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= 0, and only an electrical voltage is applied. The material parameters are depicted in . The thickness of piezoelectric layer is 7 μm.The effect of the material length scale parameter l on normalized tip deflection can be visualized by plotting normalized tip deflection versus l and hs for aluminum and brass shin, depicted in , respectively. These figures demonstrate that material length scale parameter l has a decreasing effect on the tip deflection of bimorph actuator. In addition, the decreasing rates of the tip deflections become faster with increasing length scale parameter l. show that the effect of the material length scale parameter l and thickness of elastic layer on normalized tip deflection of heterogeneous bimorph for different elastic material. We can also draw a similar conclusion about the connection between normalized tip deflection and material length scale parameter l. Furthermore, the thinner the elastic layer, the larger the decreasing rates of the normalized tip deflections. plot the ratio of the size-dependent tip deflection to the classical one versus the ratio of the symmetrical/heterogeneous bimorph actuator thickness to the material scale parameter l on a dual logarithmic coordinate diagram. From these figures it is observed that the effect of length scale parameter l stiffs the actuator. For the case of symmetrical bimorph actuator, demonstrate that the stiffener the elastic layer, the larger the difference between tip deflections obtained by the modified couple stress theory and those evaluated by the classical beam theory. In contrast, demonstrate that the softer the elastic layer of heterogeneous bimorph actuator, the larger the difference between the two groups of computed values. This opposite result is probably attributed to the different structures of the two kinds of bimorph actuator, i.e. one is symmetrical and another one is non- symmetrical.The present paper makes the first attempt to develop size-dependent constituent equations for both symmetrical and heterogeneous piezoelectric bimorph actuator by using the modified couple stress theory and the principle of minimum total potential energy. This model equation uses an internal material length scale parameter to describe the size-dependent behavior of piezoelectric bimorphs for various electrical and mechanical boundary conditions. Exact solutions for the normalized static deflection are obtained as a function of the ratio of the actuator thickness to the internal material length scale parameter. These investigations suggest the following conclusion:The simulations demonstrate that the static tip deflections of bimorph actuators are strongly dependent on internal material length scale parameter. A small internal material length scale parameter leads to a very small decrease of the normalized tip deflection. In the limit when the internal material length scale parameter goes to zero, this model reduces to classical (local) constituent equations available in the literatures for symmetrical and/or heterogeneous piezoelectric bimorph actuator. With the increase of internal material length scale parameter, the tip deflection decreases more rapidly.The effect of the thickness of the elastic layer on the normalized static deflection is discussed in this paper. When the internal material length scale parameter is fixed, the thinner the elastic layer, the larger the decreasing rates of the normalized tip deflections.When the thickness of piezoelectric layer is set to zero, the present constitutive equations for piezoelectric bimorph actuator reduced to the size-dependent Euler beam model available in the literatures.It is also concluded that the stiffness of elastic layers show directionally opposite effects on tip deflections of symmetrical piezoelectric bimorph actuator and heterogeneous one. For the former, the stiffener the elastic layer, the larger the difference between tip deflections obtained by the modified couple stress theory and those evaluated by the classical beam theory. Nevertheless, for the latter, the softer the elastic layer, the larger the difference between tip deflections obtained by the modified couple stress theory and those evaluated by the classical beam theory. This opposite result is probably attributed to the different structures of the two kinds of bimorph actuator, i.e. one is symmetrical and another one is non- symmetrical.The presented constitutive equations are expressed in a 4 × 4 matrix form, which can be used as black-box boxes in practical applications.Assessment of nonlinear distortions in modal testing and analysis of vibrating automotive structuresIn this paper, new developments for the nonparametric processing of modal test data are presented. Classically, random noise signals are applied to deal with possible nonlinear distortions during frequency response function measurements of linear dynamic systems. However, the use of multisine excitation signals allows the engineer to control much more his experiments. First of all, the nonparametric estimation of multivariable frequency response functions can be more easily based on an “errors-in-variables” stochastic framework. In addition, the application of a well-chosen multisine excitation permits improvement of the data quality, as well as the detection, qualification and quantification of nonlinear distortions during FRF measurements. To make the presented techniques available for multi-input modal testing, attention is paid to the design of optimal multi-input excitations by maximizing the Fisher information matrix as well as minimizing the crest factor of the applied excitation.In a limited amount of cases it is not possible, or very difficult, to control, or even to measure, the excitation forces acting on the structure under test (bridges excited by traffic and wind, operating machines, etc.). In most modal analysis applications, however, the excitation forces can be imposed with an actuator, and the engineer can choose which excitation signal to use.A common way of measuring Frequency Response Functions (FRF) in the 1960s consisted in using slowly varying swept sine excitations together with tracking filters. With the development of signal processing techniques, such as the Fast Fourier Transform (FFT), it became possible to use broadband excitation signals One way to avoid these errors consists in using periodic excitation signals such as multisines, which will also be used throughout this paper. Besides avoiding spectral errors, multisines offer other advantages such as optimal signal-to-noise (SNR) ratios, and a reduction of the number of periods required for averaging during the nonparametric identification of the FRF matrix (nonparametric stands for describing the dynamics of the observed system by its spectral contents i.e. a transfer function). In addition (as will be discussed in ) a synchronized set-up, with deterministic excitation using e.g. multisines, permits the use of a maximum likelihood FRF estimator developed in a “errors-in-variables” (EV) stochastic framework. As will be shown, such an estimator outperforms the traditionally-used FRF estimators such as the H1 and HvModal testing of large structures, typically encountered in the automotive and aerospace industries, certainly requires the use of multi-shaker excitation. Very early, the possibility offered by exciting multi-input systems with uncorrelated signals has been investigated. The most obvious approach consists in applying independent random noise sources to the different inputs of the system (see for instance Ref. ) is optimal in the sense that it optimizes the Fisher information matrix for amplitude constrained inputs.However, besides reducing the measurement time and improving the quality of the FRF data, the effects of possible nonlinear distortions become even more important. For this reason, most engineers still prefer the use of random noise excitation, since the contribution of nonlinearities is expected to be reduced by the averaging of random noise sequences. Nevertheless, the ideal FRF measurement method should not only provide accurate FRFs, but at the same time the presence of nonlinear distortions should be known to the engineer in order to properly judge the suitability of the FRF data for a subsequent modal analysis, which in the end is based on linear assumptions. It will be shown in this paper how the use of specially selected periodic excitation signals extends the engineer's possibilities to detect, qualify and quantify nonlinear distortions, which can have a large impact on the further modelling results if not recognized. Recently, new developments for this purpose have been presented for single input single output systems based on the use of multisines For cases where the typical input amplitudes clearly distort the structure's linear behaviour (e.g. a high level of operational input amplitudes) efficient nonlinear frequency analysis tools are available As a summary, this paper generalizes recently developed multisine-based SISO techniques to multivariable modal testing, where the aspects of multi-input experiment design, “errors-in-variables” nonparametric processing and the assessment for nonlinear distortions during testing are combined in an advanced modal test procedure. More specifically, the following contributions will be discussed:the maximum likelihood estimation of multivariable FRFs and their noise covariance matrix from MIMO multisine measurements when using a synchronized measurement setup.the optimization of multi-input excitation in modal testing, simply by the use of one single multisine realization based on an excitation scheme that maximizes the so-called Fisher information matrix.the practical assessment of the recently developed multisine-based methods for the detection and characterization of nonlinear distortions for mechanical structures and the generalization of these tools to MIMO modal testing.illustration of the benefits and at the same time ease-of-application of the different tools that were integrated in a multivariable modal testing procedure by means of experimental results for an application in the field of vibration analysis for automotive engineering.A multisine is a periodic broadband signal consisting of a sum of (co-)sines with harmonically related frequenciesThe period of the signal is T=1/f0. The amplitudes, Ak (k harmonic numbers) of the (co-)sine can be chosen arbitrarily while the phases φk are usually selected in such a way that the crest factor (i.e. the ratio of the peak and effective (RMS) value) is minimal. The amplitudes completely determine the auto-power spectrum of the signal, while the phases influence the peak value of the signal. Multisine can be considered as a generalization of stepped sine measurements. Stepped sine frequency response measurements are usually characterized by very good signal-to-noise ratios but long measurement times. Multisine makes it possible to reduce the measurement time while maintaining good SNRs By replacing classically-used random noise by multisine signals the user gets additional advantages:Leakage errors are avoided when properly used (i.e. synchronized measurements of an integer number of periods).The amplitude spectrum Ak is deterministic, resulting in a better SNR behavior, especially for a small number of averages/realizations.A full control over the amplitude spectrum is obtained such that it is possible to focus all the power in a desired frequency band, or to avoid the excitation of specific frequency bands or lines.In addition insights in the presence of nonlinear distortions can be obtained, e.g. the level of the even and odd nonlinear distortions can be separated, at the cost of an increased measurement time (factor 2 for odd to 4 or odd–odd multisines).The nonparametric estimation of FRFs (or impulse response functions) is of primary importance in many scientific investigations. This is the reason why much attention has been paid to nonparametric estimators in the literature The reason for using an EV framework relates to a typical modal test setup, where there exists a permanent fixation, a so-called stinger, between the electrodynamic shakers and the structure. Such a stinger, having a high stiffness in the longitudinal direction while being flexible in the transversal direction, serves as a interface to ensure that the forces are applied perpendicular to the structure. As a result, around the resonance frequencies of the structure, the structure will resist additional input of energy resulting in low levels of the applied force and consequently higher noise levels on the input (force) Fourier data. Practically this means that the SNR drops at the resonance frequencies and one can certainly not assume that the applied force is free of errors. This is certainly not in favour of the H1 FRF estimator, which requires that the input noise must be negligible in order to avoid biased FRF estimates. Therefore, it is certainly beneficial to work in an EV framework, which is in the case of arbitrary excitation (e.g. random noise) possible by the use of an instrumental variables (IV) method (see for instance Refs. Consider the multivariable system with Ni inputs and No outputs as shown in . If the “true” input and output signals, f0(t)∈RNi and x0(t)∈RNo, were observable at equidistant time instants tn=nτ, n=0,…,N-1, with τ the sampling period and T=Nτ the observation period, and if the sampled signals could be discrete Fourier transformed without introducing errors (which is the case for periodic signals), then, for all angular frequencies in Ω={ωk=2πk/T:k=0,…,N/2-1}, the following linear mapping would hold exactlywhere H(ωk)∈CNo×Ni stands for the multivariable FRF matrix at angular frequency ωk, while F0(ωk)∈CNi×1 and X0(ωk)∈CNo×1 are the corresponding discrete Fourier transforms of the “true” Input/Output signals.In practice, however, (as illustrated in ) errors usually affect the measured Fourier vectors, and consequently, what is observed are not the “true” Input/Output Fourier data, D0(ωk)=[F0(ωk)H,X0(ωk)H]H, but D0(ωk) together with some random perturbations, Ed(ωk)=[Ef(ωk)H,Ex(ωk)H]H (⋄H stands for the Hermitian transpose operator). The problem, thus, becomes statistical, resulting in random observations, D(ωk)=[F(ωk)H,X(ωk)H]H.Consider now the set {(Fm(ωk),Xm(ωk)):m=1,…,M⩾Ni} consisting of M observations of the Input/Ouput Fourier vectors at angular frequency ωk. Using the above notations, the following EV stochastic model relates the M measured observationsDm(ωk)=D0,m(ωk)+Ed,m(ωk)[H(ωk),-INo]D0,m(ωk)=0m=1,…,M⩾Ni.By grouping the M input and output Fourier vectors into two matrices F(ωk)=[F1(ωk),…,FM(ωk)]∈CNi×M and X(ωk)=[X1(ωk),…,XM(ωk)]∈CNo×M, the EV model D(ωk)=D0(ωk)+Ed(ωk)[H(ωk),-INo]D0(ωk)=0withD(ωk),D0(ωk),Ed(ωk)∈C(Ni+No)×Mi.e. D(ωk)=[D1(ωk),D2(ωk),…,DM(ωk)], D0(ωk)=[D0,1(ωk),D0,2(ωk),…,D0,M(ωk)] and Ed(ωk)=[Ed,1(ωk),Ed,2(ωk),…,Ed,M(ωk)].Note that for a multi-excitation setup, matrix F0(ωk) of the Ni linear independent stimuli, F0(ωk)=[F0,1(ωk),…,F0,Ni(ωk)]∈CNi×Ni has to be of full row-rank, i.e. Ni of the inputs F0,m(ωk)∈CNi×1 have to be linearly independent.An extensive list of statistical publications has been devoted to the closely related topic of EV regression analysis One way to overcome this problem is to use an instrumental variables approach as presented in Refs. In the next section, however, an alternative approach will be proposed based on repeated observations of deterministic signals. This can nowadays easily be realized in practice by applying periodic (broadband) excitations (e.g. multisines) and by measuring, say, P>1 periods of the signals. For the case of deterministic excitation, the Instrumental Variables approach then boils down to a special case, i.e. the HML estimator Nowadays, modal testing equipment has built-in generators permitting the synchronization of the measurements of the applied forces and structures responses automatically. Using a synchronized measurement setup in combination with a deterministic excitation facilitates the observation of the Input/Ouput data for a number of integer periods of the deterministic signal.Under the condition that repeated observations of the same deterministic excitation signals are available, it is possible to obtain maximum likelihood estimates of the FRFs without requiring any a priori noise information as well as the need for additional instrumental variables.For a multi-excitation setup, a set of Ni linear independent stimuli, F0(ωk)=[F0,1(ωk),…,F0,Ni(ωk)]∈CNi×Ni, are required. For the different stimuli, the resulting Input/Ouput data are measured P times (i.e. M=NiP), which leads to the following EV modelDp(ωk)=D0,p(ωk)+Ed,p(ωk)[H(ωk),-INo]D0,p(ωk)=0p=1,…,P.Note that the covariance matrix of the disturbances is not required anymore to obtain consistent estimates. This estimator belongs to the class of maximum likelihood estimators Cov(H^ML(ωk))=1P1P∑k=1PFk(ωk)*1P∑l=1PFl(ωk)T-1⊗Cε(ωk)Cε(ωk)=B^(ωk)CD(ωk)B^(ωk)H,B^(ωk)=H^ML(ωk),-INo.The probability limit (p.lim) for P→∞ results in the Cramér–Rao lower bound In the case of asynchronous periodic measurements, it is possible to use, besides the HIV estimator, FRF estimators based on nonlinear averaging techniques. FRF estimators such as the Hari, Hhar and the Hlog are also able to derive the FRF matrix with its covariance matrix under the EV noise model assumptions (a)) is obtained with a large crest factor (CF) (CF=16 for this signal). In order to get measurements with a good signal-to-noise ratio (SNR) the CF should be as small as possible. For comparison, the crest-factor of a sinewave equals 2≈1.414.Several algorithms are available to minimize the CF of multisines by specific choices for the phases φk in Eq. (d)) can be considered as being a sub-optimal multisine with equal amplitudes (to approximate white noise) and random phases uniformly distributed in [0,2π[.During modal testing, both input and output signals have to be measured, and thus, all signals should preferably have a good SNR. Assume that, for instance, the Input/Ouput signals are related to each other by a differentiator (H(s)=αs). In that case, the resulting output signal for the optimized input of (a). The CF of this signal is not optimal.Some crest-factor optimization algorithms allow to compress the input as well as the output signals (b) and (c) the simultaneously optimized Input/Ouput signals are given taking into account the transfer function between input and output. Using these algorithms, it is for instance possible to compress the force signal of a shaker together with the displacement in order not to exceed the stroke limits of the electrodynamic shakers.The quality of the MFRF estimates does not depend on the estimator only, but the excitation plays an important role too. The design of optimal excitations relies on the maximization of the so-called Fisher information matrix As multi-input modal testing requires uncorrelated inputs, 2 uncorrelated inputs are for instance readily obtained by designing one multisine that only contains odd frequency lines (f0,3f0,5f0,…) and another consisting of the even frequencies (2f0,4f0,6f0,…)The design of optimal excitations relies on the minimization of the Cramer–Rao lower bound CCR(vec(H(ωk)))=1P(F0(ωk)TF0(ωk)*)-1⊗CBD(ωk),where vec(H(ωk))=(H11,…,HNo1,H12,…,HNoNi)T, CBD(ωk)=BCDBH and B(ωk)=[H(ωk),-INo]. This result is a generalization of Theorem 8.2.5 in Ref. det(CCR(vec(H(ωk))))=1PNiNodet(CBD(ωk))Nidet(F0(ωk)TF0(ωk)*)No.As a result, the optimal input design is the one that maximizes |det(F0(ωk))|.Assume that we have designed, for a given frequency band, a multisine with optimized crest-factor. Its Fourier coefficient at angular frequency ωk will be denoted by S(ωk). Applying this signal (with normalized peak value) to the different inputs, taking into account the maximum allowed peak values Ri, i=1,…,Ni, results for observation p in the input vectorF0,p(ωk)=(R1S(ωk)Q1,p,R2S(ωk)Q2,p,…,RNiS(ωk)QNi,p)T.The question that has to be addressed now is how to choose the matrix Q∈[-1,1]Ni×Ni such that |det(F0(ωk))| attains its extremum. The answer follows from showing that the extremum is obtained when Q is a Hadamard matrix The most simple method for the detection of nonlinear distortions is the sine test, characterizing nonlinear behavior by checking on the generation of higher harmonics. However, this method is very slow and it is unacceptable that most of the available measurement time should be spent on the detection of nonlinear distortions at the cost of reduced FRF quality. Another approach, commonly-used in modal testing, is based on random noise measurements at increasing excitation levels and comparing the FRFs that should be amplitude independent in the linear range of the system. This method is also less appealing since two separate measurements are needed and a possible nonlinear load behavior of the generator can occur due the input impedance of the tested system. Another often-used test is the coherence check, which however does not allow one distinguish between noise disturbances, leakage errors and nonlinear distortions.Using random noise signals, small nonlinear distortions can still be reduced by sufficient averaging. This results in the so-called “best linear approximation” for the system, although it introduces the important disadvantages of leakage and transient effects. As a result, the class of suitable excitation signals is already restricted to broadband random multisines. Depending on the measurement procedure and specific choice of the amplitude spectrum two approaches, that allow the detection, qualification and quantification of nonlinear distortions during FRF measurements, are now discussed.This approach is based on using random multisine or so-called pseudorandom excitations in a special periodic measurement sequence. A pseudorandom signal is typically constructed with harmonic components of equal amplitudes and random phases uniformly distributed in [0,2π[, every line containing equal energy in the frequency band considered.This approach allows one to measure in the same experiment the nonlinear and disturbing noise levels. This is done by analyzing the variations over consecutively measured periods, and the variations over different realizations of the input signal as is now briefly discussed (cf. Refs. . Using the FFT, the measured input and output signals for each individual period m are denoted by F[r,m](ωk), X[r,m](ωk), with r=1,…,R indicating the different realizations for the pseudorandom input and m=1,…,M(M=NiP) indicating P measured periods of the periodic repetition of each realization according e.g. a Ni multi-input scheme maximizing the Fisher information matrix as explained in Assuming for conciseness that there is no noise on the input, both input and output relations are then given asX[r,m](ωk)=HR(ωk)F[r](ωk)+T[r,m](ωk)+SX[r](ωk)+NX[r,m](ωk)with T[r,m](ωk) a transient term, SX[r](ωk) the stochastic nonlinearities and NX[r,m](ωk) the disturbing noise. As can be seen from the output relation, the following patterns are derived:For a given realization r the variations from one period to another are only due to the disturbing noise and the vanishing transient effects. Thus averaging over consecutive periods m will only reduce the effects of the disturbing noise, while the nonlinear distortions not depending on m do not disappear if more periods are averaged (increasing M). As a result, applying a given realization of a pseudo random multisine for a sufficient number of consecutive periods yields the combined stochastic error due to both the disturbing noise and nonlinear distortions.Applying different realizations r for the pseudorandom multisine, the variations from one period to another are now due to the disturbing noise, the vanishing transient effects and the nonlinear distortions. Hence, in order to reduce the effects of the nonlinear distortions, averaging over different realizations should be increased (by increasing R). As a result, applying sufficient different pseudorandom realizations yields the stochastic error due solely to the disturbing noise.Given the random character of the applied multisine signal, this approach combines in one experiment the measurement of the “best linear approximation” of the MFRFs together with the detection of the error levels due to disturbing noise and nonlinear distortions. The generally large number of averages can be reduced by the use of CF optimized pseudorandom signal realizations The basic idea of this approach relies on exciting the system with an odd–odd multisine, where only the frequencies 4k+1,k=0,1,2,…,kmax in Eq. have amplitudes different from zero. The output spectrum X(ωk), calculated using an FFT and rectangular window again forms the basis for the detection of nonlinear distortions. As discussed in Ref. At lines 4k+1: the output consisting of the linear contribution and odd nonlinear distortions.At lines 4k+2: only the even nonlinear distortions.At lines 4k+3: only the odd nonlinear distortions.This enables both the detection and characterization of the system's nonlinear behavior. If at least P⩾2 successive periods are measured in one block, it is still possible to make the same conclusions at respectively lines P(4k+1), P(4k+2) and P(4k+3). In addition, it is also possible to derive the noise level (having a nonperiodic behavior) at the lines that are not a multiple of P since these cannot be excited by a signal with M periods in a single block (window).In the end, the engineer derives from one single experiment the broadband MFRF measurement and the detection, qualification and rough quantification of the nonlinear distortions, together with a noise analysis. The price for this is a loss in frequency resolution caused by the nonexcited lines or an increased measurement time (factor 4) by increasing the number of frequency lines to maintain the same resolution. The “best linear approximation” for the studied system is obtained by applying odd–odd multisines with optimized crest factor optionally combined with averaging over different realizations of the (random) odd–odd multisine at the cost of an increased measurement time.In practice, some additional problems can occur during modal testing using this approach. A nonlinear interaction between the generator and the studied system can generate unwanted excitations at the detection frequencies or create additional undesired harmonic components once the system becomes nonlinearly distorted. Hence, it is no longer clear what part of the output should be assigned to the system behavior and what part is due to the nonlinear interaction distortions. In that case, the output can be compensated through a first-order correction X˜(ωk)=X(ωk)-H˜(ωk)·F(ωk), where H˜(ωk) is obtained by a linear interpolation between the FRF measurements at the excited frequencies.The applicability of the presented methods was studied for the case of a typical modal test of a so-called “body-in-white” structure as shown in . The car body was suspended by means of steel cables connected to the car body through 4 sets of 3 springs connected at the front and back part of the body. Multiple-input testing was realized using 2 Bruël & Kjær shakers in the front part where the applied loading was measured using PCB force sensors. Multiple responses were measured using PCB accelerometers and the results presented for this specific study used 2 of the observed responses (1 sensor at the coupling of multiple parts by means of welding and screw joints (see ), the other on a side panel). The measurements were controlled using MATLAB software in combination with a National Instruments data-acquisition board (with synchronized 2 generators and 16 channels). Reason for this choice is the fact that until today commercially available measurement systems still do not provide sufficient freedom in the application of “exotic” excitation signals such as the odd–odd multisines.The following issues were considered during the performed modal testing experiments:Three types of different excitation signals were considered during the experiments: random noise, pseudo random (random multisine) and l∞ optimized odd–odd multisine.Multiple input testing required the generation of uncorrelated inputs. As discussed in , this can be realized by generating a single multisine (e.g. pseudo random or odd–odd) and applying, in this practical case, this signal through two (Ni=2) subsequent load realizations according to the optimal Hadamard 11-11 matrix realization. For the random noise excitation, two different random noise realizations were applied as is classically done in modal testing practice.) was applied for the odd–odd multisine excitation since only one realization was used during the experiment. In order to find the “best linear approximation” of the measured FRFs for the studied car body it is advised to use a CF optimization when applying odd–odd excitation. Notice that a CF optimization could also be applied for the pseudo random excitation. However, since this signal was applied during a sufficient number of consecutive periods and for different realizations, the averaging process generally yields a “best-practice best linear approximation” without the need for CF optimization (which also would increase the measurement time since the iterative l∞ optimization algorithm would have to be executed for each realization).Two different estimators are considered during the nonparametric processing of the acquired data in order to estimate the multivariable FRFs and their corresponding noise covariance matrix as discussed in . For the random noise experiment, the classical H1 is used, while the EV approach could be applied for the multisine (pseudo and odd–odd) cases.Three different experiments were performed in this study as summarized in . Both approaches for the detection and characterization of nonlinear distortions during the FRF measurements, as presented in , were applied for, respectively, the pseudo random and odd–odd multisine excitation. It should be noticed that the total number of averages available for the nonparametric processing and assessment of nonlinear distortions was 10 times larger for the experiment using the pseudo random excitation. This because 12 consecutive periods (2 periods waiting for vanishing transient effects) were acquired for each of the 10 pseudo random realizations. On the contrary, 12 consecutive periods were acquired for just 1 odd–odd multisine realization that has in its turn a frequency resolution that is 4 times larger than the pseudo random excitation in order to introduce detection lines in the excitation spectrum.For comparison reasons the measurement channel settings (channel ranges, anti-aliasing filters, …) were kept the same throughout this study.Consider a multisine and random noise excitation with the same number of spectral lines in the observed Fourier data. Since a multisine signal typically has a constant amplitude spectrum, every spectral line receives enough energy during a single record resulting in a good SNR for each spectral line. This is certainly not the case for a random noise excitation so that the number of required records for random noise excitation is always larger in order to obtain the same data quality compared to a multisine. As a result, a given data quality is achieved with less measurement time in the case of a multisine. When using the specially designed odd–odd multisine, the number of spectral lines is increased with a factor 4 in order to introduce the detection lines while keeping the same frequency resolution for the excited spectrum. As a result, in one record, the odd–odd multisine permits acquiring, besides system information, also information on the measurement setup (noise) and possible nonlinear behavior of the studied system, at the cost of an increased measurement time for a single record. However, with respect to achieving a certain data quality (in terms of SNR) in comparison to random noise, it still applies that the same quality is achieved with much less observed records in the case of the odd–odd multisine. shows the error levels (standard deviations) for the FRF estimates derived from the noise covariance matrices, for the three different types of excitations. These matrices are computed during the nonparametric averaging process and multivariable expressions for the H1 and HML are given in Ref. . As can be seen, the stochastic errors on the FRFs are smallest for the experiment using an l∞ optimized odd–odd multisine combined with the HML FRF estimator. The largest errors are related to the random noise excitation mainly due to lower SNR for the measured signals within a single observation window (the number of averages is the same as for odd–odd experiment), while a lower crest factor and a larger number of averages (compared to the random noise case) reduces the stochastic errors on the FRF estimates obtained by the pseudo random experiment.Although the noise levels on the measured force signals were small in the data-acquisition setup, a gain in accuracy is still obtained from taking also the input noise into account during nonparametric processing based on an EV stochastic framework. This can also be observed in , where especially in the resonances (peaks) the differences (typically 2 to 5 dB for this case) between the H1 (random noise) and the HML (pseudo/odd–odd) are due to systematic (bias) errors in the H1 FRF estimates The effects of an increasing excitation amplitude on the FRF estimates can be observed in for the experiment using random noise excitation combined with the H1 estimator. It is seen that the resonance peaks shift to lower frequencies and become broader with lower amplitude due to an increasing effect of nonlinear distortions during the FRF measurements. Physically, this behavior can be related to the nonlinear characteristics of the car body's material properties, where the damping characteristics change and the Young's modulus becomes smaller at larger vibration amplitudes and hence larger displacements result. Since the Young's modulus is also proportional to the material stiffness, the resonance frequencies tend to decrease (in this case by typically up to 1 Hz with the frequency resolution Δf=0.0125). illustrates the detection of nonlinear distortions using approach 1 with a pseudorandom excitation as discussed in . Based on the averaging-based nonparametric analysis of the response spectra (-) for the different multi-input realizations (“even” stands for 11 and “odd” for 1-1) and different pseudorandom realizations, the engineer gets a better insight in the errors on the FRF estimates, since a separation between the disturbing noise level (-•) and the level of errors due to both the disturbing noise and nonlinear distortions (-×) becomes possible. The difference between low and high excitation levels (cf. ) is clearly observed. For a low amplitude excitation, both error contributions are of the same level, while at a high amplitude the error level for the combined noise and nonlinear distortions contributions is clearly higher, typically by 10–25 dB, than the disturbing noise level. Notice also that this difference varies with the Input/Ouput locations, which is related to the car body's construction in terms of welding and screwing joints as well as the material itself (i.e. high vibration amplitudes in the panel parts of the body).More detailed information for the detection, qualification and a rough quantification is derived by approach 2 by the use of odd–odd multisine excitation. As explained in , the nonparametric analysis of the response spectrum (optionally by averaging consecutive periods) can be done by separating the spectral energy present at the excited and non excited even/odd frequency lines. This results in with the response spectrum (-), disturbing noise (-•), even nonlinear distortions (-×) and odd nonlinear distortions (-+). Again, it can be seen that for a low level of excitation the different error levels coincide, which indicates that the nonlinear distortions are of the same level as the stochastic error due to the disturbing noise (SNR for the response signals is 40–60 dB). Increasing the excitation amplitude clearly results in an increasing effect of nonlinear distortions. The levels for the even and odd nonlinear distortions are now about 20–30 dB higher than the disturbing noise, clearly indicating the dominance of nonlinear distortions in the overall error on the observed responses. Moreover, more detailed information about the character of the nonlinearities as a function of the frequency is derived by approach 2. It is noticed that the portion of even nonlinear distortions is still about 8–12 dB higher than the odd nonlinear contribution, and so for the studied body-in-white structure, the even nonlinear distortions seem to be most dominant. Another important observation is the fact that increasing the amplitude during modal testing is generally perceived as beneficial for the SNR of the measured signals, which is only correct around the linear working point of the considered structure. However, as can be seen from the results acquired on the car body, for both a low or high level of excitation the disturbing noise level remains the same, while only the nonlinear contributions are enforced during testing at higher amplitudes. It can be concluded that both approaches presented in provide powerful tools for the engineer in order to assess the presence and character of nonlinear distortions during FRF measurements and more general during modal testing. Performing the correction on the output spectrum for possible extraneous nonlinear distortions, as discussed in , yields the same results. In this case, the nonlinear distorting effects of the shakers were kept very small by the use of high quality shaker-amplifier systems in their optimal working point (range).In this paper new developments for modal testing have been discussed. First, attention has been paid to the maximum likelihood estimation of multivariable FRFs and their noise covariance matrix from multisine measurements when using a synchronized setup. It is shown that this estimator outperforms the classically-used FRF estimators. Next, the optimization of the CF of multisines as well as the application of multisines for multi-input excitation have been included in a modal testing procedure. It is shown that simply by the use of one single multisine realization, multi-input testing is possible based on an excitation scheme that maximizes the so-called Fisher information matrix. Moreover, with the application of multisine excitations, it becomes possible to measure the FRFs simultaneously with detection, qualification and quantification of the nonlinear distortions during testing. In cases where nonlinear distortions are not avoidable, random multisine testing still allows the measurement of the “best linear approximation” of the studied system. Finally, the benefits and at the same time ease-of-application of the different tools to be included in a typical multivariable modal testing procedure have been illustrated by means of experimental results for an application in the field of automotive engineering vibration analysis. where the inputs F0,p=F0,p(ωk) (ωk is omitted for simplifying notations) are considered deterministic. It will be assumed that the random vectors {Ed,p:p=1,…,P} are complex normally distributed withand CD∈C(No+Ni)×(No+Ni) an a priori known Hermitian-symmetric covariance matrix. Notice that CD accounts for possible correlations among the Input/Ouput Fourier coefficients. For a wide class of probability density functions of the time-domain noise, the Fourier coefficients are asymptotically (as the number of time samples N→∞) complex normally distributed and independent over the frequencies This results in the following (negative) log-likelihood functionℓ(H^,F^)=∑p=1PtrCD-1Dp-INiH^F^Dp-INiH^F^H.The matrices H^ and F^=[F^1,…,F^P] are the independent variables, while D=[D1,…,DP] represents the measurements. The values of the independent variables minimizing the cost function are the MLEs (H^ML,F^ML) of the true (H,F0) while the MLE of the dependent variable X0 is given byThereto the method of the Lagrangian multipliers is applied to Eq. ℓ(H^,D^,L^)=∑p=1Ptr(CD-1[Dp-D^][Dp-D^]H)+Re(tr(L^HB^D^)),where D^∈C(No+Ni)×Ni, B^=[H^,-INo]∈CNo×(No+Ni) and where L^ is a Lagrangian multiplier matrix for the constraint B^D^=0 (use of the real part of the trace of L^HB^D^ is just a convenient way of summing Re(L^jk)Re(∑lB^jlD^lk) and Im(L^jk)Im(∑lB^jlD^lk) over all j,k). In its extremum, ℓ(H^,D^,L^) must be stationary with respect to H^, D^ and L^. Setting ∂ℓ/∂Re(D^)+-1∂ℓ/∂Im(D^) equal to zero gives (notice that ℓ is not an analytic function, thus, ∂ℓ/∂D^ does not exist).Similarly, the derivative with respect to Re(H^) and Im(H^), respectively Re(L^) and Im(L^) giveAs F^∈CNi×Ni is a regular matrix by assumption, can only be satisfied when L^∈C(No+Ni)×Ni equals zero. Consequently, Eq. , the transfer matrix estimate H^ML becomesNote that a priori knowledge of CD is not required any more to obtain the ML estimate of H.Defining X^=1P∑k=1PXk and F^=1P∑l=1PFl, Eq. Starting from a sensitivity analysis, an expression for the covariance matrix of the H^ML FRF estimates can be foundwith δ(F^-1)=F^-1δ(F^)F^-1. Using the Vector vec and Kronecker ⊗ operators, this can also be written asvec(δH^ML)=(F^-T⊗INo)vec(δX^)-(F^-T⊗X^F^-1)vec(δF^)the covariance matrix of the H^ML FRF matrix is then given byCov(H^ML)=E{vec(δH^ML)vec(δH^ML)H}=(F^-T⊗X^F^-1)E{vec(δF^)vec(δF^)H}(F^-*⊗F^-HX^H)+(F^-T⊗INo)E{vec(δX^)vec(δX^)H}(F^-*⊗INo)-2herm(F^-T⊗X^F^-1)E{vec(δF^)vec(δX^)H}(F^-*⊗INo)with E the Expectation operator, where for exampleE{vec(δX^)vec(δX^)H}=E1P∑k=1Pvec(δXk)1P∑l=1Pvec(δXl)Hunder the assumptions that over the different measurements all signals and noise are stationary and the noise is not correlated, reduces toConsequently, the expression for the covariance matrix becomesCov(H^ML)=1P(F^-TF^-*)⊗CX+1P(F^-TF^-*)⊗(X^F^-1CFF^-HX^H)-1P(F^-TF^-*)⊗(X^F^-1Cov(F,X))-1P(F^-TF^-*)⊗(Cov(X,F)F^-HX^H)The determinant ofN×NmatricesA(i), i=1,…,2N2, consisting of only 1's and-1's can only be equal to-α, 0 orα, whereα=2N-1.If A(j) is singular then det(A(j))=0. On the other hand, if A(j) is regular, it has a determinant α≠0. Note that all regular matrices A(i) can be derived from A(j) by means of column and row permutations, and multiplications of columns or rows with -1. These operations can only modify the sign of the determinant so that |det(A(i))|=α,∀ regular matrices A(i). Consider the regular N×N matrix AN constructed by making all lower triangular elements including the diagonal ones equal to 1, while the upper triangular elements equal -1. For exampleBy means of linear column manipulations, it follows that det(AN)=det(BN) where BN stands for AN but with all entries (i,j) where j>i+1 equal to 0. For exampledet(A4)=1-1-1-111-1-1111-11111=1-10011-10111-11111=det(B4).Expanding with respect to the first row givesdet(B4)=1-10011-10111-11111=11-1-111-1111-(-1)1-1-111-1111.From this example it follows that det(B4)=2det(A3)=2det(B3)=22det(A2)=23, and by induction det(AN)=2N-1. Thus, α=2N-1. □Consider the convex hullQ=Co{Q(1),Q(2),…,Q(2Ni2)}in the spaceRNi×Ni, supported by all matricesQ(n)∈{1,-1}Ni×Ni, n=1,…,2Ni2, consisting of only 1's and-1's. Then, |det(Q)|withQ∈Q=[-1,1]Ni×Ni (i.e. the set of allNi×Nimatrices with entries in the interval[-1,1]), reaches its maximum value in all regular vertex matricesQ(n)of the convex polytopeQ.Firstly, it is shown that the maximum value is reached on the boundary ∂Q of the convex hull Q. Indeed, if Q* is a point interior to Q then there exists an α>1 such that αQ*∈∂Q and if det(αQ*)≠0 then |det(αQ*)|=|αNidet(Q*)|>|det(Q*)|. The second part of the proof consists in showing that |det(Q(i))|∈{0,A},∀ vertices Q(i) of the polytope Q. If Q* is a non-regular vertex matrix then |det(Q*)|=0. On the other hand, if Q* is regular then |det(Q(i))| equals some value A>0. Note that all regular vertex matrices of Q can be derived from Q* by means of column and row permutations, and multiplications of columns or rows with -1. These operations can only modify the sign of the determinant so that |det(Q(i))|=A,∀ regular vertices Q(i) of Q. Eventually, it is shown that for Q*∈∂Q, |det(Q*)| cannot exceed the value A, obtained in the regular vertex matrices. Assume therefore that there exist a matrix Q*∈∂Q with determinant equal to A and with at least one entry different from 1 or -1. Assume for example that Q11* is such an entry. The determinant of Q* can be written as det(Q*)=∑j=1Ni(-1)j+1Q1j*det(Q(-1,-j)*) where Q(-1,-j)* is an (Ni-1)-by-(Ni-1) matrix obtained by deleting the first row and the jth column of Q*. If Q11* differs from 0, then it would be possible to exceed A in a vertex which contradicts with our prior result. So, |Q11*| must equal 1 in the extremum. Otherwise, if Q(-1,-1)* equals 0, then the value of Q11* does not matter. □Elastic–plastic contact model for rough surfaces based on plastic asperity conceptA mathematical formulation for the contact of rough surfaces is presented. The derivation of the contact model is facilitated through the definition of plastic asperities that are assumed to be embedded at a critical depth within the actual surface asperities. The surface asperities are assumed to deform elastically whereas the plastic asperities experience only plastic deformation. The deformation of plastic asperities is made to obey the law of conservation of volume. It is believed that the proposed model is advantageous since (a) it provides a more accurate account of elastic–plastic behavior of surfaces in contact and (b) it is applicable to model formulations that involve asperity shoulder-to-shoulder contact. Comparison of numerical results for estimating true contact area and contact force using the proposed model and the earlier methods suggest that the proposed approach provides a more realistic prediction of elastic–plastic contact behavior.elastic contact area due to elastic deformationelastic contact area of the fictitious asperitydiameter of contact area of plastically deformed asperityelastic contact load due to elastic deformationelastic contact load of the fictitious asperitydistance between the mean of asperity heights and that of surface heightsheight of asperity measured from the mean asperity heightsdistribution function of asperity heightscritical interference at the inception of plastic deformationMany engineering problems lead to the consideration of contact between surfaces. These include studies related to friction-induced vibration and noise, thermal and electrical contact resistance, and mechanical seals, bushing, fasteners, etc. Examination of contact characteristics encompasses equivalent contact stiffness and damping for vibration and noise studies, and true contact area for issues related to mechanical seals, and electrical and thermal resistance. Accounting for contact characteristics inherently necessitates characterization of surface topography and development of probabilistic models, which relate contact area, contact stiffness, contact load and separation of surfaces.The plastic models are based on the presumption that contact is dominated by plastic flow. Such models may be best suited for load ranges that warrant large degree of plastic flow. The earliest work on plastic contact model is attributed to Abbott and Firestone Whereas the elastic and plastic models are seen to be advantageous for extreme cases of loading, in a large number of engineering applications, contact loads may fall within ranges that do not warrant adequate representation by either elastic or plastic model. This fact has led researchers to consider what is referred to as elastic–plastic models The present work proposes a new elastic–plastic model for surfaces in contact. The critical interference proposed by Chang et al. ) those that are the actual surface asperities and () the fictitious asperities which can only deform plastically. The concept of elastic and plastic asperities allows formulation of asperity deformation model which is elastic–plastic at microscopic scale as well, in contrast to the model by Chang et al. The contact between smooth and rough surface is considered. The contact model is based on the presumption that a surface can, in effect, be represented by a distribution of asperities (Fig. ). As two surfaces are brought into contact, the macroscopic contact characteristic in question is a cumulative effect of localized interactions of the smooth surface and the asperities on the rough surface. This approach has required the statistical formulation of a surface and statistical summation of microscopic contact effects to obtain probabilistic macroscopic expectation of the contact characteristic (contact area, load, and stiffness).Many of the contact models predict extreme situations; contact is purely elastic or purely plastic. However, the contact is better described, for moderate load ranges, when it includes both elastic and plastic contacts. The proposed model approximates the behavior of the intermediate load ranges, which is referred to as elastic–plastic contact model.In the derivation of the equations the contact between one asperity on a rough surface and a plane is considered. The behavior of the asperity is initially elastic. As the load is increased the elastic behavior continues to describe the deformation until a critical interference is reached. At this critical load and beyond, the asperity deforms as a purely plastic body. Hence, for every asperity there are two types of interactions. The first is the elastic contact between the plane and the surface asperity. If the interference (w) exceeds the critical interference (wc), then the interaction also includes plastic contact. The shaded volume representing the interference of the plastic asperities and the plane contribute to the plastic portion of contact whereas the remaining volume of interference contributes to the elastic contact (Fig. ). It should be noted that with the plastic contact pressure there exist an elastic quantity, which must be subtracted to obtain the net elastic contribution.The method propound to account for the net elastic–plastic contribution is shown in . Therefore if we let Q be the characteristic of contact (area, or load) then Q may be obtained by appropriately accounting for the aforementioned interactions. That isthe characteristic of contact corresponds to the contribution due to elastic interference between the plane and the plastic asperity (Qe2) must be subtracted from the characteristics of contact corresponds to the contribution due to the elastic contact between the plane and surface asperity (Qe1) to obtain the net elastic contribution. Next the contribution from plastic interaction due to the plastic interference of the plane and plastic asperity (Qp2) must be added to the result to obtain the net elastic–plastic characteristics of contact.The difference between the present work and that proposed by Chang et al. where d is the separation based on asperity heights. For N asperities, the expected number of contacts will bewhere the total number of asperities, N, the density of asperities, η, and the nominal area An are related according toFor this type of contact, the interference w may be described as In analyzing the contact, the laws describing the dependence of the local contact area, A0, and the local contact load,P0, on w are employed. Hence,The expected total contact area, At, and the expected total contact load, P, are the statistical sums of the local contributions of each asperity. Therefore,The Hertzian contact area, contact load and the maximum contact pressure between one asperity, having interference w with a plane are given as follows:In the above equations R is the average equivalent radius of curvature. In general, the maximum contact pressure may relate to the hardness where K is the maximum contact pressure factor. Tabor for w⩾wc, the contact is plastic. Using the critical interference and additionally by imposing the conservation of volume, Chang et al. It is appropriate here to reiterate the difference between the present work and that proposed by Chang et al. The method propounded in this paper is shown to represent more accurately an elastic–plastic model of the contact, through the introduction of a fictitious surface that can only deform plastically. As shown in , the critical interference (wc) is used to define a second surface. This second surface is obtained by displacement of every point on the surface by wc along the direction normal to the surface (see , to obtain the mathematical description of the plastic asperity, the mapping of a point A on the surface to a point B on the plastic asperity must be considered. It is also noted that an asperity is described (Fig. ) in terms of a frame of reference whose origin is at the asperity peak and ordinate points towards the mean plane The respective positions of points A and B are denoted by r¯A and r¯B, as depicted in . The position of point B on the fictitious asperity iswhere, u¯n is the unit normal vector to the original asperity at point A. As usual the unit vectors i¯ and j¯ are defined along ρ (or x) and y axes, respectively. Employing the notation of Greenwood and Tripp ) may be used to obtain the equation describing the plastic asperity (see Appendix A for detail). To the first approximation, the equation of the plastic asperity is given as (Appendix A)Since the plastic asperities only deform plastically, their introduction allows the reduction of Eqs. (where, Rp represents the summit radius of curvature of the plastic asperity. Based on Eq. (Clearly the formulation of the area of contact and contact force for two surfaces involve interactions of two sets of asperities. The original surface asperities which are assumed to deform elastically and plastic asperities that deform plastically. The next section presents this new mathematical model of contact.In this section the mathematical formulation of the proposed elastic–plastic contact model is presented. Using the approach in the area of contact may be described aswhere φ(s) is the dimensionless form of the probability density function for summit height distribution and β, βp, w*, and the dimensionless height of asperity s are defined as follows:It is noteworthy to mention here that the plastic asperity peaks can be viewed as being farther away from the plane by wc. We have made the approximation as to the mean plane of plastic asperity being wc below the mean plane of the surface asperities. Therefore the limits of integration are shifted by wc as presented in Eqs. (). Furthermore, in these equations the summit curvature corresponding to plastic asperities are used. Proceeding in a similar manner, the contact load may be written asPe2*(h*)=43σR1/2βp∫h*-ys*+wc*∞w*3/2φ(s)ds,The effectiveness of the proposed model is evaluated using the data and results given in Chang et al. To combine the material and surface topographic properties in contact, the plasticity index ψ is introduced according to Greenwood and Williamson The relation between separation h and σ of the surface microgeometry model and d and σs of the asperity-based model is given asthen, a form for plasticity index is obtained by substituting Eqs. ( illustrates the contact area versus separation, both given in dimensionless form, for the AFM and CEB models. While both models predict similar contact area for low plasticity index, the AFM model predicts higher values for materials of higher plasticity index. depicts the dimensionless separation h* versus dimensionless load P/AnE for different values of plasticity index ϕ as predicted by the AFM and CEB models. It is clear from the figure that the separation increases with the plasticity index for a given load. For low plasticity index (harder material), the contact is approximately totally elastic. As summarized in , lower plasticity index corresponds to larger critical interference, wc. This in turn increases effective separation for plastic asperity as seen in Eqs. (). The result is diminished contributions of plastic asperities. Hence in Eq. () Pe2 and Pp2 attain a smaller value, resulting in the following approximationTherefore material with low plasticity index may be approximated as a purely elastic body. On the other hand, for high plasticity index (softer material), the contact is approximately totally plastic and the total expected dimensionless contact load for elastic–plastic contact of (Again, a similar explanation may be used with respect to the AFM model. A high value of plasticity index corresponds to a low value of the critical interference, wc. This in turn causes Pe2≈Pe1 as suggested by Eqs. (). Therefore, the net elastic contribution is diminished resulting in the approximate Eq. (It is the intent of this subsection to evaluate the proposed model (AFT) and present a comparative study of the model with those proposed by CEB and KKPK. In doing so we present the experimental results by Kucharski et al. where a is the approach, and zmax and h are the maximum peak height and separation. illustrates the results. In this case dimensionless approach is with respect to the maximum summit height, Msh. Clearly, the proposed (AFM) model presents the most favorable agreement between the predicted contact load/approach values to that obtained by measurements. The accuracy of the AFM model is also attested to by the results shown in . The results show that the AFM model provides significantly more accurate prediction of contact load and contact area than CEB and KKPK models.In this section direct formulation of contact of rough-on-rough surfaces based on the work of Greenwood and Tripp where z1 and z2 are the heights of asperities on surfaces one and two, respectively. r is the radial distance denoting the offset between the central lines of the two asperities. For a summit radius of curvature R, the presumption of Hertzian contact leads toThe expected dimensionless contact load for elastic contact isHence, using the proposed method, the total dimensionless expected contact load for elastic–plastic behavior isand σ denotes the standard deviation of sum of asperity heights on the two surfaces.A mathematical formulation of elastic–plastic contact has been forwarded in this paper. Using the definition of critical interference the concept of elastic and plastic asperities have been developed in which a rough surface is represented by two surfaces. The first surface is the actual physical surface and is assumed to deform as a purely elastic body. The second surface is a fictitious one and it is derived from the physical surface and the critical interference. This surface is assumed to deform as a purely plastic body. The development of the elastic and plastic surfaces has facilitated the mathematical formulation of elastic–plastic contact of rough surfaces. Comparison of the proposed model with the existing models for elastic–plastic contact have been performed. The measurement results of previously performed experiments on sand-blasted steel surface Consider an asperity and assume that its shape is quadratic as proposed by Greenwood and Tripp . The figure also illustrates fictitious plastic asperity whose shape is obtained by a displacement of wc along the normal to the quadratic curve. Let u¯t and u¯n represent the tangential and normal unit vector to the quadratic at point A. The position of point A is given by vector r¯A asThe unit tangential vector is obtained asThen the description of the plastic asperity is obtained byr¯B=ρ1-wc/R1+ρ2/R2i¯+ρ22R+wc1+ρ2/R2-wcj¯.For small wcR and ρR, r¯B may be approximated byTherefore, the shape of the plastic (fictitious) asperity is given byIn silico analysis of Superelastic Nitinol staples for trans-sternal closureSuperelastic Nitinol staples, utilized routinely in foot surgeries, are proposed to be used for sternal closure application in this study. It is hypothesized that the shape memory induced superelasticity will allow multiple staples placed along the sternum to promote fast and safe recovery by maintaining constant clamping pressure at the sternotomy midline.Two different Nitinol staples of different alloying compositions, one representing the metal formed wire geometry and, the other, powder metallurgy manufactured rectangular geometry, are chosen from the literature. Austenite finish temperatures of both materials are confirmed to be appropriately below the body temperature for superelastic shape memory activation. The adopted finite element superelasticity model is first validated and, via design optimization of parametrized dimensions, the staple geometries for producing maximal clamping forces are identified. The performances of the optimized staples for full trans-sternal closure (seven staples for each) are then tested under lateral sternal loading in separate computational models.The optimized metal formed staple exerts 70.2 N and the optimized powder metallurgy manufactured staple exerts 245 N clamping force, while keeping the maximum localized stresses under the yield threshold for 90° leg bending. Testing the staple-sternum constructs under lateral sternal loading revealed that the former staple can be utilized for small-chested patients with lower expected physiological loading, while the latter staple can be used for high-risk patients, for which high magnitude valsalva maneuver is expected.Computational results prove that superelastic Nitinol staples are promising candidates as alternatives to routinely performed techniques for sternal closure.Nitinol is an intermetallic and roughly equiatomic compound between nickel and titanium that belongs to the family of shape memory alloys (SMA) and exhibits two unconventional but valuable thermo-mechanical properties that set them apart from the traditional metallic alloys. The first property is superelasticity for which the material can retain and recover its original shape despite experiencing larger strains that would cause plastic deformation for other metals (). The second property is the shape memory effect for which the material remembers the trained 3D shape at high temperatures even when highly deformed at lower temperatures (). Both the attributes of SMAs depend on changes in the solid phase atomic structure between the ordered austenite and less ordered martensite configurations in response to thermal or mechanical loading (Thanks to its unique material characteristics and great biocompatibility, Nitinol's value in medical applications was immediately realized and the alloy is being used widely today from cardiovascular stents to surgical endoscopic tools (). In this paper, the emphasized application for Nitinol will be the medical superelastic staple, typically implemented as an orthopedic solution to foot-related surgeries, e.g. phalangeal osteotomy, joint fusion, and Lapidus arthrodesis (). The success of superelastic Nitinol staples as small clamps in compressing two phalangeal bone segments together is already well-documented via clinical trials in the medical literature (A potential application of superelastic staples is in sternotomy procedure, conducted during open thoracic surgeries. However, investigating previous sternal closure studies, it was realized that such utilization of Nitinol staples for bringing together two halves of the bisected sternum has not yet been discussed. Among the available closure techniques are the stainless steel (SS) suturing wire, which is the most used method, plate-screw systems, and interlocking mechanisms (). Each closure technique has its own trade-offs with respect to cost, ease of implementation and performance. The main goal of the sternal closure is to enable safe and fast recovery of the sternum anatomy and to avoid post-surgical complications, which include dehiscence, mediastinitis, and wound infections (). Thus, the choice of closure technique is critical for the sound recovery of the patient.While Nitinol is not utilized widespread among sternal closure solutions, the successful application of thermo-reactive SMA clips has been discussed in the literature (). The most well-known example is the Flexigrip™ product by Praesidia (). The peristernal clips are malleable at low temperatures (<8 °C), as martensite dominates the lattice structure, and can be deformed easily to fit across two opposing intercostal gaps (). After loosely implanting the clips along the sternum, a hot solution is applied for thermal activation and recovery of the original memory shape, allowing the clips to tightly clamp the sternal halves together; this temperature-dependent memory-effect takes place above the austenite finish temperature (>Af ≈ 35 °C) (). However, while Nitinol clips have been observed to provide acceptable sternal wound stability, the means of intraoperative thermal activation, which is the application of a towel soaked in hot water solution, is quite inconvenient at the operative stage. Also, the surgeons are limited by the available clip sizes (ranging from 22 to 40 mm), making the size choice of the clip critical to avoid the cases for which the original memory shape would fail to exert adequate compression.To provide an alternative solution to thermo-reactive Nitinol clips for sternal closure, in this study, it is proposed that similar geometry staples, utilized in foot surgeries, can also be implemented for median sternotomy. A sample implantation procedure is demonstrated in . Suitably, the narrow temperature range in which the SMAs exhibit superelasticity over their Af, includes the human body temperature (37 °C) (). Thanks to this superelastic property, the Nitinol staple would apply constant clamping pressure across the sternotomy midline to promote stability and fast healing. Two custom Nitinol staple geometries are created via design optimization tools available in the chosen finite element (FE) software (ANSYS, v19). The mechanical performances of the staples are then proved under the anatomical sternal loading scenario. The promising results indicate that the Nitinol staple is a strong candidate for sternal closure.The initial step before carrying out the finite element analysis is to correctly define the superelastic properties of Nitinol. It is documented in the literature for a narrow temperature range over the Af, SMAs demonstrate superelasticity that allows for recoverable elastic strain up to 11%; this phenomenon is enabled by the stress-caused transformation from austenitic structure to martensitic structure (). The superelasticity material model in ANSYS is based on a simplified SMA model proposed by Auricchio in 2001 (). According to the model, the isothermal stress-strain behavior up to the elastic strain limit of the material under loading and unloading regime follows a hysteresis curve with four different critical points, which are the start and end stress values for the forward and the reverse phase transformations from austenite to martensite (). This model assumes a slightly different compression behavior in comparison to tensile, and that the elastic modulus of the austenite (EA) and martensite (EM) are not identical; for a better approximation, in this study, both the juxtaposed quantities are assumed to be identical.It must be noted that the pseudoelastic behavior of the material, along with austenite and martensite start and end temperatures are directly dependent on the chemical composition of the alloy and the means of manufacturing, i.e. powder metallurgy vs casting followed by metal forming processes (). Typically, the superelastic stress-strain response and the pertaining material parameters are characterized via tensile loading and unloading on a wire specimen, but for this study, the properties are extracted from Nitinol staple literature after a comprehensive survey. The most critical requirement was that the Af of the material was sufficiently close but below the body temperature for proper activation of the staple to achieve the desired compression.Nitinol properties from two different studies are chosen as a reference that satisfies the activation temperature condition, denoted by M1 and M2 henceforth (see M1: TiNiCo (48.8% Ni, 1.3% Co) alloy manufactured by via vacuum induction melting that are cold drawn and annealed at 400 °C for 30 min with a circular cross-section, representing the metal formed staple case., whose superelastic FE response is calibrated to the metal injection molded and sintered (5 h at 1230 °C) NiTi (50.7% Ni) by , representing the powder metallurgy staple case.Since the proposed sternal staple will have a custom geometry that is not identical to commercially available staples utilized for foot surgeries, the aim of this study is to computationally investigate the feasibility of utilizing two different manufacturing methods with different cross-sections, dimensionally optimized for the sternal application.To observe the calibration of the superelastic constants, initial FE tests are run to simulate the stress-strain behavior of M1 and M2. A 100 mm long M1 wire with a 1 mm radius and a 100 mm long M2 wire with 2 mm by 2 mm cross-section are tested under tensile loading and unloading. Tests are performed on each wire for a maximum displacement of 0.5 mm over σMF strain, while fixed at the other extremity. The simulations are conducted with 25759 elements and 5382 nodes for M1 and 18065 elements and 3200 nodes for M2. For all the simulations in this study, mesh sensitivity is checked, large deformations are enabled, and linear isotropic elasticity is assumed throughout.The main goal of the optimization is to reveal the optimal staple dimensions for the chosen dimensional ranges that will produce the maximum Fc while not inducing stresses above the chosen yield limit of the materials. Initial geometries both for M1 and M2 staples are chosen, before carrying out design optimization. The dimensional parameters that will majorly determine the Fc and the stresses for a staple geometry are the initial leg angle and the cross-section. Thus, for M1, the cross-sectional radius, r, the leg angle, α, and for M2, the cross-sectional height, h, thickness, t, and the leg angle, α, are selected as parametric dimensions.In order to characterize the Fc of the staple, FE models are created for a half staple geometry. To allow parametrization, the models are generated in ANSYS DesignModeler. The working principle of the staple is first distracting the legs with the help of a reverse-action forceps until they are approximately perpendicular to the staple bridge. To simulate the Fc at the 90°, the staple is fixed at the half-bridge cross-section and a rectangular block, that represents the cortical sternal tissue, is displaced towards the bent staple leg until the desired distraction of the leg is achieved. Via this simulation, also the stresses that will be created on the sternal tissue are calculated for which the staple geometry can also be adjusted to not create stresses that will damage the sternal tissue. The initial dimensions for the M1 and M2 staple, the boundary conditions for the simulations and the mesh are shown in The staple half-bridge length is fixed to 5 mm, such that a 5.25 mm displacement of the sternal block (bearing in mind the bridge-leg junction) opens the leg to near 90°. Also, to accommodate the average 10 mm sternum thickness, the staple legs are fixed to 11 mm for the bicortical clasp of the sternum during the optimization process. The static structural FE statistics are recorded in . A frictionless contact is defined between the sternal block and the staple; for varying initial leg angles, the starting contact gap can be far, thus, a pinball radius of 1 mm is chosen for the contact that was confirmed to produce appropriate results for all initial leg angles. The maximum Von Mises stresses (σMAX) and the force reaction at the contact are chosen as the output parameters for which the input parameters are optimized for.Employing the optimization tools in ANSYS, first, the central composite type designs of experiments are created with several sample design points (9 for M1 and 16 for M2). The designs of experiments are then utilized to find the best response surfaces using the genetic aggregation method for both models. Then, the desired objectives are introduced to the optimization tool to carry out a multi-objective genetic algorithm for finding the best dimensional parameters. The chosen dimensional parameter ranges are as follows:The parameter boundaries are selected such that the maximum anterior thickness of the staple should not exceed 3 mm as the thickest plate screw systems and interlocking mechanisms are at most 3 mm thick; else due to thin subcutaneous tissue over the sternum, there is a risk of bulging and causing discomfort for the patient. In addition, a smaller initial angle than 65° causes opposite staple legs to collide for the chosen bridge-length and an angle above 80° does not allow meaningful angular distraction for applying Fc. The optimization objectives are chosen as follows:σMAX of the staple must be below the yield strength of the alloyFc in x-direction should be maximized given the first criterionAccording to the results of the optimization, the final geometries for both M1 and M2 staples are decided upon, which are then implemented on the sternum to simulate a full closure.There are three modes of anatomical loading on the sternum, which are lateral, transversal (anterior-posterior), and longitudinal (rostro-caudal) (). As a design requirement for the sternal closure device, the most critical loading mode is the lateral loading since the forces act perpendicularly to the median sternotomy line and can cause separation of the sternal halves. Furthermore, the physiological extreme loadings caused by coughing and sneezing induce sudden lateral forces on the sternum and the method of sternal closure should be rigid enough to brace such forces. Repeated separation of the sternal halves during the first weeks of recovery and overall instability at the sternotomy midline will majorly hamper the osteosynthesis and lead to dehiscence.The forces that act on the transversal and the longitudinal directions have comparably low magnitudes (). In addition, as the sternal closure device pushes the two halves against each other, the frictional contact forces at the sternotomy midline reinforce the rigidity of the healing sternum against such loading (). Consequently, the longitudinal and transversal physiological forces impose negligible design objectives on the sternal staple. Since the characterization of the frictional behavior between the two sternal halves is challenging and not discussed in the literature prior, loading in transversal and longitudinal directions are omitted and purely lateral loading is implemented on the sternum for the FE simulations.The physiological extreme lateral loading limits are once again extracted from the previous literature. Adams et al. conducted sternal force measurement tests on healthy volunteers for different daily activities and for both regular breathing and valsalva maneuver via pressure-detecting esophageal catheters (). The maximum calculated loading was 153.9 kg for the high valsalva sneeze with a mean of 68.9 kg. This measurement is also corroborated by the calculation of Casha et al. which reveals that the theoretical strong coughing forces for large chested patients can even reach 1500 N (For FE lateral loading simulations, a solid model of a half female sternum is utilized. The sternum geometry is extracted from the open-source Visible Human Project datasets (). The geometry of the sternum and the location of the seven chosen staple leg slot holes are illustrated in . Lateral displacement is applied to the median sternotomy cross-section, similar to the FE boundary conditions of Section , in order to characterize the rigidity of the closure. The staples are initially placed with a 5.25 mm lateral offset with respect to their designated slot hole, such that at the end of 5.25 displacement, all the staple legs will be bent 90°, representing the ideal closure scenario. The FE material parameters for healthy sternal cancellous and cortical tissues are taken from the work by Furusu et al. (). The outer cortical wall is assumed to have approximately 1 mm thickness in accordance with the sternum thickness micro-CT study conducted by . The sternum is meshed with 3 mm sized tetrahedral elements (76837 nodes, 36978 elements).The results of the FE calibration test, outlined in section . It can be seen from Fig. (d) that both the M1 and M2 wires demonstrate the desired stress-strain response. For stresses over σMF, the lattice transforms completely from austenite configuration to martensite and continues to deform elastically up until the yield point of the martensite lattice.The yield point of the martensite lattices of M1 and M2 are not characterized in their respective studies; however, it has been reported that the true dislocation based yielding of Nitinol occurs above 900 MPa (). Thus, in this study, the allowable stress limit has been chosen to be 100 MPa above respective σMF limits of M1 and M2 (σM1yield = 700 MPa, σM2yield = 600 MPa). The selection of a theoretically lower yield limit for the material also introduces a safety factor for the staple design that will ensure plastic deformation will be avoided for the designated physiological sternal loading extremum.Before moving on to the optimization step, comparative validation tests utilizing the FE setup of are carried out. For the M1 staple, Lekston et al. report 26 ± 1 N clamping force for experimental bending of a 1.3 mm diameter staple leg from 60° to 90° at room temperature (). 65.43 N clamping force was calculated by the recreation of the 90° bending scenario and no detrimental stress accumulations were observed (<500 MPa). As a result, the superelastic model adopted for this study is validated for both the M1 and M2 staples.The generated response surfaces indicating the relationships between the dimensional input parameters and the FE based output parameters are illustrated in ((a) and (e) for M1 and the rest for M2). A linear extrapolated elastic model is used in this study for the understanding of the overall input-output relationship for the chosen dimensional parameter range. Since plasticity is not introduced into the FE models and Nitinol is assumed to start yielding above this stress threshold, the results with a Von Mises stress above 900 MPa do not properly convey a meaningful stress value (For the M1 staple with the circular cross-section, (a) shows that a thicker cross-section and a lower initial leg angle causes the most stresses when the staple is bent. However, (e) shows that the clamping force is primarily dependent on r, and, for a given r, α doesn't change the clamping force. Thus, the design of the M1 staple is straightforward as α should be chosen as high as possible while r should be chosen as the highest value that will produce a σMAX below σM1yield.For the M2 staple with rectangular cross-section, (c) and (d) reveal that the thickness parameter of the staple minimally affects the σMAX and should be maximized to maximize the clamping force, apparent from (g) and (h). Even though h and α have a non-linear relationship, the lowest stresses are seen when α is maximized; thus, once again, the highest h should be chosen that will keep the σMAX below σM2yield.The σMAX FE results for the initial and optimized staple geometries are presented in (a) and (b), there is detrimental stress accumulation at the lower bridge-leg junction, which is under tension due to bending. At 90° leg opening, the staple could crack and fail due to sustained localized stresses over the yield limit and plastic deformation at the lower bridge surface. For the optimized staples, shown in (c) and (d), there are no stress accumulation regions at the junction that cause a spike and the σMAX for both staples is below the designated thresholds. The evolution of σMAX is checked for the complete opening of the legs for the optimized geometries, plotted in (e) and (f). It is confirmed that at no point in bending, σMAX reaches a value above the yield strength and superelasticity is maintained throughout. Furthermore, in none of the FE models, the stresses on the sternal block exceed the yield strength of the cortical sternal tissue at parallel contact between the sternum and the staple leg, which is critical to avoid catastrophic complications caused by bone cut-through.The optimized M2 staple exerts 245 N of Fc at 90°, which means that seven of these staples are expected to apply adequate force towards the sternotomy midline to even endure the high valsalva loading reported by Adams et al. (7 × 245 N = 1715 N > 153.9 kg) (). However, this maximum threshold cannot be realistically reached using the M1 staple, as at least 22 of them would be needed to apply adequate Fc (22 × 70 N = 1540 N > 153.9 kg). Nevertheless, the full sternal closure performance comparison of M1 and M2 is presented in . Each FE model contains seven appropriately shaped slots for seven staples. The leg lengths have been properly adjusted for each slot thickness, to ensure bicortical contact; it is confirmed via FE simulations that the leg length did not affect Fc. The half-sternum is displaced in 0.05 mm increments up until σMAX exceeded 1000 MPa, representing the case for which the staples are forced to bend beyond 90° under higher than expected lateral forces and experience true yielding.In addition, for displacements that would bend the legs beyond 90°, it is observed that Fc starts to exponentially increase. This is a desired property for the staples, such that it gets exponentially harder to separate the sternal halves from each other for increasing thoracic pressures. Seven M2 staples already exert adequate total Fc to accommodate the extreme valsalva loading, but, while seven M1 staples at 90° leg bending do not provide sufficient total Fc, at 5.55 mm displacement of the sternum (0.3 mm over 90° bending at 5.25 mm mark), the total Fc reaches 1885 N which is sufficiently over the 1500 N extreme lateral loading threshold. Consequently, a seven M1 staple construct would not allow more than 0.6 mm sternal separation even for the strong cough of a large-chested patient. Furthermore, in M1 staples, it was seen that up to a certain sternal displacement over the 5.25 mm mark, σMAX increases marginally for rapidly increasing Fc, which demonstrates its ability to apply strong clamping without entering the plastic regime for repeated high magnitude loading. Finally, no substantial stresses were realized at the cortical tissue at 90° leg bending, indicating that the trans-sternal application is safe for both staples.There is no consensus on the ideal sternal closure technique thus far in the literature (). The routinely utilized SS suturing is the primarily chosen technique due to its low manufacturing cost, reliability, and familiarity of cardiac surgeons with the implantation process (). While post-surgical complications rarely arise for patients that are not high-risk, this has not stopped the development of alternative sternal closure methods to further advance towards a more optimal solution (). Plate-screw systems, interlocking mechanisms, and thermo-reactive Nitinol clips are among these types of solutions that attempt to provide better sternal rigidity in exchange for increased implant costs (). The novelty in this article lies in proposing another alternative solution to sternal closure that has not yet been discussed in the literature. It is proved computationally that Nitinol staples, successfully utilized for foot surgeries, can also be implemented to achieve rigid trans-sternal closure when their geometry is optimized for this application.The most critical comparison of the Nitinol staples is against the SS cerclage, as the increase in material and manufacturing costs must provide adequate advantages over the yardstick solution. The biggest disadvantage of the SS cerclage is the sustained cut-through damage that leads to sternum wounding and dehiscence (). This is because the standard SS wire diameter is 0.75 mm, which creates stress accumulation at the sternum contact; the cutting is even more pronounced for trans-sternal application compared to peri-sternal looping due to decreased contact area with the supporting cortical bone. Furthermore, it has been documented that the SS cerclage can also fail and break under high sternal loading (). For the Nitinol staples, the trans-sternal application is much safer as the contact area is highly increased thanks to the larger clamping leg geometry, alleviating the stress accumulation problem at the cortical tissue, which is confirmed throughout the FE simulations. In addition, for even the extreme valsalva loading, the maximum stresses on the staples are in the acceptable range. The stresses only concentrate at the lower bridge surface and even when passing the yield limit, it is less likely for the thicker staples to fail catastrophically unlike the breaking of the thin steel suture that renders a whole loop useless.Compared to the other alternative solutions, the Nitinol staples have niche benefits while providing satisfactory rigidity to the sternum. Emergency re-entry is much easier compared to plate-screw systems and the implantation steps are much more straightforward compared to interlocking mechanisms as these products typically require their specialized surgical equipment for implementation (). Ideally, for the implantation of staples, all that is needed is a surgical drill for the creation of the leg slots and reverse-action forceps to distract the arms to 90°. Against the thermo-reactive Nitinol clips, the step of artificially increasing the temperature of the clips after implantation is also completely avoided with the superelastic staples, which is among the procedural inconveniences that lead to the proposal of such a solution outlined in this study.The most critical advantage of the superelastic staple, however, is its ability to apply constant pressure to the median sternotomy midline stemming from its SMA properties. Since the staple wants to revert to its original geometry for temperatures over Af, a constant compressive force is created between the legs of the distracted staple; achieving such large strains under bending while not entering the plastic deformation regime cannot be achieved with other traditional engineering metals. The maintained clamping force to promote rapid osteosynthesis is the main allure of the proposed staples. The design can even be further enhanced with serrations and notches at the leg-sternum contact to prevent pull-out migration of the staple by increasing the traction at the leg slots (Among the limiting design considerations is the fatigue life. While Nitinol brings all the unique SMA properties, it is notorious for having very low fatigue life compared to other biomedical metallic alloys (). Thus far, the highest reported fatigue life for the superelastic Nitinol staple is still below 30000 cycles (). This is an indication that without a significant breakthrough on the material side, Nitinol implants are unsuitable for applications that impose high values of cycling strains over long periods and when repetitive high-magnitude and sudden loadings are in play (). These are among the reasons the Nitinol staple geometries were optimized for lower yield thresholds than expected to avoid fatigue fracture as much as possible while still having them exert adequate clamping force. Repeated loading, even as infrequent as sporadic coughing, that creates localized stresses near the true yielding of the alloy, would undoubtedly result in the early failure of the implant. Nonetheless, despite the low fatigue life, the reported average force created by the moderate level breathing is 41 kg by Adams et al., which can be safely braced by the multiple staple closure. Bearing in mind the healing of the sternum, triggering the synthesis of mechanically-supporting cortical tissue, the loading on the closure gradually decreases. Consequently, the staples must bear the full loading for only the first few weeks of complete sternal recovery, which typically lasts up to 4–6 weeks.Additionally, the nature of the FE analysis employed for this study is static and dynamic effects caused by the strong and sudden anatomical loading such as coughing are neglected. This is specifically a critical concern for SMA materials since they exhibit strong strain-rate dependency, a phenomenon well-established in the literature (). It has been observed that, with increasing strain rates, both the critical stress points (σMS, σMF, σAS, σAF) and the slopes of the phase change plateaus increase. Consequently, the loading-unloading hysteresis loop changes, the response of the staple is stiffer and even the maximum recoverable strain decreases. Such high-strain rates would negatively impact the overall performance of the sternal staple and could lead to earlier than expected failure. More advanced FE models, incorporating the strain-rate effect, as proposed by , can be utilized in follow-up studies to characterize the behavior of sternal staples for high valsalva maneuver.In this study, two different Nitinol alloys from the literature are chosen as superelastic sternal staple candidate materials with two different cross-sectional geometries. The M1 staple is the metal formed Nitinol wire, used by Lekston et al. as craniomaxillofacial fixators, while M2 staple is the powder metallurgy manufactured staple proposed by Saleeb et al. for general bone fracture stabilization. Conducting a design optimization analysis on parametrized staple dimensions with linearly elastic FE models, dependency trends of dimensional parameters are identified. It is found that both candidate materials, for the optimized staple geometries, are suitable for sternal application to bear the physiological loading.Since the powder metallurgy case allows the manufacturing of a more flexible geometry, the optimization results of M2 were better than the M1 staple. For the M2 staple, the thickness can be almost freely adjusted to increase the clamping force while not influencing the maximum stresses; this is the main reason the final optimized geometry turned out to be much thicker, with the ability to apply very high clamping forces, when compared to other Nitinol staples discussed in the literature. On the other hand, for the M1 staple, in terms of adjusting the cross-sectional area, only the radius could be adjusted to conserve the wire geometry, which would proportionally increase the maximum stress for increasing radius. Furthermore, while the circular cross-section must be kept uniform at the bridge-leg junction for the M1 staple, such a restriction did not apply for the M2 geometry, such that the stresses that tend to accumulate at the leg-bend did not impose a design challenge.Overall, the M1 staple is proposed to be utilized for smaller-chested patients for which the anatomical loads are expected to be on the lower end, whereas the M2 staple can be implemented in high-risk patients for full sternal closure. Another analysis that can be conducted for future work is finding the optimal number of staples and their locations along the sternotomy midline. For this study, a computational sternal loading that is comparable to an in vitro lateral loading setup is employed. This is among the limitations of this study as it has been reported in the literature that the anatomical loading is imbalanced and relatively higher separation is observed at distal sternal regions closer to the xiphoid. Fortunately, the proposed stapling strategy is adaptable such that the lower portions of the sternum can easily be reinforced by installing more staples at critical positions.This computational biomechanical study is first in the literature to discuss such a potential application and to provide insights on critical mechanical design optimizations for SMA staples that are already in use for other biomedical fixation applications. It is hypothesized that the creation of peri-sternally applied superelastic sternal implants can even quicken the implantation process by circumventing the drilling step, which will be the concentration of a follow-up study by our research group along with in vitro and in vivo experimentations of Nitinol staples to further demonstrate the feasibility of our proposed sternal closure solution.Omer Subasi: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Writing - original draft, Writing - review & editing, Visualization. Shams Torabnia: Software, Validation, Formal analysis, Investigation, Writing - review & editing. Ismail Lazoglu: Formal analysis, Resources, Data curation, Writing - review & editing, Supervision, Project administration.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Impact response of recycled polypropylene-based composites under a wide range of temperature: Effect of filler content and recyclingThis work aimed at investigating the thermal mechanical behavior of recycled polypropylene (PP)-based composites under dynamic loading. PP was blended by extrusion with different fractions of ethylene octene copolymer (EOC) as soft rubber toughening agent and talc as rigid reinforcing agent. To simulate mechanical recycling, the composites were grinded and re-extruded up to 6 times. The dynamic behavior was studied by means of a split Hopkinson pressure bar at various strain rates and temperatures. We found that neat PP and PP/talc composites presented a brittle behavior at low temperatures. The addition of EOC inclusions markedly improved the impact resistance of PP and PP/talc. The results also indicated that the impact resistance of PP/talc was improved with the recycling numbers due to a fragmentation of the talc particles during the reprocessing inducing a self-reinforcement. However, the impact resistance of PP/EOC decreased with the recycling due to chain scission mechanisms. Concerning PP/EOC/talc composite, its dynamic behavior was almost constant with the recycling number possibly induced by equilibrium between self-reinforcement and chain scission mechanisms. Complementary information about the dynamic behavior of the materials was deduced from optical microscopy investigation of the morphology after dynamic compression testing.Polypropylene (PP)-based composites are increasingly becoming preferred engineering materials in the automotive application and in particular for both exterior and interior parts. However, the increasing use of PP-based composites results in huge plastic wastes from end-of-life vehicles (ELV). For both environmental protection and waste management considerations, it is of great importance to drastically increase the re-use and recovery rate of these plastic wastes. Among different recycling methods of plastics, the mechanical recycling is the simplest and the more ecological one where the post-used ELV plastics are mechanically grinded and reprocessed to produce new structural parts The mechanical reprocessing at high temperature, intensive shearing conditions, and with the presence of oxygen and impurities could lead to thermal, thermo-oxidative and thermo-mechanical degradations of the material and consequently, can affect the properties of the resulting recycled material To the best of our knowledge, the influence of the filler content and recycling number on the dynamic behavior of PP-based composites has received little to no attention. In the automotive industry, PP-based composites are generally used for the manufacturing of bumpers. For this application, if an accident occurs, composite structure could be subjected during the impact to a single loading mode as bending, tension, and compression, or to a combination of them. In this context, dynamic compression testing is generally considered as simple and practical way to investigate the mechanical response of the materials for high strain rate impact. A detailed study of high strain rate and temperature sensitivities of non-recycled and recycled PP-based composites would be of high scientific interest for the development of a robust constitutive model. In particular, such a model could be used as a fully three-dimensional user subroutine (VUMAT) for commercial Finite Element code such as ABAQUS. The aim of this work was to study the impact of the content of ethylene octene copolymer (EOC) as toughening agent and talc as reinforcing agent on the dynamic compression behavior of recycled PP-based composites, prior and after mechanical recycling. The dynamic compression behavior was investigated by using split hopkinson pressure bars (SHPB) under a wide range of temperature and strain rate. The macroscopic mechanical properties were correlated with the morphology of the studied composites by optical microscopy (OM) observations after dynamic compression testing.A highly isotactic polypropylene (PP) supplied by Lyondellbasell was selected for this study (reference Moplen HP500 N, Frankfurt am Main, Germany). This PP had a melt flow index (MFI) of 12 g/10 min and a density of 0.9 g/cm3PP blends containing 0 wt.%, 10 wt.% and 20 wt.% of EOC or talc (PP/EOC, 100/0, 90/10, 80/20, or PP/talc, 100/0, 90/10, 80/20, respectively) were prepared by extrusion. PP with 20 wt.% of EOC and 10 wt.% of talc (PP/EOC/Talc 70/20/10) was also processed. These compositions are similar to available commercial PP composites for car bumpers Finally, tensile samples for all the materials were injected by means of a Billion 90 tons injection molding machine (Bellignat, France) with temperature profile ranging from 190 °C to 220 °C and a screw rotation speed of 180 rpm. Note that neat PP and PP-based composites were denoted as PP neat, PP/EOC x/y, PP/Talc x/z and PP/EOC/Talc x/y/z, respectively, where x, y and z are the weight percent of PP, EOC and talc, respectively. Concerning the recycling number, it was denoted as 0P, 3P and 6P. lists some main properties of the virgin and the recycled materials for which detailed information about the material characterization has been reported elsewhere A homemade split Hopkinson pressure bars (SHPB) was used to perform the uniaxial compressive high strain rate testing (). This apparatus consisted of three parts, a striker, an input bar and an output bar made of 316L steel, with lengths of 500 mm, 2903 mm and 2890 mm, respectively, and the same diameter of 22 mm. The strain gages were glued on the middle of the incident and the transmitted bars with a distance 1500 mm from the interface of the specimen and bars. The cylindrical samples with a diameter of 8 mm and a thickness of 3 mm were cut from the injected tensile samples and placed between the input bar and the output bar. It is to be noted that thin samples are more acceptable than thick samples to minimize the effects of the non-uniform stress field and inertia of samples in SHPB approach The striker was used to generate a longitudinal compressive wave. Once this compressive wave reached the incident bar, strain gages cemented on this bar recorded an incident wave ε1(t). The difference in the mechanical impedances at the interface between the incident bar and the specimen resulted in the fact that a part of the incident wave reflected back along the incident bar while the other part transmitted through the specimen and then within the transmitted bar. The reflected wave εR(t) was measured by the same strain gages cemented on the incident bar. The transmitted wave εT(t) can be obtained by the same type of strain gages glued on the transmitted bar. In addition, two speed sensors were used to measure the velocity of the striker. shows the incident, reflected and transmitted waves obtained from the SHPB device for the non-recycled PP at 25 °C and at a strain rate of 1247 s−1.Based on the classical elastic wave propagation theory, when the stress and strain fields were uniform in the specimen, the nominal stress σn(t), the nominal strain (εn(t)) and the nominal strain rate (ε̇n(t)) of the tested materials were computed by the following expressions Here Cb was the elastic wave speed in the incident and the transmitted bars (bars are made of the same materials); E was the Young’s modulus of the bars; L represented the initial thickness of specimen; A and AS were the cross sectional area of the bars and the specimen, respectively. The nominal measurements were used to derive the true ones (with the subscript t) by the following equations with a SHPB testing analysis software These equations were written for compression when strains were taken positive. Eq. was derivated from σt(t)=σn(t)(1-εn(t))2v, where ν was the Poisson’s ratio. For an incompressible plastic material, this Poisson’s ratio was equal to 0.5. In this work, a value of ν |
= 0.4 was previously measured for neat PP and PP-based composites In this study, dynamic tests were carried out at various temperatures ranging from −30 °C to 85 °C (−30 °C, 0 °C, 25 °C, 50 °C and 85 °C), and various strain rates ranging from 592 s−1 to 3346 s−1 (ε1̇=592±6.5%s-1, ε2̇=1276±7.9%s-1, ε3̇=2221±5.6%s-1 and ε4̇=3346±4.3s-1). Each test was repeated 5 times and hence, averaged strain rates and averaged curves were reported here. In the manuscript, these four strain rates were denoted as strain-rate-1, strain-rate-2, strain-rate-3 and strain-rate-4, respectively.The morphology of the materials before and after dynamic testing was studied by a pressure-controlled scanning electron microscopy (SEM) FEI Quanta FEG 200 (Hillsboro, Oregon, USA). The SEM was used with a pressure of 150 Pa and the images were recorded with the chemical contrast mode using the gaseous analytical solid-state back-scattered electron detector (GAD). To get complementary information, morphological observations were also conducted with an optical binocular Leica MZ12.5 (Wetzlar, Germany). This equipment was equipped with a digital camera model DS 2 mV coupled with an NIS Elements acquisition software Br2.30 allowing pictures to be recorded.SEM images of the cryo-fractured surfaces obtained under low magnification exhibit a good dispersion of the talc fillers in the PP matrix, as shown in a for PP/EOC/Talc 70/20/10 0P. In this figure, the high contrast images clearly show the plate-like talc fillers appearing with a bright contrast and PP matrix appearing with a dark contrast. However, at this low magnification, we cannot observe the EOC inclusions. This result may be explained by a limited chemical contrast between PP and EOC attributing to a similar chemical composition and/or by the small size of EOC inclusions (see b), well-dispersed spherical EOC inclusions within PP matrix were noted due to a topographical contrast induced by EOC inclusions in the cryo-fractured area.The experimental true stress–strain curves in compression of the non-recycled neat polypropylene and PP-based composites at different temperatures and under strain-rate-2 (ε2̇=1276s-1) are shown in . Note that the unloading part in these curves indicates the end of the dynamic test. The non-recycled neat PP and non-recycled PP/talc composites presented a brittle behavior at −30 °C and 0 °C. This is due to the glass transition temperature of non-recycled PP which is around 12 °C The materials PP/EOC 0P and PP/EOC/talc 0P had a ductile dynamic response for all the investigated temperatures. This is due to the addition of EOC inclusions as toughening agents of PP matrix that obviously increase the impact resistance of the material. In , whatever the testing temperature, in the case of PP/EOC composites 0P, the Young’s modulus and the yield stress decreased with the amount of EOC. This can be explained by the increased amount of this soft rubber phase. It is to be noted that the addition of EOC had no significant effect on the crystallinity of PP as shown in our previous study (The experimental true-stress versus true-strain curves under uniaxial compression loading of non-recycled neat PP and non-recycled PP-based composites at −30 °C, 25 °C and 85 °C for strain-rate-2 (ε2̇=1276s-1) and strain-rate-4 (ε4̇=3346s-1) are shown in . The zoom-in view of the initial part of the true stress–true strain curves are also shown in this figure. The effects of temperature and strain rate on the dynamic behavior of the materials can be clearly observed. The Young’s modulus and the yield stress increased with increasing strain rate. Furthermore, both Young’s modulus and yield stress decreased as the temperature increased.At −30 °C, neat PP 0P and PP/talc 80/20 0P exhibited a brittle behavior for the two strain rates, while PP/EOC 80/20 0P and PP/EOC/talc 70/20/10 0P had a ductile behavior. In addition, PP/EOC 80/20 0P and PP/EOC/talc 70/20/10 0P presented a strain-softening effect after the yield point for the two strain rates. In the case of strain-rate-4, PP/EOC/talc 70/20/10 0P exhibited a higher amplitude of strain-softening than PP/EOC 80/20 0P. For the testing at 25 °C and at strain-rate-4, the dynamic response of neat PP 0P showed a typical feature of true stress strain curves in which the curves can be divided into four stages: initial viscoelastic stage, transition from viscoelastic to viscoplastic stages until the yield point, viscoplastic strain-softening stage and viscoplastic plateau By comparing the dynamic responses of the materials for the strain strain-rate-2 and strain-rate-4 (), we observed that the true stress–strain curves for PP/EOC 80/20 0P and PP/EOC/talc 70/20/10 0P at −30 °C and under strain-rate-2 have smaller amplitudes of strain-softening than that under strain-rate-4 at the same testing temperature. Similar results were obtained for PP/talc 80/20 0P and neat PP 0P at 25 °C where the true stress–strain curves of strain-rate-4 had more significant strain-softening.When the materials are tested under dynamic conditions, strain rate and temperature play an important role in the true stress–true strain curve , the less important post-yield softening with increasing testing temperature and with decreasing testing strain rate may due to a lower increase of temperature within the materials. In addition, in the cases of PP/EOC 80/20 0P and PP/EOC/talc 70/20/10 0P tested at −30 °C, and in the cases of neat PP 0P and PP/talc 80/20 0P tested at 25 °C, the adiabatic condition may induce failure of the materials by adiabatic shear banding which overcomes the high strain rate strengthening effect and result in the post-yield strain-softening , the dynamic responses of the materials at 85 °C, was characterized by less marked post-yield softening and hardening compared to lower temperatures. The true stress–strain curves of neat PP 0P and PP/talc 80/20 0P at the strain-rate-4 exhibited a very small strain-softening and then a plateau. For PP/EOC 80/20 0P and PP/EOC/talc 70/20/10 0P, the true stress–strain curves showed a less important post-yield strain-hardening comparing with that at 25 °C. These observations are mainly attributed to the softening of the materials at high temperatures We do not show the dynamic responses of PP/EOC 90/10 0P and PP/talc 90/10 0P here, because they have similar behavior to PP/EOC 80/20 0P and PP/talc 80/20 0P, respectively.The impact of recycling on the dynamic responses for non-recycled and recycled neat PP and PP-based composites at 25 °C and at strain-rate-2 are represented in . With increasing recycling cycles, the Young’s modulus and the yield stress of neat PP and PP/EOC 80/20 decreased slightly. This result may be attributed to the chain scission mechanism and the increase of amorphous chain defects that soften the materials The maximum stress on the true stress–true strain curves were chosen as the yield stress for the materials which had a marked post-yield softening. In the case of the materials characterized by a post-yield hardening, the intersection point between the tangent taken at the onset of viscoelastic stage and the tangent taken at the viscoplastic stage corresponded to the yield point. Concerning Young’s modulus, it was calculated based on the slope of the true stress–true strain curve at a strain of 0.02 for all the investigated cases. To show the strain rate dependence of yield stress and Young’s modulus, these properties were plotted as function of strain rates for non-recycled neat PP and non-recycled PP-based composite for the five temperatures (see ). The variations of Young’s modulus are not perfectly linear with the logarithmic strain rate (, plots of compression yield stress/T against logarithmic strain rate, gave for all the materials, a series of almost parallel straight lines showing that the yielding of the materials can be considered as an activated rate process , because they overlapped with the figure symbols. The yield stress of the materials with standard deviation were reported elsewhere The morphological investigation for the materials after the dynamic compressive tests was shown in . In these three figures, we did not show the results for PP blended with 10 wt.% of EOC or talc because they were similar to those of PP blended with 20 wt.% of EOC or talc. Furthermore, because there was no significant difference of morphology between the non-recycled (0P) and recycled (6P) materials after dynamic testing, we only presented here the images of the non-recycled case (0P). Last, it is important to mention that only the images corresponding to materials tested at strain-rate-4 are represented in shows the optical morphology of the materials after the dynamic test at −30 °C and at strain-rate-4. In , neat PP 0P and PP/talc 80/20 0P failed in an almost explosive manner by shear banding and cracking mechanisms ). For PP/EOC 80/20 0P, the detachment of fragments at the periphery of the sample by cracking was noted. This mechanism can be at the origin of the post yield strain-softening of PP/EOC 80/20 0P at −30 °C (). For PP/EOC/talc 70/20/10 0P, besides the peripheral fragments, the OM images also show the obvious internal fragmentation of the materials. This may be the reason why PP/EOC/talc 70/20/10 0P shows greater amplitude of post yield strain-softening compared to PP/EOC 80/20 0P at −30 °C (see OM images of non-recycled and recycled neat PP and PP-based composites after the dynamic compressive testing at 25 °C and under strain-rate-4 are represented in . It can be seen that neat PP 0P only showed peripheral fragments while PP/talc 80/20 0P showed both peripheral and internal fragmentations of the materials by cracks. These fragmentations of PP/talc 80/20 may result in an important post yield strain-softening of the materials (). For PP/EOC 80/20 0P and PP/EOC/talc 70/20/10 0P, they did not exhibit peripheral crack leading to partial fragmentation of the materials. However, OM images at higher magnification for PP/EOC 80/20 0P and PP/EOC/talc 70/20/10 0P showed shearing bands. This finding can explain the limited post-yield strain-softening of PP/EOC 80/20 0P and PP/EOC/talc 70/20/10 0P at 25 °C (see For the dynamic testing at 85 °C and under strain-rate-4, the materials deformed more homogeneously till large strain levels than those at −30 °C and 25 °C. No significant cracks were observed for all the considered materials. However, the shear bandings still exist for all the materials (Commercial polypropylene (PP) was compounded with different weight percent of ethylene octene copolymer (EOC) and talc particles (0 wt.%, 10 wt.% and 20 wt.%). In order to simulate the mechanical recycling, neat PP and PP-based composites were subjected to a maximum of six extrusion procedures. For the purpose of studying the impact of recycling and of filler content on the dynamic behavior of PP-based composites, dynamic testing were done with split Hopkinson pressure bars under a wide range of temperatures and strain rates.The results showed that the considered materials were strain-rate and temperature sensitive. The addition of EOC decreased the Young’s modulus and yield stress of PP while the presence of talc fillers increased the Young’s modulus of PP. However, the yield stress for PP/talc 80/20 was slightly lower than that of PP/talc 90/10 probably due to more important damage mechanisms by matrix/filler debonding in PP/talc 80/20 compared to PP/talc 90/10 during the dynamic testing. With the increase of the recycling number, the dynamic behaviors of neat PP and PP/EOC composites decreased. The dynamic responses of PP/talc increased with increasing reprocessing cycles. In the case of PP/EOC/talc composites, the dynamic responses were not influenced by the recycling.The dynamic behaviors of the materials were correlated with their morphology by using an optical microscope. At low temperature (−30 °C), neat PP and PP/talc composites showed an explosive failure while the other materials showed partial failure as indicated by peripheral or internal fragmentations. These failures were caused by crack and shear banding mechanisms. At room temperature (25 °C), these failures were less marked since neat PP and PP/talc exhibited partial fragmentations. At high temperature (85 °C), all the materials deformed more homogeneously without significant crack at the investigated magnifications. The observed failures of the materials by optical microscopy are in good accordance with the macroscopic dynamic responses.The present study was focused on the experimental dynamic behavior of non-recycled and recycled PP-based composites. The modeling aspects about the dynamic behavior of recycled PP-based composites with the effect of filler content, recycling, temperature and strain rate will be considered in a next study.Residual stresses and structural changes generated at different steps of the manufacturing of gears: Effect of banded structures► Microsegregations lead to fiber structures that align following the plastic flow lines in forging. ► Banded structures are not completely removed by normalizing heat treatment. ► Banded structures result in hardness and residual stresses inhomogeneities. ► Conventional heat treatment models are not valid if bands and decarburization are present.Banded ferrite–pearlite structures, and in general chemically inhomogeneous structures, react non uniformly to elevated temperatures during forging and/or subsequent heat treatment processes, affecting the final stress state (plastic deformation is required to accommodate dissimilar thermal expansion behavior for each phase) and consequently leading to distortions. These unpredicted distortions are one of the major causes of rejected components and components that need to be reworked, leading to production losses.The aim of the present research work is to study the effect of forging and different thermal treatments (normalizing, quenching and tempering), i.e., the effect of different steps of the manufacturing of gears, on the final residual stress state, microstructure and hardness of AISI 4140 steel, a material that frequently presents ferrite–pearlite banded structures coming from segregation of alloying elements (such as chromium and carbon). With this purpose, portions of a forged AISI 4140 steel ring have been subjected to different thermal treatments. Residual stresses, hardness and microstructure after each treatment (forging, normalizing, quenching and tempering) have been studied experimentally and compared with the predictions of FEM simulations of heat treatment processes.In alloy steels manufacturing, during the cooling of the ingots there is a trend to form ferritic–pearlitic bands due to segregation of the alloying elements Banded ferritic–pearlitic structures have been observed in AISI 4140 steel for example by de Albuquerque et al. Banded structures are associated with microcrack formation Heat treatment of parts is a large time and energy consuming step in the manufacturing of gears and, at the same time, is highly critical because thermal treatments can generate residual stresses in the parts, and can also relieve the residual stresses generated during previous mechanical treatments (forging and machining) in the manufacturing chain, leading to distortion of the final parts, as has been observed for example by Cho et al. Previous investigations regarding the effect of thermo-mechanical treatments (like forging and quenching) on the residual stresses have been performed on different materials, like aluminium alloys In the simulations of quenching processes the material is generally considered chemically homogeneous before and during quenching, but it is known that a real material is not homogeneous at all and it contains certain compositional fluctuations due to segregations that can lead to banded structures, as has been described in the former paragraphs. Therefore, discrepancies between experimental and simulation results can have the origin in the fact that in the models material is considered homogeneous but it is really not always homogeneous (for example when the material exhibits banded structures, surface decarburization, etc.).Taking into account these difficulties of the models to predict well microstructure and mechanical properties when material is not homogeneous, in the present research work it is aimed to study the effect of forging and different thermal treatments on the final residual stress state and microstructure in AISI 4140 steel, a material that commonly presents ferrite–pearlite banded structures due to segregation of alloying elements. Therefore, the main objective of the work is to study the effect of banded structures (and also surface decarburization) in the final properties of a component subjected to thermo-mechanical treatments, because, as has been indicated previously, in literature there is no consensus regarding the effect of banded structures on the mechanical behavior of the parts. To study how banded structures react to thermo-mechanical treatments (in particular, to the processes involved in the manufacturing chain of gears), portions of a forged ring have been subjected to different thermal treatments (normalizing, quenching and tempering). In each sample, residual stresses, hardness and microstructure have been studied experimentally. These results have been compared with the predictions of FEM models of heat treatment.The material employed in this study is AISI 4140 (42CrMo4) steel. This steel, due to its good ductility, shock resisting characteristics and resistance to wear, is commonly employed in the manufacturing of bearings, dies, gears, crankshafts, spindles, axles, etc. gives the chemical composition of this steel: both the nominal composition ranges gathered in the European Standard Specification Starting from a block of AISI 4140 steel, a ring () of 270 mm outer diameter, 190 mm inner diameter and 80 mm height has been forged at 1250 °C and afterwards cooled in calm air. The forged ring has been cut into smaller pieces, and each of these ring portions has been subjected to different thermal treatments in order to analyze the effect of each of them on the final structural state (residual stresses, hardness and microstructure).Four samples have been studied, representing each of them a different step of the manufacturing of gears:Sample 1 (forged): portion of the ring forged at 1250 °C and cooled in calm air, without subsequent thermal treatment.Sample 2 (forged + normalized): portion of the ring forged at 1250 °C and cooled in calm air, subjected to subsequent normalizing at 855 °C during 1.5 h and then cooled with N2 at 0.8 bar (low pressure N2).Sample 3 (forged + normalized + quenched): sample with the same treatment as sample 2 and subsequently heated up to 840 °C and maintained at that temperature during 30 min before being quenched with N2 at 9 bar.Sample 4 (forged + normalized + quenched + tempered): sample with the same treatments as sample 3, subsequently tempered at 600 °C during 2.5 h and followed by slow cooling. are represented the time–temperature experimental curves of the different thermal treatments described previously (normalizing, quenching and tempering). Time–temperature values have been measured by means of thermocouples located at the surface of the treated samples.Residual stress depth profiles have been measured along four lines in a plane that corresponds to the central slice of each sample (In order to perform through thickness (along the previously mentioned lines) measurements of residual stresses in a non destructive way, neutron diffraction has been employed. For these residual stress measurements SALSA instrument The data acquisition mode employed was to count for a certain number of neutrons (counts) on the detector instead of fixing a constant acquisition time. Therefore the acquisition time is adapted automatically and peak profiles of similar quality are achieved. At each measurement point strain has been measured in three directions: axial, radial and tangential direction of the ring. Depending on the point and strain direction, the measurements have been done in reflection or transmission mode. In all cases a gauge volume of 2 mm × 2 mm × 15 mm has been employed. The {2 1 1} reflection monitored at 2θ |
≈ 92° has been used to determine strain (ɛi |
= (sin θ0/sin θi) − 1). LAMP software (ILL in-house program publicly available using E |
= 210 GPa for Young's modulus and ν |
= 0.28 for Poisson's coefficient.In order to correlate residual stresses with the structural changes generated by each manufacturing step, microhardness measurements and a microstructural study have been done at the same locations in the samples where residual stresses were measured. For this purpose, each specimen has been cut (after the measurement of residual stresses by means of neutron diffraction) along the central slide () and subsequently polished. Vickers hardness using 1 kg (HV1.0) has been measured in these polished surfaces, at different points along the same lines where residual stresses were previously measured.Afterwards, the samples have been etched with Nital 2% to reveal the microstructure that has been analyzed by conventional optical microscopy.FEM (Finite Element Modeling) software Sysweld® has been used to simulate thermal treatments. From these simulations, residual stress, hardness and microstructure results are obtained. These results have been compared with the experimental ones.Heat exchange coefficients for the simulations have been obtained from the cooling curves () measured experimentally (by means of thermocouples) in each heat treatment. In the simulations, all the nodes of the base of the sample have been clamped using elastic constraints, to avoid solid rigid movement. For the simulations there have been used the thermal (chemical composition, CCT diagram, density, enthalpy, thermal conductivity) and mechanical (elastic modulus, Poisson's coefficient, thermal expansion coefficients, etc.) properties of AISI 4140 steel gathered in Sysweld® database. The composition of the material of Sysweld® database is practically identical to the composition of material used experimentally, so it is assumed that material properties of the database of Sysweld® are acceptable.Nevertheless, it must be taken in mind that results of heat treatment simulations are only as good as the correctness of the input data. So, differences between the mean values of the measurements and the simulation may have their origin in the use of non-correct data. As has been indicated in the introduction, in the simulations of quenching processes the material is generally considered chemically homogeneous before and during quenching, but it is known that a real material is not homogeneous at all and it can contain certain compositional fluctuations due to segregations, that can lead to banded structures. Therefore, discrepancies between experimental and simulation results can have the origin in the fact that in the models material is considered homogeneous but it is really not always homogeneous. For this reason, a simple 2D simulation of a quenching process has been implemented to study the effect of having bands of ferrite–pearlite and surface decarburization instead of chemically homogeneous material.The degree of banding at different zones of the parts has been estimated following the ASTM International Standard E1268-01 The four samples studied present a fiber macro-structure, more pronounced in the center of the samples, and reaching the inner and outer surface of the ring, as can be seen in . In this figure there have been marked approximately the lines along which residual stress and hardness have been measured experimentally in each sample.Fiber structure is the result of microsegregation of some alloying elements: the dark zones correspond to areas where microsegregation has lead to higher chromium and carbon content, increasing the amount of pearlite in the structure. This pearlite transforms to martensite and/or bainite in later heat treatments.The banded structures generated by microsegregation tend to align following the plastic flow lines of the material during the forging process. The fiber structure is not removed in the normalizing, and remains during all the subsequent heat treatments. Normalizing does not remove banded structures because, although carbon diffusion is very fast, the differences in carbon concentration are associated to differences in chromium concentration (during chromium segregation carbon also segregates to the richest chrome bands due to the affinity of these two elements), and chromium has lower diffusion velocity. Therefore, normalizing does not produce homogenization of chromium, and therefore, chromium segregations remain, affecting also to the diffusion of carbon, because of the high affinity between carbon and chromium. show the microstructure of each sample at three different locations: close to the surface (), at the bulk in a region outside of the strongly marked fiber structured area () and at the center of the sample, where fiber structure patterns are clearly noticed (At the outermost surface layers of the studied samples () there is more presence of ferrite (brighter aspect after chemical etching with Nital), indicating a decarburization of the samples. This loss of C in the outermost surface layers leads to hardness heterogeneities (lower hardness at the decarburized layer, as will be shown below) and a reduction of wear and fatigue strength of the samples. The decarburized layers generated in forging are not eliminated in the subsequent heat treatments, but can be eliminated during subsequent machining steps in the manufacturing process, but if there is not a later machining process, these decarburized layers cause a decrease in tensile strength which could affect the service life of the product. Besides, as has been pointed out by Calliari et al. After forging, the material is composed of pearlite/bainite plus some retained austenite. The grain size is larger at the center of the forged sample than close to the surface. This opposes the observations of Mkaddem et al. Normalizing leads to a ferrite plus pearlite matrix, of finer grain size, that is transformed to bainite and martensite (plus a certain quantity of ferrite) in the quenching. Tempering produces tempered martensite plus bainite and some ferrite. As mentioned previously, the darker zones correspond to bainite/martensite, that is, to carbon enriched zones, whereas bright zones correspond to ferrite.Residual stresses and micro-hardness have been measured along the four lines mentioned previously (Section ). Nevertheless, for simplicity and because the information obtained from lines P3 and P5 are equivalent to the information of lines P1 and P4, respectively, only the results in lines P1 (, the forging process studied generates tensile residual stresses (up to around 250 MPa) in the lateral external surface of the ring and in the top and bottom surfaces, up to depths of around 3 mm. On the contrary, compressive stresses of up to −300 MPa have been measured in the inner part of the forged ring. Nevertheless, in that case the last point measured is at a distance of 39.5 mm from the external surface of the ring, and the internal surface of the ring is at around 41 mm from the external surface, so the last point measured is not at the surface, as in the other cases. Therefore, compressive stresses are generated just below the inner surface of the ring, but there is not information of the residual stresses at the outermost surface layer of the inner part of the forged ring.At this point it is worthy of mention that with neutron diffraction residual stresses cannot be measured at the very surface, as with X-ray diffraction. In the case of neutron diffraction the resolution is determined by the gauge volume, and in the present work when surface residual stresses are referred, these are not the residual stresses at the actual surface but at a depth of around 0.5 mm (that is why in the graphs of the first measurement point is not at 0 mm depth but at 0.5 mm depth).In those zones of the samples where there have been observed changes in the fiber orientation and more accumulation of fibers, i.e., in the center of the part and near the inner surface of the ring, there have been measured also some variations in the residual stresses and hardness. To see it more clear, in there have been superimposed to the hardness and residual stress profiles some pictures of macrographs (portions of the complete macrographs shown in ), indicating the zones of the macrostructures where changes in stress and hardness profiles are also observed.Residual stresses are slightly more tensile in these zones observed darker in the macros, which are the limits of the zone of the parts with more marked banded structure (these limits have been marked with dashed red line in ). Hardness remains practically constant throughout the sample except when crossing these limits, where a slight increase in hardness is observed; this increase in hardness can be associated to the higher amount of carbon in the darker zones of the fibers.Therefore, fiber structures imply inhomogeneities in hardness and in the final residual stresses generated. At the surfaces of the samples, lower hardness values have been measured, reflecting the surface decarburization mentioned previously.Normalizing reduces the mean hardness of the sample from around 300 HV1.0 (mean hardness after forging) to around 200 HV1.0 in the bulk of the sample. As there is a certain surface decarburization, surface hardness is even lower (around 160 HV1.0 after normalizing). On the other hand, normalizing leads to a more homogeneous stress state, and slightly relieves the detrimental surface tensile stresses generated by forging (surface stresses after normalizing are less than 100 MPa).Again, residual stresses and hardness are slightly higher at the darkest zones, i.e., when crossing the limits of the zone with a very different macrostructure (). At the center of the sample, at a distance to the outer surface of around 20 mm (), less tensile or slightly compressive residual stresses have been measured, and at the end of line P1, just below the inner surface of the ring, there is a peak of compressive residual stresses (These changes are observed also in the forged sample and in the other studied samples). These zones of material with compressive stresses correspond to zones next to the border line marked in , and match up with a zone of higher density of fiber lines. This is specially clear below the inner surface of the ring (), where the mean density of fiber lines (that, moreover, are nearly parallel to the surface) measured according to ASTM International Standard E1268-01 After quenching, the residual stress state is again less homogeneous and with tensile residual stresses at the surfaces of the ring (inner, outer, top and bottom surface). Just below the inner surface of the ring, a peak of strong compressive stresses has been measured. That is the zone with compressive stresses after the previous treatments (zone of the samples with high density of fiber lines), which after quenching results in still more compressive stresses, and higher hardness. This higher hardness is associated to the fact that bands are richer in chromium and carbon, and chromium enhances the quenchability of the steel and carbon leads to higher hardness.Austenitizing prior to quenching, as well as normalizing, is supposed to “erase” the stress history of the material (austenitizing reduces residual stresses to the value of the yield strength of austenite), so the final stresses after quenching (and similarly after normalizing) would be the resultant stresses of the rapid cooling process. As normalizing and austenitizing prior to quenching do not eliminate banded structures (due to the low diffusivity of chromium mentioned in Section ), these banded structures are the responsible of the inhomogeneities in residual stresses and hardness observed in quenched sample. This is clear when macrostructures are related with stress and harness profiles: as in forging and normalizing cases, changes in residual stresses and hardness are produced in those zones of the samples where there exist differences in the density of fiber lines.Tempering has a similar effect than normalizing: leads to more homogeneous stresses and hardness, and reduces the tensile stress peaks (tempering is a stress relief process), as well as hardness. The inhomogeneities observed are the result of the different response to cooling of the different zones of the part with dissimilar chemical composition due to segregations, as it is observed in the other thermal treatments, and has been discussed in the previous paragraphs.As a summary of the results presented in preceding paragraphs it can be concluded that during the manufacturing of the steel, there is chromium segregation that results in zones of the material richer in chromium and also richer in carbon, due to the high affinity of these two elements. During forging, these segregation bands tend to align following the material flux, i.e., align following plastic deformation lines; the banded structure is more evident at the center of the ring, where there is higher amount of deformation, and higher strain rate. The zones with more density of bands present also inhomogeneities in hardness and residual stresses: below the inner surface of the ring, the high amount of deformation results in thinner bands aligned parallel to the surface, which are associated with compressive stresses. In the limits of the zone with higher density of bands (darker macrostructure) an increase in hardness and a reduction of residual stresses is observed.The original fiber structures are not eliminated by the different thermal treatments, resulting in hardness and residual stresses variations in the zones with banded structure, and especially in those zones where there are changes in the density of fiber lines, in all the studied states of material (normalized, quenched and tempered).During forging, a certain surface decarburization takes place, resulting in a decrease of surface hardness. This decarburization is not eliminated during the subsequent heat treatments, and therefore hardness inhomogeneities associated to this surface loss of carbon are not eliminated.In conclusion, in those zones of the part where chemical inhomogeneities exist (enriched and poorer areas of the material generated by segregations of alloying elements), there is a different response to thermo-mechanical treatments, resulting in hardness and residual stress inhomogeneities. show the comparison of residual stress and hardness profiles measured experimentally with those obtained in the simulations done using Sysweld® software, for normalizing and quenching processes.In the case of normalizing, the simulations give nearly null residual stresses and a constant hardness of 200 HV all throughout the part. These simulation results follow the trend and magnitude of experimental results closely, as experimental values give a mean hardness of 200–225 HV1.0 and mean residual stresses between −50 and +50 MPa (i.e., practically null). However, the theoretical calculations do not reproduce the local changes in hardness and residual stresses measured experimentally and associated to the presence of segregation (banded structure) and surface decarburization: in the decarburized surface hardness is lower, and this decrease in hardness is not reproduced by the simulation; regarding residual stresses, the compressive stresses measured below the inner surface of the ring, associated to the high density of fiber lines located in that zone, are not predicted by the simulations.The differences between experimental and simulation profiles are more significant in the case of quenching: simulations predict tensile stresses at the surfaces and up to around 5 mm, and compressive stresses of −100 MPa along the remainder of the thickness of the sample. Experimental results show that tensile stresses are generated at the surface layers, but not up to such a depth. The strong compressive stresses observed experimentally below the inner surface of the ring are not reproduced by the simulations, exactly the same as in the normalizing process. Regarding hardness, the mean hardness measured experimentally (around 400 HV1.0) is slightly higher than that obtained from the simulations (around 300 HV, and at the surface 350 HV), and again the simulations do not reproduce the hardness changes associated to segregation bands and surface decarburization. In fact, quenching simulations predict an increase in hardness at the surface (the normal case in quenching: the high cooling rates produce martensite of higher hardness at the very surface), whereas experimentally surface hardness is lower than the bulk, due to decarburization.Therefore, it can be concluded that conventional simulations of thermal treatments do not reproduce experimental results (hardness, residual stresses, etc.) when banded microstructures are present in the material. This, in fact, is an expected result since the results of simulation are only as good as the data input, and in that case, in the simulation it is considered that the material is chemically homogeneous, and it is not the real situation, as chemical inhomogeneities exist both in the surface (due to the loss of carbon associated to decarburization) and in the bulk of the sample (due to chromium and carbon segregation that leads to ferrite–pearlite bands).To study the effect of banded structures and decarburization in the values of residual stresses and hardness, simpler simulations (in two dimensions) have been performed. Concretely, a two-dimensional mesh with bands (in green in (a)) has been generated for the simulation of quenching of a banded structure (similar to the banded structure of AISI 4140 steel shown in (b)), that presents also surface decarburization. (For interpretation of the references to color in this text, the reader is referred to the web version of the article.) To simulate surface decarburization, the properties assigned to the surface layer are the properties of the same steel, but with 1/4 of the carbon content. To simulate a banded structure, it has been assumed that just before quenching the bands defined in the model mesh are bands of pearlite, whereas the rest of the material is austenite. are gathered contour maps of hardness and mean residual stresses obtained from the simulation of quenching of the banded and decarburized 2D sample. An important reduction in hardness is observed in the decarburized surface and a light increase in hardness in the segregation bands. More tensile stresses are generated in the decarburized surface layer and at the pearlite bands after quenching. These changes in residual stresses and hardness reproduce reasonably well the changes observed experimentally in the forged and heat treated samples.Therefore, it is clear that when simulating heat treatments of materials with inhomogeneous microstructures (segregations bands, surface decarburization, etc.), if these inhomogeneities are not taken into account the simulations will not predict properly the final state (hardness, residual stresses, etc.) of the part.Further investigation based on 3D-modeling has to be performed in order to analyze the effect of internal microstructure inhomogeneities on macroscopic physical properties of components under thermal and mechanical treatments. Nevertheless, it is supposed that if the density of fiber lines increases, there would be an increase in macroscopic average residual stresses and hardness.Based on the observations of this work, the following conclusions can be made:In the manufacturing of gears, the microsegregations produced during the production of the steel tend to form fiber structures that align following the plastic flow lines during forging processes. These fiber structures are not completely removed by the normalizing process, and are still present during all the subsequent heat treatments performed on the parts.Fiber structures result in inhomogeneities in terms of hardness and residual stresses. This is related to the different response to thermo-mechanical treatments of the enriched (due to segregation) and poorer areas of the material.During forging process, surface decarburization of the parts takes place. This carbon loss in the outermost surface layers leads to hardness heterogeneities (lower hardness) and a reduction of wear and fatigue strength of the samples. The decarburized layers can be eliminated during subsequent machining steps in the manufacturing process, but if there is not a later machining process, these decarburized layers are not completely removed, being a source of service life problems associated to their lower strength.If microstructure inhomogeneities (such as ferrite–pearlite bands and decarburization) are not taken into account in the simulation of heat treatments, the simulations will not predict properly the final state (hardness, residual stresses, and more important: distortions) of the part. The 2D simulations performed considering banded structures and decarburization reproduce reasonably well the changes observed experimentally in the forged and heat treated samples.Wear and corrosion properties of (Ti1–xCrx)N coatings produced by the ion-plating method(Ti1–xCrx)N coatings were deposited by an ion-plating technique in a reactor with two evaporation sources, Ti and Cr, which were evaporated by electron beam and resistance heating, respectively. The Ti and Cr concentrations in the coating were controlled by the Ti:Cr evaporation ratio. This study evaluated the wear and corrosion properties of the (Ti1–xCrx)N coatings. The wear properties were evaluated from the surface morphology, Cr content (x) in the coatings and the effects of the wear debris as well as the transferred layer on the wear behavior were also examined. The wear resistance was found to increase when Cr was added to TiN. It was found from corrosion experiments that, at vs.·(SCE) <0.5 V, all samples showed an electrochemical behavior similar to that of the CrN coating, irrespective of the Cr content (x) of the coatings. The coatings showed good passivity and the corrosion current was very small, regardless of the Cr content. Above 0.5 V, however, like the CrN coatings, the passivity disappeared and corrosion current increased abruptly.TiN coatings are extensively used in all types of cutting operation. These coatings enhance tool life, improve the surface finish and increase productivity. However, as mechanical components are used in increasingly aggressive environments, new coating materials with improved properties such as corrosion and oxidation resistance are needed While there are many reports regarding the structure and hardness of (Ti,Cr)N coatings, few studies have been reported describing wear and corrosion properties of (Ti,Cr)N coatings. Jehn et al. In this study, the wear and corrosion properties of (Ti1–xCrx)N coatings were systematically investigated using various test methods.(Ti1–xCrx)N coatings were deposited by reactive ion-plating. Ti and Cr were evaporated by electron beam and resistant heating, respectively. The concentrations of Ti and Cr were controlled by the Ti/Cr evaporation ratio. (Ti1–xCrx)N coatings with similar compositions of metals and nitrogen could be produced through a feedback control of the nitrogen flow rate and the total evaporation rate of the metals. Ar and NH3 were introduced after the chamber pressure was evacuated to approximately 2×10−6 torr. The thickness and deposition rates of the coatings were approximately 2.0 μm and 700 Å/min., respectively. The detailed deposition conditions for the (Ti1–xCrx)N coatings are presented in . High speed steel (HSS, SKH-9) was used as the substrate material. The substrate was polished by Al2O3 powder with diameters up to 0.3 μm, then ultrasonically cleaned in acetone for 10 min. and finally dried with N2 gas.The Ti and Cr concentrations were determined by energy dispersive spectroscopy (EDS), and the coating thickness was measured using an α-step profilometer. The surface morphologies of the specimens were observed using scanning electron microscopy (SEM).The wear properties of the coatings were examined with a CSEM pin-on-disk type tribometer. A Cr-steel ball, 10 mm in diameter, was placed on the specimen and rotated at 191 rev./min., which is equivalent to a sliding speed of approximately 0.1 m/s. A normal load of 5 N was applied and the total number of turns was 5000. After the tests, the sample surface was observed by both SEM and the α-step profilometer. The composition of the particles that were rubbed off the sample during the wear test was determined by EDS.The corrosion properties of the coatings were examined with an EG&G 273A potentiostat. The experiments were performed in a well-stirred 0.8-M NaCl solution of pH 7 in deionized water using 1.09887 Titrisol as a buffer solution. The reference electrode used was a saturated calomel electrode (SCE). The potentio-dynamic polarization tests were carried out with a scan speed of 2 mV/s. The surface morphology and the composition of the coatings after the potentio-dynamic tests were studied using SEM, α-step profilometer and Auger electron spectroscopy (AES). The potentio-static polarization tests were also performed to investigate the stability of the passive layers on the (Ti1–xCrx)N coatings at 0.3 V. The corrosion experiments were carried out at 25°C while the apparatus was exposed to the air.The (Ti1–xCrx)N coatings deposited in this study formed solid solutions of TiN and CrN at all concentrations with the lattice parameter of the coatings decreasing gradually with increasing x. The TiN microhardness showed a value approximately 2000 HK, which increased with increasing Cr content (x) and showed maximum value of 6000 HK at x=0.8. At higher x values, the hardness decreased slightly to that of the CrN coating. The microhardness of the CrN coating was approximately 4500 HK, which is higher than the value usually reported. The critical load values from the scratch test were above 25 N at all concentrations. The structure and mechanical properties of the (Ti1–xCrx)N coatings have been reported in a previous publication shows the surface profiles of the (Ti1–xCrx)N coatings after the wear test. In the case of TiN, the coating had entirely worn off and the substrate surface was exposed. This was not the case with (Ti,Cr)N and CrN coatings, which did not wear off. On the contrary, the wear tracks were piled up by other particles. The wear track of the (Ti0.15Cr0.85)N coating was investigated by SEM and EDS, and the results are shown in . No scratches could be found along the track in the SEM image (a), while some sections of the track were covered by reddish-brown particles. EDS determined Fe to be the main component of these particles (c shows the EDS results of the coatings without the wear test. shows the surface morphology and the results from EDS analysis of the Cr-steel ball after the wear test of the (Ti0.15Cr0.85)N coating. From this it can be seen that considerable wear occurred on the Cr-steel ball, and the composition of the particles was found to be the same as that of the Cr-steel ball. This phenomenon could be also found in other (Ti1–xCrx)N coatings. Yoon et al. shows the wear volume of the Cr-steel ball after the wear test for the (Ti1–xCrx)N coatings. The wear volume increased with the increasing coating hardness, and the (Ti0.15Cr0.85)N coating, which had the highest hardness, showed the best wear property. shows the potentio-dynamic polarization curves of the (Ti1–xCrx)N coatings investigated in this study. The TiN coating did not show any passivation region, which is contrary to that of the CrN coating. The (Ti,Cr)N coatings, however, showed two clearly distinguished regions at approximately 0.5 V (vs·SCE). Below 0.5 V, all samples showed an electrochemical behavior similar to that of the CrN coating, which was independent of the chromium content (x). Above 0.5 V, on the other hand, the (Ti,Cr)N coatings lost their passivity and the corrosion current increased significantly. Moreover, the corrosion current increased more rapidly, as the Cr content (x) in the coatings increased.To investigate the corrosion property of the CrN coating more clearly, potentio-dynamic polarization tests on the CrNx coatings were performed, and the results are shown in . By changing the NH3 flow rate, CrNx coatings with various nitrogen contents (x) could be obtained. Mixed phases of pure Cr and Cr2N were observed at low NH3 flow rates (<15 sccm), while Cr2N and CrN mixed phases formed at flow rates between 15 and 30 sccm. A single CrN phase was observed, when the NH3 flow rate was over 30 sccm.However, the corrosion properties of the CrNx coatings showed a similar behavior in all the samples, regardless of the nitrogen content (x). As x in the coating increased, the corrosion potential (Ecorr) corresponding to the zero current moved to higher positive potentials. However, above 0.5 V (vs·SCE), all samples lost their passivity and the anodic corrosion current increased abruptly.The typical corrosion behavior of the CrNx coatings can be understood from the potentio-pH equilibrium diagram (Pourbaix diagram) a shows a schematic diagram for the corrosion resistance of Cr to pure water. The hatched regions indicate the theoretical corrosion domains, while the non-hatched regions represent the theoretical immunity and passivation domains. Chromium shows a passivation region up to approximately 0.65 V [vs. SHE (standard hydrogen electrode), which corresponds to approximately 0.4 V vs. SCE] at pH 7. However, above that voltage, chromium converts to soluble ions and passivation of the chromium layer is no longer stable in the passivation region, three different kinds of chromium oxides appear in the diagram: Cr(OH)3; Cr2O3; and Cr(OH)3·nH2O. Among them, a potential-pH equilibrium diagram for Cr(OH)3 is shown in b. The line (A) represents the following reaction:This equation shows the relative stability between Cr and the passive chromium oxide, Cr(OH)3. If CrN is substituted for Cr, the reaction is as follows:The line is then shifted to line (A)′ as shown in , which is still within the passive oxide region. Similar results can be obtained for other oxides. This means that, when the potential increases, the Cr2N and CrN coatings would change into chromium oxide, just like Cr. Thus all the CrNx samples, regardless of the nitrogen concentration, x, will show the same transpassivity voltage of 0.5 V at which the Cr oxides begin to dissolve, although the chromium nitrides will transform to oxides at higher voltages than pure Cr.To investigate the corrosion properties of the (Ti1–xCrx)N coatings more clearly, the potentio-dynamic polarization tests were stopped at 0.8, 1.0 and 1.2 V, respectively. After each test, the surface roughness was measured by the α-step profilometer and the change in concentration of the coatings was investigated by AES and EDS. shows the surface profiles of the CrN coating. The corrosion proceeded over the whole surface and the amount of dissolved volume increased, as the voltage was increased from 0.8 to 1.2 V. On the other hand, corrosion on the TiN coating was proceeded by local attacks. Pits could be observed on the TiN coating surface and Fe was detected around the pits by EDS. As discussed previously, the chromium oxide layers are no longer stable at voltages above 0.5 V (vs·SCE) and corrosion would proceed over the whole surface. However, oxides of Ti are stable up to approximately 1.6 V at pH 7 AES depth profiles of the (Ti0.62Cr0.38)N (b) coatings after the corrosion test up to 1.2 V shows that the Cr content in the oxide layer decreased considerably, while the Ti concentration remained constant. It is supposed that the Cr-oxide is dissolved selectively from the oxide layer. shows the potentio-static polarization curves of the (Ti1–xCrx)N coatings at 0.3 V where (Ti,Cr)N showed a passivation region at that voltage. A significant increase in the corrosion current was observed for the TiN coated sample after approximately 2 h. However, the corrosion current for both the (Ti,Cr)N and CrN coatings was barely detected during the test, showing almost perfect corrosion resistance at that voltage.This study investigated the wear and corrosion properties of (Ti1–xCrx)N coatings that were deposited by an ion-plating technique in a reactor with two evaporation sources.In wear tests, the TiN coated sample was entirely worn out and the surface was exposed. In contrast, no wear marks on the surfaces of the (Ti1–xCrx)N and CrN coated samples were observed. Instead, pile-up along the wear track was found and this was the result of wear from the softer Cr-steel ball. Along the outside of the wear track, reddish-brown particles were observed that were shown to be Fe-oxide. However, this did not accelerate the wear of the coating as is usually observed in three-body abrasion wear. The wear volume of the Cr-steel ball increased with the increasing hardness of the coatings and (Ti0.15Cr0.85)N coating showed the best wear properties.The corrosion properties of the (Ti1–xCrx)N coatings showed the same transpassivity potential as observed in the CrN coatings. A passive layer was already formed when the Cr content (x) in the (Ti1–xCrx)N coatings was 0.3. Above 0.5 V, selective Cr-oxide dissolution was observed and only Ti-oxide remained. This phenomenon is related to the inherent electrochemical properties of Cr. From the potentio-static polarization test, (Ti,Cr)N coatings showed almost perfect corrosion resistance in the passivation region, contrary to TiN.Hierarchical microstructure design to tune the mechanical behavior of an interstitial TRIP-TWIP high-entropy alloyWe demonstrate a novel approach of utilizing a hierarchical microstructure design to improve the mechanical properties of an interstitial carbon doped high-entropy alloy (HEA) by cold rolling and subsequent tempering and annealing. Bimodal microstructures were produced in the tempered specimens consisting of nano-grains (∼50 nm) in the vicinity of shear bands and recovered parent grains (10–35 μm) with pre-existing nano-twins. Upon annealing, partial recrystallization led to trimodal microstructures characterized by small recrystallized grains (<1 μm) associated with shear bands, medium-sized grains (1–6 μm) recrystallized through subgrain rotation or coalescence of parent grains and retained large un-recrystallized grains. To reveal the influence of these hierarchical microstructures on the strength-ductility synergy, the underlying deformation mechanisms and the resultant strain hardening were investigated. A superior yield strength of 1.3 GPa was achieved in the bimodal microstructure, more than two times higher than that of the fully recrystallized microstructure, owing to the presence of nano-sized grains and nano-twins. The ductility was dramatically improved from 14% to 60% in the trimodal structure compared to the bimodal structure due to the appearance of a multi-stage work hardening behavior. This important strain hardening sequence was attributed to the sequential activation of transformation-induced plasticity (TRIP) and twinning-induced plasticity (TWIP) effects as a result of the wide variation in phase stability promoted by the grain size hierarchy. These findings open a broader window for achieving a wide spectrum of mechanical properties for HEAs, making better use of not only compositional variations but also microstructure and phase stability tuning.Currently, there is considerable interest in the field of high-entropy alloys (HEAs) not only due to their configurational entropy-driven phase stability of massive solid solutions [] and in part good mechanical properties [] but also because they open up a practically infinite compositional space for future solid solution alloy development []. The original design concept of HEAs was directed towards mixing of more than five alloying elements at near equimolar concentrations with the aim of forming a single-phase solid solution []. Numerous studies have focused on designing new compositions to improve the mechanical properties of HEAs by incorporating further strengthening mechanisms such as precipitation hardening [] and interstitial solid solution strengthening (e.g., by adding carbon) [] besides the intrinsic substitutional solid solution strengthening.The recent development of non-equiatomic HEAs with metastable bulk phases has introduced a more efficient way to improve strength and ductility simultaneously by triggering transformation induced plasticity (TRIP) [] and/or twinning induced plasticity (TWIP) effects []. This novel metastability-engineering strategy opens up even more space for mechanism-driven HEA design owing to the tunable stability of the solid solution phases.Although substantial research efforts have been devoted to the compositional design of HEAs, few studies have been conducted to also utilize microstructure control for tuning their mechanical properties []. Since the mechanical response of structural materials, such as strength, ductility and toughness, are highly sensitive to microstructure [], it is important to understand and design specific microstructure features in close concert with the vast compositional degrees of freedom of HEAs to further broaden their mechanical property spectrum.In the current work, an interstitial carbon alloyed HEA (iHEA), 49.5Fe-30Mn-10Co-10Cr-0.5C (at. %), was chosen for conducting such a microstructural design study. The composition was tuned for a stacking fault energy (SFE) regime that allows joint and sequential activation of phase transformation from face-centered cubic (FCC) matrix to hexagonal close-packed (HCP) martensite and mechanical twinning during room temperature deformation []. The sequence or respectively overlap in the activation of these two effects, together with dislocation slip, depends not only on the loading scenario but also on the microstructures. More specific, both mechanisms have been reported to show strong dependence on grain size and local partitioning of the alloying elements [], nucleation and growth of HCP-martensite and twins involve specific dislocation patterns and interactions at grain boundaries, formation of stacking faults and passages of Shockley partials. Grain refinement influences dislocation pile-ups in front of grain boundaries, thus setting the back stresses level. Consequently, higher external stresses are required to generate more dislocations and stacking faults. Also, nucleation of both, mechanical twins and HCP-martensite require specific configurations of stacking faults at the grain boundaries so that their frequency scales inversely with grain size []. In addition, pre-existing dislocations increase the mechanical stability of the FCC structure as they inhibit the motion of mobile dislocations and constitute effective barriers to the growth of martensite lamellae []. Therefore, both, grain refinement and pre-existing substructures can lead to the higher resistance to deformation-induced martensitic transformation and twinning of the FCC matrix [Based on the characteristics of the TWIP-TRIP-assisted iHEA and the grain size effects on the phase transformation and twinning discussed above, we propose here a novel approach to improve the mechanical properties of an iHEA by hierarchical microstructure design []. Experimentally, this was achieved by means of recovery and partial recrystallization of the cold-deformed alloy. A series of bimodal and trimodal microstructures covering a wide range of grain sizes from 50 nm to tens of micrometers were developed so as to manipulate the phase stability of the FCC matrix to different levels of metastability []. In this way, HCP-martensitic transformation and twinning can be expanded to larger strain domains and in smaller scales upon deformation. As a consequence, the work hardening rate is expected to be enhanced, which, in turn, gives rise to the improved ductility and tensile strength. The systematic investigation is conducted to fundamentally understand the effects of grain-structure hierarchy on deformation mechanisms, work hardening behavior and final mechanical properties of the iHEA. The new insights obtained from merging synergetic effects from both, compositional and microstructural tuning can serve as an important guidance for future developments of advanced HEAs with superior mechanical properties.The iHEA used in the present study has a nominal composition of 49.5Fe-30Mn-10Co-10Cr-0.5C (at. %). The chemical composition measured by inductively coupled plasma (ICP) mass spectrometry is listed in . Hot rolling was performed on the as-cast alloy at 900 °C to a thickness reduction of 50%, followed by homogenization at 1200 °C for 2 h in an Ar atmosphere and then water quenching. The as-homogenized plate presented a single FCC structure and equiaxed grains with an average size of 65 μm. Cold-rolling was performed on the as-homogenized plates to a thickness reduction of 67%. The as-cold-rolled specimens were then subjected to tempering at 400 °C and annealing at 650 °C and 750 °C for different times to create a series of different microstructures. All the heat treatments were conducted using a dilatometer with a heating rate of 10 K/s and a cooling rate of 50 K/s which was approximately equivalent to that of water-quenching.The microstructures of as-cold-rolled and heat-treated specimens were characterized in the cross-section of the rolling direction (RD) and the normal direction (ND) of the sheets, while the tensile samples were analyzed in the cross-section of the RD and the transverse direction (TD). Electron backscattered diffraction (EBSD) measurements were performed using a Jeol JSM-6500F field emission gun scanning electron microscope (SEM) equipped with a high resolution camera and a TSL-OIM data analysis software. All inverse pole figure (IPF) maps were plotted using the ND as reference axis. Electron channeling contrast (ECC) imaging was coupled with the EBSD analysis to reveal deformation substructures by a Zeiss-Merlin SEM. X-ray diffraction (XRD) measurements were performed by using a Meteor0D energy dispersive point detector with Cobalt source operated at 40 kV and 30 mA. Transmission electron microscopy (TEM) analysis was performed using a FEI-TITAN at an acceleration voltage of 300 kV. TEM thin foils were prepared by mechanical grinding followed by electro-polishing with a solution of 5% perchloric acid in acetic acid.Regular dog-bone shaped tensile samples with a thickness of 1 mm were machined from the alloy sheets by electron discharge machining. The total length of the specimen is 20 mm, and the gauge length and width are 4 mm and 2 mm, respectively. Room temperature tensile tests were conducted at a constant speed of 4 μm/s which is equivalent to a strain rate of 0.001/s by using a Kammrath & Weiss tensile device. The macroscopic strain distribution and evolution were measured by a digital image correlation (DIC) technique with Aramis software (GOM GmbH). Nano-indentation tests were performed using a Hysitron TriboScope nano-indentation system with a Berkovich shaped indenter with a maximum load of 2500 μN.a). Deformation during cold-rolling was highly localized in the shear bands resulting in regions with large lattice distortion beyond the resolution limit required for reliable EBSD indexing, shown as black bands in the EBSD maps (a–c). A dual-phase structure consisting of deformation induced HCP-martensite and FCC phase is formed (b). By ECC imaging, nano-grains are observed inside the shear bands mixed with nano-lamellae (d). Moreover, micro-shear bands with the thickness of sub-micrometers are found penetrating through the parent grains (e.g. Region II in a). Enlarged ECC image of the micro-shear band inside the HCP-martensite grain is displayed in e. The volume fraction of the HCP-phase is about twice that of the FCC phase from the quantitative XRD analysis according to the Rietvelt method (f). There is no BCC or BCT martensite identified by either EBSD or XRD technique.It is worth mentioning that, besides the shear-banded regions, the strain distribution in the large grains is also heterogeneous. In the kernel average misorientation (KAM) map with the 1st nearest neighbor correlation (c), the KAM values indicate the densities of the geometrically necessary dislocations (GNDs) []. It can be seen that the retained FCC grains have higher dislocation densities compared to the deformation induced HCP-martensite grains. Accordingly, the former should possess higher driving forces for subsequent recrystallization than the latter. Furthermore, HCP-martensite exhibits a near-basal texture with the {0001} direction along the ND of the as-rolled sheet, while the retained FCC phase shows a {101} fiber texture, i.e., {101}//ND and {111}//TD, in the inverse pole figure (IPF) map ( reveals the microstructures of specimens tempered at 400 °C for 3 min and 10 min. Both specimens consist of a single FCC phase, indicating that deformation induced HCP-martensite reversely transformed to FCC phase during tempering (). At such a low temperature (∼0.3Tm), no evidence of recrystallization is found. The large grains show mainly two orientation components, {101}//ND (green) and close to {111}//ND (blue and purple) in the IPF maps (). The {101} oriented grains (type I) correspond to the residual FCC phase as they inherited the grain orientations from the texture developed upon rolling. The {111} oriented grains (type II) are the reversely transformed FCC phase associated with the prior HCP-martensite which had a near-basal texture ({0001}//ND). This is because the reverse phase transformation from HCP to FCC upon heating is a shear transformation following the S-N relationship (i.e. (111)FCC//(0001)HCP and [101¯]FCC//[112¯0]HCP) []. In addition, the retained FCC grains show higher dislocation density compared to the reversely transformed ones (see KAM map, ). The image quality (IQ) maps overlaid with the grain boundaries () also show that a larger number of low angle grain boundaries (LAGBs) appear in the retained FCC grains. Twins are identified mostly in the reversely transformed FCC grains (marked by red lines in the IQ maps, shows the ECC images and TEM analysis of the substructures in as-tempered specimens. Nano-twins with thicknesses ranging from 10 nm to 70 nm are found in the reversely transformed FCC grains (b). Some of them were sized below the resolution limits of EBSD. Dislocations and stacking faults (SFs) also present in some of the large grains (c). In the vicinity of the shear bands, nano-sized grains can be seen (d). To confirm these observations, TEM bright field (BF) and dark field (DF) images are shown in d and e (where the dashed line separates the matrix from the shear-banded region). In the DF image, nano-grains are clearly observed in the shear bands.The nano-indentation tests conducted on the shear bands and also in the middle of the large parent grains for reference showed a large difference in hardness values, ∼7.4 GPa and ∼4.5 GPa, respectively. In general, the bimodal microstructures consisting of large parent grains with pre-existing nano-twins and nano-grains in the vicinity of shear bands were produced after tempering. reveals the partially recrystallized microstructures of the specimens subjected to annealing at 650 °C for 3 min and 10 min and 750 °C for 3 min. A single FCC phase formed for all annealing conditions (). No thermally induced HCP-martensite is observed after cooling. Statically recrystallized (SRX) dislocation-free grains form at the expense of the deformation structures (see KAM maps, ). It can be seen that recrystallized grains preferentially nucleate in the vicinity of the shear bands in the specimen annealed at 650 °C for 3 min (a). With increasing the annealing time to 10 min, besides the shear-banding related recrystallization, a large portion of the retained FCC grains undergo recrystallization, as marked by the white arrows in b. At a higher annealing temperature of 750 °C, the volume fraction of SRX grains increases dramatically (c). Moreover, annealing twins form in the recrystallized grains, while much finer mechanical twins are found in the un-recrystallized grains (marked by white lines in phase maps, shows the partitioned EBSD maps of the hierarchical microstructure of the specimen annealed at 650 °C for 10 min in the way of un-recrystallized grains and recrystallized grains with two different levels of sizes (medium >1 μm and small <1 μm). Most of the medium-sized recrystallized grains (1–4 μm) formed by consuming the large parent grains (). For comparison, smaller grains with average size below 1 μm mainly nucleated in the vicinity of the shear bands. The un-recrystallized grains were segmented by micro shear-bands into smaller parts with sizes ranging from 10 to 35 μm. Overall, a trimodal microstructure was attained after annealing at 650 °C for 10 min consisting of: (i) large un-recrystallized grains with nano-twins (∼45 vol %); (ii) medium-sized recrystallized grains with sizes of 1–4 μm (∼33 vol %) and (iii) small recrystallized grains with sizes less than 1 μm (∼22 vol %) (The ECC image of the retained FCC grain shows blocks of deformation substructure (c). At higher magnification, a high density of dislocation walls is observed inside the block cells (d). In contrast, numerous mechanical twins with dislocations inside the twin lamellae can be seen in the reversely transformed FCC grains (e and f). Nano-grains are found inside the micro shear-bands with an average size of around 100 nm (g). Nano-carbides (M23C6, where M represents the substitutional elements Fe, Mn, Co and Cr []) are mainly observed in the recrystallized regions associated with shear bands (h). This is related to the highly concentrated plastic deformation in the shear bands which gives rise to locally increased defect concentrations, strain energy and dissipative heating. Thus, the diffusion rate of carbon is assumed to be higher in the shear bands, which results in the favored formation of carbides in these regions during the subsequent annealing. In addition, a higher number density of carbides is detected along the chain of the nano-grains (h), which indicates that such nano-particles pinned grain boundaries, preventing their motion.The engineering stress-strain curves of the specimens subjected to tempering and annealing with different hierarchical microstructures are shown in a. As a comparison, the engineering stress-strain curves of the fully recrystallized microstructures with average grain sizes of 4 μm and 160 μm from preview work [a (dash lines). The true stress-strain curves superimposed with their corresponding strain hardening plots are displayed in b. The yield strength, ultimate tensile strength (UTS), elongation to fracture and uniform elongation of the specimens at different conditions are summarized in c together with the volume fraction and the average size of SRX grains (A high yield strength of ∼1.3 GPa and a UTS of ∼1.5 GPa are observed for the tempered specimens with bimodal microstructures, although the total elongation is only 12%–14%. After annealing at 650 °C for 3 min, where recrystallization mainly occurred at shear bands, a good combination of yield strength (824 MPa), UTS (1.05 GPa) and ductility (33%) is attained. As a comparison, for the specimens annealed at 750 °C for 3 min with a higher recrystallized volume fraction (85%), the ductility is substantially enhanced from 33% to 60%, yet, at sacrificing some of the yield strength which drops from 824 MPa to 555 MPa, but the UTS only slightly decreases (1050 MPa–938 MPa). These observations indicate that a more pronounced work hardening behavior appears with a larger amount of SRX grains. It is also found that not only the uniform elongation (4%–38%) but also the post-necking elongation (10%–24%) is improved with increasing the volume fraction of recrystallization from 41% to 85%. Comparing with the fully recrystallized structure with an average grain size of ∼4 μm, the yield strength of the trimodal structure annealed at 750 °C increases from 485 MPa to 555 MPa, while the UTS and total elongation are at similar levels. The fine-grained material annealed at 900 °C for 3 min also showed a mixture of large grains (up to 8 μm) and smaller grains (∼1 μm) []. Nevertheless, the yield strength and the UTS of the materials with trimodal microstructures annealed at 750 °C are substantially enhanced compared to those of specimens with uniform coarse-grained structure (∼160 μm) and their ductility is slightly improved.The work hardening rate of the tempered samples decreases linearly with true strain until necking, while a multi-stage strain hardening response appears in the annealed specimens with trimodal grain structures. Specifically, the specimens subjected to annealing at 650 °C (≤ 55% SRX) show three-stage work hardening behavior, while the specimens annealed at 750 °C (≥ 85% SRX) present clearly four stages of strain hardening with a sudden increase of the work hardening rate at early strains (2–5%).To correlate the work hardening behavior with the underlying deformation mechanisms upon uniaxial tensile loading, the microstructural evolution of two different hierarchical grain structures (650 °C for 3 min and 750 °C for 3 min) are compared for a range of local strains (3%–45%). It should be noted that the recrystallized volume fraction of the former material (650 °C) is 50% smaller than that of the latter one (750 °C). In the grain size distribution map (c), it can be seen that the volume fraction of small grains (<1 μm) of the specimen annealed at 650 °C is higher than that of the sample subjected to annealing at 750 °C, but the medium-sized recrystallized grains (1–6 μm) in the former is less than that in the latter. At a low strain of 3%, HCP-martensite lamellae are only found in the large parent grains in the specimen annealed at 650 °C, but in both parent grains and medium-sized recrystallized grains in the sample annealed at 750 °C according to EBSD analysis (a and b). The fraction of the HCP-martensite of the former (∼0.2 vol %) is also lower than that of the latter (∼0.5 vol %). In the large parent grains, the HCP-martensite lamellae are found along the pre-existing twin boundaries (as shown in the enlarged IQ map, ECC imaging was applied to analyze the formation of HCP-martensite lamellae and twins at submicron scales. In the specimens annealed at 750 °C for 3 min, numerous fine HCP-lamellae and twins are observed in the medium-sized recrystallized grains and most of them penetrate the entire grain (a). Multiple variants of HCP-martensite or twinning systems are activated in the grain with orientation {101}//ND (marked by the black rectangular in the IPF map, ). In the recrystallized grains, incoherent annealing twin boundaries (showing facets) also serve as nucleation sites for HCP-martensite and twins (b). The thickness of HCP-martensite and twin lamellae at this stage was very thin, viz. below the EBSD resolution limit. In the ultrafine recrystallized grains with size below 500 nm (c), stacking faults and partial dislocations can be seen near grain boundaries. In the large parent grains, besides the martensite growing along the pre-existing twinning plane, partial dislocations and thin martensite lamellae are observed inclining at mainly two sets of angles (i.e., 35–40⁰ and 90⁰) to the pre-existing twin boundaries (marked by red arrows in d). In the specimen annealed at 650 °C for 3 min, stacking faults and partial dislocations are found in the large parent grains and they are blocked by the pre-existing dislocation substructures (To demonstrate the effect of grain size on the formation of HCP-martensite during deformation, the microstructures of the specimen annealed at 750 °C for 3 min at local strains of 10% and 30% are shown in ), a higher fraction of HCP-martensite with larger thickness is detected in both parent grains and medium-sized recrystallized grains compared to those at the strain of 3% (2 vol % vs. 0.5 vol %). Moreover, higher KAM values are found along grain boundaries, particularly concentrated in the region of small SRX grains (<1 μm). This is attributed to the strong interactions of dislocations with grain boundaries and formation of stacking faults in front of the boundaries. Annealing twin boundaries are also strong obstacles for dislocation movement. The reactions of dislocations with twins lead to the transition of twin boundaries to random high angle grain boundaries (HAGBs) partially (see white arrows in c). With increasing the local strain to 30% (), the overall volume fraction of HCP-martensite largely increases (8 vol %) and the martensite lamellae in the small recrystallized grains (∼1 μm) are thick enough to be detected by EBSD.At a high local strain of 45%, exceeding the global uniform elongation value, some of the large parent grains are found mostly transformed to HCP-martensite in the specimen annealed at 750 °C for 3 min (a). The HCP phase shows a lower dislocation density than the FCC matrix. In the specimen annealed at 650 °C for 10 min, the volume fraction of deformation induced HCP-martensite (13 vol %) is much lower than that in the specimen annealed at 750 °C for 3 min (33 vol %) at the same local strain (b). This is mainly due to the inhibition of the growth of martensite plates by pre-existing twin boundaries in the large parent grains in the former material.A schematic plot of creating hierarchical microstructures through thermomechanical processing (from homogenization to cold rolling to tempering/annealing) is shown in . The as-homogenized materials had an equiaxed recrystallized microstructure with a single FCC phase. Upon cold rolling, deformation induced HCP-martensite formed with retained FCC matrix leading to a dual-phase microstructure and severe shear bands appeared upon deformation to 67% which is equivalent to a true strain of 1.1. When the as-rolled sheet was subjected to heat treatment at and above 400 °C, deformation induced HCP-martensite reversely transformed to FCC matrix through displacive transformation following the S-N relationship [], while twins which co-existed with martensite lamellae prevailed in the parent grains. After tempering at 400 °C for short times (3 min and 10 min), recovery was dominant in the large parent grains and nano-grains remained in the shear bands. Thus, single-phase bimodal microstructures consisting of large unrecrystallized grains with pre-existing nano-twins and nano-grains in the vicinity of the shear bands were produced.During annealing, static recrystallization took place particularly in the vicinity of shear bands due to their largely concentrated deformation and the higher density of dislocations. Nano-grains also appeared as the precursors for recrystallization, and thus no incubation time was required and more nucleation sites were available for recrystallization. As a consequence, the recrystallization kinetics of the shear bands was much higher and the size of the recrystallized grains was finer compared to those of the large parent grains. In the residual FCC grains, cell blocks appeared with dense dislocation walls (DDWs). This was also observed in other FCC metals, such as in Ni subjected to large strain cold-rolling [] upon tensile testing. Cell blocks are formed by activating multiple slip systems simultaneously and they are separated by dislocation boundaries that are geometrically necessary [] showed that in a single FCC phase twinning-assisted HEA, 8 slip systems can be equally stressed in the grains with the orientation of <001> along the tensile direction. This is due to the fact that these slip systems have the same Schmid factor which is higher than that for mechanical twinning. Therefore, the retained FCC grains showed a preferred orientation of (110)//ND and (100)//RD together with dense dislocation cell structures. On the contrary, the reversely transformed FCC phase contained multiple nano-twins. Also, in regions adjacent to the shear bands and the micro-shear bands, the dislocation density was higher (KAM values of 1–2) compared to those in the grain interiors (KAM<1) (). This observation was related to the highly localized deformation created by shear banding where the crystals adjoining to the shear bands rotated and formed GNDs to accommodate strains which caused a local increase in the misorientation as reflected by the KAM values []. As such, both the retained and reversely transformed parent grains recrystallized through the formation of LAGBs and rotation and coalescence of subgrains. Yet, the recrystallization kinetics of the retained FCC grains was higher than that of the reverted ones due to the higher dislocation densities in the former. In this way, trimodal grain structures were produced characterized by small recrystallized grains associated with shear bands, medium-sized grain recrystallized from parent grains and unrecrystallized large grains.The specimens subjected to tempering at 400 °C with bimodal microstructures exhibited much higher yield strength compared to those annealed at the higher temperatures. This is mainly attributed to the pre-existing nano-twins and dislocations in the large parent grains and nano-grains remained in the shear bands. Therefore, the yield strength can be considered as the summation of the strength contributions from twin boundaries, dislocations and grain refinement, written by equation where σi is the initial yield strength of the current iHEA with the average grain size of 65 μm. The terms indicated by f represent the volume fraction of the grains associated with different microstructural features, such as pre-existing nano-twin boundaries (TW), dislocations (DIS) and grain refinement (GR) by nano-grains or static recrystallization, and Δσ refers to the increase of the yield strength caused by each strengthening mechanism.It is well-known that the yield strength can be improved by grain refinement which is expressed as the Hall-Petch relation [Here, ky is the strengthening coefficient by grain refinement and d is the average grain diameter. By plotting the Hall-Petch relation in a large range of grain sizes from 2.2 μm to 160 μm (data extracted from current and previous work []), the values of ky (573MPa⋅μm−1/2) and σ0 (179 MPa) were derived. The strengthening coefficient ky in this case is consistent with those reported in the Fe-Ni-Co-Al-Cr HEAs with and without the addition of carbon (574 and 534 MPa⋅μm1/2) [] and the equiatomic Co-Cr-Fe-Mn-Ni HEA (494 MPa⋅μm1/2) [], but it is much higher than that stated in Fe-Mn steels (365MPa⋅μm1/2) []. The volume fraction of recrystallized grains, fSRX, was measured from EBSD analysis according to the grain orientation spread (GOS) of which the dislocation-free recrystallized grains were less than 1⁰.Upon annealing, the large parent grains underwent recovery where dislocation dipoles with opposite sign annihilated, thus the density of retained statistically stored dislocations (SSD) was expected to be very low. The increase in yield strength owing to the pre-existing dislocations, therefore, was mainly due to GNDs which form arrays of subgrains with small misorientations. The density of GNDs (ρGNDs) can be expressed as a function of the misorientation angle (θ) and the unit length (u) [where b is the magnitude of the Burgers vector (2.55 × 10−10 m) of the FCC phase. Taking u=10−5 m, the density of the GNDs in the annealed samples was then estimated to be around 1014/m2 []. The contribution of the GNDs to the yield strength can be considered by using Taylor hardening law [Here, M is the Taylor factor (3.06), α is a constant (0.2) and G is the shear modulus which was determined to be 76 GPa for this iHEA as measured by impulse excitation technique. The fractions of the GNDs of 1014/m2 (KAM values above 1) were obtained from the KAM plots [With knowing the contribution of grain refinement and dislocations to the yield strength, the role of pre-existing nano-twins was able to be derived. It was reported that the yield strength was related to the twin spacing, described by the twinning Hall-Petch relation (equation where λ is twin spacing and kt is the strengthening factor by twin boundaries. shows the ECC images of twins in annealed specimens. It can be seen that twin spacing became broader at higher annealing temperatures due to the migration of twin boundaries by the movement of Shorkley partials. The volume fraction of the grains with nano-twins was assumed to be the fraction of un-recrystallized and yet reversely transformed FCC grains. The dependence of the increase in the yield strength due to the nano-twins, ΔσTW, with average twin spacing was then plotted in d together with the grain size Hall-Petch relation. The derived strengthening coefficient of nano-twins, kt (195MPa⋅μm1/2) was much smaller than the grain boundary strengthening coefficient. The similar phenomenon was also reported in a Fe-Mn steel with pre-existing nano-twins produced by dynamic plastic deformation and subsequent annealing []. This indicates that nano-twin boundaries did not act as effective obstacles as the high angle grain boundaries for dislocation transmissions. The pre-existing twin boundaries had two-fold effects. At first, the coherent twin boundaries on the (111) plane provide glide plane for partial dislocations where the slip plane and the Burgers vector are parallel to the twin boundaries which help to facilitate HCP-martensitic transformation and twinning []. Secondly, some of the twin boundaries block the motions of dislocations as grain boundaries. When the incoming dislocations interact with twin boundaries, they either dissociate into partials along the twins or transfer through the twins depending on the nature of the dislocations and the stress state []. In this case, the pre-existing twin boundaries show an angle with respect to the slip planes (For the tempered samples, the augmentation of the yield stress due to nano-twins can be calculated by extrapolating the plot of the twinning Hall-Petch relation. It was found that the increase of the yield strength due to nano-twins and dislocations were around 468 and 57 MPa, respectively. Hence, the shear-banded microstructure contributed about 522 MPa of the yield strength. Given that the volume fraction of the shear bands was about 35%, a yield strength of 1.5 GPa could be achieved in the nanostructures in the shear bands. A ratio of the yield strength of the nanostructures in the shear bands with respect to the large grains with nano-twins was around 1.66, which is consistent with the nano-indentation results (7.4 GPa/4.5 GPa). The contributions of nano-twins, dislocations and grain refinement to the increase of yield strength were summarized in e. It can be seen that the nanostructures in the shear bands and the pre-existing nano-twins in the parent grains made the primary contributions to the improvement in the yield strength of the bimodal microstructures created by tempering. In the annealed specimens with trimodal grain structures, nano-twins in the unrecrystallized grains played a larger role to the increase of the yield strength than the grain refinement by recrystallization.In the following, we discuss the correlation of the work hardening behavior and the strength-ductility synergy with the formation of HCP-martensite and twinning in the hierarchical microstructures. According to the models proposed by Mahajan et al. for HCP-martensite [], a normal stress of 531 MPa was required for activating both mechanisms with assuming the stacking fault energy of 18 mJ/m2 in the current iHEA (see appendix). This critical stress was lower than the actual yield strength of all the tempered and annealed specimens.The tempered specimens with bimodal microstructures showed an almost linear decrease of the work hardening rate until necking. Since both, the pre-deformation substructures and the nano-grains largely increased the stability of the FCC matrix, formation of HCP-martensite and mechanical twinning were inhibited to some extent. Plastic deformation was, hence, achieved mainly by dislocation slip and led to localized deformation. According to the Considère criterion, plastic instability is reached when the work-hardening rate is surpassed by the true stress, ∂σ/∂ε≤σ []. Therefore, in the tempered specimens, the work-hardening rate was not sufficiently high to prevent early necking resulting in the limited uniform elongation.Interestingly, the annealed samples with trimodal microstructures exhibited multistage work hardening behavior (see the schematic plot in c). In the first stage, the work hardening rate continuously decreased in all specimens, which is related to the rearrangement of the dislocations []. At higher strains, it was found that the different types of trimodal grain structures probed in this study showed a more complex, viz., multistep work hardening response. Specifically, specimens annealed at 650 °C went through three stages of strain hardening whereas four-stage work hardening behavior appeared in the specimens annealed at 750 °C with a sudden increase at low strains (2–5%, stage II) (c). This is attributed to the difference in the volume fraction of recrystallized grains in the former case (55 vol %) opposed to the latter one (85 vol %). Accordingly, the latter case involves a higher amount of medium-sized recrystallized grains (1–6 μm) (c) which have relatively low phase stability relative to smaller crystals. Therefore, the rapid increase of the work hardening rate in stage II was ascribed to the nucleation of HCP-martensite lamellae and nano-twins in the medium-sized recrystallized grains in the specimens annealed at 750 °C. Although the volume fractions of the HCP-martensite and twins were fairly low at early strains, it was noticed that the thicknesses of such lamellae were very thin (a few nm to 100 nm) which greatly refined the microstructure, thus reducing the mean free path of dislocations, an effect known as dynamic Hall-Petch effect []. It was also reported that thinner twins could promote dislocation-twin interactions and leave more space for dislocation storage resulting in more pronounced work hardening []. In this case, both martensite lamellae and twins served as obstacles for dislocation glide. On the contrary, in the specimens annealed at 650 °C, the pre-existing dislocations trapped free mobile dislocations and the smaller grain size increased the back stresses which also affected dislocation motion. Both effects impeded formation of stacking faults. Therefore, nucleation of HCP-martensite and twins in the specimens annealed at 650 °C was sluggish at low strains and no obvious increase in strain hardening was observed in this regime.The strain hardening in stages III and IV of all annealed specimens showed a similar trend characterized by the further decline in the work hardening rate, however, with a lower decreasing slope at the last stage. For the specimen annealed at 750 °C, the nucleation rate of HCP-martensite and twin lamellae in stage III was lower compared to that in stage II. The reason for this effect is that when the critical stresses for nucleation of HCP-martensite and twins were reached, growth rather than nucleation of such lamellae prevails. Therefore, the further decrease of the mean free path for dislocations by such lamellae was modest, reducing work hardening. Stage IV occurred roughly at strains of 10%, 12% and 18% for the specimens annealed at 650 °C for 3 min, and 10 min and 750 °C for 3 min, respectively, corresponding to a similar true stress level of around 1100 MPa. It is related to the nucleation and growth of HCP-martensite and twins in the ultrafine SRX grains since higher stresses are required to nucleate twins and/or HCP-martensite under such spatially confined conditions [] reported that the critical shear stress to initiate twins in a Fe–15Mn–2Al–2Si–0.7C steel increased from 62 MPa to 316 MPa with decreasing grain size from 84 μm to 0.7 μm which followed a Hall-Petch type relationship. Yoo et al. [] found that the critical stored energy for the formation of the strain-induced martensite in an austenitic steel increased from 5.5 J/g to 9 J/g with decreasing grain size from 2 μm to 300 nm and the volume fraction of martensite reduced in smaller grains. These findings are consistent with the current observations, and hence, the true stress of ∼1100 MPa is correlated to the critical stress required to grow HCP-martensite and twins in sub-micrometer sized grains. Therefore, due to the wide variation in the phase stability promoted by trimodal grain structures, the TRIP and TWIP effects were stimulated successively in grains with different sizes. Through such utilization of the size and substructure dependence of the TRIP and TWIP effects we expanded the work hardening rate into a sequence of distinct and successive mechanism regimes, enhancing the materials’ strength-ductility ranges. Overall, it is thus shown that different types of hierarchical microstructures, including grains of difference size, texture, softening stage and substructure, can significantly affect the deformation modes and the associated work hardening response in such metastable HEAs, enabling tuning them for different types of strength-ductility profiles.As discussed above, a large spectrum of mechanical properties with the yield strength ranging from 555 MPa to 1.3 GPa, UTS from 930 MPa to 1.5 GPa and total elongation from 60% to 14% was achieved through the hierarchical microstructural design. The combinations of strength and ductility reported here covered properties ranging from the strong maraging steels []. Here this was achieved in a carbon interstitial HEA with well-tuned stacking fault energy coupling with hierarchical microstructures introduced by conventional thermomechanical processing. The current study not only revealed the fundamentals of the processing-microstructure-properties relationship of the iHEA but also pointed out the importance of designing microstructures that take advantage of the wide compositional degrees of freedom of HEAs for future composition and microstructure-sensitive alloy development strategies.In this work, we presented systematic investigations on hierarchical microstructural design and the corresponding mechanical properties of an interstitial carbon alloyed high-entropy alloy (Fe50Mn30Co10Cr10C0.5, at. %) showing joint activation of martensitic phase transformation and mechanical twinning upon loading. The main conclusions are:A hierarchical microstructural design strategy was successfully employed to enhance the mechanical properties of an interstitial TRIP-TWIP-assisted HEA. The fundamental principle is to introduce several grain classes of different size, softening stage, texture and substructure which individually influence the mechanical stability of the FCC matrix. This effect was used to tune the local onset of phase transformation and mechanical twinning over much larger strain domains, enabling to realize and utilize a likewise wide spread of the associated strain hardening stages, ideally resulting in multistage work hardening.Upon tempering and annealing, HCP-martensite transformed reversely to FCC matrix, whereas the mechanical twins that had co-existed with martensite lamellae prevailed in the parent grains. In the tempered specimens, bimodal microstructures were produced consisting of nano-grains (∼50 nm) in the vicinity of shear bands and recovered parent grains (10–35 μm) with pre-existing nano-twins. Upon annealing, trimodal microstructures were created via partial recrystallization, characterized by small recrystallized grains (<1 μm) associated with shear bands, medium-sized grains (1–6 μm) recrystallized through subgrain rotation or coalescence of parent grains and retained large un-recrystallized grains.The enormous improvement in yield strength of the bimodal microstructure from 555 MPa to 1.3 GPa relative to the 95 vol % recrystallized specimen (with an average grain size of 2.2 μm) was attributed to the appearance of pre-existing nano-twins and nanosized grains.In specimens with trimodal microstructures, ductility was improved from 14% to 60% compared to those with bimodal microstructures due to the appearance of a multistage work hardening behavior. Specimens with less than 55% recrystallization exhibited three stages of strain hardening, whereas for those containing 85% recrystallization and above, four-stage work hardening behavior was observed with a steep increase at low strains (2–5%). This work hardening sequence was due to the activation of TRIP and TWIP effects over a large strain regime, which was associated with the difference in phase stability promoted by the grain size hierarchy. Particularly, the resistance to the decrease of the work hardening rate in the last stage of strain hardening was attributed to the formation of martensite and twins in grains of sub-micrometer size (<500 nm).It has been well established that activation of TRIP and TWIP effects strongly depends on the stacking fault energy (SFE). TRIP is normally found in the FCC structured metals with SFE below 20 mJ/m2, while TWIP was reported in the materials with higher SFE between 18 and 40 mJ/m2 []. The SFE of the present iHEA is expected to be around 18–20 mJ/m2, since TRIP and TWIP mechanisms occurred concurrently upon deformation and no B.C.C. α′-martensite was observed []. The SFE of Fe-30Mn-0.5C (at.%) was found to be around 20 mJ/m2 [] and Co and Cr are both HCP-phase stabilizing elements and thus decrease the SFE []. Therefore, the SFE of the 49.5Fe-30Mn-10Co-10Cr-0.5C (at.%) iHEA is assumed to be 18 mJ/m2 for the following calculation. The SFE, Γsf, can be determined by equation Here, ΔGFCC→HCP is the Gibbs free energy difference between the FCC phase and the HCP-martensite, σFCC/HCP is the interface energy (5–15 mJ/m2), and ρm is the molar surface density of the {111} plane (2.94 × 10−5 mol/m2). Therefore, ΔGFCC→HCP can be derived from equation with taking the interface energy of 10 mJ/m2.According to the HCP-martensite nucleus model proposed by Mahajan et al. [], the formation of HCP-phase involves Shockley partial dislocations gliding on every second (111) plane. The critical stress for the growth of the HCP-nucleus can be expressed by equation τtr=2σγ/ε3btr+3GbtrLtr+hΔGF.C.C.→H.C.P.3btrHere, G is the shear modulus, btr is the Burgers vector of the partial dislocation (0.147 nm) and Ltr is the length of the nucleus.Formation of deformation twins in FCC also involves a6<112¯> Shockley partials but gliding on the successive {111} plane, suggested by Mahajan and Chin []. The critical stress for twin growth, τtw, can be estimated by equation Here, L0 is the width of twin embryo (260 nm) []. At the SFE of 18 mJ/m2, the shear stress required to grow martensite and twins are very close, about 174 MPa. By considering a Taylor factor of 3.06, a normal stress of 531 MPa is required to grow HCP-martensite and twins. The lowest yield strength among all the annealed specimens was 555 MPa in this work, thus the predicted stresses for HCP-martensitic transformation and twinning both below the bulk yield stresses.Microstructure, mechanical properties and superplasticity of the Al–Cu–Y–Zr alloyThe phase composition, mechanical properties, and superplastic deformation behavior of a novel Al-4.7Cu-1.6Y-0.3Zr alloy were analyzed. The precipitation of Al3(Zr,Y) dispersoids was observed during a homogenization treatment. The precipitates have an L12 structure and a mean size of 17 and 19 nm at 540 and 590 °C, respectively. The sheets exhibit a yield strength of 292 MPa, an ultimate tensile strength of 320 MPa, and an elongation of 5.3% after simple thermomechanical treatment and annealing at 100 °C. The Al-4.7Cu-1.6Y-0.3Zr alloy exhibits superplasticity with m > 0.4 and elongation of 300–400% within a temperature range of 550–580 °C and a strain rate range of 1 × 10−4 to 1 × 10−3 s−1.In aluminum-based alloys, nanoscale L12-type Zr and Sc-bearing precipitates provide strengthening due to the Orovan mechanism [] and significant grain refinement due to Zener pinning of the grain boundaries []. The yield strength additionally improves via Hall-Petch relationships []. As a result, Zr and Sc minor additions help improve the mechanical properties at room temperature [] of various aluminum-based alloys. Several previously published studies [] demonstrated that Y is a prospective alloying element for Al and its alloys due to the formation of similar nanoscale L12 precipitates. Al3(Y,Zr) dispersoids with sizes in the range of 17–37 nm are formed in the Al–Zr–Y alloy after annealing at 500°С []. Minor Y addition helps improve the mechanical properties of aluminum via the same mechanisms; therefore, Y is a promising analogue of expensive Sc [Yttrium as an alloying element that demonstrates additional advantages for aluminum alloys. The addition of 0.05–0.10 wt% Y decreases the solidification range, causing increased castability of Al–5%Cu []. Due to grain refinement of the as-cast structure by the peritectic Al3Y phase, Y decreases the hot tearing susceptibility of the Al–5%Cu alloy []. The quasi-binary Al-4.7Cu-1.6Y alloy exhibits a good combination of casting properties, hot cracking susceptibility, and mechanical properties at room temperature []. Therefore, complex alloying of aluminum with Cu, Y, and Zr should lead to a bimodal size distribution of secondary phases in the aluminum matrix—fine precipitates of Al3(Zr,Y) and coarse particles of crystallization-originated eutectic Al8Cu4Y (τ1) and AlCuY phases [The bimodal distribution of particles improved the grain refinement due to their effect on recrystallization []. First, fine nanoscale precipitates inhibit grain growth via the Zener pinning effect [], and second, coarse microsize particles increase the nucleation rate via the particle-stimulated nucleation effect []. The involvement of both grain refinement mechanisms helps form a stable and fine grain structure, providing good ductility, formability and superplasticity of the sheets processed via simple thermomechanical treatment []. Thus, the combination of high recrystallization resistance, increased mechanical strength and superplasticity are expected in a novel Al–Cu–Y–Zr alloy. This study focuses on the analysis of the phase composition, grain structure, mechanical properties, and superplastic behavior of a novel Al-4.7Cu-1.6Y-0.3Zr alloy.A novel Al-4.7Cu-1.6Y-0.3Zr alloy and a recently developed Al-4.7Cu-1.6Y alloy [] were studied. The Zr-free Al-4.7Cu-1.6Y alloy was studied as a reference. The Al-4.7Cu-1.6Y-0.3Zr alloy was produced in a laboratory Nabertherm S3 (Nabertherm GmbH, Lilienthal, Germany) furnace. Pure aluminum (99.99%) and Al-53.5Cu, Al–9Y, Al-3.5Zr master alloys (“ligatures”) were used in the alloy preparation. The melting temperature was 750°С. Ingots with a size of 40 × 20 × 120 mm3 were cast into a water-cooled copper mold. The casting-cooling rate was approximately 15 K/s. The as-cast ingots were homogenized in a Nabertherm N30/65A furnace. The ingots of 20 mm in thickness were rolled to 10 mm (50% reduction) at 450 °C and, subsequently, to 1 mm (90%) at room temperature.The alloy microstructure and phase composition were studied using a TESCAN VEGA 3LMH scanning electron microscope (SEM) equipped with XMAX-80 energy-dispersive X-ray and electron backscatter diffraction (EBSD) HKL NordlysMax detectors. The EBSD maps were processed in the area of 200 × 200 μm2 with a 0.4-μm step size to identify high angle grain boundaries (HAGBs) and low angle grain boundaries (LAGBs). The strain-induced changes in the microstructures of the sample volumes and surfaces were studied at a strain of 0.7 (100%) with a strain rate of 5 × 10−4 s−1 and temperature of 580 °C. Several cross scratches were produced on the polished surfaces of the samples prior to tensile tests to evaluate the surface changes in the grain structure.Disc-shaped samples with a diameter of 3 mm and a major axis parallel to the deformation direction were used for transmission electron microscopy (TEM). The TEM studies were performed using a JEOL JEM–2000 EX microscope. The discs were electrochemically thinned by twin-jet polishing using a Struers Tenupol in an A2-type electrolyte at a temperature of (0 ± 1) °C and a voltage of 20 V. The grain structure of the alloy was studied using a Neophot 30 light microscope (LM) with a polarized light.The mechanical properties were determined at room temperature based on the results of the tensile and Vickers hardness (HV) tests. The uniaxial tensile tests were performed with a strain rate of 4 mm/min using a Zwick/Roell Z250 testing machine. The tested samples had a gage length of 20 mm, a width of 6 mm, and a thickness of 1 mm.The superplastic characteristics were studied by uniaxial tensile tests on a Walter Bay 100 N test machine. The traversing rate was controlled to maintain constant strain rates during the sample tensile testing. Samples with a gauge section size of 6 × 1 mm2 and a length of 14 mm were cut parallel to the rolling direction. The m-index that characterizes the strain rate sensitivity of the alloy was determined via step-by-step increasing of the strain rate tests within a temperature range of 500–580°С. Tests at constant strain rates were carried out within a strain rate range of 1 × 10−4 to 1 × 10−2 s−1 and a temperature range of 460–580 °C.The grain structure of the as-cast Al-4.7Cu-1.6Y-0.3Zr alloy is shown in ). It is notable that the Zr-free alloy had the same mean grain size [], which suggested the formation of a supersaturated Al–Zr solid solution upon casting.The dendrites of the Al-based solid solution were the main microstructural element in the as-cast state, with a volume fraction of 80% (). Fine crystallization-origin phases were observed organized in colonies on the periphery of the dendrite cells of the aluminum solid solution (). The colonies consisted of platelets with a thickness of approximately 200 nm and compact inclusions (). Three types of secondary phases were identified in the as-cast state: (1) Cu- and Y-enriched platelets (A-type, dark gray), Cu- and Y-enriched rims around the (Al) dendrite cells (light gray, B-type), and Cu-rich areas (white, C-type) (). Zirconium-bearing secondary phases were unobserved, and the 0.3 wt%Zr completely dissolved in the aluminum-based solid solution, as shown by the SEM-EDS analysis. The as-cast microstructure of the studied alloy was similar to that of the Zr-free alloy []. Solidification of the (Al), η(AlCu), τ1(Al8Cu4Y), and τ6(Al,Cu)11Y3 phases is suggested according to Ref. [Homogenization annealing was performed at 540 (b, d) for 3 and 24 h. Homogenization led to fragmentation and spheroidization of the Al8Cu4Y and (Al,Cu)11Y3 eutectic-origin phases. The mean size of the Y-bearing inclusions increased from 200 nm after casting (c) and to 1.9 μm after annealing at 590°С (d) for 24 h. The Cu-rich phases partially dissolved during annealing. The copper content in the aluminum solid solution increased from 1.1% in the as-cast state to 1.3% after annealing at 540°С for 3 h and to 1.8% after annealing at 590°С for 3 h ( a, b). The results demonstrate a similar behavior of the crystallization origin phase upon the annealing of Zr-free and Zr-bearing Al–Cu–Y alloys [The TEM study identified spheroidal precipitates () after 3 h of annealing at both 540 and 590 °C. The precipitates exhibited a mean size of 16 ± 5 nm and 19 ± 7 nm at 540 and 590 °C, respectively. The precipitates displayed typical L12 phase diffraction patterns with superlattice reflections (SAEDs in inserts in ). Most likely, the precipitates belong to the Al3(Zr,Y) phase []. It is notable that many precipitates exhibited structural faults characterized by sharp lines of no contrast inside the precipitates. Such planar defects were previously observed in the Al3Zr [] phases, and their formation is typically associated with the start of the L12→D023 transformation []. The precipitates were organized in lines (c), and they were randomly distributed inside the dendrite cells ( a, b), which suggests heterogeneous and homogeneous nucleation mechanisms [Ingots annealed at 540 and 590°С for 3 h were subjected to thermomechanical treatment. The intermetallic particles were more homogenously distributed in the aluminum matrix after rolling compared to in the as-annealed state (). The particles had a mean size of 1.7 ± 0.2 μm and a volume fraction of 20% in the sheets prehomogenized at 540°С and 1.9 ± 0.2 μm and of 11% in the sheets prehomogenized at 590°С. Thus, 9% of the inclusions were dissolved upon increasing the temperature from 540 to 590°С.The as-rolled samples were annealed at different temperatures for 1 h. The hardness evolution vs annealing temperature curves are presented in a, c. The data for the Zr-free alloy are shown in for comparison. A banded grain structure was observed after annealing at up to 250 °C. Annealing at 350 °C or higher resulted in a recrystallized grain structure (microstructure in a, c). The hardness level of the Al-4.7Cu-1.6Y-0.3Zr alloy was 10 HV higher than that of the Zr-free alloy at all annealing temperatures (). However, the recrystallization start temperature was within the same temperature range of 250–350°С (see the grain structures in Ref. [The hardness vs. time curves at low annealing temperatures (<250 °C, below the recrystallization start temperature) were different for the Zr-bearing and Zr-free alloys ( b, d). The hardness value decreased upon annealing for both alloys. During annealing at 150 and 180°С for 6 h, a slight hardness decrease of 10–16 HV was observed in the Zr-bearing alloy, while the decrease in the Zr-free alloy was 20–30 HV (b, d). Thus, the softening was significantly lower in the Al-4.7Cu-1.6Y-0.3Zr alloy in comparison with that in the similar Zr-free material. The lower softening effect in the Zr-bearing alloy can be explained by the formation of Al3(Zr,Y) dispersoids, which provided Zener pinning and Orovan strengthening mechanisms (It is notable that the hardness level of the samples prehomogenized at 590°С after 6 h of annealing at 150 and 180°С was higher than that of the samples pre-homogenized at 540°С. Such behavior can be explained by the higher copper concentration in the aluminum solid solution after annealing at 590°С. illustrates the results of the tensile tests of the as-rolled and as-annealed conditions. Higher strength values were achieved in the rolled alloy prehomogenized at 590°С due to the higher Cu content in the aluminum solid solution compared to that at 540°С. A good combination of strength and ductility was observed both after rolling and after rolling with subsequent annealing at 100°С for 1 h—the alloy exhibited a yield strength of 303–292 MPa, an ultimate tensile strength of 328–320 MPa, and an elongation to failure of 5.0–5.3%.Recrystallization annealing at a temperature of 580 °C (0.97 Tmelt) for 20 min led to the formation of a homogenous equiaxed grain structure in the Al–Cu–Y–Zr alloy (b and c) and a nonhomogeneous grain structure with areas of coarse and fine grains in the Al–Cu–Y alloy (a). In the Zr-bearing alloy, the mean grain size was 7.8 ± 0.5 μm and 8.2 ± 0.4 μm in the samples preannealed at 540 °C for 3 h and at 590 °C for 3 h, respectively. The Al–Cu–Y alloy exhibited a coarser grain structure with a mean grain size of 11.3 ± 1.1 μm.The fine-grained Zr-bearing alloy exhibited a sigmoidal shape of the stress-strain rate logarithmic curves, with a maximum strain rate sensitivity m-index of 0.4–0.5 within a strain rate range of 1 × 10−4 - 2 × 10−3 s−1 at 580 °C (a). It is notable that the Zr-free alloy exhibited m > 0.3 at strain rates below 1 × 10−3 s−1. The Zr-free alloy demonstrated a mean elongation of 175% and 225% at a strain rate of 1 × 10−3 s−1 and 1 × 10−4 s−1, respectively (b, red curves). In the Al-4.7Cu-1.6Y-0.3Zr alloy prehomogenized at 540°С, the elongation was 250 and 325% at a strain rate of 1 × 10−3 s−1 and 1 × 10−4 s−1, respectively (b, black curves). The samples of the Al-4.7Cu-1.6Y-0.3Zr alloy prehomogenized at 590°С exhibited a mean elongation of 295 and 355% at a strain rate of 1 × 10−3 s−1 and 1 × 10−4 s−1, respectively (b, blue curves). These samples exhibited the maximum elongation of 400% corresponding to a constant strain rate of 5 × 10−4 s−1 at 580 °C (b). The elongation to failure decreased to 300% and 230% at strain rates of 1 × 10−3 s−1 and 2 × 10−3 s−1, respectively. Therefore, the Al-4.7Cu-1.6Y-0.3Zr alloy prehomogenized at 590°С exhibited 300%–400% elongation, whereas the Zr-free alloy did not exceed 200% elongation within a constant strain rate range of 1 × 10−4 s−1 to 1 × 10−3 s−1.EBSD orientation maps, crystallographic texture maps, grain boundaries misorientation angle distributions, and grain sizes obtained from the samples strained at 0.7 at 580 °C and 5 × 10−4 s−1 are presented in (a–f). The samples, which were prehomogenized using different modes, exhibited similar grain structures and grain sizes after superplastic deformation (true strain of 0.7). The HAGBs were dominated by a mean grain boundary misorientation angle of approximately 45° (see dotted lines in e and f). The grain sizes were 10.2 ± 0.9 μm and 11.3 ± 1.0 μm for the samples prehomogenized at 540 °C and 590 °C, respectively. EBSD data indicate relatively weak textures for both samples independently of the homogenization regime. The textures consisted of several components with a range of orientations. Specifically, goss, brass, cubic, copper, and S crystallographic texture components were presented.g and h demonstrate the microstructures of the surfaces of the deformed samples at strain 0.7 at 580 °C and 5 × 10−4 s−1. This regime provided high m of 0.45–0.50 under both homogenization modes. A value of m ≈ 0.5 and a weak texture, which were observed in the studied samples, were considered as grain boundary sliding features []. The grain boundary sliding is a dominant superplastic deformation mechanism for many superplastic materials []. The grain rotation and shifts of marker lines (grains A, B, and C and dotted lines in g and h) were observed on the surfaces of as-deformed samples. These phenomena are typical of superplastic deformation through grain boundary sliding []. The dislocation slip/creep and diffusion creep are considered the mechanisms that accommodate grain boundary sliding []. The contribution of these mechanisms to a total strain can be significant []. The “striated regions” (red arrows in g and h) indicate that a diffusion creep mechanism operated in the process of superplastic deformation []. Folds that appeared on the surfaces of several grains (black arrows in g and h) derived from the mechanism of intragranular dislocation sleep/creep. Therefore, surface observations indicated that all typical deformation mechanisms were operating in the superplastic flow of the studied Al–Cu–Y–Zr alloy.The low strain rate of superplasticity and low elongation was a result of the coarser grain structure of the Zr-free alloy. Despite their similar grain size, the Al-4.7Cu-1.6Y-0.3Zr alloy samples prehomogenized at 590 °C demonstrated better superplasticity compared to the samples prehomogenized at 540 °C due to the higher Cu content in the Al solid solution. The solute may have a direct effect in promoting the studied alloy superplasticity []. According to several experimental observations [], diffusion creep plays a significant role in the superplastic deformation of Al–Mg- and Al–Cu-based alloys. The increasing elongation with increasing Cu in the aluminum solid solution also suggested the significance of the diffusion creep mechanism in the superplastic deformation of the studied alloy. Most likely, copper may enhance the diffusion rate of the solvent self-diffusion in the aluminum, similar to the way that P increases the self-diffusion in Fe [], Au and Ag increase the self-diffusion in Pb [] and Cd and In increase the self-diffusion in Ag []. To clarify the differences in superplastic deformation behavior of samples with similar grain sizes and different solute content, further investigations of the contributions of the grain boundary sliding as well as the diffusion creep and dislocation creep mechanisms to the total strain are necessary.The investigated alloy may be a prospective composition for the development of novel heat-resistant materials for the aerospace industry due to the high thermal stability of the eutectic phases and Al3(Zr,Y) precipitates. The studied Al-4.7Cu-1.6Y-0.3Zr alloy may be successfully used as a cast and wrought alloy due to its good combination of castability, room-temperature mechanical strength, creep resistance and superplasticity. To increase its mechanical properties, the investigated alloy can be additionally alloyed with Mg and Mn. Due to its good castability, the alloy is a promising material for use in additive manufacturing by laser selective melting. However, investigated alloy was melted of pure aluminum (99.99%) and further investigation of the residual Fe and Si on phase composition and properties is required.The phase composition and microstructure evolution during thermomechanical treatment and mechanical properties at room temperature and superplasticity at elevated temperatures in a novel Al-4.7Cu-1.6Y-0.3Zr (wt.%) alloy were studied. The most important results are summarized as follow:Yttrium provided for the formation of the Y-rich (Al8Cu4Y and (Al, Cu)11Y3) constituent phases and supersaturated aluminum solid solution in the as-cast state. The Y-free and copper enriched (AlCu) constituent phase were also identified.Due to the decomposition of the as-cast solid solution supersaturated by 0.3 wt%Zr and 0.1 wt%Y, the coherent L12-structured Al3(Zr, Y) precipitates with an average size of 16 and 19 nm formed during homogenization annealing for 3 h at 540 and 590 °C, respectively. As compared with the reference Zr-free alloy, the Al–Cu–Y–Zr alloy demonstrated an enhanced recrystallization resistance upon annealing of thermomechanically treated sheets due to the Al3(Zr,Y) dispersoids.The homogenization annealing increased the Cu content in the aluminum solid solution from 0.7 in the as-cast state to 1.1 wt% at 540 °C and to 1.8 wt% at 590 °C as a result of the dissolution of non-equilibrium Cu-rich phases. Increasing solute Cu was the reason for the improvement of the alloy superplasticity in the samples with the same initial mean grain sizes of ≈8 μm. As a result, the Al-4.7Cu-1.6Y-0.3Zr alloy prehomogenized at 590 °C exhibited superplasticity with m > 0.4 and elongation to failure of 340–400% at a temperature of 580 °C and a strain rate range of 1 × 10−4 to 1 × 10−3 s−1. The strain-induced grain growth to 10–11 μm and a weak texture were identified at a superplastic strain of 0.7 with a strain rate of 5 × 10−4 s−1 regardless of the homogenization mode. The structural features of the grain boundary sliding, dislocation slip/creep and diffusion creep mechanisms on the surface of the as-deformed sample were evidenced.The alloy developed in this study exhibits a good combination of strength and ductility after thermomechanical treatment which includes homogenization at 590°С for 3 h, hot and cold rolling, and subsequent annealing at 100°С for 1 h. The alloy demonstrated a yield strength of 292 MPa, an ultimate tensile strength of 320 MPa and an elongation of 5.3%.The alloy is a prospective composition for the development of novel heat-resistant materials due to the high thermal stability of the eutectic phases and L12-structured coherent nanoscaled Al3(Zr,Y) precipitates. The mechanical properties of the alloy can be improved by additional doping with Mg and Mn, and their effect on the properties of the developed alloy is still to be studied. Further investigation of residual Fe and Si on the phase composition and properties of the alloy is also required.Non-homogeneous and multi-axial stress distribution in concrete specimens during split Hopkinson tensile testsA split Hopkinson bar set-up is often used for the dynamic testing of materials. Test execution is relatively simple, and interpretation of test results is considered to be straightforward. Classical treatment of Hopkinson bar test results is based on the assumption of a homogeneous, uniaxial stress state in the specimen. However, non-axial stress components inevitably accompany the axial stress. These stresses have a large influence on the mechanical behaviour of concrete. To investigate the dynamic tensile properties of concrete, a split Hopkinson bar set-up was built. To obtain the full understanding, numerical simulations of the behaviour of the test set-up have been performed. The results are presented in this paper.Aircraft accidents, collisions, earthquakes, seawaves, vibrating machines etc., imply heavy dynamic loading on civil constructions from 100 to 5000 s−1) material testing Although commonly used for compression testing, with some adaptations, the concept of the split Hopkinson bar set-up and the basic principle of interpretation can be used for dynamic tension The experimental set-up of a split Hopkinson bar test consists typically of an input bar, a test specimen and an output bar. For compression testing the specimen can simply be sandwiched between input and output bar, whereas for tensile testing the specimen has to be attached in some way to the input and output bar. gives a schematic representation of a typical Hopkinson set-up for tensile testing of materials. The anvil at the outer end of the input bar is hit by an impactor, which is generally pneumatically accelerated. A tensile strain wave ϵi, the so-called incident wave, is thus generated and propagates along the input bar towards the specimen. Upon reaching the specimen, the wave is partly reflected back into the input bar to form the reflected wave ϵr, and is partly transmitted to the output bar to form the transmitted wave ϵt. The waves ϵi, ϵr and ϵt are usually measured by means of strain gauges. These strain gauges are located at well chosen points on the input and output bar, away from the specimen. The so recorded signals have, thus, to be shifted forward or backward, towards the interface planes with the specimen, in order to obtain the forces and displacements at both ends of the specimen.As mentioned previously, for the extraction of the time histories of strain, strain rate and stress in the specimen from the waves ϵi, ϵr and ϵt at the interfaces of the bars with the specimen, the following assumptions are classically made:a uniaxial stress state is supposed to exist in both Hopkinson bars and specimen; from the recorded strain waves, particle speeds and stresses at the bar–specimen interface planes are calculated using the one-dimensional wave propagation theory,a homogeneous stress state is supposed to exist in the specimen; radial and axial inertia of the specimen itself are neglected, and the specimen is supposed to be able to expand or contract freely in the radial direction, without any influence of the bars.With these assumptions, the time histories of strain, strain rate and stress in the specimen can be obtained from the following equations with Eb being the modulus of elasticity of the Hopkinson bars; As, Ab, the cross-section area of the specimen, and of the Hopkinson bars respectively; Cb, the velocity of propagation of longitudinal waves in the Hopkinson bars; and Ls, the specimen length.For the calculation of the stress history within the specimen, some authors Similarly the strain rate can be calculated byCertainly, in the range of small strains, gives a result closer to the real value of the stress When the incident wave is sufficiently long in comparison with the specimen length, axial inertia of the specimen could be neglected in a first approximation; quasi-static equilibrium is established after a certain time. Indeed when a stress wave reaches the specimen, part of it is reflected at both interfaces and travels back and forth within the specimen, making the axial stress in the specimen approximately uniform after a few reflections , the major advantage of classical Hopkinson bar tests, for high strain rate materials testing and characterisation, is clear: stress and strain history in the specimen are obtained independently of each other, and no assumptions concerning the behaviour of the material have to be made.At this moment, some remarks have to be stated. As mentioned, the strain–time histories ϵi(t), ϵr(t) and ϵt(t) required in the are those existing at the interface planes, so that the recorded signals have to be shifted towards the specimen interface planes. Therefore, the material of the Hopkinson bars is normally chosen such that they remain linear elastic under the applied stresses, thus allowing the use of the elastic wave propagation theory in the interpretation – when testing low impedance materials as foams, it can be necessary to use visco-elastic bars Since Hopkinson bar tests have been used for dynamic material testing, researchers have been well aware of the fact that neither the stress state in the specimen is far from being purely uniaxial, nor perfectly homogeneous. For several reasons, small non-axial stress components inevitably accompany the axial stress. Correction terms were proposed by Kolsky In compression testing, the influence on the stress state of eventually occurring frictional effects in the interface plane between the specimen and Hopkinson bar was also soon recognised; it was noticed that the existence of frictional forces can lead to a bad estimate of the true dynamic behaviour of the material. Some authors proposed criteria for the specimen dimensions, such that these frictional forces could be neglected Upon conceiving and building the experimental set-up, the authors observed that the fabrication of bone-shaped concrete specimens is not realistic. And because of the very low tensile strength, mechanical fastening of the specimens is impossible. Therefore, glueing to the Hopkinson bars of drilled cylindrical specimens has been put forward. In the interface planes, the radial displacements of Hopkinson bars and concrete specimen are thus equal, causing additional non-axial stresses in bars and specimen. In order to obtain a good understanding of what happens inside the specimen, and to be able to develop an adequate material model, numerical calculations by means of finite elements, of the experimental set-up, have been performed.Different materials have been used for the Hopkinson bars, as well as different bar and specimen diameters. The results presented in this paper, show that the non-axial stresses cannot be neglected, and moreover that the stress state is not homogeneous in the specimen. This is a very important conclusion, as is well known that the mechanical behaviour, statically as well as dynamically, of (quasi-)brittle materials, such as rocks and concrete, is largely influenced by the presence of non-axial stress components Numerical simulations have been performed to obtain the full three-dimensional stress and strain histories during a split Hopkinson bar tensile experiment. The stress situations within the specimen, as well as in the bars, were studied. Whereas the input and output Hopkinson bars do remain in a linear elastic state of stress, indeed, the material under test is being damaged and is eventually totally broken down. This implies that for a correct simulation of the behaviour of the test specimen, an adequate material model should be used. Numerical simulations that include specimen damaging and degradation are, however, very complex and do constitute a complete study by themselves: topics of non-linear, non-elastic behaviour, of strain rate dependance, of large deformations, of localisation and of numerical convergence have to be addressed. Moreover, full three-dimensional, non-linear dynamic simulations are very demanding as far as computing power is concerned. The numerical modelling and simulation of the dynamic behaviour of (quasi-)brittle specimens and the most important associated problems have been studied recently The simulated concrete specimens had the same diameter as the Hopkinson bars, and were supposed to be glued to both bars. Simulations were done for diameters of 10, 25 and 50 mm. Specimen length was chosen to be 10 mm, in accordance to the second assumption for straightforward interpretation. Referring to these dimensions, it must be noted that due to material heterogeneity, specimen diameter and length should of course be large enough in relation to the aggregate size. In their study, the authors focussed their modelling and experimental work on specimens of micro-concrete and fibre reinforced micro-concrete. Aggregate size was in all cases lower than three millimetres, and the authors have noticed that a specimen length of 10 mm and a specimen diameter of 25 mm fitted very well for this type of material The lengths of the input and output bars were 2000 and 1000 mm, respectively. For the simulations, both steel and aluminium bars were used. Aluminium bars have an acoustic impedance that is closer to that of concrete than steel bars, usually resulting in higher strain rates in the specimen. resumes the material properties, used in the numerical simulations.Loading consisted of hitting the input bar with a tensile pulse, with a rise time of 10 μs as depicted in Such a rise time is representative for that observed in the experiments.For the simulations, the finite element code SAMCEF was used. It provides an unconditionally stable implicit integration scheme for the time integration, which is called the Hilber–Hughes–Taylor method and on the element dimensions by the following equation where Le is the distance between two integration points in the direction of the wave propagation. These considerations resulted in a time step of 0.2 μs.For the spatial discretisation, axial-symmetric isoparametric elements of the second degree were used, with two translational degrees of freedom in every node. Within the specimen the element length was 2 mm and the element width was, for all bar diameters, 2.5 mm or less. For the longer input and output bars, elements of 9 mm length by 6 mm width maximum were used. Near the interface with the specimen, the mesh in the bars was gradually refined. The number of elements varied between 762 for the 10 mm diameter bars, and 1324 for the 50 mm diameter bars. shows the mesh used for bars and specimen of 50 mm diameter.During the analysis special attention was focussed on the development of non-axial stresses in the bars and the specimen, as well as on the homogeneity of stresses within the specimen.It was observed that the radial and tangential stresses accompanied the incident wave, while running along the input bar: as soon as loading starts oscillating, radial and tangential stress waves were found to develop (. The oscillations are due to the interaction of the initial three-dimensional stress pulse with the free boundaries of the cylinder; this gives rise to bouncing of stress release waves between these boundaries shows the history of the axial and radial stress components, calculated for a point on the central axis of a steel input bar with a diameter of 50 mm; the point is located at 1000 mm from the free end and specimen. The tangential stress component in this point is equal to the radial component.Due to coupling between axial and radial stress components through Poisson’s effect, oscillations with the same frequency can be observed in the axial stress history. A greater Poisson’s ratio gives rise to a greater amplitude of radial and tangential stresses; using a zero Poisson’s ratio, non-axial stress waves were found to vanish. Increasing the diameter of Hopkinson bars and specimen also increases the amplitude of the oscillations.Upon reflection and transmission at the specimen interface, these non-axial stresses become more important, due to imposed compatibility of radial displacements in the interfaces of bars and specimen. By coupling between the normal stress components, this is reflected again in the existence of additional tangential stresses.The reader should remember the fact that specimen and bars are glued together here, thus, imposing compatibility of radial displacements indeed. However, the authors came to the important conclusion that, due to friction in the interfaces of bars and specimen, exactly the same multi-dimensional stress situation does occur in classical compression testing – except of course from the sign of the stresses. It is hereby supposed that in classical compression testing by means of split Hopkinson bars, the bars and the specimen are simply put in close contact with each other, theoretically allowing for relative sliding. Indeed, when calculating the ratio of shear stress |σrz| to normal stress |σzz| () for all elements located at the interfaces, it is found that the maximum value of this ratio is always in the order of 0.05, exceptionally 0.07, whereby σzz remains always compressive. Even with careful surface preparation and with adequate lubrication, it seems unlikely that such low static friction coefficients are obtained. According to the friction laws of Amonton, it must therefore be concluded that no relative sliding in the interfaces can occur, and that the interfaces behave virtually as bonded interfaces, thus leading to the same radial and tangential stresses in the specimen.shows the radial stress distributions at 500 μs, along the central axis of a 10 and 50 mm diameter specimen, as well as in the adjacent parts of the input and output steel bars. As expected, the highest values of the radial stress are found close to the interfaces indeed; they decrease rather quickly when moving from the interface. As can be expected also, the simulations showed a larger extent of influenced zone for the larger specimen diameters, whereas the maximum value of the radial to axial stress ratio increased with the diameter.gives the time history of the axial and radial stress component in the first concrete element, just behind the interface input bar-concrete, in case of a bar diameter of 50 mm and steel bars. Note the oscillations, which were already present in the incident stress wave, and which are now superposed on the radial stress component within the specimen. Similar conclusions apply concerning the tangential stress component, as tangential and radial stresses show quite similar time histories and distributions.shows some subsequent stages of deformation of the specimen in case of a diameter of 50 mm and aluminium Hopkinson bars; for clarity, real deformations have been largely amplified. From these images it is obvious that the state of deformation and stress of the specimen is indeed far from purely uniaxial, and is moreover far from being homogeneous either.As a further example of the non-homogeneity of the stress state within the specimen, depicts the distribution of stresses at a scale that is normalised against the maximum value of the axial stress component. The diagrams correspond to , at 522 μs. Radial and tangential stresses vary from a maximum value on the specimen axis to nearly zero (zero for the radial stress) at the specimen surface. The highest values of the shear stress are generally found in the outer ring. When looking at a video of the subsequent stress distribution frames, rapid varying stress waves are clearly observed.summarises the mean and maximum values of the ratio of radial to axial stress, that were found in the simulations, for different bar materials and different specimen diameters.Numerical simulations were performed for a split Hopkinson bar experiment on micro-concrete, loaded in tension. Two different materials were compared for the input and output bars, and three different diameters were used for bars and specimens.It has become clear that the importance of non-axial stress components and heterogeneity of stress distribution in split Hopkinson bar specimens, cannot be neglected. In the case of (quasi-)brittle materials with a well-known sensitivity to multi-axial states of stress, such as concrete, these aspects should have a significant effect on actual damage onset and evolution. This leads to the conclusion that straightforward data reduction of Hopkinson bar experiments is no longer a valid procedure, in the process of development of adequate material models for this type of materials under dynamic conditions.The amplitude of the non-axial stress components, related to the amplitude of the applied axial stress, depends on the mechanical properties of the specimen and Hopkinson bars, as well as on their dimensions; radial as well as tangential stress can easily exceed 10% of the actual axial stress.It has been found that numerical simulations are a valuable tool for conceiving dynamic test set-ups, as well as for gaining understanding of what happens during an experiment and later interpretation of results. It has become the authors feeling that the development of dynamic material models for concrete, based on Hopkinson bar tests or other tests, will necessitate the combination of experiments and simultaneous numerical simulations of the complex stress and strain histories and distributions involved.Structure and residual stress evolution of Ti/Al, Cr/Al or W/Al co-doped amorphous carbon nanocomposite films: Insights from ab initio calculationsHere, we selected Ti, Cr, and W as the representative metal elements to composite with Al atom in order to generate co-doped amorphous carbon (a-C) films using ab initio calculations. Results show that compared with the pure and mono-doped cases, the Ti/Al, Cr/Al, or W/Al co-doped a-C films exhibit a general tendency of stress reduction. Particularly, it is noted that with the co-doping of Ti (1.56 at.%)/Al (1.56 at.%), Cr (1.56 at.%)/Al (4.69 at.%), or W (1.56 at.%)/Al (1.56 at.%), the residual stress is reduced by 83%, 78.9%, and 90.6%, respectively, without deteriorating the mechanical properties. Structural analysis reveals that the co-doping of Ti/Al, Cr/Al, or W/Al brings the critical and significant relaxation of distorted C–C bond lengths, as well as the formation of a weak covalent interaction for Ti–C, Cr–C, and W–C bonds and the ionic interaction for Al–C bonds, which account for the giant residual stress reduction. Consequently, by the synergistic effect of small amounts of soft ductile weak-carbide-forming metals and hard-carbide ones, it provides the theoretical guidance and desirable strategy to design and fabricate the a-C films with low residual stress and other novel performance/functions.Co-doping Ti/Al, Cr/Al, or W/Al into a-C films into carbon matrix could exhibit an extremely low residual compressive stress due to the relaxation of highly distorted bond structures and the formation of weak bond characteristics in carbon matrix in comparison with that of Ti, Cr, W, or Al mono-doped and pure a-C films, without deteriorating the mechanical properties.Amorphous carbon (a-C) films have emerged as the key ingredients for the developments of many protective materials and advanced devices Recently, multiple metal elements co-doping has been taken into account recently to overcome these barriers and explore new functions. Jansson et al. In the present work, we focused on the residual stress and structure evolution of metal co-doped a-C films using ab initio calculations based on density functional theory (DFT). Hard-carbide-forming metals (Ti, Cr, or W) and soft ductile weak-carbide-forming metals (Al) were selected as the representative doped metal elements to composite the co-doped systems. The residual stress and bulk modulus were calculated, and the bond structure including bond angles and bond lengths and bonding feature were examined to elucidate the stress reduction mechanism induced by co-dopants. We observed that co-doping Ti/Al, Cr/Al, or W/Al into a-C films into carbon matrix could exhibit an extremely low residual compressive stress due to the relaxation of highly distorted bond structures and the formation of weak bond characteristics in carbon matrix in comparison with that of Ti, Cr, W, or Al mono-doped and pure a-C films. If one notes the optimized designing with the selected co-doped metal characteristics, our results could not only account for the physical and chemical properties in experiment, but also present a new straightforward strategy to tailor the a-C films with low residual stress and other novel performance/functions.Compared with classical molecular dynamics (MD) methods which require predetermined empirical potential parameters for specified compositions, the superiority of the parameter-free ab initio simulation method is obvious. All the spin-polarized calculations were carried out using the Vienna ab initio simulation package based on DFT During the AIMD simulation, the system was first equilibrated at 8000 K for 1 ps to become completely liquid and eliminate its correlation to the initial configuration using NVT ensemble with a Nose thermostat for temperature-control and a time step of 1 fs; then, the samples were quenched from 8000 to 1 K at cooling rate of 1.6 × 1016 |
K/s. For the subsequent geometric optimization of amorphous structure, a full relaxation of the atomic positions based on conjugated gradient method Since we focused on the small amount of co-doped metal concentration without invoking severe changes in carbon matrix, the total concentrations for two metals in Ti/Al, Cr/Al, or W/Al co-doped systems were selected ranging from 3.12 to 7.81 at.% with different ratios, corresponding to 2, 3, 4 and 5 atoms in 64-atom systems, respectively. In order to provide more representative models of the real metal doped system than the direct substitution of carbon by metal atoms in pre-generated pure carbon networks, Ti, Cr, or W with Al atoms were introduced by substituting carbon atoms in the liquid carbon state with an external equilibrium at 8000 K for 0.5 ps Before characterizing the structure of Ti/Al, Cr/Al, and W/Al co-doped a-C films, the RDF, g(r), in the systems with high metal concentration was analyzed firstly to define the Ti, Cr, W, Al, and C atoms being bonded or non-bonded with each other, as shown in . The distance to the first minimum in RDF (inset values of ) was set as the cutoff distance Rcut for the C–C, C–Me, and Me–Me bonds shows the final structures of Ti/Al co-doped a-C films by using the cutoff distance of to determine the nearest neighbor atoms. Pure and Ti/Al mono-doped cases are also considered. We find that all the films are amorphous, which will be described later by RDF. gives the tetra-coordinated C content for each case. For pure a-C film, the structure is dense, and the tetra-coordinated C content is 56.2% (), which is consistent with previous work ), the similar behavior of hybridized structure with Al content is also observed. However, co-doping Ti/Al into carbon matrix seems to modify the structure seriously, as illustrated in , which will induce the significant change of properties; after co-doping Ti 1.56 at.% and Al 1.56 at.% into the a-C film simultaneously, the tetra-coordinated C content of 73.44% is obtained. Besides, noted that for the co-doped films with constant Ti content, the tetra-coordinated C content as a function of Al content decreases gradually following the increase of three-coordinated C content and five-coordinated hybridized structures. shows the RDF spectra of pure, Ti/Al mono- and co-doped a-C films. First, it reveals that for each case the film shows the typical amorphous character, that is long-range disorder and short-range order. For pure a-C film, the 1st nearest neighbor peak is located at 1.50 Å, which is in agreement with the previous experimental , the positions of 1st nearest-neighbor peak shift to 1.51, 1.51 and 1.52 Å, respectively, demonstrating the evolution of atomic bond structure and properties.The biaxial stress, σ, and bulk modulus, B, are computed by the equationswhere P is the hydrostatic pressure, Pxx, Pyy and Pzz are the diagonal components of the stress tensor, V is the system volume, B is the bulk modulus; the pressure, P, is converted to the biaxial stress, σ, by multiplying the pressure by a factor of 1.5, according to the method of McKenzie (Eq. shows the residual compressive stress and bulk modulus of Ti/Al co-doped a-C films as a function of Ti/Al concentrations. Pure and Ti/Al mono-doped cases are also evaluated. Our previous study . In general, the mechanical properties of a-C films mainly depend on the tetra-coordinated C interlink matrix. This can account for the behavior of bulk modulus with Ti concentrations and also proves that Ti as a hard-carbide formatting metal has little effect on mechanical properties However, after introducing Ti and Al into a-C films simultaneously, the drastic evolution of residual stress is presented in and the bulk modulus also shows the similar behavior to that of the tetra-coordinated C content (). As the concentrations of Ti and Al are 1.56 and 1.56 at.%, respectively, the film exhibits the lowest residual stress of about 4.6 GPa. In respect to pure a-C film, co-doping Ti and Al could reduce the residual stress by 83%, while in Ti/Al mono-doped cases the stress only drops by 47% or 36%, respectively. This is well consistent with previous work In order to elucidate the properties in terms of the doped metal concentrations and provide further insight to the stress reduction mechanism, more direct evidences for the atomic bond structure including both the bond angle and length distributions of Ti/Al co-doped a-C films are analyzed firstly. Previous study has revealed that the high residual compressive stress of a-C films is mainly originated from the distortion of both the bond angles and bond lengths of carbon network, which are less than 109.5° and 1.42 Å, respectively . In pure a-C film, the fraction of distorted bond angles is 41.4% and that of distorted bond lengths is 21.7% ). Nevertheless, after co-doping Ti (1.56 at.%) and Al (1.56 at.%) into films, the synergistic effect of Ti and Al atoms on the structure brings the fraction of distorted bond lengths to be significantly decreased to 16.2%, while the fraction of distorted bond angles slightly increases to 41.9%. This contribution agrees well with the calculation results () and experiments study where a drastic reduction of residual stress is visible In addition, the evolution of electronic structure such as the bonding characteristics caused by Ti/Al co-doping is also of great importance for optimizing the design strategies and providing the further insight for the residual stress reduction mechanism. The spin resolved density of states shows that the obvious hybridization occurs between Ti-3d, Al-3s or Al-3p and C-2p atomic orbitals, and the highest occupied molecular orbital (HOMO) mainly consists of Ti-3d, Al-3p and C-2p atomic orbitals. The charge density distribution of HOMO is given in . It illustrates that the Ti and C atoms are connected by the charge distribution (b). This is the typical character of covalent bond, but the charge accumulation between Ti and C atoms is much smaller than C–C covalent bond c). This indicates that the bond characteristic between Al and C atoms is ionic. Since the HOMO characteristics also contributes to the system rigidity except the tetra-coordinated C content, the Ti and Al atoms could form the weak covalent for Ti–C and ionic bond for Al–C separately in Ti/Al co-doped a-C systems and thus play the role of a pivotal site to reduce the bond strength and directionality drastically, where the distortion of atomic bond structure can occur without the significant increase of the strain energy due to the formed weak bond characteristics. Consequently, the drastic relaxation of distorted C–C bond lengths and the formation of weak bond characteristics between Ti/Al and C atoms are supposed to be the fundamental reasons why the residual stress is significantly decreased due to the Ti/Al co-doping.Similar to the Ti/Al co-doped case, the Cr/Al and W/Al mono- and co-doped a-C systems were also evaluated using the same method. shows the final structures and the calculated properties including the residual compressive stress and bulk modulus. It reveals that all of the films are amorphous (). Compared with the pure and Cr/Al mono-doped cases (a), co-doping Cr/Al into a-C matrix could further decrease the residual compressive stress; when the co-doped Cr and Al contents are 1.56 and 4.69 at.%, respectively, the residual stress reduces to 5.6 from 24.2 of Cr (1.56 at.%) and 20.1 GPa of Al (4.69 at.%) mono-doped cases, while the bulk modulus increases to 322.7 from 317.8 (only Cr 1.56 at.%) and 309 GPa (only Al 4.69 at.%). By contrast with pure a-C film, the co-doping of Cr/Al could decrease the compressive stress by 78.9% with the increase of bulk modulus by 2.9%. The analysis of distorted bond structure and bond characteristics is shown in . It indicates that when Cr 1.56 at.% and Al 4.69 at.% are doped into a-C film simultaneously, the fraction of distorted bond angles (< 109.5°) slightly increases to 44.2% from 40.9% of Cr (1.56 at.%) and 42.7% of Al (4.69 at.%) mono-doped cases, but that of distorted bond lengths (< 1.42 Å) drops to 12.4% remarkably from 22.4% of Cr (1.56 at.%) and 16.9% of Al (4.69 at.%) mono-doped cases. Moreover, the electronic structure (a) shows that the co-doped Cr and Al atoms also bond with C atoms in the form of weak covalent and ionic bonds, respectively. So the combination of critical relaxation of the C–C distorted bond lengths and weak bond characteristics caused by Cr/Al co-doping contributes to the obvious reduction of the residual compressive stress.b shows that compared with the compressive stress of pure a-C, W 1.56 at.%, and Al 1.56 at.% mono-doped cases (corresponding to 26.6, 9.0, and 17 GPa, respectively), it is seriously reduced to 2.5 GPa when the W 1.56 at.% and Al 1.56 at.% are co-doped. Especially, it is observed that the bulk modulus increases to 332.6 from 333.5 (only W 1.56 at.%) and 318.4 GPa (only Al 1.56 at.%). In contrast with pure case, the co-doping of W/Al could lead to the compressive stress decreased by 90.6% following the increase of bulk modulus by 6%. Furthermore, the fractions of distorted bond angles for W (1.56 at.%) or Al (1.56 at.%) mono-doped films are 42.7% and 42.2%, and those of distorted bond lengths are 15.3% and 20.1%, respectively, as shown in b. Although the fraction of distorted bond angles (< 109.5°) shows a little increases (44.1%), that of distorted bond lengths (< 1.42 Å) declines up to 11.6% drastically. On the other hand, b also shows the similar bond characteristics, weak covalent bond for W-C and ionic bond for Al–C. These factors account for the behavior of the residual stress caused by W/Al co-doping.In this study, ab initio calculations based on DFT were employed to prepare Ti/Al, Cr/Al, or W/Al co-doped a-C films by a two-step process composed of melt-quenching from liquid and geometric optimization. The residual stress and bulk modulus were calculated, and the atomic and electronic bond structure was analyzed to clarify the stress reduction mechanism. Compared with pure and mono-doped a-C films, the co-doping of Ti/Al, Cr/Al, or W/Al could reduce the residual stress remarkably without the expense of mechanical properties; as Ti (1.56 at.%)/Al (1.56 at.%), Cr (1.56 at.%)/Al (4.69 at.%), or W (1.56 at.%)/Al (1.56 at.%) were co-doped, the residual compressive stress reduced to 4.6, 5.6, and 2.5 GPa separately from 26.6 GPa of pure case. The structure analysis revealed that although co-doping Ti/Al, Cr/Al, or W/Al into a-C film causes the slight increase of fractions of the distorted bond angles smaller than 109.5°, the fractions of the distorted bond lengths smaller than 1.42 Å drastically declined to 16.2%, 12.4%, and 11.6%, respectively, from 21.7% of pure a-C film. On the other hand, electronic structure calculation indicated that weak covalent interaction was formed between Ti, Cr or W and C atoms, while the ionic interaction was observed for the Al–C bond. Therefore, the co-doping of Ti/Al, Cr/Al, or W/Al could not only provide the key relaxation of distorted C–C bond lengths, but also play a pivotal site to reduce the increase of strain energy change caused by distortion of bond structure due to the formed weak bonding characteristics, which can resulted in the giant residual stress reduction. The current result provides further insight into the structure and stress reduction mechanism for the previous experimental work, but the more important is that it provides a straightforward possibility by using the synergistic benefits from the binary doped metal feature to fabricate the new nano-composite carbon-based films with high performance for the promising wider applications.Ultra-high molecular weight polyethyleneModification of UHMWPE by ion, electron and γ-ray irradiationDue to good wear resistance Ultrahigh Molecular Weight Polyethylene (UHMWPE) is the material of choice for the load bearing surfaces of total joint implants. In order to improve its performance polymer parts are often modified by the use of ionizing radiation. Here we report on the use of electron and ion beams and γ-rays for the purpose. UHMWPE samples were irradiated with 600 keV and 1.5 MeV electron beam with doses ranging from 50 to 500 kGy and bombarded with 1–10 MeV He- and 9 MeV Cl-ions to fluences ranging from 1012 to 5 × 1016 |
ions/cm2. Co-bomb was used for γ-ray irradiation. Polymer radiolysis due to the irradiations was studied by means of nuclear reaction analysis (NRA) using the 1H(15N, αγ)12C reaction. Hydrogen release increases with the applied dose and was correlated to the linear energy transfer (LET). Irradiated polymers oxidize rapidly when exposed to the air. Oxygen uptake profiles were determined using RBS. Correlation between radiolysis and oxidation has been revealed. Enriched in oxygen region extends to the depth at which radiation induced hydrogen release took place. Once started oxidation proceeds until the saturation concentration of about 10 at.% was attained.Ultra-high molecular weight polyethylenePolymers are one of most frequently used engineering materials. However, further expansion of polymer applications is seriously limited by their poor mechanical properties and low abrasion resistance. To solve this problem different, mostly chemical, methods of polymer modifications have been proposed. These treatments usually affect the bulk of materials whereas the key issue in many applications are the surface properties. Since several decades γ-ray irradiation was successfully applied for improvement of mechanical properties of polymers. It produces extended cross-linking leading to the increase of hardness and better abrasion resistance. Unfortunately, irradiated polymers oxidize rapidly when exposed to the air and as a consequence become brittle. Therefore, modified polymers cannot support dynamic loads, which usually produce microcracks leading to enhanced abrasion due to microparticle production upon friction. Recently, the use of multiphase polymer materials combining different bulk and surface properties has been proposed It has been demonstrated in our previous work that light ion bombardment of energies ranging from 60 keV to 300 keV can be successfully applied for the purpose Materials used were 2 mm thick UHMWPE plates as supplied by Goodfellow (UK) of molecular weight Mw |
= 120,000 g/mol, degree of crystallinity Xc |
= 65% and density of 0.95 g/cm3. 1–10 MeV He- and 9 MeV Cl-ion bombardment with the fluence ranging from 1 × 1012–2 × 1016 |
cm−2 was carried out at Forschungszentrum Dresden, Germany. Electron and γ-ray irradiations were performed at the Institute of Nuclear Chemistry and Technology, Warsaw, Poland. UHMWPE samples were irradiated with 600 keV and 1.5 MeV electron beam with doses ranging from 50 to 500 kGy. Conventional Co-radiation source was used for γ-ray irradiation. In order to avoid dose rate effects, which are primarily due to the target heating, the power deposited by bombarding beams was always kept well below 100 mW.Hydrogen profiling was performed at Forschungszentrum Dresden using the 6.385 MeV resonance of the nuclear reaction 1H(15N, αγ)12C Statistical Molecular Recombination Model (MRM) explaining the mechanism of hydrogen release induced by ion irradiation was proposed by Adel et al. shows hydrogen release profiles, i.e. the number of H atoms that were released from the 100 nm depth interval located at the given depth for 9 MeV Cl-ions. It was calculated as a difference in measured hydrogen depth profiles for pristine and bombarded samples. Also shown are the LET and the density of displaced atoms (damage) as calculated using the SRIM code Release of hydrogen under electron beam and γ irradiation of polymers under study is very small: for the highest dose used of 500 kGy released were less than 10% of the initial amount. The reason is the very low LET. So, the probability of creating H2 molecules is very low.In order to compare effects of different types of radiation the ion fluence has to be expressed in Greys (1 Gy = 1 J/g). Comparison of the effectiveness of various energetic ions, electrons and γ-rays is shown in . One notices the same dependence of the hydrogen release on the deposited energy with one exclusion, however, i.e. 9 MeV Cl-ions. Much higher hydrogen release in this case could be attributed to the non-linear processes occurring at high deposited energy density and energetic δ-rays production.Oxygen profiling has been performed by applying typical RBS spectra analysis methods using RUMP Hydrogen release and oxygen uptake as a function of 9 MeV Cl-ions fluence is shown in . It demonstrates the typical correlation of these two effects: even small amount of radicals created by radiation can initiate oxidation; on the other hand the saturation in oxygen can be attained at relatively low fluence of 1 × 1013 |
Cl/cm2. For samples bombarded to low fluences continuous oxygen uptake upon prolonged storage in the air (aging) was observed. This is due to the fact that the number of created free radicals is small and the distance between them is rather large. Very important observation is that in any case the maximum oxygen concentration of 8–10 at.% was not exceeded. For samples bombarded to low fluence of He-ions the initial oxygen concentration is below 1 at.%. After the storage for two years the saturation in oxygen was attained, however, the oxidized layer extends only over the modified depth, which corresponds roughly to the incident ion range. This observation has also important consequences for electron or γ-ray irradiation of polymers. Since the oxidation eventually extends over the whole modified layer in this case layers of several cm thickness become oxidized and the mentioned above beneficial effect of shock absorbing hard surface layer on soft substrate will not appear.Radiolysis and oxidation of UHMWPE due to low energy He and Ar bombardment has been already discussed in detail in our previous publications lists ions and their energies used in this study. With respect to the polymer modification the most important parameters are LET and its relation to the nuclear stopping power Sn. The high LET and low Sn are desirable. Following the data in and keeping in mind that modified layers of several μm thickness are desirable the first choice are high energy, i.e. about 10 MeV, medium mass ions like Cl. As can be seen in high energy Cl-ions provide high LET and acceptable low damage. The second choice are He-ions of MeV energy. Release of hydrogen upon irradiation of polymers is well explained by the Molecular Recombination Model also in the studied ion energy range as well as for electrons and γ-rays. This model assumes that only molecular hydrogen can outdiffuse from the irradiated polymers.Oxidation of polymers takes place once the irradiated sample was exposed to the air. Oxygen diffuses into polymers where it interacts with free radicals produced by the irradiation. Oxidation mechanism is well explained by the Bolland's model Following this argument even low number of radicals in the near surface region can start the oxidation process. Oxidation rate is hence reaction controlled and depends on the initial concentration of radicals. This explains why for polymer samples irradiated with electron beam and γ-rays initial oxidation was very low. Consequently, transformations of the polyethylene microstructure takes place over a period of years. Why this process stops when the local oxygen concentration of 8–10 at.% is attained is not clear. Observed spread of this concentration can be attributed to different crystallinity of studied polymer samples.A novel method for the fabrication of Al-matrix nanocomposites reinforced by mono-dispersed TiAl3 intermetallic via a three-step process of cold-roll bonding, heat-treatment and accumulative roll bondingA novel method to fabricate aluminum metal-matrix composites reinforced by mono-dispersed TiAl3 intermetallic particles, by cold-roll bonding, heat treatment, followed by accumulative roll bonding (ARB), is demonstrated. Roll bonding of 1100-Al sheets inserted with Ti powder was carried out at room temperature with 50% thickness reduction. Complete conversion of the initial Ti particles into TiAl3 intermetallic was achieved by a post-rolling annealing treatment at 590 °C for 2 h, which results in the formation of coarse TiAl3 particles along the interface of the original 1100-Al sheets. Subsequent ARB process was applied to break up and disperse the TiAl3 phase, and after 5 cycles of ARB, an aluminum-matrix composite with mono-dispersed TiAl3 particles of submicron sizes was achieved. The Al matrix also undergoes dynamic recrystallization during the ARB process to result in a fine-grained microstructure (size less than 500 nm). The hardness, tensile strength and elongation of the Al/TiAl3 composite were found to increase with the number of ARB cycles. The tensile strength of the Al/TiAl3 composite after the 5th cycle reaches 400 MPa, which is significantly higher than the 300 MPa of monolithic 1100-Al processed in the same way. The tensile elongation of the Al/TiAl3 composite after 5 cycles of ARB exhibits a good value of ∼8%, with a ductile fracture mode. This is the first successful attempt to achieve Al-matrix nanocomposites reinforced by mono-dispersed TiAl3 intermetallic based on an ARB method.Due to their superior properties including low density, high specific strength, stiffness and creep resistance, aluminum-based metal matrix composites (AMMCs) are attractive structural materials for aerospace and automotive applications. Traditional methods for fabricating AMMCs include powder metallurgy (PM) [] first employed accumulative roll-bonding (ARB) to fabricate AMMCs, and since then, the use of ARB to fabricate AMMCs reinforced by ceramics, metal particles or carbon fibers have been studied []. As the reinforcing phase in AMMCs, intermetallics have several advantages over ceramics, carbon fibers and pure metals, including compatible coefficient of thermal expansion with the Al matrix, low density, and high thermal stability []. Past attempts to fabricate intermetallic-reinforced AMMCs by the ARB method usually involved a post-ARB heat treatment (HT) step to activate the formation of the desired intermetallic compound in the Al matrix. For instance, Al3Mg2-containing AMMCs were fabricated by ARB of Al plates and Mg foils and vacuum annealing, and good distribution of intermetallic particles was achieved in the Al matrix after 6 cycles of ARB []. However, the ARB-HT protocol does not always result in the formation of a monolithic type of intermetallic phase, or a mono-dispersed distribution of the latter in the matrix, which is a requirement for good applicability of the composite. For example, Mozaffari et al. [] have attempted the fabrication of Ni-aluminide-containing AMMCs by ARB of Al/Ni laminates followed by HT, but instead of achieving a unitary Ni-Al intermetallic reinforcing phase with uniform dispersion, different types of Ni-Al intermetallic compounds were obtained in the Al matrix with non-uniform distribution.In this work, we focus on fabricating TiAl3-reinforced AMMCs by the ARB process. TiAl3 is one of the more attractive tri-aluminide intermetallic compounds because of its low density, relatively inexpensive constitutive elements, low synthesis temperature and high strength []. However, the use of bulk TiAl3 in engineering (e.g. aerospace) applications is limited by its poor ductility, especially at ambient temperature when its fracture mode is brittle intergranular or brittle cleavage. However, using TiAl3 in submicron-particle forms as the reinforcing phase in a ductile matrix like Al may result in a composite with high strength and at the same time good ductility [] have successfully fabricated Ti-aluminide-containing Al/Ti laminate composites by using the ARB-HT route as mentioned above, but the Ti aluminides in that case were not uniformly dispersed within the Al metal matrix. In this paper, we show that a novel “CRB-HT-ARB” fabrication route, based on three processing steps of (i) cold-roll bonding (CRB) of Al plates sandwiching Ti particles to achieve bonded Al/Ti sheet, followed by (ii) heat treatment (HT) to convert the Ti addition into TiAl3, and finally (iii) accumulative roll bonding (ARB) to break up the TiAl3 particles within the Al matrix, can achieve AMMCs with very uniform distribution of TiAl3 reinforcing phase. The resultant TiAl3-reinforced AMMCs are also found to exhibit significantly higher strength compared with the starting 1100-Al material, and still with excellent ductility.1100-Al sheets were cut into 100 × 50 × 1 mm3 sections parallel to the original sheet rolling direction and then annealed at 370 °C for 1 h. Pre-rolling annealing treatment reduced strip hardness and, therefore, increased bond toughness and made more bonding possible at lower thickness reductions. The chemical composition and mechanical properties of the as-received and annealed Al sheets are shown in 99.9% pure Ti particles, supplied by Merck ((a and b)), were prepared to apply between two Al strips before the CRB process. To achieve powders with small size and narrow range of size, ball milling was used. Milling was made in a Retsch PM100 planetary ball mill using 5 balls in atmosphere of argon for 7 h. The ball to powder weight ratio and speed of container were 10:1 and 500 rpm, respectively. Morphology of Ti particles, with irregular shape, after milling is shown in (c and d). The particle size distribution of Ti was determined by digital image processing (DIP) technique [). After milling, average size of Ti particles decreases from 45 μm to 0.8 μm.Before the cold rolling process, the surfaces of the aluminum sheets were scratch brushed with a stainless steel brush of 0.25 mm wire diameter, in order to remove surface contamination and to roughen the surface for better roll bonding results. An ethanol-base suspension was used for applying Ti powders with good distribution on Al sheets. After surface brushing, suspension was sprayed on the Al sheet surface. Then, Ti particles deposited and ethanol evaporated in air, so that the Al surface uniformly covered with Ti particles. Then, Al sheets with and without Ti powders were put on each other, stacked, and both ends riveted. The stacked strips buttoned at both end by steel wire and were roll bonded as soon as surface preparation was finished.The subsequent processing steps are shown schematically in 0.5 wt % of Ti powder was sandwiched between Al sheets, and then the Al sheet/Ti powder/Al sheet material was cold rolled by 50% at rolling speed 2 m/min, in a laboratory rolling mill with a roll diameter of 220 mm. The resultant rolled samples at this stage are referred to as CRB. The CRB samples were then heat treated at 580 °C and 590 °C for 2 h, followed by furnace cooling to room temperature. The strips fabricated up to this stage are called CRB-HT hereafter.Each CRB-HT strip was cut into two pieces. After repeating the scratch brushing treatment as described, the two pieces were stacked and then cold rolled again by 50% reduction (Von Mises equivalent strain: |ɛeq| = 0.8 per cycle). The rolling was done at the same rolling speed as in Step 1, at room temperature without adding new reinforcement Ti particles. The cutting, scratch brushing, stacking, and roll-bonding processes were repeated for up to five cycles. The strips fabricated up to this stage are called CRB-HT-ARB hereafter.To form a basis for comparison, the above steps with the same conditions were also applied to monolithic Al without adding any Ti particles. The strips produced from this procedure are called Al-ARB hereafter. The samples for microstructure analysis were cut from the CRB-HT, CRB-HT-ARB and Al-ARB samples. Microstructural characterization was carried out in a Hitachi S-3400 field emission scanning electron microscope (SEM) equipped with an energy dispersive spectrometer (EDS), and a Transmission Electron Microscope (FEI Tecnai G2 20 Scanning TEM). Tensile test samples were machined from the strips, according to the ASTM standard, with the tensile axis along the rolling direction. The gauge width and length of the tensile samples were 6 mm and 25 mm, respectively. Tensile tests were performed at room temperature using a tensile machine (HounsfieldH50ks) at a crosshead speed of 1 mm/min. The total elongation of the specimens was determined as the difference between the gauge lengths before and after testing. Nanoindentation tests were performed using an Agilent G200 Nanoindenter equipped with a Berkovich tip in the load control mode with a maximum load of 10 mN, and hardness was measured using the Oliver–Pharr method []. X-ray diffraction (XRD) analyses were performed in a Philips X'Pert MPD diffractometer with Cu Kα radiation (ƛ = 0.1541 nm) to determine the phases in the roll bonded materials.The objective of annealing the rolled specimens in the CRB-HT process was to convert the Ti addition into TiAl3. Two heat treatment temperatures for 2 h, namely, 580 °C and 590 °C, were attempted, and shows the SEM micrographs and elemental distributions of the resultant microstructures. From the low-magnification micrographs in (a, c), it can be seen that at the CRB-HT condition, the added Ti content remains mostly as particles at the interface of the Al layers. These particles, with the expected high Ti contents as confirmed by EDX elemental distributions shown in (b) shows a typical particle at the CRB-HT-580 °C condition, in which the EDX-measured Al and Ti contents at locations A, B and C are given in . Both the image contrast and the elemental distributions indicate two clear zones of the particle – an inner zone with high level of Ti content with 85Ti-15Al composition, surrounded by a layer with a composition close to Ti-3Al, which corresponds to that of the TiAl3 phase. It is also interesting to see that in (b), while the interface between the inner rich Ti zone and the outer Ti-3Al layer is sharp and dense, that between the Ti-3Al phase and the Al matrix is diffuse and heavily voided. In fact at temperatures less than 660 °C, Al is the only diffusing species []. Hence, large pores form at the prior Al sites. Big voids formed as a result of the coalescence of pores which resulted in the formation of locally isolated diffusion Couples. The voids are likely Kirkendall voids that are formed in the Al/Ti diffusion couple, due to the difference in atomic volumes between Al and the Ti-3Al. In any case, (b) shows that after CRB-HT at 580 °C, although there is evidence for the formation of the TiAl3 phase, the heat treatment temperature of 580 °C for 2 h is not sufficient to turn all Ti into TiAl3. (d) shows a typical particle at the CRB-HT-590 °C condition. After heat treatment at the higher temperature of 590 °C, the particle appears homogeneous and EDX measurements show that the composition inside (point D in ) is Ti-3Al which corresponds to the TiAl3 phase. At the same time, the particle is also decorated by Kirkendall voids along its interface with the Al matrix.The fact that all the added Ti is consumed and TiAl3 indeed forms after the CRB-HT-590 °C condition is proven by XRD as shown in . It can be seen that after the first CRB process, the XRD profile exhibits peaks corresponding to only the Al matrix and the added Ti particles, but after the CRB-HT at 590 °C, almost all Ti is turned into TiAl3 phase. For this reason, the CRB-HT-590 °C condition was used for the subsequent processing. A comparison of the principal Al peaks in the XRD patterns obtained before and after the HT process indicates a shift for the diffraction peaks towards higher angles, which means reduction in the lattice size after the HT process. This is likely a consequence of increase in dislocation density and internal stresses and also inter-diffusion between different atoms accompanying the formation of Al-Ti solid solution. shows the hardness distributions along the thickness of the CRB and CRB-HT-590 °C samples. The average hardness values of Al and Ti in the CRB condition are 0.45 and 2.3 GPa, respectively. The values change significantly after annealing at 590 °C for 2 h, with the hardness of Al dropping to 0.3 GPa, and a high hardness of approximately 6 GPa for the TiAl3 phase formed., the CRB-HT-590 °C condition is sufficient to turn all the added Ti into TiAl3, but from (c), the TiAl3 formed still exist as particles along the interface of the bonded Al strips. The main purpose of the subsequent ARB process was therefore to break up the TiAl3 particles and disperse them uniformly throughout the Al matrix. Also, the continuous plastic deformation in the ARB process should help eliminate the Kirkendall voids which would otherwise be detrimental to the mechanical properties of the resultant AMMCs. (a–e) show SEM micrographs of the AMMCs produced in different cycles of the ARB process. (a) shows that after the first rolling cycle, the original intermetallic particles, which were less than 100 μm in size, began to break up, so that the resultant microstructure consists of both larger deforming particles and smaller fragments of broken up particles, as well as large particle-free zones in the Al matrix. During subsequent rolling cycles, the intermetallic particles were further broken down into smaller ones, and their average size was reduced to less than 10 μm after the 3rd cycle ((e) shows the microstructure after the 5th rolling cycle, at which the particle size became less than 0.5 μm. According to (e), after the 5th rolling cycle, the uniformity of the particle distribution is improved remarkably, without any noticeable particles-free zones in the Al matrix, and also, no more Kerkendall voids can be seen in the microstructure. It can therefore be concluded that the distribution of the reinforcement particles becomes more uniform as the number of rolling cycles increases, and five rolling cycles would be enough to achieve an AMMC microstructure with a well dispersed distribution of the reinforcing intermetallic particles and a void-free matrix. It is also worth noting that the phase constituents of the material are not disrupted by the ARB process. The particle near point E in (e) was scanned by EDX and the result shown in indicates that, compared with point D in the CRB-HT-590 °C condition ((d)), the composition exhibits nearly no change, suggesting that the phase remains to be TiAl3 after the ARB process.TEM microstructures and the corresponding selected area diffraction (SAD) patterns on the rolling plane of the ARB processed Al/TiAl3 composites after the 1st, 3rd and 5th cycle and also Al-ARB after the 5th cycle are shown in (a) shows the microstructure after the 1st cycle of ARB at equivalent strain εeq = 0.8. In this case, the Al grains have large size (∼5 μm), due to the HT process preceding the ARB rolling, and the microstructure is indicative of the severe ARB deformation of the Al matrix from the well-annealed state of the CRB-HT step. Due to the bending of the TEM foil, the bend contours were rather narrow, but the top part of the micrograph was close enough to a Bragg diffraction condition to reveal the dislocations there, which exhibit a small spacing of ∼0.1 μm, or a high density of ∼1014 m−2. For the specimen after the 3rd ARB cycle at εeq = 2.4, (b), interestingly, the dense dislocation structure has subsided drastically, and the microstructure now consisted of equiaxed grains ∼0.8 μm large with low dislocation contents, which are likely the result of dynamic recrystallization accompanying the ARB process. The SAD pattern exhibits dotty diffraction rings of the FCC structure with a lattice constant of ∼4.05 Å, indicative of the fine grained Al matrix, and the uneven intensity of the diffraction rings suggests a strong texture of the fine-grained state. The microstructure also shows a sparse dispersion of submicron-sized TiAl3 particles which would not be discernible in the lower-magnification SEM micrograph in (c). The microstructure after the 5th ARB cycle at εeq = 4 is shown in (c and d). The related SAD pattern (inset in (c)) consists of discrete diffraction spots falling on the Debye–Scherrer circles of the Al structure, indicating the presence of a large number of randomly oriented fine grains in the selected area for the SAD pattern. The TiAl3 phase dispersion is less discernible in the bright-field image in (c), due to the deformed, fine-grained structure in the Al matrix, but in (d) where the foil thickness is smaller, the TiAl3 particles are clearly visible and there is a good distribution of TiAl3 particles was achieved in the Al matrix after 5 cycles of ARB, and the higher-magnification images show that the size of TiAl3 reached to 200 nm; it can therefore be concluded that a nanocomposite of Al/TiAl3 was successfully achieved after five cycles of ARB process. For comparison, the TEM microstructure of monolithic Al that had gone through the same CRB-HT-ARB process but without Ti addition, i.e. the Al-ARB state, is shown in (e). Again, the microstructure after the 5th ARB cycle exhibits fine, dynamically recrystallized grains of generally submicron sizes.The results of grain size calculations from TEM images are shown in . Grain size of Al matrix after CRB-HT step decreases by increasing the number of ARB cycles. Also particles become finer by progressing of ARB. According to (d) the grain size of Al matrix in ARB-processed sample after 5th cycle reach to ∼500 nm while it is ∼700 nm for monolithic Al under same condition. This observation can be related to extra grain refinement at the interface particle/Al matrix by intermetallic particles. As shown in (d), there are fine grains around the intermetallic particle. collectively indicate that, during the ARB cycles subsequent to the well-annealed state immediately after the CRB-HT step, dynamic recrystallization takes place in 1100 Al, resulting in a fine-grained structure after 5 cycles of ARB. Such dynamic recrystallization phenomenon during ARB has in fact been previously reported in Al []; the interest here and in the following, however, is the breaking up of the TiAl3 phase during the ARB process to form a uniform dispersion of reinforcing particles accompanying more grain refinement, and the resultant effect on the mechanical properties of the fine-grained Al.The engineering stress–strain curves of the samples after Steps 1 and 2, and also those of the as-received Al and Al-ARB materials as controls, are shown in (a), the CRB process leads to significant strengthening but much reduced elongation as compared to the initial 1100-Al, which are typical effects of cold working. After the heat treatment at 590 °C, the CRB-HT material exhibits lower strength than the initial (as-received) 1100-Al. It has some of the ductility recovered compared to the CRB cold-worked state, although the elongation is still smaller than the as-received 1100-Al.The engineering stress–strain curves of the ARB-processed samples are presented in (b). After the first cycle of ARB, compared to the CRB-HT state in (a), the elongation is decreased and strength increases remarkably. Interestingly, subsequent ARB cycles lead to gradual improvement of both strength and elongation. (c) summarizes the elongation of the Al/Ti-AMMCs and monolithic Al at different treatment steps studied in this work. The elongation of the composite and monolithic Al after the first ARB cycle declines drastically from the CRB-HT state, but improves gradually by increasing the number of ARB cycles. In particular, the elongation of the TiAl3-AMMC treated after five ARB cycles exhibits a good value of approximately 8%. The biggest advantage of the present TiAl3-AMMCs, however, is its much improved strength by the ARB treatment. It can be seen from (d) that, although the tensile strength of 1100-Al is also improved by the ARB treatment; the strength improvement in the TiAl3-AMMC by the ARB process is much more significant. After the 5th ARB cycle where a homogeneous distribution of fine TiAl3 particles in ultra-fine Al grains is achieved in the microstructure (), the final TiAl3-AMMC has a significantly higher strength than monolithic Al without Ti addition treated with the same ARB procedure (i.e. the Al-ARB material). The final strength of approaching 400 MPa for the present TiAl3-AMMC is indeed a high value among Al based materials.The mild strengthening of the monolithic 1100-Al after high ARB cycles may be attributed to the grain refinement and strain hardening during the ARB process []. However, as stated above, the strength of the TiAl3-AMMC after the 5th ARB cycle is significantly higher than that of monolithic 1100-Al after identical processing. This implies that the submicron-sized TiAl3 particles can serve as highly effective reinforcing phase in AMMCs.(a–c) show the fractographs of the as-received 1100-Al, CRB and CRB-HT samples, respectively. The as-received, monolithic 1100-Al exhibits typical ductile fracture characterized by large and equiaxed dimples, which correspond to the large elongation of the material. In the CRB state, the fractured surface exhibits a mixed mode involving both ductile fracture in the Al matrix and cleavage fracture occurred in the interface of Ti particles and the Al matrix. The much smaller dimples in the Al matrix indicate limited plastic deformation which is evidently a result of the prior cold work, and the small elongation of the sample is likely initiated by cleavage along the Al/Ti interface. In the CRB-HT state, the 2 h heat treatment at 590 °C should lead to a much softer and ductile Al matrix than the as-rolled 1100-Al, while the TiAl3 particles formed are hard as shown in . The large size of the TiAl3 particles would intensify local stress, and the strength of their interfacial region with the Al matrix would be reduced by the dense Kerkendall voids nearby. In the failure morphology near an Al/TiAl3 interface as shown in (c), cleavage of the interface can be seen, and at the same time, a large amount of micro-sized and larger Kerkendall voids up to about ten microns in size are also present in the fractured Al matrix nearby. The growth and quick coalescence of the dense Kerkendall voids in the neighborhood of the Al/TiAl3 interfaces are likely an important factor for the low ductility of the CRB-HT material compared to the monolithic 1100-Al, as seen in The fractography of the TiAl3-AMMC after the 5th ARB cycle is shown in (d). As stated above, after the 5th ARB cycle, fine TiAl3 particles are uniformly distributed in the Al matrix. The fractograph in (d) shows that some micron-sized TiAl3 particles exist in the dimples, indicating a classical particle-induced ductile fracture behavior in which the fracture of the composite is initiated from crack formation at the particle/matrix interfaces []. In general, the large difference in elastic modulus between the reinforcement particles and the metal matrix should cause significant stress localization near the reinforcing particles leading to interfacial cracking. On the contrary, for the monolithic Al treated by the same ARB process ((e)), the fracture mode is shear ductile rupture characterized by large dimples similar to that of the as-received 1100-Al.The obtained results from nanoindentation tests of the Al matrix at different ARB cycles of the present AMMC samples shows a highest value of 1.5 GPa after the 5th ARB cycle. The nanoindentation hardness of the TiAl3 particles (about 6 GPa) remains much higher than that of the Al matrix during the ARB process, and the hardness of the Al matrix increases mildly with the number of ARB cycles. Two key effects of TiAl3 in Al matrix may be expected: (1) the harder TiAl3 phase impedes dislocation motion in the soft Al grains during ARB, resulting in increased dislocation density in the matrix near the matrix–reinforcement interfaces, and (2) during the plastic deformation process, the slip pattern in the regions near the TiAl3 is different from that in the other regions; thereby, geometrically-necessary boundaries (GNBs) are formed ((b)). GNBs with large misorientations can lead to an increase in strength [Al/TiAl3 composites with monodispersed TiAl3 reinforcing particles were fabricated using 1100-Al sheets and Ti powder via a novel procedure of cold rolling, annealing, followed by accumulated roll-bonding process. The phase composition, microstructure, and mechanical properties of the composites were investigated. The conclusions are summarized as follows:Cold-roll-bonding 1100-Al plates sandwiching Ti particles, followed by annealing at 590 °C for 2 h, result in complete conversion of the initial Ti particles into TiAl3, despite the fact that the TiAl3 particles are not homogeneously dispersed in the Al matrix and also there are high amount of Kirkendall voids around these particles.The subsequent accumulative roll-bond process can gradually break up and disperse the TiAl3 particles and also decrease Kirkendall voids. Uniform distribution of TiAl3 particles of submicron sizes can be obtained in the Al matrix after five cycles of the accumulative roll-bond process.The hardness, strength and ductility of the Al/TiAl3 composites increase with the number of accumulative roll-bond cycles. The tensile strength of the Al/TiAl3 composite after the 5th cycle is 400 MPa, which is significantly higher than that of the initial 1100-Al, or monolithic 1100-Al undergoing the same process but without Ti addition. The elongation of the Al/TiAl3 composite after the 5th accumulative roll-bond cycle is ∼8% with a ductile fracture mode.The final grain size of Al matrix after 5 cycle of ARB is ∼500 nm and TiAl3 intermetallic particles with size of 200 nm distribute uniformly in Al matrix. So rolling, annealing, followed by accumulated roll-bonding process is a successful route for fabrication of AMMCs nanocomposite.Numerical and experimental determination of three-dimensional multiple crack growth in fatigueThis work is concerned with the assessment of propagation of multiple fatigue cracks in three-dimensions. Computational modelling of fatigue crack propagation is made together with detection and monitoring of the crack shape development. The boundary element method (BEM) is used for automating the modelling of crack propagation in linear elastic as well as elastic–plastic regimes. Strain at several positions on the specimen surface near the crack mouth is measured to monitor crack initiation, shape development and closure levels. Examples are provided to validate the model by comparing the experimental results with those obtained by numerical predictions.Generally speaking, fatigue cracks will almost always be initiated at the surface, from regions of high-stress concentration due to changes in geometry or geometric discontinuities created during fabrication. In a welded structure, the weld will contain small defects, which could enhance crack growth even from the first few stress cycles. Propagation and coalescence of these initial cracks could lead to the formation of a dominant crack, such that subsequent propagation could result in the failure or instability of the component.It is important to give an accurate estimate of the life expectancy of mechanical and structural components that can be expressed in a number of fatigue cycles. Normally, cracks can be detected by trained technicians. Cracks up to a certain size are accepted and are, in fact, allowed in the initial design of the component by making use of the concept of damage tolerance.Fatigue crack propagation is perhaps the most thoroughly studied area of fracture mechanics. However, the theoretical relations that have been so far developed are in many cases not fully capable of treating the crack growth process that occur in service when the effects of the environment, load frequency and/or crack closure are also considered. The problem can be further complicated by multiple crack growth in three-dimensions.During the last decade, numerical methods have been used widely as a powerful tool to solve problems involving cracks. The finite element and boundary element methods (BEM) are cases in point. Availability of the high-speed digital computers have made it possible to obtain accurate estimates of fatigue for detecting on and monitoring crack shape development.The work to be presented subsequently was developed by researchers from INTEMA (University of Mar del Plata, Argentina) within the framework of the European Community Programme INCO DC 950956 “High Performance Computing Simulation for Structural Integrity Analysis”. Collaborators of the project were those from the Wessex Institute of Technology (UK), the Centre of Supercomputing of Galicia (Spain), the Federal University of Rio de Janeiro (Brazil) and INTEMA (Argentina).The numerical simulation of general mixed-mode crack growth requires the capability of predicting the direction and amount of crack growth as well as the robustness to updating of the numerical model to account for the changing crack geometry. Since the advent of BEM in the late sixties, it has developed into a powerful computational method to solve fracture mechanics problems. In most cases, the BEM formulation does not require integration over the problem domain; hence domain discretization is not necessary Several techniques have been developed for modelling fracture problems using the BEM. Among them is the dual boundary elements method (DBEM) which incorporates two independent boundary integral equations, such that the displacement equation is collocated on one of the crack surfaces and the traction equation on the other. Effectiveness of the method for solving single and multiple three-dimensional elastic crack problems can be found in Linear elastic and elastoplastic boundary element formulations employed in this work are those proposed in Bilinear quadrilateral and triangular elements are used to discretize linear elastic problems. gives the schematic of a crack. A portion of the crack front is shown together with details of the crack extension procedure. The relative displacements of the crack surface are used in the near crack tip displacement field equations to obtain the local mixed-mode stress intensity factors ΔKAmong the criteria for computing the local out-of-plane direction of crack growth, the minimum strain energy criterion is adopted in this work where a11,a12,a22 and a33 are functions of the propagation angle θ, . The derivative of S(θ) with respect to θ can be obtained from , while the stationary value of S(θ) can be calculated by solvingusing the bisection method numerically. Finally, Smin is obtained by comparing the values of S(θ) at stationary points d2S(θ)/dθ2>0. Local magnitude of propagation vectors are computed from stress intensity factor ranges using the two-parameter crack growth relation.Once the position of the new crack front is known, the model geometry is updated for each load step. This is simply done by adding new elements along the old crack fronts, the size and orientation of which are given by the propagation vectors. A localized model remeshing is also done at the zone where cracks intersect free surfaces using triangular elements. This strategy minimizes the extra computation necessary to solve the new configuration and proves to be suitable for the automatic simulation of multiple cracks approaching each other Elastoplastic DBEM models require the discretization of not only the boundary but also of the domain regions. To this end bilinear volume (brick) cells are used. They are placed around the crack fronts as shown in . Note that internal cells consisting of `rings' are placed around the crack front. For the latter, energy domain integral methodology is used. The details can be found in In this work, an attempt will be made to analyze elastoplastic fatigue crack growth by solving successive elastoplastic models without accounting for the previous plastic deformation. This simplification is only partially justified for the examples analyzed. It is based on experimental observation that crack closure levels due to plasticity developing behind the advancing crack front were are found to be negligible for the range of crack depths under consideration.An extensive experimental program for sample weld specimens has been carried out at INTEMA using fracture mechanics models to retrieve fatigue data. Experiments on ferritic and duplex steels were used to examine mechanisms of fatigue initiation, crack growth and coalescence, and to assess the effects of closure for weld toe geometry in addition to study the effect of environment on crack growth rates.Fatigue tests were performed on three-point-bending specimens where the in-depth crack propagation rates remained approximately constant during the whole test. Specimens with single and multiple cracks emanating from natural weld defects were tested. The same is done for artificial notches that were cut using electro-erosion copper tools. Environmental effects were studied by comparing results obtained for specimens tested in air and artificial normalized seawater under controlled electrochemical conditions for load frequencies ranging from 3 to 10 Hz.The main objective of tests for welded crack specimens was to study the effect of the weld toe irregularity as a means of enhancing fatigue resistance Crack initiation and early growth were monitored together with closure levels using local measurements of strain at several positions on the specimen surface near the crack mouth . Variations in elastic deformation field near the crack mouth can then be used to determine initiation, local crack depths and closure level as the test progresses. Refer to the schematics in for the method of solution. For a strain gauge situated very close to the crack plane, crack growths of can be detected accurately. When strain gauges indicated initiation, ink stain and/or beach marking techniques were applied to record the crack size and shape, such that “post-mortem” observation can be made and information related to the evolution of crack growth can be obtained.Crack closure constitutes one of the main extrinsic factors affecting fatigue crack propagation In what follows, results obtained for a series of specimens containing two coplanar semicircular cracks are compared with numerical predictions in order to demonstrate the capabilities of the developed methodology. depicts a typical post-mortem view of a fracture surface of one of the specimens, in which the initial notches, as well as ink marks showing the evolution of the crack shape can be seen. (a) and (b) are top views of the specimen surface after 230 000 and 580 000 cycles, respectively. Obtained variations of the strain–stress curve slopes P/P0 at the position of selected gauges are shown in (a) and (b). An accurate correlation between the change in P/P0 ratio and the position of the outer crack tip can be seen. This is given by the sudden change in the value of P/P0 registered by strain gauge 9 after 580 000 cycles, (a), which matches the position of the crack tip in On the other hand, the strain gauge method was only able to give qualitative information about the coalescence process, as it can be seen in (b). It shows a nearly constant value of P/P0 registered by strain gauge 5. This limitation is attributed to the fact that strain gauge dimensions are of the same order of the distance between the two cracks. Hence the position of individual crack tips cannot be distinguished, , very good agreement was obtained between predicted and actual crack shapes up to relative crack depth values a*/H=1.4, where the method looses sensitivity.Numerical predictions are in good agreement with experimental results. shows the evolution of the crack shape and discretization for a model containing two coplanar semicircular cracks. The geometry and material properties correspond to those used in . They are compared with those from the reference. Very good agreement is found in general between them. They differ only for outer distance for the terminal crack growth.In some of these experiments, deviation of the adjacent tips was observed just before coalescence, where the crack tips may pass each other before coalescence as shown in . This behavior is due to the misalignment of the crack initiation sites from the machined notches. The numerical model also predicts this behavior. shows the evolution of the crack shape for two offset semicircular parallel cracks. Shaded elements on the cracks indicate the original model geometry. Also shown in are the triangular elements introduced on the specimen surface during the rediscretization process after each crack growth increment. The subfigure at the top right-hand side shows crack growth on the free surface.Experimental results obtained for a full penetration welded joint were used for comparison with elastic and elastoplastic numerical predictions. The specimen was welded using an automatic submerged arc welding (SAW) process in a horizontal position. Weld was completed after 16 passes and the specimen was not constrained during the welding process nor stress relieved or pre-heated. An initial notch was cut in the zone of the weld toe, and the weld reinforcement was then machined down in order to avoid the stress concentration effect. The material properties are: Young modulus , Poisson's ratio ν=0.3, yield strength and m=3.2. The specimen was tested in a three-point bending configuration with a nominal stress range at the location of the crack and a load ratio R=0.1. The “map” of the evolution of the fatigue crack is shown in where the dark area corresponds to the initial notch. Closure levels were not considered since they were found to be negligible for the range of cracks depths under consideration.In order to insure the growth of a single crack with a mild front, the initial notch was cut. Although this cut was made using a thin tool, the blunted notch front could not simulate a crack. Taking this into account, the numerical analysis was started from the geometry corresponding to 1275×103 cycles. The resultant discretization of the elastic model is shown for the deformed configuration in (a) where a few elements on the top surface were removed in order to show details of the crack extension process. Also shown are model dimensions and a schematic of the applied load. In order to analyze the example with an acceptable degree of mesh refinement, it was decided to exploit the near symmetry of the problem geometry. Assuming a symmetry plane as shown in (b), only half of the problem was analyzed. Boundary discretization of the crack tip area is shown in detail in the subfigure. Starting from the crack front profile at 1275×103 cycles, three growth increments of and 490×103 cycles were made, for the elastic model, while only the first two were modeled for the elastoplastic case.Predictions for the crack shape using both models are in good agreement with experimental data, . Some deviations are observed only for the last load steps in regions close to the free surface. Many uncertainties involved in the experimental data such as the occurrence of residual stresses or variations of mechanical properties in the zone of the welded joint could account for this deviation. From the view point of the numerical modelling, a significant factor to be considered could be the crack discretization. The present procedure of automatic updating the crack geometry consists of adding new elements along the crack front while keeping the number of elements constant along it. For cracks under consideration, they would grow in such a way that the aspect ratio increases constantly. Elements on the crack front tend to span over larger and larger portions of the crack. The model would loose accuracy as the simulation progresses.Numerical and experimental assessments of multiple fatigue cracks in three-dimensions are made in this work. The BEM is used in conjunction with automatic modelling of crack growth for the linear elastic and elastic–plastic regimes. Measurements of strain at several locations on the specimen surface near the crack mouth are used to monitor crack initiation, shape development and closure levels. The proposed methodology is a powerful tool for estimating the life expectancy of structural components.Further work is needed to define appropriate intrinsic fatigue crack growth models that take into account the elastic–plastic behavior of metals. It is worth noting that the ligament of material between crack fronts as they approach each other have low constraint to plastic deformation while the portion in the interior could be more constrained. This affects not only the growth but also plasticity induced crack closure. These considerations should be kept in mind when selecting coalescence criteria for multiple surface cracks.Crack closure due to plasticity developing behind the advancing crack tip and crack arrest due to compression ahead of the crack tip could affect fatigue growth of short cracks. Physical contact between the crack faces could be possible and added to the formulation.Growth and coalescence of multiple cracks are relevant to fatigue growth. The multiple crack growth prediction method could be applied to study stress corrosion cracking (SCC) where colonies of multiple cracks could occur at the surface of buried pipes Effects of composition and thermal annealing on the mechanical properties of silicon oxycarbide filmsThere is an increasing trend to incorporate silicon carbide (SiC) into silicon oxides to improve the mechanical properties, thermal stability, and chemical resistance. In this work the silicon oxycarbide (SiOC) films were deposited by RF magnetron co-sputtering from silicon dioxide and silicon carbide targets. Subsequently rapid thermal annealing was applied to the as-deposited films to tune the mechanical properties. Energy dispersive spectroscopy, scanning electron microscopy, Fourier transform infrared spectroscopy and ellipsometry were employed to characterize the compositions and microstructure of the films. The residual stress of the films was calculated from the film–substrate curvature measurement using Stoney's equation. The film stress changed from compressive to tensile after annealing, and it generally increased with carbon contents. The Young's modulus and hardness were investigated by the depth-sensing nanoindentation, which were found to increase with the carbon content and annealing temperature. A thorough microstructural analysis was conducted to investigate the effect of carbon content and annealing temperature on the mechanical properties of SiOC films.Silicon-based ceramics (silicon oxides, silicon nitrides, silicon carbides and their combinations) are important structural and electronic materials for various applications in semiconductor and microelectromechanical systems (MEMS) Common fabrication techniques for these ceramics include melting, chemical vapor deposition (CVD), and sol–gel pyrolysis In semiconductor and MEMS applications, mechanical properties such as modulus, hardness and residual stress play key roles to determine the device's performance and structural reliability In this work, we fabricate silicon oxycarbide films, and study the effect of composition on the mechanical properties of the films before and after rapid thermal annealing. The SiOC films with different compositions of oxygen and carbon contents, were deposited by RF magnetron co-sputtering from silicon dioxide and silicon carbide targets. Subsequently RTA was applied to these films in order to alter the mechanical properties and stress states. Energy dispersive spectroscopy (EDS), scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR) and ellipsometry were employed to characterize the compositions and microstructure of the films. The residual stress of the films was calculated from the film–substrate curvature measurement using Stoney's equation, and the Young's modulus and hardness were investigated by the depth-sensing nanoindentation. Moreover, a thorough microstructural study was conducted to investigate the effect of carbon content and annealing temperature on the measured mechanical properties of SiOC films.SiOC films were deposited on n-type (100) silicon wafer substrates at room temperature (23 °C) by a Discovery 18 RF magnetron sputter (Denton Vacuum Inc.). All silicon substrates were pre-cleaned with piranha solution (hydrogen peroxide and sulfuric acid with a volume ratio of 1:3) for 10 min, then rinsed with deionized water and dried with nitrogen. SiOx or SiCy films were directly sputtered from pure (>99.9% purity) silicon dioxide or silicon carbide targets (Kurt J. Lesker Inc.) at a fixed RF power of 300 W, respectively. The deposition rate of SiOx was 12.4 nm/min, and that of SiCy was 4.6 nm/min. The rate of SiOx was about three times of the SiCy. In other word, using a RF power of 100 W on the silicon dioxide target should result in comparable amount of SiOx versus SiCy obtained from 300 W RF power on the silicon carbide target. Subsequently, three SiOC films with different carbon/oxygen ratios were deposited by co-sputtering the SiO2 and SiC targets. The composition variation was achieved by varying the RF power applied to SiO2 target at 50 W, 100 W and 200 W, while maintaining the RF power of SiC target at 300 W (listed in ). The flow rate of argon was 25 sccm (standard cubic centimeters per minute) to maintain a sputtering pressure at 4 mTorr during the deposition. The thickness of each film was controlled in ∼1 μm.After the deposition, rapid thermal annealing was applied to the specimens using a RTP-600S rapid thermal processing system (Modular Process Technology Corp.). Each specimen was subjected to 400 °C, 600 °C and 800 °C annealing for 10 min in a nitrogen ambient environment, respectively.A JSM-6100 scanning electron microscope (JEOL Ltd.) equipped with an energy dispersive spectroscopy (EDS, from Oxford Instruments) was used to quantitatively analyze the composition of the sputtered SiOC films. An accelerating voltage of 5 kV was selected for the electron beam. This was the minimum voltage required to obtain successful element analysis for Si, O and C. In addition, the low voltage ensured the interaction between beam and samples was confined within the 1 μm top layer of the films A SUPRA 55VP scanning electron microscope (SEM, from Carl Zeiss) was employed to obtain high-resolution surface micrographs of the SiOC films. The accelerating voltage was set to 2 kV, the aperture was 30 μm, and the working distance was 4.9 mm. The signals from both the Inlens and Second-electron (SE2) detectors were mixed to obtain optimal image quality.The chemical bonding structures were identified by Fourier transform infrared spectroscopy (FTIR) with an IFS 66 FTIR spectrometer (Bruker Inc.). A MCT-B detector and a K–Br beam splitter were employed in the analysis to obtain the mid-infrared (MIR) absorption spectra (4000–400 cm−1). A background spectrum of bare silicon wafer was first obtained to normalize the spectra of SiOC films, eliminating the contributions from the substrate, instrumentation and atmosphere. A total of 256 scans were performed with a resolution of 4 cm−1 for the background and each SiOC specimen. The obtained spectra were analyzed using the OPUS 5.5 software package (also from Bruker Inc.).The change of thickness before and after the thermal annealing was used to represent the microstructure revolution in the films. The thickness was measured by a VASE ellipsometer (J.A. Woollam Co., Inc.). The ellipsometer featured variable wavelength and angle of incidence allowing flexible measurement capabilities of thickness and optical constants of thin films. The change in polarization as the light reflects or transmits from the material. The polarization is expressed by amplitude ratio and phase difference between the incident and reflective lights. The wavelength used for the SiOC films was in the range of 600–1100 nm, in which the majority interference pattern occurred. The sampling rate was 10 nm/point, and the measurements were conducted in three incident angles, i.e. 65°, 70° and 75°.The model used to fit the experimental data consists of three layers: a Si wafer substrate, a Cauchy layer for the film and a surface roughness layer. The thickness non-uniformity option was applied in the Cauchy layer to take into account the uneven thickness in the sputtered films. Both the thickness and optical constants (refractive index and absorption coefficient) were determined by data regression, in which the object was to find the global minimum of mean square error (MSE).The curvature of the film–substrate system was measured by an Alpha-Step 500 Surface Profiler (KLA Tencor). Subsequently the curvature was used to calculate the residual stress in the film by the Stony's equation where σ is the residual stress, t is the thickness, κ is the curvature after deposition, and κ0 is the curvature of the substrate before deposition. E′ is defined as the biaxial modulus and equals E/(1 − |
ν), where E is Young's modulus and ν is the Poisson's ratio. The subscript s stands for substrate and f for film. Because the thickness ratio to the wafer is only 0.2% in this work, the Stony's equation should be sufficient to calculate the residual stress without causing serious errors , therefore the measured residual stress is independent of mechanical properties of the film.The Young's moduli and hardness of the SiOC films were characterized by a TI 900 Triboindenter (Hysitron Inc.). A standard Berkovich tip (also from Hysitron Inc.) with a tip radius of approximately 150 nm and a half-angle of 65.35° was chosen for the experiments. The tip area function was calibrated with a standard fused silica sample. The tip was installed overnight before the day of testing in order to reach the thermal equilibrium and minimize the drift. Regular constant-rate loading nanoindentation tests (loading/unloading rate: 400 μN/s) were performed on SiOC films without the maximum load holding period. Each sample was indented at 6 different locations and the results were averaged. The Young's modulus was measured by fitting the unloading segment of load–displacement (P–h) curve to an empirical power-law relation (where hc is the contact depth, a and m are fitting constants. Measurement of the elastic modulus follows from its relationship to contact area and the measured unloading stiffness through the relationwhere Er is the reduced modulus, β is the geometric constant for the tip, S |
= |
dP/dh is the experimentally measured stiffness of the upper portion of the unloading data, and A is contact area. For a Berkovich tip, β equals 1.05 Meanwhile, the hardness of the films can be derived from the peak load Pmax divided by the projected contact area at peak load A:The stoichiometric composition of the deposited films was investigated by EDS technique. As the accelerating voltage used in this work 5 kV is different from the default in the quantitative analysis, it is crucial to use the correct accelerating voltage in the spectra condition during analysis. The EDS spectra of all five films are shown in . The elements C, O and Si were easily identified from the absorbance peaks at 0.25 keV, 0.5 keV and 1.7 keV, respectively. The corresponding atomic concentrations of Si, O and C in atomic concentration (at.%) were also summarized in . The Si content is in the range of 24.2–46.41 at.%, which agrees well with the 25–40 at.% reported by Ryan and Pantano The SEM micrographs of the SiOC films were obtained with the magnification of 100k. As shown in , the SiOx and SiCy have distinct surface characteristics. The surface of SiOx consists of relatively large clusters, while SiCy is closely packed with much finer clusters. The three SiOC films show a noticeable transition from silica-like loose structure to silicon carbide-like dense structure. The results agree with the density measurement from Ryan and Pantano Since sputtering is a relatively low temperature process, the deposited films on unheated substrates are generally amorphous presents the FTIR absorption spectra of SiOC films with various carbon contents. The spectra exhibit characteristic peaks centered at 780, 810, and 1060 cm−1, corresponding to Si–C–Si stretching mode The residual stress in the films was calculated from the curvature of the film–substrate system by using the Stoney's equation. Before film deposition, the averaged initial curvature of the silicon wafer substrate was measured from the profiler as −2.05 × 10−2 |
m−1. After deposition, the curvatures of SiOC films subjected to three RTA temperatures (400 °C, 600 °C and 800 °C) were measured. The residual stress was calculated based on the properties of the wafer (E′s |
= 180 GPa The resulting residual stresses for different carbon contents under different annealing temperatures were plotted in . For the as-deposited films, the residual stresses are generally compressive for all films. The development of compressive stress is associated with “atomic shot peening” mechanism For the effect of annealing temperature, all five films experience increases in residual stress from compressive to tensile ((a)). Similar behavior has been reported by Chaker et al. for PECVD SiC films . It implies that the films under different carbon contents all experience the reduction of thickness after the thermal annealing, and the amount of reduction increases with higher annealing temperatures.Moreover, SiCy is more sensitive to the post-deposition thermal treatment. The residual stress changes from compressive (−290.6 MPa) at the as-deposited state to high tensile (770.9 MPa) after the 400 °C RTA treatment. It indicates that using only thermal treatment is not sufficient to control the residual stress of silicon carbide films.For the effect of carbon content, the residual stresses of all RTA treated films show monotonic increases from compressive to tensile with increasing carbon contents ((b)). The thermal annealing consists of both heating and cooling steps, in other words, the net change of temperature is zero for a complete cycle. Therefore the thermal stress is zero for the annealed films, and any change in stress reflects the change in the intrinsic stress. In the RBM model, silicon atoms randomly bond with oxygen and carbon atoms to form a homogeneous O–Si–C network with five different tetrahedral coordinates, in which y |
= 4 − |
x and x may vary from 0 to 4. The O–Si–O covalent bonds inside the Si–O tetrahedral structure have a fixed arrangement. In comparison, the Si–O–Si bridging bonds connecting the tetrahedral units are flexible. Without inducing change in potential energy, the Si–O–Si bond angle (normally about 144°) can be varied in a wide range from 110° to 160°, and the bond can also rotate freely around the Si–O axis It is worth noting that the minimum stresses occurred for the 53.8% carbon content film at the as-deposited state (−36.93 MPa), 31.7% and 41.7% carbon content films after 400 °C RTA treatments (−21.16 MPa and 20.43 MPa, respectively). In other words, we realized a “stress engineering”, through which the stress can be manipulated by controlling compositions and annealing temperatures.Constant-rate of loading nanoindentation tests without the holding period were performed on all SiOC films. The representative load–displacement curves of the nanoindentation on SiOC films are shown in and (b). The maximum indentation depth at the peak load of 2 mN in the SiOC films was less than 130 nm, which counts for approximately 13% of the film thickness (∼1 μm). Therefore, the effect of silicon substrate on the Young's modulus and indentation-hardness could be negligible . The elastic constants of diamond Berkovich tip were Ei |
= 1141 GPa and vi |
= 0.07 The effect of residual stress on the modulus and hardness varies for different types of materials. For high modulus-to-yield strength (E/σy) materials (such as metals and alloys), the residual stress has large effect on the “pile-up” of contact area , the change of contact area will consequently affect the modulus and hardness. However, the “pile-up” phenomenon rarely happens in low E/σy materials (such as glasses and ceramics). Bolshakov and Pharr proposed a convenient measurable parameter to identify the amount of pile-up The calculation results were presented in and (b). Both the Young's modulus and hardness of as-deposited SiOC films show monotonic increases with increasing carbon contents. For instance, the Young's modulus of SiOC films increased from 68.14 GPa to 272.08 GPa, and the hardness increased from 6.89 GPa to 23.37 GPa. The measured Young's modulus of SiOx 68.14 ± 1.79 GPa, is in good agreement with that of silicon dioxide as obtained by the microindentation test (E |
= 67 ± 1.5 GPa) ). However, both the modulus and hardness are lower than those of bulk SiC single crystal. Since the sputtered deposited films are generally amorphous, it is therefore more likely to form numerous point defects. In addition, the reduction of the short-range order and strength of inter-atomic bonding due to the ion bombardment could also contribute to the lower modulus and hardness.For the effect of thermal annealing, both the modulus and hardness generally increase with increasing annealing temperatures. SiCy is more sensitive to annealing than SiOx in both modulus and hardness. For instance, the relative increase of modulus (from the as-deposited state to 800 °C annealing) for SiOx is 4.83%, and that for SiCy is 18.81%; the increase of hardness for SiOx is 13.35%, and that for SiCy is 54.81%. The increase of annealing temperature results in the growth of modulus and hardness could be due to the microstructure evolution. Therefore, FTIR absorption spectra of both the as-deposited and annealed SiOC films were measured and compared. The representative spectra of SiOx and SiCy were plotted in . It clearly shows that the absorption peaks shift to higher wavenumber (blue shift) in both spectra. The peak shifting for all SiOC films are summarized in (c). SiOx shifts the least with a slope of 4.8 × 10−3 |
cm−1/°C, while SiCy has much larger shifting with a slope of 2.41 × 10−2 |
cm−1/°C. Awad et al. has reported a similar behavior for CVD deposited SiC films It is worth noting that the hardness is more sensitive to annealing than the modulus, for both SiOx and SiCy films. Hardness depends not only on the bonding strength between atoms, but also on the microstructure that prevents plastic flow. Due to the much smaller cluster size and more densely packed structure, the strengthening cluster boundaries of SiCy can be responsible for the enhanced hardness. Indeed, we find that the hardness of the SiCy film at 600 °C and 800 °C annealing (34.53 GPa and 36.18 GPa, respectively), are comparable to the bulk SiC single crystal Amorphous SiOC films with varied composition of oxygen and carbon content (ranging from SiOx to SiCy) were deposited by RF magnetron sputtering. The residual stress, Young's modulus and hardness were measured and found to be closely correlated to the film composition and post-thermal annealing temperatures. The change from compressive to tensile stress after thermal annealing was attributed to the structural relaxation. The increasing stress with higher carbon content was due to the bonding configuration of Si–O–Si and Si–C–Si bonds. The modulus and hardness generally increased with higher carbon content and annealing temperatures, which can be related to the bond density change and film densification. This work presents a versatile approach to control the mechanical properties of SiOC films, which will provide more opportunities for SiOC to be integrated into the MEMS field. We believe this microstructure-based theory will not only contribute to a better understanding of thermomechanical issues concerning the sputtered SiOC films, but also provide insights into the analysis of similar responses of other amorphous physical vapor deposited (PVD) or CVD materials.Stability of retained austenite in high carbon steel – Effect of post-tempering heat treatmentThis work represents a fundamental study that investigates the effect of post-tempering heat treatment on hardness and the stability of retained austenite in dual phase high carbon steel. This influence was investigated focusing on micro to nano-scale stability of retained austenite and nanomechanical properties of the individual grains. Depending on heat treatment history of dual-phase high carbon steel, austenite grains will have different mechanical stability. In this study, samples with and without post-tempering heat treatment were produced while keeping other processing condition similar. Microstructural investigations, hardness test, and compression test were carried out on both samples to identify the characterization of different phases. The dislocation density and deformation mechanism of phases was affected by the tempering due to the redistribution of C content within the grains. Tempering facilitated the diffusion of carbon from martensite to retained austenite and the formation of nano carbides in the martensite matrix, therefore, decreased the hardness of martensite. The overall hardness of the material was decreased by ~16%. However, the stability of retained austenite at nano and bulk scale increased significantly as a result of tempering. These results revealed a valuable understanding for designing the low alloyed high carbon steel for industrial application.There is a continuous and significant interest in the development of low cost, low alloyed high carbon steel which has a combination of high hardness, strength, and ductility. This can be achieved through the combination of martensite and a significant amount of retained austenite where the austenite provides the toughness []. To produce good combinations of strength and toughness from the martensitic structure, conventional quenching and tempering heat treatments have long been applied to steels []. A number of studies indicate that tempering along with carbide formation can stabilize the metastable austenite and increase the toughness []. It has been reported that the post-tempering along with the cryogenic treatment on AISI M2, AISI D2, and X105CrCoMo18 steels induced the carbide precipitations homogeneously, reduced the residual stresses in the microstructure without reducing the hardness and Young's modulus which improved the fracture toughness []. Another study indicates that the impact toughness measured at sub-zero Celsius temperatures actually depends on the fraction of austenite []. The metastable retained austenite is considered as a detrimental phase for the low carbon steel []. However, it is an advantageous phase for high carbon steel because of its strain hardening effect []. Over the past few decades, noticeable investigations have been directed toward microstructural development, mechanical properties and work hardening behavior of dual phase steels. Due to desirable wear properties, hardness and low production expenses, high carbon steels are among the most widely used alloys in the industries [The objective of the current investigation is to study the effect of post-tempering heat treatment on the properties of dual-phase high carbon steel. In dual-phase high carbon steel, if the composition and microstructure are the same, the strength and hardness of carbon steel mostly depend on the carbon content []. Martensitic transformations through quenching develop stress within the microstructure. Applying an appropriate tempering process can relieve the stress and hence, reduces the dislocation in the martensitic matrix which reflects in the mechanical response of the high carbon steel. Thus, it is well known that the properties in martensitic steels are strongly influenced by tempering treatment []. In order to be able to design/customize cost-effective high carbon steels for industrial applications, it is crucial to understand the optimum heat treatment schedule and post-tempering condition and their effect on the structure and properties of high carbon steel.This research aims to clarify the effect of low-temperature post-tempering condition by investigating the stability and solid-state transition of retained austenite from macro to nano-scale. It addresses the hardness of each phase and the overall microstructure in high carbon steel with or without post-tempering heat treatment. For this purpose, two high carbon steels with and without post-tempering conditions but similar initial microstructures and compositions were investigated under various compression stresses. By standardized compression tests on the bulk samples, the consequence of pressure on the evolution of retained austenite to HCP (hexagonal close-packed) martensite and BCT (body-centered tetragonal) martensite transformation at the macro-level is investigated. Nano-indentation experiment helps to evaluate this stress-induced phase transition at the nano level. The microstructures and the phase transformations are investigated using electron backscattering microscopy and quantitative X-ray diffraction analysis before and after the compression deformation. The carbon percentage in the microstructure is determined by electron probe micro-analysis to find out the stacking fault energy of the retained austenite which influences the phase transformation behaviour.High carbon steels with the chemical composition (Fe – 1.0%C – 0.2%Si – 1.0%Mn – 0.6%Cr) and with or without post-tempering heat treatment after austenitizing and quenching process were investigated in this study. The compositions of the high‑carbon steel samples were measured by Spark Emission Spectrometry. Sample A was quenched in water from the austenite temperature and air-cooled at room temperature without post-tempering heat treatment. Sample B was quenched into the water from austenite temperature and then air cooled at room temperature and after that tempered at 150 °C for 90 min. Both the samples had a similar structure of Martensite and Retained austenite (RA).For the compression tests, the samples were cut into small sizes (4 mm × 4 mm × 4 mm) using a diamond cutter at a very slow speed (0.01 mm/s) to minimize both the heat effects and shear stress, thereby ensuring that retained austenite was not inadvertently transformed as the sample was prepared. Standard metallographic wet grinding and polishing methods were used to prepare the samples for X-ray analysis. A PANalytical Empyrean XRD instrument was used with unfiltered Co-Kα radiation at 45 kV and 40 mA current for quantitative XRD to measure the volume fraction of phases from a 2θ spectrum. The compression deformation experiment was performed at room temperature with an Instron 8510 instrument operating at 0.10 mm/min cross-head speed over a loading pressure at 500 MPa–3500 MPa. After X-ray diffraction characterization, an orientation microscopy investigation of transformed austenite and martensite was conducted by electron back-scattered diffraction (EBSD) technique, using an Oxford system attached with a Carl Zeiss AURIGA® CrossBeam® field emission gun scanning electron microscopy (FEG SEM) workstation. To determine the steel's quantitative carbon and manganese content in the microstructure, an electron probe micro-analysis (EPMA) was conducted using a Jeol JXA 8500F Hyper probe machine. Nano-indentation tests were carried out to investigate the stability and hardness of the phases in load control mode on a TI 900 Hysitron Tribolab system at loads up to 8000 μN with a Berkovich three-sided pyramidal diamond tip indenter (nominal angle of 142.3° and radius of 100 nm). Micro Vickers hardness tests were also performed to obtain macroscopic hardness at 0.2 HV load for all 4 samples.After indentation, the indented areas were analyzed again by EBSD to determine any changes in their structure. Martensitic transformation within a single grain of RA was studied using TEM. The focused ion beam (FIB, XT Nova Nanolab 200, at 30 kV) technique was performed to mill the cross-sectional TEM thin foils beneath the nano-indentation. A protective layer of platinum was deposited over the surface of the indents with a built-in gas injection source system. In the initial thinning, the Ga + beam was accelerated to 30 kV with a current of 5 nA, which was used to mill a staircase on both sides of the plate area. Then, the plate was further thinned to a foil of less than 100 nm with a lower Ga + current of 0.1 nA. The damaged layers formed during the initial high energy milling were removed by applying smaller beam currents during subsequent cleaning and final thinning processes. Finally, the thin foil was lifted out and transferred onto the Cu grid prepared for TEM investigation.The resulting microstructures after the heat treatment were resolved by electron backscatter diffraction (EBSD). It is clearly seen from the quantitative analysis of the XRD spectrums [] that the applied heat treatment results in martensite/austenite microstructures with an almost similar fraction of phases (). Only 1% retained austenite of sample B was decomposed and might be transformed to martensite or carbides due to the additional post-tempering temperature [The microstructure and dislocation density of martensite in different specimens were evaluated at first before the compression deformation. The EBSD phase mappings and kernel average misorientation (KAM) mappings are shown in . The KAM maps indicate short-range orientation gradients within individual grains. Local variations in the lattice orientation reflect lattice curvature that can be associated with residual strain and geometrically necessary dislocations (GNDs) []. Different levels of KAM were observed within the martensite blocks in all specimens, which is indicative of the heterogeneity of strain developed through the microstructure that varies with the tempering.The misorientation near some of the austenite-martensite grain boundaries displays a shift in the distribution toward higher local misorientations. Sample A is showing more misorientation compared to sample B. Increased misorientation angle is an indication of more dislocation density in the structure. Due to the tempering of martensite, the dislocation density in the microstructure reduces [] in sample B. Dislocation density and carbon content in the microstructure correlates with the hardness of microstructure. Higher dislocation density and high carbon content in the microstructure results in high hardness. To measure the overall hardness of the samples conventional Vicker's hardness test was performed. shows variations in the hardness of the heat-treated samples. Although the samples have very little discrimination in volume percent of RA (), there lie large variations in microhardness because of dislocation density variation and redistribution of carbon content.An additional tempering schedule in the heat treatment changed the dislocation density of the structure in sample B where the dislocation density in the martensite decreases. Higher dislocations are associated with the high hardness. The hardness of the sample after tempering is ~615 HV which is lower than the hardness of the sample without tempering ~750 HV. To understand the discrimination among the overall hardness of the samples it is important to investigate the nano-hardness of each phase.The average nano-hardness of individual austenite and martensite grains in sample A was 8.38 and 9.57 with a standard error of 0.19 and 0.17 respectively. On the other hand, the average hardness of individual RA and martensite grains in sample B was 7.11 GPa and 7.43 GPa with a standard error of 0.11 and 0.010 respectively. The actual hardness of austenite is much less than this values because, during the nanoindentation, the metastable austenite transforms to martensite and shows elevated hardness. In the case of sample A, the stability of RA was less compared to the RA of sample B which might be the reason behind the higher hardness of RA. As the indenter tip gave load on RA grain, the amount of martensite transformed from the metastable RA was more in sample A and because the martensite is harder than RA, the nanoindentation showed higher hardness. On the other hand, the hardness of martensite depends mostly on the carbon content and dislocation density in the microstructure. Higher carbon content and dislocation density in the microstructure is associated with the high hardness which was observed in the case of sample A (The tempering of martensite reduces the carbon content in the microstructure, promotes the formation of the transition carbide and softens the martensite of sample B. During tempering, carbon diffuses from the martensite to the RA matrix due to the carbon redistribution []. Elevated carbon content in the austenite grain should increase the hardness; however, the hardness was significantly less. This is because, the increased carbon content increases the SFE of the austenite grain [] and make the grain stable which needs more energy to transform into martensite, so there was less martensitic transformation compared to sample A. In the case of sample A, the hardness of austenite grains are associated with the martensitic transformation which triggered the higher hardness as the martensite is a harder phase than austenite. This is in line with the previous research where it has been proven that the stable austenite grains attained comparatively less hardness [As mentioned earlier, a factor that influences the RA to martensitic transformation is the stacking fault energy (SFE). The SFE is related to the C and Mn content [] and therefore an elementary analysis in the RA was conducted using EPMA. Both C and Mn elements are the strong austenite stabilizers []. But the Mn content within the austenite grains is similar due to the negligible Mn partitioning between the austenite and surrounding martensite []. According to the EPMA analysis, the Mn content of the austenite grains does not vary significantly, based on the spatial distribution of the martensite phase, and therefore a uniform Mn content was revealed. But there was inhomogeneity in the C content of the samples. The C content in the ten austenite phases for each sample (based on EPMA data) and the calculated SFEs are listed in ; it was found that the SFE varies within around 13–20 mJ m−2 range. The literature shows the formation of martensite occurs below 18 mJ m−2 SFE [The microstructure in sample A obtained after quenching from austenite consists of plates and laths of martensite which is supersaturated with carbon. The carbon percent of this structure is much higher than the martensite of sample B. In high‑carbon steels, the precipitation of excess carbon begins with the formation of transition carbide, such as, ε-carbide which can grow at temperatures as low as 50 °C []. From the EPMA results, it was clearly seen that there is a redistribution of the carbon content as an effect of the tempering. In sample A, martensite has more C in wt% compared to the sample B and the higher dislocation density which might be the reason behind high hardness of sample A (The microstructure attained directly after quenching from austenite consists of plates and laths of martensite which was supersaturated with carbon. After the tempering for sample B, nano scale carbide precipitation formation was predicted within the grains of martensite which were investigated by the TEM dark field and bright field images (&3b). Similar kind of nano scale carbides has been reported by the other researchers in low-temperature tempering of martensite in medium carbon steel []. As mentioned before, transition carbides can form at the temperature as low as 50 °C in case of high carbon steel []. The carbides grow through a displacive mechanism and do not need the redistribution of substitutional atoms, i.e. iron atoms. The partitioning of the carbon occurs naturally. This could be also the reason behind the elevated carbon content in the RA of sample B where after quenching the sample was tempered at 150 °C for 90 min. From the EDS analysis, it was found that the carbides were iron carbides (c). It should be noted that this kind of nano-scale precipitation of carbides in the matrix was not seen in sample A without the tempering treatment, which is in line with the previous research [To depict the phase stability of metastable RA at the nano scale, we performed several indentations on the austenite grains in each sample and analyzed them based on the nano indentation load-displacement curve and microstructural defects.After confirming the effect of heat treatment on the C content, SFE and hardness of RA, nano-scale testing were carried out to determine the phase transformation behaviour and stability of individual RA grains. EBSD images were used to understand the morphology of phases before and after nano-indentation. Sample A and B are presented here which had larger variations in hardness. shows the EBSD micrograph of individual austenite grains of sample A and B before and after nano-indentation. Comparatively larger grains of austenite were selected for nanoindentation. Although the same load of 8000 μN was applied for each round of indentations, the penetration depth of the indenter varied significantly. The indentation depth was larger in the case of sample B compared to sample A (). Due to the reduced stacking fault energy, the RA of sample A is more susceptible to transform to martensite. As the martensitic structure is distorted and shows more microstructural misorientation, the kernel average misorientation (KAM) around the indentation of sample A is slightly more than that of sample B. When the martensitic transformation of RA starts, the hardness also starts to rise due to the strain hardening effect. The measured hardness of RA of sample A was 8.3 GPa which indicates a larger amount of martensite was nucleated because of the less stable austenite grains in sample A compared to sample B. The hardness of RA of sample B was measured 6.7 GPa.By analyzing the loading and unloading curve – and the indentation depth against the indentation force – Young's modulus and hardness values of these microcrystalline structures could be determined []. Understanding the nanomechanical properties of the individual grains is very important given the heterogeneity of the microstructure of the bulk sample. Nano-indentation techniques can also generate valuable information about the phase change phenomena through analysis of the loading and unloading curve; the indicative tool for approximating the force at which austenite transforms to martensite at the nano-level [To illustrate the detailed analysis of the reason causing the large hardness scatter of austenite between the two samples, the nanoindentation load-displacement curves for different grains need to be critically analyzed. Load-displacement (P–h) curves for the austenite phases at both samples are presented in . To develop a comprehensive understanding of RA and its transformation mechanism, it is important to determine the elastic deformation regime in the P– curves. The Hertzian elastic contact solution was calculated and employed for this purpose.It is clearly seen that the actual load-displacement curve deviated from the calculated Hertzian elastic contact (green dashed line in The load at which the first pop-in occurs in the plastic region of the p-h curve is known as the critical load (Pc) for the martensitic transformation, which is an indication of the mechanical stability of individual RA grain []. A higher Pc means increased mechanical stability of RA grain. summarises the critical load and nano-hardness from the nanoindentation load-displacement curve of each sample on several austenite grains. When the martensitic transformation of RA starts the hardness also starts to rise due to the strain hardening effect. Higher dislocation density due to the nanoindentation is also a barrier for the indenter tip to further penetrate which is another reason for higher hardness. As mentioned before, the distorted regions around the indentation in sample A were more compared to the sample B (a&4b), are indicative of the more martensitic transformation and strain hardening effect in sample A which occurred due to compression deformation at the nano-level.To obtain direct evidence of martensitic transformation and dislocation formation as an effect of plastic deformation within the indented RA grain in high carbon steel, TEM investigation was carried out on the cross-sections of indents which demonstrated the martensitic transformation of retained austenite. Here the TEM result of only one indent is presented. For this purpose, indent on sample A (a) was selected which shows clear martensitic transformation by EBSD micrograph. shows the bright-field TEM image of the RA grain after nano-indentation with selected area electron diffraction pattern (SAED) in two selected spots under the indentation. Spot 1, close to the indenter and the SAED pattern of this region, showed a number of discrete and elongated lights indicating dislocation and elongation of the atoms after severe plastic deformation. The SAED pattern of this spot illustrates only the martensite phase. Spot 2, comparatively far away from the indentation shows the coexistence of newly formed martensite and retained austenite where these two phases are showing Kurdjumov–Sachs orientation relationship (K-S OR).In order to better understanding the variations in the hardness of different heat treated steel, a macro-scale study of the mechanical stability of the samples' RA and other phases under compression deformation were carried out using the volume fraction calculating methods from XRD spectrum analyses (ASTM-E975-13) [The XRD patterns of each sample after compression at different loadings are presented in (only the dominating peaks are illustrated here). In the XRD spectra (111)γ peak represents the RA and the decrease in this peak represents a decrease in the RA %. The RA phase showed a greater reduction by falling up to ~9% at 3000 MPa compression for sample A; however, it was stable at further compression (up to 3500 MPa). In contrast, at 3500 MPa compression stress, the RA in sample B had decreased to ~23%. When RA achieves sufficient energy from the induced compression throughout the compression deformation test, HCP martensite is created by the overlapping of the stacking faults and BCT martensite nucleates at the intersection of the shear while the dislocation piles-up on closely placed slip planes. As a consequence of this transformation, the volume of RA declines progressively with the increase in applies stress (). Steels with low stacking fault energy are prone to BCT martensitic transformation []. HCP Martensite is considered as an intermediate phase in case of deformation-induced martensitic transformation []. At the initial stage of deformation, both HCP and BCT transformation takes place, however, at the final stage of deformation BCT martensitic transformation triggers []. So it has been reported that, when the stability of RA increases, it needs more activation energy to reach the final stage of deformation where the BCT martensitic transformation dominates significantly [The evolution of the RA percent with increasing compressive stress was determined by XRD measurements after interrupting compression on the bulk specimen. The quantitative results are shown in . Differences in the austenite mechanical stability are clearly observed in the different conditions. The mechanically more stable austenite is found in sample B, wherein sample A, the harder martensite and mechanically less stable RA was more evident (These results indicate that a more gradual decrease in the austenite volume fraction occurred in response to stress in the case of sample B when compared to sample A. shows that both samples had a comparable RA percentage prior to compression testing. However, sample B had higher barrier energy for transformation so more compression was needed to trigger the RA to martensite phase transformation (~1000 MPa). For sample A the transformation started at ~500 MPa. By increasing the compression, the volume of RA in sample B decreased, but at a slower rate when compared to sample A. shows a sequence of EBSD measured phase maps that are taken from deformed samples after final loading conditions. Overall, the grain size of the retained austenite decreased with the compressive load as the deformation creates new boundaries and thus divides the original grains into smaller sizes.An overall comparison between these maps shows a variation in the area fractions of RA due to the compression deformation which complements with the XRD results. If the grain size of the retained austenite decreases, the stacking fault energy increases. As the SFE increases, it acts as a barrier to the further transformation of RA which makes the finer grain sized RA mechanically more stable []. This was seen in the case of sample B as the compression progresses the transformation occurred up to 3000 MPa compression load, further compression did not have any effect on the finer-grained RA. Also in the previous study, it was found that dislocation content was highest when more stress-induced HCP martensite was created from retained austenite []. To understand this deformation phenomenon, microstructures of sample A and sample B after 1500 MPa compression is presented in The occurrence of phase transformation and grain refinement depends on the relationship between the rate of strain and the mobility of the grain boundaries of metals and alloys. Here the ongoing transformation of high angle boundaries was detected due to the development of geometrically necessary boundaries. Because of the deformation, misorientations within the microstructure increased and transformed into high angle boundaries. It is also evident from the literature that, in the case of two-phase materials, the development of high angle grain boundaries takes place more rapidly compared to single phase materials and leads to the significant refinement of the original microstructure []. The consequence of this phenomenon is the formation of finer grain due to compression deformation (). Here the misorientation angles were mapped considering the misorientation angle less than 5° within a grain. Due to the compression deformation, when the misorientation angle is more than 15°, was considered as a new grain boundary. Therefore refinement of the grain portrayed less misorientation [] which is clearly observed after the final deformation in the case of sample A (b). As the stability of RA in sample B was more, it resists more to transformation, created more HCP martensite and hence developed more dislocation density compared to the sample B which is understandable by the KAM map (This paper studied the effect of the post-tempering heat treatment on the stability of retained austenite in high carbon steel from macro to nanoscale. By utilizing standard compression testing on bulk material and nanoindentation testing on individual austenite grains of high carbon steel before and after tempering, we delivered important insights into the strain induced phase transformation and deformation behavior of metastable RA. The mechanical stability of RA was increased by additional tempering at a very low temperature (150 °C for 90 min) which was due to the carbon enrichment of the austenite matrix. Tempering facilitated the nanoscale carbide precipitation and reduced the carbon content in the martensitic matrix; hence, the hardness of the martensite grains and bulk steel decreases significantly. The mechanical stability of RA under compressive loads increased in the tempered steel, as represented in XRD patterns and EBSD micrographs after applying different compressive loads in bulk samples. In the nanoscale study, induced critical load that corresponded to martensitic transformation was higher in the sample with tempering, which is well aligned with our macro-scale results.Velocity dependence of strength and healing behaviour in simulated phyllosilicate-bearing fault gougeDespite the fact that phyllosilicates are widespread in fault zones, little is known about the strength of phyllosilicate-bearing fault rocks under brittle–ductile transitional conditions. In this study, we explored the steady state strength and healing behaviour of a simulated phyllosilicate-bearing fault rock, i.e. muscovite plus halite and brine, at room temperature, normal stresses of 1–9 MPa, atmospheric fluid pressure and sliding velocities of 0.001–13 μm/s, using a rotary shear apparatus. While 100% halite and 100% muscovite samples exhibit rate-independent frictional/brittle behaviour, the strength of mixtures containing 10–50% muscovite is both normal stress and sliding velocity dependent. At low velocities (< 1 μm/s), strength increases with increasing velocity and normal stress, and a mylonitic foliation develops. This behaviour results from pressure solution in the halite grains, which accommodates frictional sliding on the phyllosilicate foliation. The pervasive muscovite foliation, which coats all halite grains, prevents significant healing. At high velocities (> 1 μm/s), velocity-weakening frictional behaviour occurs, along with the development of a structureless, intermixed, cataclastic microstructure. The steady state porosity of samples deformed in this regime increases with increasing sliding velocity. We propose that this behaviour involves competition between dilatation due to granular flow and compaction due to pressure solution. Towards higher sliding velocities, dilatation increasingly dominates over pressure solution compaction, so that porosity increases and frictional strength decreases. During periods of zero slip, pressure solution compaction occurs, causing a significant strength increase on reshearing. Our results imply that cataclastic overprinting of mylonitic rocks in natural fault zones does not require any changes in temperature or effective pressure conditions, but can simply result from oscillating fault motion rates. Our healing data suggest that foliated, aseismically creeping fault segments will remain weak and aseismic, whereas segments that have slipped seismically will rapidly re-strengthen and remain in the unstable, velocity-weakening regime.In the past few decades considerable experimental effort has been focused on quantifying the frictional behaviour of faults. Results from room temperature and/or dry sliding experiments on bare rock interfaces and simulated gouge-filled faults have typically shown static and dynamic sliding friction at 0.6–0.9 times the applied normal stress (e.g. ). Early experiments on bare rock surfaces by ) have shown an increase in static friction, that is the maximum friction following a “hold” period of zero slip, with increasing hold duration. These experiments also show a decrease in dynamic friction with increasing sliding velocity, a phenomenon known as velocity-weakening. By contrast, simulated fault gouges (e.g. ) in general show a lower rate of increase in static friction with hold duration. Moreover, they show an increase in dynamic friction with increasing sliding velocity for pervasive shear over a wide range of sliding velocities, i.e. a velocity-strengthening effect. With ongoing shear displacement, however, simulated fault gouges exhibit a transition from velocity-strengthening to velocity-weakening behaviour associated with localization of shear.Reduction of dynamic friction through velocity-weakening behaviour is a requirement to produce unstable slip on a fault, i.e. a stick–slip event in the laboratory or an earthquake in nature, and is therefore of major interest in relation to seismogenesis. Increasing static friction during periods of zero slip, otherwise known as strength recovery or fault healing, is also of major interest in relation to understanding the earthquake cycle (e.g. ). A coupled description of static and dynamic friction in relation to fault slip behaviour was first established with the development of the rate- and state-friction (RSF) laws by . These have been successfully applied to quantify the effects seen in numerous rock friction experiments and have shown that static friction and its time dependence represent a special case of velocity-dependent friction.Significantly, most previous studies of friction on bare fault surfaces and simulated gouge-filled faults have focused on room temperature experiments (e.g. ). Such experiments exclude the hydrothermal fluid–rock interactions that are known to be important in the upper to middle crustal depth range corresponding to the seismogenic zone and its base at the brittle–ductile transition (e.g. ). Effects of fluid–rock interaction have been demonstrated in several experimental studies on gouge-filled faults (e.g. ) and have a clear influence on the sliding and healing behaviour. These effects include stabilization of sliding behaviour (i.e. a transition from velocity-weakening to velocity-strengthening) and a stronger healing propensity often attributed to solution transfer effects (e.g. ). However, there is a lack of systematic analysis and quantification of these effects, and the number of studies of the micromechanical processes involved and their relevance to nature is limited. Indeed, most experiments performed on simulated gouge under wet, reactive conditions have focused on pure single phase materials or else are influenced by incomplete mineral reactions. They are also limited in the duration and in the total amount of strain that could be reached, so that the internal microstructural development is highly immature (). By contrast, natural fault rocks often contain a significant proportion of weak phyllosilicates, either inherited from the host rock or formed by mineral reactions, which form an interconnected network or foliation indicative of high shear strain. Such foliations have often been suggested as an explanation for the observed weakness of some faults, such as the San Andreas Fault and others (e.g.), though it remains unclear how these weak faults may be capable of producing large earthquakes.Recent large strain, rotary shear experiments, performed by Bos, Niemeijer and Spiers () on rock analogue materials consisting of halite plus phyllosilicate mixtures have shown large effects of phyllosilicate content and foliation development. These experiments were done under simulated brittle–ductile transitional conditions where cataclasis and solution transfer operate in the halite, without the operation of plastic processes such as dislocation creep. At low sliding velocities, combined slip on the developing phyllosilicate foliation and solution-transfer of intervening halite clasts yield velocity-strengthening behaviour plus slow healing characteristics. A microphysical model for the inferred deformation process predicts low steady state fault strength and aseismic slip in mature phyllosilicate-bearing faults at mid-crustal depths ( on wet halite/muscovite mixtures, but at higher sliding velocities, have recently revealed dramatic velocity-weakening behaviour, not seen in the two end-member compositions. Such behaviour may also be important in natural fault rocks containing phyllosilicates. If so, it could play a significant role in controlling seismogenesis and the entire the seismic cycle on faults under the reactive hydrothermal conditions of the brittle–ductile transition. However, the microphysical mechanisms underlying the observed velocity-weakening behaviour are not yet understood. Moreover, the healing behaviour in the velocity-weakening regime is unknown and the relevance to nature is unverified.In this study, we have investigated the large strain sliding and the healing behaviour of simulated faults containing halite–muscovite gouges at velocities covering both the velocity-strengthening and velocity-weakening regimes. Under the chosen conditions, pressure solution, cataclasis and phyllosilicate foliation development and destruction are active, as anticipated for nature under brittle–ductile transitional conditions (e.g. ). Our aim is to determine the healing behaviour of the mixtures as a function of sliding velocity and to explain the microphysical mechanisms responsible for the observed velocity-weakening and healing effects. Finally, we speculate on the possible implications of our results for natural faults, assuming that the processes observed in our experiments also occur in natural fault zones.The experiments were performed at room temperature on simulated, muscovite-halite fault gouges, using a rotary shear apparatus located in an Instron 1362 loading frame to apply normal load to the simulated fault. Tests were done both dry and in the presence of brine. The apparatus has been described in detail elsewhere (). In brief, the sample assembly consists of a pair of toothed stainless steel rings (the wall rock rings of , teeth height = ∼ 0.1 mm) sandwiching a layer of halite–muscovite gouge. The assembly is sealed, using O-rings, between an inner steel confining ring and an outer steel confining ring, which houses a pore fluid inlet and outlet. Within the rotary-shear machine, the sample assembly is rigidly gripped by a stationary upper forcing block and a lower forcing block linked to a servo-controlled drive system. The servo-controlled drive is used to apply rotational sliding velocities of 0.001–10 μm/s to the gouge with a resolution of 0.0003 μm/s. Shear displacement is measured using a potentiometer with a resolution of 0.001 mm, geared to the lower (rotating) forcing block. Shear stress on the gouge is measured using a torque gauge couple, with a resolution of 0.01 MPa, mounted on the upper forcing block. Normal stress is applied using the Instron loading ram and can be held constant to within ∼ 0.02 MPa. Most of the present experiments were conducted under a normal stress of 5 MPa. Displacement occurring normal to the fault zone is measured using a Linear Variable Differential Transformer or LVDT (1 mm full scale, 0.01% resolution) located in the centre of the sample assembly.Sample material consisted of mixtures of granular halite with a median grain size of 100 μm (determined using a Malvern particle sizer), plus 10–80 wt.% muscovite with a median equivalent spherical diameter of 13 μm (as stated by the supplier, Internatio B.V., Zutphen, the Netherlands). Pure halite and pure muscovite samples were used as control experiments. In setting up each run, about 8 g of material were loaded into the sample assembly, yielding an initial gouge thickness of ∼ 2 mm. All samples were then subjected to dry compaction, under a normal load of 1 MPa for ∼ 15 min. Except where otherwise specified (), samples were subsequently dry-sheared to a displacement around ∼ 50 mm at a velocity of 1 μm/s and 5 MPa normal stress. This was done to produce a reproducible microstructure. In most experiments, the pore fluid system was then connected to the sample assembly, which was in turn evacuated and flooded with saturated brine (i.e. saturated with respect to the NaCl in the gouge). The pore fluid was subsequently kept at atmospheric pressure by means of evaporation-proof draining to air.Two broad categories of experiments were performed to investigate the effects of sliding velocity, composition and normal stress.Continuous sliding experiments carried out in velocity stepping mode, normal stress stepping mode, or at constant velocity and constant normal stress.Slide–hold–slide experiments, performed using different sliding velocities and constant normal stress.The continuous sliding experiments consisted of 24 separate experiments. These included a series of 11 velocity-stepping experiments performed on brine-flooded samples of different composition (0, 10, 20, 50, 80 and 100 wt.% muscovite). The tests were carried out by shearing at a constant sliding velocity of 1 μm/s until a steady state shear stress level was attained, usually after a displacement of ∼ 3 mm. The velocity was then stepped up or down and the new sliding velocity held constant until a new steady state shear stress level was reached. The aim of this series of experiments was to determine the rate dependence of steady state shear strength for a range of gouge compositions. Most of these tests were carried out at a constant normal stress of 5 MPa, though the normal stress was also stepped in a few cases to determine its effect on gouge shear strengths. In addition, four stress-stepping experiments were performed at constant sliding velocity on wet samples with 20 wt.% muscovite using the same experimental procedure, but without the dry run-in phase. A further series of 5 large displacement experiments was carried out on wet samples with 20 wt.% muscovite at a constant sliding velocity of 0.03, 0.1, 1, 5 and 13 μm/s and at a constant stress of 5 MPa (including a dry run-in phase). These were done to investigate the high strain microstructure (shear strain of 30). The remaining continuous sliding tests consisted of 4 control experiments, performed dry and using silicone oil instead of brine. For more details, we refer to our previous paper dealing with velocity-stepping experiments on the same material (The slide–hold–slide (SHS) experiments () were carried out with the aim of investigating the transient and healing behaviour of mixtures containing 80 wt.% halite and 20 wt.% muscovite plus brine at different sliding velocities. This series of 5 tests involved the same initial dry compaction and shearing procedure described above, followed by a wet “run-in” sliding stage at 1 μm/s, until a steady state shear stress level was reached. The sliding velocity was then stepped to a chosen SHS reference sliding velocity until a new steady state shear stress was reached. The rotary drive was then halted and the sample allowed to “stress relax” for a chosen hold time. We measure no displacement or back lash when the motor was halted. After the desired hold, sliding was restarted at the same reference velocity, by switching on the motor, and continued until steady state was re-attained. This slide–hold–slide procedure was repeated 2 or 3 times for reference SHS sliding velocities of 0.01, 0.03, 0.1, 1, 2, 3, 5 and 10 μm/s, using hold periods of 60 s, 600 s, 1200 s and 6000 s. We employed slide–hold–slide cycles at different reference velocities within individual tests in order to avoid any effects of sample variability and to investigate the influence of increasing displacement (shear strain). An exception to the above SHS procedure is test shs3, which was slid directly after the dry run-in stage at the desired reference sliding velocity of 10 μm/s. The shear stiffness of the machine was measured using a dummy sample of steel. It was found that the stiffness varied from 0.02–0.08 MPa/μm and stress relaxation curves were accordingly corrected.At the end of all experiments, sliding was halted and the normal load was removed. Residual brine was flushed rapidly from the sample assembly with hexane and the entire assembly was removed from the testing machine and dried at 50 °C for ∼ 2 h. Finally, the sample was extracted and impregnated with blue-stained epoxy resin. Standard thin sections were cut parallel to the sliding direction and normal to the shear plane.The final porosities of the gouge samples studied in all constant velocity tests (Mus5, Mus6, Mus7, Mus8, Mus23) and all slide–hold–slide tests were determined by image analysis of thin sections and Thermo Gravimetric Analysis of propylene carbonate-saturated samples. Porosity determination using image analysis was done by defining a pixel threshold for detecting pores filled with blue-stained resin in 10 microstructural images at the same magnification. The images were converted to a black-and-white image using the UTHSCA ImageTool and a manual grey scale threshold. The porosity was obtained from the relative proportion of black pixels, yielding an area-based porosity. Porosity determinations using TGA were conducted by evacuating of about 0.1 g of sample material and subsequently impregnating this with propylene carbonate. Propylene carbonate is a liquid with a high boiling point (240 °C) which does not dissolve halite in significant amounts. The sample was then placed in a DuPont Instruments 1090 Thermal Gravimetric Analyzer and heated at a rate of 10 °C/min up to a temperature of 130 °C at which point significant evaporation starts. It was then kept at this temperature for 40 min, while the weight loss was continuously measured. The porosity was determined by assuming a constant surface evaporation rate at 130 °C, so that deviations from a linear weight loss must be due to evaporation from the pores. The weight loss due to evaporation from the pores was then used to determine the porosity of the sample. Measurements for each sample were repeated three times. The absolute standard error in our TGA porosity determination is about 1.5%. Values obtained from TGA agree well with those available from image analysis. lists the 24 continuous sliding experiments, along with corresponding data on dry run-in displacement, normal stress, sliding velocity, total wet displacement and final gouge thickness (cf. ). A similar list of the 5 slide–hold–slide experiments and supporting data is given in The final porosities of the samples obtained from our constant velocity tests (Mus5, Mus6, Mus7, Mus8 and Mus23) and slide–hold–slide tests, as measured using image analysis and TGA, are listed in . The final porosity of the gouges was also calculated from our mechanical compaction data, obtained using the LVDT, and using the gouge density and the measured initial thickness of the sample assembly. However, in numerous cases we found negative values for the final porosity calculated in this way, probably due to minor material loss from the edges of the samples during the experiments. We accordingly corrected our mechanical compaction data for material loss, using a linear fit of compaction strain versus displacement obtained from experiment Mus12 in which silicone oil was used as the pore fluid. Pressure solution compaction does not occur under these conditions, because halite is not soluble in silicone oil. The porosity (Porosity–Exp) values listed in are the values obtained from the thus corrected compaction data. They agree well with the porosities determined using both image analysis and TGA. Note that the final porosity of the gouges increases systematically with increasing sliding velocity (We present data from a typical velocity-stepping experiment (Mus2) in . In all such experiments, upon a change in sliding velocity, an instantaneous effect on the measured shear stress (strength) was observed. This was followed by a gradual approach to a new steady state strength as seen in conventional rate- and state-dependent friction experiments (). Sample compaction rate was observed to increase sharply upon a step down in velocity and to decrease and even become negative upon a step up in velocity.Representative results from the complete set of velocity-stepping tests, showing the dependence of steady state shear strength of our gouge samples on sliding velocity, are presented in b. Reproducibility between experiments performed at the same conditions was good, showing differences in shear strength up to ∼ 10%. The pure muscovite sample (Mus1) showed no measurable velocity-dependence of steady state shear strength (∼ 1.8 MPa) over the entire velocity range (0.03–10 μm/s) investigated. The pure halite sample showed a very slight velocity dependence, with the steady state shear strength increasing from a value of ∼ 4.3 MPa at a velocity of 0.003 μm/s to a maximum of ∼ 5.2 MPa at 3 μm/s. At higher velocities, the steady state strength decreased slightly, falling to around 4.6 MPa at the highest velocity (13 μm/s).In contrast to the pure end-members, all mixed muscovite–halite samples show a pronounced dependence of steady state shear strength on sliding velocity, reaching a maximum strength at ∼ 1 μm/s (b). In addition, strength clearly decreases with increasing muscovite-content. All halite–muscovite mixtures are weaker than the pure halite sample over the entire velocity range investigated, while at the lowest sliding velocities investigated, samples with 20–50 wt.% muscovite are even weaker than the pure muscovite sample. The velocity dependence of shear strength is most pronounced in mixtures with low to intermediate muscovite content (i.e. 10 wt.% to 50 wt.%). The samples with 20 wt.% muscovite increased over 250% in strength, from a minimum value of ∼ 1.4 MPa at 0.001 μm/s to a maximum of ∼ 3.7 MPa at 1 μm/s. At higher sliding velocities, the steady state strength decreased again, reaching a value of ∼ 2.2 MPa at 13 μm/s. Two regimes of behaviour could thus be distinguished for the halite–muscovite samples, namely a velocity-strengthening regime at low sliding velocities (< 1 μm/s) and a velocity-weakening regime at high sliding velocities (≥ 1 μm/s)., we present typical shear stress and normal displacement versus time data sets extracted from the complete sequence of SHS cycles performed within experiments shs2 and shs5 (see ). Note that the experimental data shown are for displacements beyond both the dry and wet run-in stages. The steady state sliding behaviour obtained prior to and between hold periods was generally similar to that observed in the velocity-stepping experiments, both in terms of steady state shear stress levels and in terms of strain weakening and transient response to velocity-steps. An exception was sample shs3 (wet run-in at 10 μm/s), which showed significantly lower steady state shear stress values (∼ 30%) than those determined in the velocity-stepping series, as well as regular stick–slip cycles during sliding at 10 μm/s.All SHS cycles showed rapid shear stress relaxation from the instant that the drive motor was halted (see ). In addition, significant compaction and shear displacement were observed during the hold periods. At low SHS reference velocities (< 1 μm/s), the shear stress drops at a low rate, and only small amounts of horizontal and vertical displacement are accumulated. With increasing SHS reference velocity, the shear stress relaxation rate during individual hold periods increases, with a maximum observed at 1 μm/s (though the lowest shear stress level was observed in the sample deformed at 10 μm/s). Both horizontal (shear) and vertical (compaction) displacement accumulated during hold periods increase with increasing SHS reference velocity. Shear displacement, for example, is approximately half an order of magnitude larger at a SHS reference velocity of 10 μm/s than at 0.1 μm/s, while compaction is even one order of magnitude larger.Upon re-shear, distinctly different behaviour was observed for SHS cycles performed in the velocity-strengthening regime (sliding velocity < 1 μm/s) than for SHS cycles in the velocity-weakening regime (sliding velocity ≥ 1 μm/s). When sliding was re-started in the low velocity regime, a more or less gradual increase in shear stress occurred until a steady state shear stress was achieved at a similar level to the shear stress prior to the hold period (see a and b). Dilatation, recovering about 80% of the compaction that occurred during the hold, was observed upon re-shear. In the high velocity regime, on the other hand, a sharp peak in shear stress was observed upon re-shear, accompanied by significant dilatation usually recovering all of the compaction that occurred during the hold (c and d). Also, the absolute amount of compaction and dilatation was much larger in the high velocity regime. After the peak, the shear stress rapidly decreased to a steady state level similar to that prior to the hold period.The starting microstructure of the samples prior to brine addition was investigated using a sample extracted from an experiment that was terminated directly after the dry run-in stage, i.e. after a dry shear strain of ∼ 40 (sample Mus24, ). In this sample, halite clasts with a size close to the starting grain size fraction (60–110 μm) are obvious and represent ∼ 30 vol.% of the gouge. These appear to be little affected by deformation, since they are mostly equiaxed. However, the matrix of the sample consists of a fine-grained mixture of halite and muscovite. Some regions of the gouge (∼ 20 vol.%, especially near the edges of the gouge) are relatively enriched in muscovite and contain fewer halite clasts than other regions. Such regions sometimes form narrow poorly defined zones lying in the Riedel shear orientation, i.e. inclined at 20–30° to the shear direction. Locally, the matrix also shows a weak foliation orientated at 30° to the fault zone boundary (a and b). It was inferred in an earlier paper (see ) that this shear band was probably produced during the last part of the dry run-in, since at this time stick–slip cycles occurred which are well-known to be associated with shear localization (a). The overall grain size of the halite is significantly reduced in comparison with the starting material, although numerous larger clasts are still present. These larger clasts consist of elongated grains often with long tails that sometimes show trails of fluid inclusion (Samples Mus7 and Mus8, deformed wet at higher sliding velocities (5 and 13 μm/s) are relatively structureless on the microscopic scale and show a large variation in halite grain size (b–c). The larger clasts in these samples are blocky and irregular compared to the clasts in the low velocity sample. The matrix muscovite grains do not define a clear foliation. They usually coat the smaller halite grain boundaries but not the entire surface of larger clasts. In contrast to the low velocity samples, considerable porosity is developed, especially at the highest velocity (Mus8, see ). The porosity is both distributed over the sample as well as locally clustered to form zones of higher porosity. Besides the difference in porosity, there is little further difference in the microstructures of sample Mus7 (5 μm/s, show the microstructure of sample shs4 which was deformed to a shear strain of ∼ 85 in both velocity regimes. The appearance of this gouge is very heterogeneous. The overall halite grain size is significantly reduced in comparison to sample shs2. However, there are still a number of larger, sigmoidally shaped or tailed halite clasts present. Some of these clasts show intragranular fractures (b). The matrix consists of regions of very fine-grained mixtures of halite and muscovite and regions with less muscovite and more porosity. Some of the more porous zones appear aligned in a poorly defined Riedel shear orientation.The aim of the present work is to investigate the large strain slip and healing behaviour of halite–muscovite fault gouges in both the velocity-strengthening and in the velocity-weakening regimes, to explain any differences in behaviour in terms of the microphysical mechanisms involved, and to speculate on the possible implications of our results for natural fault zones. In order to set about interpreting our results, we begin by considering a number of important theoretical concepts relating to the strength and healing of gouge-filled faults. We then proceed to consider the microphysical mechanism that might be responsible for the observed velocity-weakening under steady state conditions. We go on to compare and mechanistically analyse the strength recovery behaviour seen in slide–hold–slide experiments performed in both the velocity-strengthening and the velocity-weakening regimes. Finally, we will discuss some of the implications that our work may have for deformation of natural phyllosilicate-bearing fault zones under hydrothermal conditions., and taking into account possible changes in grain boundary and pore wall surface areas, the combined energy and entropy balance for a representative volume of fault rock during deformation can be written as:assuming a closed system with respect to solid mass. In this relation, τ is the shear stress acting on the fault rock, γ̇ is the shear strain rate, σn is the effective normal stress on the fault (compressive positive), ε̇ is the normal strain rate (compaction positive), ḟ is the rate of change of Helmholtz free energy of the solid phase per unit volume, Δ̇ denotes the volume specific energy dissipation rate by all irreversible processes, Ȧsub gb is the rate of change in grain boundary surface area per unit volume, γgb is the grain boundary surface energy, Ȧsub gb is the rate of change of solid–liquid interfacial area per unit volume and γsl is the solid–liquid interfacial energy. For clarity, note that the left-hand side of Eq. represents the rate at which work is done on unit volume of fault rock by the externally applied stresses. The right-hand side represents the sum of the energy dissipation rates of all microscale processes operating per unit volume (Δ), plus changes in the Helmholtz free energy stored in the solid part of the system, plus changes in surface energy caused by changes in grain boundary and pore wall area. Dividing now by γ̇ (), the measured shear stress or shear strength can be written:where ⅆεⅆγ represents an instantaneous dilatation angle tanΨ=ⅆεⅆγ analogous to that familiar in soil mechanics (e.g. The quantity τx can be interpreted as representing the contribution to measured shear stress of all energy dissipation and storage processes operating in the gouge. Ignoring minor changes in Helmholtz free energy, it is evident from (5.2) and (5.3) that strengthening of a homogeneously deforming granular fault gouge may occur for three basic reasons. First, gouge compaction may increase the packing density so that upon reshearing the gouge needs to dilate, requiring work against the normal stress (ⅆεⅆγσn). Second, the gouge may strengthen through an increase in contact bonding between particles in the gouge. The increased bonding may increase the grain boundary friction coefficient and/or the grain boundary cohesion. This then increases the average contact sliding strength in the gouge and thereby the total frictional dissipation (ⅆΔⅆγ) due to intergranular slip on re-shearing. Third, the gouge may strengthen by an increase in grain contact area (relative to pore wall area) which may be disrupted on re-shear. This increases strength only when the sliding contact has a cohesive strength. In general, fault gouge healing will be a combination of the three.Our results from the velocity-stepping experiments have shown two clear regimes of steady state behaviour for the halite–muscovite mixtures: velocity-strengthening at velocities below 1 μm/s and velocity-weakening at velocities above 1 μm/s. We have shown here and in our previous work () that the velocity-strengthening regime is associated with intense phyllosilicate foliation development. In our previous paper, we presented strong evidence that this regime is characterized by a steady state flow mechanism involving frictional sliding on the foliation accommodated by pressure solution of the intervening halite grains. A microphysical model was presented that is capable of predicting the observed velocity-strengthening behaviour. The model is based on a steady state microstructure (), where the phyllosilicate foliation wraps around elongate halite grains. The shear stress supported by the gouge at a particular sliding velocity is then the sum of the shear stress for sliding on the foliation plus the shear stress taken up by driving pressure solution. The strengthening with increasing velocity is caused by an increasing influence of pressure solution on the total shear stress, i.e. increasing dissipation by pressure solution.We argue here that the switch to velocity-weakening behaviour occurs when the rate of pressure solution is too slow to accommodate the imposed shear displacement and the gouge has to dilate to accommodate slip, causing the onset of cataclasis. This argument is based on the observation that the velocity-weakening regime is associated with a chaotic cataclastic microstructure (see ). However, purely cataclastic deformation is not expected to show a strong rate-dependence, whereas we have found a marked, inverse dependence of steady state shear strength on velocity (b). This velocity weakening effect could potentially be explained by severe grain size reduction in the halite with increasing velocity, thus enhancing pressure solution rates in the halite and reducing the stress required for pressure solution to accommodate slip on phyllosilicates. However, since the velocity weakening behaviour that we observe is reversible with velocity-stepping direction (see a), we believe that an effect of grain size reduction thereby enhancing pressure solution rates, can be ruled out. Another possibility is that the proportion of healed, cohesive contacts decreases with increasing sliding velocity, due to a shorter average contact lifetime (cf. Dieterich-type healing). However, if this is the explanation of the velocity-weakening, the same would occur in the pure halite sample, but we did not observe a strong velocity-weakening in this sample. Moreover, the lack of healing observed in halite–kaolinite samples () and in our low velocity samples, implies that phyllosilicate–halite contacts do not heal readily. Therefore, we believe that a Dieterich-type healing mechanism cannot explain the observed strong velocity-weakening.On the basis of the chaotic, intermixed, cataclastic microstructures, we propose instead the hypothesis that the velocity-weakening regime is due to competition between a) shear-induced dilatation caused by granular flow of the gouge and b) compaction of the gouge through pressure solution of the halite. Such a mechanism should lead to an increase in porosity with increasing shear rate, at steady state, as granular dilatation becomes more effective compared to compaction by pressure solution. This will produce a decrease in mean grain contact area and intergranular slip-surface inclination/amplitude (dilatancy angle for granular flow). A decrease of the average inclination of actively sliding grain contacts (i.e. the dilatancy angle for granular flow) will lower the normal force on the contacts, thereby reducing the friction on the contacts. Focusing first on the steady state behaviour, the proposed mechanism should thus lead to:Increasing steady state porosity with increasing steady state velocityZero compaction rate at mechanical steady stateA decrease in granular dilatancy angle with increasing steady state sliding velocity.The first of these is confirmed by the porosity measurements made on samples deformed at constant sliding velocity, i.e. at 0.03, 0.1, 1, 5 and 13 μm/s and 5 MPa normal stress (see ). The final porosity of these samples increases from near-zero at the lowest sliding velocity to ∼ 13% at the maximum sliding velocity. Zero compaction rate was almost never measured, however. This could be due to the fact that we did not achieve true steady state in our experiments, or more likely because of minor but ongoing material loss from the simulated fault zone. Direct determination of the granular dilatancy angle from our compaction data is not possible because our volumetric data are a combined signal of compaction by pressure solution and dilatation by granular flow. We therefore evaluate our hypothesis further by qualitatively testing its implications versus our observations in slide–hold–slide tests.Our SHS results for the velocity-strengthening regime (< 1 μm/s), characterized by foliation development, show an increase in compaction rate and gradual shear stress relaxation during the hold periods plus a gradual increase in shear strength upon re-shear accompanied by significant dilatation (). The re-shearing behaviour has been analysed by calculating the dilatation rate ⅆεⅆγ and τx for an SHS reference velocity of 0.1 μm/s and a hold period of 6000 s (). This shows that there is hardly any peak discernible for the shear stress (τ) or for τx, whereas the dilatation rate ⅆεⅆγ shows a broad maximum. This implies that most of the strength recovery was due to dilatational work done against the normal stress. This behaviour resembles that for foliated clay-bearing synthetic fault gouges reported earlier by . These authors explained the observed compaction and stress relaxation as caused by the operation of pressure solution. The absence of a peak strength upon re-shear was explained by a low proportion of healing-prone halite–halite grain contacts due to the presence of a pervasive phyllosilicate foliation. The absence or low amount of healing of these gouges was thus attributed to the absence of contact strengthening and/or increase during the hold periods. Since the behaviour seen in our SHS tests in the velocity-strengthening regime is identical, the same explanation would seem to apply.Our SHS results for the velocity-weakening regime (≥ 1 μm/s, samples shs1, shs4 and shs5) show increasing syn-hold compaction with increasing SHS reference velocity (c), as well as rapid shear stress relaxation during hold periods (a) and a strong increase in shear strength on re-shearing (b–d). This results in a peak strength which gradually decays to a steady state value, the peak being accompanied by only minor dilatation. If we assume that the steady state velocity-weakening behaviour is indeed due to the mechanism of compaction versus dilatation inferred in , then in the SHS experiments, the faster syn-hold compaction observed for higher SHS reference velocities (c) can be explained by a higher porosity being maintained during faster steady state sliding. This would result in a higher pressure solution compaction rate than at low sliding velocity, due to the smaller grain contact area and the higher grain contact stress (e.g. Support for our hypothesis that gouge behaviour is controlled by competition between pressure solution compaction and dilatation due to granular flow can be obtained by a comparison of pre-hold and syn-hold compaction behaviour. Our qualitative model implies that 1) the compaction rate at the start of and during individual hold periods should increase systematically with increasing gouge porosity and SHS reference velocity and 2) the granular dilatation rate (i.e. the granular dilatancy angle) just prior to the hold period should increase with pre-hold steady state porosity and hence SHS reference velocity. The granular dilatation rate just prior to the hold can be obtained by subtracting the volumetric strain rate just after the start of the hold from the volumetric strain rate just before the start of the hold. The results are shown in and indeed show an increasing compaction rate and dilatation rate with increasing SHS sliding velocity.We now analyse the effects of reshearing on strength seen in the velocity-weakening regime. To do this we again use the measures of strength τ and τx introduced in b–d, we show representative data on the evolution of τ, τx and the measured dilatation rate (− dε/dγ) with displacement for three different sliding velocities after a hold period of 6000 s. The curves for τx correspond to the measured shear stress τ almost perfectly at all SHS velocities. This means that dilatational work (σn |
· |
ε̇) contributes negligibly to strength evolution and that strength is determined by dissipative processes or changes in stored energy within the system. Note that the peak in dilatation rate consistently postdates the peaks in τ and τx by ∼ 20 μm in displacement, which again implies that dilatation contributes almost negligibly to strength evolution (). Instead, virtually all strengthening is caused by an increase in τx.As explained earlier, this implies that strengthening was either due to an increase in average contact strength, thereby increasing the amount of frictional dissipation through intergranular slip, or due to an increase in average grain contact area relative to pore wall area. We cannot distinguish between the two on the basis of our mechanical results, although the increase of the amount of compaction during hold periods with increasing SHS velocity might indicate a larger increase in contact area with increasing SHS velocity. The observed increase in strengthening with increasing SHS velocity might be explained by an increase in contact area during hold periods.In analysing SHS tests, it is customary to define the degree of restrengthening or healing (Δμ) as the difference between the peak shear stress and steady state shear stress prior to each hold period, normalized with respect to the applied normal stress. shows how this depends on hold time for our complete set of SHS experiments (with the exception of SHS reference velocities of 0.01 and 0.03 μm/s, which were similar to the results for 0.1 μm/s and of test shs3). The linearised healing rate (Δμ per order of magnitude of healing time, i.e. the slope in a) is also indicated. The healing rate is observed to increase steadily with increasing pre-hold sliding velocity, with the healing rate at 10 μm/s being almost 1.5 orders of magnitude higher than at 0.1 μm/s. In b we show the dependence of Δμx (the difference between the peak and steady state values of τx, normalized by the normal stress) as a function of hold time. Again, an increase in healing rate is observed with increasing sliding velocity. In c we show the maximum measured dilatation rate (− dε/dγ)as a function of hold time. No clear dependence of maximum dilatation rate on hold time or sliding velocity is visible, although dilatation rate tends to be higher after longer hold times. d shows the dependence of Δμ, Δμx and − (dε/dγ)max on SHS sliding velocity for a fixed hold period of 6000 s. This illustrates that with increasing SHS sliding velocity, healing rates increase as a result of faster compaction due to higher steady state porosity being sustained at high SHS sliding velocity. show that at low sliding velocities, post-hold strengthening is minor and mostly due to dilatation. We infer that changes in τx, i.e. in contact friction and/or strength, are unimportant and do not influence strengthening in the low velocity regime. This is because there are few halite–halite contacts to be disrupted, as concluded by for NaCl plus kaolinite. At high sliding velocities, however, restrengthening is almost entirely (∼ 90%) due to an increase in τx (or Δμx, see ). This is due to a decrease in porosity which causes an increase in the dilatancy angle for granular flow, hence an increased contact friction. Increased cohesive strength at halite/halite contacts may also play a role in this regime.We will now discuss sample shs3. In this case, there was no initial wet sliding stage at low sliding velocity and stick–slip cycles occurred after a short amount of slip. The absence of initial slow sliding is likely to have resulted in a loose gouge where localization could easily be achieved, as evidenced by the occurrence of stick–slip. This is similar to the deformation behaviour observed during part of the dry run-in stage (It is evident from the above that our results for the halite–muscovite mixtures in the velocity strengthening regime are similar to the results reported by for halite plus kaolinite. However, there are some important differences. The main difference between the present experiments and the previous work of Bos and coworkers lies in the effect of using of muscovite instead of kaolinite as the phyllosilicate phase. Surprisingly, the different phyllosilicate phase and grain size has led to a different mechanical behaviour in the high velocity regime. Firstly, our muscovite-bearing mixtures have clearly shown velocity-weakening behaviour at high velocities, whereas , 2001) reported only a slight velocity-effect at sliding velocities above 1 μm/s for salt–kaolinite mixtures. The microstructures of the salt–kaolinite mixtures deformed at high sliding velocities are similar to those deformed at low sliding velocity and show only minor porosity (). Secondly, our samples heal significantly faster than kaolinite-bearing samples, in the velocity-weakening regime, even when there is no foliation present in the kaolinite–salt mixtures (Many natural fault zones exhumed from brittle–ductile transitional depths contain significant amounts of phyllosilicates. Moreover, pressure solution and cataclasis are known to be important deformation mechanisms in fluid-rich rocks at such depths (e.g. ). The present results accordingly imply a possible influence of phyllosilicate content, foliation development, cataclasis and pressure solution on mid-crustal fault mechanics, including both steady state and transient aspects. We therefore speculate upon the following possible implications of our present work, although we are aware that a microphysical model, and/or experiments under hydrothermal conditions on real fault rock materials such as quartz plus muscovite, are needed to validate extrapolation of our results to nature.A first and obvious implication is that the occurrence of brittle deformation textures (i.e. cataclasites) together with ductile deformation textures (i.e. mylonites) does not necessarily imply a change in deformation temperature or effective pressure conditions. Equally, our results indicate that an increase in shear strain rate, through an increase in fault displacement rate or a decrease in fault zone width, can create chaotic, cataclastic gouges by causing a transition from velocity-strengthening (stable) fault creep to a granular flow process accompanied by pressure solution compaction. Because this process is velocity-weakening, self-enhancing behaviour is initiated leading to an instability and possibly a seismic event. Similarly, oscillating fault motion rate can easily produce multiple cataclastic overprinting of mylonitic rocks.Secondly, it is worth noting that the healing rates we measured at the highest sliding velocity are about one order of magnitude higher than healing rates of quartz–feldspar gouges determined at room temperature and/or dry (e.g. ). A direct comparison of our healing data with estimates of fault-healing rates based on earthquake stress drop observations would not be appropriate. However, since the same mechanisms operate under upper to mid-crustal conditions, healing of natural fault zones can be expected to be dominated by solution-transfer processes and the transition from velocity-strengthening to velocity-weakening would also occur when pressure solution is too slow to accommodate the imposed displacement.Finally, the present data on the rates of restrengthening of our simulated fault gouges in the velocity-strengthening and velocity-weakening regimes imply a strong effect of the velocity history of a fault gouge on its healing rate and seismicity. A mature phyllosilicate-bearing fault rock can be expected to slip aseismically at low rates with low friction and a low healing propensity forming a mylonitic fault rock. At high strain rates, however, the same fault rock might slip seismically with high friction and a high healing propensity, forming a chaotic, cataclastic fault rock. In such a scenario, the geometry and heterogeneity of the fault zone, together with pore fluid pressure and/or composition, will initially determine which parts of the fault zone can slip aseismically and which parts might slip seismically. With ongoing displacement, stably sliding portions will tend to remain weak and stable, while unstable portions will rapidly heal and thus remain strong and unstable.In this study, we have investigated the large strain sliding and healing behaviour of simulated fault gouge using a muscovite–halite system under room temperature conditions, normal stresses of 1–9 MPa, atmospheric fluid pressure and sliding velocities of 0.001–13 μm/s. Under these conditions pressure solution, cataclasis and phyllosilicate foliation development and/or destruction are active, as anticipated for nature under the brittle–ductile transitional conditions. We investigated the steady state sliding behaviour and performed a series of slide–hold–slide tests to investigate the transient behaviour of the gouges in both the velocity-weakening and velocity-strengthening regimes reported previously. Our aim was to explain the observed velocity-weakening and healing behaviour in terms of a microphysical mechanism. We also aimed to speculate on the possible implications of our work for phyllosilicate-bearing natural fault zones under hydrothermal conditions.Synthetic fault gouges composed of muscovite plus halite are characterized by a strong velocity-dependence of shear strength, showing velocity-strengthening behaviour at low velocities (< 1 μm/s) and velocity-weakening at high velocities (≥ 1 μm/s).In the low velocity regime, halite–muscovite gouges develop a mylonitic microstructure and deform by slip on the muscovite foliation with accommodation by pressure solution of the intervening halite grains. These gouges show little or no healing in slide–hold–slide tests, probably due to the low porosity (low compaction potential) of these samples and the absence of halite–halite contacts that can heal by solution transfer processes.In the high velocity regime, halite–muscovite gouges develop a chaotic, intermixed, cataclastic microstructure due to deformation by granular flow involving pervasive intergranular sliding plus competition between intergranular dilatation and pressure solution controlled compaction. A higher porosity develops towards higher sliding velocities due to an increase in the relative importance of dilatation compared to compaction. The increase in porosity at high sliding velocity causes reduced intergranular friction due to a lower inclination of sliding grain contacts (i.e. dilatancy angle for granular flow) which leads to the observed velocity-weakening.Gouges deformed in the high velocity regime exhibit strong, velocity-dependent healing in slide–hold–slide tests, as a result of compaction during the hold period. This increases the inclination of sliding contacts (i.e. dilatancy angle) and increases intergranular friction. Increases in cohesive strength of halite–halite contacts through cementation might also play a role in the restrengthening.The overprinting of mylonitic rocks by cataclasites does not necessarily require a history of uplift, since such overprinting relations can be formed by changing the strain rate in the fault zone. Multiple overprinting of cataclasites and mylonites more likely implies a history of highly variable fault displacement rates than a complex uplift history.The large difference between healing rates in the low velocity and high velocity regimes observed in the present experiments implies that mature phyllosilicate-bearing fault zones might slip aseismically where a mylonitic foliation with a low healing and low restrengthening potential is developed. In contrast, other parts of the fault zone, where a cataclastic microstructure is developed with a high healing and high restrengthening potential, will tend to slip seismically.Effect of surface nanostructuring in solution treated and thermally aged condition on LCF life of AA7075Low cycle fatigue (LCF) behavior of the AA7075 was studied in the solution treated-ultrasonic shot peened and the peak aged (ST-USSP-PA) condition and was compared with that of the peak aged and ultrasonic shot peened (PA-USSP) as well the peak aged-ultrasonic shot peened and stress relieved (PA-USSP-SR) condition, studied earlier. LCF tests were carried out under fully reversed axial strain control at different total strain amplitudes (Δεt/2) from ±0.38% to ±0.60%. LCF life was highest in the ST-USSP-PA followed by the PA-USSP and PA-USSP-SR conditions. It was found that nanostructure of comparable size (~22 nm) was developed up to a depth of ~50 μm in all the three conditions, however, there was much variation in the type, size, distribution and number density of the metastable of η precipitates in the three conditions. While the size of the strengthening precipitates η′ was ~20 nm in the ST-USSP-PA, it was much smaller (~10 nm) in the other two conditions. High resolution TEM examination revealed high density of dislocations in the matrix and also within the equilibrium η precipitates in the PA-USSP condition whereas dislocations were not observed in η precipitates of the PA-USSP-SR and ST-USSP-PA conditions. Highest fatigue life in the ST-USSP-PA condition is attributed to more homogeneous distribution, larger size and higher volume fraction of the strengthening precipitates η′ and consequent increase in the resistance against fatigue crack initiation.Aluminium and its alloys are widely used for several components in aerospace and the aeronautical industries because of their high specific strength and corrosion resistance. The AA7075 is an age hardening Al alloy with high strength, however, exhibits relatively low fatigue resistance. Since majority of fatigue cracks initiate from the surface, the microstructure at the surface plays an important role on fatigue resistance. Surface microstructure [] affect the process of fatigue crack initiation from the surface and crack propagation in the modified surface region. Several techniques of surface modification have been used to induce compressive residual stress in the surface and sub-surface region of structural components []. Relative efficacy of several surface modification techniques those have been applied hitherto is still a matter of research.Ultrasonic shot peening (USSP) is a simple process of grain refinement potentially up to nano scale in the surface region by severe plastic deformation (SPD) without altering the chemical state of the material and without creating a sharp interface between the USSPed surface and the substrate []. USSP is based on mechanical impacts of hard metallic balls on the material at high strain rate to create highly deformed layer at the surface. The local impacts of hard balls cause extensive work hardening, confined to surface region and lead to grain refinement to nano scale and induce residual compressive stress in the surface region. Severe shot peening of a low alloy steel caused marked increase in the depth affected by residual stresses and the magnitude of the stress on the surface in respect of conventionally shot peened. Further, despite the high surface roughness, fatigue strength was improved by 10% compared to the non-peened specimen []. Fatigue strength of a 316L stainless steel was significantly improved both in the region of LCF and even more in that of HCF through surface mechanical attrition treatment (SMAT). The effect was further enhanced by annealing treatment at 400 °C following surface nanostructuring [Several studies have been carried out on fatigue behavior of the surface nanostructured materials, developed through different SPD processes. LCF life of the AA2014 was enhanced by 400% using USSP treatment, through surface nanostructuring and the associated compressive residual stresses. There was further enhancement of fatigue life following stress relieving treatment of the USSP treated specimens by complete removal of the residual substrate tensile stress induced by USSP []. LCF life of the alloy Ti-6Al-4V at the lowest strain amplitude of ±0.6% was enhanced by four times, following USSP treatment with 3 mm hard steel shots for 5 min, however, the enhancement was reduced to nearly one and half time following the stress relieving treatment at 400 °C [] studied the effect of peening intensity on the reverse bending fatigue of the AA7075-T651 and observed 15–50% increase in the high cycle fatigue life, and attributed to compressive residual stress induced by the USSP. Ramos et al. [] studied the effect of ultrasonic shot peening and microshot peening on fatigue behavior of the AA7475-T7351 and found that both of these surface treatments enhanced the fatigue life.The influence of the morphologies of precipitates of the ultrafine grained (UFG) AA6060 (Al0.5Mg0.4Si) produced by ECAP (Equi channel angular pressing), was studied on its LCF behavior []. LCF life of the specimen subjected to two passes of ECAP and aged (E2aged) was found to be less than that of the as ECAPed (E2). The lowering of fatigue life in the E2aged was attributed to shearing of fine precipitates, resulting from the aging treatment, by dislocations and formation of planar slip. ECAP is a process of bulk grain refinement whereas the present work is related to surface nanostructuring through USSP in which only the surface region is nanocrystallized to very small depth and the bulk of interior remains unaffected and coarse grained. While the extremely refined grains in the surface region of the USSP treated specimen delay the process of fatigue crack initiation from the surface, the interior coarse grains reduce the rate of fatigue crack propagation. Thus, the composite type of microstructure in the USSP treated specimens significantly enhances the fatigue life. In contrast to the detrimental effect of aging treatment on the LCF life of the E2aged AA6060, in the present investigation there was beneficial effect of the aging treatment on the fatigue life in the ST-USSP-PA condition. This is the main aspect of present work and is discussed in detail in the later sections.In our earlier investigation LCF of the coarse grained (80 μm) AA7075 in the peak aged condition was found considerably increased by USSP of the peak aged specimens for 180 s []. The enhancement in fatigue life was attributed to refinement of the coarse grains (80 μm) into ultrafine grains of ~20 nm in the surface region and the associated compressive residual stress. The current investigation was undertaken to study the effect of peak aging, following USSP in the solution treated condition on the fatigue life and to compare with those of the PA-USSP (peak aged and ultrasonic shot peened) and PA-USSP-SR (peak aged-ultrasonic shot peened and stress relieved) conditions, carried out in our earlier investigation []. An attempt has been made to correlate the observed LCF behavior of the AA7075 with microstructural features of the bulk material and modified surface regions in the three different treated conditions, referred to above.The AA7075 was procured from M/s Hindalco Industries Limited, Renukot, India, as a cylindrical bar of 54 mm diameter and 1000 mm length with nominal composition Al-4.89Zn-2.12 Mg-1.52Cu-0.33Si-0.21Cr-0.007Fe-0.09Mn (wt%). Blanks of 12.5 mm diameter and 110 mm length were prepared and solution treated at 470 °C for 30 min, quenched in water and pre-aged at 120 °C for 24 h, subsequently were heated to 200 °C and soaked for 10 min, followed by a secondary aging at 120 °C for 24 h. This aging treatment is designated as peak aging (PA).X-ray diffraction of the differently treated specimens was carried out by Rigaku X-ray diffractometer (The Rint 2000) with Cu Kα radiation in 2θ range from 15° to 60°. Major peaks of Al (111), (200), (220) and (311) were used to calculate the crystallite size and microstrain. Contribution of instrumental broadening from the assumption of spherical grains was corrected using a standard Si sample for calibration. Residual stress in surface region of the USSP treated specimens was determined by XRD using Sin2ψ method. (111) pole was used instead of (311) pole to avoid the noise effect, also error in measurement at (311) was significant at lower stress values. The Bragg's reflection for (111) pole is at 38.4°, elastic modulus used was 76 GPa and Poisson coefficient was taken 0.29. Residual stress measurements were made on a Brukers™ D8 Discovery system. This equipment was equipped with microfocus (with minimum spot size of 50 μ, with suitable laser tracking) and an area detector (Vantec™). Residual stress was estimated following the methodology of Durga et al. []. The surface removal was done through controlled electropolishing. Electro-polishing was performed in a Struers™ Lectropol-5, at room temperature, with 16 V DC using an electrolyte of 90:10 (by volume) methanol and Nitric acid. The dimension of the sample was measured with a micrometer with a least count of 10 μm. Electron transparent TEM foils of the USSP treated surface regions were prepared by sectioning thin slice from the surface region using a slow speed precision cutter and reducing its thickness to ~50 μm by mechanical grinding from the side opposite the USSP treated surface. Discs of 3 mm diameter were punched out from these thinned strips and TEM foils were prepared by electrolytic thinning of these discs in the electrolyte containing 20% nitric acid in methanol, cooled to −30 °C, at 20 V, using the twinjet electropolisher (TenuPol-5). A TECNAI G2 T20 transmission electron microscope operating at 200 kV, equipped with a high-angle annular dark field (HAADF) detector was used to characterize microstructure of the surface region. Fracture surfaces of the LCF tested specimens were examined by Zeiss EVO18 scanning electron microscope.Microhardness was measured by Shimadzu microhardness tester at an applied load of 50 g with dwell time of 10s. Tensile tests were performed at room temperature on a 100 kN Instron 5982 universal testing machine, at a strain rate of 5 × 10−3 s−1. Tensile specimens of dog-bone shape with gauge section of 15 mm × 5 mm × 2 mm were used and two specimens were tested in each condition to check the reproducibility. Cylindrical LCF specimens with gauge section of 15 mm length and 5.5 mm diameter, shoulder radii of 25 mm, and threaded ends of 30 mm length and 12 mm diameter were machined from the heat-treated blanks. The gauge sections of the PA (peak aged) and ST (solution treated) fatigue specimens were subjected to USSP for 180 s, continuously rotating the test specimens using a motorized device to ensure uniform USSP. Stress relieving treatment for the PA-USSP treated specimens, was carried out at 90 °C for 4 h and the peak aging treatment of the ST-USSP treated specimens was performed in the same way as that of the base PA specimen. LCF tests were carried out using a servo hydraulic MTS™ of 50 kN (Model 810) under the total strain control mode with triangular wave form and fully reversed axial loading at different total strain amplitudes of ±0.38%, ±0.40%, ±0.45%, ±0.50%, ±0.55% and ±0.60%, at a constant strain rate of 5 × 10−3 s−1. One specimen was tested for each thermal treated condition at respective total strain amplitudes. The number of cycles for crack propagation (Np) was calculated by drawing a line on the largest region of the fracture surface showing striations, determining the interstriation spacing at mid-point on the line to have average value of the interstriation distance taking into account the magnification of the image and dividing the length of the line drawn by the average interstriation spacing. The number of cycles for crack initiation (Ni) was determined as Nf-Np.X-ray diffraction patterns of the AA7075 in the PA-unUSSP, PA-USSP, PA-USSP-SR and ST-USSP-PA conditions are shown in . XRD peaks are analyzed to characterize the phases in the above conditions. In all the specimens most intense diffraction signature is observed from FCC Al. This indicates that the matrix of all the specimens in the above four conditions remains the same. The heat treatment brings about changes only in the structure, shape, size, morphology and distribution of precipitates. In between the 111 and 200 diffraction peaks of Al, a number of minor peaks may be seen in the PA-unUSSP specimen. However, the nature and presence of those peaks changes as the specimen is USSP treated or stress relieved following USSP. The d-spacings of those peaks match closely with those of the hexagonal hP12 MgZn2 phase. This phase is commonly referred to as η phase in aluminium alloys literature.This phase has several structural variants which are slightly different in terms of their lattice parameters. It is not possible to distinguish them from the diffraction patterns. The structural variants of η phase is termed as η′. The differentiation between η′ and η appears impossible. It can be concluded that in the PA-unUSSP specimen apart from the FCC aluminium grains, hexagonal MgZn2 type phase is present. In the PA-USSP specimen even though the diffraction peaks remain intact, the diffraction peaks corresponding to MgZn2 are reduced to a large extent. This may be attributed to fragmentation of the precipitates into much finer size and sparse distribution or dissolution of some of them in the matrix due to the USSP treatment. Again, in the PA-USSP-SR specimen similar peaks reappear which indicate that reprecipitation or coarsening of precipitates occurred during the stress relieving treatment, following the USSP. In the ST-USSP-PA specimen also similar peaks may be observed. It appears from the X-ray diffraction that the heat treatment and USSP cause some changes in the precipitates in this alloy which needs to be investigated further in order to correlate them with the observed properties. The average crystallite size was calculated using the Scherrer and Wilson equation [where t is effective crystallite size, λ is X-ray wavelength, θ is Bragg angle and B is line broadening. The average crystallite size of the matrix (αAl) in the surface region of the PA-USSP, PA-USSP-SR and ST-USSP-PA specimens was ~19 nm, ~22 nm and ~21 nm respectively. Thus, there was formation of nanostructure in surface region of the specimens almost of comparable size in all the above three conditions. The mean micro-strain was calculated from the XRD data using the Williamson-Hall equation [where ε is root mean square of micro-strain. Micro-strain in the PA-USSP, PA-USSP-SR and ST-USSP-PA condition was found to be 0.320, 0.307 and 0.304% respectively.The variation of the residual stress from the USSP treated surface towards interior was determined in XRD, sequentially removing thin layers of the material electrochemically. Its variation is shown in The variation of the residual stress shows that it was compressive in nature and maximum in the sub-surface region. The maximum compressive residual stress was −305 MPa by the PA-USSP condition. The magnitude of the compressive stress was reduced to 239 MPa and 117 MPa for the PA-USSP-SR and ST-USSP-PA specimens respectively. The maximum compressive stress was there in the subsurface region as there was relatively less stress relaxation in the subsurface region with respect to that at the surface. Additionally, the maximum residual stress in this case may also be substantiated in terms of the heat treatment history and the precipitate structure to be discussed in later part of the paper. It is evident from the profile of the stress distribution that the major compressive stress was relieved from thermal exposure of the specimens at higher temperatures, upto the depth of ~250 μm and the nature of the residual stress was still compressive.The microstructural and chemical information of the PA-unUSSP specimen is given in . The bright field TEM micrograph and the corresponding diffraction pattern of the PA-unUSSP specimen are shown in a and in the inset respectively. In the bright field image, coarse and faceted grains of the FCC aluminium are observed. The grains are mostly strain free and fringe contrast arising out of grain boundaries is also clearly visible. Occasional presence of dislocations, mostly in the grain body, is clearly discerned. In addition to that, a large number of precipitates are seen to be distributed in the grain body. The precipitates could be divided into three categories based on their size and morphology. The elongated rod like precipitates ~100–200 nm long and ~30–50 nm wide may be observed in the grain body. There are nearly spherical or faceted precipitates of ~50–100 nm size, randomly distributed in the grain. In addition to these there are lumpy precipitates of ~100–200 nm size in the grains. These precipitates are relatively less in number. In the diffraction pattern in the inset quite a few very sharp spots are observed. The sharp spots correspond to 0.138 nm, 0.118 nm and 0.09 nm which closely resemble with d-spacings of FCC aluminium. However, they do not maintain the angular relationship with respect to FCC aluminium. The authors conclude from this observation that some of the spots are from the precipitate phases and the d-spacings match closely with the hexagonal MgZn2 phase and cubic Al18Cr2Mg3 phase. A high resolution phase contrast image from one of the nearly spherical and faceted precipitates is shown in b. In the image, lattice fringe contrast distributed over two dimensions could be clearly distinguished. The FFT from the precipitate (inset) measures 0.18 nm which closely matches with the hexagonal MgZn2 phase or the cubic Al18Cr2Mg3 phase.In order to ascertain the phase, the precipitate was chemically mapped by STEM-EDS technique. The STEM-EDS map from the precipitate is shown in d. It is clear from the map that the precipitate is rich in Cr and Mg. There is aluminium in it; however, the aluminium content is lesser than that in the surrounding matrix. This confirms that the almost circular or faceted precipitates are cubic Al18Cr2Mg3 phase which is commonly termed as E-phase in literature. A high resolution phase contrast image of the elongated rod like precipitates is shown in c. Lattice fringes are observed in the image. The FFT from the high-resolution image (inset) measures 0.19 nm and 0.23 nm which are characteristic d-spacings of the hexagonal MgZn2 phase. However, in order to ascertain this observation, the precipitates were chemically mapped by STEM-EDS. The STEM-EDS map from the precipitate is shown in e. It is clear from the map that the elongated precipitates are rich in Mg and Zn. This conforms that the elongated precipitates are hexagonal MgZn2 phase which are commonly referred to as η phase in literature. The structure of the precipitates and their crystallographic relationship with the matrix has been further probed by high resolution microscopy and nano-beam diffraction. The high-resolution phase contrast image of the E-phase is shown in . In the high resolution image cross fringe pattern could be easily observed which is very close to that of the cubic Al18Cr2Mg3 phase. The nano-beam diffraction pattern from the precipitate is presented in d. In the diffraction pattern a prominent hexagonal array of the spots is observed. The hexagonal array of the spots corresponds to 0.142 nm which closely matches with (220) of FCC aluminium. It can be concluded that the dark hexagonal array of the spots arises from FCC aluminium when it is oriented along [111] zone axis. In addition to that in the diffraction pattern a couple of other spots could also be observed. The other spots correspond to 0.206 nm which closely matches with 444 of the cubic Al18Cr2Mg3 phase.This indicates that the E-phase grows into the aluminium matrix in oriented fashion in which there is an in-plane rotation between the FCC aluminium and the E-phase. The high-resolution phase contrast image of the η phase is shown in b. Even though lattice fringes could be easily discerned, the crystal is multiply faulted which can be ascertained from the contrast and extensive streaking in the FFT (inset). The nano-beam diffraction pattern from the η-phase is displayed in c. In the diffraction pattern a number of scattered spots could be observed which is due to the simultaneous interaction of the electron beam with the precipitate and the matrix. In the diffraction pattern, the spot corresponding to 0.23 nm arises from the FCC aluminium and the spots corresponding to 0.217 nm and 0.222 nm arise from the hexagonal MgZn2, η-phase. No particular orientation relationship between this phase and the matrix phase could be discerned.TEM bright field image and the corresponding diffraction pattern of the PA-USSP specimen are displayed in (inset). In the bright field image, a drastic change in microstructure could be observed following the USSP treatment. All through the microstructure mottled contrast is present which signifies the presence of residual strain in the microstructure. The grains have fragmented and their size has been reduced to ~100–200 nm. The grains are polygonal in nature and are separated by sharply defined grain boundaries. The appearance of a greater number of spots in the PA-USSP case corresponds to sampling of several grains in the TEM field of view. This is in contrast to the PA-unUSSP condition where a fewer spots are observed. This further supports the grain refinement induced by USSP treatment. All the Debye rings in the diffraction pattern could be indexed to FCC aluminium. It might be interesting to note that Debye rings corresponding to precipitate phases are not seen in the diffraction pattern. This might indicate that during USSP, intense mechanical strain along with localized heat, that is produced, tends to dissolve some of the precipitates back into the matrix. A similar bright field image from some other region of the specimen is displayed in b. In this micrograph also very fine distributed grains are observed. This fine grain structure arises partially due to the fragmentation of grains and the precipitates during the USSP treatment. There might still be some GP zones also with speckle contrast. However, deep into the thickness of the specimen unfragmented grains and precipitates are observed. The precipitate in c and d corresponds to η-phase and E-phase respectively.TEM micrographs and the diffraction patterns from the PA-USSP-SR specimen are displayed in (a-e). The bright field image from the specimen in a indicates that residual stress has been relieved to a large extent after the stress relieving treatment. However, the grains are still fine and their size lies in the range of 100–200 nm. This confirms that stress relieving treatment relieves stress, however, it does not lead to grain growth to a large extent. The diffraction pattern in the inset is still spotty ring which is due to fine grain structure and the Debye rings match quite well with FCC aluminium. b is bright field image from some other region of the specimen where very fine grain structure is observed. The fine grains match quite well with FCC aluminium, and η′ precipitates. Some of these fine structures may also be GP zones. In c apart from fine grains, two types of precipitates are observed which are either needle shaped or faceted polygonal in shape. The diffraction patterns from the precipitates are shown in d, the most intense spots are from aluminium. The other scattered spots match with the η phase. In e, again the intense spots are from FCC aluminium and the scattered spots match with the E-phase, as discussed earlier. It appears from this study that due to the USSP treatment the precipitates either dissolve or get fragmented to very fine size. However, after stress relieving treatment the precipitates reappear.In the ST-USSP-PA condition there is more homogeneous distribution of the strengthening precipitates (GP-zones and η′). The discontinuous ring in the SADP inset () signifies presence of nanograined structure even after the peak aging treatment. The mottled contrast in the microstructure indicates presence of residual strain. The microstructure following the aging treatment shows clusters of very fine platelets (b); the typical round clusters of GP-zones/E-phase and fine platelets of η′ precipitates. The η′ precipitates with average size of 5.1 nm × 23.8 nm are distributed homogeneously throughout the matrix and were oriented in a particular direction. The density of these precipitates is found to be higher as compared with those of the other two conditions. An HRTEM of the individual η′ precipitate is shown in c, its FFT in the inset shows that these precipitates are aligned parallel to (100) planes. Alignment of the η′ precipitates may be attributed to the tendency of the precipitate to grow along elastically soft direction in order to reduce the interfacial strain energy.The variation of microhardness from the USSP treated surface towards interior in transverse sections of the different specimens is shown in . The hardness is highest in the surface region and gradually decreases with increase in the depth from the surface. The level of the microhardness profile is highest for the ST-USSP-PA and is followed in decreasing order by the PA-USSP and PA-USSP-SR. As expected, the hardness in the PA-unUSSP condition is lowest and constant. The microhardness in the PA-unUSSP condition was 154Hv. The microhardness on the surface of the ST-USSP-PA, PA-USSP and PA-USSP-SR conditions was 184, 173 and 168 Hv respectively. While the micro hardness in the PA-USSP and PA-USSP-SR conditions coincided with that of the PA-unUSSP at the depth of ~800 μm from the surface, the hardness of the ST-USSP-PA was still higher.The engineering stress-strain curves of the AA7075 in the three different conditions are shown in and the tensile properties are presented in . It may be seen that the strength and ductility parameters are highest in the ST-USSP-PA condition and lowest in the PA-USSP-SR. An intermediate behavior is exhibited in the PA-USSP condition. However, the degree of work hardening is highest in the PA-USSP-SR condition. The highest strength in the ST-USSP-PA condition is attributed to precipitates and refinement of grains. In the case of PA-USSP specimen also the high strength is attributed to precipitates and refined grain size and accumulated strain. In the case of stress relieved specimen the drop in strength is due to strain relaxation. However, this results in an increment in the uniform strain. The degree of work hardening was highest in the PA-USSP-SR condition. shows cyclic stress response of the AA7075 in the PA-USSP, PA-USSP-SR and ST-USSP-PA conditions at different total strain amplitudes. There is rapid hardening in the initial stage from cycle 1 to 2 except in the ST-USSP-PA condition of Δεt/2 = ±0.40%. The rate of cyclic hardening decreases from the second cycle to nearly 100 cycles. The rate of cyclic hardening further decreases from 100 cycles till before fracture. The level of the cyclic stress response curves at Δεt/2 = ±0.40% and ± 0.50% is highest for the ST-USSP-PA condition followed by that of the PA-USSP and PA-USSP-SR respectively. On the other hand at the highest strain amplitude of ±0.55%, is highest in the PA-USSP-SR followed by that in the ST-USSP-PA and lowest in the PA-USSP condition.Coffin–Manson relationship between the plastic strain amplitude (Δεp/2) and the number of reversals to failure (2Nf) is used to analyze the fatigue behavior in the different conditions, as given below.where ε'f and c are fatigue ductility coefficient and exponent respectively. The Coffin-Manson plots for the different conditions are shown in . The numerical values of the LCF parameters determined from the plots in . It may be seen that in the ST-USSP-PA condition the values of ε'f and c are lowest and fatigue life is highest. The variation of the number of cycles to failure at different total strain amplitudes for the different conditions is shown in . LCF life is reduced following stress relieving treatment of the USSP treated specimen; on the other hand fatigue life is increased in the ST-USSP-PA condition and is highest among the three conditions.The highest fatigue life in the ST-USSP-PA condition in respect of the other two conditions may be analyzed from which shows variation of the two components of fatigue life, Ni and Np. It may be seen from that both Ni and Np for the ST-USSP-PA condition are more or less comparable to the other two conditions at the highest strain amplitude of ±0.60%; however, at the lower strain amplitudes from ±0.55% to ±0.38%, Ni is significantly enhanced for the ST-USSP-PA in comparison with those of the other two conditions. Further, the difference between Ni and Np increases markedly with decrease in the strain amplitude. On the other hand, there is not much difference in Np for the three conditions. Thus, it is obvious that high fatigue life in the ST-USSP-PA condition is essentially due to high resistance of the material in this condition against fatigue crack initiation.The fractured surfaces of the specimens tested at the intermediate strain amplitude of Δεt/2 = ±0.45% for the above three conditions are shown in . Fatigue cracks may be seen to initiate from the surface (marked with yellow arrows) in all the conditions and there is no sub-surface crack initiation. The number of crack initiation sites is more in the USSP treated specimen ( a). The mode of crack propagation is transgranular and the direction of fatigue crack growth (FCG) is shown by arrows in a′, b′, c′. An approximation was made for the rate of crack propagation estimating the inter-striation spacing in Stage-II crack propagation. The average inter-striation spacings determined from the fractographs of the PA-USSP, PA-USSP-SR and ST-USSP-PA are found to be 0.75, 1.21 and 0.63 μm/cycle, respectively. Thus, it is obvious from these data that the rate of crack propagation is lowest in the ST-USSP-PA condition.In the present investigation the microstructure of the AA7075 aluminium alloy with different thermal history and USSP treatment has been studied in detail and the mechanical behavior of the alloy has been correlated with the microstructural components. A number of interesting observations have been made which are discussed in the following sections:The AA 7075 alloy in the peak aging condition shows large faceted grains of FCC aluminium. Apart from that a large number of precipitates are observed in the matrix. The lumpy precipitates are cubic Al18Cr2Mg3 phase which has a complex crystal structure. This phase is likely to augment strength and hardness of the alloy. Further, long rod/needle shaped precipitates of η-phase also be seen. The η-phase is hexagonal MgZn2 Laves phase. There is another phase termed as η′ which is also very closely related to the η phase. Both the phases being hexagonal Laves phase are hard and brittle and are likely to increase the strength and hardness of the alloy. It is important to note that η-phase may accommodate other alloying elements from the matrix forming a pseudo ternary Laves phase and in course of that it might undergo polymorphic transformation to η′. Even though both the phases are related, they are supposed to have different mechanical behavior due to their different alloying elements addition and different states of order. The signature of presence of all these phases was obtained from the XRD and TEM analysis.Significant change in microstructure took place due to the USSP treatment. Huge strain accumulation took place during the USSP treatment and grains were considerably refined. More importantly, in the XRD and in TEM study of this alloy after the USSP treatment signature of the precipitates could not be observed. It may be due to extensive refining of the precipitates or selective dissolution of the precipitates in the matrix. During the USSP treatment local temperature may go very high hence selective dissolution is a finite probability. Stress relieving treatment after USSP resulted in reprecipitation of the phases once again. Signature of those phases could be observed from the X-ray and electron diffraction. However, USSP treatment after the solution treatment only leads to strain accumulation and grain refinement in the alloy. Peak aging after this leads to stress relaxation and precipitation of the same phases. This systematic microstructural development leads to the evolution of mechanical properties which will be discussed in the following sections.It has been observed that during the USSP treatment extensive grain refinement takes place and prior or subsequent heat treatment affects the precipitate shape, size and distribution in the alloy. As a consequence of that a systematic variation in mechanical properties was observed. After the USSP treatment, grain refinement takes place in the alloy. The extent of refinement and the depth to which the refinement takes place depends upon the time and intensity of the impacts of the shots on the material. It can be concluded that the interface between the base material and the USSP layer is diffused structural interface without any sharp distinctive boundary line between the USSP modified layer and the base material. In the present case, even though the USSP parameters were kept constant, microstructure of the parent material being different, different mechanical properties were exhibited.From the hardness profile, it is discerned that the PA-unUSSP specimen shows uniform hardness. In the ST-USSP-PA specimen hardness is highest because of severe plastic deformation caused by the USSP and subsequent extensive precipitation from the peak aging. Hardness profile in the PA-USSP condition is above that of the PA-unUSSP because of severe plastic deformation due to USSP and is lower than that of the ST-USSP-PA because of the damage of the strengthening precipitates in the PA-USSP condition. The relatively lower level of hardness profile in the PA-USSP-SR than that of PA-USSP is due to annihilation and rearrangement of dislocations after the stress relieving treatment. A similar trend is seen in relative values of the yield strength (YS), ultimate tensile strength (UTS) and strain to fracture.] also observed enhanced tensile strength in the AA7075 in the solutionized, cryo-rolled and peak aged condition and attributed to the improved work hardening rate. The low dislocation density, following peak aging treatment of the ST-USSPed specimen left much room for dislocation accumulation before saturation, increased the degree and rate of work-hardening. The high density of nanosize precipitates was effective in pinning and accumulation of dislocations to increase the work-hardening rate [Refinement of surface grains and induced high compressive residual stress from the USSP treatment enhanced fatigue life of the AA7075 as reported in our earlier publication []. As mentioned in the introduction, the present investigation was undertaken to study the effect of pre and post USSP thermal treatment on the LCF life of the alloy AA7075. In all the three conditions: PA-USSP, PA-USSP-SR and ST-USSP-PA, the USSP treatment was identical for 180 s with shots of 3 mm diameter. However, the initial condition of the AA7075 was peak aged for the PA-USSP and PA-USSP-SR, whereas it was solution treated for the ST-USSP-PA. Further, while no thermal treatment was given to PA-USSP, stress relieving treatment was given to PA-USSP-SR, whereas peak age hardening treatment was given to ST-USSP and it was designated as ST-USSP-PA.As mentioned earlier, ultrasonic shot peening led to development of nanostructure in surface region of the specimens, in all the three conditions, as established by the XRD and TEM analyses. The original coarse-grains were refined to nano-scale by severe plastic deformation of the surface region from repeated multidirectional impacts of the hard steel shots. It is evident from the characteristic ring-shaped SAD pattern of the USSP treated surface region that an extremely fine-grained structure developed with high angles of misorientation of the grain boundaries. There was decrease in the volume fraction of the precipitates, in particular of the coarse ones, due to the USSP treatment, suggesting their fragmentation and dissolution in the matrix as evident from the XRD plot (), in line with the earlier observation made by Krishna et al. in the ultrafine grained Al–4Zn–2Mg alloy produced by cryorolling []. Along with the nanosized grains some η and E-phase particles were also present in the PA-USSP-SR condition, distributed heterogeneously in the matrix. Further, there was no change in the size of surface grains following the stress relieving treatment, however, there was recovery and reduction in the dislocation density and increase in the size of the precipitates (). The stress relieving treatment led to increase in the size and volume fraction of the coarse precipitates η as compared with that in the PA-USSP condition. However, there was no effect on the fine precipitates of η′ (b). On the other hand, in the ST-USSP-PA condition volume fraction of the coarse precipitates was low and the fine precipitates were relatively larger in size and more uniformly distributed than that in the initial peak aged condition (b). It is due to high density of dislocations produced by the USSP of the solution treated specimen, to act as nucleation sites for the precipitates. On the other hand the GP-zones formed during the USSP process got transformed into η′ on aging and thus contributed to overall increase in the volume fraction of η′. The size of the strengthening precipitates was relatively larger (~23 nm) in the ST-USSP-PA condition in comparision with those in the PA-USSP and in PA-USSP-SR conditions (~7-8 nm). Large number of grain boundaries in the nanostructured surface region enhanced the rate of diffusion and the kinetics of precipitation to result in more homogeneous distribution of the strengthening precipitates []. In the USSP treatment of the ST specimen some GP zones formed during the USSP and during the post USSP aging these GP zones got transformed to η′, thus a more homogeneous distribution of the strengthening precipitates occurred.The HRTEM micrographs and their corresponding inverse fast Fourier transform (IFFT) images for the different conditions are shown in . The density of dislocations in the USSP treated condition was estimated to be 3.7675 × 1016 m−2 and most of the dislocations are observed to surround the second phase η particles (a′). These dislocations of high density were not able to pass/glide the precipitates and increased the hardness in the USSP affected region. At high strain the dislocations were able to pass through the precipitates and cause their fragmentation. The high density of dislocations, generated during the USSP treatment was drastically reduced to 5.9612 × 1015 m−2 in the stress relieved condition due to recovery. The decrease in dislocation density and partial relieving of the compressive residual stress () caused decrease in hardness in the surface region (). The increase in grain boundary fraction resulting from the USSP enhanced the rate of diffusion and consequent formation of nano precipitates which retarded the mobilization of dislocations and caused strengthening of the AA7075 []. These nanosized precipitates compensated for the fall in the dislocation density (9.2146 × 1015 m−2) and also the fall in the compressive residual stress and the overall strength of the AA7075 was enhanced. These observations are in line with those of Cheng et al. [] who reported that there were smaller precipitates in the AA2024 due to cryo-rolling and subsequent aging, and also their density was high to cause strengthening.There is considerable difference in the cyclic stress response of the alloy in the three conditions []. It may be seen that there is significant increase in the stress amplitude in the second cycle itself in the PA-USSP and PA-USSP-SR and the increase is relatively more in the PA-USSP-SR than that in the PA-USSP. Further, the cyclic stress amplitude rises progressively up to about 100 cycles in the PA-USSP and thereafter remains constant till before the fracture, whereas the stress amplitude continuously increases up to nearly 2000 cycles before stabilization in the PA-USSP-SR condition. Also, the degree of work hardening is higher in the PA-USSP-SR as compared with that in the PA-USSP, at almost all the strain amplitudes from ±0.38% to ±0.60%. The relatively higher stress amplitude in the first cycle in the case of the PA-USSP at the lower strain amplitudes from ±0.38% to ±0.45% in respect of that of the PA-USSP-SR is due to initial high density of dislocations in the PA-USSP condition. The relatively lower cyclic stress amplitude in first cycle of the PA-USSP than that in the PA-USSP-SR, at the high strain amplitudes from ±0.50% to ±0.60%, is due to the effect of the precipitates formed during the stress relieving treatment of the PA specimen, following the USSP treatment. The degree of cyclic work hardening is highest in the PA-USSP-SR among the three conditions and it is due to the initial low density of dislocations resulting from the stress relieving treatment coupled with precipitation of fine precipitates from the SR treatment.Nanostructuring in the surface region has been reported to delay the process of fatigue crack initiation and the high compressive residual stresses associated with gradient microstructure in the sub surface region to retard the process of fatigue crack propagation []. It may be noted that in general, the number of cycles for crack initiation (Ni) is higher than the number of cycles for crack propagation (Np). In the ST-USSP-PA condition there is large difference between the Ni and Np and the difference between Ni and Np progressively increases with decrease in the total strain amplitude. Ni may be seen to increase rapidly at the lower strain amplitudes of ±0.40% and more so at ±0.38%. It is due to the presence of the strengthening precipitates in the nanostructured surface layer, which made dislocation movements more difficult under the applied cyclic stress, due to which the process of fatigue crack nucleation was delayed and Ni was increased (Ductile materials exhibit higher life under strain controlled low cycle fatigue in which the major fraction of the fatigue life is spent in the process of fatigue crack propagation, whereas strong materials show better resistance under stress controlled high cycle fatigue (HCF) where large fraction of fatigue life is spent in the process of fatigue crack initiation. Therefore, it may be inferred from that surface nanostructuring induced by the USSP treatment is more effective in enhancing fatigue life at decreasing strain amplitude as compared to that at the higher strain amplitude. Nanostructured surface layer displays higher yield strength as per the Hall-Petch relationship, whereas strain hardening increases the mechanical strength through dislocation entanglement, and further permanent deformation is delayed []. Grain refinement causes shortening of slip distance due to which the level of stress concentration is reduced and the resistance against fatigue crack initiation is improved and thus fatigue life is enhanced []. Also, compressive residual stress plays a significant role in improving the ductility by suppressing cracking in the surface and sub-surface region. In residual stress remains compressive up to a depth of ~250 μm from the surface. This makes the affected region hard and the un-affected coarse grained region soft and a large strain gradient is developed under loading due to gradient residual stress which promotes further accumulation of dislocations and produces extra strain hardening and crack propagation is also arrested to some extent [Thus, the enhancement in LCF life in the ST-USSP-PA condition is due to homogeneous precipitation of extremely fine GP-zones and η′ precipitates along with the nanostructured surface layer as no grain growth was observed due to low temperature of aging. The decrease in dislocation density and fall in the residual stress was compensated by the relatively large size of the strengthening precipitates (~24 nm). LCF life of the PA-USSP-SR specimens was found to be less as compared with that of the PA-USSP condition. It can be seen from that the difference between Np and Ni was very low which indicates that relieving of the compressive residual stress from the surface region () resulted in decrease of both Ni and Np and consequently the LCF life was decreased. Stress relieving treatment did not alter the microstructure in the surface region; the grains were of nano size and there was no grain growth. In the AA2014 the stress relieving treatment resulted in increase of LCF life and it was attributed to complete removal of the tensile residual stress generated from the USSP treatment in the sub surface region, however an opposite trend was observed in the alloy Ti-6Al-4V []. In addition, the very high increase in the yield strength in the nanostructured region due to highly effective blockage of dislocations by nanograins and demonstrated in the 316L stainless steel [] would be very favorable and important factor for increasing Ni. Further, linkage of slip, if any, from one to other nanograin to form large slip would be highly difficult due to large difference in the orientation of grain boundaries in the nanostructured region.Three different treatments namely (1) PA-USSP, (2) PA-USSP-SR and (3) ST-USSP-PA were given to the AA7075 to study the effect of pre and post USSP thermal treatments on microstructural changes and the LCF behavior at RT. The following conclusions are drawn from this investigation.The coarse surface grains of ~80 μm were refined to nanoscale of comparable size of ~22 nm in all the three conditions referred to above. There was appreciable variation in the type, size, distribution and number density of the strengthening precipitates in the three conditions.At the lower strain amplitudes, the LCF life was found to be highest in the ST-USSP-PA condition which had high number density of η′ precipitates, more uniform distribution and larger size of these precipitates despite lowest compressive residual stress in the surface region. Further, there was also no damage of the strengthening precipitates as these formed after the USSP treatment.The highest LCF life in the ST-USSP-PA condition at the lower strain amplitudes was essentially due to the increase in the resistance of the nanostructured region against the process of fatigue crack initiation.The LCF life was lowest in the PA-USSP-SR among the three conditions which may be attributed to decrease in the dislocation density, fall in the compressive residual stress and damage of the strengthening precipitates due to the USSP treatment after peak aging and consequent reduction in their effective size.The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.Vaibhav Pandey: Writing- Original draft preparation, Conducting experiments, Methodology, Investigation. Manish Kumar Singh: Visualization. Joysurya Basu: Conceptualization. K. Chattopadhyay: Supervision. N. C. Santhi Srinivas: Co-Supervision. Vakil Singh: Writing- Reviewing and Editing.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Structure-based selection of surface engineering parameters to improve wear resistance of heterogeneous nickel- and iron-based alloysHeat treatment, low energy elevated-temperature nitrogen ion implantation, and combination of these techniques were selected to analyze the influence of surface structure parameters on tribological properties of precipitation hardening nickel-based alloys and chromium steels. It was demonstrated that wear resistance of investigated alloys did not correlate well with the surface hardness for both sliding and abrasive modes of wear. Details of microstructure including inclusion morphology, interface microstructure, and stress–strain state induced by preceding treatments of blocks should be taken into account to explain properly wear behavior of blocks.Most of microstructures, produced by surface engineering techniques such as laser treatment, ion implantation, etc. are metastable and characterized by increased level of inner energy. One of the most typical results of surface processing to improve mechanical properties of materials is precipitation of hard particles. The crucial role of residual stresses, precipitate concentration, size, shape, and matrix–inclusion interface microstructure for tribological applications was demonstrated elsewhere Two types of alloys were investigated in this research: (1) precipitation–hardening Ni–Cr alloys containing predominantly spherical coherent and isomorphic precipitates; (2) nitrogen ion implanted chromium steels containing non-coherent and -isomorphic nitrides. These alloys are considered as promising tribological materials for severe applications and for applications in chemically aggressive environments The present work examines the influence of precipitate size, concentration, and morphology of inclusions, matrix–inclusion interfaces, residual and inter-phase stresses on wear behavior of precipitate containing alloys. By correlating microstructural and tribological changes in these materials, increased understanding of wear mechanisms and their correlation with prior surface engineering parameters is sought.Precipitation–hardening XH77TЮP, XH67BMTЮ, XH56BMTЮ alloys, chromium-containing 20X13, and 40X13 steels were selected to facilitate understanding of hard fine precipitates influence and surface processing parameters on friction and wear behavior of materials. shows the chemical composition of the alloys. Favorable combination of structural parameters makes selected Ni–Cr alloys essentially attractive for research. Particularly, precipitation of hard γ′-phase inclusions in XH77TЮP and XH56BMTЮ alloys results in inter-phase elastic strains of different signs: compressive strains for XH77TЮP alloy, when γ′-phase crystal lattice parameter (ap) exceeds that for matrix phase (am) and tensile strains for XH56BMTЮ alloy when ap<am. Matrix and γ′-phase in XH67BMTЮ alloy have the same lattice parameter so ageing does not lead to crystal lattice deformation (). All blocks were ground to Ra=0.32 μm and washed in alcohol before wear tests and/or ion implantations.Nitrogen is one of the most promising elements for surface modification of metals and alloys. Blocks were implanted with 3 keV nitrogen ions at an ion current density of 2.0 mA/cm2. The total fluence of ions was 3×1019 |
cm−2. The temperatures of ion implantation were selected on the basis of preliminary research Microhardness was measured at 1 N. Optical and electron microscopy were used for metallographic study of blocks. X-ray diffraction analysis (Cu Kα irradiation, U=30 kV, I=10 mA) was carried out to study surface layer microstructure. The concentration of γ′-phase precipitates was determined by electrochemical extraction.A tester with reciprocating movement (average velocity 0.016 m/s, BOSH 320 abrasive band with 50 μm size Al2O3) has been used for abrasive wear tests. Specific pressure for abrasive wear tests was 0.02 MPa. Weight losses were determined after each 35 m of running.Ten blocks were used for each wear measurement (both sliding and abrasive) so statistically significant mean values could be obtained. The accuracy of wear tests estimated to be 10%.Heat treatment of Ni–Cr alloys involved 0.5 h homogenization at 1350 K (XH77TЮP blocks), 1430 K (XH67BMTЮ blocks), and 1470 K (XH56BMTЮ blocks) quenching and ageing of blocks. Diffraction lines of single-phase blocks were very narrow. XH77TЮP and XH67BMTЮ block ageing resulted in diffraction lines broadening. Aged blocks consisted of γ-phase matrix and hard intermetallic γ′-(Ni3(Al, Ti)) precipitates. Parameters of heat treatment () were selected so to obtain two sets of blocks: blocks with different concentration of 20/30 nm size precipitates; blocks containing the same concentration of precipitates with different size (25–100 nm). The crystal lattice parameters for XH77TЮP, XH67BMTЮ, XH56BMTЮ alloys were 0.3571, 0.3593, and 0.3601 nm correspondingly.Ion implantation of Ni–Cr alloys yields a modified surface layer, which is 1–3 μm thick (). X-ray analysis did not reveal Ni3N inclusions in the layer, but supplementary diffraction lines show the formation of nitrogen solid solution (). Noticeably broadened diffraction lines of CrN were also observed.Heat treatment of steel blocks prior to implantation involved initial hardening by heating to 1300 K (20X13 steel) or to 1320 K (40X13 steel) and quenching in the oil. Data for surface hardness are presented in . 20X13 blocks had the needle-shaped martensite structure with lattice parameter a=0.2873 nm. 40X13 blocks had the same structure (a=0.2874 nm) with traces of Cr23C6 carbides. Ion implantation at 620 K influenced a 10–15 μm thick layer. X-ray data demonstrate that ion implantation yields precipitation of nitrogen-rich ε-(Fe, Cr)3N phase inclusions with comparatively small amount of α″-(Fe, Cr)8N inclusions in the deeper layer. Ion implantation at 670 K influences a 15–18 μm thick surface layer. Surface layer consists of ε-(Fe, Cr)3N, γ′-(Fe, Cr)8N inclusions, and αN-martensite. Ion implantation at 720–770 K increased the depth of modified layer up to 20 μm. A great deal of thermodynamically stable CrN precipitates (10–12 nm in size) and traces of ε-nitrides were observed in blocks implanted at 720 K. Surface layer of blocks implanted at 770 K contains only CrN inclusions. High temperature implantations result in decomposition of oversaturated α-solid solution and diffraction lines narrowing. Carbide inclusions in the surface layer of these blocks were not observed.Wear rates for single-phase quenched Ni–Cr alloys presented in show that XH77TЮP blocks reveal the worse wear resistance as compared to XH67BMTЮ and XH56BMTЮ blocks. XH77TЮP and XH67BMTЮ blocks containing comparatively small concentration of γ′-precipitates (1–10 vol.%) revealed slightly improved wear resistance. Further growth of γ′-phase content resulted in wear resistance decrease. The best wear resistance of XH56BMTЮ blocks was observed for the single-phase state. The precipitation of γ′-phase inclusions results in wear resistance decrease. Data of show the influence of γ′-precipitates size on the wear resistance of blocks. As easy to see size increase up to D=100 nm (for alloys with the same concentration of γ′-phase) slightly increase wear of blocks.Ion implantation resulted in 20–30% wear resistance improvement, but the effect was observed only during running-in period.The typical microphotographs of Ni–Cr blocks, subjected to sliding wear, are presented in . A comparatively low concentration of evenly distributed dislocations was observed in single-phase blocks. Surface layer of blocks consists of small 20–200 nm grains elongated in the direction of friction and cellular structure with broad dislocation boundaries in the deeper layer. The wear rates for steel blocks are presented in and demonstrate that the highest wear resistance was observed for blocks treated at 770 K.Dramatic broadening of diffraction lines took place also after wear tests (). The maximum values of Δβ were observed for single-phase blocks and blocks with a low concentration of γ′-phase (5–6%).Data for abrasive wear of Ni–Cr alloys and steels are presented in correspondingly. In the case of XH77TЮP and XH67BMTЮ blocks the maximum wear rates were observed for single-phase alloys. Ageing and γ′-phase content increase improved wear resistance of blocks. On the contrary, high concentration of γ′-phase precipitates in XH56BMTЮ blocks lowered their wear resistance. The increase of precipitate size up to D∼100 nm did not influence wear resistance of Ni–Cr alloys. Extremely small thickness of implanted layer did not allow to detect the influence of ion beam processing on the wear resistance these alloys.Data presented demonstrate that in the case of Ni-based alloys both homogeneous and heterogeneous microstructures can be obtained by proper heat treatment. Ion implantation of these alloys influences comparatively thin surface layer (1–3 μm), which consists of nitrogen solid solution in γ-phase matrix.In the case of sliding wear structural parameters responsible for dislocations and microcracks behavior control wear resistance of blocks. The energy of dislocation sliding in single-phase Ni–Cr alloys is comparatively low. Friction induces intensive plastic deformation of the surface layer and development of dislocation substructures. These substructures favor relaxation of elastic energy in the area of microcrack mouths, and prevent further development of crack ). As a consequence wear resistance of blocks appeared to be comparatively high.The precipitation of comparatively small amount of γ′-phase (<10 vol.%) in XH77TЮP and XH67BMTЮ alloys does not change the mechanism of surface layer plastic deformation under friction. Precipitates in these alloys are located far apart from each other and do not influence noticeably plastic deformation. Multiple γ′-precipitates cutting by dislocations ) and facilitates microcracks formation. Increased brittleness and small work-hardening of the surface layer in this case (In the case of sliding wear of alloys abrasive effect of hard inclusions (both embedded into the surface and pooled out from the surface during wearing) explains wear increase for blocks containing large γ′-phase precipitates.Even small concentrations of γ′-precipitates decrease wear resistance of XH56BMTЮ blocks in spite of surface hardness growth. The main reason is that in XH56BMTЮ blocks precipitates are subjected to hydrostatic tension favorable for nucleation and development of microcracks.Abrasive wear resistance of XH77TЮP and XH67BMTЮ blocks correlates well with their hardness. In the case of XH56BMTЮ blocks surface hardness increase after aging was accompanied by decrease of wear resistance. The increase of γ′-phase particle size up to ∼100 nm did not influence noticeably abrasive wear resistance.Ion implantation of steels at 620–670 K results in formation of comparatively deep and hard (10–20 μm) modified ε-(Fe, Cr)3N surface layer. Comparatively low toughness of this layer explains poor wear resistance of the surface. High temperature ion implantation (720–770 K) results in precipitation of fine hard CrN inclusions in comparatively ductile matrix of tempered martensite. This structure reveals lower surface hardness, but high sliding wear resistance () demonstrated steels with the hardest surface. Particularly ion beam processing at 770 K results in comparatively low surface hardening and poor wear resistance.Wear resistance of heterogeneous alloys for both sliding and abrasive wear does not correlate well with the surface hardness. Details of microstructure should be taken into account to explain properly wear behavior of blocks.Abrasive wear resistance and surface hardness of XH77TЮP and XH67BMTЮ blocks increase with the growth of precipitates content. On the contrary ageing of XH56BMTЮ blocks results in lower abrasion resistance in spite of surface hardness increase.The maximum sliding wear resistance for XH77TЮP and XH67BMTЮ blocks was observed for homogeneous alloys and alloys with comparatively small concentration of γ′-precipitates. The precipitation of γ′-phase inclusions in XH56BMTЮ blocks intensifies surface wearing.The highest abrasive wear resistance was observed for steels subjected to ion implantation at 670–720 K. Ion implantation at 770 K was the most efficient to provide high sliding wear resistance of steels.On tension–compression yield asymmetry in an extruded Mg–3Al–1Zn alloyThe tension–compression yield asymmetry of an extruded Mg–3Al–1Zn alloy was examined by changing load directions and grain sizes in room-temperature mechanical tests. A criterion for the activation of deformation modes was proposed to analyze the effect of load direction on twinning activity. When the load angle was 45°, the twin area fractions after tension and compression resembled each other, and the corresponding ratio between compression yield stress and tension yield stress equaled 1.02. As the load direction was parallel or perpendicular to the extrusion axis, the yield stress and twinning activity in tension differed obviously from those in compression, resulting in marked tension–compression yield asymmetry. Although grain-coarsening promotes twinning in tension along extrusion axis, it cannot reduce the yield asymmetry. Further, the contributions of twinning to strain during yield deformation were evaluated based on the quantitative statistic of twin area fraction.Owing to the low-asymmetry HCP structure, a variety of deformation textures are produced during the plastic processing process of wrought magnesium alloys, such as the fiber texture in extruded magnesium alloys and the plate texture in rolled magnesium alloys. The presence of deformation texture in magnesium alloys often result in tension–compression yield asymmetry, making the compression yield stress only 1/2 or 3/4 of the tension yield stress along extrusion or rolling direction It has been shown that large numbers of twins occur in magnesium alloy at low strain level, which is quite different from FCC or BCC metals In plastic processing of Mg alloys, resulting texture and grain size are usually coupled together depending on processing parameters. For example, the extrusion ratio always influences texture and grain size simultaneously during the extrusion process. Hence, it is necessary to investigate the effects of extrusion texture and grain size respectively to elucidate the essence of the tension–compression yield asymmetry in extrusion Mg alloys. However, such comprehensive study has not yet reported to date. Since the yield asymmetry produced by texture can exhibit when the extruded Mg alloys are subject to tension–compression deformation along different load directions respect to the extrusion axis, the geometric effect of texture i.e. orientation factor, can be independently investigated by stressing along various load directions regardless of the coupling disturbance of grain size. In this paper, room temperature tension and compression tests were carried out to investigate the effects of load direction and grain size on the tension–compression yield asymmetry of an extruded AZ31 Mg alloy. X-ray diffraction and optical microscopy were employed to quantitatively analyze the texture and microstructure respectively. Further, the role of deformation twinning in the tension–compression yield asymmetry was identified and the contributions of twinning to tension and compression yield deformation were evaluated.The material used in this study is an Mg–3Al–1Zn alloy (AZ31) extruded at 250 °C with an extrusion ratio of 9. shows the extrusion microstructures in cross-section (b), which illustrates twin-free equal-axial grains with an average grain size of 8.9 ± 0.3 μm. The texture of extruded AZ31 bar was measured by X-ray diffraction is shown in (the reflecting surface is normal to the extrusion direction). It is seen that the intensity of basal pole distributes in circles around the extrusion axis. The father from the extrusion center, the intensity becomes greater, exhibiting an obvious ring-like extruded texture with most basal planes oriented nearly parallel to the extrusion direction.Commonly, the occurrence of twinning in wrought magnesium alloys is governed by the coupled effects of texture and grain size. Therefore, it is necessary to separate the two factors to investigate their individual effects on twinning. Since the effect of texture on twinning is mainly realized by the geometry condition which requires a specific angle between c axis and the load direction To examine the effect of load direction on tension–compression yield asymmetry, mechanical test specimens were machined from extruded bars along three angles θ (0°, 45°, 90° respectively) relative to extrusion direction. The tensile specimens were in form of sheet with a gauge length of 10 mm and a thickness of 2 mm. The compression specimens were cylindrical with a diameter of 8 mm and a height of 12 mm. The concrete machining scheme is shown in (Only half of the extruded bar is shown; the machined specimens and extruded bar are displayed with different colors).It has also been shown that the characteristic basal texture of wrought Mg alloys don’t markedly change after anneal at temperature lower than 450 °C shows the uniaxial tension and compression yield stresses and CYS/TYS along three load directions. It is seen that, when the angle θ between load direction and extrusion axis is 0°, the tension yield stress is obviously greater than compression yield stress and the CYS/TYS equals 0.84, showing typical tension–compression yield asymmetry of extruded Mg alloy.When load angle θ increases to 45°, CYS/TYS reaches 1.02; the tension–compression yield asymmetry nearly disappears. When θ continues to increase to 90°, i.e., the load direction is perpendicular to the extrusion direction, the relative magnitude between TYS and CYS reverse and then CYS is greater than TYS, making CYS/TYS increase to 1.28. It is indicated in that, with the increase of θ from 0° to 90°, the CYS/TYS moves from the underside of tension–compression yield symmetry line (CYS/TYS = 1) to the upside of this line, showing remarkable dependence of macro-yield properties on load direction. Considering the fiber basal texture in this extruded AZ31 Mg alloy, the geometry condition for twinning and the polarity of twinning is fundamentally responsible for the tension–compression yield asymmetry.To further clarify the effect of load direction on tension–compression yield asymmetry, we observed the microstructures after tension and compression deformation along three load directions, as shown in . It is shown that the change of twinning activity with θ is quite similar with that of tension and compression yield stresses. When tension along θ |
= 0° (f), twinning barely occurs, whereas twinning occurs considerably when compression along θ |
= 0° (c). When load angle θ |
= 45°, the twined grain fractions after tension and compression are nearly the same. The above results verify the dependence of tension–compression yield asymmetry on the load direction arises from the difference of twinning activity in characteristic basal texture of extruded AZ31 Mg alloy.Additionally, the twin lamellas in any twinned grain are almost parallel to each other and equally-spaced without double-twins, suggesting the twinning mode is simple, as also observed by Proust et al. There are three main deformation modes in Mg alloys that can be activated at room temperature: (0 0 0 1) basal <a> slip, {101¯0} prismatic <a> slip and {101¯2} tensile twinning Since a deformation mode is more readily to be activated with lower CRSS and greater orientation factor, we consider the minimum yield stress of a deformation mode as the criterion for its activation. The yield stress of a deformation mode M along the load direction is represented as:Where σsM, τcM and mM are the yield stress, the CRSS and the orientation factor or Schmid factor of the deformation mode M respectively. According to the studies of Agnew illustrates the change of yield stresses of above-mentioned three deformation modes with the angle ψ between c axis and load direction based on the computation with equation , during which the values are averaged over Bunge angle φ2 for each mode. For ideal fiber basal texture, the relation between θ and ψ is:a, for tension perpendicular to extrusion axis (a), θ |
= 90°, ψ |
= 0°, the yield stress of {101¯2} twinning is much lower than basal slip and prismatic slip, therefore the {101¯2} twinning is first activated. As ψ increases, the yield stress of basal slip declines rapidly to approach that of {101¯2} twinning. When ψ increases to 45°, the yield stress of {101¯2} rises drastically, making the basal slip with the minimum yield stress operate first. When ψ continues to increase to 90°, i.e. the tension axis is parallel to extrusion direction, the {101¯2} twinning cannot be activated due to the geometric condition, while the yield stress of prismatic slip becomes the minimum and dominates the deformation with the resulting macro-yield stress two times as much as that in tension with ψ |
= 0°.b), the variation of yield stresses of basal slip and prismatic slip with ψ is similar to that in tension, but, for the yield stress of {101¯2} twinning, it is not the case. When 0 < |
ψ |
< 46.8°, the {101¯2} twinning cannot be activated due to geometric condition, but the yield stress of basal slip is the minimum and govern the deformation. With the increase of ψ, the yield stress of twinning decreases rapidly, and becomes less than that of basal slip and operates first when ψ is above 78°. This is in agreement with the observed large number of twins in compression along extrusion direction. In addition, the yield stresses of {101¯2} twinning at ψ |
= 45° in tension and compression are nearly equal, which is also in accordance with the observed similar twin area fractions after yield deformation in tension and compression along θ |
= 45°. Therefore, the proposed criterion for the activation of deformation modes can account for the strong dependence of twinning activity and tension–compression yield asymmetry of extruded-textured Mg alloy on load direction.Studies on grain-size dependence of twinning stresses of different crystalline structures have shown that twinning stress has higher grain-size dependence than the stress required for slip activation, i.e. the Hall-Petch slope of twinning kT is greater than the Hall-Petch slope of slip kS that both TYS and CYS increase with the decrease of grain size, showing obvious fine-grain strengthening. Moreover, the changing rate of yield stress differs between different load manners: the decreasing rate of CYS with increasing grain size is faster than that of TYS, which is consistent with the higher Hall-Petch slope of twinning than that of slip. As a result, the CYS/TYS decreases with increasing grain size and therefore the tension–compression yield asymmetry is slightly enhanced. But it should be noted that, the change of this asymmetry with increasing grain size is limited compared with the remarkable effect by changing load direction.To elucidate the mechanism of tension–compression yield asymmetry from a microscopic view, we used metallographic microscope to observe the microstructures after yield deformation of various grain sizes, as shown in It is seen that twinning seldom occurs in tension of AZ31 Mg alloy of various grain sizes along the extrusion direction, especially for small grain size in a. But with the increase of grain size, due to the faster decrease of twinning stress compared to slip, twinning becomes a soft mechanism, leading to an increase of twinned grains and showing the promoting effect of grain coarsening. While in compression, the twinned grain fraction and parallel twin lamellas in a twinned grain significantly increase with increasing grain size, which exhibits the combined promoting effect of grain size and load direction on twinning.It has been mentioned above that, the tension–compression yield asymmetry is closely related to the twin area fraction. Although the increase of grain size helps to twinning activation, the difference between TYS and CYS widens () and the tension–compression yield asymmetry becomes slightly stronger due to the more remarkable frequency of twinning in compression. It is worth noting that, as the grain size decreases, the CYS/TYS gradually approaches the tension–compression asymmetry line (CYS/TYS = 1) as shown in . It can be predicted according to the greater Hall-Petch slope of twinning Another object of this work is to evaluate the importance of twinning during the yield stage, i.e. to determine the contribution of twinning to total strain by quantitatively statistic of twin area fraction after yield deformation. The twin area fractions after tension and compression yield deformation of various grain sizes are shown in It is indicated that, the twin area fraction increases with increasing grain size after both tension and compression, but their increasing rates are quite different: the twin area fraction increases with grain size in tension is much faster than in compression. This shows the combined promoting effects of load direction and grain size on twinning in compression. In contrast, the limited activating effect of grain-coarsening on twinning still cannot counteract the suppressing effect of extrusion basal texture on {101¯2} twinning in tensile deformation.To quantitatively evaluate the role of twinning in the yield deformation of AZ31 Mg alloy, we adopted the following equation given by Brown and Agnew Where ɛtwin is the accommodated strain by twinning along load direction, s is the shear amount of {101¯2} twinning, m¯ is the average orientation factor of {101¯2} twinning system, and v is the twin volume fraction. By orientation distribution function (ODF) test, we determined m¯ of {101¯2} twinning to be 0.25 and replaced the twin volume fraction with twin area fraction approximately. For {101¯2} twinning, s is equal to 0.13 Upon calculation, the contributions of twinning in yield deformation for various grain sizes are illustrated in , which shows the increase of twinning contribution with grain size for both tension and compression. For a fixed grain size, the contribution of twinning in compression is much higher than in tension, and the gap between them continuously increases with grain size. When the grain size is 28.1 ± 2.3 μm, the contribution of twinning in compression reaches 18.8%, almost five times as much as the value 2.9% in tension. The great gap of twinning contribution once again embodies the combined effect of load direction and grain size on twinning in compression. It needs attention that the twin area fraction ratio between compression and tension at various grain sizes is well above the ratio between CYS and TYS, suggesting the complicated relation between twin area fraction and tension–compression yield asymmetry which requires further research to clarify.In this work, we examined the tension–compression yield asymmetry of an extruded AZ31 Mg alloy by varying load directions and grain sizes in tension and compression tests. The contribution of {101¯2} twinning during the yield deformation in tension and compression was evaluated respectively. The results are summarized as follows:With the increase of the angle θ between load direction and extrusion axis from 0° to 90°, CYS/TYS moves from the underside of the symmetry line (CYS/TYS = 1) to the upside of this line, showing significant dependence of tension–compression yield asymmetry on load direction.A criterion based on the minimum yield stress of deformation modes was proposed and used to account for the reason for the load manner dependence of twinning and yield stresses, which proves the tension–compression yield asymmetry originates from the transition for activation mode between {101¯2} twinning and slip.In the grain size range of 8.9–28.1 μm, grain-size coarsening promotes the {101¯2} twinning activation, but cannot reduce the tension–compression yield asymmetry, suggesting the smaller effect of grain size comparing with load direction.With the increase of grain size, the contribution of {101¯2} twinning to the yield strain increases both in tension and compression. For a fixed grain size, both the twin area fraction and the contribution of twinning in compression are much higher than in tension, and the gap between them continuously increases with grain size, showing the combined actions of load direction and grain size on twinning in compression of textured Mg alloy.Trans. Nonferrous Met. Soc. China 22(2012) 1588Ã1593 Grain size effect on cyclic oxidation of (TiB 2 +TiC)/Ni 3 Al composites CAO Guo-jian 1 , XU Hong-yu 2 , ZHENG Zhen-zhu 2 , GENG Lin 2 , Naka Masaaki 3 1. School of Materials Science and Engineering, Harbin University of Science and Technology, Harbin 150040, China; 2. School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, China; 3. Joining and Welding Research Institute, Osaka University, Ibaraki, Osaka 567-0047, Japan Received 18 August 2011; accepted 28 October 2011 Abstract: (TiB 2 +TiC)/Ni 3 Al composites were prepared by mechanical alloying of elemental powders and subsequently spark plasma sintering. Microstructure of (TiB 2 +TiC)/Ni 3 Al composite sintered at 950 °C was finer than that of composite sintered at 1050 °C. The influence of grain size on cyclic oxidation behavior was investigated. Cyclic oxidation results showed that the composite sintered at 950 °C had smaller mass gains than the composite sintered at 1050 °C. XRD and EDS results indicate that finer grain size is beneficial for increasing the oxidation resistance by improving the formation of a continuous TiO 2 outer layer and a continuous Al 2 O 3 inner layer on the surface of the composites sintered at 950 °C. Key words: nickel aluminides; composites; grain refinement; oxidation; mechanical alloying 1 Introduction Intermetallic compound Ni 3 Al is of a great interest for its attractive applications in aerospace and power industries as a high-temperature structural material due to its low density, high strength and good oxidation resistance at elevated temperatures [1,2]. However, the practical use of Ni 3 Al is still severely restricted by its low-temperature brittleness and poor high-temperature creep resistance. One approach to enhance the high-temperature strength and the high-temperature creep resistance is to reinforce the brittle intermetallic matrix with appropriate volume fraction of ceramic phases, which may provide a good combination of high-temperature strength, creep resistance, environmental stability with adequate ambient temperature ductility [3,4]. For application at high temperature, it is essential that mechanical properties of Ni 3 Al were improved without lowering its high-temperature oxidation resistance. Ni 3 Al exhibits an excellent oxidation resistance because of its capability of forming a continuous Al 2 O 3 layer below an outer layer of NiO and an intermediate layer of NiAl 2 O 4 at high temperatures [5]. However, the addition of ceramic particles like TiB 2 and (or) TiC may reduce the oxidation resistance by the formation of discontinuous oxide layers. Some researchers [6Ã8] reported that Ni 3 Al compound with fine microstructure obtained good anti-oxidation ability since increased grain boundaries (GBs) can promote the selective oxidation of Al to form continuous oxide layer in cyclic oxidation of Ni 3 Al. It is reasonable to deduce that grain refinement may be a possible way to optimize the oxidation performance of (TiB 2 +TiC)/Ni 3 Al composites. The effect of grain size on oxidation resistance of Ni 3 Al matrix composites has not been researched quit well. To achieve fine microstructure, spark plasma sintering (SPS) is an effective technique, which fabricates materials by charging a high pulsed electric current directly through powders in a graphite die under externally applied pressure [9Ã11]. In this study, the microstructure and cyclic oxidation of (TiB 2 +TiC)/Ni 3 Al composites were examined. Effect of grain size on cyclic oxidation performance was investigated. 2 Material and methods In this work, 20%(TiB 2 +TiC)/Ni 3 Al composites (volume fraction), in which the volume ratio of TiB 2 to TiC was 1:1, were prepared by using mechanical alloying Foundation item: Project (QC2010110) supported by Heilongjiang Province Natural Science Foundation, China Corresponding author: CAO Gao-jian; Tel: +86-451-86392517; E-mail: [email protected] DOI: 10.1016/S1003-6326(11)61360-5 CAO Guo-jian, et al/Trans. Nonferrous Met. Soc. China 22(2012) 1588Ã1593 1589 method. Starting powders used in this study were elemental Ni (99.9% purity, 3 È�m), Al (99.9% purity, 3 È�m), Ti (99.9% purity, 10 È�m), B (99.7% purity, 1 È�m) and C (99.7% purity, 1 È�m) powders. The elemental powders were ball milled in a vibration ball milling machine equipped with water-cooled chambers for 30 h prior to sintering by SPS. The ball-to-powder mass ratio was 10:1. Ball milling was performed under an Ar gas atmosphere to prevent the oxidation of the powders during the process. After ball milling, the powders were sintered in a DR. SINTER type SPSÃ1050 apparatus (Sumitomo Coal Mining Co. Ltd.). The powders were heated in a vacuum of 10 Pa to 950 °C (or 1050 °C) at a heating rate of 150 °C/min for a holding time of 10 min. During SPS process, a uniaxial pressure of 65 MPa was applied to punches. And then, after a cooling process with a rate of 100Ã40 °C/min, (TiB 2 +TiC)/Ni 3 Al composites were achieved. Samples with dimensions of 10 mm×10 mm×1 mm were cut from the composites by an electro-discharge machine. All samples were metallographically polished, and then cleaned ultrasonically in acetone, and dried in air. The mass and the size of the samples were measured carefully before oxidation exposure. Cyclic oxidation experiments were conducted at 900 °C in air. The samples were withdrawn from furnace every 2 h and cooled to room temperature, weighed before being put back into the furnace. The mass change during exposure was measured by an electron balance with a sensitivity of ±0.01 mg. Microstructure of the composites was observed by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Phases in sintered composites were identified by X-ray diffraction (XRD). The oxidation scales formed at 900 °C for 2 h and 50 h were examined by Ä®Ã2È™ mode XRD with a 3° incident angle (Ä®). Cross-section of the oxidation samples was observed by SEM equipped with an energy-dispersive spectroscope (EDS). Before SEM observation, the composites before and after oxidation were metallographically polished without erosion. For convenient, the 20%(TiB 2 +TiC)/Ni 3 Al composites fabricated at 950 °C and 1050 °C were signed as IC-950 and IC-1050, respectively. The composites synthesized at 950 °C and 1050 °C exhibited relative density of 99.1% and 99.8%, respectively, as measured by the Archimede’s method. 3 Results and discussion 3.1 Microstructure of composites XRD patterns of the 20%(TiB 2 +TiC)/Ni 3 Al composites fabricated by mechanical alloying and SPS at 950 °C and 1050 °C are shown in Figs. 1(a) and (b), respectively. Both composites consist of Ni 3 Al, TiB 2 and TiC. No other phases are found in the XRD patterns. Hardness of the composites was tested by using Vickers-hardness. The hardness values of IC-950 and IC-1050 were 8.5 GPa and 9.1 GPa, respectively. These values are much higher compared with coarse Ni 3 Al compound, which was reported by PAUL to be 3 GPa [12], meaning that ceramic addition and grain refinement can effectively improve the hardness of the composites. Fig. 1 XRD patterns of (TiB 2 +TiC)/Ni 3 Al composites sintered at 950 °C (a) and 1050 °C (b) Grain sizes of phases in the composites could be estimated by Scherrer equation according to peak broadening. However, the estimated grain sizes of different composites are in the same magnitude, which is not coincident with Fig. 2. The reason for this is that the peak broadening is not only due to the reduction of the particle size but also due to the significant residual strain. Fig. 2 Backscattered electron images of (TiB 2 +TiC)/Ni 3 Al composites sintered at 950 °C (a) and 1050 °C (b) CAO Guo-jian, et al/Trans. Nonferrous Met. Soc. China 22(2012) 1588Ã1593 1590 Backscattered electron (BSE) images of both sintered composites are shown in Fig. 2. Gray areas are ceramic phases (TiB 2 or TiC) and bright area is Ni 3 Al phase. It can be seen that although both composites are nearly uniform, the microstructures of IC-1050 is more even than those of IC-950. The microstructure in IC-950 is much finer than that in IC-1050. This can be approved by TEM observation shown in Fig. 3. The spacing between ceramic particles in IC-950 is greatly reduced compared with IC-1050. Bright field TEM images of both composites shown in Fig. 3 show that grains in both composites are essentially equiaxed. The grain sizes of Ni 3 Al and ceramic particles are in the same magnitude in each composite. The average grain sizes in IC-950 and IC-1050 are Ã40 nm and Ã300 nm, respectively. These indicate that lower sintering temperature can effectively stunt grain growth in the composites. Fig. 3 TEM bright-field images of (TiB 2 +TiC)/Ni 3 Al composites sintered at 950 °C (a) and 1050 °C (b) 3.2 Cyclic oxidation of composites Mass changes of both composites cyclically oxidized at 900 °C for 50 h are shown in Fig. 4. Compared with IC-1050, IC-950 shows considerable improvement in oxidation resistance. The excellent oxidation resistance for IC-950 is due to the formation of a dense TiO 2 scale in a short time, and the formation of double continuous oxide layers after longer oxidation. These can be testified by XRD and SEM observations on the oxide scales formed on both composites. Surface morphologies of the oxide scales formed on both composites after 2 h oxidation in air at 900 °C are shown in Fig. 5. The oxide scales formed on IC-950 are much finer and denser than those formed on IC-1050. Pores are obviously seen in the oxide scales formed on Fig. 4 Cyclic mass change curves of (TiB 2 +TiC)/Ni 3 Al composites oxidized in air at 900 °C Fig. 5 SEM images showing surface morphologies of oxide scales formed on (TiB 2 +TiC)/Ni 3 Al composites after 2 h oxidation in air at 900 °C: (a) IC-950; (b) IC-1050 CAO Guo-jian, et al/Trans. Nonferrous Met. Soc. China 22(2012) 1588Ã1593 1591 IC-1050. Dense oxidation scale is beneficial for increasing oxidation resistance. Cross-sectional morphologies of both composites after 50 h oxidation in air at 900 °C are shown in Fig. 6. IC-950 sample formed double sound continuous oxide layers after 50 h exposure. TiO 2 layer with a thickness of around 3 È�m is on the top. Al 2 O 3 layer with a thickness of around 6 È�m is under the TiO 2 layer. Underneath the layers, there is an internal oxidation zone (IOZ) with a thickness of 12 È�m. No continuous oxide layer is found on the surface of IC-1050 sample. Oxidized depth of the IC-1050 sample is around 27.5 È�m, which is much thicker than the oxidation layer on IC-950. Fig. 6 SEM images showing cross-sectional morphologies of oxide scales formed on (TiB 2 +TiC)/Ni 3 Al composites after 50 h oxidation in air at 900 °C: (a) IC-950; (b) IC-1050 The XRD (Fig. 7(a)) and EDS results indicate that the oxide scales on IC-950 mainly consist of TiO 2 (B) and minor TiO 2 (rutile) after 2 h oxidation, while the oxide scales on IC-1050 is in reverse. TiO 2 (B) is a polymorph of TiO 2 . The crystal structure of TiO 2 (B) is Fig. 7 XRD patterns of (TiB 2 +TiC)/Ni 3 Al composites cyclic oxidized at 900 °C for 2 h (a) and 50 h (b) basically the same as that of VO 2 (B) [13,14]. TiO 2 (B) is a metastable polymorph [13]. However, our results indicate that this phase can be present at 900 °C. Previous works [15,16] reported that when particle size decreases to sufficiently low value, the total free energy of rutile becomes higher. They also suggested that the number of potential nucleation sites is the rate-limiting factor to rutile formation. These hypotheses suggest that the TiO 2 (B) were formed and stable in this work owing to their surface or interfacial energy [17]. Meanwhile, the finer microstructure in IC-950 can provide more nucleation sites due to their smaller size of ceramic particles and great density of grain boundaries, which indicates that the ratio of TiO 2 (B) transformation to rutile is smaller in IC-950 than in IC-1050. As a result, there is more TiO 2 (B) formed which is more stable in IC-950 than in IC-1050. Experiments to determine the precise relation between the formation of TiO 2 (B) and oxidation conditions are in progress. For the oxide scales formed on IC-950 after 50 h exposure, the XRD (Fig. 7 (b)) and EDS results indicate that the outer oxide layer mainly consists of TiO 2 (B) and the inner oxide layer mainly consists of Al 2 O 3 . In IOZ, Al 2 O 3 was formed due to the selective oxidation of Al between the oxide layers and the substrate. The oxide scales formed on IC-1050 consist of major TiO 2 (rutile) and a small amount of Al 3 BO 6 and NiAl 2 O 4 . The discontinuous oxide mixtures cannot effectively protect the substrate from the inward diffusion of oxygen [18]. With a similar volume fraction of ceramic particles, IC-950 rather than IC-1050 can form continuous oxide scales. This is related to the different microstructure of the composites, which can be summarized as follows: 1) the spacing between ceramic particles is much smaller in IC-950 than in IC-1050; 2) the grain size of ceramic phases in IC-950 is finer than that in IC-1050; 3) the grain size of Ni 3 Al in IC-950 is finer than that in IC-1050. CAO Guo-jian, et al/Trans. Nonferrous Met. Soc. China 22(2012) 1588Ã1593 1592 With these characteristics, IC-950 exhibits an increased ability to grow TiO 2 (B) and alumina for the following reasons. Both TiC and TiB 2 will be oxidized at the tested temperature obeying the following equations [19]: TiC+2O 2 ĺTiO 2 +CO 2 TiB 2 +5/2O 2 ĺTiO 2 +B 2 O 3 At the onset of oxidation, ceramic particles in both composites nucleate TiO 2 . Taking into account that distribution of ceramic particles in the Ni 3 Al matrix was homogeneous, and supposing that the unit cell for the space distribution of ceramic particles in Ni 3 Al matrix has a simple cubic structure, the spacing between the initially formed TiO 2 nuclei (d) can be roughly expressed by: 3 4ÊŒ 2 3 dr V §· ¨¸ ©¹ where r is the average radius of the ceramic particles and V is the volume fraction of ceramic particles. The calculated d was 30 nm for IC-950 and Ã225 nm for IC-1050, which means that the spacing between TiO 2 nuclei in IC-950 is dramatically reduced compared with IC-1050. This can also be clearly seen in Fig. 3. As a result, TiO 2 formed on IC-950 is finer than that on IC-1050. As mentioned previously, the more TiO 2 nuclei could stabilize the TiO 2 (B) phase. Consequently, there is more TiO 2 (B) in the oxide scales formed on IC-950 due to its finer microstructure than that on IC-1050. Meanwhile, the density of TiO 2 (B) (3.64 g/cm 3 ) is lower than that of rutile (4.13 g/cm 3 ) [13]. This indicates that it is easier for TiO 2 (B) to cover the composite surface due to its larger volume than rutile. As a result, it is easier for IC-950 to form a dense and continuous TiO 2 (B) layer than IC-1050 (Fig. 6). The growth of TiO 2 (B) on IC-950 can perturb the reaction rate by acting as a gaseous diffusion barrier. Reversely, pores can be clearly seen on the surface of IC-1050 after 2 h oxidation, as shown in Fig. 5. This indicates that rutile as major phase formed on IC-1050 cannot effectively cover the composite surface. And the pores act as quick channel for oxygen diffusion and in turn decrease the oxidation resistance of IC-1050. Furthermore, Ni 3 Al is finer-grained in IC-950 and abundant GBs would enhance Al diffusion to the oxidation front and consequently promote the lateral growth of alumina [6Ã8]. Once a continuous Al 2 O 3 layer formed, the growth of TiO 2 and NiO was obstructed. In contrast, during the oxidation of IC-1050, broad spacing between alumina nuclei makes it impossible for them to form a continuous layer. Ni-rich phase, bright area in Fig. 6, was obviously seen in the oxide scales on IC-1050. As a result, the microstructure has a great influence on the oxidation performance of the (TiB 2 +TiC)/Ni 3 Al composites. 4 Conclusions 1) The (TiB 2 +TiC)/Ni 3 Al composite sintered at 950 °C has a finer microstructure than that sintered at 1050 °C. 2) The microstructure of the (TiB 2 +TiC)/Ni 3 Al composites has a great impact on oxidation. 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A novel ultrafine-grained Ni 3 Al with increased cyclic oxidation resistance [J]. Corrosion Science. 2011, 53: 1616Ã1620. ᱊㉦ሎᇌá‡�(TiB 2 +TiC)/Ni 3 Al໡ড়ᴤáᕾ⦃⇻࣪ᗻ㛑ⱘᕅડ Ѓߔڳ 1 ē༘ဳ۾ 2 ēᄂჳᘦ 2 Ä“Ù› ॿ 2 ēઑۯჾੜ 3 1. જᇨⒼ⧚Ꮉ໻ᄺ á´¤á⾥ᄺϢᎹ⿟ᄺ䰶ˈજᇨⒼ 150040Ë— 2. જᇨⒼᎹϮ໻ᄺ á´¤á⾥ᄺϢᎹ⿟ᄺ䰶ˈજᇨⒼ 150001Ë— 3. ໻䯾໻ᄺ ᥹ড়ⷨã�Šá ”ˈ᮹ᴀ໻䯾 567-0047 ᨬ 㽕˖䞛⫼ᬒ⬉ã„�â¾�á„¤âš»ã’§âŠ©à Šà»›(TiB 2 +TiC)/Ni 3 Al ໡ড়ᴤáÇ„à³¼ 950 °C ϟ⚻㒧ⱘ(TiB 2 +TiC)/Ni 3 Al ໡ড়ᴤá ⱘ㒘㒛↨೼ 1050 °Cϟ⚻㒧ⱘ(TiB 2 +TiC)/Ni 3 Al໡ড়ᴤáⱘ㒘㒛᳈㒚ᇣDŽá‡�⚻㒧â�½á‘ºß¿ßšÐŽ 950 °Cà© 1050 °Cⱘ ໡ড়ᴤáà³¼ 900 °Cϟ䖯㸠ᕾ⦃⇻࣪ᗻ㛑⌟䆩DŽ㒧ᵰ㸼ᯢˈ೼ 950 °Cϟ⚻㒧ⱘ໡ড়ᴤáⱘᕾ⦃⇻࣪䋼䞣ᤳ༅㽕ᇣ Ѣ೼ 1050 °Cϟ⚻㒧ⱘ໡ড়ᴤáⱘDŽ᱊㉦㒚ࡽá³�࣪Ѣ೼⇻࣪䖛⿟∛á˜�ⱘä—�ᢽᗻ⇻࣪ˈՓᕫ䖲ã“�ⱘ TiO 2 à© Al 2 O 3 ⇻ ࣪ã�°á•«Ò¹à³¼à»¡à§œá´¤á㸼䴶ᔶ៤ˈҢ㗠ᦤ催໡ড়ᴤáⱘᡫ⇻࣪ᗻ㛑DŽ ݇䬂䆡˖Ni 3 Al˗໡ড়ᴤá˗᱊㉦㒚࣪⇻˗࣪˗ᴎẄড়䞥࣪ (Edited by YANG Hua) prepared by pressureless melt infiltration with porous TiC/Ni 3 Al preforms [J]. Materials and Manufacturing Processes, 2011, 26: 586Ã591. [5] QIN F, ANDEREGG J W, JENKS C J, GLEESON B, SORDELET D J, THIE P A. X-ray photoelectron spectroscopy studies of the early-stage oxidation behavior of (Pt, Ni) 3 Al(111) surfaces in air. [J] Surface Science, 2008, 602: 205Ã215. [6] LIU W, NAKA M. In situ joining of dissimilar nanocrystalline materials by spark plasma sintering [J]. Scripta Materialia 2003, 48: 1225Ã1230. [7] CHOUDRY M S, DOLLAR M, EASTMAN J A. Nanocrystalline NiAlüProcessing, characterization and mechanical properties [J]. Materials Science and Engineering A, 1998, 256: 25Ã33. [8] SHEARWOOD C, FU Y Q, YU L, KHOR K A. Spark plasma sintering of TiNi nano-powder [J]. Scripta Materialia, 2005, 52: 455Ã460. [9] BECHER P F, PLUCKNETT K P. Properties of Ni 3 Al-bonded titanium carbide ceramics [J]. Journal of European Ceramic Society. 1997, 18: 395Ã400. [10] BANFIELD J F, VEBLEN D R, SMITH D J. The identification of naturally occurring TiO 2 (B) by structure determination using high-resolution electron microscopy, image simulation, and distance-least-squares refinement [J]. American Mineralogist, 1991, 76: 343Ã353. [11] BANFIELD J F, VEBLEN D R. Conversion of perovskite to anatase CAO Guo-jian, et al/Trans. Nonferrous Met. Soc. China 22(2012) 1588Ã1593 1593 and TiO 2 (B): A TEM study and the use of fundamental building blocks for understanding relationships among the TiO 2 minerals [J]. American Mineralogist, 1992, 77: 545Ã557. [12] ZHANG H, BANFIELD J F. Thermodynamic analysis of phase stability of nanocrystalline titania [J]. J Mater Chem, 1998, 8: 2073Ã2076. [13] GRIBB A A, BANFIELD J F. Particle size effects on transformation kinetics and phase stability in nanocrystalline TiO 2 [J]. American Mineralogist, 1997, 82: 717Ã728. [14] KOGURE T, UMEZAWA T, KOTANI Y, MATSUDA A, TATSUMISAGO M, MINAMI T. Formation of TiO 2 (B) nanocrystallites in sol-gel-derived SiO 2 -TiO 2 film [J]. J Am Ceram Soc, 1999, 82: 3248Ã3250. [15] BAI C Y, LUO Y J, KOO C H. Improvement of high temperature oxidation and corrosion resistance of superalloy IN-738LC by pack cementation [J]. Surface and Coatings Technology, 2004, 183: 74Ã88. [16] RUDOLPH P, BRZEZINKA K W, WÄSCHE R, KAUTEK W. Physical chemistry of the femtosecond and nanoscecond laser-material interaction with SiC and a SiCÃTiCÃTiB 2 composite cerGrain size effect on cyclic oxidation of (TiB2+TiC)/Ni3Al composites(TiB2+TiC)/Ni3Al composites were prepared by mechanical alloying of elemental powders and subsequently spark plasma sintering. Microstructure of (TiB2+TiC)/Ni3Al composite sintered at 950 °C was finer than that of composite sintered at 1050 °C. The influence of grain size on cyclic oxidation behavior was investigated. Cyclic oxidation results showed that the composite sintered at 950 °C had smaller mass gains than the composite sintered at 1050 °C. XRD and EDS results indicate that finer grain size is beneficial for increasing the oxidation resistance by improving the formation of a continuous TiO2 outer layer and a continuous Al2O3 inner layer on the surface of the composites sintered at 950 °C.Upheaval buckling of surface-laid offshore pipelineOffshore pipelines operating under high pressure and temperature are subjected to upheaval buckling. Pipeline behaviour in upheaval buckling depends on a number of factors including the shape of pipeline imperfection, installation stresses, loading types, seabed sediment behaviour and the flexural stiffness of the pipe. Current method of predicting upheaval buckling is based on simplified shapes of pipeline imperfection developed for idealized seabed conditions. To account for the effect of internal pressure, the pressure load is represented using an equivalent temperature. However, the applicability of these idealizations on the prediction of upheaval buckling has not been well-investigated. In this paper, the three-dimensional finite element modelling technique is used to investigate the applicability of idealized shapes and their effects on the upheaval buckling of pipeline for a seabed condition at offshore Newfoundland in Canada. The finite element model is then used to conduct a parametric study to investigate the effects of installation stress, loading types, seabed parameters and the flexural stiffness of the pipe. Finally, a design chart is developed to determine the optimum height of seabed features to manage pipeline stability against upheaval buckling under different temperature and pressure loadings.Offshore oil and gas development activities have grown rapidly over the past few decades to meet the global energy demand. Pipeline, as the most viable mean for transporting oil and gas, are being used worldwide for transporting offshore oil and gas. However, offshore pipeline design faces a number of engineering challenges, which require proper understanding of the behavior of the pipelines on and in the seabed under various operating conditions. Upheaval buckling was recognized as an important design consideration for offshore pipelines in the early 1980s when a few upheaval buckling incidents occurred in the North Sea Upheaval buckling is a mode of pipeline deformation (upward) that overstresses the pipe wall and may lead to fracture The offshore pipeline transporting oil with high internal pressure and high temperature (HP/HT) experiences high compressive force normal to the pipe cross-section when the pipe is constrained along longitudinal direction. The pipe buckles laterally, vertically or obliquely when this compressive force exceeds the critical buckling force. Theory and laboratory-scale experiments demonstrate that the high internal pressure alone can cause upheaval buckling (Palmar and King 2008). The surrounding soil offers resistance to buckling of the pipeline. The soil resistance is generally greater against lateral buckling than the upheaval buckling In addition to the operating conditions (high pressure and high temperature), the upheaval buckling of subsea pipelines is greatly affected by initial imperfection (out-of-straightness) of the pipelines For the structural stability assessment of pipelines subjected to upheaval buckling, several analytical solutions were developed for critical buckling forces using beam formulations with assumed shapes of localized imperfections Where ΔTp is the temperature change required to result in the same effect as that of an internal pressure of p. The other parameters in the equation such as D, t, E, α and ν correspond to pipe outer diameter, pipe wall thickness, modulus of elasticity, coefficient of thermal expansion and Poisson’s ratio, respectively. Eq. is based on the assumption of fully restrained longitudinal expansion of the pipeline, which is expected for pipelines undergoing upheaval buckling. Longitudinal expansion of offshore pipelines is inhibited by the friction between the pipelines and the seabed soil The objective of this study is to investigate the influence of local seabed conditions on the upheaval buckling of offshore pipelines using three-dimensional (3-D) FE modelling. The initial shape of unburied pipeline laid on imperfect seabed is developed by FE modelling. The developed shape is compared with the existing models for initial imperfection A real seabed profile of offshore Newfoundland in Canada is first considered for this study. Seabed profile and the geotechnical information of the subsea soil along a potential pipeline project were obtained through collaboration with Husky Energy. shows the seabed profile over the length of 350 m from a reference point. A length of 350 m is employed in the analysis based on a preliminary study revealing that the length is sufficient for the analysis of the upheaval buckling. represents profile with respect to the depth of water. also shows elevation of the seabed profile with respect to an arbitrary datum located at 76 m below the water surface. The figure reveals that seabed is irregular and has an upward prop of about 2.2 m height between the distance of 150 m and 250 m. Pipe laid on this seabed will develop an initial shape of imperfection that will be governed by the shape of the seabed, stiffness of the seabed and the flexural rigidity of the pipeline.Several different idealized profiles for subsea pipeline exist in the literature to represent the initial shape of pipeline imperfection. Taylor and Tran Lo |
= wave length of imperfection = |
5.8259(HEIq)14x |
= distance measured from the symmetric point of imperfectionq |
= submerged otherwise self-weight of pipeline per unit lengthE |
= modulus of elasticity of pipe materialFor infilled prop imperfection where the pipeline is perfectly fitting with the seabed, the proposed shape of imperfection is y=H[0.707−0.26176π2x2Lo2+0.293cos(2.86πxLo)]) to develop universal design curve for upheaval buckling.) to account for possible undulations of the seabed. is assumed to result in the infilled prop type imperfection (or basic contact undulation) of the pipeline. The shapes given in Eqs. would thus represent the idealized initial shape, which are investigated here for comparison. However, the initial shape given by Eq. is used to model the pipeline imperfection for the parametric study.In the above idealized imperfection shapes, only Eq. includes a term for flexural rigidity (EI) of the pipeline. The effects of soil stiffness are not incorporated in any of the equations above. A FE modelling technique is used in this research to investigate the effect of pipe flexural rigidity and seabed soil stiffness on upheaval buckling of pipeline.The purpose of the FE analysis presented in this paper is threefold. In step 1, the initial shape of imperfection of pipeline is investigated. A pipe is allowed to fall on a flexible seabed under gravity to obtain the initial shape of imperfection. In step 2, upheaval buckling associated with the increase of temperature and/or internal pressure is investigated. The effects of upheaval buckling on pipeline with an initial shape of imperfection obtained from the FE analysis and those obtained from idealized imperfection shapes are compared. It is to be noted that upheaval buckling prediction using the idealized imperfection shape neglects the residual stress in the pipe resulting from pipeline installation. The effect of residual stress resulting from falling pipeline to the seabed under the gravity load is included in the analysis. In step 3, a remedial measure against upheaval buckling is investigated.A commercially available FE software “Abaqus” is used in this study. The pipeline and seabed is modeled using 8-noded linear brick element with reduced integration and hourglass control option (Abaqus element type C3D8R). The outer diameter (D) and wall thickness (t) of the pipeline are 219.1 mm and 18.3 mm, respectively. A wall thickness of 8 mm is also considered to study the effect of flexural stiffness of pipeline. The sheathing on pipelines is not considered in this study. The seabed is extended sufficiently along the transverse direction to avoid the effect of boundary condition. The surface-to-surface interaction between the pipeline and seabed is used. The seabed soil is generally assumed as an elastic material. The effect of soil plasticity is found to be less significant on the upheaval buckling of the surface laid pipe, as demonstrated in . This is due to fact that the seabed soil does not undergo significant deformation during upheaval buckling of pipeline. plots the buckling amplitude against temperature considering an elastic and an elasto-plastic seabed. Mohr-Coulomb model is used to account for the soil plasticity. Soil parameters are estimated based on the information from a geotechnical investigation report for the site. The soil at the site (very dense gravelly sand) is considered highly permeable and the drained condition is simulated. A study is conducted with a seabed thickness of 2 m and 3 m to investigate the effect of seabed thickness on FE simulation of the pipeline responses. No significant difference on the upheaval buckling is found for the two thicknesses. A thickness of 2 m is therefore used in the FE modelling. The effect of upward seepage from the seabed is not considered. The upward seepage from seabed is not anticipated for the site considered, based on the information in the geotechnical investigation report.The bilinear elastic material model is used for the steel pipe material. However, the effects of bilinear material model is expected to be negligible for the study presented here, since the pipe stress during upheaval buckling is not significantly higher (often less) than the yield strength. The material parameters used in the general analysis are listed in show the values used in the parametric study.Analysis is performed in different steps using automatic time increment in each step. The dynamic implicit method is used for the analysis, which is computationally efficient (less time required) with respect to the dynamic explicit method. The implicit and explicit methods are found to provide similar results Step 1: The pipe is first placed horizontally at the crest level of the upward prop on the seabed (). The pipe is then allowed to deform under gravity load. At this level of analysis, pipe deformation at the crest of the prop is restrained. The nonlinearities in geometry and material are included in the analysis.Step 2: Temperature and/or pressure of the pipe having an initial shape with imperfections at the seabed temperature is increased to investigate upheaval buckling. Applied temperature is thus increased with respect to ambient seabed temperature. For the simulation, the pipe ends are fully restrained. The pipe between the ends is set free to move and/or rotate. The initial shape obtained from FE analysis in step 1 is first investigated. Pipe with idealized imperfections (Eqs. Step 3: In this step, the relation of the prop height on the initiation of upheaval buckling is investigated under different temperature and pressure loads.The result of dynamic analysis of snap-through buckling is often influenced by the time period used in each step compares the shapes of initial imperfection derived using the idealized shapes (Eq. ) and from FE analysis. For the idealized shapes, a wavelength, Lo of 96 m is used for a height of imperfection, H of 2.2 m. The wavelength is assumed from 144.5 m to 240.5 m along the length of pipeline ( indicates that the differences of the initial shapes given by Eqs. are not significant. However, the idealized initial profiles differ from that obtained from FE analysis. The FE analysis accounts for the real shape of the seabed. The seabed profile is also included in the figure. In , the shapes from the FE analysis match the shape of the seabed except around the prop. The pipe appears to be penetrated/embedded into the flexible seabed under the gravity load. The seabed embedment could not be simulated using 2D analysis shows the effects of seabed imperfection on the pipe upheaval buckling due to temperature load. The results obtained based on an initial shape obtained from FE analysis and the one given by Eq. (idealized shape) are compared in the figure. The idealized shape was obtained for an imperfection height of 2.20 m and wavelength of 96 m. The maximum longitudinal stress and the maximum deflection at the crest of imperfection are plotted in . The compressive stress is plotted along the positive y-axis. (a), pipe deflections against the rise of temperature are not significant up to the temperature required to initiate upheaval buckling (critical buckling temperature). Beyond the critical buckling temperature, pipe deflection increases at a higher rate. (a) indicates that the critical buckling temperature calculated based on simplified idealization of the initial shape (Eq. ) is around 8 °C while the temperature based the initial shape obtained from FE analysis is around 25 °C. The idealized profile thus provides a much conservative estimate of the buckling initiation temperature. At very high temperature (beyond 75 °C), the two curves for pipe deflections become close to each other, indicating that the pipe deformation is independent on the initial shape beyond that temperature. However, the simplified idealization of the initial shape results in the calculation of a significantly high longitudinal stress in the pipe wall. The longitudinal stress calculated based on the idealized shape is consistently higher in (a) than the stress calculated using the FE based initial shape.(a), no snap-through instability is observed, which is attributed to the high amplitude of initial imperfection (i.e., 2.2 m) for the pipes investigated. Run et al. (b) shows the vertical deflection along the length of pipeline at a temperature of 35 °C, which is greater than the critical buckling temperature (8 °C or 25 °C). Due to the presence of local undulation on the seabed, the shape of the pipeline profile obtained from FE analysis is not symmetric about the crest. As a result, the location of maximum deflection varies around the crest and is not always at the crest of the initial shape. The decrease in the longitudinal stress at the crest in (a) with temperature up to the critical buckling temperature (i.e., 25 °C) is attributed to the variation of the location of the maximum deflection. The longitudinal stress increases consistently with temperature beyond critical buckling temperature when the effect of the local seabed feature is insignificant. For analysis with an idealized initial shape, the profile is assumed to be symmetric about the crest. Therefore, the maximum deflection is always at the crest of the initial profile and the longitudinal stress increases consistently with temperature.The above comparison implies that the initial shape of pipeline influences upheaval buckling behavior of pipeline. The simplified idealization of the initial profile is found to provide conservative (higher) estimations of critical buckling temperature and pipe wall stress.During installation of subsea pipeline on undulated seabed or uneven trenched bottom, stresses develop in the pipe wall. The stress is defined herein as installation stress or initial stress. The effect of the installation stress on the upheaval buckling behavior is often neglected when the pipeline is assumed to have an initial shape given in the simplified equation (i.e., Eq. The initial stress condition is simulated here using FE analysis to investigate the effects. In order to account for the initial stress condition, an idealized seabed is first developed using Eq. . The pipe is then laid on the seabed under gravity, as discussed in Section . The resulting initial shape of the pipeline was found to match with the shape of the idealized seabed. Temperature and/or pressure load are then applied to the pipe. To model a pipe without installation stress (i.e. initially unstressed), the seabed and pipe are modelled according to the shape given by Eq. . The pipeline is then subjected to the loads. shows the maximum deflection of the pipe due to temperature load or pressure load. The imperfection height of 2.2 m is considered to develop the idealized seabed. The initial non-zero (negative) deflection in is the penetration of the pipeline into the seabed under the gravity load. It can be seen in the figure that the critical buckling temperature and the critical buckling pressure are influenced by the initial stress conditions. The critical buckling temperatures with initially unstressed and initially stressed conditions are 7.25 °C and 10.25 °C, respectively. The critical buckling pressures of the pipe are 19.5 MPa and 27.0 MPa, respectively. The critical buckling temperature and pressure are thus underestimated for the pipes with no initial stress. For the pipe considered, the critical buckling temperature and the pressure are underestimated by 41% and 38%, respectively. Neglecting of the installation stress would thus provide conservative estimation of the buckling behavior.A parametric study is conducted to identify the effects of flexural stiffness of the pipe, soil conditions and the loading types on the upheaval buckling of the pipelines. The parametric study is conducted for an idealized seabed profile that is expected to provide an initial shape of the pipe recommended in the design codes (i.e., Eq. ). Pipe laying on the seabed is simulated to account for the installation stress on the pipe wall, as discussed above. An idealized profile with an imperfection height of 1 m and wavelength of 96 m is considered.Two different wall thicknesses (i.e., 8 mm and 18.3 mm) for a 219.1 mm diameter pipe are considered to investigate the effects of the flexural stiffness of the pipeline. Moments of inertia for the pipes are calculated to be 29.60 × 106 |
mm4 and 58.67 × 106 |
mm4, respectively. shows the maximum deflection of the pipeline (at the crest of the imperfection) due to temperature and pressure loads. As seen in (a), the upheaval buckling behavior under temperature load is not affected by the pipe stiffness for the two pipe thicknesses considered. However, under the loading of internal pressure, the critical buckling pressure is higher for the pipe with higher flexural stiffness as shown in (b). Due to the increase of the wall thickness from 8 mm to 18.3 mm (increase of the flexural stiffness from 29.60 × 106 |
mm4 to 58.67 × 106 |
mm4), the critical buckling pressure is increased from 16 MPa to 42.5 MPa (about 166%).The effects of stiffness and strength parameters of subsea soil on upheaval buckling of pipeline are investigated using FE modelling. A seabed condition consisting of granular soil is considered. The granular soil condition is encountered at the seabed of offshore Newfoundland. Analysis was conducted with typical lower bound and upper bound values of the friction coefficients between the pipeline and the soil (after, Hobbs plots the maximum pipe deflections with pipe temperature for a lower bound and an upper bound values of soil modulus, Es (i.e., 10 MPa and 300 MPa) and the interface friction, f (0.2 and 0.8) for granular soil. Two idealized imperfections obtained using Eq. with imperfection height (H) of 1000 mm and 400 mm and a wavelength of 96 m are examined. In , pipe deflection shows a sudden jump at the critical buckling temperature (around 35 °C) for the imperfection height of 400 mm, while the rate of deflection suddenly increase at the critical temperature (around 15 °C) for the imperfection height of 1000 mm. As discussed earlier, for the pipe with high imperfection height (i.e., 1000 mm), no snap through buckling occurs. As a result, the sudden jump is not observed. For the pipe with 400 mm of imperfection height, a snap through buckling is expected. The snap through buckling process involves transformation of the strain energy of the system into the kinetic energy that stabilized after a short period of fluctuation reveals that the critical buckling temperature is not affected significantly by the seabed soil conditions for the surface laid pipeline considered. The critical buckling temperature appears to depend predominantly on the height of imperfection.Upheaval buckling of offshore pipelines is caused by the high pressure and high temperature during operation. The current practice of accounting for the effect of the internal pressure is to apply an equivalent temperature that is calculated from the pressure using Eq. . However, the study presented above reveals that the behavior of the pipeline could be different under the temperature and the pressure loads. As a result, the approach of using equivalent temperature for the pressure load may not always be applicable. The effects of the temperature and pressure loads are studied here with applications of the temperature and the internal pressure to the pipe using 3D FE analysis. To date, the effect of high pressure on upheaval buckling has not been studied with direct application of internal pressure.The validity of the assumption of representing a pressure load by an equivalent temperature load is first examined. A pipe subjected to 35 °C of temperature and 20 MPa of internal pressure is considered. The pipe is subjected to an imperfection (Eq. ) with a height of 400 mm and wavelength of 96 m. Analyses are performed with application of each of the loads independently and with representation of the pressure by an equivalent temperature (Eq. ). The equivalent temperature corresponding to a pressure of 20 MPa is calculated to be 10 °C that results in a total temperature load of 45 °C for the pipe. Analysis is also performed with back-representation of the temperature by an equivalent internal pressure using Eq. . The total equivalent pressure of the pipe is calculated to be 91 MPa. The results of analyses with the three approaches of idealization are compared in . As shown in the figure, the maximum pipe deflections calculated using the different approaches of the idealization are different. The maximum deflection calculated using equivalent temperature is higher than the deflection calculated using actual loading condition with application of temperature and internal pressure. Idealization of the pressure load by an equivalent temperature would thus provide a conservative estimate of the pipe behavior. On the other hand, idealization of temperature load by an equivalent pressure would provide unconsevative estimation of the pipe deflection. The calculated maximum pipe deflection is significantly less when using the equivalent pressure (The comparison of results from different approaches of modelling the temperature and pressure loads reveals that idealization of the pressure load using equivalent temperature and vice versa may not be applicable for analysis of upheaval buckling.Apparently, no buckling is expected with an equivalent internal pressure of 91 MPa with the level of imperfection considered (). However, for a higher level of imperfection, a pressure load may also initiate upheaval buckling. shows the results of analysis conducted with different heights (amplitudes) of initial imperfection under the temperature and pressure loads. In , “T” and “P” in the parentheses correspond to the temperature and pressure loads, respectively. The deflection amplitude of the pipe is plotted against the temperature and the pressure in the figure. The figure reveals that only internal pressure can cause upheaval buckling if the amplitude of the imperfection is high. The rate of pipe deflection suddenly increases at the pressures of 25 MPa, 45 MPa, 65 MPa and 90 MPa for the imperfection height of 2200 mm, 1000 mm, 600 mm and 400 mm, respectively. Thus, the critical buckling pressure increases with the decrease of the height of the imperfection (dashed line). For an imperfection of 200 mm height, the critical buckling pressure is not reached within an internal pressure of 100 MPa. As expected, the critical buckling temperature also increases with the decrease of the height of the imperfection (dash-dot line). The height of the imperfection can therefore be controlled to increase the critical buckling temperature and pressure in order to minimize the upheaval buckling, if the method is economically viable. In the following section, a method is proposed to optimize the height of imperfection as a measure to control upheaval buckling.Seabed profile along the route of the pipeline may include features (i.e., imperfections) of different heights that influence the shape of the initial imperfection of the pipeline. As demonstrated in the above study, the shape of the imperfection significantly affects the behavior of pipe subjected to upheaval buckling. The critical buckling temperatures and/or pressures would be lower for the pipe traversing over higher features. The pipelines traversing higher features are therefore prone to upheaval buckling at lower temperatures and/or internal pressures. In this regard, the height of the features or imperfections could be reduced through excavation to increase the safety of the pipe to a manageable level. The design height of the imperfection would depend on the operating temperature and pressure of the pipeline. Pipelines under different operating conditions are investigated using 3D FE analysis to develop a design chart for selection of the optimum imperfection height based on the anticipated operating condition of the pipeline. The critical buckling temperatures are calculated for different operating pressures of the pipeline under three different imperfection geometries. A pipe with a diameter of 219.1 mm and wall thickness of 18.3 mm is considered for this study. The geometry of the imperfection is expressed as the ratio of height (h) and wavelength (L) of the pipeline imperfection. presents the design chart relating the critical buckling temperature with the operating pressure for the pipeline with four different conditions of imperfection. It reveals that the critical buckling temperature decreases linearly with the operating pressure of the pipeline for each of the imperfections. With reduction of h/L, the critical buckling temperature is increased. The design chart in could be used to determine the optimum imperfection height to manage pipeline stability against upheaval buckling.The subsea pipeline operated at HP/HT is subjected to upheaval buckling. The upheaval buckling is influenced by several factors including initial imperfection, soil properties, loading type and pipe stiffness. 3D FE models are developed using ABAQUS software to study the effects of these factors on the buckling behavior of subsea pipelines. A real seabed profile of offshore Newfoundland in Canada is examined. The idealized shape of imperfections are also considered for comparison. A method is proposed to determine the optimum height of imperfection for different load combinations. Based on the analysis, the following conclusions can be drawn:The initial shape of pipeline subjected to gravity load depends on the shape of seabed profile and differs from the idealized shapes recommended in the design codes/literature. The initial shape should be properly modelled to predict the pipeline behavior in upheaval buckling.For the pipeline and seabed condition considered, the critical buckling temperature is underestimated by the idealized shape of imperfection. The installation stress on the pipe is also found to influence the critical buckling loads on the pipelines. For the pipe with no installation stress, the critical buckling temperature and the critical buckling pressure are underestimated.The effects of soil stiffness and pipe-soil interface friction on the upheaval buckling behavior of the surface-laid pipe are not significant. The flexural stiffness of the pipeline has less effect on the critical buckling temperature and has significant effect on the critical buckling pressure. Critical buckling temperature and critical buckling pressure decreases with the increase of the imperfection height.Idealization of the pressure load using equivalent temperature and vice versa is not always applicable for the analysis of upheaval buckling of pipeline. The temperature-pressure interaction diagram can be developed for the assessment of critical loads under the effect of combined loads. A design chart using the interaction diagram is developed to determine the optimum height of a seabed feature to control upheaval buckling.A crosslinking strategy to make neutral polysaccharide nanofibers robust and biocompatible: With konjac glucomannan as an exampleNeutral polysaccharides such as konjac glucomannan, starch and pullulan are abundant in nature and have unique property. Their nanofibers hold great potential for biomedicine, which however, are seldom applied in the field due to the lack of crosslinking method. In this work, we report a periodate oxidation - adipic acid dihydrazide (ADH) crosslinking strategy to prepare robust and biocompatible neutral polysaccharide nanofibers. Neutral polysaccharides with adjacent dihydroxyl groups are firstly partially oxidized with periodate to give dialdehyde polysaccharides, and their electrospun nanofibers are then crosslinked with ADH to form dihydrazone crosslinkers. The resulting crosslinked neutral polysaccharide nanofibers exhibit high water resistance and excellent mechanical properties because of the high reactivity of Schiff base crosslinking reaction. Moreover, the crosslinked neutral polysaccharide nanofibers show good biocompatibility due to the low toxicity of ADH. These robust and biocompatible neutral polysaccharide nanofibers are expected to seek extensive applications in a variety of biomedical fields.Polysaccharides represent an important class of biomedical materials attributing to their biocompatibility, biodegradability as well as potential bioactivity (). Among the various types of polysaccharides, neutral polysaccharides are of richest resources. For example, cellulose and starch are the two most abundant polysaccharides in nature (). Moreover, since neutral polysaccharides are free of charges, they interact weakly with bioentities including proteins, DNAs, or cells. This unique property makes them ideal for a variety of specific biomedical applications such as drug delivery, antifouling, cell encapsulation, etc (). Nanofibrous structure fabricated by electrospinning technique possesses the properties of high specific area, high porosity, and mimicking natural extracellular matrix’s structure. These features benefit many biomedical applications including wound healing, tissue engineering, and drug delivery (However, despite of the abundancy and unique property of neutral polysaccharides, there are very few biomedical applications of neutral polysaccharide nanofibers till now. This is due to the lack of crosslinking method for neutral polysaccharide nanofibers. The reconstituted polysaccharide nanofibers dissolve quickly upon contacting with biological fluids because polysaccharides are water soluble. Crosslinking is thus necessary to improve their water resistance and mechanical strength (). The general approach to crosslink neutral polysaccharide nanofibers was to use glutaraldehyde (). This approach suffers from the low crosslinking reactivity (acetalization reaction) () and the high toxicity of glutaraldehyde (), which lead to poor water resistance, poor mechanical strength, and poor biocompatibility of the resulted nanofibers. Therefore, in order to pave the biomedical applications of neutral polysaccharide nanofibers, it is important to develop a new crosslinking strategy for neutral polysaccharide nanofibers with high efficiency and biocompatibility.Firstly oxidizing polysaccharides into aldehyde polysaccharides with periodate and then crosslinking the oxidized polysaccharides with multi-amino compounds to form Schiff base crosslinkers is a versatile method for the preparation of polysaccharide hydrogels (). Previously we crosslinked the nanofibers of an ionic polysaccharide, pectin, with a periodate oxidation - adipic acid dihydrazide crosslinking strategy based on similar principles, which showed good efficiency and biocompatibility (). In this manuscript, we use this periodate oxidation - adipic acid dihydrazide crosslinking strategy to prepare robust and biocompatible neutral polysaccharide nanofibers. As shown in , neutral polysaccharides with adjacent dihydroxyl groups in saccharide residues are firstly partially oxidized with periodate to give dialdehyde polysaccharides. The electrospun nanofibers of dialdehyde polysaccharides are then crosslinked with adipic acid dihydrazide (ADH) to form dihydrazone crosslinkers between the polysaccharide chains. The resulting crosslinked neutral polysaccharide nanofibers exhibit high water resistance and excellent mechanical properties because of the high reactivity of the Schiff base reaction between aldehyde and hydrazide groups (). Moreover, the crosslinked neutral polysaccharide nanofibers show good biocompatibility due to the low toxicity of ADH (). This work not only greatly paves the biomedical application of neutral polysaccharides, but also provides a new class of biomedical materials.Konjac glucomannan (KGM) (≥25 Pa s at 1% solution, Hubei Yizhi Konjac Biotechnology Co. Ltd, China), potato starch (Sigma-Aldrich, China), or pullulan (Sigma-Aldrich, China) was dissolved in water and mixed with NaIO4 (Alladdin, China) solution. The molar ratios between NaIO4 to saccharide units in polysaccharides were set at 10%–60% for KGM and 30% for starch and pullulan. After being stirred in dark for 16 h at ambient temperature (25 °C), the solutions were dialyzed against a large volume of water and then lyophilized. The obtained dialdehyde polysaccharides were then dissolved homogeneously with polyethylene oxide (PEO, Mν = 1000 kDa, Aladdin, China), Triton X-100 and dimethyl sulfoxide (DMSO) in water to reach polymer concentration of 3% for KGM and 10% for starch and pullulan, a polysaccharide/PEO mass ratio of 80:20, a Triton X-100 concentration of 1.0 wt.%, and a DMSO concentration of 5.0 wt.%, respectively. The solutions were electrospun under a spinneret diameter of 0.6 mm, a flow rate of 300 μL/h and a positive high voltage of 5–10 kV, and nanofibers were collected at a distance of 20 cm from the spinneret. The electrospun dialdehyde polysaccharide nanofibers (20 mg) were crosslinked with excess amount of ADH by being soaked in ADH solution (50 mmol/L, 20 mL) in ethanol/water mixture solvent (80/20 v/v) for 8 h at ambient temperature and under moderate shaking (100 rpm). The crosslinked nanofibers were washed with plenty of deionized water, ethanol and chloroform sequentially, and vacuum dried.FTIR spectra were collected with a FTIR spectrometer (iS10, Thermo Scientific Nicolet) equipped with a photomultiplier detector. The samples were homogeneously mixed with patassium bromide at a weight ratio of 1:100 and pressed into tablets. Spectra were obtained by recording 48 scans between 2000 and 800 cm−1 with a resolution of 4 cm−1. Scanning electron microscope (SEM) images were collected with a SEM (XL-30 ESEM FEG, Micro FEI Philips) at an acceleration voltage of 20 kV. The samples were sputter coated with a thin layer of gold before measurements. Young's moduli of the nanofiber membranes were determined with a universal testing machine (Instron 1121). The membranes with a thickness of approximately 0.05 mm were cut into a dimension of 6 mm × 20 mm, wet with simulated body fluid (SBF) and drawn at a rate of 1 mm/min to obtain stress-strain curves. Young's moduli were calculated from the stress-strain curves. Three parallel samples were tested. To examine the swelling properties of the nanofibers, the nanofibers (M1, ≈5 mg) were immersed in SBF (2 mL) at 37 C for 24 h, then centrifuged at 1200 rpm for 15 min and weighed (M2). The swelling ratio of the nanofibers is calculated as (M2−M1)/M1. Three parallel samples were tested. To examine the water resistance of the nanofibers, the nanofibers (10 mg) were incubated in SBF (20 mL) at 37 °C. At desired time points, the nanofibers were taken out, washed with plenty of deionized water, ethanol and chloroform sequentially, and vacuum dried. The mass of the nanofibers were weighed with a balance and the morphologies of the nanofibers were observed with SEM. Three parallel samples were tested.L929 mouse fibroblast cells (ATCC, US) were seeded in a 96-well plate at a density of 3000 cells/well and cultured in Dulbecco’s modified Eagle’s medium with 10% fetal calf serum for 24 h at 37 °C in a humidified atmosphere containing 5% CO2. Nanofibers (20 mg) were soaked in cell medium (2 mL) for 24 h at 37 °C and the leachates were then added to cell wells (n = 5). After 24 h’ culture at 37 °C, cell viabilities were tested with MTT assay. To culture cells on nanofiber membranes, the membranes were tiled into 24-well plates and L929 cells were seeded on the membranes at a density of 10,000 cells/well. After being cultured at 37 °C for 1, 3, and 7 days, fluorescent imaging of live/dead cells on membranes were performed after staining cells with Calcein AM/Propidium iodide (PI) double stain kit (Keygen Biotech., China) and SEM imaging of cells were carried out after fixing the cells with glutaraldehyde.We selected konjac glucomannan (KGM), a typical neutral polysaccharide mainly composed of β-1,4-linked ), to test the feasibility of the periodate oxidation - ADH crosslinking strategy.KGM could be readily oxidized upon incubating with sodium periodate in acidic aqueous solution (pH 4) and at ambient temperature for hours. The periodate oxidation afforded aldehyde groups in oxidized KGM, which was proved by FTIR characterization (a) and hydroxylamine hydrochloride titration (Supporting Information, Experimental Section and Fig. S1). As shown in a, the peak at 1730 cm−1 in the FTIR spectrum of pristine KGM is assigned to the low amount of acetyl groups in KGM (). In the spectrum of the 30% oxidized KGM (OKGM30), this peak become much stronger because of the generation of aldehyde groups by oxidation. The degree of oxidation was tunable by varying the feed ratio of sodium periodate and pristine KGM (Supporting Information, Fig. S1). The oxidized KGM could be readily electrospun into nanofibers with low amount of aiding reagents (see Experimental Section) (b). These oxidized KGM nanofibers could be crosslinked by immersing in ADH aqueous solution because the aldehyde groups of oxidized KGM react with the hydrazide groups of ADH to form dihydrazone crosslinkers. The crosslinking reaction was verified by the diminishing of the peak at 1730 cm−1 (consumption of aldehyde groups) and the appearance of the peaks at 1670 and 1540 cm−1 (formation of hydrazone linkers) in the FTIR spectrum of ADH-crosslinked OKGM30 nanofibers (OKGM30-ADH) (For comparison, we have also prepared crosslinked KGM fibers by putting pristine electrospun KGM nanofibers in glutaraldehyde (GA) vapors. The preparation process and the verification of crosslinking are provided in the Supporting Information (Experimental Section and Fig. S2). To investigate the effect of oxidation degree on the properties of ADH crosslinked OKGM nanofibers, we prepared OKGM with 10%, 20% and 30% oxidation degrees by varying the feed ratio of sodium periodate and pristine KGM (Supporting Information, Fig. S1). The resulting crosslinked nanofibers are named as OKGM10-ADH, OKGM20-ADH and OKGM30-ADH, respectively.The periodate oxidation - ADH crosslinking strategy could retain nanofibrous morphology for KGM nanofibers, while GA crosslinking strategy could not. As shown in b, after crosslinking by immersing in aqueous ADH solution, OKGM10-ADH, OKGM20-ADH and OKGM30-ADH all show well-defined nanofibrous morphology, which is similar to the as-spun OKGM nanofibers. In contrast, after the crosslinking with GA vapor, the KGM-GA nanofibers fused with each other, which caused the decrease of the porosity of the nanofiber mat significantly. The original nanofibrous morphology of the nanofibers is undistinguishable in the area where fusion is serious. The different capabilities to retain nanofibrous morphology of the two crosslinking strategies are probably attributed to the different activities of Schiff base reaction and acetalization reaction. During the crosslinking process, the KGM/OKGM nanofibers are exposed to aqueous conditions. Water molecules diffuse into nanofibers, leading to the swelling/dissolution of KGM macromolecular chains and resulting in the loss of nanofibrous structure. At the same time, crosslinking reaction leads to the linking of KGM/OKGM macromolecular chains, preventing their dissolution and fixing the nanofibrous structures. Therefore, the retaining of nanofibrous structure is dependent on the rate of the crosslinking reaction. The crosslinking reaction between GA and KGM is an acetalization reaction, while that between ADH and OKGM is a Schiff base reaction. As we know, acetalization is a thermodynamically unfavorable reaction, and it does not occur spontaneously. Although catalysts (usually acids) can activate acetalization, the reaction rate is still slow and the efficiency is low (). In comparison, Schiff base reaction occurs spontaneously without the needs of any catalysts and the reaction proceeds very fast and efficiently (). Therefore, the periodate oxidation - ADH crosslinking strategy could better retain the structure of nanofibers than GA crosslinking strategy.The mechanical strength of OKGM-ADH nanofibers can be dramatically higher than that of KGM-GA nanofibers. As shown in a, the Young’s modulus of KGM-GA nanofiber membrane is 2.7 MPa. The Young’s moduli of OKGM20-ADH and OKGM30-ADH nanofiber membranes are 5.5 and 13.1 MPa, respectively. Generally, for porous membranes, the higher the porosity is, the lower the mechanical strength is. Here, although the porosity of OKGM20-ADH and OKGM30-ADH nanofiber membranes is obviously higher than KGM-GA nanofiber membrane (b), the mechanical strength of the former is much higher than that of the latter. This result indicates higher crosslinking density in OKGM-ADH nanofibers than in KGM-GA nanofibers. We should note that the theoretical crosslinking density in OKGM-ADH nanofibers is much lower than that in KGM-GA nanofibers. In OKGM-ADH nanofibers, as each pair of aldehyde groups in each oxidized saccharide residue can react with two ADH molecules and form two dihydrazone crosslinkers, the theoretical crosslinking density of OKGM10-ADH, OKGM20-ADH and OKGM30-ADH nanofibers may reach 20%, 40% and 60%, respectively. By contrast, in KGM-GA nanofibers, each pair of adjacent dihydroxyl groups in each saccharide residue can react with one GA molecule and form one acetal crosslinker, so the theoretical crosslinking density can reach 100%. The actual crosslinking densities of OKGM-ADH nanofibers were determined based on 2,4,6-trinitrobenzene sulfonic acid assay (Table S1). For OKGM10-ADH nanofibers, 50.5% of the aldehyde groups in dialdehyde KGM reacted with ADH and formed dihydrazone crosslinkers during crosslinking reaction, generating a crosslinking density of 10.2%. For OKGM20-ADH and OKGM30-ADH nanofibers, 84.9 and 80.4% of the aldehyde groups in dialdehyde KGM reacted with ADH and formed dihydrazone crosslinkers, generating the crosslinking density of 34.0% and 48.2%, respectively. These results demonstrate that the Schiff base crosslinking reaction between dialdehyde KGM and ADH has high efficiency, especially in the case of high KGM oxidation degree. As the Young’s modulus of KGM-GA nanofibers is only comparable to that of OKGM10-ADH nanofibers, the acetalization crosslinking efficiency between pristine KGM and GA is probably very low. It is likely that lots of alcohol groups in KGM did not react with GA, or, although some alcohol groups did react with the aldehyde groups at one end of GA, the other end of the GA did not react with other alcohol groups in KGM (Supporting Information, Fig. S2), so KGM was not actually crosslinked at these sites.OKGM-ADH nanofibers can swell to a much higher extent than KGM-GA nanofibers (b). KGM-GA nanofibers had poor stability in SBF, probably due to its low crosslinking density as discussed above. They lost 66% of their initial dry mass after one day’s soaking in SBF. Hence, the determined swelling ratio is thus very low (0.6). In comparison, all OKGM-ADH nanofibers had good stability in SBF. They did not lose dry mass significantly after one day’s soaking in SBF and swelled 4.6–5.8 times. Higher swelling ratio is observed at higher KGM oxidation degree. It is possible that the dihydrazone domains in the crosslinked KGM nanofibers can bond water through hydrogen bonding interaction. OKGM-ADH nanofibers with high KGM oxidation degree own more dihydrazone domains (Table S1), thus can swell to a higher extent in SBF. The high swelling ratios of OKGM-ADH nanofibers indicate that they are highly hydrophilic and absorbent, and may be good as dressings for wound healing.The water resistance of OKGM-ADH nanofibers is dramatically higher than that of KGM-GA nanofibers. As shown in , upon incubation in simulated body fluid (SBF) at 37 °C, KGM-GA nanofibers lost nanofibrous structure completely and 64% of its initial mass in 1 day, and degraded totally in 1 week. In contrast, all the OKGM-ADH nanofibers retained the nanofibrous structure in SBF over 1 week. With the increased degree of oxidation, the degradation rates of OKGM-ADH nanofibers decreased. The OKGM30-ADH nanofibers could still retain approximately 80% of their initial mass even after being incubated in SBF for 4 weeks. The water resistance of OKGM-ADH nanofibers are also attributed to their high crosslinking density originated from the high activity and efficiency of Schiff base reaction. These results also indicate that the OKGM-ADH nanofibers are degradable. The degradation mechanism may involve scission of the KGM main chain () and hydrolysis of the hydrazone crosslinkers (). The degradability of the OKGM-ADH nanofibers is beneficial for their biomedical applications.The biocompatibility of OKGM-ADH nanofibers is also better than that of the KGM-GA nanofibers. a shows the viability of L929 mouse fibroblast cells cultured in medium containing the leachates of crosslinked KGM nanofibers for 24 h. Cells cultured in blank medium were used as positive controls. For KGM-GA nanofibers, the cell viability of the nanofiber leachates was only 80% at low concentration (0.31 and 0.63 mg/mL), and it dropped to 70% or lower at higher concentration (1.25–5 mg/mL), indicating their moderate toxicity. For all the OKGM-ADH nanofibers, the cell viability kept at around 90% at all tested concentrations, suggesting good biocompatibility of these nanofibers. The biocompatibility of the OKGM-ADH nanofibers is further proved by the fact that they can support the growth of cells on the surface of the nanofiber membranes (b). Cells could survive, attach, and proliferate on the surface of these OKGM-ADH nanofiber membranes. Cells proliferated fastest on nanofiber membrane of highest degree of oxidation (OKGM30-ADH). We should also notice that although cells could grow on OKGM-ADH nanofiber membranes, their attached number, spreading extent and proliferating rate were not high. And, the cells did not infiltrate into the membranes. These results suggest that the OKGM-ADH nanofiber membranes may fit more for wound healing applications, e.g., as wound dressings or anti-adhesion membranes. For tissue engineering applications, further modifications to enhance cell adhesion and infiltration are probably needed.The better biocompatibility of OKGM-ADH nanofibers compared to KGM-GA nanofibers is mainly attributed to the much better biocompatibility of ADH than GA. GA itself is highly toxic () while ADH is of low toxicity and widely used in bioconjugating and crosslinking chemistry (). In the crosslinking process, the crosslinking reagents must enter the inside of the nanofibers and the residual unreacted crosslinking reagents are difficult to be completely removed after crosslinking. Therefore, the toxicity of the crosslinking reagents greatly affects the biocompatibility of the nanofibers. The low toxicity of ADH leads to the great biocompatibility of polysaccharide nanofibers prepared by the periodate oxidation - ADH crosslinking strategy.The periodate oxidation - ADH crosslinking strategy is generally applicable to nanofibers of many other neutral polysaccharides besides KGM. We choose another two neutral polysaccharides, starch and pullulan () to test the versatility of the crosslinking strategy. As shown in , crosslinked starch and pullulan nanofibers prepared with the strategy showed well-defined nanofibrous morphology and good water resistance. They retained nanofibrous morphology and over 93% mass after being incubated in SBF for a week. Moreover, they both showed excellent biocompatibility, which is supported by the cell viability of over 80% at leachate concentration of 5 mg/mL. These results demonstrate the versatility of the periodate oxidation - ADH crosslinking strategy for neutral polysaccharide nanofibers.In summary, we have developed a periodate oxidation - ADH crosslinking strategy to make robust and biocompatible neutral polysaccharide nanofibers. In comparison to the glutaraldehyde crosslinking strategy, the periodate oxidation - ADH crosslinking strategy is more effective because of the high efficiency of Schiff base reaction and more biocompatible because of the low toxicity of ADH. As the results, the nanofibrous morphology, mechanical strength, water resistance and biocompatibility of neutral polysaccharide nanofibers crosslinked with this strategy are far better than those of nanofibers crosslinked with glutaraldehyde. These robust and biocompatible neutral polysaccharide nanofibers are expected to seek extensive applications in a variety of biomedical fields.Supplementary material related to this article can be found, in the online version, at doi:The following is Supplementary data to this article:Experimental details for determination of degree of oxidation, preparation of glutaraldehyde crosslinked KGM nanofibers, and determination of crosslinking density of OKGM-ADH nanofibers. Dependence of degree of oxidation of KGM on the feed ratio of sodium periodate and pristine KGM, FTIR of glutaraldehyde crosslinked KGM nanofibers, and crosslinking densities of OKGM-ADH nanofibers.Phosphorus grain boundary segregation in steel 17-4 PHA correlation between grain boundary etching of a martensitic steel and phosphorus segregation was established. Using metallographic experiments, the phosphorus diffusivity D in the steel and the Gibbs free energy ΔGP of phosphorus grain boundary segregation were determined: Phosphorus intergranular segregation is known to reduce grain boundary cohesion of steels. For ferritic or martensitic steels, this segregation can lead in some cases to much higher ductile-to-brittle transition temperatures Previous studies have shown that it is possible to detect P segregation by very simple metallographic techniques using picric acid-based reagents A commercial 17-4 PH steel from UGINE was used in this study. Its composition is listed in . In the quenched state, the Vickers hardness is 350, the microstructure is fully martensitic and the average grain size is 17 μm. Two precipitation mechanisms occurring in the martensite phase can increase the hardness of the steel: copper precipitation and α′ chromium-rich phase precipitation Twenty millimeter long cylindrical samples (φ=15 mm) of 17-4 PH steel were cut from the as-received bars, annealed 1 h at 1050 °C and water quenched. The samples were then heat-treated in the furnace in air to induce phosphorus grain boundary segregation. The various conditions as shown in were chosen to have different amounts of phosphorus segregation in the grain boundaries and a sufficiently high hardness level in order to obtain fully brittle intergranular fractures, instead of ductile fractures. For example, it is not possible to obtain an intergranular fracture after a 4 h annealing at 600 °C, even at low temperature, because the hardness is too low (Hv=350). On the other hand, after 15,700 h (22 months) at 320 °C, α′ precipitation induces an increase of hardness (Hv=420) and it is then possible to have some fully intergranular fractures even at room temperature. In other words, intergranular fracture requires both P segregation and sufficiently high hardness.After heat treatments, the samples were removed from the furnace and quenched in air. The heat-treated steel was then subjected to AES and metallographic examinations.Notched samples (≈1×1×20 mm3) were machined from the material after heat treatments. These notched samples were then fractured at room temperature in the chamber of the Auger spectrometer in a vacuum of about 7×10−8 Pa. The fractured sample was then immediately transferred in the analysis chamber and analysed using a cylindrical mirror analyser MAC 2 from RIBER. The vacuum in the analysis chamber was about 7×10−9 Pa. The primary beam energy was 3 keV. The size of the analysed area was chosen in order to get an average analysis from several grain boundary facets (≈50) at the same time. shows typical intergranular fracture obtained in the ultra-high vacuum chamber and the corresponding Auger spectrum.One of the main difficulties of studying interfacial segregation by AES is the quantification of the amount of segregated element: the sensitivity factors of both segregated (here phosphorus) and matrix (here mainly iron and chromium) are very dependent on the spectrometer specifications. That is why it is necessary to use a standard material Neglecting the Si, Mn, Ti and V elements, the phosphorus fractional monolayer content XP in the standard sample is given by is the phosphorus peak height at 120 eV, is the iron peak height at 703 eV and α is a spectrometer dependant constant. Since the peak height ratio measured on the standard sample is 10.0 and the phosphorus fractional monolayer content is 0.369, the constant α can thus be calculated: α=0.0369.The quantification of phosphorus grain boundary segregation in 17-4 PH steel needs to take into account that phosphorus occupies a zone only one atom wide where λ is the attenuation length of the Auger electrons emitted by the phosphorus atoms, θ is the angle of emission from the surface normal, a is the thickness of the segregated layer, is the iron peak height for pure iron and is the chromium peak height for pure chromium is taking into account that phosphorus is randomly distributed on both side of the intergranular fracture.The thickness a of the segregated layer is 1 monolayer and the attenuation length λ is about 2 monolayers for phosphorus It was previously shown that it is possible to detect phosphorus intergranular segregation in steels by metallographic techniques using picric acid-based reagents and that the depth of the grain boundary grooves formed during etching is proportional to the intergranular fractional monolayer content of phosphorus ) and surface preparation (mechanical polishing until a 3 μm diamond finish), samples were chemically etched in a picric acid-based reagent made of ethanol, picric acid (60 g l−1) and benzalkonium chloride (20 g l−1) used as a wetting agent. The etching temperature was maintained between 19 and 23 °C using a temperature-controlled circulator bath. 20 ml of reagent were used for 1 cm2 sample area and the samples were etched for 1 h. shows the evolution of grain boundary grooving after etching with annealing time at 460 °C.The grain boundary groove depth can be measured by iterative surface polishing using a 3 μm diamond paste. A Vickers indentation was previously made on the etched surface in order to measure the thickness of the eroded layer at each polishing step (). The sample was polished until no more intergranular groove is observed on the surface. The maximum intergranular groove depth h is then given by:where di is the initial diagonal length of the Vickers indentation and df the final diagonal length of the Vickers indentation. illustrates iterative polishing of a sample annealed 1000 h at 460 °C (in that case, the grain size was about 200 μm). The uncertainty on the h value measured by this technique can be estimated to be about 0.1 μm.Using this technique, the maximum intergranular groove depth was measured for each heat treatment indicated in . The results of both AES and metallographic technique are summarised in . The correlation between phosphorus segregation and grain boundary etching is evidenced in . Assuming a linear relation between XPGB and h (in μm), we get:The evolution of phosphorus grain boundary fractional monolayer content with time was measured at 430, 460, 500 and 600 °C using the metallographic technique described above. The phosphorus grain boundary fractional monolayer content was calculated using Eq. shows the evolution of the grain boundary groove depth and phosphorus grain boundary fractional monolayer content with time at these temperatures.The phosphorus grain boundary equilibrium fractional monolayer content was obtained at 600 °C (XPGB=0.098), which enables to estimate the Gibbs free energy ΔGP of phosphorus grain boundary segregation in steel 17-4 PH. Using the Langmuir–McLean formalism, ΔGP is given by:where XPB is the phosphorus atomic fraction in the bulk (XPB=286 at. ppm), XP,MaxGB is the saturation value of XPGB and R=8.314 J mol−1 |
K−1. For α-iron or ferritic steels, some authors For short annealing times, the evolution of XPGB is given by the simplified kinetic McLean law where D is the phosphorus diffusivity at the annealing temperature and d is the grain boundary thickness. Assuming a grain boundary thickness of 0.5 nm . Plotting these values in an Arrhenius diagram (), we get the Arrhenius parameters of phosphorus diffusivity in 17-4 PH steel (D=D0exp(−Q/RT), D0: pre-exponential factor and Q: activation energy):The evolution of phosphorus diffusivity with temperature in α-iron was extrapolated from the values proposed by Matsuyama et al. . In the temperature range that was investigated in this study (430–600 °C), the phosphorus diffusivity in 17-4 PH is very closed to the one given by It can also be concluded from our results that there is no accelerating effect due to martensite lath packet boundaries (α boundaries) and lath boundaries The main conclusions of this paper can be stated as follows:Phosphorus grain boundary segregation can be detected in 17-4 PH steel by a very simple metallographic technique using a picric acid-based reagent. A linear relationship between the amount of phosphorus segregated at grain boundaries and the depth of intergranular grooves formed during etching was found.Gibbs free energy of phosphorus grain boundary segregation in 17-4 PH steel was estimated to be −43.1 kJ mol−1 at 600 °C.Phosphorus diffusivity in 17-4 PH steel is given by: m2 |
s−1. It is very closed to the value of phosphorus diffusivity in α-iron proposed by Matsuyama et al. Study on interfacial adhesion strength of single glass fibre/polypropylene model composites by altering the nature of the surface of sized glass fibresPolypropylene (PP) compatibly sized glass fibres (GFs) were treated with boiling water and toluene, respectively, to reveal the interactions of water and toluene with different components in the sizing of sized GF and their influences on the interfacial adhesion strength of GF/PP model composites. Compared to control GF/PP model composites, about 30% increase of interfacial adhesion strength was achieved for composites with water-treated GF, whereas a small decrease of interfacial adhesion strength was revealed for composites with toluene-treated GF. X-ray photoelectron spectroscopy, Fourier transform infrared spectroscopy, Zeta-potential measurement, and water contact angle measurement demonstrated that the boiling water-treated GFs posses a more polar and hydrophilic surface with homogeneously distributed derivatives of 3-aminopropyltriethoxysilane, which is related to a higher interfacial adhesion strength for water-treated GF/PP model composites. In contrast, hot toluene-treated GFs led to a more hydrophobic surface with low molar mass PP and surfactants enriching on the outermost surface.The interphase between reinforcement GF and matrix in GF/polymer composites is of vital importance since the mechanical properties of composite materials are mainly determined by whether the mechanical stresses can be efficiently transferred from matrix to the reinforcing fibres It is noted that under aqueous condition the functional groups, mostly amino group, of (hydrolyzed and condensed) silanes and the polar groups of surfactants and additives are able to interact with the surface silanol group of the GF via H-bonding, electrostatic interaction or dipole–dipole interaction Extracting GF with hot water is similar to aging. The aging of sizings was already investigated by Ishida and Koenig in 1979 At elevated temperature, toluene is a good solvent for PP, polymeric film former of PP compatible sizings, and the physically adsorbed polysiloxane In this work, surface sensitive analysis methods (dynamic contact angle measurement, atomic force microscopy (AFM), X-ray photoelectron spectroscopy (XPS), and Zeta-potential measurement) were used to probe the changes of surface properties of as-spun and differently treated GFs. The influence of hot water and toluene treatments on the interfacial adhesion strength of single fibre/PP model composite was studied using single fibre pull-out test.Toluene (Acros) and γ-APS (Degussa) were used as received. Water was deionized to a resistivity of 15 MΩ cm using a Millipore Elix 5 water purification system. E-glass fibres sized by γ-APS in conjunction with PP film former (about 1:2.6 in dry weight ratio) were spun at the Leibniz Institute of Polymer Research Dresden using a continuous spinning device comparable to industrial ones. The average diameter of used sized GF is 15 μm. The as-prepared sized GF is named M1. M1 was extracted with boiling water and toluene for 8 h using a Soxhlet extractor with the aim to selectively extract sizing layer, the resulting GFs are referred as M1-W and M1-T (shown in ), respectively. An isotactic polypropylene (weight average molecular weight (Mw) = 23.8 × 104 |
g/mol) compounded with 2 wt.% MAH-g-PP (Polybond 3200) was used as matrix.High temperature gel permeation chromatography (HT-GPC) was performed at 150 °C using trichlorobenzene as solvent and eluent on a PL GPC220 (Polymer Laboratories) equipped with 2 PL Mixed B LS separating columns using triple detection (refractive index, light scattering, and viscosity). Room temperature GPC was carried out on a PL GPC220 (Polymer Laboratories) equipped with a PL Mixed-C column using tetrahydrofurane as solvent and eluent.XPS investigations were performed on a Kratos AXIS Ultra X-ray photoelectron spectrometer. Areas of approximately 300 × 700 microns were analyzed with a monochromatic Al Kα X-ray source. The samples were analyzed via angle-resolved XPS (AR-XPS) at normal (90°) and glancing (60°, 30°, and 15°) take-off angles (TOAs) in order to investigate the sizing surface chemistry as a function of analysis depth. The TOA is the angle between the analyzer and sample surface. At a 90° TOA, the XPS is capable of analyzing the top 8 nm of the sample surface, while at a 15° TOA only the top 2–2.5 nm of the sample surface is investigated. Due to the insulating nature of the samples, charge neutralization of the sample surface was required. Survey spectra were collected from six different areas of each sample at 90° TOA and 2 areas of each sample at 60°, 30°, and 15° TOAs. The survey spectra were collected over a wide binding energy range (0–1300 eV) and were used to evaluate all of the elements present (except H and He) within the sample surface. The survey spectra were acquired at a pass energy of 160 eV and a step size of 1 eV. The high-resolution spectra were dissected by means of the spectra deconvolution software. The parameters of the component peaks were their binding energy, height, full width at half maximum, and the Gaussian–Lorentzian ratio.Tapping mode AFM measurements were carried out using Dimension 3100 (Digital Instruments, Santa Barbara) at room temperature. The values of root-mean-square roughness (Rq) and maximum height roughness (Rmax) were calculated over the AFM images (3 μm × 3 μm).Electrokinetic properties, Zeta-potential as a function of pH, of sized GFs were obtained by electrokinetic analysis (EKA) on an electrokinetic analyzer (Fa. Anton Paar KG, Austria).The dynamic advancing contact angle (θa) and receding contact angle (θr) measurements on single GFs were performed on a tensiometer K14 (Krüss GmbH, Hamburg, Germany).The FTIR investigations were carried out on a Bruker IFS66 spectrometer. Transparent polymer films of PP film former and its acetone insoluble part with a thickness of 250 μm were prepared by compression molding at 190 °C. All extractions were analyzed in form of KBr pellets.The NMR spectra were collected on a Bruker DRX 500 NMR spectrometer at 500.13 MHz for 1H NMR spectrum and 125.75 MHz for 13C NMR spectrum. The signal assignment was done by 1H–1H COSY and 1H–13C HMQC 2D NMR experiments using the standard pulse sequences provided by Bruker. For internal calibration the solvent peaks of DMSO-d6 were used: δ (13C) = 39.60 ppm; δ (1H) = 2.50 ppm. 13C NMR spectrum was used for peak assignment and is not shown at here.Single fibre pull-out test was performed on single fibre model composites to study the interfacial adhesion strength. The fibres were end-embedded 300 μm deep into matrix at 200 °C with a heating and cooling rate of 50 K/min. From each force–displacement curve, the force Fd at the start of debonding and the embedded length, le, were derived. The apparent adhesion strength τapp was determined according to Eq. The local adhesion strength τd and the critical interphase release rate Gic were calculated according towhere p and q(Gic) are terms depending on fibre and matrix properties and specimen geometry The organic content of M1 fibre is 1.1 wt.% determined by pyrolysis following DIN EN ISO 1172. The average sizing thickness is about 36 nm assuming a homogenous sizing was formed and the density of sizing is 1 g/cm3. The commercially available PP film former is in the form of aqueous dispersion with a solid content of 35 wt.%, which was added drop-wise to acetone to get an acetone soluble part (Part-I) and an acetone insoluble part (Part-II), the weight ratio of Part-II to Part-I is about 4:1. Part-I was subjected to NMR, FTIR, and GPC analyses while Part-II was analyzed using FTIR and HT-GPC. The results are shown in for 1H NMR spectrum and FTIR spectra, respectively. The NMR spectrum of Part-I () revealed that the main fraction of Part-I is alkyl polyethylene glycol ether. The peak assignment is detailed in following. The triplet peaks centered at 0.85 ppm are assigned to the CH3 of alkyl group. The intensive peak at 1.24 ppm arises from the of alkyl group. A group of multiplet peaks between 3.3 and 3.6 ppm, except the resonance peak of H2O at 3.51 ppm, are due to the resonance of . Additionally, Part-I has a small amount of low molecular amines, most likely N-methyl ethylamine and/or its derivatives. The singlet peak at 2.37 mainly arises from the CH3N of N-methyl ethylamine, while the quadruplet peaks between 2.76 and 2.80 are attributed to the resonance peak of of N-methyl ethylamine next to methyl group, which gives raise to the triplet peaks around 1.06 ppm. On the other hand, the FTIR spectrum of Part-I (d) shows only the typical absorbance bands of alkyl polyethylene glycol ether. In detail, the strong absorbance bands between 1080 and 1150 cm−1 are attributed to the stretching vibration of CO, the intensive band at 1464 cm−1 arises from the bending vibration of CH2, while the broad band between 3200 and 3600 is assigned to the stretching vibration of OH and/or NH. GPC analysis revealed that the number average molecular weight (Mn) of Part-I is 920 g/mol with a narrow polydispersity index of 1.25. The main component of Part-II is MAH-g-PP, as revealed by FTIR in e. Except the typical absorbance bands of isotactic-PP, additional bands at 1775 and 1735 cm−1 are attributed to the stretching vibration of anhydride and other carbonyl groups. HT-GPC showed that Part-II has Mn of 75,400 g/mol, which is quite close to that of PP dispersion (80,600 g/mol). Moreover, Part-II has also a tiny amount of surfactant or other low MW components, as a weak peak at low molar mass region was present in the HT-GPC curve.Extracting M1 fibre in hot water and toluene, respectively, both led to a weight loss, the weight loss of M1 fibre is slightly higher in the case of hot water treatment (). It is noted that both hot water and toluene extracted mainly one component from the sizing layer, basing on the following observations. The extract in hot water was subjected to FTIR analysis and the result is shown in b and c shows the FTIR spectra of acetone soluble part of PP dispersion and the extract of only γ-APS sized GF using hot water, respectively. For the extract of only γ-APS sized GF (b), the absorbance bands at 2923 and 2852 cm−1 are assigned to asymmetric and symmetric stretching vibration of >CH2, the strong and broad peak at 1029 cm−1 is the typical stretching absorbance band of SiSi. The absorbance bands between 1650 and 1130 cm−1 are attributed to the stretching vibration of carbonyl group and bicarbonate salts due to the interaction between the amino group of γ-APS based components and environmental CO2 and water a and b one can conclude that the wash-out of M1 fibre in hot water mainly is γ-APS based components. Since the intensity of the peaks at 2923 and 2852 cm−1 is stronger in a, alkyl polyethylene glycol ether could be also included. However, the wash-out might also comprise small molecular amines and small amounts of PP, which bond or interact with physically adsorbed γ-APS based components and were extracted into water with physically adsorbed γ-APS based components.Upon extraction in hot toluene, mainly alkyl polyethylene glycol ether was washed out as revealed in the FTIR spectrum (d). However, components with Mn of 23,800 g/mol were detected by HT-GPC, this fraction can be assigned to PP or the complex of PP with γ-APS, since it is known that the physically adsorbed γ-APS based components do not posses such high MW The impact of solvent treatment on the surface properties of GFs was firstly studied by mapping the surface topography using tapping mode AFM. presents AFM height images of M1-T and M1-W fibres as well as M1 fibre, the surface roughness data of GFs are summarized in a shows that the surface of M1 fibre looks like pine tree bark characterized by the irregular islands in a sea. Upon extraction with hot toluene, the surface of M1-T fibre turns rougher (b), which probably is due to the swelling of toluene in sizing during extraction, which collapsed or shrank in the course of drying at 80 °C under vacuum. Correspondingly, the Rq and Rmax values increase from 3.5 and 41.5 nm to 9.6 and 88.6 nm, respectively. On the other hand, extracting M1 fibre in hot water did not change the surface topography of the resulting fibres as much as in hot toluene. There is only a small increase in both Rq and Rmax values.Water contact angle measurements were performed to obtain information concerning the hydrophobicity of the sizing of single fibres. summarizes dynamic advancing contact angles (θa) and receding contact angles (θr) as well as the hysteresis value (θa |
− |
θr). The control M1 fibre has θa of 94.3° and θr of 68.5°. After toluene extraction, θa and θr of M1-T fibre increase a little bit to 99.2° and 72°, respectively. As FTIR and HT-GPC analyses revealed that surfactants and PP with low MW were extracted into hot toluene, the higher water contact angle is related to the enrichment of low MW PP on the topmost surface since PP with lower MW has lower surface tension compared to the high MW analogues AR-XPS was used to probe the radial distribution of sizing components within the sizing, the average surface compositions in atomic percentage are presented in . The C 1s high-resolution spectra were curve-fitted with four peaks. The corresponding peak assignments are listed in . The peaks of interest in the C 1s spectra are C-1 and C-2, which correspond to CO chemical states, respectively. C-3 and C-4 correspond to different types of surface oxidation of the carbon. In addition, the N 1s high-resolution spectra were curve-fitted with two peaks, which correspond to amine and protonated amine chemical states. Here, only the degrees of nitrogen protonation are reported in For the M1 fibre, a 20% increase in C and 40% decrease in N were found at 15° TOA versus at 90° TOA, while the percentage of CC bonds remained constant and there was a 10% decrease in CO bonds. This agrees with the results of contact angle measurements indicating the non-polar components of polymeric film former enrich on the outermost surface. In addition, it was determined that at 90° TOA 10% of the amine groups were protonated while no protonation was observed at the air/sizing interface. Usually it is assumed that the protonation of the amino group is mostly induced by the interaction of amino groups with silanol groups either via intra-molecule or inter-molecule H-bondings For the toluene washed fibre (M1-T), at TOA of 90°, a 5% decrease in C was detected while the N percentage was similar to the M1 fibre. This small drop in C correlates to the FTIR and GPC results, which revealed surfactants and PP in the toluene extract. In addition, a 30% increment in C and 35% decrease in N were observed at 15° TOA in comparison with at 90° TOA. These results are similar to those found for the M1 fibre prior to extraction. Moreover, CC bonds show about a 10% increase while about 40% reduction in CO bonds was found compared to the M1 sample, which is in a good agreement with the FTIR analysis of the wash-off of M1 fibre in hot toluene. On the other hand, a 5% drop in CO bonds were observed as the TOA was decreased. The large increase in the C-2 peak is probably due to an enrichment of the CO bonds from either polyethylene glycol or oxidation of the outermost surface of the fibre or more amino groups are present in the outermost surface upon extraction as observed by Zeta-potential measurement. Moreover, it was found that 20% of the amine groups at TOA of 90° were protonated while no protonation was found at the outermost surface of the fibre.For the water washed fibre (M1-W), at TOA of 90°, a 15% drop in C and 40% decrease in N were observed compared with the M1 sample. A 10% increase in CO bonds were observed compared to the M1 sample. This suggests that the boiling water extraction removed physically adsorbed and/or chemisorbed coupling agent and surfactants from sizing and consists with the FTIR analysis on the wash-off of M1 fibre using hot water. Furthermore, a 12% reduction in C was detected at TOA of 15° versus at TOA of 90°, while the N percentage remained constant as a function of probing depth. In addition, it was observed that almost 50% of the amine groups at TOA of 90° have been protonated, while 35% were protonated at the outermost surface. This agrees with the contact angle observation that the polar groups are present on the outermost surface, thus creating a hydrophilic surface. On the other hand, the C-1 and C-2 percentages remained constant as a function of depth probed into the surface. This suggests that the concentration of aminosilane does not change greatly within the detected information depth.To better understand the influence of solvent treatments on the surface properties of GFs, Zeta-potential of GF was determined using EKA to derive information about the surface functional groups. The Zeta-potential – pH curves are shown in . Compared with M1 fibre, a significant shift in iso-electric point (IEP) to the basic region after toluene treatment or to the acidic region after water treatment was found. After toluene treatment a significant amount of surfactant and a part of the PP film former were removed. As a consequence, the basic NH2-groups of the aminosilane are more accessible, correspondingly the Zeta-potential at the plateau shifted to higher positive values, meanwhile the IEP also moved from 7.0 to more basic value. On the contrary, after water treatment the Zeta-potential of M1-W fibre at native pH shifted from positive to negative and preferably acidic groups were detected at the surface, moreover the IEP was shifted to about pH 4. These results also suggest the hydrolysis of siloxane groups and migration of aminosilane from sizing/fibre interface to air/sizing interface.From above analyses the radial chemical compositions of GF sizing layer become clear and are presented in following. After sizing application and drying, the sizing of control fibre (M1) shows enrichment of aminosilane in the sizing/GF interface while PP film former predominating at the air/sizing interface. The driving force for this is related to the low surface free energy of PP and the good affinity between aminosilane and GF surface. Upon extraction in hot toluene, the low MW fraction of PP film former and surfactants are partly washed off, making the amino groups of aminosilane more accessible; however, the low MW PP and surfactants enrich on the outermost surface. Extracting sized GF in hot water can wash-off physically adsorbed and chemisorbed aminosilane and surfactants. Under high humidity and high temperature, polysiloxane hydrolyzes and distributes evenly throughout the detected information depth. Moreover, hot water extraction led to GF with a more hydrophilic surface.Interfacial shear strength is an evaluation of the efficiency of the interface to transfer the applied stress from the matrix to the fibre before interfacial debonding occurs. In-house single fibre pull-out test device was used to determine the interfacial adhesion strength of differently treated GF/PP model composites. shows a modest decrease of the local adhesion strength τd and Gic when M1 fibre was extracted in toluene, the τd and Gic slightly drop from 13.1 MPa and 5.5 J m−2 to 10.6 MPa and 3.7 J m−2, respectively. Based on the results of Zeta-potential measurement this was not expected, since it revealed a better accessibility of the amino groups of aminosilane, which can prompt the formation of the covalent bond between amino group and anhydride group. However, if the enrichment of low MW PP and surfactants at the outermost surface is taken into consideration, the modest drop in interfacial adhesion strength is reasonable and could relate to the presence of weak points in the interphase. This is consistent with our previous observation that the bond strength was especially low when low MW PP was applied as film former PP compatibly sized glass fibres (GFs) were subjected to extraction either in hot water or in toluene to simulate a different attack of sizing depending on the media and in depth altering of the sizing, respectively, and to obtain indirect information about the gradient within the interphase ranging from the air/sizing interface to the sizing/glass interface. FTIR and GPC anaylses on the wash-offs, surface properties of GFs and the interfacial adhesion strength of single fibre/PP model composites upon extraction in different liquids proved to be surface sensitive methods, revealing the chemical composition within the sizing. Extracting control GF in hot toluene, surfactants and the low molecular weight fraction of PP film former are partly washed off, making the amino groups of aminosilane more accessible; however, the enrichment of low molecular weight PP and surfactants on the outermost surface creates weak points in the interphase. The latter one overwhelms the former one leading to slight decrease in interfacial adhesion strength. On the other hand, extracting control GF in hot water could wash-off physically adsorbed and chemisorbed aminosilane and surfactant. Meanwhile polysiloxane hydrolyzes and distributes evenly throughout the sizing thickness, as a result of this the observed interfacial adhesion strength value shows a 30% increase. Further works will be dedicated to nano-indentation and nano-TA studies on differently treated GFs and corresponding composites to evaluate the mechanical property and chemical composition gradient within sizing/interphase thickness with the aim to deepen the understanding on the correlation between the surface/interphase properties and composite material mechanical properties.Spheroidization behaviour of a Fe-enriched eutectic high-entropy alloyA cost-effective Fe-enriched eutectic high-entropy alloy (EHEA), Fe35Ni25Cr25Mo15, was designed and prepared to avoid the use of expensive Co that is commonly used in HEAs. However, the as-cast Fe-enriched EHEA was associated with brittleness. The present work aims to evaluate the possibility and feasibility of spheroidization of the lamellar structure of the EHEA in order to improve the ductility. Due to the high cooling rate of arc-melting, the as-melted Fe35Ni25Cr25Mo15 EHEA was found to be a pseudo eutectic alloy comprised of alternant σ phase (Cr0.22Mo0.18Fe0.6-type intermetallic) and face centred cubic (FCC) phase. The lamellar structure in the Fe-enriched EHEA remained stable up to 800 °C. The instability of the lamellar structure occurred at temperatures over 800 °C, which was resulted from migration of high-density faults (i.e. lamellar termination and ledges in the lamellae). However, the Fe35Ni25Cr25Mo15 EHEA still exhibited brittleness even after spheroidization at 1100 °C for 168 h due to the formation of the hard and brittle σ matrix in the pseudo Fe35Ni25Cr25Mo15 EHEA as a result of decomposition of the lamellar structure. Therefore, in contrast to the softening of traditional eutectic alloys, spheroidization treatment was considered as invalid to improve the ductility of pseudo-eutectic HEA with high fraction of intermetallic phase. The present work provides a valuable reference for those who aim to improve the ductility of brittle EHEA through spheroidization.Unlike traditional alloys containing one or two principal elements, high entropy alloys (HEAs) normally consist of 3 or more principal elements []. For as-cast HEAs, research over the last decade has shown that the most non-equiatomic HEAs with multi-phases exhibit superior mechanical properties compared with the most equiatomic single-phase HEAs [] and dual-phase (DP) eutectic high-entropy alloys (EHEAs) in particular [] firstly proposed to use eutectic alloy concept to design HEAs, aiming at good castability and composite structure to resolve the strength-ductility trade-off. The directly casting AlCoCrFeNi2.1 DP EHEA exhibit both high strength and ductility in a wide temperature range, which outperform most of conventional cast alloys and also HEAs reported previously []. In addition, based on a pseudo binary strategy proposed by Jin et al. [], three groups of AlCoCrFeNi-based EHEAs with tensile fracture strengths of ∼1.0 GPa and elongations of over 10% were developed. Similarly, a quaternary Fe20Co20Ni41Al19 EHEA with nano-lamellar structure presented an ultimate tensile strength of 1.3 GPa and an elongation of 17.1% at room temperature, which is superior to most reported as-cast HEAs [Except for the above EHEAs, most other reported EHEA systems exhibited ultra-high strength but substantial brittleness. This includes the as-cast CoFeNi2V0.5Nb0.75 and Co2Mo0.8Ni2VW0.8 EHEAs. []. These alloys showed high ultimate compression strength (UCS) of around 2 GPa, but low compression fracture strain (εc) below 15%. In addition, almost all the current EHEAs (e.g. AlCoCrFeNi2.1, Fe20Co20Ni41Al19, CoFeNi2V0.5Nb0.75 and Co2Mo0.8Ni2VW0.8) contain expensive metals, such as Co or Mo, which increased the overall cost of the alloys. Hence, the critical challenges to applicate this type of EHEA are to enhance their ductility and decrease the cost. To address this problem, we previously designed a low-cost Fe-enriched dual-phase EHEA – Fe35Ni25Cr25Mo15 []. But, as-cast Fe35Ni25Cr25Mo15 alloy also showed high brittleness at room temperature.Adopting the concept of spheroidization from traditional eutectic alloys, the present work aims to evaluate the feasibility of spheroidization of the lamellar structure of EHEAs in order to improve ductility. The brittle Fe-enriched EHEA (Fe35Ni25Cr25Mo15) [] was used as an example. The instability of the lamellar structure in this EHEA under high temperature annealing was investigated and the influence of spheroidization on the room-temperature mechanical properties was evaluated.To lower the cost of HEAs, the overall design strategy was to avoid the use of expensive Co that is commonly used in HEAs. Based on Yu and co-workers’ previous work [], a new cost-effective Fe35Ni25Cr25Mo15 EHEA was designed through increasing the ratio of Fe to Mo in an equiatomic Fe25Ni25Cr25Mo25 HEA to produce more ductile face centred cubic (FCC) phase because the latter was predominated by brittle intermetallic phase. It has been commonly considered that Fe and Ni are FCC stabilizers, while Cr and Mo are intermetallic forming elements []. Hence, the EHEA can be designed through adjusting the ratio of Fe/Ni to Cr/Mo. In addition, to ensure the high oxidation and corrosion resistance, Cr content was retained at 25 at.%. As Fe is much cheaper than other elements while Mo is the most expensive one in the FeNiCrMo alloy system, the ratio of Fe to Mo was accordingly increased to obtain the dual phase (DP) eutectic structure consisting of FCC and intermetallic phase. The proposed Fe-enrich EHEA exhibited high strength at room temperature. Due to its composite structure and high Cr content, this new alloy should possess potential applications as high-temperature materials. But, reducing its room-temperature brittleness remains a great challenge.The designed Fe35Ni25Cr25Mo15 EHEA was prepared in an arc-melting furnace using a water-cooled copper mould in an argon atmosphere. Before arc-melting, commercial-grade metal powders (Fe, Ni, Cr and Mo) with 99.9 wt.% purity were mixed and then compacted into small cylinders of 14 mm in diameter and 20 mm in length. Then, the compacted cylinders were melted in the arc furnace. To ensure the chemical homogeneity, each ingot was remelted four times with processing parameters of 250 A current and 28.5 V voltage. Mild oxidation was notified on the top surface of the ingots. This was attributed to the high specific surface area of the powders used. However, since samples for mechanical property tests and microstructure characterization were cut from the middle of the bar ingots, the effect of surface oxidation can be reasonably ignored. Rectangular bar ingots with dimension of about 120 mm × 12 mm × 8 mm were cut to various sizes for heat treatment, microstructural characterization and mechanical property tests. Spheroidization treatments were conducted in an air furnace within a temperature ranging from 600 °C to 1100 °C for 24, 72, and 164 h followed by air-cooling.The phase constituents were identified through X-ray diffraction (XRD; Bruker D8) using Cu Kα radiation at a scanning rate of 1° min−1, and a 2θ angle ranging from 20° to 100°. Metallographic samples with a thickness of around 2 mm were mounted with electroconductive resin. The mounted samples were then mechanically ground and polished followed by etching using an aqua regia etchant (HNO3 + 3 HCl). The microstructure was examined in a scanning electron microscopy (SEM; JEOL-6610) and the chemical compositions were analysed using energy-dispersive spectrometry (EDS). Transmission electron microscopy (TEM) samples were prepared using a Focused Ion Beam (FIB) method in a FEI Scios Dual Beam system and examined in a TECNAI F20 TEM with operating voltage of 200 kV.Differential Scanning Calorimetry (DSC; NETZSCH thermische analyse) analysis was carried out over a temperature ranging from 20 °C to 1450 °C at a heating and cooling rate of 10 °C min−1 in an argon atmosphere. The DSC samples with dimension of 4.3 mm in diameter and 3 mm in length were cut from the bar ingots, and then ground and polished before testing. After the DSC, microstructural characterization of these samples was also performed using the JEOL-6610 SEM. Hardness was measured using a Struers Vickers hardness tester with a load of 5 kg and a dwell time of 12 s. Due to the brittleness of the alloy, mechanical properties were measured through compression tests. Test samples were machined to the size of 5 mm in diameter and 10 mm in length. The testing was conducted on a 100 kN Shimadzu AGS-X machine fitted with video extensometer at a strain rate of 5 × 10−4 s−1 at room temperature, and representative compressive true stress-strain curves were presented.(a, b) show the backscattered electron (BSE) morphology of the arc-melted Fe35Ni25Cr25Mo15 EHEA. The as-cast alloy exhibited a typical lamellar eutectic (LE) structure (non-faceted/non-faceted) with small amounts of anomalous eutectic (AE) structure. From the high magnification image in (b), a high-density of faults can be identified in the lamellar structure, including lamellar terminations (marked as blue arrows) and some ledges in the lamellae (red arrows). The EDS mapping in (c) shows chemical contrast of two phases, including a Fe and Ni enriched phase and a Mo enriched phase in the lamellae. The XRD spectrum in (d) confirms the dual-phase structure of the as-cast Fe35Ni25Cr25Mo15 EHEA. The phases are an FCC solid solution and a Cr0.22Mo0.18Fe0.6-type body-centred tetragonal phase (σ phase). TEM was performed to further verify the phase constituents in the alloy.To understand the formation sequence of the LE and AE revealed in shows the DSC heating (a) and cooling curves (b) of the as-cast EHEA. Although the heating curve shows one endothermic peak, indicating simultaneous melting of the two phases in both the LE and AE regions at ∼1318 °C, three exothermic peaks can be identified in the cooling curve between 1350 °C and 1288 °C, corresponding to different phase transformations during solidification. To understand the phase transformations occurred during DSC cooling, the microstructure of the sample after DSC test was examined and is shown in . Three distinguishable microstructures, pro-eutectic σ phase (marked as P), LE structure and AE structure can be observed, which differ from the microstructure of the as-cast samples. This difference in microstructure results from the different cooling rates during the DSC versus the arc-melting used to prepare the samples. In contrast to the slow cooling rate during the DSC test (10 °C min−1), the typical cooling rate for arc-melting is much higher (103–104 °C s−1) [], which inhibited the formation of the pro-eutectic σ phase in the as-cast sample. Slow cooling during DSC enabled primary σ phase to form. This result indicates that the Fe35Ni25Cr25Mo15 alloy is a hyper-eutectic alloy. According to previously published results on traditional eutectic alloys, the AE structure tends to form at high undercooling as a result of irregular or partial remelting [In addition, the formation of the various microstructures during solidification are marked near the corresponding exothermic peaks on the DSC cooling curve. During solidification of the EHEA, the primary σ phase forms first, corresponding to the smallest peak in , it is observed that the volume fraction of AE is higher as compared with the primary σ phase and LE region, hence it corresponds to the highest (3rd) exothermic peak in the DSC cooling curve and thereby the second peak is related to the formation of the LE region.(a–g) show optical microscopy (OM) images revealing the morphological evolution of the EHEA when annealing at various temperatures from 600 °C to 1100 °C for 24 h. The lamellar eutectic structure remained stable up to 800 °C. With annealing at temperatures over 800 °C, the lamellar eutectic structure started to pinch off, coarsen and spheroidize. The lamellar structure completely decomposed at 1000 °C and 1100 °C, though the microstructure was not fully spheroidized. This result indicates that, in the current as-cast EHEA, although the lamellar structure was destabilized over 800 °C, full spheroidization required much longer annealing time. shows the hardness variation of the EHEA with annealing temperature. The hardness of the samples annealed below 800 °C remained similar to the as-cast alloy, which is consistent with the similar microstructures observed in these samples ((a–d)). Whereas, due to the decomposition of the lamellar structure, the hardness of the samples annealed at temperatures over 900 °C is gradually reduced. As spheroidization is regarded as one of the most effective approaches to increase the ductility of eutectic or eutectoid alloys, longer time annealing at 1100 °C was conducted to maximize spheroidization of the LE in the EHEA. shows XRD spectra of the Fe35Ni25Cr25Mo15 alloy after annealing at 1100 °C for different time, indicating the same phase constituents (dual FCC and σ phase) as the original as-cast alloy. Thus, the annealing did not cause phase transformation. (a–d) are BSE images of the Fe35Ni25Cr25Mo15 alloys annealed at 1100 °C, which show two distinguishable phase features (a white region and a grey region) with the contrast due to their differing chemical compositions. EDS analysis indicated that the grey areas were Fe and Ni enriched FCC phase and the white areas were Cr and Mo enriched σ phase. As aforementioned, although the lamellar structure decomposed after 24 h annealing, complete spheroidization did not occur. An increased annealing time up to 72 h significantly improved the spheroidization. However, further annealing up to 168 h did not promote further spheroidization of the alloy. For longer annealing times above 72 h, the microstructure consisted of the σ phase as the matrix with spheroidized FCC phase.To verify the phase constituents shown in . The TEM bright field image and corresponding selected diffraction patterns in (a–c) confirm the two phases to be FCC and σ phase in the as-cast alloy. The TEM-EDS mapping ((d)) indicates that the FCC phase is Fe and Ni enriched (grey area in (a)), while the σ phase is rich in Cr and Mo (white area in (a–d) indicates that the spheroidized alloy is comprised of spheroidized FCC phase (grey area in (d)) and the σ phase matrix (white area in (d)) after annealing at 1100 °C for 168 h.]. However, most lamellar structures in eutectic alloys contain defects, such as lamellar terminations, ledges in the lamellae and colony/grain boundaries, which induce coarsening of the lamellar structure at higher temperatures. Depending on the defects, coarsening can occur through a continuous mode (fault migration) or a discontinuous mode (grain boundary migration) []. Currently, the fault migration theory is widely accepted for understanding the instability of lamellar structures at high temperatures. As shown in In addition, increasing the temperature from 800 °C to 1100 °C promoted atomic diffusion and fault migration, therefore fostering the spheroidization as shown in (a–g). According to the model developed by Cline et al. [], the fault migration rate in binary eutectic can be expressed as follows:where VF is the fault migration rate, D is the diffusion coefficient, γ is the interfacial energy between the α and β phases, Cα and Cβ are the concentrations of solutes in both phases (Cα > Cβ), λ is the inter-lamellar spacing, λα is lamellar thickness of solute rich phase, T is temperature and V¯α is the partial molar volume of solute rich phase. For a given eutectic alloy, the parameters in Eq. can be assumed to be invariant except the temperature T and diffusion coefficient D. Thus, the fault migration rate VF is mainly defined by the value of D/T [], the diffusion coefficient D in Pb-Sn eutectic alloys increased up to several orders of magnitudes when the temperature T surpassed a critical value. Therefore, the high temperature annealing treatments over 800 °C may significantly increase rates of diffusion in the Fe35Ni25Cr25Mo15 EHEAs and thereby the velocity of fault migration. Combined with the high-density faults in the eutectic structure of the Fe35Ni25Cr25Mo15 alloy, instability is substantially increased at elevated temperature. shows that spheroidization in the current alloy was not fully completed at 1100 °C even after 168 h ((a–d)). As the microstructure after annealing for 72 h was similar to that for 168 h, the potential to achieve full spheroidization at 1100 °C is limited. Higher temperatures are necessary to complete the spheroidization. A similar result was reported by He et al. [] in a CoCrFeNiNb0.65 EHEA. Partial spheroidization occurred in this alloy at 900 °C after 24 h, but the majority of the spheroidization process was not complete. In addition, using deep etching and tilted sample observation with SEM, Lei et al. reported that the observed spheroids in the NiAl-Cr(Mo) eutectic alloys that were annealed at 1150 °C for 400 h were actually cylindrical in shape []. Higher annealing temperatures were required to break the cylindrical phase into spheres. For instance, spheroidization of a NiAl-Mo eutectic alloy was only completed at around 1575 °C for 100 h []. Thus, it is reasonable to believe that full spheroidization of lamellar eutectic in EHEAs is challenging, and generally requires very long time and/or high temperatures.(a) shows the hardness of the EHEA after annealing at 1100 °C for various time. Compared with the as-cast alloy, annealing led to a slight decrease in hardness, but the annealing time had marginal impact. The corresponding true compressive stress-strain curves of the Fe35Ni25Cr25Mo15 EHEA are shown in (b). The as-cast alloy exhibited high ultimate strength of 1874 MPa with low strain to fracture (ductility) of 3.7%. Annealing at 1100 °C for 72 h only slightly enhanced the strain to fracture to 6.5% with reduction in ultimate strength to 1570 MPa. Whereas, 168 h annealing decreased both the ultimate strength and strain to fracture.The decrease in ultimate compression strength of the Fe35Ni25Cr25Mo15 EHEA after annealing at 1100 °C originated from decomposition of the lamellar structure due to its shape instability at elevated temperatures. show the close correlation between the eutectic morphology and mechanical properties of the alloy. From (a–d), one can see that annealing at 1100 °C led to coarsening and spheroidization of the lamellae in the Fe35Ni25Cr25Mo15 alloy. The interlamellar spacing was remarkably increased from ∼0.4 μm to ∼4 μm. The bigger interlamellar spacing resulted in a reduction in ultimate compression strength.Generally, due to the substantial reduction in the volume fraction of interphase boundaries, spheroidization will significantly improve the ductility of eutectic alloys in sacrifice of the strength. However, the Fe35Ni25Cr25Mo15 EHEA still exhibited brittleness after spehroidization. This was attributed to the formation of brittle and hard σ matrix as a result of the spheroidization although the FCC phase was spheroidized ((c, d)). As aforementioned, the Fe35Ni25Cr25Mo15 EHEA is a pseudo eutectic alloy resulting from the fast rate of cooling after arc-melting (). Its hyper-eutectic composition may be associated with higher fractions of the brittle σ phase in the arc-melted EHEA than for equilibrium EHEAs. Thus, the high-proportioned σ phase in the lamellae evolve to the matrix after spheroidization and should be responsible for the brittleness of the spheroidized Fe35Ni25Cr25Mo15 EHEA., it is reasonable to consider that σ phase acts as the matrix even after longer time or higher temperature annealing, indicating that the brittleness cannot be eliminated by fully spheroidization. Therefore, spheroidization treatment was invalid for the ductility improvement of the brittle pseudo eutectic EHEA with higher fraction of intermetallic phase. This conclusion probably would be true for traditional eutectic alloys provided intermetallic matrix formed after spheroidization of the alloys. However, this is quite unlikely because traditional eutectic alloys do not contain sufficient alloying elements to form intermetallic phases as the matrix. Further studies will provide solid conclusions.The arc-melted Fe-rich Fe35Ni25Cr25Mo15 EHEA is a pseudo eutectic alloy formed due to the high cooling rate during solidification. The microstructure comprises a primarily lamellar eutectic structure with small amount of anomalous eutectic structure. Both consist of Mo-Cr enriched σ phase and Fe-Ni enriched FCC phase.(2)The lamellar structure of the EHEA was stable up to 800 °C when annealing for 24 h. Above this temperature, morphological instability of the microstructure originating from the migration of high-density faults (i.e. lamellar termination and ledges in the lamellae) occurred. In addition, with increasing annealing temperature, the instability increased significantly due to the higher velocity of fault migration.The as-cast alloy exhibited high ultimate compression strength of 1874 MPa but low ductility of 3.7%. Unlike traditional eutectic alloys, spheroidization treatment was invalid for the ductility improvement of brittle pseudo-eutectic HEA with higher fraction of intermetallic phase. The brittleness of the spheroidized Fe-enriched EHEA was originated from the the hyper-eutectic composition and thereby the formation of a brittle and hard σ matrix after decomposition of the lamellar structure.Characterization and modeling of localized compaction in aluminum foamUniaxial compression tests on aluminum foam reveal formation of bands of localized compaction, initiating near peak stress, and becoming clearly defined during the subsequent stress drop. Band formation is modeled as a bifurcation from uniform deformation due to a constitutive instability. Theoretical predictions and experimental observations are in reasonable agreement.Specimens were cut from Cymat structural grade aluminum foam to dimensions 27 mm × 27 mm × 54 mm, using wire electro-discharge machining per ASTM standards Results from a representative specimen (C5a18) are shown in . The stress–strain plot shows nominal stress (force divided by original cross sectional area) vs. nominal strain (cross head displacement divided by original length), both positive in compression. The three axial surface strain contour plots relate to the three loading stages, A (pre-peak), B (peak), and C (post-peak), labeled on the stress–strain plot. Because the current work focuses on compaction band initiation, the stress–strain curve is shown only through the stress drop, although all specimens were loaded to approximately 5% axial strain. The complete stress–strain plots, characterized by a large stress drop and jagged sloping plateau, are similar to those reported by other authors for brittle foams ) show accumulated surface axial strain, with progressively darker shades representing increasingly compressive strain. At loading stage A, prior to peak stress, deformation consists of multiple isolated zones of localized compaction, distributed across the specimen face. At peak stress, B, strain begins to localize into a single zone of localized axial compaction. During the stress drop, C, a large portion of the specimen shortening goes into the compaction band, which is now well defined. Comparing strain maps for B and C reveal several zones of local unloading (e.g., left side above band) that occur during the stress drop, as the specimen continues to shorten. also shows evolution of the “total” Poisson’s ratio, νt (the negative of the ratio of the lateral and axial strain increments, including elastic and inelastic portions), which will be utilized in the theoretical predictions. Through peak stress, νt is relatively constant, and then decreases rapidly such that νt |
≈ 0 shortly after peak stress. appears to be roughly perpendicular to the axial direction (band angle of ≈0°, where the band angle is defined as the angle between the band normal and the axial direction), determination of the observed band angle also requires examination of the non-photographed faces. For each specimen, the observed band angle was estimated by fitting a plane through the four points where the band intersected the corners of the specimen. Clearly this method is an approximation, however, since the exact location of the band inside the specimen is also unknown, this method was deemed adequate to provide an initial estimate of the band angle. In future work, X-ray computed tomography could facilitate more accurate determination of band angle. The estimated observed band angles (see Bands of localized compaction have also been observed in field and laboratory specimens of high porosity sandstone subject to axisymmetric compression Clearly the localization conditions are influenced by the choice of constitutive relation. For porous rock, Issen and Rudnicki The slope of the plastic potential for axisymmetric (or uniaxial) compression is given by β=-3b/(3-b), where b is the ratio of the inelastic volume strain, dεvp, to inelastic axial strain dεap (both positive in compression), b=dεvp/dεap). This reasonably favorable agreement is noteworthy, considering the difficulties and assumptions (discussed next) involved in determining predicted and observed band angles. Additionally, at peak stress, Et is zero, and from , notice that νt, the slope of the lateral vs. axial stress curve, goes to zero slightly past the stress peak. These observations compare favorably with Rudnicki’s predictions of compaction band formation in transversely isotropic materials at peak stress (Et |
= 0), if νt |
= 0 Since only uniaxial tests were conducted, the yield surface slope, μ, cannot be determined, so associated flow, μ |
= |
β, was assumed. However, band angle predictions would change if μ |
≠ |
β. Additionally, the theoretical continuum approach used here assumes that the specimen size to cell size ratio is large. While the specimens studied here satisfy the suggested conditions for bulk material behavior (i.e., a minimum specimen dimension is six to 10 cells The Cymat manufacturing process results in denser material at the foam panel faces (corresponding to the specimen ends), such that compaction localization typically occurs in the less dense middle section of the specimen. Certainly this density gradient, as well as the inhomogeneous cell microstructure (in particular, certain cell geometries that are prone to collapse, see Refs. Uniaxial compression tests on aluminum foam reveal the formation of bands of intense localized compaction, “compaction bands”, oriented approximately perpendicular to the loading direction. Digital image correlation was used to produce maps of surface axial strain, which show that near peak stress the deformation mode transitions from multiple zones of isolated compaction, to a single compaction band. The stress peak is followed by a large stress drop, during which a significant amount of the specimen shortening is absorbed by a band, which becomes clearly defined. Some unloading is observed in material outside the band. The theoretical framework developed by Rudnicki and Rice Thin-walled cold roll-formed steel sectionsFatigue behaviour of thin-walled cold roll-formed steel sectionsThis paper presents experimental research aimed at addressing the fatigue behaviour of thin-walled cold roll-formed steel sections, very commonly used in rack structures. This research is performed under the FASTCOLD-RFCS project, which aims to fill an existing gap on fatigue design rules. A new design S-N curve is derived from an innovative testing methodology, which supports the current revision of the Eurocode 3 (EN 1993-1-9). Additionally, a local fatigue approach, encompassing residual stresses from numerically simulating the manufacturing process and structural elastoplastic stress analysis supported by the Theory of Critical Distances, returned consistent fatigue life predictions for the tested profiles.Thin-walled cold roll-formed steel sectionsReliable storage and retrieval (S&R) logistic systems based on rack structures are the backbone of resilient industries, where the recent significant growth of e-commerce has been contributing to fatigue damage intensification (fatigue cracking) on the members of these structures. Moreover, logistic rack structures commonly use thin-walled cold-formed mild steel members, and EU regulations do not cover the fatigue design for these cases: EN 1993-1-1 shows a typical fatigue failure mode observed in a shuttle rail used in a real-world application; the observed cracking increases maintenance costs and, in extreme cases, can compromise the structural integrity of the structure.Sheet metal-forming is a manufacturing process that induces permanent plastic deformations and can be conducted above the material’s recrystallization temperature (hot-forming), minimizing residual stresses Within this research, numerical studies were performed by Souto et al. This research is based on a case study consisting of a thin-walled rail obtained by cold roll-forming, which is used to guide pallet carrier shuttles. These specific rails are known as Z-rails due to the global geometry of their section, as shown in presents the derived mechanical properties measured along the longitudinal/rolling direction of the profile, while where σ is the true stress and ∊p is the true plastic strain. The remaining parameters (K, n, and ∊0) are empirically determined material constants; for the S355MC steel, the derived values are shown in a shows the selected points used as an input in numerical models to define the elastoplastic behaviour of the S355MC steel, in tabular form. It should be noted that 197 points were selected, where the true plastic strain ranges from 0 to 1. Also, the first point was modified aiming at capturing the yield plateau of the experimental yield curves.To verify that the selected points model correctly the S355MC material, a uniaxial test was simulated in both MSC Marc and Abaqus/CAE, where a unit cube with isostatic boundary conditions was subjected to a uniaxial load. Both models are using the elastic material properties shown in and a hardening curve defined by the selected points shown in a. It should be noted that both models applied hexahedral elements (8 nodes with 8 integration points corresponding to full integration); this element type is also the one used in further simulations. As shown by the results presented in b, a very good match is visible between the numerical and experimental data until the maximum stress, meaning that the material’s elastoplastic behaviour is being correctly modelled. After the maximum stress, the experiments show necking and a reduction of the stresses is apparent, while the true stress increases as predicted by the Swift model., cracking in real world vs. experimental setup). shows all the holes for the bolted supports (also see ). Fatigue testing is done through load control and a loading ratio of R=0.1 was used for all tests to guarantee minimum contact conditions and stable testing conditions. In real applications, the loading is not as simple as the one considered in this testing setup due to the action of sets of wheels and various shuttle axes, where a cycle counting procedure and a damage accumulation model could be considered. Finally, an Instron hydraulic system was used with a 100 kN rated load cell. shows the final design of the experimental setup used in a downward (). For the downward loading scenario, the best results were obtained with the actuator depicted in . Regarding the upward loading scenario, it became clear that the rail behaves differently when comparing to the downward case. To correct this issue and to ensure optimal results, a steel clamp was added to the mid-span support (see c-d), further increasing the local stiffness of the web; a steel plate was also added between the load actuator and the rail (see Finally, to determine the lifetime for each specimen in terms of number of load cycles endured by the profile, a strain gauge (CEA-06-250UM-120) was used as a crack detection method. For the downward loading scenario, a strain gauge was placed on the web (see Disregarding preliminary tests used in the iterative development of the proposed fatigue setups, presents the full fatigue testing matrix for full-scale Z-rails. A total of 36 specimens were tested, two at a time. The load values were defined after some trial tests to cover fatigue lives approximately in the range between 5×104 and 5×106 cycles (run-out).This section presents the main numerical details of the various finite element models that were created during this study. Respectively, the following sections refer to numerical models used for: i) elastic stress range computations for building S-N curves disregarding residual stresses; ii) simulating the cold roll-forming process, aiming to obtain the Z-rail’s internal residual stresses; iii) simulating fatigue loading considering previous residual stresses, aiming to apply a local fatigue life prediction approach.For S-N data derivation, finite element models were used to compute the elastic stress ranges at which the Z-rail specimens were subjected to during experimental fatigue testing. In these models, the rail’s material is considered elastic; thus, there are no considerations for manufacturing residual stresses, which is a common situation for design stages, where residual stresses should be accounted in the resistance S-N curves and not in the actions. These models were built in Abaqus/CAE observing the following characteristics:Regarding the geometry of the rail, a total length of 880 mm was considered (distance between clamping bolt holes in ), however, to save on computational costs, the model uses the symmetry in the Z-rail’s length axis; thus, only half of the total length is modelled (440 mm).Regarding the material properties of the rail, the S355MC steel is considered elastic (elastic properties shown in ). The rail is also considered solid and homogeneous.Regarding the remaining parts present in the model, namely the load actuator shown in Regarding the load stepping procedure, it should be noted that non-linear geometry effects are considered.Regarding boundary conditions, symmetry conditions are included, as stated above. Besides that, the rail’s web (end facet) is fixed on both ends, and since in the real setup the rail is supported on both ends by bolted connections, this is a simplification to save on computational costs due to a simpler geometry to mesh; however, since major stresses/strains are localized in the mid-span of the rail, this is assumed to be an acceptable simplification. Finally, the mid-span support is modelled by fixing the internal surface of the mid-span bolt holes.Regarding load conditions, the actuator is displaced until half of the intended load is achieved (magnitude of reaction force at the actuators reference/control point), due to symmetry. It should be noted that the actuator is free to rotate along the rail’s length axis. shows the mentioned finite element models created in Abaqus/CAE for downward and upward loading scenarios. To validate these models, two monotonic tests were conducted (for a total of 4 specimens tested). Using the results from these tests, shows a satisfactory match between stress values obtained from the elastic numerical models and stress values obtained from strain gauges, where registered strains were converted to stresses according to the following constitutive law:Small deviations may be due to the uncertainty of the strain gauge location with respect to the numerical finite element node and the area of influence of the strain gauge together with some degree of uncertainty of the global experimental boundary conditions, which are typical of full-scale testing.This section presents some details of the finite element model used to simulate the cold roll-forming process of the Z-rail, which includes the determination of plastic strain histories and internal residual stresses. The COPRA RF software The modelled roll-forming machine is based on CAD drawings of the real machine made available by the manufacturer and the Z-rail’s roll-forming flower diagram is seen in . In total, 18 accurately drawn stations are present in the model, where most are separated by a 500 mm distance, ensuring representative kinetics are simulated.A pre-cut strip of 900 mm (intended rail’s length) was modelled, and regarding the finite element mesh, in the transversal direction, element edge size is approximately 2 mm for the corner/bend regions and 12 mm for the straight segments. Along the longitudinal direction, element edge size is around 8 mm. Across the thickness, 3 element layers are used. The mesh is comprised of continuum hexahedral elements with 8 nodes and 8 integration points (tri-linear, full integration). shows the roll-forming model, where the forming rolls are considered as analytical rigid parts and contact interactions between the rolls and the strip are automatically defined and divided into several load cases by the software. Regarding the S355MC steel, its elastoplastic behaviour was defined by the elastic properties from a, in tabular form. The von Mises yield criterion was considered, as well as an isotropic hardening rule. In this study, the roll-forming simulation does not have considerations about friction. On effect, a common (quasi-static) simplification of the roll-forming process was made: the strip is fixed in place with boundary conditions that prevent rigid-body motion, while the rolls move towards the strip without actually rolling (since contact is frictionless). This still captures both the transversal and longitudinal deformations that the strip must go through to produce a Z-rail.In this study, the so-called modified Morrow model where Δ∊ is the elastoplastic strain range evaluated locally where the peak values are verified; σm is the mean stress within the load cycle, also evaluated locally; Nf is the estimated number of load cycles to failure; E is the Young’s modulus of the material; σf′ and b are, respectively, the fatigue strength coefficient and exponent; ∊f′ and c are, respectively, the fatigue ductility coefficient and exponent.Regarding the fatigue constants, results were obtained from the literature for a S355 steel presents these constants that were used in this study to represent the S355MC steel fatigue properties. These constants represent the fatigue behaviour of the material tested with 5 mm thickness and mirror polished surfaces under uniaxial tension–compression loading (R=-1).Using the obtained Z-rail geometry and residual stress/strain field from the finite element model presented in As the experimental data supporting the Morrow fatigue damage relation was derived from uniaxial tensile-compression tests and the Z-rail profile will be subjected to local bending, with significant stress/strain gradients across thickness, the Theory of Critical Distances (TCD) In the present study the PM and LM are tested. Regarding the definition of the critical distance parameter, L, it is understood as a material property, and based on the proposed study by El Haddad et al. Recent advances in the TCD have been proposed in the literature aiming at combining notch stress gradient effects with size effects and probabilistic approaches Using the fatigue testing setup for full-scale thin-walled profiles presented in , the experimental fatigue life was determined for 36 Z-rail specimens (18 tested in downward loading, and another 18 tested in upward loading).As previously mentioned, strain gauges were used as a crack detection method and the registered strain spectrums were plotted for further analysis (for convenience, strains were converted into stresses by using the constitutive law shown in Eq. (2)). In a downward loading scenario (a shows an example of a single specimen tested in a downward loading case, where an endurance of 325,000 cycles is assumed. Regarding the upward loading scenario (c-d), the strain gauge is now placed in a less-than-ideal but possible location; the determination of the lifetime of a specimen is still possible due to significant stress range variations in the plot. These local variations indicate the presence of a crack. b shows an example of a single specimen tested in an upward loading case, where an endurance of 240,000 cycles is assumed. In this loading condition, higher scatter was observed in the strain spectrum due to the higher influence of various friction pairs in the process and through-thickness cracks were verified.The process of analysing each individual stress range plot was assisted by previous periodical visual inspections and written records on crack development by the laboratory staff. Combining these records with the plots increased the confidence of the declared fatigue life values for any given specimen.For S-N data derivation, there is still the matter of computing the stress ranges that each specimen was subjected to during experimental fatigue testing. To this end, the finite element models presented in shows the simulation of a downward and upward loading scenarios (9 kN example). The usage of elastic stress ranges instead of actual elastoplastic ones aims at generating S-N data directly comparable with design S-N curves often based on pseudo-elastic stress ranges. Alternatively, a strain measure would be preferable for S-N data presentation due to the local plastic strains generated.Based on experimental fatigue life and computed peak values of elastic maximum principal stresses, presents the obtained S-N curves. The ASTM E739-91 standard a, the obtained data (except a single outlier point) fits within the 2 standard deviations confidence band. The inverse slope of the obtained global fatigue strength curve is m=5.96, which is higher than the reference value of the Eurocode 3 b, there is a very slight difference between the upward and the downward loading scenario, where the downward loading scenario presents a lower fatigue strength, indicating that this loading scenario is the most damaging. This effect could be justified by the tensile residual stresses developed at the corner’s inner surface, while compressive residual stresses are generated at the corner’s outer surface (as shown further in the paper). a also presents a comparison between the obtained S-N curve and curves from Eurocode 3. The category of 160 MPa (with m=3) for plain material is already present in current versions of the standard. However, a current draft made available by the CEN/TC 250 aiming the future revision of Eurocode 3 proposes a new detail category of 180 MPa with an inverse slope of m=5a, both curves from Eurocode 3 are conservative, however, the new inverse slope of m=5 that is proposed in the Eurocode 3 draft is a much better match with the obtained results. The category of 180 MPa S-N curve with m=5 gives a consistently conservative design curve for the Z-rail profiles. This curve still shows an extra fatigue strength safety factor of approximately 1.67 (=300/180). were one can see the multiple initiation sites at parallel planes and their coalescence in one single fatigue crack plane. also shows a fracture surface with multiple cracks (bottom centre), fatigue striations (bottom right) and clear transition from crack opening to a crack closure scenario (bottom left). represent the manufacturing residual strain/stress fields obtained for the simulation of the Z-rail profile. Considering the fatigue/structural loading that these rails are subjected to, the most relevant residual stresses to be analysed are the transversal ones. To obtain the transversal residual stresses, an element-local coordinate system was used for each element. b, where, as previously stated, there is a very slight difference between an upward and a downward loading scenario, where the downward loading scenario presents a lower fatigue strength, indicating that this loading scenario is the most damaging. However, again, this effect is minimal, which could be likely due to eventual residual stresses relaxation during cyclic elastoplastic loading. presents the fatigue life prediction vs. the experimental fatigue life criterion. To have a good fatigue life prediction, all points in should fall in a narrow band around the 45 degrees line. The criteria of 2×|0.5× (dashed lines) and 4×|0.25× (dotted lines) were plotted and one can realize that some points fall outside these bands, however, in the safe predictions side. The consistency of the safe predictions could be justified by the use of the peak values of the fatigue damage driving parameters. One can also see that the predictions regarding the upward loading conditions were more conservative than the predictions performed for the downward cases, which could be justified by the way the load in the numerical model was applied (point load in the numerical model vs. linear load distributed by a plate in test). presents the predictions performed using the TCD coupled with the modified Morrow model, with the critical distance presented previously. Both the PM and LM were used and the three criteria for the correction of the mean stress effects on the fatigue limit, from R=-1 to R=0.1. presents the mean squared errors for the predictions. One can see that the PM yields the best predictions. In addition, the Goodman criterion produced the best results, followed by the Gerber, which is consistent with the literature Innovative fatigue design assessment procedures for thin-walled cold-formed members were investigated in this research, using the Z-rail profile as a case study. The manufacturing residual stress effect on the fatigue resistance was also investigated. The main innovative points shown in this research are:The use of a purpose-built fatigue testing setup for full-scale Z-rail profiles to generate representative cracking and to determine experimental fatigue endurances.The construction of a master S-N curve that encompasses two loading scenarios (downward and upward cases, which were emphasised during this work) based on elastic maximum principal stresses.The simulation of the cold roll-forming manufacturing process was coupled with structural loading using elastoplastic FEA; this allowed to include manufacturing residual stresses in the fatigue modelling.The TCD was coupled with the modified Morrow model, where two different philosophies of the TCD were explored, the PM and LM methods. Additionally, a mean stress correction was applied using three classical equations proposed by Goodman, Gerber, and Soderberg.The main concluding remarks can be summarized as follows:The purpose-built fatigue testing setup was very successful in generating representative fatigue cracking: the obtained failure modes are very similar to the ones observed in real-world applications, while being possible to identify macroscopic fatigue crack initiation and test two profiles simultaneously.The obtained master S-N curve based on elastic maximum principal stresses supports the current revision of the Eurocode 3, namely the inclusion of new detail categories with m=5. The detail category of 180 MPa is demonstrated to be enough conservative for safe design.The usage of the TCD was key for a reliable comparison between the experimental and numerical results of fatigue lifetimes. The PM combined with the Goodman equation returned the best fatigue life predictions.C.D.S. Souto: Methodology, Software, Formal analysis, Data curation, Writing - original draft, Visualization. V.M.G. Gomes: Conceptualization, Methodology, Investigation. M. Figueiredo: Investigation. J.A.F.O. Correia: Validation, Writing - review & editing. G. Lesiuk: Validation, Writing - review & editing. A.A. Fernandes: Supervision, Project administration, Funding acquisition. A.M.P. De Jesus: Conceptualization, Writing - review & editing, Supervision, Project administration, Funding acquisition.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Finite-element analysis and design of aluminium alloy CHSs with circular through-holes in bendingFinite-element analysis (FEA) was performed in this study on the flexural behaviour of aluminium alloy circular hollow sections (CHSs) with circular through-holes subjected to gradient and constant bending moments. The non-linear finite-element models (FEMs) were established and verified by the corresponding experimental results. The material and geometrical non-linearities, as well as the initial geometrical imperfections, were taken into account in the FEMs. The validated FEMs were employed in an extensive parametric study on a total of 408 specimens, which have the cross-section slenderness ratio (D/t) and hole size ratio (d/D) ranged from 5 to 150 and from 0.2 to 0.8, respectively. The influences of the cross-section slenderness ratio and hole size ratio of the CHSs, as well as the quantity and location of the circular through-holes on the flexural strengths of aluminium alloy CHSs with circular through-holes, were carefully evaluated. The test and FEA flexural strengths are compared with the design flexural strengths determined by the modified direct strength method (DSM) and the modified continuous strength method (CSM) developed for aluminium alloy flexural members. The comparison indicates that the current design guidelines are conservative for aluminium alloy CHSs with circular through-holes in bending. Therefore, the design equations are proposed on the basis of the modified CSM for the flexural strengths of aluminium alloy CHSs with circular through-holes. A reliability analysis was carried out to evaluate the modified DSM, the modified CSM and the proposed design equations. It is demonstrated that the proposed design equations are of high precision and reliability for aluminium alloy CHSs with circular through-holes in bending.Aluminium alloy materials have got increasing attention over the past few years in the construction industries such as building curtain walls, pedestrian bridges and many spatial structures, which benefit from the superior material properties of lightweight, attractive appearance, excellent anti-corrosion and easy manufacture. It was observed in the steel buildings that floor beams with holes at web could help the laying of the pipes and ducts for electric wires, internet cables, heating, air-conditioning and water supply. The aluminium alloy members with holes are also a good choice for a replacement, even if the reduction of the ultimate strengths and the complexity of the design rules usually resulted from the introduction of the multiple holes.The early research on aluminium alloy members was carried out by Bijlaard and Fisher [] dating back to 1950s. The aluminium alloy flexural members with various cross-section forms including H-section, square and rectangular hollow sections (SHS and RHS) were all well studied. Both experiments and numerical simulations were carried out by Moen et al. [] on the rotational capacities of aluminium alloy beams under moment gradient. The finite-element model (FEM) established in the numerical analysis successfully predicted the load-deflection behaviour of the compact aluminium alloy beams subjected to local buckling. Eberwien and Valtinat [] investigated the bending moment versus curvature relationship of an aluminium alloy symmetrical cross section by using the fullness method, which was also extended to two material systems in the study. The direct strength method (DSM) derived by Schafer and Peköz [] for carbon steel members in bending was extended by Zhu and Young [] to the design of aluminium alloy SHS flexural members. It was found that the DSM was modified with high precision and reliability for the prediction of the flexural strengths of aluminium alloy SHS tubes. Piluso et al. [] studied the ultimate response of temper T4 and T5 aluminium alloy beams subjected to non-uniform bending. The empirical design formulations were obtained for predicting the rotation capacities of aluminium alloys. However, few types of researches were conducted on aluminium alloy flexural members with holes. Zhou and Young [] ever investigated the web crippling of aluminium alloy SHSs with circular web holes. A unified design equation was proposed for web crippling.As a convenient and time-efficient tool, finite-element analysis (FEA) was widely carried out to predict the strengths and behaviour of aluminium alloy flexural members. A FEM with high precision and reliability is pre-requisite for the parametric study of aluminium alloy flexural members. A numerical study was performed by De Matteis et al. []. The verified FEM was used in the parametric study to evaluate the bending capacities determined by the design rules and the continuous strength method (CSM). Wang et al. [] studied the local buckling behaviour of extruded I-shaped beams in aluminium alloy of 6000 series. A FEM was established for the parametric study on 24 specimens, which was calibrated well against the experimental results. An extensive numerical analysis was performed by Castaldo et al. [] on the ultimate behaviour of RHS temper T4 and T6 aluminium alloy beams under non-uniform bending considering the governing geometrical parameters. The empirical relationships to predict both the non-dimensional ultimate flexural resistance and the rotation capacity of RHS temper T4 and T6 aluminium alloy beams were obtained by means of multivariate non-linear regression analyses. However, the aforementioned FEA all focused on aluminium alloy flexural members without holes. Up to the authors’ knowledge, the FEA on aluminium alloy flexural members with holes was rare, not to mention aluminium alloy circular hollow sections (CHSs) with circular through-holes in bending.This paper presents the FEA on the flexural behaviour of aluminium alloy CHSs with circular through-holes in bending. The FEMs were established for aluminium alloy CHSs subjected to gradient and constant bending moments, which were calibrated by the corresponding experimental results. The validated FEMs were employed in an extensive parametric study on aluminium alloy CHS flexural members. The modified DSM and the modified CSM were evaluated by the numerical results for the flexural strengths of aluminium alloy CHSs. The modified CSM was further modified for aluminium alloy CHSs with circular through-holes in bending. In addition, a reliability analysis was carried out to evaluate the modified DSM, the modified CSM and the proposed design equations.] conducted the simply-supported bending tests on aluminium alloy CHSs with circular through-holes, as shown in . The specimens were fabricated by extrusion of CHS 150 × 7 and CHS 202 × 7.5 using heat-treated aluminium alloys of 6061-T6 and 6063-T5, respectively, which were considered as high strength and normal strength materials, respectively. A total of 12 specimens were subjected to gradient and constant bending moments, in which 8 perforated aluminium alloy CHSs were tested by punching multiple circular through-holes with the nominal diameters of 0.3D, 0.45D and 0.6D at the cross sections that evenly positioned along the longitudinal direction of the specimens, another 4 imperforated aluminium alloy CHSs were tested for comparison. The mechanical properties of aluminium alloys were obtained from longitudinal tensile coupon tests, which are summarized in . The simply-supported bending tests were conducted using a hydraulic jack with steel triangle and steel roller at two ends of the specimens, which were used to simulate hinge support and roller support, respectively. The stiffening bearing components were designed at the loading points to preclude the premature failure of local buckling at the location subjected to the maximum bending moment and shear force. The failure modes, ultimate bending moments, testing curves of bending moment versus curvature, as well as strain distributions along half of CHS cross sections of all specimens were obtained.The failure modes and ultimate bending moments of all specimens were determined, which are also presented in . The comparison indicated that the ultimate loads of all specimens in three-point bending were smaller than those in four-point bending due to the weakening effect of the shear force in the gradient moment zone. Whereas, the ultimate bending moments of all specimens in three-point bending were greater than those in four-point bending owing to the larger lever arm of bending. On the other hand, it was also found that the flexural strengths of the specimens reduced by introducing circular through-holes. And the decrease of the flexural strengths by increasing the diameter of circular through-holes was larger than that by increasing the quantity of circular through-holes.The current design guidelines of American Specification (AA) [] in Australian/New Zealand Standard (AS/NZS), and Chinese Code [], as well as the modified DSM and the modified CSM were evaluated by comparing the test flexural strengths with the design flexural strengths for both imperforated and perforated aluminium alloy CHSs. The comparison demonstrated that the current design guidelines were all quite conservative. In addition, the modified DSM and the modified CSM were also found to be quite conservative for aluminium alloy CHSs with circular through-holes subjected to gradient and constant bending moments.The general-purpose finite-element software ABAQUS [] was employed to simulate the behaviour of aluminium alloy CHSs with circular through-holes in bending. The aluminium alloy CHSs, the profiled stiffening steel components used in the tests to accommodate the CHSs, and the interfaces between aluminium alloy CHSs and contacted stiffening steel components were carefully modelled in the FEA. The measured specimen dimensions, initial geometrical imperfections and mechanical properties determined by tensile coupon tests were all incorporated in the FEMs. The residual stress profiles resulted from the extrusion of aluminium alloys were ignored in finite-element modelling, which have little effect on the behaviour of aluminium alloy CHSs in bending. Furthermore, the partial safety factor related to the resistance model uncertainties in the FEA was not considered in this study, although the FEM is always affected by the model uncertainties [The aluminium alloy CHSs were modelled by using the four-node hyperbolic shell element with reduced integration (S4R), which is suitable for the numerical analysis of thin-walled structures with thin or medium thickness. Each node of S4R element has six degrees of freedom including translational displacements along the x, y and z directions and rotational displacements around the axes of translational displacements. The optimum finite-element mesh size was chosen as 14 × 14 mm (length by width) for aluminium alloy CHSs based on the convergence studies, which could provide accurate results with minimum computational costs. The finer meshes were employed at the vicinity of circular through-holes along the longitudinal direction of the CHSs to take the possible stress concentrations into consideration. In addition, the profiled stiffening steel components at loading points and end supports of the specimens were modelled by using the analytical rigid body.The mechanical properties of aluminium alloys in ] include Young's modulus (E), 0.2% tensile proof stress (σ0.2), ultimate tensile stress (σu) and fracture strain (εf). The measured non-linear stress-strain curves were employed in finite-element modelling, which consist of the elastic property involving Young's modulus and Poisson's ratio of 0.3 with the stress up to the proportional limit, and the plastic property involving large plastic strains. Furthermore, the engineering curves of static stress (σ) versus static strain (ε) were converted to true curves of true stress (σtrue) versus logarithmic plastic strain (εpl) by using the conversion equations specified in ABAQUS [] as σtrue=σ(1+ε) and εpl=ln(1+ε)-σtrue/E, which is illustrated in The initial geometrical imperfections usually include local and overall geometrical imperfections, in which the overall geometrical imperfections can be ignored for aluminium alloy thin-walled flexural members due to its insignificant influence. Therefore, the local geometrical imperfections were considered in the FEMs by conducting the Eigen-value analysis, from which the buckling mode was achieved by using the (*BUCKLE) step in ABAQUS library. The initial local geometrical imperfections were included in finite-element modelling based on the first-order buckling mode obtained from the Eigen-value analysis that normalized to 1.0, which was factored by the measured magnitude of t/10 as recommended by Zhu and Young [], where t is the wall thickness of aluminium alloy CHSs.The compression force was applied through the profiled stiffening steel component to the mid-span of the specimens, which were therefore in three-point bending. While, the compression force was applied through the profiled stiffening steel components to two loading points of the specimens simultaneously, which were therefore in four-point bending. The profiled stiffening steel components in the FEA were modelled by the analytical rigid body, whose Reference Points were free to move in the direction of the applied loads and along the longitudinal direction of the specimens, as well as rotate around the bending axes. The compression force was applied in the numerical analysis by means of displacement control at the Reference Points. The load-displacement non-linear analysis following the Eigen-value analysis was performed by adopting the (*RIKS) step in ABAQUS library. The non-linear geometrical parameter (*NLGEOM) was employed to take the non-linear deformation behaviour of the specimens under the loading application into consideration. The contact interaction played an important role in the load transferring between the rigid stiffening steel components and the deformable aluminium alloy CHSs, which was modelled by using a contact pair “Master-slave” algorithm in ABAQUS library. In addition, the hinge support and roller support at two ends of the specimens were modelled by the analytical rigid body with Reference Points being restrained against the relevant degrees of freedom.A total of 12 perforated aluminium alloy CHSs subjected to gradient and constant bending moments were analyzed. The numerical results of all specimens including the failure modes, ultimate bending moments and deformation curves of bending moment versus mid-span deflection are compared with the corresponding experimental results to verify the FEMs. The comparison of the ultimate bending moments obtained from the experiments (MEXP) and FEA (MFEA) is summarized in . Good agreement of the comparison (MEXP/MFEA) is reached with the mean value of 1.03 and coefficient of variation (COV) of 0.038, while the maximum difference of the comparison is 9%.In addition, the comparison of the failure modes of all specimens obtained from the experiments and FEA is also given in . It is shown from the comparison that the flexural buckling failure occurred for all specimens in the experiments, which is predicted by the FEA as plotted in a. In particular, the specimen HC150 × 7-n6-d90-B3 was subjected to the combination of local and flexural buckling failure in the experiments, which is also predicted by the FEA as plotted in b. It is found that the typical failure modes observed in the experiments are accurately captured by the FEA.On the other hand, the deformation curves of the specimens HC150 × 7-n6-d90 subjected to gradient and constant bending moments obtained from the experiments and FEA are also compared in , where the horizontal axis represents the mid-span deflection and the vertical axis refers to the bending moment. It is demonstrated from the comparison that the testing curves agree well with those predicted by the FEA. Therefore, the FEMs were validated to be accurate by good agreement between the experimental and numerical results in terms of the failure modes, ultimate bending moments and deformation curves of bending moment versus mid-span deflection, which can be used to estimate the strengths and behaviour of aluminium alloy CHSs with circular through-holes in bending.It is demonstrated that the validated FEMs accurately simulated the strengths and behaviour of aluminium alloy CHSs with circular through-holes in bending, which were employed in an extensive parametric study on a total of 408 specimens to evaluate the effects of critical geometrical parameters including the cross-section slenderness ratio (D/t) and hole size ratio (d/D) of the CHSs, as well as the quantity and location of the circular through-holes. The specimens consisted of 12 cross sections with the outer diameter (D) and wall thickness (t) ranged from 50 to 300 mm and from 2 to 10 mm, respectively, while the overall lengths (L) were determined from 1000 to 2800 mm accordingly. Hence, a wide range of cross-section slenderness ratio (D/t) from 5 to 150 was involved in the parametric study, which extended the classification of cross sections from the stocky section to slender section. In addition, the quantity of circular through-holes was chosen as 1, 2, 4 and 6 with the hole size ratio (d/D) ranged from 0.2 to 0.8, where d is the diameter of circular through-holes. For the beams with one circular through-hole only, the location of the hole was arranged according to the distance (x) between the supporting end and the center of the hole. While, for the beams with multiple circular through-holes, the locations of holes were determined symmetrically by the distance (x) between the supporting end and the center of the first hole as well as the uniform interval (s) of adjacent holes. In the meanwhile, the imperforated aluminium alloy CHSs were also simulated for comparison. One-half of specimens were simulated in three-point bending with the compression force applied to the mid-span of the specimens, which resulted in the uniform shear force with the shear span along the half-length of the specimens. While, the other half of specimens were simulated in four-point bending with the compression force applied through a spreader beam, which resulted in the pure bending moment between two loading points with the moment span of 500 and 700 mm for the specimens with the overall lengths of 1000 and 1600 mm, as well as 2200 and 2800 mm, respectively.The similar labelling rules adopted in the experiments were also used in the parametric study. The labels of the specimens were defined according to the cross section and overall length of the CHSs, the quantity, diameter and location of the circular through-holes, as well as the loading and boundary conditions. One of the labels “C200 × 2-L2200-n2-d100-1-B3” defines a perforated aluminium alloy CHS flexural member. The first letter ‘‘C’’ represents the CHS with the subsequent expression ‘‘200 × 2″ denotes the nominal outer diameter (D) of 200 mm and wall thickness (t) of 2 mm. The second notation ‘‘L2200″ represents the nominal overall length (L) of 2200 mm. The third notation ‘‘n2″ represents the quantity of circular through-holes of 2. The fourth notation ‘‘d100″ refers to the nominal diameter (d) of circular through-holes of 100 mm. The fifth notation “1” refers to the location of circular through-holes for the beams with one or two holes. It should be noted that the distance (x) between the supporting end and the center of the first hole for the beams with the fifth notation “2” is smaller than that of the beams with the fifth notation “1”. Both of them are smaller than that of the beams without fifth notation. If the third, fourth and fifth notations are not shown in the label, it indicates the imperforated aluminium alloy CHS. The last notation ‘‘B3″ refers to three-point bending. If the notation is “B4”, it refers to four-point bending. The prefix letter “B” denotes bending.The details of all specimens in the parametric study including the cross section of the CHSs, the diameter, quantity and location of the circular through-holes are summarized in for aluminium alloy CHSs with the outer diameter (D) of 50, 100, 200 and 300 mm, respectively, with the definition of symbols clearly shown in . The high strength aluminium alloy type 6061-T6 was employed in the parametric study for all specimens, whose mechanical properties are summarized in with the corresponding engineering and true stress-strain curves plotted in . The initial local geometrical imperfections were chosen as t/10 in the parametric study for all specimens on the basis of the suggestions of Zhu and Young [], where t is the wall thickness of aluminium alloy CHSs.The ultimate bending moments (MFEA) of all specimens in the parametric study were obtained from the FEA, as presented in . The flexural strengths of aluminium alloy CHSs decreased by introducing circular through-holes, which destroyed the continuity of flexural members. Besides, the ultimate bending moments (MFEA-3) of the specimens in three-point bending are found to be generally higher than the ultimate bending moments (MFEA-4) of the specimens in four-point bending, which were verified by the experimental investigation in a companion paper []. The influences of the critical geometrical parameters including the diameter, quantity and location of the circular through-holes on the flexural strengths of aluminium alloy CHSs were evaluated separately.The influence of the diameter of circular through-holes on the flexural strengths of the specimen C200 × 6-L2200-B4 in four-point bending was investigated in . The comparison shows that the flexural strengths of aluminium alloy CHSs in four-point bending slightly reduced up to 0.60% and 6.97% by introducing one circular through-hole at the mid-span of the specimen with the diameters of 0.2D and 0.5D, respectively. Whereas, the reduction significantly rose up to 36.51% by raising the diameter of circular through-hole to 0.8D. The similar reduction of the flexural strengths of aluminium alloy CHSs occurred regardless of the quantity of circular through-holes positioned symmetrically along the longitudinal direction of the specimens.The influence of the quantity of circular through-holes on the flexural strengths of the specimen C300 × 6-L2800-B3 in three-point bending was also investigated in . The comparison exhibits that the reduction of the flexural strengths of aluminium alloy CHSs in three-point bending slightly increased from 0.18% to 0.26%, from 19.98% to 20.79%, and from 49.74% to 59.70% by raising the quantity of circular through-holes from 1 to 6 for the specimens with the same diameters of 0.2D, 0.5D and 0.8D, respectively.Furthermore, the influence of the location of one or two circular through-holes with the same diameter of 0.5D on the flexural strengths of the specimen C200 × 10-L2200-B3 in three-point bending was also investigated in , respectively. The comparison indicates that the difference of the flexural strengths of aluminium alloy CHSs with the same diameter and quantity of circular through-holes at different locations depends on the distance between the location of circular through-hole and the loading point. The larger is the distance, the larger is the flexural strength, which may attribute to the location of circular through-holes that within the moment span or shear span of the specimens.The current design guidelines are available in AA [] for aluminium alloy members in bending. Furthermore, the DSM developed by Schafer and Peköz [] which was adopted in North American Specification (NAS) [], as well as the CSM proposed by Gardner [] and later modified by Buchanan et al. [] also provide design guidelines for aluminium alloy members in bending. It should be noted that the aforementioned design specifications have no design guidelines for aluminium alloy members with circular through-holes in bending. Whereas, the modified DSM [] could be used to predict the flexural strengths of aluminium alloy CHSs with circular through-holes by replacing the elastic and plastic moduli of the gross section with the elastic and plastic moduli of the effective section, respectively.] for imperforated aluminium alloy SHS and RHS beams and columns. The design equations of modified DSM were verified to be accurate and reliable as follows:MDSM−M={Myλl≤0.7131−0.15McrlMy0.3McrlMy0.3Myλl>0.713in which, λl=My/Mcrl; My=fySg.where Mcrl is the critical elastic moment for local buckling, Sg is the modulus of the gross section, and fy is the static 0.2% proof stress.The CSM was also extended by Buchanan et al. [] to aluminium alloy CHS beams. Aluminium alloy non-slender (λc‾≤0.3) and slender (0.3<λc‾≤0.6) CHS cross sections were considered in this method. The design equations of modified CSM were verified to be accurate and reliable as follows:Forλc‾≤0.3,MCSM−M=Mpl[1+EshEWelWpl(εcsmεy−1)−(1−WelWpl)/(εcsmεy)2]Forλc‾≤0.3εcsmεy=4.44×10−3λc‾4.5≤min(15,0.5εuεy)For0.3<λc‾≤0.6εcsmεy=(1−0.224λc‾0.342)1λc‾0.342in which, Mpl=Wplfy; Esh=fu−fy0.5εu−εy; σcr=E3(1−ν2)2tD; εu=0.13(1−fyfu)+0.06; λc‾=fyσcr.where Wel and Wpl are the elastic and plastic section moduli, respectively, σcr is the critical elastic buckling stress, fy and fu are the yield and ultimate stresses, respectively, and εy and εu are the yield and ultimate strains, respectively.The ultimate bending moments of aluminium alloy CHSs with circular through-holes obtained from the experiments (MEXP) and FEA (MFEA) are compared with the design flexural strengths calculated using the modified DSM and the modified CSM, as displayed in . The cross sections and mechanical properties as summarized in were used to calculate the ultimate bending moments. The design flexural strengths were obtained from the modified DSM and the modified CSM by replacing the elastic and plastic moduli of the gross section with the elastic and plastic moduli of the effective section, respectively. It should be noted that the modified CSM is inapplicable to the specimens with the slenderness (λc‾>0.6), such as the specimens with the cross section of CHS 300 × 2 in . The mean values of the comparison in terms of test and FEA-to-design flexural strength ratios Mu/MDSM-M and Mu/MCSM-M are 1.47 and 1.28, having the COVs of 0.264 and 0.168 for the modified DSM and the modified CSM, respectively. It is shown from the comparison that the modified DSM and the modified CSM are both conservative for aluminium alloy CHSs subjected to gradient and constant bending moments.The comparison of the test and FEA flexural strengths with the design flexural strengths shows that the modified DSM and the modified CSM are conservative for aluminium alloy CHSs with circular through-holes in bending, in which, the modified DSM was ever extended to perforated cold-formed steel flexural members []. Whereas, the modified CSM provided relatively accurate results with smaller COV compared to the modified DSM. Therefore, the modified CSM was further revised to estimate the flexural strengths of aluminium alloy CHSs with circular through-holes.The effects of the critical influential factors including the cross-section slenderness ratio and hole size ratio of the CHSs, the quantity and location of the circular through-holes, as well as the loading and boundary conditions on the flexural strengths of aluminium alloy CHSs with circular through-holes was evaluated in the numerical work. The comparison indicates that the cross-section slenderness ratio has a great influence on the flexural strengths of the specimens. While, the reduction of the flexural strengths of the specimens resulted from the circular through-holes with the hole size ratio (d/D) ranged from 0.2 to 0.8 greatly increased. Furthermore, the quantity of circular through-holes is found to be important to the flexural strengths of the specimens, especially by increasing the hole size ratio (d/D) up to 0.8. While, the influence of the location of circular through-holes on the flexural strengths of the specimens depends on the distances between the center of the circular through-holes and the loading points. In addition, the flexural strengths of the specimens in three-point bending are generally greater than those of the specimens in four-point bending. Therefore, all these influential factors need to be taken into account in the proposed design equations on the basis of the modified CSM [] for the flexural strengths of aluminium alloy CHSs with circular through-holes.The design equations for the flexural strengths of aluminium alloy CHSs with circular through-holes are proposed on the basis of the numerical results, which particularly considered the influences of the circular through-holes including the hole size ratio (d/D), the location (x/l0) and quantity (s/l0) of the circular through-holes as follows:MCSM−P={[1−(dD)−0.527n+5.527](xl0)−0.139[1−(sl0)17.307]MCSM−Mλc‾≤0.31.09[1−(dD)−0.641n+6.255](xl0)−0.172[1−(sl0)22.594]MCSM−M0.3<λc‾≤0.6where d is the diameter of circular through-holes, D is the outer diameter of CHSs, n is the quantity of circular through-holes, x is the location of the hole which is defined as the distance between the supporting end and the center of the first hole, s is the interval of adjacent holes, l0 is the effective span of the beam which is defined as the distance between the two supporting ends.It should be noted that the weakening effect of holes on the flexural strengths of aluminium alloy CHSs has been taken into account by including the hole size ratio (d/D) in the proposed design equations. Hence, the elastic and plastic moduli of the gross section rather than the effective section need to be used in the computation of MCSM-M.The ultimate bending moments of aluminium alloy CHSs with circular through-holes obtained from the experiments (MEXP) and FEA (MFEA) are compared with the design flexural strengths (MCSM-P) calculated using the proposed design equations, as displayed in . The mean value of the comparison in terms of test and FEA-to-design flexural strength ratio Mu/MCSM-P is 1.05, having the COV of 0.100.In addition, a reliability analysis was carried out based on the recommendations specified in AA [] to evaluate the modified DSM, the modified CSM and the proposed design equations for aluminium alloy CHSs with circular through-holes. The target reliability index (β) recommended as the minimum limit in AA [] was adopted in this study as 2.5, which means the design rules with the reliability index larger than or equal to 2.5 are considered to be reliable. The resistance factor (φ) was chosen as 0.90, while the load combination of dead load (DL) with the load factor of 1.2 and live load with the load factor of 1.6 was employed in the reliability analysis for the modified DSM, the modified CSM and the proposed design equations with the ratio DL/LL equaling to 0.2. The mean values (Mm and Fm) of material and fabrication factors given in AA [] are 1.10 and 1.00, respectively, having the COVs (VM and VF) of 0.06 and 0.05, respectively. The mean values and COVs of the load ratio including Pm and VP were also employed in the reliability analysis. The correction factor (CP) was also involved to take the effect of a small number of specimens into consideration. The reliability indices (β) were determined from the equation of β=ln(1.5MmFmPm/ϕ)VM2+VF2+CPVP2+0.212, which are equal to 2.85, 3.03 and 2.66 for the modified DSM, the modified CSM and the proposed design equations, respectively, as presented in . It is demonstrated that the proposed design equations could achieve more accurate and reliable results, which are recommended to be used for the flexural strengths of aluminium alloy CHSs with circular through-holes.The FEA and design of aluminium alloy CHSs with and without circular through-holes in bending were carried out in this paper. The FEMs incorporating the material and geometrical non-linearities, and the initial geometrical imperfections were developed and validated by the corresponding experimental results, which were employed in an extensive parametric study on a total of 408 specimens. The effects of the critical geometrical parameters including the cross-section slenderness ratio and hole size ratio of the CHSs, as well as the quantity and location of the circular through-holes on the flexural strengths of aluminium alloy CHSs with circular through-holes were evaluated in the parametric study. The test and FEA flexural strengths are compared with the design flexural strengths determined by the modified DSM and the modified CSM developed for aluminium alloy flexural members. The comparison indicates that the current design guidelines are conservative for aluminium alloy CHSs with circular through-holes in bending. Furthermore, the design equations are proposed based on the modified CSM for aluminium alloy CHSs with circular through-holes in bending, which were also verified by the experimental and numerical results. A reliability analysis was carried out to evaluate the modified DSM, the modified CSM and the proposed design equations. It is demonstrated that the proposed design equations provide more accurate and reliable results, which are recommended to be used for aluminium alloy CHSs with circular through-holes in bending.Enclosed please find the revised manuscript by Ran Feng, Chengdong Shen, Junwu Lin and entitled “Finite-element analysis and design of aluminium alloy CHSs with circular through-holes in bending”, which is submitted to be considered for publication in Thin-Walled Structures.We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.Critical elastic moment for local bucklingDesign strength obtained from modified CSMDesign strength obtained from proposed design equations based on modified CSMDesign strength obtained from modified DSMUltimate bending moment obtained from experimentUltimate bending moment obtained from FEAUltimate bending moment in three-point bending obtained from FEAUltimate bending moment in four-point bending obtained from FEAMean value of test and FEA-to-design strength ratioInterval between center of adjacent circular holesCoefficient of variation of fabrication factorCoefficient of variation of material factorCoefficient of variation of test and FEA-to-design strength ratioDistance between supporting end and center of first holeLogarithmic plastic strain converted from engineering static strainTrue stress converted from engineering static stressDetermination and evaluation of Holmquist-Johnson-Cook constitutive model parameters for ultra-high-performance concrete with steel fibersUltra-high performance concrete (UHPC) features with exceedingly high strength and fracture energy, and thus is regarded as a promising structural material to resist impact and blast loadings. Particularly, adding steel fibers can significantly enhance the impact resistance of UHPC. To facilitate the simulation of the behavior of UHPC structures with various steel fiber ratios against extreme loadings, selecting an appropriate constitutive model and determining its parameters should be highly emphasized. The Holmquist-Johnson-Cook (HJC) model is widely used in the simulation of the conventional concrete subjected to impact and explosion, whereas there are rare studies on calibrating the parameters of the HJC model for UHPC. In this study, a set of HJC model parameters for UHPC with considering the volume ratio of steel fiber ranging from 0% to 3% were firstly determined based on existing test data, originating from the Split-Hopkinson pressure bar (SHPB) test, triaxial test, uniaxial loading test, and Hugoniot test. To verify the correctness of the calibrated parameters of HJC model, UHPC slabs under the contact explosion condition were then tested, and a finite element model (FEM) with the calibrated parameters implemented was thereby established to reproduce this experiment numerically. Finally, the existing bullet penetration experiment was also verified with the numerical procedure. The results show that finite element simulations by employing the HJC model with calibrated parameters agree well with the experiments. The successful applications and evaluation of the HJC model with calibrated parameters in this work can provide guidance in simulating the behavior of UHPC with certain prescribed steel fiber ratio subjected to the impact and blast loading.Protection of structures against extreme loadings, such as explosion and penetration loads, has become a serious public concern in recent decades. Ultra-high performance concrete (UHPC) is a promising material to promote the protective capability of structures owing to its high compressive strength of over 150 MPa and fracture energy of 20-40 kJ/m2, and the excellent protection capability of UHPC is attributed to the use of proper fibers []. Existing experimental results show that UHPC maintains excellent impact and blast resistance []. Yet, to enhance the understanding on the performance of UHPC structures under the high strain rate loading, blasting experiments are desirable, but it is limited due to the high cost and dificculty in obtaining the explosive. Therefore the numerical simulation becomes a favourable alternative. As a result, an appropriate constitutive model with well-calibrated parameters is the key to achieve high-fidelity simulation results.The Holmquist-Johnson-Cook (HJC) model, Riedel–Hiermaier–Thoma (RHT) model, and Karagozian & Case Concrete (KCC) model are classic models used for the numerical simulation of penetration and blast processing The HJC model is an excellent constitutive model for the simulation of UHPC structures subjected to explosion and penetration loadings and has been employed in a few studies []. To simulate the experiment of projectile penetrating UHPC plate target, Tai modified the strength and damage parameters of NC in the original HJC model ]. Therefore, to accommodate to UHPC with considering the steel fiber, the parameters of the HJC model need to be updated accordingly.In this study, a set of HJC model parameters for UHPC with considering the volume ratio of the steel fiber being 0%, 1%, 2%, and 3% are firstly determined based on the published test data, originating from the SPHB test, triaxial test, uniaxial loading test and Hugoniot test. Then, to verify the correctness of the calibrated parameters, contact explosion tests were conducted, where the volume ratio of the steel fiber for UHPC slabs is 2%. In addition, the bullet penetration tests performed by Li et al. and Jun et al. [] were also involved for verification purpose, where the volume ratio of the steel fiber in the UHPC target specimens being 0%, 2% and 3% was considered. Finite element models (FEM) were established accordingly to simulate the behavior of the UHPC targets for both tests, where the HJC model with calibrated parameters was employed. The results of numerical simulations were discussed and compared with experimental results. It shows that the FEM employing the HJC model with calibrated parameters can successfully reproduce the dynamic behavior of UHPC slabs under the contact blast loading, and favorably predict the penetration depth of the UHPC target under bullet penetrating.The HJC constitutive model, proposed by Holmquist et al., mainly includes three parts: the equation of yield surface, equation of damage evolution, and equation of state, as shown in The equation of yield surface is given aswhere σ*=σ/fc′ and P*=P/fc′ are the normalized equivalent stress and hydrostatic pressure, respectively, σdenotes the actual equivalent stress, P is the actual pressure; ε˙*=ε˙/ε˙0 is the dimensionless strain rate, where ε˙ and ε˙0=1.0s−1 are the actual and reference strain rates, respectively; A is the normalized cohesive strength; D is the damage (0≤D≤1.0); B is the normalized pressure hardening coefficient; C is the strain rate constant; N is the pressure hardening exponent; and Smax is the normalized maximum strength that can be developed.D=∑ΔεP+ΔμPεPf+μPf=∑ΔεP+ΔμPD1(P*+T*)D2≥EFMINwhere ΔεP and ΔμP are correspondingly the equivalent plastic strain and plastic volumetric strain during a cycle of integration; εPf+μPf is the plastic strain up to fracture under constant pressure P; D1 and D2 are damage constants; T*=T/fc′is the normalized maximum tensile hydrostatic pressure, where T is the maximum tensile hydrostatic pressure the material can withstand; EFMIN is a material constant used to suppress fracture from weak tensile waves.P={Kelasticμ,P≤PcrushPcrush−Plockμcrush−μplock(μ−μcrush)+Pcrush,Pcrush<P<PlockK1μ¯+K2μ¯2+K3μ¯3,P≥Plockwhere μ=ρ/ρ0−1 is the volumetric strain, ρ and ρ0 are the current density and initial density, respectively, Kelastic=Pcrush/μcrush is the elastic bulk modulus, where Pcrush and μcrush are the pressure and volumetric strain, respectively, when the material begins to undergo plastic deformation, μplock and Plock are the volumetric strain and pressure, respectively, when the air voids are completely removed from the material, μ¯=(μ−μlock)/(1+μlock)is the modified volumetric strain, μlock is the volumetric strain when the density ρ reaches the grain density ρgrain, and K1, K2 and K3 are constants.There are five parameters to be calibrated for the equation of yield surface: A, B, N, C,Smax. The normalized cohesive strength parameter A is assumed to be 0.30 [], which is obtained from a large number of experiments. B and N can be determined from the triaxial test of UHPC, where the effect of the strain rates and damage can be ignored because of the quasi-static loading and small damage during the first loading. This method was also employed by Ren et al. to determine the parameters of the HJC model for high strength concrete where σ*=(σ1−σ3)/fc′ and P*=(σ1+σ2+σ3)/3fc′. The triaxial test data of UHPC given by Ren et al. and Zhu is shown in ]. Here Ren et al. studied two batches of cylindrical UHPC specimens with the uniaxial compressive strengths of 95 MPa and 129 MPa, where the steel fiber ratio of these specimens is 2%, and the confining pressure ranges from 0 MPa to 100 MPa , and the fitting curve is σ*=0.3+1.781P*0.810 with R2=0.9879, as shown in . This high correlation result further confirms the assumption presented in the initial HJC model. Hence, B=1.781 and N=0.810 are determined.The strain rate constant C can be determined by the SHPB test of UHPC specimens. The published test data of the SHPB test is shown in , and the strain rate constant C is the slope of the fitted line, i.e., C=0.019. Therefore, all the experimental data can be well fitted by the same line, indicating that the strain rate constant C is independent of the uniaxial compressive strength and steel fiber ratio. The experiment performed by Wu et al. The normalized maximum strength Smax was determined as Smax=3.5 by Tai, where an extrapolation approach for the experimental data was employed In summary, the values of all strength parameters for UHPC material are A=0.3, B=1.781, N=0.810, C=0.019 and Smax=3.5.The equation of damage evolution has three parameters that need to be determined, which are D1, D2 and EFMIN.All three parameters can be obtained from the uniaxial loading test of the UHPC specimens. The hypothetical failure surface can be obtained from the uniaxial loading test results as shown in The values of all damage parameters are listed in . It is worth noting that, according to , as the volume ratio of the steel fiber increases, EFMIN and D1 increase, leading to the reduction of the damage D. This is consistent with the fact that the toughness of UHPC increases with increasing the volume ratio of the steel fiber.The equation of state has seven parameters that need to be determined, which are Pcrush, μcrush, Plock, μlock, K1, K2 and K3. Pcrush and μcrush are the pressure and volumetric strain, respectively, when the plastic deformation starts for specific material where E is the elastic modulus and υ is the Poisson ratio. According to the Chinese specification DBJ43/T325—2017 The porosity of UHPC is determined through experiments to be about 10.5% , Plock, K1, K2 and K3 are obtained as 3.63, 101.2, -199.5 and 329.2, respectively, as shown in . The values of pressure parameters are summarized in So far, all necessary parameters of the HJC model for UHPC with the volume ratio of steel fiber ranging from 0% to 3% were calibrated.To verify the improved HJC model with calibrated parameters for the UHPC material, six reinforced UHPC slabs were tested under the contact explosion condition, as listed in . The dimension of the slabs is 120 cm × 120 cm × 20 cm (or 40 cm). The steel fibers are mixed with a volume ratio of 2% in UHPC, where the length of the fiber is 13 mm, the diameter is 0.20 mm, and the tensile strength is over 2100 MPa. The layout of the steel reinforcement/rebar in the specimens is represented in , where the plane spacing and layer spacing of the reinforcement are 6 cm and 14.2 cm (or 34.2cm for slabs with height 40 cm) respectively. The yield stress and diameter of the rebar is 400 MPa and 9 mm, respectively. All of these specimens were steam cured by an automatic control machine. The procedure of steam curing completely conforms to the China Standard DBJ43/T325—2017 Uniaxial compression tests were conducted on UHPC specimens with the dimension of 100 mm × 100 mm × 300 mm using a computer-controlled electromechanical servo hydraulic pressure testing machine to determine the static uniaxial compressive strength and young's modulus of UHPC, as shown in . There were in total six specimens tested, three of which were used for the determination of the compressive strength and the other three were used for measuring the young's modulus. The testing procedure strictly conformed to the China Standard GB/T 50081-2019 The tensile strength of UHPC was also determined by a bending test, as shown in . The testing procedure completely conforms to the China Standard DBJ43/T325—2017 The test results of all specimens, represented by the diameter and depth of the crater and spall, are summarized in . Since the damage of the crater and spall does not show a regular circle pattern, the averaged diameters in all four directions are considered, as shown in . Generally speaking, the diameter and depth of the crater on the impacted face increase with the increase of the TNT charge weight. The damage on the rear face of the slabs is dependent not only on the TNT charge weight but also on the thickness of the slabs. For example, the rear face of the slab with a thickness of 20 cm is seriously damaged with the charge weight of 1200 g, resulting in severe spalling with a diameter of 44.4 cm, whereas the rear face of the slab with a thickness of 40 cm is just cracked even with the charge weight of 2400 g. The damage patterns for specimens U-20-800 and U-40-2000 are presented in , respectively. It is noteworthy that the diameter and depth of the crater are 20.2 cm and 4.5 cm, respectively, for the case with the charge weight of 800 g, and they are 30.3 cm and 7.5 cm correspondingly for the case with the charge weight 2000g.Based on the experimental test, finite element model (FEM) was established by using the LS-DYNA software to verify the damage pattern of the UHPC slab, where only a quarter of the UHPC slab was modeled for efficiency purpose, as shown in . As exhibited, this model consists of four parts: air, explosive, reinforcement and concrete, where the reinforcement is modeled with BEAM161 element, and the others are modeled with SOLID164 element. BEAM161 is an important explicit 3D (three dimensional) beam element in LS-DYNA, allowing to deal with finite strains that occur in many practical applications. SOLID164 is employed for the 3D modeling of solid structures, which is defined by eight nodes featuring with the following degrees of freedom at each node: translations, velocities, and accelerations in the nodal x, y, and z directions. The grid within 40 cm around the TNT was densified because of complex stress changes in this area, and the grid far away from TNT was relatively coarse. To ensure that the simulation results were not affected by the number of the elements, the dimension of the element was reduced with a scale of 0.9 each time until the relative error resulted from reducing the element size dis not exceed 5%. Therefore, the final element size near the TNT and densified zone was about 0.48 cm. Fluid-structure interaction was considered in this model to transmit stress waves at the interface between air and reinforced concrete. The Lagrange grid was used for concrete and rebar, and the Euler grid was selected for the explosive and air. Symmetry boundary conditions were adopted on the two symmetry planes and non-reflecting boundary conditions were imposed on the surround sides of air to avoid the reflected stress wave. The coupling of UHPC and reinforcement was realized through the key world card “*CONSTRAINED_BEAM_IN_SOLID”. Besides, the key world card “*INITIAL_DETONATION” was used to define the initial time of the TNT explosion at 0 µs and the location of the detonation on the central point. The calculation time step was set as 0.3 µs.The air is assumed as an ideal gas, which is modelled by an equation of state, defined as where E0air is the initial energy density of air, ρ0airandρair refer to the initial and present densities of air, respectively, and γair is the adiabatic index, namely the fraction between the specific heats under constant pressure and volume conditions. The parameters for the Equation of State are summarized in In this work, the Jones-Wilkins-Lee equation of state (JWL EOS) was adopted to model the TNT and it prescribes the pressure generated by explosives [P=AT(1−ωTR1TνT)e−R1TνT+BT(1−ωTR2TνT)e−R2TνT+ωTE0TνTwhereAT,BT,ωT, R1T, R2T are constants, E0T is the initial internal energy per unit volume (energy density) of TNT, νT=ρ0T/ρT is the relative volume, and ρT and ρ0T are the present and initial densities of the explosive. The parameters of JWL EOS for TNT are listed in The Mat Piecewise Linear Plasticity was employed in rebar modeling. The material parameters are listed in ]. The HJC constitutive model with calibrated parameters in is employed for modeling the UHPC slabs.The simulation result for the specimen U-20-800 is taken as an example for illustration purpose, as presented in . It is noted that the TNT begins to explode at the beginning, and then the stress waves generated by the TNT explosion are transmitted to the surface of the concrete slab at the 14 µs, resulting in compressive stress (31.36 MPa) on the concrete slabs, as shown in (a). Then, the compressive stress becomes progressively larger (the maximum pressure is 14.76 GPa at 16 µs) because of the TNT explosion. A funnel-shaped crater is formed around the explosive position in the slab because of the compressive failure of the UHPC, and the crater gradually expands outward along with the time. At 46 µs, as shown in (b), the compressive stress wave propagates to the rear surface of the slab and is reflected to form a tensile stress wave, which results in spalling on the rear face. At 67 µs, as shown in (c), the explosion crater stops expanding because the stress waves dissipate quickly in the process of propagation in the concrete. The total calculation time of this simulation is 140 µs, by which the compressive stress wave propagates to the fringe of the slab.The comparison between the exprimental and simulation results for the specimen U-20-800 is shown in . The diameter and depth of the simulated explosion crater are 18.2 cm and 4.8 cm, respectively, which are favorably close to the corresponding experimental results that are 20.2 cm and 4.5 cm, and the relative errors are -9.9% and 6.7%, respectively. The diameter of the simulated spalling is 19.7 cm, which is close to the corresponding experimental results that is 19.2 cm and the relative errors is 2.6%. The simulation results for all specimens are summarized in . The maximum relative error between the experimental and numerical results is 13.1% with respect to specimen U-40-1200. This indicates that the HJC model with the parameters determined in this study can well simulate the dynamic performance of UHPC in the explosion test.The improved HJC model with calibrated parameters is further verified with the bullet penetration experiments, where a total of 9 specimens are involved, containing 3 specimens in Ref. , where the volume ratios of the steel fiber for UHPC target are 0%, 2%, and 3%, and the velocity of the bullet ranges from 553 m/s to 1113 m/s. The schematic diagram for the setup of the penetration test is shown in , where the diameter and length of the target are 750 mm and 700 mm, respectively, in Ref. , where the bullet weight is 329 g and 54.2 g, respectively.To reproduce the bullet penetrating the UHPC target, a quarter of the test arrangement was modeled by using the finite element method, as shown in . Each of the models shown in this figure consisted of two parts, the UHPC target and the bullet, which retained exactly the same properties as in the references and were assigned with the explicit 3D structural solid element (SOLID164). The elements in the zone within 1.5 times of the actual penetration depth and within three times of the bullet diameter were densified because of the complex stress changes in this zone. Similarly, to ensure the simulation results to be independent of the element number, the dimension of the element was reduced with a scale of 0.9 each time until the relative error on the penetration depth did not exceed 5%. Therefore, the final adopted element size for the bullet and in the densified zone was around 0.3 cm. This procedure was also executed in determining the calculation time step to ensure the simulation results to be independent of the time step. As such, 0.3 µs (similarly, the unit system of the model is cm-g-µs) as the calculation time step was an appropriate one. Symmetry boundary conditions were imposed on the centerline of the target. In the tests of Refs. The HJC model with the parameters determined in was employed for modeling the UHPC targets. The material model of Mat Johnson Cook coupled with EOS Gruneisen was adopted to establish the casing of the projectile. The material model of Mat Johnson Cook is defined as follows:σ=(Aj+Bjεnj)(1+cjlnε˙*)[1−(T−TroomTmelt−Troom)mj]where Aj, Bj, cj, nj and mj are constants; ε is the equivalent plastic strain; T is the actual temperature; Troom is the room temperature; and Tmelt is the melt temperature of material. The fracture principle of this material model isε≥max{[D1j+D2jexp(D3jσ*)](1+D4jlnε˙*)[1+D5j(T−TroomTmelt−Troom)]}where D1j, D2j, D3j, D4j and D5j are constants. The EOS Gruneisen is defined as follow:P={ρ0Cg2μ[1+(1−γ02)μ−ag2μ21−(S1−1)μ−S2μ2μ+1−S3μ3(μ+1)2+(γ0+aμ)Eg,forcompressedmaterialsρ0Cg2μ+(γ0+agμ)Eg,forexpandedmaterialswhere Cg is material speed of sound; γ0, ag, S1, S2 and S3are constants; Eg is the internal energy of material. The values of all parameters for the material model of Mat Johnson Cook and EOS Gruneisen are listed in The Erosion Surface to Surface (ESTS) algorithm was employed for the contact between the target and bullet. The erosion criterion is set on the tensile strain, and when the tensile strain reaches the critical value, the failed element will be immediately deleted from calculations. This strategy is also adopted in Ref. shows the simulation results of the penetration process for the specimen UHPC-SF-1, where the compressive strength of the target is 140 MPa and the ratio of the steel fiber is 3%, as given in Ref. refers to the damage factor D in the HJC model, where D = 0 means no damage and D = 1 means the occurrence of failure for the target. The initial velocity of the bullet is 553 m/s. A damage zone is formed during the bullet penetrating the target, and the degree of the damage is gradually weakened from the inside to the outside. The velocity of the projectile decreased to 0 m/s at 510 μs, as shown in (c). However, the destruction of the UHPC target does not stop immediately since the stress waves are still propagating inside the target. The stress waves stop completely at 600μs, as shown in shows the time histories of the bullet velocity and displacement/penetration in the UHPC target for the specimen UHPC-SF-1. It is observed in that the simulation result of the penetration depth is 12.8 cm, which is consistent with the test data of 12.9 cm in Ref. The comparison of the penetration depth between the simulated and tested results for all specimens, presented in Refs. . It can be observed that the maximum relative error between the simulation results and the test data is 8.46%, indicating that the HJC model with the parameters calibrated in this study can favorably simulate the dynamic performance of UHPC in the penetration test.In this work, a set of parameters of the Holmquist-Johnson-Cook (HJC) model (including strength parameters, damage parameters and pressure parameters) for ultra-high performance concrete (UHPC) with the steel fiber volume ratio of 0%, 1%, 2%, and 3% were determined based on the published test data. The strength parameters were derived from the triaxial test data and SPHB test data. The damage parameters were obtained through uniaxial loading tests. According to the Hugoniot test data, the pressure parameters were obtained.A contact explosion test was conducted to verify the correctness of the parameters, in which a series of UHPC slabs with a steel fiber volume ratio of 2% were subjected to blast loadings. Besides, the penetration tests that were conducted by Liu et al. and Jun et al. [] were also involved, where the bullet penetrated the UHPC targets with a steel fiber volume ratio of 0%, 2% and 3%. The finite element model employing the HJC model with the determined parameters for the two tests were established and evaluated. The numerical phenomenon including the propagation principle of stress wave in explosion test and the damage situation for UHPC target in penetration test were discussed. In addition, the numerical results including the diameter and depth of the blast crater and the penetration depth agree well with the experimental results. It is thus proven that the HJC model with the determined parameters can adequately and effectively simulate the dynamic behavior of UHPC subjected to impact and explosion.Wenzheng Wan: Software, Investigation, Formal analysis, Data curation, Writing – original draft. Jian Yang: Resources, Conceptualization, Methodology, Funding acquisition. Guoji Xu: Supervision, Project administration, Writing – review & editing. Yikang Liu: Writing – original draft.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Development of a fretting–fatigue mapping concept: The effect of material properties and surface treatmentsFretting–fatigue induced by combined localized cyclic contact motion and external bulk fatigue loadings may result in premature and dramatic failure of the contacting components. Depending on fretting and fatigue loading conditions, crack nucleation and possibly crack propagation can be activated. This paper proposes a procedure for estimating these two damage thresholds. The crack nucleation boundary is formalized by applying the Crossland high cycle fatigue criterion, taking into account the stress gradient and the ensuing “size effect”. The prediction of the crack propagation condition is formalized using a short crack arrest description. Applied to an AISI 1034 steel, this methodology allows the development of an original material response fretting–fatigue map (FFM). The impact of material properties and surface treatments is investigated.Fretting is a small amplitude oscillatory movement, which may occur between contacting surfaces that are subjected to vibration or cyclic stress. Combined with cyclic bulk fatigue loading, the so-called fretting–fatigue loading can induce catastrophic cracking phenomena which critically reduces the endurance of assemblies. Considered to be a plague for modern industry, fretting–fatigue is encountered in all quasi-static contact loadings subjected to vibration and cyclic fatigue and thus concerns many industrial branches (helicopters, aircraft, trains, ships, trucks, etc.) , fretting–fatigue loading can be characterized by the superposition of a heterogeneous cyclic stress gradient related to the contact loading, and a homogeneous fatigue bulk loading.Indeed, the contact stress decreases asymptotically below the interface. From this typical stress distribution, cracking damage will evolve in three different ways. Below a threshold fretting–fatigue condition, no cracks are nucleated and the system runs under safe crack nucleation conditions. Above this threshold, two evolutions can be observed: for intermediate loading conditions, a crack will nucleate; however, due to the very sharp decrease of the contact stress below the interface, it will finally stop. This typical behavior defines the safe crack arrest domain During the past decades, a significant effort has been made to formalize both the crack nucleation and the crack arrest conditions. The crack nucleation phenomenon is commonly addressed by transposing conventional multiaxial fatigue criteria The objective of this work is to combine these two approaches in order to describe the different types of fretting–fatigue damage through the synthetic form of a fretting–fatigue mapping concept (). The three damage behaviors are reported as a function of fretting loading (Y-axis) and fatigue loading (X-axis).Then the plain fatigue parameter along the X-axis will be determined from conventional fatigue tests whereas the plain fretting damage along the Y-axis will be identified from plain fretting conditions. Finally, the combined fretting–fatigue test will permit to be identified, respectively the crack nucleation and crack arrest boundaries in the intermediate domains. To rationalize this analysis, the fatigue stress amplitude is normalized by the fatigue limit (σa/σd) whereas fretting loading, restricted to the partial slip condition, is quantified though the ratio Q*/μP. Like for any fatigue problem, the mean stress level plays a critical role in the damage evolution. Both fretting and fatigue loadings have therefore been related to the corresponding stress ratii RQ and Rs respectively. To avoid any perturbation induced by this latter aspect, this investigation is developed for pure alternated stress conditions (i.e. R |
= |
RQ |
= |
Rs |
= −1). By introducing this new mapping concept, the present investigation develops a combined experimental and modeling methodology to identify the damage boundaries and to provide an explicit description of the various types of fretting–fatigue damage. Finally, the impact of material fatigue properties, but also various surface treatments like shot peening or HVOF coatings, is discussed and schematically transposed into the fretting map description.Fretting–fatigue phenomenon involves numerous complex mechanisms, which is why, to establish a predictive methodology, the investigation must be calibrated on a well known material. The material used for the experimental investigation and the construction of the model is a low carbon steel alloy, AISI 1034. Fully investigated by Gros To investigate material property effects, the global fretting–fatigue response of a low alloyed steel 30NiCrMo8 is modeled and compared in the discussion A similar 2D cylinder/plane configuration was chosen both for plain fretting and fretting–fatigue test experiments. The radius of the 52100 steel cylinder is R |
= 40 mm and the pad length L |
= 6 mm, giving plane-strain conditions near the central axis of the fretting scar. Both AISI 1034 planes and fatigue specimens used respectively for plain fretting and fretting–fatigue tests display a T |
= 12 mm thickness. The normal load is fixed at P |
= |
Fn/L |
= 227 N/mm, inducing a maximum Hertzian pressure of p0H |
= 450 MPa and a Hertzian contact half-width of aH |
= 320 μm. In order to minimize edge-effects, the contact pad thickness and the transverse width of the plane specimen were machined to the same size. Hence, whilst the side faces of the contact are traction-free, approximate plane-strain conditions are present along the centreline of the contact. This means that the pressure distribution decreases from a maximum value along the central region to a lower value towards the contact ends, and eliminates any stress singularity problems , two different test apparatuses were involved to quantify respectively the fretting and the fatigue influences in cracking processes.The plain fretting stress conditions were achieved on a dedicated fretting wear test The fretting–fatigue apparatus is based on the conventional principle first introduced by the Oxford group A laser extensometer is adapted to measure the relative displacement between the pad and the fatigue specimen at the contact point. It allows the fretting loop to be plotted, which guarantees better control of the partial sliding condition.A dedicated system based on a ball bearing adjustment allows a single pad contact configuration to be implemented. The dispersion induced by contact misalignment and friction dispersion is reduced because only one contact needs to be adjusted. Besides, unlike the symmetrical configuration which requires a complex finite plate thickness correction, the whole specimen thickness can be considered for the stress analysis, which justifies the semi-infinite contact hypothesis.This fretting–fatigue setup enables the application of a negative loading ratio. In the present investigation, all the tests were performed for alternated fatigue loading conditions (R |
= −1).Stress analysis of a fretting contact is highly dependent on the applied friction coefficient. Different approaches have been developed to determine this value The studied pressure condition is quite high compared to the yield stress of the material (p0H/σy |
= 1.28). If a full sliding configuration is assumed, the very high friction coefficient will promote a generalized plastic deformation within the interface. However, because very small partial slip conditions are imposed, the plasticity is in fact constrained in narrow domains localized on the top surface sliding domains. Expecting plasticity to have a minor impact, we assume an elastic description of the contact and subsurface stress field distribution.The specimen thickness T |
= 12 mm is defined so that each solid could be considered as an elastic half space, hence the solution for the pressure distribution is Hertzian The contact pressure contribution is assumed to be constant and static due to the very small displacement amplitude:The description of the cyclic shear contribution is more complex Hence, symmetrical shear stress field distributions are alternately imposed at the tangential force amplitudes +Q* and −Q*.The elastic fretting–fatigue stress description is developed using an on-phase fretting–fatigue loading condition. As shown by Nowell and Hills Again, symmetrical shear stress field distributions are alternately imposed at tangential force amplitudes +Q* and −Q* depending on the imposed bulk loading (By contrast to the plain fretting condition, the dissymmetry of the sliding distributions promotes a larger sliding domain at the trailing edge of the contact.If larger bulk stresses are applied (i.e. e |
+ |
c |
> |
a), reverse slip takes place at one edge of the contact. Complex integral equations must then be solved to extract the shear stress field distribution.Both fretting and fatigue loading are in phase and related to an alternating loading condition (stress ratio R |
= −1). The stress loading path can therefore be expressed by the two amplitude states, the so-called loading and unloading conditions respectively (The maximum loading state conditioning the crack nucleation risk and the crack propagation is located at the trailing edge (X |
= −1) at the loading condition.When the size of the contacting bodies is large compared to the contact size, a good approximation might be to consider each body as an elastic half-plane. With this approximation, once the surface stresses are known, the subsurface stresses induced by the contact loadings can be found by superposing half-plane Green's functions. For example, a general pressure distribution may be approximated in a piecewise-linear fashion by overlapping triangular elements To predict the fretting–fatigue crack nucleation risk at the fatigue limit condition (i.e. 106 |
cycles), Crossland's multiaxial fatigue description is applied ), and the maximum value of the hydrostatic pressure (Ph max).The non-cracking condition is expressed by:ξa=12maxt0∈Tmaxt∈T12(S(t)−S(t0)):(S(t)−S(t0))1/2with S, the deviatoric part of Σ; σd, the alternating bending fatigue limit; τd, the alternating shear fatigue limit.The cracking risk can then be quantified through a scalar variable:The cracking condition is then expressed as:If dC is greater than or equal to 1, there is a risk of cracking;If dC remains less than 1, there is no risk of cracking.The first step of the methodology is to calibrate the model by iterating the experimental crack nucleation limit defined from plain fretting tests. To identify the experimental crack nucleation threshold, the following procedure is applied.Keeping the pressure and the test duration constant, various tests are performed at different tangential force amplitudes. In the present investigation we focus on high cycle endurance conditions so we consider that the crack nucleation limit is reached at 106 cycles. Cross-sections at different places along the median axis of the fretting scars are then taken. The maximum crack lengths observed are plotted versus the applied tangential force amplitude (). A linear approximation can be considered (The crack nucleation condition is usually defined for an arbitrary crack length. Depending on the crack length, different crack nucleation thresholds might be considered, which complicates the crack nucleation analysis. This paradox is here resolved by defining the crack nucleation threshold as the limit tangential force amplitude (QCN*) below which no crack can be observed (b |
= 0). To determine this value, the following strategy is applied: assuming a linear evolution of the crack length versus the tangential force amplitude, we extrapolate the crack nucleation threshold (QCN*) when this linear extrapolation crosses the X-axis (i.e. crack length b |
= 0 μm). To confirm this value, few tests are then performed just below this extrapolated value to verify that no cracks have nucleated. For the studied condition we determine QCN*=100N/mm (The multiaxial fatigue analysis is then performed for the threshold crack nucleation condition. Confirming the experiments, shows that the maximum crack risk is located at the contact borders, but the computed value dC is around 2. As mentioned previously, the current point stress analysis critically over-estimates the cracking risk. Indeed, the cracking risk analysis under severe stress gradient conditions requires that more representative averaged stress states defined over intrinsic length scales be considered A pertinent cracking risk analysis will consist first in identifying a representative stress state, taking into account the stress gradient (ΣR), then in applying a multiaxial fatigue analysis. Taylor ΣR3D(x,y)=Σ¯(V(M(x,y),ℓ3D))=125∑i,j=−22ΣMx+i⋅ℓ3D4,y+j⋅ℓ3D4A crack displays a planar morphology so there is a physical justification to consider a plane averaging procedure rather than a volume approach. Indeed, although it is simpler to implement, a volume averaging procedure involves out-plane stress components and therefore can induce discrepancy. The “2D” representative stress state can be approximated by the mean loading state averaged over a square area, whose edges are assimilated to the physical length “ℓ2D”. In fretting–fatigue problems, a crack nucleates at the surface trailing edge of the contact and usually propagates perpendicularly to the fatigue loading. The square area can therefore be assumed to be normal to the surface and the fatigue directions with one edge located on the top surface. For the studied 2D plain strain configuration, the analysis is reduced to a “y” line averaging procedure (The following formulation is hereafter considered:ΣR2D(x)=Σ¯(L(M(x,y=0),ℓ2D))=15⋅∑i=04ΣMx,i⋅ℓ2D4This method is equivalent to the point stress analysis and does not involve an averaging procedure. However, rather than considering the surface stress discontinuity to predict the cracking risk, fatigue analysis is performed from a stress state defined below the surface at a critical distance called “ℓ1D”. Likewise for the averaging procedures, this infers a significant reduction of the maximum loading state and therefore, a better integration of the stress gradient effect. For the studied 2D cylinder plane configuration, the surface representative stress state related to the contact surface is expressed by the following expression:Different methodologies can be applied to extrapolate the former length scale parameters. Some approaches consider the crack length marking the transition from short to long crack propagation regime; others are based on grain size. In the present investigation, we adopt a reverse identification methodology involving iterative procedures to extrapolate the optimized length values predicting the experimental plain fretting crack nucleation condition (i.e. p0H |
= 450 MPa, aH |
= 320 μm, μt |
= 0.85, QCN*=100N/mm) illustrates this methodology by plotting the evolution of the predicted cracking risk as a function of the 3D length scale parameter (i.e. process volume approach). A pertinent prediction of the cracking risk is found for ℓ3D_Crossland=45μm. This dimension is very close to the Austenite grain size of the AISI 1034 alloy, which supports the hypothesis of a correlation between the length scale parameter and the microstructure To establish the experimental crack nucleation boundary under fretting–fatigue conditions, the following methodology was applied. Three fatigue stress levels were defined. For each fatigue level, different tests were performed, adjusting the fretting tangential force amplitude by monitoring the test apparatus stiffness. Like for plain fretting investigations, the test duration was fixed at 106 cycles. After the test, cross section observations were performed to see if any cracks had been activated. The studied loading conditions are compiled in plots the experimental damage as a function of the imposed fretting and fatigue loading conditions defining the so-called crack nucleation fretting–fatigue map (CN-FFM).The experimental crack nucleation boundary is estimated by separating both cracking and non-cracking domains. It is characterized by an initial sharp decrease followed by a quasi constant evolution. Hence, the threshold crack nucleation boundary stabilizes at 80% of the plain fretting condition in the middle fatigue stress range (i.e. σa/σd |
< 0.5). The application of a fatigue bulk stress decreases the admissible fretting loading. However, its influence appears less effective than expected. This suggests that for the studied medium–low fatigue stress range (i.e. σa/σd |
< 0.5), the crack nucleation process is mainly controlled by the contact loading. Further experiments are now required to investigate the crack nucleation process in the high fatigue stress region (i.e. σa/σd |
< 0.5) in order to see until which fatigue stress condition the influence of the contact predominates, and how the crack nucleation boundary converges toward the fatigue limit (σa/σd |
= 1).To formalize the crack nucleation boundary, the multiaxial Crossland fatigue criterion is applied and the different length scale approaches compared. As expected, the conventional point stress analysis clearly underestimates the safe crack nucleation domain (). It shows an asymptotic decrease from the plain fretting condition (i.e. Q*/μP |
= 0.18) to zero at the fatigue limit (i.e. σa/σd |
= 1.0). This convergence toward a zero tangential loading is consistent with the fact that the stress state at the contact borders defined from the point stress methodology is dependent on the tangential force only. Therefore, when the bulk loading reaches the fatigue limit, the threshold tangential force amplitude is obviously equal to zero.The length scale approaches (i.e. crack nucleation process volume, crack nucleation process surface and critical distance method), display quasi superimposed evolutions which suggests that, apart from numerical implementation considerations, none of them can be preferred to describe the stress gradient effect induced by fretting loading.They show a quasi-linear decrease of the admissible tangential loading from the plain fretting condition down to a small residual positive value when σa/σd |
= 1. This residual tangential force, estimated near Q*/μP |
= 0.05, is in fact required to compensate for the compressive stress state induced by the static normal component. Unlike the point stress analysis, length scale approaches consider a loading region where the mean stress level controlled by the normal loading is not zero but compressive. This suggests that for low fretting and high fatigue loading conditions, crack nucleation could be observed outside the contact region. Such a peculiar situation has been confirmed in different experimental investigations, and indirectly supports the applied length scale descriptions to quantify the crack nucleation risk under fretting–fatigue conditions.The length scale approaches are clearly more realistic than the conventional point stress to predict the safe crack nucleation domain. However the predictions are still uncertain:They provide a very good description of the crack nucleation process for the low fatigue stress range (i.e. σa/σd |
< 0.1).Within the intermediate fatigue stress domain (i.e. 0.1 < |
σa/σd |
< 0.5), the length scale approaches predict a quasi-linear decrease of the crack nucleation boundary, whereas experiments conclude that the admissible fretting loading stabilizes. The higher the bulk stress, the larger the discrepancy with the models.Convergence is however expected for the higher fatigue stress range (0.5 < |
σa/σd |
< 1.0), which unfortunately cannot be addressed in the present investigation due to technical limitations. Indeed, due to high compressive stress levels, the experimental results have been corrupted by buckling instabilities of fatigue specimens. Current developments allowing shorter fretting–fatigue specimen configurations are expected to solve this limitation.To verify if the discrepancy observed for the intermediate fatigue stress domain could be explained by crack nucleation formulations, other descriptions like Dang Van confirms similar evolutions between the multixial fatigue criteria and equivalent dispersion versus the experiments. It shows that whatever the multiaxial fatigue formulations, the stress gradient calibration from plain fretting condition systematically provides pessimistic estimations of crack nucleation boundaries. Moreover, the very small difference between the fatigue criteria suggests that the fretting–fatigue stress condition, characterized by a “quasi” bi-axial stress state, is not appropriate to discriminate between the former multiaxial formulations.The present investigation clearly demonstrates that the discrepancy between the experimental crack nucleation boundary and multiaxial modeling is not related to the length scale averaging procedure or the fatigue crack nucleation formulation. Alternative hypotheses must be considered, like plasticity, which interacts with the stress distribution and introduces local residual stresses, or the current length scale methods which are established from fixed length values but could be optimized by considering variable length scale dimensions as a function of the stress gradient fluctuations.However, one important conclusion of this work is the fact that a multiaxial fatigue analysis combined with a length scale approach calibrated from plain fretting conditions enables a conservative approximation of the crack nucleation boundary under fretting–fatigue loadings. Due to its capacity to be generalized for any stress configurations like subsurface stress discontinuities, the crack nucleation process volume approach combined with the simple Crossland formulation will be preferred and applied in the following development.Crack tip stress intensity factors have been found using the distributed dislocation method which is described in detail in ). A problem equivalent to the original would be the superposition of the body without a crack subjected to the external fretting–fatigue load (A) and a cracked body devoid of external loads but whose crack line traction and shear are equal and opposite to the stress components along the line of the crack (B), so that after summing the two (A |
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