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= 289 K, As |
= 333 K and Af |
= 357 K (b, the austenitic pseudoelastic alloy shows a complex three-step transformation upon cooling from the high temperature phase, which is typically related to the presence of small- and large-scale microstructural heterogeneities a and b show that, at room temperature (295 K), the alloy with 50.3 at.% Ni is martensitic while the alloy with 50.7 at.% Ni is fully austenitic. No further effort was made to rationalize DSC chart features.Uniaxial tensile tests, with dog-bone tensile specimens identical in dimensions to those reported previously a, the martensitic and pseudoelastic alloys show typical tensile curves, with stress plateaus at 200 MPa (martensitic alloy) and 330 MPa (pseudoelastic alloy). It is clear that the two alloys differ in tensile strength and rupture ductility. shows specimens after rupture (stress–strain histories reported in a). The martensitic alloy keeps its deformed shape while the pseudoelastic alloy almost fully recovers the total strain imposed during tensile loading. b documents the difference between the martensitic and the pseudoelastic alloys at a higher strain resolution for a loading/unloading experiment taken to a maximum strain of 4%. The pseudoelastic alloy shows nearly complete strain reversibility, while the martensitic alloy exhibits full irreversibility, if the back transformation is not thermally induced (one-way effect) In our test program, we need to establish the temperature Md above which stress-induced martensite no longer forms, because mechanical tests above Md allow for the assessment of the mechanical properties of austenite. For this purpose, we performed additional isothermal loading and unloading tests on our pseudoelastic alloy (maximum strain: 4%; strain rate: 0.05 mm min−1) at temperatures below, at and above room temperature, some of which are shown in a. The evolution of the loading and unloading stress–strain curves in a illustrates that the pseudoelastic reversibility which characterizes the room-temperature experiment (295 K) is no longer observed at 373 and 473 K, where the irreversible strain reflects the plastic deformation of austenite. In contrast, at lower temperatures (218 K) the same type of pseudoplastic stress–strain curve is observed as exhibited by the martensitic material at room temperature. The observed irreversible strains as a function of temperature from all tests performed to determine Md are presented in b suggest that a test temperature of 423 K (dashed line) is safely above Md and can be used to assess the mechanical properties of austenitic NiTi. Throughout the present study we refer to our SMA with 50.7 at.% NiTi as pseudoelastic material (when the formation of stress-induced martensite needs to be considered) and as austenite when the test is performed above Md (when stress-induced martensite can no longer form).Fracture mechanics experiments were performed using a miniature CT specimen geometry Prior to CT testing, fatigue pre-cracks were introduced using cyclic tensile loading between 0.03 and 0.55 kN at a frequency of 20 Hz in a servo-hydraulic test rig (Schenck PC 160). Different crack lengths (a) were obtained (7.57 mm < |
a |
< 11.80 mm) to yield a/W ratios ranging from 0.473 to 0.738. These specimens were tested using the same Zwick/Roell Z100 rig as used for the tensile experiments described earlier. The tests were performed in displacement control (displacement rate: 0.05 mm min−1). Typical raw data for different a/W ratios from pseudoelastic miniature CT specimens at 295 K are shown in shows that all experiments yield a maximum load indicating crack propagation. As we expected, the experiment performed for the smallest a/W ratio (0.500) yielded the highest maximum loads. However, even in this case, there is no sharp load drop (as was observed for Al 7075), but a deviation from linearity occurs before the maximum load is reached. This indicates that the response of our pseudoelastic CT specimen to mechanical loading cannot be fully accounted for on the basis of linear elastic fracture mechanics (LEFM). This type of deviation from linearity becomes even more pronounced as a/W ratios increase. We intuitively associate this effect with microstructural processes in front of the crack and we investigate these processes later. With this limitation in mind, we assessed whether prominent LEFM parameters like KIC can account for crack stability in our alloys. We used the well-known equations for KI and KIC to calculate a loading parameter K∗ and a critical parameter for crack propagation Kmax∗ (the star indicates that we appreciate that the severe constraints imposed by the LEFM are not fully met). For K∗, we used:f(a/W) can be obtained from the crack geometry In addition to these CT tests, in situ CT experiments were performed using a miniature tensile device built by Kammrath & Weiss GmbH. shows our miniature CT specimen as mounted in this miniature test rig. Although testing is limited to much smaller displacement rates, this miniature test rig allows for reproduction of the mechanical data shown in obtained with a standard size test machine. This miniature test rig can be integrated into a scanning electron microscope as well as into a beam line of a synchrotron radiation facility. Using this miniature test rig, SEM images were collected using a Jeol JSM-840A scanning electron microscope operating in secondary electron imaging mode at 20 kV and a working distance of 20 mm to observe the crack tip of a martensitic (a/W |
= 0.513) and a pseudoelastic (a/W |
= 0.506) CT specimen subjected to different loads between 0 and 3500 N.In addition to these in situ SEM experiments, we also present results from a series of in situ diffraction experiments on a pseudoelastic NiTi CT specimen obtained with this miniature test rig at the beam line BW5 of the Hamburg Synchrotron Laboratories (HASYLAB) at the German Electron Synchrotron (DESY). Diffraction measurements were performed with a 99 keV (λ |
= 0.0125 nm) X-ray beam in transmission geometry for 60 s. An ion chamber and a diode (Keithley, Model 428) were used to locate the crack tip and to position the CT specimen by measuring the initial and transmitted beam intensity. The cross-section of the beam was 100 × 200 μm2 and the sample-to-camera distance was approximately 1.0 m. Complete Debye–Scherrer diffraction rings were obtained by an image plate (MAR345) of 345 mm diameter with a 100 μm pixel size and a 16-bit dynamic range. Calibration diffraction patterns were collected from LaB6 (NIST Standard Reference Material SRM-660). Diffraction patterns were collected on the pseudoelastic NiTi CT specimen (a/W |
= 0.550) for an unloaded (P |
= 0 N) and a loaded (P |
= 2860 N) condition.The pseudoelastic NiTi CT specimen was oriented, with respect to the synchrotron beam, in two experimental configurations (perpendicular to the beam (a and b) and at a 45° angle to the beam (a and b). In the first configuration, a diffraction map was obtained with the synchrotron beam perpendicular to the miniature pseudoelastic NiTi CT specimen, a. The detailed results of this study are reported in Ref. a indicate that the size of the plastic zone in front of the crack in the center of the specimen is significantly smaller (<1 mm) than the in-plane dimensions of crack size (1.6 mm) and depth (7.2 mm), which ensures that plane strain conditions are met. b shows the limits of the two zones where stress-induced martensite is detected in our pseudoelastic CT specimen: one close to the crack tip (tensile in nature) and the other one at the far end of the CT specimen (compressive in nature). It is important to realize that the transmitted beam in the configuration shown in a provides volume-average data. It indicates the presence of martensite, even for cases where stress-induced martensite only forms at the surfaces of the CT specimen (plane stress conditions) and not in the center (plane strain condition). In the second configuration (our key experiment), the miniature CT specimen is positioned at 45° with respect to the incident beam (a). The geometry of this experiment is set up to keep the beam from crossing the plane stress surface regions and at the same time avoiding the compressive zones at the end of the CT specimen as illustrated in a. When stress-induced martensite is detected, it is only associated with the central crack tip regions. b shows a photograph of the miniature CT specimen prior to the 45° diffraction experiment.We first consider the mechanical response of our three types (martensitic, pseudoelastic and austenitic) of miniature CT specimens. From raw data like those shown in , K∗(Δ) curves can be calculated using the equation given above. a and b shows these stress intensity vs. displacement curves for the martensitic and pseudoelastic SMAs at 295 K (room temperature). c shows the stress intensity vs. displacement curves for the austenitic material at 423 K (above Md). In the early stages of loading, all K∗(Δ) curves show linear elastic behavior and the K-concept rationalizes the data reasonably well. In all three cases, clear maxima are observed, which indicate the start of macroscopic crack propagation. There is always a deviation from linearity before Kmax∗ is reached. a shows that this effect is much stronger and occurs significantly earlier in martensitic NiTi SMA than in the pseudoelastic (c) NiTi SMAs. This deviation is still a significant feature of the K∗(Δ) curves of the pseudoelastic alloy, while it almost completely vanishes in the austenitic alloy. It seems reasonable to assume that the strong nonlinearities in the martensite are related to large-scale detwinning processes. In the martensitic NiTi SMA, statistically oriented martensitic variants exist prior to loading. Upon loading, favorably oriented martensitic variants grow. This microstructural evolution is associated with large-scale macroscopic deformation. Daymond et al. suggest that detwinning starts at stresses which are significantly lower than those triggering the formation of stress-induced martensite in the pseudoelastic alloy. Therefore, larger parts of a martensitic CT specimen are affected by non-elastic processes than in the pseudoelastic CT specimen. In the analytical part of our study, we will show that small deviations from linearity in the pseudoelastic CT specimens are associated with the formation of stress-induced martensite in specimen volumes which are still large enough to cause a macroscopic effect in the P(Δ) curves (b). While the evolution of a detwinned martensitic variant structure requires mechanical deformation in the martensitic material, stress-induced martensitic variants form directly with preferential orientations.The tiny deviations in the austenitic alloy are most probably related to crack tip blunting processes associated with dislocation plasticity b and c shows that there are sharp drops in K∗ values after Kmax∗ in the pseudoelastic and austenitic alloys. Here, instable cracks propagate fast. In contrast, martensitic CT specimens show a slow and steady decrease in K∗ values with increasing displacement, indicating slow crack propagation.While the K∗(Δ) curves for martensitic and pseudoelastic NiTi differ, the two materials are characterized by the same critical Kmax∗ value, which indicates the loading condition where macroscopic cracks start to propagate. This is shown in , where Kmax∗ values are plotted as a function of specimen geometry a/W for the three alloys considered. shows that Kmax∗ is independent of specimen geometry for all three material states, within the validity range of ASTM E399-90 ) properties, martensitic and pseudoelastic NiTi SMAs are characterized by very similar Kmax∗ values (31 and 34MPam, respectively). This strongly suggests that, despite the different macroscopic behavior of the CT specimens prior to crack propagation, macroscopic cracks in both alloys grow into a similar microstructure: detwinned martensite. Our result on Kmax∗ of martensitic and pseudoelastic NiTi is in good agreement with the values reported by Daymond et al. This conclusion is indirectly supported by the fact that the austenitic CT specimen (i.e. our pseudoelastic alloy tested at 423 K, above Md) shows the significantly higher Kmax∗ value of 53MPam. Our results show that a NiTi SMA with 50.7 at.% Ni shows a lower resistance to crack propagation when martensite forms in front of the crack tip prior to crack propagation as compared to the case where cracks grow into austenite without martensite at the crack tip. In this respect, SMAs differ from typical engineering materials where we expect a decrease of KIC with increasing temperature, because higher temperatures result in lower elastic constants and generally promote plasticity.a and b show the response of crack tip regions of martensitic and pseudoelastic NiTi as observed using SEM during in situ mechanical loading. Loads increase from 0 N (tops of a and b) to 2700 N (martensitic NiTi, bottom of a) and 3500 N (pseudoelastic NiTi, bottom of a and b, the SEM micrographs reveal three important features of cracks in NiTi.First, crack tips stay sharp and do not exhibit the typical features associated with crack tip blunting a and b. However, these deviations are not due to blunting processes. Crack tip blunting is associated with dislocation processes Secondly, a closer inspection of the two series of micrographs shows that there is microscopic crack extension in both materials before Kmax∗. This can be seen when comparing the two SEM micrographs for the crack tip in martensitic NiTi loaded up to 2000 and 2700 N. At 2000 N, a small subcrack at approximately 45° to the main crack grows upward. At 2700 N, it has become the dominant crack, leaving the old crack tip (marked by white arrows pointing to the upper right in the last two micrographs in a) 15 μm behind. Similarly, a microscopic crack extension is observed for the pseudoelastic NiTi at loads of 2750 and 3500 N. As illustrated by white arrows pointing up in b, the distance of the crack tip from a ledge increases by 5 μm. In view of the dependence of K∗ on a (see the above equation), the contribution of these microscopic undercritical crack growth events to the deviations from linearity observed in a and b is negligible. However, under cyclic loading conditions, the cyclic accumulation of such microscopic crack extensions may well account for the type of crack growth characteristics observed by Robertson et al. Finally, a number of microstructural features in the martensitic and pseudoelastic NiTi SMAs close to the crack tip can be observed. At 0 N load, a shows randomly oriented martensitic variants in weak secondary electron contrast. Both materials show traces of pre-fatigue cracking, as can be clearly seen at 0 N load in the pseudoelastic NiTi (b, 45° striations along the upper crack surface). The pseudoelastic NiTi CT specimen shows striations, which originate at the crack tip. With increasing load, these striations increase in density and size (b). Similar observations (at lower contrast) can be made for the martensitic NiTi CT specimen (a). These observations provide microstructural evidence for detwinning processes (martensitic NiTi, a) and the formation of stress-induced martensite (pseudoelastic NiTi, b), which we believe are responsible for the decrease in the stiffness of our CT specimens (deviation from linearity in the K∗ vs. displacement curves shown in In order to prove the presence of stress-induced martensite in front of the crack in the center of the CT specimen (plane strain conditions) of our pseudoelastic NiTi SMA, two diffractograms are shown in a and b. Although complete diffraction rings were collected, only one-quarter is shown for clarity. a shows diffraction data obtained after unloading. All diffraction rings have been identified and are consistent with the lattice constants of the austenite B2 structure. No martensite is observed. Although not shown here, the Debye–Scherrer diffraction rings from the CT specimen prior to loading are identical to those observed after unloading (one loading/unloading cycle). As can be clearly seen in b, additional diffraction rings appear when the specimen is loaded. These rings indicate the presence of stress-induced martensite and correspond to the lattice constants of the martensite B19′ structure (a and b show that stress-induced martensite forms under plane strain conditions in front of a crack in a CT specimen. This suggests that a martensitic zone forms in the crack tip region of a pseudoelastic SMA CT specimen, which is similar in nature to the well-known plastic zone that forms in ductile engineering materials (like Al 7075 and many others). The fact that all martensitic features disappear after unloading suggests that we observe reversible forward- and reverse transformations at the crack tip during loading of the CT specimen. We can exclude the formation of stabilized martensite, which cannot retransform, because it is hindered by the presence of dislocations. We cannot exclude, however, that dislocations also affect the formation of stress-induced martensite in front of the crack tip; further work is required to clarify this point.In the present study, we investigated crack extension under static loading in three NiTi material states: martensitic (50.3 at.% Ni), pseudoelastic (50.7 at.% Ni, T |
≪ |
Md) and austenitic (50.7 at.% Ni, T |
> |
Md). We used miniature CT specimens, which represent a reasonable compromise between the requirements for mechanical testing and the microstructural objectives of our study (small size for in situ experiments, transparency to synchrotron beam). With these miniature CT specimens, we performed mechanical and microstructural experiments. From the results obtained in the present study, the following conclusions can be drawn:CT specimens of both martensitic and pseudoelastic NiTi alloys show P(Δ) curves, which are similar to those typically observed for ductile engineering materials and show deviations from linearity prior to the onset of macroscopic crack growth. However, crack tip blunting was not observed. Instead, we suggest that the growth of favorably oriented martensitic variants (fully martensitic NiTi) and the formation of stress-induced martensite (pseudoelastic NiTi) account for these deviations from linearity. In the fully austenitic material state, these deviations from linearity are negligible.Using standard fracture mechanics procedures for KIC, a critical parameter for macroscopic crack extension is obtained (referred to as Kmax∗ throughout this work). Martensitic and pseudoelastic NiTi have very different thermal properties and tensile test characteristics but show similar Kmax∗ values (31 and 34 MPa m, respectively). In both cases, cracks grow into detwinned martensitic variant microstructures. In contrast, austenitic NiTi tested above Md, where no stress-induced martensite forms, shows a higher resistance to crack extension of 53MPam.In situ SEM studies show that crack tip blunting does not occur in martensitic and pseudoelastic NiTi. Therefore, it cannot account for the deviations from linearity observed in the P(Δ) curves. Microscopic crack growth events are observed in martensitic and pseudoelastic NiTi prior to Kmax∗, but the associated crack extensions are so small that they do not affect the macroscopic specimen behavior. The growth of favorably oriented martensitic variants (martensitic NiTi) and the formation of stress-induced martensite (pseudoelastic NiTi) in sufficiently large parts of our miniature CT specimen rationalize the deviations from ideal elastic behavior. Evidence for these processes was observed in the crack tip regions of martensitic and pseudoelastic NiTi.In situ synchrotron diffraction experiments prove that stress-induced martensite can be detected ahead of a crack in the center of the specimen (plane strain condition) in a pseudoelastic CT specimen (thickness: 10 mm). The plane strain type of loading does not prohibit the formation of martensite. Our results suggest that the stress-induced formation of martensite in front of a crack produces process zones which exhibit the well-known dog-bone features associated with plastic zones in structural engineering alloys. It remains to be clarified whether dislocations also affect the process zone, where stress-induced martensite forms.Influence of mercury environment on the fatigue behavior of spallation neutron source (SNS) target container materialsThe high-cycle fatigue behavior of 316 LN stainless steel (SS), the prime candidate target-container material for the spallation neutron source (SNS), was investigated in air and mercury at frequencies from 10 to 700 Hz with a R ratio of 0.1. A decrease in the fatigue life of 316 LN SS in air was observed with increasing frequency. However, little influence of frequency on fatigue life was found in mercury. An increase in the specimen temperature at 700 Hz seems to be the main factor that contributed to the decrease of the fatigue life in air, relative to that at 10 Hz. However, because of the cooling effect of mercury, only a small temperature increase was found at 700 Hz, and, therefore, there was little frequency influence in mercury. At 10 Hz, a shorter fatigue life of 316 LN SS was measured in mercury than in air at stresses greater than yield strength, which may have resulted from liquid metal embrittlement (LME). At lower stresses, no difference in fatigue lives between mercury and air was detected at 10 Hz. At 700 Hz, the fatigue life in mercury was longer than in air. The fatigue endurance limit measured at both frequencies in mercury and in air was approx. 350 MPa.Type 316 stainless steel (SS) has been widely used in the nuclear industry, because of its excellent ductility, corrosion resistance, and irradiation performance. Recently, 316 LN (low carbon, nitrogen-containing) SS was selected as a container material for the mercury target of the Spallation Neutron Source (SNS) at the Oak Ridge National Laboratory (ORNL) The target material for the bombardment of a proton beam will be liquid mercury (Hg) contained in the 316 LN SS container. The function of the neutron-source system is to convert a short-pulsed, high-power high-energy proton beam into a short-pulsed, low-energy neutron beam optimized for use in neutron-scattering instruments The phenomenon of LME was first reported in 1874, but a comprehensive text on the subject was not published until 1960 The present studies focused on the fatigue behavior of 316 LN SS in air and mercury within the test frequency range from 10 to 700 Hz using an advanced high-frequency electrohydraulic machine.The SNS is an accelerator-based instrument that provides pulsed beams of neutrons by bombarding a mercury target with 1 GeV protons shows a cutaway view of the target and beam-tube region.A heavy liquid-metal target was selected over a water-cooled solid target for many reasons. These include higher neutron production, increased power-handling capability, and the absence of radiation damage to the liquid target. However, the target container material will experience radiation damage. The performance of the target container material to the intended service is crucial to the successful operation of the SNS facility. The configuration of the target container of the SNS is shown in . The container is a four-walled structure. The outer two walls define a protective shroud cooled by water in an enclosed channel, and the inner two walls form a mercury channel. The mercury serving as the target material is contained by the innermost wall.Fatigue tests and analyses of the 316 LN SS container material, in addition to a comprehensive battery of other tests and calculations Research results on the fatigue properties of 316 LN SS have been reported in the literature Type 316 LN SS is an austenitic stainless steel with the chemical composition shown in . The geometry of the cylindrical-bar specimen used is illustrated in . The specimen has a total length of 118.8 mm, a gage length of 19.0 mm, and a diameter of 5.1 mm. In order to conduct fatigue tests in a mercury environment, an attached container of 304 stainless steel was used (). The gage section of the specimen was immersed in mercury enclosed in the container. The container was attached to the specimen with a silicone-rubber adhesive sealant, which could be removed from the specimen after the test, and reused. During fatigue tests, the gage section of the specimen remained in contact with the mercury in the container.Two state-of-the-art electrohydraulic material test systems (MTS) were used in the present study. One has a frequency range from 0.001 to 60 Hz and is capable of being operated in a vacuum as low as 10−6 torr. It can be used to run tests at temperatures as high as 2000°C in either vacuum or inert gas. The second machine is an advanced, high-frequency, electrohydraulic MTS machine with a frequency range from 20 to 1000 Hz and a loading capacity of ±25 kN. Servovalves are activated by voice coils to achieve frequencies up to 1000 Hz. To avoid testing noise at 1000 Hz, the machine is situated in a well-designed, soundproof room equipped with a heat pump, which has the cooling capability to prevent overheating of the servovalves. In the mercury-environment fatigue test, an airflow system (Model MINI-PAC) was used to filter the air near the specimen to eliminate the possibility of mercury entering the room. Following the fatigue tests in mercury, the specimens were washed in acetone with an ultrasonic cleaning machine (Model FS20) for 1 h.High-cycle fatigue (HCF) tests at different stress levels were conducted in air and mercury under a load-control mode using a R ratio of 0.1, where R=σmin/σmax, σmin and σmax are the applied minimum and maximum stresses, respectively. High-frequency tests in the frequency range of 10 to 700 Hz were performed using the 1000 Hz machine to study the frequency effect on fatigue behavior. To assure the reliability and repeatability of the fatigue test results in mercury, some fatigue experiments conducted at the University of Tennessee, Knoxville (UTK) were compared with the ongoing test program at the Oak Ridge National Laboratory (ORNL). The experimental details in the mercury-environment fatigue tests at ORNL were similar to those described above.A high-speed and high-sensitivity, thermography-infrared (IR) detection method was used to observe changes in the specimen temperature during fatigue. This technique uses IR radiation emitted from the surface of a material to determine its temperature. The equipment employed in the experiment is a state-of-the-art, high-resolution, Raytheon-Radiance-HS IR imaging system — an IR camera, which has a temperature resolution up to 10−2°C and a spatial resolution of 5.4 μm. Under the snapshot mode, the IR camera has a tunable data-acquisition speed up to 6,100 Hz, and was used to measure the specimen temperature during fatigue testing. A thin sub-micron graphite coating was applied on the specimen gage-length section of the as-machined sample to decrease the surface-heat reflection. Following fatigue tests, a scanning-electron microscope (SEM), Model Cambridge S-360, was used to observe the fracture surfaces.Fatigue experiments were conducted at different stress levels. Test results in air are illustrated in . In this test series, efforts were mainly focused on tension–tension fatigue tests with a R ratio of 0.1. shows that the yield-strength of 316 LN SS is approx. 288 MPa and ultimate tensile strength is about 587 MPa at a strain rate of 0.01 s−1. The maximum stresses used in the present fatigue tests were between approx. 270 and 540 MPa (, the 316 LN SS exhibits a fatigue endurance limit of about 350 MPa at 10 Hz (R=0.1), and fatigue tests conducted at 700 Hz also showed a similar limit. At the stress level near 350 MPa, the fatigue data exhibit some scatter. This is probably due to an increase in sensitivity of the crack-initiation behavior to the specimen preparation and microstructure.As discussed previously, the target-container will be subjected to several types of loading conditions in its service environment. One of the loads on the target container is the thermal stress to the container, induced by direct heating from the proton beam. Another is the load transferred from the mercury pressure waves caused by beam pulses. As a result, the SNS target-container is subjected to fatigue loading at various frequencies. Thus, the influence of test frequency was investigated. shows the results of HCF (high cycle fatigue) tests of 316 LN SS at the frequencies of 10 and 700 Hz. The fatigue life in air at the frequency of 700 Hz is shorter than that at 10 Hz, although the fatigue endurance limit tends to be comparable in both conditions. The difference in the fatigue lives at the two frequencies seems to increase with increasing maximum stress levels.Further tests were performed concerning the temperature development in the 316 LN SS during HCF tests. The temperature variations during fatigue tests were determined using the IR camera, and they are illustrated in . Efforts were aimed at confirming the suggestion that an increase in the specimen temperature during a high-frequency test could be responsible for decreasing the fatigue life.During fatigue testing, the temperature on the specimen gradually rose to reach a steady-state temperature after some time During the initial period of fatigue, the temperature variation is due to thermoelastic and inelastic effects , the steady-state temperature measured by thermography is plotted as a function of the test frequency. At 10 Hz and σmax=439 MPa, the steady-state temperature is approx. 25°C in the air-environment fatigue test, which is much lower than that of 270°C at 700 Hz in the steady state. Correspondingly, the fatigue lives of 316 LN SS are longer at 10 Hz than at 700 Hz (The temperature difference gives a possible explanation for the effect of test frequency on fatigue lives in air. Since the steady-state temperature generally decreases with decreasing σmax, that the temperature difference between 10 and 700 Hz would decrease with decreasing σmax., the fatigue lives at 10 and 700 Hz in mercury appear to be similar in contrast with the results in air (), i.e., there is little influence of test frequency on the fatigue life in mercury. Note that the fatigue data at 10 Hz in mercury developed at UTK and ORNL are in good agreement, especially for the maximum stress levels above 420 MPa. However, at lower stress levels (⩽420 MPa), some scatter of fatigue lives was observed., the specimen temperature in the mercury-environment fatigue test at 700 Hz with the σmax=439 MPa was approx. 78°C, while at 10 Hz the temperature was approx. 25°C. The difference in specimen temperatures at these two frequencies in mercury is much smaller than the difference in air. Thus, the apparent frequency effect for the fatigue tests in mercury is not as significant as that in air.In the previous section, the test results were examined as a function of frequency in air and mercury. Here, the same results are examined at a fixed frequency.Fatigue tests at the stress levels greater than 400 MPa in mercury at 10 Hz have shorter lives as compared with those in air (). However, for tests at lower stress levels (⩽400 MPa), the material has comparable fatigue lives in mercury and air. For fatigue tests at higher stress levels (e.g. 400 MPa), LME is suggested to be the main factor that decreases the fatigue life of 316 LN SS. At higher stress levels, mercury may have more chance to interact directly with the fresh surface in the crack-tip area due to the larger plastic deformation. Thus, there is a greater possibility of better contact of the mercury with the fresh metal surface at higher stresses. Moreover, at high stress levels, the fatigue life is generally determined by the crack-propagation process. During the crack-growth period at high stress levels, the crack opening displacement (COD) is relatively large, which facilitates the penetration of mercury into the crack tip and the contact with the fresh crack surface. Correspondingly, the penetration depth of the mercury may be increased during a high-stress fatigue test, and wetting of the freshly cracked surface by mercury may be enhanced. These trends result in the mercury effects at high stress levels (The SEM micrographs of the fracture surfaces of the specimens tested at 10 Hz in air and mercury showed different fracture mechanisms. are micrographs of the crack-initiation site and the crack-propagation region of 316 LN SS tested at 10 Hz in air, respectively. The specimen tested in air showed typical transgranular (TG) cracking throughout most of the fracture surface and a dimpled fracture in the overload region.In contrast, the specimen tested in mercury exhibited intergranular (IG) cracking near the crack-initiation site, as shown in is the intermediate region showing where the cracking mode changed from IG to TG. In this region, the grain boundaries are already difficult to discern, and the broken surface exhibits a quasi-cleavage appearance. At the center part of the specimen, the fracture mechanism in the crack-growth region changed to a transgranular mode (). The intergranular-cracking region is believed to be a direct result of LME. But intergranular cracking seems not to be a widespread fracture mechanism for the 316 LN SS tested in mercury. This trend corresponds to the results reported by other authors [4–7].At low stress levels (⩽400 MPa), the fatigue lives in mercury are comparable with those in air at low stress levels as shown in . This trend can be explained as a result of lack of the penetration and wetting of mercury at low stresses. presents the S–N curve for 700 Hz in air and mercury. Obviously, LME is not a factor in the fatigue behavior of 316 LN SS at 700 Hz in mercury. In fact, longer fatigue lives in mercury than in air were observed. Thermography tests showed that temperature might be the dominant factor that contributed to the difference in the fatigue life at 700 Hz in air and mercury. For the fatigue test at 700 Hz and σmax=439 MPa with a R ratio of 0.1, the specimen temperature in air was much greater than that in mercury, approx. 270 versus 78°C (). Mercury serves as a heat sink and effectively lowers the specimen temperature at 700 Hz, which results in longer fatigue lives in mercury than air., decreasing σmax decreases the difference in the fatigue lives in air and mercury. This trend can be expected to result from the fact that decreasing σmax reduces the specimen temperature in air The SEM micrographs of the specimens tested at 700 Hz in air and mercury are presented in . Whether at the crack-initiation site or in the crack-propagation region, any difference in cracking modes in air and mercury is difficult to distinguish. The initiation site showed similar TG features in air (). However, some striations, although difficult to resolve on the fracture surface of the specimens tested in air, indicate a greater extent of ductile fracture in air than mercury. The somewhat brittle appearance of cracking in mercury seems to suggest that LME may have occurred in specimens tested in mercury. shows striations on the surface of specimens tested in mercury, which are not as clear as those in air () exhibit typical TG cracking in the crack-propagation region, which means LME, if present, is not significant enough to result in an obvious difference in the fracture mode. The SEM micrograph of the specimens tested at 700 Hz in mercury did not show IG cracking (). However, there was TG cracking and some faint striations in , which were similar to those observed in the specimens tested in air (). This trend suggests that there is no significant LME in mercury at 700 Hz, because of the higher frequency and less time in each fatigue at 700 Hz, which decreases the mercury effect, relative to that at 10 Hz (The present studies investigated two main factors that could have significant effects on the fatigue life of 316 LN SS in air and mercury: test frequency and environment. These two effects are summarized in The extent of the frequency effect on the fatigue life varies with the test environment. For the fatigue tests conducted in air, specimens generally have shorter fatigue lives at the high frequency of 700 Hz than those at the low frequency of 10 Hz. This trend is evidently the result of a greater increase in the specimen temperature at 700 Hz. Decreasing the applied maximum stress level decreases the frequency effect in air.In contrast, for the mercury-environment fatigue tests, specimens show insignificant difference in the fatigue lives at 10 and 700 Hz. As the mercury acts as a heat sink, the difference in the specimen temperature induced at 10 and 700 Hz is not large enough to show an obvious frequency effect on the fatigue life.The environmental effect depends on both the stress level and test frequency. Fatigue tests conducted at the low frequency of 10 Hz have shorter fatigue lives at high maximum stress levels (⩾400 MPa) in mercury, as compared to those in air. This trend is believed to result from LME in mercury. At lower applied stress levels, the fatigue lives in mercury and air are comparable.For the fatigue tests carried out at the high frequency of 700 Hz, longer fatigue lives in mercury were observed, relative to those in air for the higher stress (⩾400 MPa). However, decreasing the applied stress level at 700 Hz decreases the difference in the fatigue lives in air and mercury.The specimen temperature developed during fatigue can greatly influence the effects of test frequency and environment on the fatigue life.There is a frequency effect between 10 and 700 Hz in air. The greater specimen temperature at 700 than 10 Hz reduces the fatigue life at 700 Hz.There is no significant frequency effect between 10 and 700 Hz in mercury.Fatigue specimens tested at 10 Hz and applied maxmum stress levels over 400 MPa in mercury exhibit shorter lives, as compared to those in air, which may be due to liquid metal embrittlement.Fatigue lives at 700 Hz in mercury were found to be generally longer than in air, resulting from a temperature effect due to the cooling effect of mercury compared with air.The fatigue endurance limit measured at both 10 and 700 Hz in air and in mercury was approx. 350 MPa.Effects of multiple delaminations on the compressive, tensile, flexural, and buckling behaviour of E-glass/epoxy compositesThe goal of this study is to investigate the effect of multiple delaminations on the compressive, tensile and flexural strength of E-glass/epoxy composites and to evaluate their effects on the first critical buckling and re-buckling loads. Artificial delaminations of different sizes were inserted into four interlayers of [45°2/0°2/−45°2/90°2]s oriented E-glass/epoxy composite using a hand lay-up method and a hot press. The effects of through-the-width strip, circular and peanut shaped delaminations and triangle and inverted triangle patterned delaminations through the thickness direction were investigated experimentally. According to the results, the presence of multiple large delaminations influences the compressive and flexural strength and critical buckling load significantly. However, tensile strength is less affected by multiple delamination.Laminated composites, also known as advanced materials, are widely used in a variety of engineering applications. Though these materials offer several advantages, they must be used with caution. Damage mechanisms involved in laminated composite materials are unlike that of conventional metal materials. One of the most important types of damage encountered in laminated composite materials is the decomposition of two layers. This damage is known as delamination, which is not visible to the naked eye. The material strength decreases significantly due to delamination. The out-of-plane forces such as low velocity impact loading cause interlaminar stresses and delamination In recent years, significant research has been carried out towards understanding the effects of delamination on the mechanical properties of polymer-matrix composites. Chen and Sun Most of the studies focus on the effects of single delamination. Kutlu and Chang To determine the buckling and post-buckling behaviour of single and double through-the-width delaminated composites, a novel layerwise theory was proposed by Ovesy et al. Most studies involve one or two embedded artificial delaminations. However, delamination damage can occur at multiple interlayers of laminated composite plates and their dimensions are generally different. On the other hand, the overall mechanical properties (such as compressive, tensile and flexural strength and critical buckling load) have not been investigated simultaneously in most studies. In this study, triangle and inverted triangle patterned delaminations through the thickness direction were investigated experimentally. Polytetrafluoroethylene (PTFE) films of different sizes were inserted to four interlayers of angle-ply E-glass/epoxy composite to create artificial delaminations. The effect of the multiple delaminations of different sizes on the compressive, tensile and flexural strength and critical buckling load were determined experimentally. The effect of the length of the biggest delamination and the length of the other delaminations (lower level delaminations) and the effect of the delamination shape (through-the-width-strip, circular and peanut) were also investigated.The laminated composite materials with and without artificially embedded multiple delamination damage were manufactured using a hand lay-up method at the Izoreel Company, Izmir. Ciba Geigy Bisphenol A Epoxy CY-225 resin and Ciba Geigy Anhyride HY-225 hardener were stirred in a mass ratio of 100:80 to form the matrix material. The cure process was carried out using a hot press at 0.15 MPa at 120 °C for 150 min. The composite plates were subjected to a post cure process at the same pressure and 100 °C for two hours. Fibre volume ratio of the obtained composite material was 65%. The fibre orientation of the laminated composite material to be used for all experiments was chosen as [45°2/0°2/-45°2/90°2]s. The resulting layer thickness was 3.8 mm. During manufacture, PTFE films, 150 μm thick, was used to create an artificial delamination.Three different delamination geometries (through-the-width strip, circular and peanut shaped) and two different delamination types through the thickness direction (triangle and inverted triangle patterned delamination) were used. The characteristics of delaminations are as follows:IA: inverted triangle patterned delamination through the thickness direction (IB: triangle patterned delamination through the thickness direction (Through-the-width and large delamination is termed as strip delamination.It simulates transverse line loading damage or low velocity line loading impact damage.It simulates low velocity point impact damage.It simulates low velocity point impact damage.Although the real delamination damage resulting from low velocity impact is generally peanut shaped, the circular form is chosen because of easy applicability in many numerical and experimental studies. In this study, the errors made by applying circular shaped delamination instead of peanut shaped delaminations were determined. In order to compare the effects of the strip, circular and peanut shaped delaminations on the compressive strength, the biggest strip delamination length, the biggest circular delamination diameter and the biggest peanut shaped delamination length were chosen as 60 mm.The compression tests of composite specimens, with and without delaminations, were performed according to the ASTM . To prevent buckling of the specimens under the compressive load, the side support plates were used on both sides of the compression test fixture. A speed of 1.25 mm/min was chosen for the test, as recommended by the standard. The specimen length (L) is 150 mm and the specimen width (w) is 100 mm. Compressive strength was determined according to Eq. There is no existing improved tension test standard for the delaminated composites. For this reason, tension tests of the control and delaminated specimens were carried out according to ASTM ). The test speed was 0.5 mm/min. Tension tests were continued until the specimen broke. Tensile strength is determined according to Eq. Pmax: maximum force obtained from the test machine (N)The flexural tests on composite specimens, with and without delamination, were performed according to ASTM . According to the standard, the diameter of the loading rollers and the support rollers are 5 mm and 3.2 mm, respectively. The distance between the support rollers (s) is 16 times the specimen thickness (t). The distance between the loading rollers is half the distance between the support rollers. The width of the four point bending specimen is chosen as 12 mm. Test speed was calculated according to Eq. s: distance between the support rollers (mm)Z: outer fibre’s strain rate (mm/mm) (Z value is considered to be 0.01 based on the standard Pmax: maximum force obtained from the test machine (N)The composite specimens, with and without delamination, were fixed at the bottom edge and subjected to a uniaxial compression from the top edge. Unlike the compression test, the other two edges were not supported. Since there isn’t any standard for the buckling test, the specimen length (L) is chosen to be 150 mm and the specimen width (w) is chosen to be 100 mm. Both Type IA (inverted triangle patterned delamination through the thickness direction) and Type IB (triangle patterned delamination through the thickness direction) specimens were used for the buckling tests. The placement of the delaminated specimen is shown in All experiments were performed using a Shimadzu AG-X-250 universal testing machine at the Mechanical Laboratory of Cumhuriyet University. Compression, tension, flexural and buckling test specimens were prepared using a diamond saw. All tests were repeated three times only due to the difficulty of preparation of the composite specimens with artificially embedded delaminations.The compressive strength of composite specimens, with and without artificial multiple delaminations, was determined based on the ASTM standard. This standard is designed to determine the residual compressive strength of real delaminated polymer matrix composites following low velocity impact. The compression load versus displacement graphs of the control specimen and through-the-width strip delamination damaged specimens (Type IA and Type IB) are shown in . While there are no fluctuations in the compression load-displacement graph of the control specimen, 4 regions indicating fluctuations (ups and downs in the graph) are observed in the load-displacement graph of multiple through-the-width strip delaminated specimens. Each one of the fluctuation regions in the graph indicates a fracture in one of the sub-laminates. During the breaking of each sub-laminate, a loud sound was heard. Composite specimen continued to carry the load until the last and the thickest sub-laminate was broken. The damages were initially observed at the lower edge (where it is connected to the support) of the control specimen (a). However, all delaminated specimens were broken in the middle. The crack originated from the delaminated region and advanced towards the edge of the specimen in the through-the-width strip, circular and peanut shaped delaminated specimens (Firstly, the effects of the biggest strip delamination length (a) on the compressive strength were determined in both the triangle and inverted triangle patterned delaminated specimens (Type IA and Type IB). The biggest delamination lengths (a) were 40 mm, 60 mm and 80 mm b determines the dimensions of other lower delaminations (lower level delaminations) and b value was 4 mm. Each test was repeated three times. The results obtained are given in . While the biggest delamination length (a) increases, the compressive strength decreases in both through-the-width strip delaminated specimens. The compressive strength in the Type IA specimen (for a = 40 mm) decreases by 63.5% compared with the control specimen. The difference between the compressive strengths of control specimen and Type IB specimen (for a = 40 mm) is 55.63%. Considering that the biggest delamination length increases from 40 mm to 80 mm, the compressive strength decreases by just 3.99 MPa in a Type IA specimen and 11.56 MPa in a Type IB specimen. As a result, when the biggest delamination is close to the edge (near surface delamination), the effect of the delamination length on the compressive strength is not significant. When the biggest delamination is in the middle interface of the specimen, the compressive strength varies substantially and the effect of the delamination length is significant. The presence of multiple large through-the-width strip delamination damage (the biggest delamination size: 40 mm–80 mm × 100 mm) causes approximately a 60% reduction. Aslan and Sahin In order to compare the effects of the strip, circular and peanut shaped delaminations on the residual compressive strength, the biggest strip delamination length, the biggest circular delamination diameter and the biggest peanut shaped delamination length were chosen as 60 mm and b was chosen as 4 mm. The results are shown in . Compared to the control specimen, the compressive strengths of through-the-width strip, circular and peanut shaped delaminated specimens decrease by 64.47%, 22.77% and 19.43%, respectively. The error generated by choosing circular shaped delamination instead of peanut shaped delamination is only 4.14%.After examining the effects of the biggest strip delamination length on the compressive strength, the effects of the other lower delamination lengths are considered. The results are shown in . When b increases, the compressive strength increases to a small extent in both through-the-width strip delaminated specimens. When the b value increases from 2 mm to 6 mm, the difference in the compressive strength is 7.8% in case of Type IA specimen and 11.47% for the Type IB specimen.In summary, the compressive damage mechanism of delaminated composites depends on shape, size and position through the thickness of delaminations The tensile strengths of the composite specimens, with and without artificial multiple delaminations, were determined according to the ASTM standard. Only the control specimen and the Type IB (triangle patterned delamination in the thickness direction) specimens were used for the tensile test. The biggest delamination lengths (a) were 40 mm, 60 mm and 80 mm b is constant and a value of 4 mm was used. Each test was repeated three times. All the layers in the control specimen and Type IB specimens broke suddenly with a loud sound. The broken Type IB tensile specimen is shown in . The results obtained from the tensile test are given in . It is seen from the table that when the length of the biggest delamination is 40 mm, the tensile strength decreases by 18.20%. Similarly, if the length of the biggest delamination is 80 mm, the tensile strength decreases by 23.39%. Reis et al. While the biggest delamination length (a) increases, the tensile strength decreases slightly. The presence of multiple large delamination damage does not significantly affect the tensile strength as much as it affects the compression strength.The four point bending test was carried out to determine the flexural strengths of the composite specimens. Control specimen and Type IB (triangle patterned delamination in the thickness direction) specimens were used for the flexural test. The specimen was loaded until either it broke with a loud sound or the strain reached 5%. Breakages occurred in the middle and bottom surface of the four point bending specimen (). Each test was repeated three times. The results obtained from the four point bending tests are given in . It is seen from the table that when the length of the biggest delamination is 40 mm, the flexural strength decreases by 20.91%. Similarly, when the lengths of delaminations are 60 mm and 80 mm, the flexural strength decreases by 62.15% and 75.76% respectively. According to the test results, while the biggest delamination length (a) increases, the flexural strength decreases significantly. Amaro et al. A typical load-displacement curve obtained from the buckling test is shown in . A line was drawn over the Hooke line to determine the critical buckling load. The point where the load-displacement curve separates from the plotted line gives the critical buckling load. The load was removed immediately after the first buckling. After determining the first critical buckling load, the composite specimen was subjected to a buckling load again (re-buckling). Re-buckling loads of all specimens were determined. Parlapalli et al. While the control specimens buckled globally, all multiple through-the-width strip delaminated specimens buckled locally from the delaminated region (). The effects of the biggest strip delamination length (a) on the critical buckling load were determined in both the triangle and inverted triangle patterned delaminated specimens (Type IA and Type IB). The results are shown in . While the biggest delamination length (a) increases, the critical buckling load decreases in both through-the-width strip delaminated specimens. Compared to the control specimen the critical buckling load of the Type IA specimen, with the biggest delamination lengths of 40 mm, 60 mm and 80 mm, decreases by 9.93%, 55.34% and 58.90%, respectively. However, in case of Type IB specimens the critical buckling load for the same lengths decreases by 48.34%, 63.40% and 67.27%, respectively. Based on the results it can be inferred that when the biggest delamination is placed at the interface close to the surface instead of the middle interface, the composite material is more resistant to the buckling load. Similar results were obtained by Mohammadi and Shahabi After investigating the effects of the biggest strip delamination length (a) on the first critical buckling load, re-buckling tests were carried out. The re-buckling results are given in . The difference between the re-buckling and first buckling loads for the control specimen is very small. After the first buckling, the load was immediately removed and therefore, the damages occurring in the control specimen during the first buckling do not propagate. When the biggest delamination is placed at the interface close to the surface (Type IA), re-buckling load decreased by ∼50% compared to the first critical buckling load. However, when the biggest delamination is placed at the middle interface (Type IB), the re-buckling load decreased by about 15–30%. This difference can be explained based on large local buckling deformation occurring in the Type IA specimens.The effect of the lengths of the other lower level delaminations on the critical buckling load is shown in . When b increases, the critical buckling load increases in both through-the-width strip delaminated specimens. When the b value increases from 2 mm to 6 mm, the difference between the critical buckling loads is 25.90% in Type IA specimen and 18.85% in Type IB specimen. However, Hwang and Liu The effects of multiple delaminations on mechanical properties were determined in this study. Triangle and inverted triangle patterned delaminations were considered. Through-the-width strip, circular and peanut shaped delaminations were also investigated. Based on the results we infer that:Multiple large through-the-width strip delaminations reduce the compressive strength by approximately 60%. The size and location of delamination significantly affect the compressive strength.When the effects of different delamination shapes on the compressive strength are compared, it is seen that the effect of the peanut shaped delamination is less than that of circular shaped delamination. The effect of the through-the-width strip delamination is the most considerable among the three delamination shapes (through-the-width strip, circular and peanut).Presence of multiple large delaminations influences the tensile strength marginally.When the biggest delamination length increases, the flexural strength decreases. The biggest delamination lengths of 40 mm and 80 mm reduce the flexural strength by 20.91% and 75.76%, respectively.When the biggest delamination is placed at the interface close to the surface (near surface delamination) instead of the middle interface, the composite material is more resistant to buckling load. However, an opposite result was found in case of the compression tests.After the first buckling, the load was removed and the composite specimen was subjected to re-buckling. The difference between the first buckling and re-buckling load is approximately 50% for Type IA specimen and 15–30% for Type IB specimen. This shows that after the first buckling, the composite specimens, with and without delamination, continue to carry the load.Boron nitride nanotube reinforced polylactide–polycaprolactone copolymer composite: Mechanical properties and cytocompatibility with osteoblasts and macrophages in vitroBiodegradable polylactide–polycaprolactone copolymer (PLC) has been reinforced with 0, 2 and 5 wt.% boron nitride nanotubes (BNNTs) for orthopedic scaffold application. Elastic modulus of the PLC–5 wt.% BNNT composite, evaluated through nanoindentation technique, shows a 1370% increase. The same amount of BNNT addition to PLC enhances the tensile strength by 109%, without any adverse effect on the ductility up to 240% elongation. Interactions of the osteoblasts and macrophages with bare BNNTs prove them to be non-cytotoxic. PLC–BNNT composites displayed increased osteoblast cell viability as compared to the PLC matrix. The addition of BNNTs also resulted in an increase in the expression levels of the Runx2 gene, the main regulator of osteoblast differentiation. These results indicate that BNNT is a potential reinforcement for composites for orthopedic applications.Biodegradable polymers are classified as the second generation bio-implant materials PLC copolymer scaffolds are proposed for the bone and cartilage tissue regeneration in this study. However, the PLC scaffold has elastic modulus and tensile strength that do not match with the properties of the bone tissue or cartilage. Subchondral, trabecular and cortical bone tissues show higher elastic modulus BNNTs have excellent elastic modulus of 1.22 TPa Given its proposed biomedical application, cytotoxicity of BNNTs is a very important issue. Recently, Chen et al. In the present study, PLC–BNNT composites have been synthesized and their mechanical properties and biocompatibility have been evaluated. The effects of BNNT addition on the macro- and nano-scale mechanical properties of the PLC copolymer have been studied. Cytotoxicity of bare BNNTs with osteoblast and macrophage cells has been evaluated. Biocompatibility of the PLC–BNNT composite has also been investigated via interaction with the human osteoblasts. Gene expression study of osteoblast cells grown on PLC–BNNT composite has been performed to obtain an insight on overall growth, proliferation and differentiation of osteoblasts with the change in composition.-lactide and ε-caprolactone (PLC) in 70/30 M ratio was obtained from Purac Biomaterials, Illinois, USA. BNNTs used in this study were obtained from Nanoamor, Houston, USA. The size distribution of as-received BNNTs measured from scanning electron microscopy (SEM) images of dispersed nanotubes shows length distribution of 0.43–5.8 μm (mean, 1.98 μm); outer diameter range of 32–145 nm (mean, 71 nm) and aspect ratio varying between 15 and 84 with an average of 40.The compositions used for this study were 100 wt.% PLC, PLC–2 wt.% BNNT and PLC–5 wt.% BNNT, which will be referred as PLC, PLC–2BNNT and PLC–5BNNT, respectively, hereafter. For preparing the composite films, 1 g of PLC was mixed with 20 ml of acetone to form a colloidal solution by constant stirring at ∼313 K. BNNTs for each composition were mixed in 20 ml of acetone. BNNT–acetone dispersion was ultrasonicated for 1 h and then mixed with colloidal PLC–acetone solution. The final mixture was ultrasonicated for 15 min before casting in a 55 mm diameter glass Petri dish. For the PLC film, 20 ml of acetone was mixed in colloidal solution and ultrasonicated before casting. This was done in order to keep the processing parameters same for the three composites. The composite films were cured at the room temperature in vacuum for 24 h. Subsequently, they were peeled off from the glass surface. The thicknesses of the free-standing films were ∼500, 250 and 200 μm for PLC, PLC–2BNNT and PLC–5BNNT, respectively. Acetone was chosen instead of chloroform because the latter has been reported to be a poor dispersant for BNNT X-ray diffraction of BNNTs was carried out using Cu Kα (λ |
= 1.542 Å) radiation in a Siemens D-500 X-ray diffractometer operating at 40 kV and 40 mA. Micro-Raman spectroscopy of BNNTs and the composite films were performed using a Spectra Physics (Model 3900S, California, USA) with Ti-sapphire crystal as target, with a laser power of 18 mW and the detector from Kaiser Optical Systems Inc. (Michigan, USA). Transmission electron microscopy (TEM) images of BNNTs were captured using Philips PW 6061 transmission electron microscopy system (model CM 200, Eindhoven, The Netherlands). JEOL, JSM-633OF field emission scanning electron microscope was used for the microstructural characterization. a (as-received BNNT) was captured at 15 kV whereas micrographs of PLC/PLC–BNNT films were recorded at 5 kV. Lower operating voltage has been used for polymer samples to avoid their heating and damage. Working distance was maintained at 36.4 mm for all samples. Density of the composite films was measured geometrically.Tensile samples were made from the free-standing PLC, PLC–2BNNT and PLC–5BNNT films. Tensile samples were 25 mm long and 5 mm wide, with a gauge length of 5 mm. These tests were carried out using EnduraTEC, ELF3200 series tensile machine using a load cell with maximum load of 245 N and 0.02% accuracy of the maximum load. The maximum allowable cross-head movement was 12 mm. Three tests were carried out for each composition at a cross-head speed of 6 mm min−1. Tensile sample preparation and testing were performed following ASTM-D3039M-08 procedure. Extensometer was not used for the strain measurement as tensile samples were small and lightweight to support the weight of extensometer. For calculation of engineering stress in the material, cross-sectional area of the three films were calculated separately using sample dimensions and thickness of the films before testing.Hysitron Triboindenter, Minneapolis, MN, USA, with 100 nm Berkovich pyramidal tip, was used for the nanoindentation testing to study nano-scale mechanical properties of PLC, PLC–2BNNT and PLC–5BNNT composites. Tip-area calibration was done using a standard fused quartz substrate of known modulus (69.6 GPa). Indentation was performed with a constant load rate for 10 s and the peak load was confined up to 90 μN. Elastic modulus (E) had been calculated from the load–displacement curves using the Oliver–Pharr method Human osteoblasts ATCC CRL-11372 (ATCC, Manassas, VA) were seeded at a density of 1000 cells per well in 6-well polystyrene Petri dishes (Corning, New York) at 307 K (34 °C), 5% CO2 in a 1:1 mixture of Ham’s F12 Medium Dulbecco’s Modified Eagle’s Medium, with 2.5 mM -glutamine. The phenol red-free base media was supplemented with 10% Fetal Bovine Serum (Atlanta Biologicals, Lawrenceville, GA), 100 UI ml−1 of penicillin and 100 μg ml−1 of streptomycin (MP Biomedicals, Irvine, CA). Murine macrophages (J774 Eclone, provided by Dr. M.A. Barbieri, Florida International University) were seeded in the same manner in Dulbecco’s Modified Eagle’s Medium supplemented with 10% Fetal Bovine Serum and 1% sodium pyruvate (Atlanta Biologicals, Lawrenceville, GA), 100 UI ml−1 of penicillin and 100 μg ml−1 of streptomycin (MP Biomedicals, Irvine, CA) at 310 K (37 °C). Osteoblasts and macrophages were allowed to attach to the plastic surface for 24 h, after which the medium was replaced by fresh medium supplemented by bare BNNTs at 1 μg ml−1 concentration (typically 2 ml of medium were added to the three experimental wells). Simultaneously, a series of osteoblasts and macrophages cultured in medium without BNNT was set up. Control wells were set up with a triplicate of medium without osteoblasts or macrophages.Both types of cells were cultured for 2.5 days with bare BNNTs prior to the cytotoxicity test, which was performed with the CytoTox 96 Non-Radioactive Cytotoxicity Assay kit (Promega, Madison, WI) following the manufacturer’s recommendations. Cytotoxicity test performed is a colorimetric assay that quantitatively measures lactate dehydrogenase (LDH), a stable cytosolic enzyme released into the culture medium upon cell lysis. Released LDH in culture supernatant is measured with a coupled enzymatic assay which results in the formation of a red formazan product that can be measured at 490 nm with a spectrophotometer and is proportional to the number of cells lysed. Student’s t test was performed to find out the 95% confidence interval.Osteoblasts were cultured in the same way described above. Prior to the experiment, PLC composite films (1 cm × 1 cm surface area) were sterilized for 5 h by UV irradiation before being placed into 6-well polystyrene Petri dishes (Corning, New York). For cell viability studies, osteoblasts were seeded at a density of 5000 cells per well in 2.5 ml of medium and grown in an incubator at 307 K, 5% CO2. After 2.5 days, cells grown on the PLC composite films were stained for 2 min with a phosphate buffer saline 1× solution containing 15 μg ml−1 of fluorescein di-acetate (FDA) (MP Biomedicals, Irvine, CA) and 4.5 μg ml−1 of propidium iodide (PI) (Fisher Scientific, Waltham, MA) Osteoblasts, cultured in the same way described earlier, were seeded at a density of 5000 cells per well in 2.5 ml of medium and grown in an incubator at 34 °C, 5% CO2.After 2.5 days, cells grown on the PLC–BNNT composite films were washed with a phosphate buffer saline 1× solution and collected by trypsinization for 5 min. Total RNA was extracted with the Cells-to-cDNA II kit (Ambion) following the manufacturer’s instructions. Cells were incubated in a lysis buffer to rupture the membranes and release the nucleic acids. Endogenous RNAses were inhibited by heat treatment and genomic DNA degraded by DNAse I action. The total RNA was reverse transcribed into cDNA and subsequently used for real time PCR amplification with SYBRGreen.The differentiation of osteoblasts on the PLC and BNNT polymer films was evaluated by assessing the expression of the transcription Runx2 (also known as cbfa1), the master regulator of osteoblast development.Comparative determination of Runx2 transcript levels was performed by real time semi-quantitative RT-PCR using the SyBr Green detection on a ABI 7300 Cycler (Applied Biosystems, Foster City, CA, USA) using primers: Fw CCA CCA CTC ACT ACC ACA CCT ACC and Rv CAT GGC GGA AGC ATT CTG GAA GG. Because the levels and the quality of mRNA may vary slightly according to the different types of culture conditions (i.e., polymer films), the transcripts were quantified relative to the GAPDH housekeeping gene using the primers: Fw CCA CCC ATG GCA AAT TCC and Rv TGGGAT TTC CAT TGA TGA CAA G, by determining the difference between the crossing point (Cp) of amplification of the target RNA and the GAPDH RNA (delta Cp GAPDH). The Cp is defined as the point when the amplification starts the exponential phase. Comparison of transcript levels then relies on differences between the delta Cps (delta-deltaCp, ddcp). We considered the transcript level in cells grown on PLC polymer as a reference. Therefore, the numbers of fold activation were calculated as follows. Given the relation: nb fold = nb copies target/nb copies reference,nb_fold=10[log(nb_copies_target)-log(nb_copies_reference)] shows the SEM and TEM images of the as-received BNNTs. SEM image shows nice clean BNNTs, whereas TEM picture shows the presence of both long cylindrical tubes and bamboo type structures. Ma et al. . It shows peaks corresponding to different phases of boron nitrides. Maximum number of peaks with high intensities is generated by hexagonal boron nitride (h-BN) phase present in the material. This indicates that the sample primarily consists of BNNTs, which are the tubular structures formed out of h-BN sheets shows the micro-Raman spectrum for the as-received BNNTs and the polymer composite films. BNNT shows a peak at 1368 cm−1 that is attributed to the E2g mode . The shift in the peak to higher wave number is attributed to the compressive stress present in the polymer matrix in the composite system . The fracture surfaces, in this study, were obtained by manually stretching the polymer film till the point of fracture. Thickening of BNNT from its original diameter of 70–100 to 90–200 nm indicates polymer coating on its surface. Neck formation with larger diameter present at the base is also an indicator of the wetting of BNNTs by PLC. The reasons for good bonding between BNNT and PLC matrix are discussed in detail in Section PLC copolymer film shows lower density than the PLC–BNNT composite films. Geometrically measured density was 0.71, 1.15 and 1.33 g cm−3 for PLC, PLC–2BNNT and PLC–5BNNT composite films, respectively. Theoretical density of PLC is not available in the literature due to varying PLC and PLA ratio. The density of BNNT used in this study is 2.25 g cm−3. Using the geometrical density of porous PLC film (0.71 g cm−3) as the baseline, the computed density (using rule of mixture) for addition of 2 and 5 wt.% BNNT is 0.74 and 0.78 g cm−3, respectively. The measured density is 55% and 71% higher than computed density for PLC–2BNNT and PLC–5BNNT composite films. This difference is due to the large porosity content of the PLC film which has been used as baseline for computations. SEM images of the cross-section of the composite films show that PLC is highly porous than PLC–5BNNT (). High magnification images of cross-sections (insets in ) also show inter-laminar pores in PLC as compared to dense structure in PLC–5BNNT with few small pores and smoother surface. Processing conditions being the same, the change in porosity of the composite films is attributed to the presence of BNNT in the PLC matrix. The effect of BNNT on the porosity of the composite film is understood in terms of interaction between PLC and BNNT in solution. In the present study, acetone has been used as the dispersant instead of chloroform. Although the latter is known to be a better solvent for PLC copolymer, dispersion of BNNT is very poor in chloroform, which may lead to poor mechanical properties of the composite . Yum and Yu have shown an improvement in the wettability of BNNT with the polymer as compared to water shows a schematic representation of this concept. shows the engineering stress–strain behavior for PLC and PLC–BNNT composite films up to a strain of 2.4 (240% elongation), obtained from the uniaxial tensile tests. The gauge length of the tensile sample was 5 mm. Maximum cross-head movement possible being 12 mm, the strain value is limited up to 2.4. Stress–strain behavior shows a gradual increase in the tensile strength with the addition of BNNT from 2.67 MPa in PLC to 4.98 and 5.59 MPa for PLC–2BNNT and PLC–5BNNT, respectively. Tensile strength at 2.4 strain increases by 87% and 109%, with addition of 2 and 5 wt.% BNNT, respectively. The error bars in show a small error (<5%), which suggests a homogeneous behavior of the composites at the macroscale length. Tensile samples from the three films returned back to their original shape without any visible deformation after a maximum strain of 2.4 was achieved. Addition of a second phase (ceramic) to a flexible matrix often shows a negative effect on its deformability. This negative effect becomes more prominent where the matrix is a very flexible polymer such as PLC. But in PLC–BNNT composite films, even with addition of BNNTs, the deformability of the PLC is not affected up to 240% elongation. Such behavior is attributed to the high flexibility of BNNTs Increase in the tensile strength, by nano-size reinforcement, is obtained by creating a large interface area between matrix and the reinforcement for effective load transfer. Further, the fiber type geometry of the reinforcement makes them more effective in increasing the tensile strength of the matrix. SEM images of the fracture surface of PLC–5BNNT () show the BNNTs bridges within PLC matrix. Dangling BNNTs with the other end fully embedded in the polymer matrix are also observed in b. BNNTs behave as rigid reinforcements and provide benefits of short fiber strengthening. The strengthening of PLC by BNNT can be explained by shear lag model, which is well accepted for polymer–CNT composites and other short fibers where σf is the fracture strength of fiber (24 GPa for BNNT where τi is the shear strength at fiber–matrix interface or matrix adjacent to interface, σm is the fracture strength of the matrix, lf and df are the length (1.98 μm) and diameter (71 nm) of the fiber, respectively, and Vf is the volume fraction (0.03 for PLC–5BNNT) of the fiber in the composite. The fracture strengths of PLC (σm) is reported to be 41 MPa , is 36.34 MPa. The experimental value (5.59 MPa) is found to be much lower than the calculated value. The lower experimental value of tensile strength of PLC–BNNT composite is attributed to the following:First, the porosities present in PLC matrix results into a lower σm (2.67 MPa) as compared to the fracture strength for PLC (41 MPa) used for calculation of σc.Second, the experimentally obtained values of strength of the composite are not fracture strength of the composites, but tensile strength at a strain of 2.4 (limit of the instrument). Hence, the actual fracture strength of the polymer composite films is expected to be much higher. However, the overall comparison of tensile strength values for PLC and PLC–BNNT composite films indicates a significant positive effect of the BNNT addition to PLC matrix.Elastic modulus of the PLC–BNNT composites was evaluated using nanoindentation technique. Nanoindentation provides localized mechanical properties. More than 50 indents have been performed in each composite film covering different regions situated a few millimeters apart. In each region, the indents were made at a distance of 9 μm from each other. Total area covered by the indents was greater than 2592 μm2 in each sample. The statistical distribution of the elastic modulus, measured from individual indents, thus provides the mechanical property of the composite at macroscale length. It should also be noted that the nanoindentation experiments do not account for the macroscale features in the composites, like porosities. The indents were made on non-porous areas of the cross-section of the composite film.A representative load vs. displacement curve for each composition has been presented in . The same load function was used for all the samples, with a peak load of 90 μN and loading time of 10 s with constant loading rate. As shown in , none of the films could achieve the peak load, as they could not provide enough resistance to the indenter, during penetration, to reach the peak load in the given loading time. But, when compared amongst them, it is clearly seen that with the addition of BNNT, the indentation depth decreases and peak load increases. This is due to the strengthening achieved through BNNT reinforcement that resists the elastic deformation of the composites. also shows full recovery of the indentation depth during unloading. This observation supports the results of tensile tests on high ductility of the PLC and PLC–BNNT composite films. shows the average and statistical distribution of elastic modulus for the three PLC–BNNT composites determined by nanoindentation. The average elastic modulus values for PLC, PLC–2BNNT and PLC–5BNNT composite are 0.081, 0.16 and 1.19 GPa, respectively. Average elastic modulus of the PLC copolymer increased by 100% with 2 wt.% BNNT and 1370% with 5 wt.% BNNT additions. There is more scatter in the E value for PLC–BNNT composites due to the fine spatial resolution of the measurement technique, as discussed earlier. The scatter originates from the difference in the stiffness of the regions with and without BNNTs. PLC samples show the lowest scatter. But, even with the scatter in the data, the total range of E values becomes significantly higher with the BNNT addition. presents a comparison of the increase in the tensile strength and elastic modulus of PLC–5BNNT composites with PCL, PLA and PLC copolymer composites with different second phase reinforcement (including CNTs) reported in the literature Cytotoxicity assay for bare BNNT was performed with osteoblast and macrophage cells to evaluate the suitability of using BNNTs for orthopedic implants. The assay that has been used in this study measures the cell death, by rapid and accurate quantification of the release of lactate dehydrogenase (LDH), a stable cytosolic enzyme released from lysed cells. The amount of LDH released, which is proportional to the number of dead cells, is quantified through a colorimetric assay by measuring the absorbance at 490 nm. Absorbance value of the culture medium without any cells or BNNT was considered as background and subtracted from the experimental absorbance values obtained for the cells cultured with and without BNNT. Comparative measurement was performed and cytotoxicity values obtained for the cells cultured without BNNT were considered as the reference (value set to 1.00). Results, reported in , show a non-significant cytotoxicity induced by the BNNT for both osteoblasts and macrophages cell lines. To the best of the authors’ knowledge no other study has reported on the cytotoxicity of BNNT on osteoblast and macrophage cells. The literature shows two studies about the cytotoxic effect of BNNT on live cells – by Chen et al. on human embryonic kidney cells Cytotoxicity can also be caused by fiber geometry by incomplete internalization (phagocytosis) by macrophages. It is observed that fibers with length <17 μm are not cytotoxic to murine alveolar macrophages (∼13 μm diameter) The viability of osteoblast cells is defined as the ratio of live to dead cells. FDA stains the grain boundary of the live cell in green color, whereas, PI stains the nucleus of the dead cell in red. The viability ratio obtained through counting the cells under the fluorescence microscope shows higher count for PLC–2BNNT and PLC–5BNNT composites with 90 ± 2% and 91 ± 4%, respectively (). The osteoblast viability for PLC film has been found to be as low as 59 ± 4% (p value <0.05). The fluorescent images in present a representative picture of live and dead cells on the three PLC composite films. Fluorescence microscopy images after 2.5 days of growth show a typical lens shape characteristic of osteoblasts, suggesting the presence of normal cell behavior on PLC, PLC–2BNNT and PLC–5BNNT composite films with no significant difference in the cellular morphology. These results indicate that the addition of BNNTs improve the biocompatibility of the PLC copolymer in terms of osteoblast cell viability. The cross-section of polymer films in shows the presence of large pores in the PLC matrix. These large pores act as asperities to increase the surface roughness of the polymer film that can affect the viability of cells. Khosroshahi et al. have shown that higher surface roughness (micrometer) obstructs osteoblast cell proliferation In order to evaluate the effects of PLC–BNNT composites on the differentiation state of osteoblasts, the levels of expression of the transcription factor Runx2 have been assessed by semi-quantitative real time PCR. Runx2 (also known as Cbfa) is a master regulator of osteoblastogenesis and coordinates the integration of signaling events and other transcription factors involved in this process ). The positive effect of the presence of BNNTs on accelerated osteoblast differentiation and growth could be due to the natural affinity of protein to BNNTs. Zhi et al. Biodegradable PLC–BNNT composite films, with improved mechanical properties and biocompatibility, have been successfully synthesized for their possible application in orthopedic scaffolds. PLC–5BNNT composite shows an impressive 1370% improvement in the elastic modulus of the composite. Tensile strength of PLC–BNNT composite is also increased by 109%, without having any adverse effect on elasticity up to 240% elongation. Enhanced elastic modulus and tensile strength of the composite is attributed to the excellent mechanical properties of BNNT along with its uniform distribution and good interfacial bonding with the polymer matrix. Cytotoxicity assay of bare BNNTs on osteoblast and macrophage cells shows that presence of BNNT does not increase the number of dead cells and hence are biocompatible to these cells. Osteoblast cell viability study on polymer films reveals a 30% increase in live to dead cells ratio with BNNT addition in PLC. Gene expression study of osteoblast cells, grown on the composite films, shows fourfold and sevenfold increase in levels of expression of the transcription factor Runx2 in PLC–2BNNT and PLC–5BNNT, respectively. Gene expression results indicate accelerated osteoblast differentiation and growth in the presence of BNNT, which might be related to the natural affinity of BNNT for proteins.Certain figures in this article, particularly Figures 2, 3, and 7–14, are difficult to interpret in black and white. The full colour images can be found in the on-line version, at Predictive durability of polyethylene terephthalate toward hydrolysis over large temperature and relative humidity rangesThe hydrolytic stability of poly(ethylene terephthalate) (PET) has already been largely reported. The chemical reactions induced by damp-heat exposure are well–known, and various kinetic expressions for the degradation have been presented. Using the data from previous studies, a new model for degradation is proposed. This model combines the effect of temperature and humidity in a single equation. Three parameters are utilized: the classical pair of activation energy (Ea) and pre-exponential factor (f0), and the reaction order (n) to the relative humidity (RH). The model may be used to fit the degradation data from various sources describing the hydrolysis over a large range of conditions (40–100 %RH, 60–160 °C). In addition a prediction of the crystallinity changes brought about by hydrolytic chain scission was performed. Prediction of useful lifetime in moist heat is also possible (hydrolysis of 0.2% ester moieties in the polymer).PET is a thermoplastic material widely used in the form of fiber, sheet and film. It presents a specific interest for many applications. PET ageing has been reported under a variety of conditions [] have been methodically studied and described. It is for instance well-known that thermal oxidative degradation occurs at high temperatures [], and is inhibited below the melting temperature (Tm). This degradation mode may thus occur during processing, but not in the final objects. On the other hand, studies have also been carried out under very harsh conditions: elevated temperatures and high water pressure. These conditions alter PET in depth, and are even the ones envisioned for recycling PET by depolymerization [In-between these two extremes, PET might undergo significant chemical changes in a standard environment, especially under the combined effects of water and temperature. The hygrothermal degradation of PET has been reported numerous times. All authors concluded that both RH and temperature promote hydrolysis [PET hydrolytic degradation consists in the transformation of ester groups to the corresponding carboxyl acids and alcohols. This chain scission directly corresponds to a decrease in the molar mass of this polyester (A concomitant increase in the density has commonly been described []. This so-called chemi-crystallization is a straight forward consequence of the chain scission. It results from the preferential water diffusion in the amorphous phase of the polymer. The reduction of the molar mass within the amorphous phase may then provide enough mobility for the polymer to crystallize []. Despite the apparent simplicity of the hydrolysis process, the reaction rate is difficult to define mathematically. Several models have been proposed in the literature so far []. These models can be sorted according to the order of the reaction rate. A rate law is a mathematical equation that shows the dependence of reaction rate to the molar concentrations of reactants at constant temperature:Half-order model with [COOH] the carboxylic acid concentration (mol.g−1) and k the reaction rate constant (mol1/2.g−1/2.s−1):Second-order model with Nt the number of chain scission per unit mass (mol.g−1), [COOR] and [H2O] the concentration in ester and water (mol.g−1) and k the reaction rate constant (g.mol−1.s−1):Assuming a constant water concentration, this is often reduced to a first-order or pseudo-first order expression:In both cases, the reaction is supposed to be thermally activated, and to follow an Arrhenius Law:where Ek the activation energy (J.mol−1), R the gas constant (8.314 J mol−1 K−1) and f0 the pre-exponential factor.In summary, a very careful study of literature reveals that several questions remain unanswered []. The first reports on the hydrolytic degradation of PET as a function of both temperatures and humidity (60–130 °C and 20–100% RH; 60–175 °C and 23–100 %RH respectively) may be found as early as 1960s []. Initially, it was postulated that hydrolysis occurred through random chain scission process []. The second assumption concerned the diffusion of water, which was considered sufficiently elevated to not affect the kinetic [On the mathematical standpoint, the hydrolytic reaction has been considered as a pseudo first order model. It seemed enough to account for the effect of temperatures and relative humidity on the chemical degradation. It even seems relatively straightforward to adjust the model to the experimental data at low to medium degradation []. The hydrolysis can however become eventually significantly larger than predicted by the model for advanced degradations. To explain this, an additional of modification of degradation mode during ageing has been assumed []. As a result, only the initial part of the curve is modeled in the pioneering reports [It has also been pointed out that the sample thickness may influence the degradation kinetic []. All other things remaining equal, it would mean that water diffusion can influence the reaction. The assumptions of constant water concentration (Equation ]. This could explain why several studies concluded in favor of a second order reaction [In the 1990s, the morphological changes induced by the degradation have been investigated []. A PET film sunk in boiling water for 14 days, reveals a strong chemi-crystallization []. The chain scission favors an average of 5–6 monomers units in the crystalline phase. Because the chain scission essentially occurs within the amorphous phase, the relative amount of ester groups accessible to water molecules gradually decreases during hygrothermal degradation. This positive feedback is the typical behavior of a second order reaction. This auto-accelerating reaction may not be solely attributed to chemi-crystallization. An additional autocatalytic phenomenon could originate from the formation of hydrophilic acids and alcohols that favors water diffusion.Several authors also mentioned that the hydrolysis of PET induces a reduction of the molecular weight with a constant polydispersity index []. This corresponds to a random chain scission mode.Finally, it seems that the initial microstructure of PET influences the hydrolysis kinetic []. For instance, water diffusion and thus hydrolytic degradation is hindered within the crystalline phase. A simple rule of mixture was proposed to account for the effect of initial crystallinity [With [COOR]0 the initial reactive ester concentration in the amorphous phase (mol.g−1), Mn0 the initial number average molecular mass (g.mol−1), M the Molar mass of the PET monomer (g.mol−1) unit and χcv the volume percent crystallinity (vol%).The first attempt to study the combine effect of temperature and RH concluded that the order of the reaction with humidity was close to 1.3 for Polyethylene Butadiene (PBT) polymer []. It was later proposed that the reaction rate was proportional to RH for a thin PET film (0.5 mil, 85 °C) []. In contrast, thick sheet (10-mil) showed pronounced curvatures suggesting the influence of a diffusion process with a second order in water. This evidence for a higher order, may also originate from the plasticizing effect of water on PET [Where [P] and [H2O] are respectively the molar concentration (mol.g−1) of the repeat unit and water and k the reaction rate constant (mol−2.g2.s−1).From short literature survey, it appears that the PET degrades through random chain scission. The process remains largely controlled by water diffusion. The amorphous phase is therefore primarily concerned. The auto-accelerated character of the reaction seems established. From the literature, a large scatter has been observed in the activation energy of PET hydrolysis, ranging from 90 and 150 kJ mol−1 []. This is a big concern because it prevents the reasonable estimation of material's lifetime.The current study establishes a new reliable kinetic expression for the degradation of PET submitted to the combined effect of temperature and humidity. With this model, one estimates the crystallinity after hydrolytic chain scissions, and the life-time of real objects with a variety of PET morphologies.PET films were aged at 70 °C and 90 %RH in climatic chamber [] for various durations, up to 200 days. Multilayer films produced by REXOR Company (38, France) as high barrier materials have also been tested up to 870 days []. They are composed of three layers of PET (12 μm) coated with aluminum (80 nm) and a one of polyethylene (50 μm). The layers are assembled with three adhesive layers (2 μm) of polyurethane.The crystallinity of the PET was evaluated by DSC. The measurements were carried out on a DSC-7 instrument (Perkin-Elmer). The instrument was calibrated with an indium (Tm = 156.6 °C, ΔHm = 28.4 J g−1) and a zinc (Tm = 419.5 °C) standards. An empty aluminum pan was the reference. The average mass of samples was taken between 5 and 10 mg, measured precisely. The samples were heated from 30 to 300 °C at 10 °C.min−1. Three distinct measurements were performed for each type of sample. The amount of semi-crystalline phase was determined with the integrated signal of the melting peak. The area of this peak is proportional to the weight fraction of crystalline polymer χcm (wt%):With ωPET the weight fraction of PET in the multilayer, ΔHm the measured enthalpy, and ΔHm∞ the heat of fusion of 100% crystalline PET (125 J g−1) []. The weight fraction ωPET was obtained from the thicknesses of the different layers i composing the film ei (PET, PU, aluminum and PE) and their density ρi:The volume crystallinity χcv (vol%) was evaluated by:with ρPETa and ρPETc, the density of the amorphous and crystalline PET phases, respectively equal to 1.337 g cm−3 and 1.476 g cm−3 [Various approaches have been proposed to characterize both chemical and physical consequences of PET hydrolysis. Titration and IR spectroscopy may reveal a gradual increase of hydroxyl and carboxyl groups, corresponding to chain scissions []. IR Spectroscopy also indicates structural modifications, like crystallization. The latter remains however easier to follow with X-ray diffraction, density and differential scanning calorimetry (DSC) []. The reduction of the molecular weight may be assessed by size-exclusion chromatography (SEC), gel permeation chromatography (GPC), viscosity measurement, light-scattering, end-group titration, and MALDI-MS []. Some authors also gave indirect evidences for chain scission, through deterioration of the mechanical properties. Tensile and bending strengths, fracture toughness, and hardness of PET decline with its hydrolysis [The number average molar mass Mn is undoubtedly the best parameter to monitor for three reasons. The first is a direct quantification of the chain scission. The second is a high sensibility, even in the early stages of hydrolysis. The third, and most important, is that the effect of hydrolysis on Mn has been reported many times the literature. These previous measurements can now be used to consolidate our data and reinforce the resulting model.An ideal case of hydrolytic degradation was hypothesized. We assumed random chain scission and the absence of autocatalysis, auto-acceleration, and diffusion control of the reaction. In addition, esterification was considered as negligible. In short, we assumed that the degradation solely depends upon temperature (T in K) and relative humidity (RH). This results in Ref. [with Ea the activation energy (J.mol−1), R the ideal gas constant (8.314 J mol−1 K−1) and f0 the pre-exponential factor (a parameter). The rate of hydrolysis at a given temperature can therefore be expressed as follow:This is a first order reaction with nester the number of moles of ester links per mole of polymer. The number of ester groups per chain is:With Mn the number average molar mass and M the molar mass of the monomer unit, namely 192 g mol−1 for the PET.This can be further simplified by neglecting the chain-ends:ln(nnester(t)nester(t0))=ln(Mn(t)Mn0)=−f0×e−EaRT×RHn×t=F(t)The molecular weight of PET is commonly extracted from the viscosity in solution. This provides the so-called viscosity average molar mass Mv, in practice close to the weight average molar mass Mw [We first selected the literature reports depending on their descriptions of the ageing conditions. Experimental data can be utilized only if the RH and temperature [] are controlled and described carefully. Equation was then tentatively adjusted to each individual data series (a “series” being defined as data from a single article). The data for each series was obtained with the same morphology of PET. A numerical regression was performed with the least square method.The values for Ea, f0 and n were first determined for all the conditions tested by Allen et al. []. This concerns the hydrolytic degradation of amorphous PET between 60 and 90 °C at 45% relative humidity and in water immersion. In addition, these severe conditions were maintained up to 500 days. shows the experimental data (symbol) and the best fit with Equation (line) for various ageing conditions. The proposed model describes fairly well the variations of Mn in this broad range of temperature and relative humidity. The optimized parameters values are presented in The model has further been applied to other cases from the literature with more degraded states either from higher degradation temperatures []. The resulting parameters were also gathered in The analysis of the fit parameters indicates a very broad distribution for the activation energies Ea between 70 and 130 kJ mol−1. If this concurs well with the literature [], it seems to refute the physical meaning of the activation energy. The drive frequency seems however to also vary randomly and widely. The comparison between Ea and ln(f0) confirmed the strong interdependency that was even linear in the present case. The two parameters (Ea, f0) are correlated and should thus always be given together for meaningfulness. The scatter in the literature data can actually be reduced with the proper data treatment, especially by performing a single treatment of the overall data previously mentioned (). This reduces the uncertainties generated by the studies in a narrow temperature range (Δ30 °C). For this, Equation ln(−ln(Mn(t)Mn0))−ln(t)−nln(RH)=ln(f0)−EaRTIn this model, three independent parameters were used: n, Ea, and f0. The RH dependency was first optimized to get the best Arrhenius plot. This lead to n = 1.57 ± 0.10. Then, the corrected molar mass for all data point could turned into a new and unique Arrhenius plot, . In this graph, each point represents an individual data series for one temperature from . For example, the violet symbols (open and closed) represent the conditions tested by Allen et al. [The values for Ea and ln(f0) could then be determined and shown in The uncertainty was determined assuming normal distribution as [Here F(t) is the generic function (Equation ) dependent on variable Ea and f0. The covariance term was neglected.In order to validate the developed model, it was further applied to other experimental conditions (T, RH) and correlated with data from the literature [a show the predicted degradation at 70 °C and 80 %RH. It corresponds to the hydrolysis of recycled PET pellets with an initial crystallinity at about 30 wt%, and an initial number-average molar mass around 10 500 g mol−1 14. b represented the experimental data of different PET morphology which were hydrolyzed at 87 °C in water immersion [] and the model for the same condition. The three PET tested (PET fiber grade granule, partly oriented yarn (POY) and fully drawn yarn (FOY) obtained from drawn of POY with drawn ratio of 2.065) presented the same initial weight-average molar mass, 32 500 g mol−1 and the crystallinity was increased from POY to granule to FDY. c depicted the loss of molar mass for PET films of different thicknesses (12.7 and 250 μm) at 90 °C and 75 %RH []. In each case, the developed model matches very well the hydrolysis data collected in the literature [) was developed to illustrate the direct link between the three parameters time, temperature and relative humidity:Some experimental data presented in the literature have been merged in a single chart (). With the equivalent time, that accounts for RH and temperature, they all fall on a single master curve that fairly follows the model developed for the hydrolysis.The morphology of PET alters the kinetic of hydrolysis. The crystallinity (c) play an important role. Thin and amorphous samples follow the most critical side of the kinetic simulation. The model presented in the present work may however be safely used to estimate all the hydrolysis data collected in the literature, regardless of the initial structure. The only limitation is plausibly related to Tg. All the data presented were gathered above the Tg of PET [], and it is likely that the law would fail to predict the degradation in the glassy state. illustrates the isolated influence of temperature and humidity on the degradation kinetic. A power-law and exponential dependence have been obtained depending on the RH and temperature, respectively. Two plots were made varying one parameter while keeping the other constant. a shows effect of temperature (at 90 %RH), while b points the influence of RH (at 70 °C).These plots confirm the influence of the temperature is more pronounced than that of the relative humidity.The previous master curves are developed with the molecular weight. The later are very useful to develop and validate kinetic expression. Nevertheless, the Mn parameter may sometimes become out of reach, when the PET is embedded in a more complex structure []. Mn may also appear a bit conceptual, and not directly related to practical applications. For these reasons the hydrolysis should also be tracked with other structural parameters.It is well accepted that the density, related to the crystallinity, increases over time during hydrothermal ageing []. Most of these studies argue that the hydrolysis in this crystalline phase can be neglected by lack of water diffusion. In addition, the preferential hydrolysis in the amorphous phase favors the chemi-crystallization of PET [In order to amplify the application range of the model, the relationship between molecular weight and crystallinity was carefully studied. presents a large series of data from the literature during the hydrolytic degradation. The crystallinity resulting from chemi-crystallization is shown as a function of the PET molecular weight. The changes of the crystallinity, Xcm, with the molar mass, Mn, can be empirically compared to a power-law equation:Where ME represents the molar mass between entanglements (g.mol−1). From ME for PET is close to 0.70 kg mol−1. This is confirms the order of magnitude obtained by Fayolle et al. [ allows determine the crystallinity of a PET sample as a function of the ageing time knowing the temperature and humidity. This chart was prepared for 70 °C/90 %RH and presented in The results from the model were further compared to experimental data obtained in these conditions (70 °C and 90 %RH). The results originated from measurements within the structure of multilayered materials []. A remarkable agreement is obtained between the two very different approaches. The model is consistent with the previous results without using any adjustable parameter (). Only after 800 days seemed the crystallinity to digress from the model, but remained in uncertainties range.In order practically use this model, there is a need for a lifetime criterion. Because PET is often used for its very good toughness, a mechanical threshold was examined. More precisely, the embrittlement due to chain scission may be considered as a good way to categorize the loss of usability. The ductile-to-brittle transition is usually defined with a critical mass MnF []. For PET, this critical mass value ranges between 3500 and 7500 g mol−1. This value corroborates with the 7000 g mol−1 of a former study []. In the present case, and with an initial mass of 21 kg mol−1, a drop to 30% of this initial value would correspond. is a representation of the combined effect of RH and relative humidity on PET practical durability. The criterion was defined with 30% of the initial molar mass. For comparison, the Tg dependence on RH [] was superimposed. As mentioned previously, the calculated lifetime is likely to be underestimated below Tg.It is striking to note that the ductile-fragile transition is estimated at 8 days with your model (Equation ) for 100 °C and 100 %RH. This result is however in good agreement with the experimentally observed embrittlement of PET after 7 days in these conditions []. For the photovoltaic (PV) community, the accelerated ageing test (according to standard IEC 61215) [] is conducted at 85 °C and 85% RH. PV with PET-based back sheets show loss performance correlated to PET physical change occurring between 40 and 80 days []. This result also agrees the calculations (37 ± 5) days in these conditions.PET hydrolysis was described with a simple equation based on random hydrolysis process without auto-catalyst and diffusion control. The model is an extension of the Arrhenius law to accounts for the detrimental effect of the relative humidity. Three parameters are needed: the standard couple pre-exponential factor-activation energy, and the kinetic order of the reaction with RH. The model properly describes the data from a large literature mining.Concerning the purely Arrhenius plot, the broad distribution for the activation energies reported in the literature was confirmed, at a first glance. It actually results from the very strong interaction between the two parameters (Ea, f0) that should thus always be given together for meaningfulness. The scatter in the literature data may be lowered with a better data treatment. An activation energy of 100 kJ mol−1 seems reasonable for the hydrolysis mechanism.For the combined effect of temperature and humidity, the proposed model was successfully applied to fit all the literature data reporting the hydrolysis of PET in the rubbery state. The kinetic order with respect to RH was found close to 1.5.A chemi-crystallization is associated with the PET hydrolysis. The crystallinity of initially amorphous PET follows a power-law with respect to the molecular weight. This equation has been optimized and applied to the hydrolysis of complex PET-based systems, otherwise hard to characterize.A ductile to fragile transition of PET was hypothesized for a 30% molecular weight loss. This criterion allows to define the lifetime of the PET after hydrolysis in any constant ageing conditions. The predictions from this model match the experimental data published on complex PET systems (photovoltaic backsheets, envelop of vacuum insolation panels). One could now try and develop the model with variable ageing conditions, closer to real service.Preparation of respirable nanoparticle agglomerates of the low melting and ductile drug ibuprofen: Impact of formulation parametersDuctile and low melting point drugs exhibit challenging behaviour during both particle size reduction and spray drying as considerable amount of heat is involved in both processes. In this study, a systematic approach was employed to understand the preparation and in-vitro performance of respirable nanoparticle agglomerates by coupling wet milling and spray drying for ibuprofen, which is a drug with a low melting point and challenging mechanical properties. Wet milling in the presence of two stabilizers differing in their thermal properties and subsequent spray drying of the suspensions were employed after the addition of mannitol and/or leucine. The effects of the stabilizer type and the amounts of mannitol (matrix former) and leucine (dispersibility enhancer), on the yield of the process, the particle size, the redispersibility (i.e. reformation of nanoparticles upon rehydration) and the aerosolization (fine particle fraction, FPF%) of the nanoparticle agglomerates were evaluated using standard least squares model and a 23 full factorial design (3 factors at 2 levels plus four centre points). All factors investigated were found to have a significant effect on the yield of nanoparticle agglomerates (p < 0.05). The size of the nanoparticle agglomerates was mainly dependent on the leucine to drug ratio and the type of stabilizer (p < 0.05), while mannitol to drug ratio was the only significant factor affecting the redispersibility of the formulations (p < 0.05). The FPF%, determined using a fast screening impactor, was found to be dependent on both the leucine and mannitol to drug ratio (p < 0.05). This study demonstrates the successful preparation of respirable nanoparticle agglomerates of low melting point and ductile ibuprofen and the usefulness of the design of experiments as a tool to understand the impact of the formulation parameters on their fabrication and in-vitro performance.Nanocrystals are nanosized drug particles. Nanocrystals are typically produced in the form of nanosuspensions, which are submicron, colloidal dispersions of nanosized drug particles, stabilized by surfactants, polymers, or a mixture of both Solidification of the nanosuspensions has been explored to combine the advantages of liquid nanosuspensions (i.e. enhanced dissolution and solubility) with the benefits of solid formulations (i.e. stability, easier handling, enhanced patient compliance) producing nanoparticle agglomerates suitable for oral and pulmonary delivery. Spray drying is a single-step process for the conversion of a liquid feed into a dried particulate form. It is a popular process from an industrial perspective as it is more cost- and time-effective compared to freeze drying Spray drying is also a fundamental particle engineering technique for pulmonary drug delivery due to its simplicity, adaptability and scalability. Spray drying is a rapid solidification procedure and the obtained particles (at least from solution feed) are usually amorphous. Amorphicity is regarded as a disadvantage for respirable particles as it is associated with the danger of recrystallisation upon storage, which may influence adversely the stability, dissolution, absorption and aerosolization efficiency of the product Addition of generally recognised as safe (GRAS) excipients in the liquid feed before spray drying is a common strategy to manipulate the properties and thus the performance of the dry powders. Mannitol is a non-reducing sugar, which has been approved by regulatory authorities for use in inhalable pharmaceutical products Leucine is an endogenous amino acid, which exhibits aerosolization-enhancing properties Ibuprofen was selected as a poorly water-soluble model drug with a low melting point (75–78 °C) and challenging mechanical properties as it exhibits a high brittle-ductile transition point of 854 μm In this study, wet milling of ibuprofen using two different stabilizers, namely hypromellose (HPMC) and -α-tocopherol polyethylene glycol 1000 succinate (TPGS), followed by spray drying, after the addition of excipients, was assessed. Different grades of HPMCs have been found to be the most effective stabilizers in terms of particle size reduction and short-term physical stability of ibuprofen nanosuspensions Ibuprofen (IBU, Shasun Pharmaceuticals, India) with volume mean diameter D4,3: 64.5 ± 8.3 μm was used. Pharmacoat 603 (low viscosity hypromellose, HMPC 2910, Shin-Etsu Chemical Co., Japan) and -α-tocopherol polyethylene glycol 1000 succinate (TPGS, Sigma Aldrich, USA) were used as stabilizers. Mannitol (Pearlitol® 160C, Roquette Frères, Lestrem, France) and -leucine (Sigma Aldrich, USA) were used as a matrix former and a dispersibility enhancer of the nanoparticle agglomerates, respectively. Hyclone™ Water for Injections (Thermo Scientific, UK) was used for the preparation of nanosuspensions. Methanol and acetonitrile were HPLC grade and all other reagents were of analytical grade.Nanosuspensions were prepared by wet bead milling using a laboratory planetary mill (Pulverisette 5, Fritsch Co., Germany). 0.5 g IBU, the stabilizer (10% w/w of IBU) and 10 g of milling beads (0.5 mm diameter aluminium borosilicate glass grinding beads, Gerhardt, UK) were weighed into each glass vial of 14 mL capacity and suspended in 10 mL Water for Injections. The vials were placed into a stainless steel milling pot with a maximum loading capacity of 8 vials. Rotation speed (200 rpm), milling duration (6 cycles) and stabilizer concentration (10% w/w of IBU) were selected based on preliminary studies. Each milling cycle comprised 30 min rotation followed by 20 min pause. At each pause, the nanocrystal size was determined and at the end of the milling procedure, the nanosuspensions were allowed to cool to room temperature and collected by withdrawal using a pipette for separation from the milling beads.Malvern Nano ZS (Malvern Instrument, UK) was used for size measurements by dynamic light scattering (DLS) yielding the intensity-weighted mean hydrodynamic diameter of the bulk population (z-average) and the polydispersity index (PI) as a measure of the width of size distribution. 20 μL of nanosuspension was diluted with 10 mL of saturated IBU solution, prepared by filtration of a suspension through a 0.1 μm disposable syringe filter to avoid extensive dissolution and was then shaken vigorously for 30 s by hand before being transferred to disposable sizing cuvettes. The measuring parameters were: dispersant refractive index of 1.338 and viscosity of dispersion medium 0.89 cP. All measurements were performed in triplicate.The obtained nanosuspensions were solidified by spray drying immediately after preparation. 10 mL of nanosuspension were diluted to 100 mL with an aqueous solution of mannitol and/or leucine to obtain the proportions reported in . Spray drying was performed using a laboratory scale spray dryer (Mini B-290, Buchi Labortechnik, Switzerland) fitted with a high performance cyclone. On the basis of preliminary experiments, the following parameters were employed: inlet temperature of 70 °C, outlet temperature of 50 ± 2 °C, feed rate of 5 mL min− 1 and atomizing gas flow rate of 0.5 L s− 1. The collected nanoparticle agglomerates were weighed and stored in a desiccator over silica gel for subsequent testing.Yield was calculated as the ratio of the mass of the particles collected after spray drying to the mass of solids (drug and excipients) introduced in the feed suspension. The drug quantity used in the calculations was the amount weighed in the milling pots before the wet-milling step.Particle size distributions of the nanoparticle agglomerates were determined by laser diffraction using a HELOS/BR laser diffractometer (Sympatec, Germany) which was fitted with the micro-dosing unit ASPIROS and the dry disperser RODOS. Samples were placed in the feeder and pressurized air at 4 bar was used to disperse them in the measurement chamber, while the feeding velocity was kept constant at 50 mm s− 1. An R2 lens detector (0.25–87.5 μm) and the particle size distribution analysis software Windox 5 (Sympatec, Germany) were used. The D10, D50 and D90 particle sizes (i.e. the size in microns at which 10%, 50% and 90% of the particles are smaller) were recorded. Measurements were carried out in triplicate.The morphology of the starting materials and the nanoparticle agglomerates was investigated using scanning electron microscopy (SEM). Samples were placed on to double-sided electro-conductive adhesive tape, which was fixed onto an aluminium stub and then sputter-coated with gold (10 nm thickness). SEM micrographs were taken using a FEI Quanta 200 FEG ESEM (FEI, Netherlands), at 5.00 kV.X-ray powder diffraction (XRPD) was employed to assess the crystallinity of the starting materials and the nanoparticle agglomerates. XRPD patterns were obtained with a bench-top diffractometer (Rigaku Miniflex 600, Japan). Cu Kα radiation at 15 mA and 40 kV with a step of 0.02° and a speed of 5°min− 1 was used, covering a 2 θ of 5–40°. Miniflex Guidance (Rigaku, Japan) was the analysis software.Differential scanning calorimetry (DSC) was performed using a TA DSC Q200 calorimeter (TA Instruments, USA) previously calibrated with indium. Accurately weighed powder samples (1–3 mg) were sealed into crimped standard aluminium pans (TA) and heated under nitrogen flow (50 mL min− 1) from 25 °C to 30 °C above the expected melting point at a heating rate of 10 °C min− 1.Thermogravimetric analysis (TGA) was used for determining the residual moisture content of the spray-dried formulations. TGA was performed with a Discovery TGA (TA Instruments, USA) controlled by TRIOS (TA) software. Weighted powder samples (1–5 mg) were placed into aluminium cups (TA) and heated under nitrogen flow (50 mL min− 1) from 25 to 120 °C at a heating rate of 10 °C min− 1. The residual moisture content was calculated as the weight loss between 25 and 120 °C.5 mg of nanoparticle agglomerates were dissolved in 50 mL methanol, and ibuprofen concentration was assayed using an HPLC system (Agilent 1100 Series, Agilent technologies, Germany). The stationary phase was a Luna® (150 × 4.60 mm, 5 μm) column (Phenomenex Co., California, USA) kept at 30 °C. The mobile phase comprised acetonitrile and aqueous trifluoroacetic acid solution (0.1% v/v) at 50/50 volumetric ratio. The mobile phase flow rate was 1 mL min− 1, the injection volume was 10 μL and the detection wavelength 214 nm. The retention time for ibuprofen was 7.4 min. The correlation coefficient of the calibration curve was R2 |
= 0.9999 for a concentration range of 5–600 μg mL− 1, indicating acceptable linearity.Redispersibility index (RDI%) was determined according to Yue et al. where, z-average0 is the intensity-weighted mean particle diameter of the nanosuspensions prior to spray drying measured by DLS and z-average is the corresponding value of nanosuspension reconstituted from nanoparticle agglomerates upon rehydration. For the measurement of redispersibility, around 100 mg of each spray-dried powder was added to a glass vial containing 10 mL of an aqueous saturated IBU solution and it was shaken vigorously for 30 s by hand before being transferred to disposable sizing cuvettes. The saturated solution of ibuprofen was prepared by filtration of a drug suspension through a 0.1 μm disposable syringe filter in order to avoid extensive dissolution. A RDI value close to 100% indicates that the spray-dried nanoparticle agglomerates exhibit complete reconstitution after rehydration to particles of similar size as the primary nanocrystals after nanomilling and before the solidification step.The paddle method was applied by using USP apparatus type II (Pharma Test, Germany), at 37 °C and 50 rpm stirring speed. The dissolution medium was 500 mL of deionised water (freshly boiled and cooled, pH: 6–7). At specific time intervals up to 120 min, 5 mL of dissolution medium was withdrawn, filtered through a 0.1 μm disposable syringe filter and placed in HPLC vials for assay, while being immediately replaced with 5 mL of fresh medium. The HPLC conditions for the assay were as for drug content determination. Dissolution tests were conducted in triplicate for each formulation.The aerodynamic assessment of the nanoparticle agglomerates was carried out using the fast screening impactor, FSI (MSP 185 FSI, Copley Scientific, UK). The FSI was developed based on the abbreviated impactor measurement concept. It divides the particles discharged from the inhaler into two parts: the coarse fraction and the fine fraction (aerodynamic diameter < 5 μm). The coarse fraction collector was equipped with an insert that enables a cut-off of 5 μm at 30 L min− 1. The particles not captured in the coarse fine collector followed the airstream and deposited in the fine fraction collector where a filter captured all of them. The FSI was connected to a high-capacity vacuum pump (Model HCP5, Copley Instruments, UK). Based on results from preliminary studies the bottom plate of the pre-separator was coated with 1% w/v silicone oil in hexane in order to reduce particle bounce that is created from the additional 5 μm cut-off plate. The actual flow rate was measured using a calibrated flow meter (Flow Meter Model DFM 2000, Copley Instrument Ltd., UK) prior to each run, to ensure that a flow at 30 L min− 1 was achieved. Gelatin hard capsules (size 3) were filled with accurately weighed amounts of product (ranging from 12.5 to 28 mg depending on the drug loading of each formulation) corresponding to about 10 mg of IBU. The capsules were placed in the inhaler device (Cyclohaler®) fitted to the impactor via an airtight rubber adaptor and tested at 30 L min− 1 for 8 s (total volume: 4 L). The capsules were discharged into the FSI and after dispersion the particles were collected on a glass fiber filter (76 mm, Pall Corporation, USA) and extracted in methanol. Analysis of the extracts from the capsules, mouthpiece and each part of the FSI was performed with HPLC. The HPLC conditions for the assay were as for drug content determination. Each formulation was tested in triplicate. The fine particle fraction (FPF%) of the formulations was the ratio of the drug mass depositing on the fine fraction collector divided by the recovered dose. The fine particle dose (FPD) was calculated as the total mass deposited on the fine fraction collector divided by the number of doses (n = 3).A full factorial design 23 (3 factors at 2 levels) was used allowing the estimation of the main effects and the two-way interactions. The three independent variables used at two levels in the design were: type of stabilizer (X1), mannitol to drug ratio (X2) and leucine to drug ratio (X3). Dependent variables: yield, volume median diameter (D50), redispersibility index (RDI%) and fine particle fraction (FPF%), were selected as responses (). The design matrix included 8 runs plus four centre points (). Centre points were added to the design space to identify any non-linearity in the responses. The design space was constructed and analyzed using the JMP 12.1.0 software (SAS Institute, USA). To reduce systematic errors, all the experiments were completely randomized. The standard least squares model (including multiple linear regression analysis and ANOVA) was fitted in to model the data. The significance and validity of the model was estimated by ANOVA. The parameter estimates and the probability values (p-values) of the effects and two-way interactions of each response are given. p-values < 0.05 were deemed to be statistically significant.Both stabilizers were able to produce nanosuspensions of ibuprofen after 180 min of wet milling. The results of z-average size and polydispersity index (PI) of nanosuspensions obtained with both stabilizers as a function of milling time are presented in (). More specifically, after 180 min nanosuspensions stabilized with HPMC and TPGS exhibited a z-average size of 533 ± 28 nm and 663 ± 12 nm, respectively.The starting material, with a volume mean diameter D4,3: 64.5 ± 8.3 μm () initially showed rapid size reduction during milling, especially with HPMC as stabilizer. In the case of HPMC, submicron particles of ibuprofen were produced in 60 min while for TPGS this occurred in 90 min. The breakage rate of crystals was high initially and with further milling time the size continued to decrease, but at a slower rate for both stabilizers. This is a common profile as breakage rate kinetics have been found to follow a first-order exponential decay The results reported in this study can be favorably compared with those obtained by rapid expansion of supercritical solutions Comminution of ibuprofen in water using a Lena DM 100 nanoparticle production machine, equipped with a heat exchanger and operating in the recirculation mode, resulted in nanosuspensions with z-average size around 450 nm The yield was selected as a response characterizing quantitatively the overall productivity of the process. For the experimental conditions applied the yield ranged from 27.3% to 72.5% (). The generated model was significant and the response was modeled with high accuracy (adjusted R2: 0.96, All the three independent variables were identified as significant with a positive effect on the yield of the process (p < 0.05, ). The positive effect of increasing the leucine and mannitol to drug ratios may be attributed to the increased concentration of the solids dissolved in the feed suspension, prior to the spray-drying step. Spray drying of nanosuspensions stabilized with TPGS led to the lowest yield of 27.3%. This low yield may be attributed to the low melting point of TPGS resulting in melting and adhesion of the nanoparticle agglomerates to the drying chamber and cyclone. Replacing TPGS with HPMC, which is a non-thermolabile stabilizer increased the yield. The yield of the process was found to maximize by increasing the leucine to drug ratio. This may be explained by the fact that leucine accumulates on the surface of the particles forming a coating around them and thus protecting them from high temperatures during spray drying. Similar results were reported regarding the spray drying of hydro-alcoholic solutions of β-estradiol where the powder yield increased with increasing leucine content in the formulation a, b) higher yields are obtained when HPMC was used as the stabilizer of ibuprofen nanosuspensions, and when high leucine and mannitol to drug ratios were used in the formulations prior to the spray-drying step.The SEM images of the formulations prepared based on the full factorial design are shown in . Spray drying of ibuprofen nanosuspensions stabilized either by HPMC or TPGS in the absence of excipients resulted in aggregated particles of irregular morphology with size outside the acceptable range for pulmonary drug delivery (Addition of mannitol and/or leucine resulted in the promotion of spherical particles with mean size approximately 2–3 μm that is suitable for pulmonary drug delivery. The surface of the spray-dried particles appears not to be smooth and a closer inspection reveals the presence of nanoparticles indicating the composite structure of the particles where ibuprofen nanocrystals are embedded in a matrix of mannitol and/or leucine (i.e. nanoparticle agglomerates).The nanoparticle agglomerates containing leucine consist of individual particles (e.g. patterns 1 −+, 2 −+, ). This may be attributed to the accumulation of leucine at the surface of the particles preventing any particle fusion. A high leucine to drug ratio resulted in wrinkled particles (patterns 1 ++, 2 ++, ). A wrinkled morphology was interpreted as an indication of hollow particles as the particle density was found to decrease as the “wrinkleness” of the particles was increased The nanoparticle agglomerates appear to be porous with holes and dimples in the particle surface due to the evaporation of liquid that escapes from the inner of the droplet through the solid crust built up in the course of the drying process on the surface of the droplet The particle size of the nanoparticle agglomerates obtained was measured by laser diffraction as a volume diameter (). The dried powders obtained exhibited a median diameter D50 between 2.15 and 16.04 μm and the data are in good agreement with the particle size observed by SEM. The results were analyzed in the experimental design performing ANOVA for particle size, focusing on the D50 value and the model was found significant (p < 0.05, Leucine to drug ratio and the type of stabilizer used were identified as formulation variables with the most significant effects on the D50 (). Their “negative” effect is interpreted as size reduction, which is desirable for pulmonary drug delivery. The observation regarding the influence of leucine on particle size is in agreement with the study of Sou et al. A significant interaction was identified between leucine to drug ratio and the type of stabilizer, with a positive parameter estimate, despite the fact that the factors had individually negative effects on the D50 (), indicating a synergistic rather than an additive interaction between HPMC and leucine to drug ratio. Use of the non-melting HPMC as a nanosuspension stabilizer and the addition of a high leucine to drug ratio leads to further particle size reduction than the individual factors alone.As shown in the surface plot, spray drying of ibuprofen nanosuspensions stabilized with HPMC and containing a high leucine to drug ratio is able to produce nanoparticle agglomerates with particle size around 2–3 μm that is suitable for pulmonary drug delivery (). On the other hand, spray drying of ibuprofen nanosuspensions stabilized with TPGS results in larger particles, while addition of both high leucine and mannitol to drug ratios was required in order to produce particles smaller than 4 μm (d). This indicates that the selection of stabilizer is vital not only for the step of nanosuspension production, but it may also influence the downstream process of spray drying by affecting the properties of the nanoparticle agglomerates produced.Redispersibility is an important quality attribute of nanoparticle agglomerates as it is a prerequisite for the reformation of nanoparticles upon rehydration of the larger particles with potential enhancement of therapeutic efficacy. Particularly, for nanoparticles of low melting drugs such as ibuprofen, thermal stresses during spray drying may lead to phase and composition changes of formulations causing irreversible aggregation and loss of the advantages of nanoformulations ). The redispersibility results were analyzed in the experimental design performing ANOVA for particle size focusing on the RDI% value and the model was found significant (p < 0.05, The mannitol to drug ratio was identified as the only significant factor affecting redispersibility (p < 0.05, ) with higher mannitol to drug ratio leading to RDI% values closer to 100%. The role of mannitol as a redispersibility enhancer can be explained by the formation of a continuous matrix around the nanocrystals during the spray-drying step, preventing their irreversible aggregation. Upon rehydration, mannitol as a hydrophilic excipient dissolves and the nanosuspensions are reconstituted.), nanoparticle agglomerates of ibuprofen with enhanced redispersibility (RDI% value close to 100%) were obtained only when high mannitol to drug ratios are present in the formulations prior to the spray-drying step.The results of assayed ibuprofen content in the nanoparticle agglomerates are given in . Spray drying of nanosuspensions without mannitol and/or leucine appeared to have lower drug loading than the nominal. This may be attributed to the melting of TPGS during spray drying that led to drug loss due to deposition on the walls of the drying chamber and cyclone. For the spray-dried nanosuspensions containing mannitol and/or -leucine the assayed ibuprofen content is close to the nominal content indicating that the addition of these excipients prevented ibuprofen loss or powder segregation during the production process.The XRPD patterns of the starting materials are shown in . Raw ibuprofen exhibited sharp peaks in the range of 2 theta: 15–25° that are characteristic of the drug -leucine indicated a highly crystalline structure (2 theta: 6°, 12°, 24°, 31°, 37°) The diffractograms of all runs prepared according to the DoE are shown in b. The diffractograms of patterns 1 −− and 2 −− (without matrix former and dispersibility enhancer) showed peaks at similar 2 theta positions to those of the raw ibuprofen. For the nanoparticle agglomerates of ibuprofen containing mannitol and/or leucine, the diffractograms were a summation of the patterns of their components. No new peaks or halo could be detected in the XRPD patterns indicating the absence of generated amorphous content during the process.The DSC was used to assess the thermal behaviour of the starting materials and nanoparticle agglomerates of ibuprofen (). The DSC thermogram of ibuprofen showed an endothermic peak at 76 °C corresponding to the melting of the drug. The nanoparticle agglomerates of ibuprofen without mannitol and leucine exhibited the same endothermic peak shifted to a slightly lower temperature (a), while those containing mannitol exhibited thermal behaviour depending on the stabilizer.More specifically, the nanoparticle agglomerates of ibuprofen containing mannitol and stabilized with TPGS exhibited two endothermic peaks (patterns 2 ++, 2 +−, b) as expected: the melting peak at around 70 °C, which relates to the melting of the drug and a sharp endothermic peak at 168 °C which relates to the melting of mannitol (Pearlitol: 160 °C). For the nanoparticle agglomerates of ibuprofen containing mannitol and stabilized with HPMC, apart from the melting of ibuprofen, an endothermic peak at 150 °C was followed by an exothermic event and then an endothermic melting at 168 °C (patterns 1 ++, 1 +−, b). The thermal events observed in the DSC of patterns 1 ++ and 1 +− could be attributed to the formation of the metastable δ-form of mannitol (m.p. 150–158 °C) that is followed by crystallization to the α- or/and β-form, and the melting of the respective crystal form Overall, the XRPD and DSC data suggest that the engineered nanoparticle agglomerates retain their crystallinity during wet bead milling followed by spray drying. The preservation of the crystalline state is advantageous, ensuring the long-term physical stability of the formulations during storage.Thermogravimetric analysis of the spray-dried powders indicated that the moisture content of the powders ranged from 1.1 to 4.7% w/w (). These values compare favorably with other studies which report moisture content of spray-dried powders in the region of 5–10% w/w ). This is in agreement with the results reported by Yamasaki et al. The dissolution profiles of ibuprofen and the nanoparticle agglomerates prepared according to the matrix of the full factorial design are shown in . Nanoparticle agglomerates stabilized with either HPMC or TPGS exhibited enhanced dissolution profiles compared to ibuprofen. In the case of the raw ibuprofen, < 40% was released in the first 20 min, while the nanoparticle agglomerates achieved complete dissolution in < 5 min. The exceptions to this were the spray-dried nanosuspensions of ibuprofen without matrix former (patterns 1 −− and 2 −−) which exhibited a higher dissolution rate compared to ibuprofen but slower than the nanoparticle agglomerates containing mannitol and/or leucine. In the case of TPGS, this may be associated with the formation of large aggregates with size around 50 μm and poor redispersibility (). Thus, the selection of suitable process and formulation parameters is of paramount importance in order to ensure that the dissolution benefit of nanoparticles is retained after spray drying.Fine particle fraction (FPF) was selected as a quality attribute describing the aerodynamic performance of a dry powder for inhalation. The European Pharmacopoeia (2.9.18 preparations for inhalation: aerodynamic assessment of fine particles, Ph. Eur. 8.0) suggest that a pressure drop over the inhaler of 4 kPa is broadly representative of the pressure drop generated by the patients using dry powder inhalers during inhalation ) and the model generated was found to be significant (p < 0.05, Leucine to drug ratio and mannitol to drug ratio were identified as the most significant factors on the FPF (.). The positive effect of leucine can be linked with its properties as a dispersibility and aerosolization enhancer. In contrast to other amino acids such as alanine and glycine, leucine has been found to reduce capsule retention and increase both the emitted and the fine particle fraction of formulations Regarding the positive effect of mannitol to drug ratio, it may be attributed to the good spray-drying properties of mannitol which facilitates the formation of spherical particles with narrow and unimodal particle size distribution c, d), both leucine and mannitol to drug ratio have a significant effect on the aerodynamic performance of the nanoparticle agglomerates, resulting in a large FPF increase from 10% to over 65%. Therefore, a combination of high leucine and mannitol to drug ratios is required in order to maximize the FPF of the nanoparticle agglomerates of the low melting and ductile ibuprofen.Nanosuspensions of the poorly water-soluble, low melting point and ductile drug ibuprofen stabilized with HPMC and TPGS were successfully produced and were further spray dried with or without the addition of excipients (mannitol and/or -leucine) employing a full factorial design. Design of experiments is a useful approach in order to gain insight into the formation of inhalable nanoparticle agglomerates using wet milling followed by spray drying. Leucine to drug ratio, mannitol to drug ratio and the type of stabilizer were found to be significant (p < 0.05) factors affecting the yield of the particles obtained by combining wet milling and spray drying. The particle size response was mainly dependent on the leucine to drug ratio and the type of stabilizer employed (p < 0.05). Mannitol to drug ratio was found to be the only critical parameter affecting redispersibility of nanoparticle agglomerates (p < 0.05), and both leucine to drug ratio and mannitol to drug ratio were found to be significant factors affecting FPF (p < 0.05). While the importance of the type of stabilizer on the formation of nanosuspensions has been previously reported Maria Malamatari, MPharm, PhD is Research Associate in the University of Greenwich. She obtained her undergraduate degree from the Aristotle University of Thessaloniki (MPharm, 2012). During this time, she undertook her pre-registration training at General Hospital Patision in Athens and an Erasmus placement at UCL School of Pharmacy on the dissolution of poorly water-soluble drugs. From 2012 to 2016, she carried out her PhD in the Centre for Doctoral Training in Targeted Therapeutics and Formulation Sciences at UCL. Dr. Malamatari's research interests include particle engineering for pulmonary drug delivery, nanoparticle-based formulations and solid state properties of pharmaceutical materials.Satyanarayana Somavarapu, MPharm, PhD is Lecturer in Pharmaceutics in UCL School of Pharmacy where he has a large research group. Dr. Somavarapu's main research interests are related to the mucosal delivery of vaccines, pulmonary delivery of siRNA and chemotherapeutic agents using nanotechnology, ocular delivery of novel therapeutic molecules and nanotechnology for the delivery of phytochemicals. He has over seventy publications, including twenty journal articles, over fifty peer-reviewed abstracts and several international conference presentations. He also has six patents on vaccine formulations.Kyriakos Kachrimanis, MPharm, PhD is Associate Professor of Pharmaceutics in the Aristotle University of Thessaloniki where he is currently the Head of the Department of Pharmaceutical Technology. Dr. Kachrimanis' expertise includes the following fields: solid state properties of pharmaceuticals, modeling and simulation of pharmaceutical materials and processes, mechanical properties of powders and compacts, “in line” monitoring of pharmaceutical formulation processes by analytical techniques, application of multivariate statistics and machine learning methods and particle engineering for pulmonary drug delivery. He has published over forty scientific articles in peer-reviewed journals and several international conference presentations.Graham Buckton, BPharm, AKC, PhD, DSc, FRSC, FRPharmS, FAPS is Emeritus Professor of Pharmaceutics in UCL School of Pharmacy. Prof. Buckton has research interest in the amorphous state, powder processing, surface science, solid and inhalation drug delivery. He served a 10-year term as Editor of the International Journal of Pharmaceutics. He is a member of the Chemistry, Pharmacy and Standards sub-committee of the Commission on Human Medicines. He was the 2003 British Pharmaceutical Conference Science Chairman. Until September 2012 he was CEO of Pharmaterials Ltd., which is the contract research company that he founded in 2000. In 2012 he founded Buckton Consulting.Kevin MG Taylor, BPharm, PhD, FRPharmS is Professor of Clinical Pharmaceutics in UCL School of Pharmacy. Prof. Taylor has more than 25 years' experience in research in the areas of formulation science, medicines manufacture and drug delivery. Prof. Taylor sits on the UK's Commission on Human Medicines (CHM) and is Chair of the Chemistry, Pharmacy and Standards Expert Advisory Group of CHM. He is Chair of the British Pharmacopoeia Commission (BPC) and is a member of the UK Delegation to the European Pharmacopoeia Commission and the Inhalanda Working Party of the European Pharmacopoeia.Strain hardening of cold-rolled lean-alloyed metastable ferritic-austenitic stainless steelsMechanical properties and strain hardening of two pilot-scale lean-alloyed ferritic-austenitic stainless steels having metastable austenite phase, present at 0.50 and 0.30 volume fractions, have been studied by means of tensile testing and nanoindentation. These ferritic-austenitic stainless steels have high strain-hardening capacity, due to the metastable austenite phase, which leads to an improved uniform elongation and higher tensile strength in comparison with most commercial lean duplex stainless steels. According to the results, even as low as 0.30 volume fraction of austenite seems efficient for achieving nearly 40% elongation. The austenite phase is initially the harder phase, and exhibits more strain hardening than the ferrite phase. The rate of strain hardening and the evolution of the martensite phase were found to depend on the loading direction: both are higher when strained in the rolling direction as compared to the transverse direction. Based on the mechanical testing, characterization of the microstructure by optical/electron microscopy, magnetic balance measurements and EBSD texture analysis, this anisotropy in mechanical properties of the cold-rolled metastable ferritic-austenitic stainless steels can be explained by the elongated dual-phase microstructure, fiber reinforcement effect of the harder austenite phase and the presence and interplay of rolling textures in the two phases.In recent years ferritic-austenitic duplex stainless steels have been used in a large number of industrial applications, such as oil and chemical storage tanks, heat exchangers, marine transport vehicles, etc. Duplex stainless steels possess an excellent combination of mechanical properties, e.g. high yield strength, and corrosion resistance. There is potential for improved ductility, if the austenite phase has sufficiently low alloy content to be metastable. Lean metastable ferritic-austenitic stainless steels, with lower alloying additions in comparison to conventional duplex grades, are very potential materials to be used in construction and many industrial applications due to their competitive price and improved formability.Transformation induced plasticity (TRIP) is a distinctive property of metastable austenitic steels, giving them an excellent combination of strength and ductility due to an increase in plasticity during a phase change. The formation of strain-induced martensite increases work hardening of the material and leads to higher values of ultimate tensile strength and uniform elongation. TRIP effect can also be induced in ferritic-austenitic steels if the austenite phase is designed correctly. However, it is more complex to design the austenite stability of duplex steels since the composition of the austenite phase depends on both the steel chemistry and the thermal history, which affect the partitioning of alloying elements between the two phases. Furthermore, the phase morphology and size influence the transformation behavior.Mechanical behavior of duplex stainless steels is influenced by microstructural features such as volume fraction, morphology and spatial distribution of the constituent phases, and also by the deformation mode of the phases. Stress and strain are not uniformly distributed, and the actual load sharing between the phases is dependent on the property mismatch and microstructural features. Plastic deformation of the body-centered cubic, high stacking fault energy ferrite is mainly dominated by dislocation glide due to numerous slip systems In a cold-rolled two-phase material, like duplex stainless steel, each phase will have a different response to an applied strain. Plastic deformation is influenced by inhomogeneous deformation within the phases, because of the complex morphology, i.e. heavily banded microstructure, and variation of stress within the phases. The phase boundaries, laying mostly parallel to the rolling direction (RD), are strong barriers to dislocation motion in the two-phase structure. Cold-rolled duplex stainless steels exhibit a strong anisotropy due to their two-phase structure. During industrial rolling process, not only the morphology of the microstructure changes from coarse-grained isotropic in the cast slab to fine-grained anisotropic in the coil, with both phases elongated in the rolling direction, but also clear and intense crystallographic rolling textures develop, especially in the ferrite phase Mechanical properties of ferritic-austenitic stainless steels can be modified by designing the austenite phase to be metastable In this study the mechanical properties and strain hardening of two pilot-scale ferritic-austenitic stainless steels are investigated. The experimental alloys were designed to be lean alloyed and have a metastable austenite phase in order to exploit the beneficial TRIP effect. The studied alloys have different austenite volume fractions, 0.50 and 0.30, in order to see whether a lower austenite fraction is adequate for achieving improved mechanical properties. This is unlike in former published studies on metastable lean duplex stainless steels, e.g. The studied ferritic-austenitic stainless steels were prepared as 65 kg laboratory cast ingots (named F50 and F70). The 48 mm thick ingots were reheated at 1265 °C for 60 min and conventionally hot rolled to a thickness of 3.5 mm. Subsequently, the hot bands were cold rolled to a 1.5 mm thickness and annealing was carried out at 1050 °C for 5 min followed by water quenching. The studied ferritic-austenitic stainless steels were alloyed with low levels of nickel, which was partly replaced by manganese and nitrogen. The austenite phase in the studied stainless steels is designed to be metastable, in order to utilize the TRIP effect for improved combination of strength and elongation. The chemical composition of the test materials is presented in . For comparison, a commercial lean duplex stainless steel LDX 2101 was studied. Its chemical composition is also presented in . It was a cold-rolled and annealed product of 1.5 mm thickness and 2B surface finish.The microstructure of the test materials was studied by optical microscopy with Nikon Epiphot 200 microscope. The specimens were ground up to 2500 grit with SiC abrasive papers and then electro-polished with A2 electrolyte at 35 V for 20–25 s. A modified Beraha etchant (1.0 g K2S2O5, 15 ml HCl and 85 ml H2O The content of the ferrite phase in the initial state and the transformed α′-martensite in the deformed specimens was measured with a Satmagan equipment. Satmagan is a magnetic balance measurement that is used to determine the content of the ferromagnetic phase in a specimen (size 6×15 mm). In a Satmagan measurement a saturating magnetic field is applied to the specimen that is placed in a sample holder. The magnetic field causes a force that is recorded by adjusting a potentiometer. The relation between the potentiometer reading S and the total content of the ferromagnetic phases is expressed as where K is a constant, Cfm is the content of the ferromagnetic phases, Msat is the saturation magnetisation of the ferromagnetic phase and ρ is density. The value of constant K is determined by empirical calibration. In this investigation the calibration constant determined by Rintamaa The volume fractions of the ferrite and austenite phases were also measured by optical image analysis using Image-J software. The volume fractions were determined in threshold mode from 10 optical micrographs taken from different locations in the material microstructure and a mean value was calculated.Uniaxial tensile testing was performed with a MTS 810 servo-hydraulic material testing system and a MTS 632.12C-20 extensometer at ambient temperature. According to standard SFS-EN ISO 6892-1, the initial stain rate was 1.1 mm/min until 1.5% strain, after which the strain rate was increased to 30.2 mm/min.Nanoindentation experiments were performed using a CSM instrumented indentation tester. A three-sided pyramidal Berkovich diamond indenter tip with nominal angle of 65.3° was employed. Analyses for the calculation of hardness were conducted by the method used by Oliver and Pharr ) under the optical microscope, the representative indentations of each phase were selected. Indentations located close to grain or phase boundaries were ignored, as well as unsuccessful indentations with anomalies in the shape of the load-displacement curve or indentations located too close to neighboring indentations.Electron backscattering diffraction (EBSD) measurements of the crystallographic texture and grain sizes of the phases were done with Zeiss Ultra 55 field emission gun scanning electron microscope (FEG-SEM) equipped with an Oxford Nordlys F+ EBSD system. The EBSD data acquisition and analysis were performed using the HKL Channel 5 software from Oxford Instruments.The volume fractions of ferrite and austenite phases in the studied materials, determined with the Satmagan equipment and with optical image analysis, are presented in . The stainless steels F50 and LDX 2101 consist of almost equal volume fractions of ferrite and austenite, whereas the stainless steel F70 consists of about 70% ferrite and 30% austenite. The results attained with the two methods are comparable.Optical micrographs of the test materials, taken from a cross-section of rolling vs. normal direction of the cold-rolled sheets, are presented in (a)-(c). The Beraha etchant colored the ferrite phase darker and left the austenite phase lighter. It can be seen that the distribution of the two phases and mean lamellar spacing in the elongated rolling microstructure differ markedly between the three materials. In (d) a SEM backscattering electron image revealing grain and phase boundaries is presented for the stainless steel F70. The grain size of ferrite is markedly larger than that of austenite.The measured true stress-true strain curves for the test materials, tested in uniaxial tensile loading along the rolling direction and the transverse direction, are presented in . The step in the curves is due to the change of strain rate after 1.5% strain. A distinct increase in the slope is seen in the curves of F50 and F70 after about 0.13 true strain, which is an indication of increased strain hardening. Tensile properties of the studied materials, together with the mean lamellar spacing, are presented in . Yield strength of the two-phase stainless steels is higher than the typical values of austenitic and ferritic single-phase stainless steels (~300–400 MPa). The commercial LDX 2101 has the highest yield strength and stainless steel F70 the lowest. The ultimate tensile strength is highest in stainless steel F50, having about 50% volume fraction of metastable austenite. The uniform elongation and elongation to fracture are markedly higher in stainless steels F50 and F70 in comparison to LDX 2101.The strain hardening rate, i.e. the first derivative of the true stress-true strain curve, dσ/dε, of the stainless steels F50 and F70 as a function of true strain is presented in (a)-(b). Strain hardening rates exhibit very high values in the beginning of deformation. After that the strain hardening rates decrease rapidly up to strains of about 0.08–0.1. This initial steep drop has been suggested to be a result of the onset of formation of α′-martensite accommodating some strain Evolution of the strain-induced α′-martensite content as a function of tensile strain was examined by Satmagan measurements and optical microscopy. The total content of ferromagnetic phases, i.e. ferrite and α′-martensite, present in the material at different strain levels, determined with Satmagan, is presented in (a). The volume fraction of ferrite phase remains constant, so the difference between the Satmagan reading at the initial stage and after straining represents the fraction of α′-martensite. The α′-martensite volume fraction at the maximum strain before break of the tensile specimens was higher when loaded in the rolling direction. For stainless steel F50 these volume fractions were 0.35 in the rolling direction and 0.30 in the transverse direction, and for stainless steel F70 0.20 and 0.14, respectively. The volume fraction of the austenite transformed to α′-martensite as a function of tensile strain is presented in Microstructures of stainless steels F50 and F70 after 15% tensile strain in transverse to rolling direction are shown in . The volume fraction of strain-induced α′-martensite is 0.14 in stainless steel F50 and 0.05 in F70.), in both test materials F50 and F70 the austenite is the stronger phase. This may be because of the nitrogen content and the smaller grain size of that phase in comparison to ferrite. The initial indentation hardness of the austenite phase is 5.0 (±0.4) GPa in F50 and 5.2 (±0.5) GPa in F70 with no tensile strain. The initial indentation hardness of the ferrite phase is 4.5 (±0.9) GPa in F50 and 3.9 (±0.5) GPa in F70.As a response to tensile straining, the hardness of the austenite phase increases due to increasing number of dislocations. Austenite accumulates more deformation than ferrite Inverse pole figure maps for fcc austenite phase and bcc ferrite phase of F50 and F70 are presented in . The orientation distribution of the grains is more random in austenite, whereas ferrite seems to have a stronger texture in both materials. The pole figures for the fcc and bcc phases of F50 and F70 are presented in . The z0 axis corresponds to normal direction (ND) and y0 axis to transverse direction (TD). The texture of ferrite is characterized as typical rolling texture with the major texture component being the rotated cube texture component {001}<110> and also α-fiber orientations, i.e. <110> parallel to the rolling direction The volume fractions of austenite and ferrite in the studied materials, determined with a magnetic method and optical analysis were comparable. However, the estimation of the phase fractions from optical micrographs can be affected by the prior etching procedure. The Beraha etchant used here selectively attacks the ferrite phase. For steels F50 and LDX 2101 the ferrite volume fraction based on the optical analysis seems somewhat overestimated in comparison to the magnetic method. The spatial distribution of the two phases and mean lamellar spacing in the elongated rolling microstructure differ markedly between the studied three materials. The mean lamellar spacing () and ferrite grain size is the largest in stainless steel F70 with the lowest austenite content. The presence of the austenite phase in higher volume fractions in F50 and LDX 2101 restricts the grain growth of the ferrite phase, which has faster recrystallization and recovery kinetics Yield strength of the studied two-phase stainless steels () is higher, from 426 to 612 MPa, than the typical values of austenitic and ferritic single-phase stainless steels (~300–400 MPa). The commercial LDX 2101 has the highest yield strength, possibly due to the high level of alloying elements and finer microstructure, i.e. the smallest mean lamellar spacing. A high volume fraction of phase boundaries increases the yield strength in duplex materials The ferritic-austenitic stainless steels F50 and F70 with metastable austenite have notably better mechanical properties when strained in the rolling direction than in the transverse direction. The rate of strain hardening () is higher when the material is tested in the rolling direction. Strain hardening also continues to higher strain levels in RD direction than in TD direction. According to Satmagan magnetic balance measurements, the maximum volume fraction of α′-martensite in the tensile specimens was higher when loaded in the rolling direction. For stainless steel F50 these volume fractions were 0.35 in the rolling direction and 0.30 in the transverse direction, and for stainless steel F70 0.20 and 0.14, respectively. More strain partitioning in austenite occurs in the stainless steel F50 having higher initial austenite volume fraction than F70, resulting in a higher strain-induced α′-martensite content. However, considering the initially lower volume fraction of austenite in F70, it is more reasonable to compare the volume fraction of the austenite transformed to α′-martensite as a function of tensile strain (b). For stainless steel F50 these volume fractions were 0.66 in the rolling direction and 0.55 in the transverse direction, and for stainless steel F70 0.63 and 0.45, respectively. The direction dependence of the martensite transformation is stronger in F70.There is some austenite still remaining in the microstructure of stainless steels F50 and F70 at the maximum strain levels. For optimal strain hardening behavior of the material, a gradual and nearly complete transformation of austenite to martensite is desired Austenite grain size may have an effect on strain-induced martensite transformation, but the results reported have been somewhat conflicting. According to some results, austenite stability increases with a decrease in grain size ), in both test materials F50 and F70 the austenite is the stronger phase. The relative hardness and yield strength of the constituent phases in duplex stainless steels depend largely on the nitrogen content of austenite: at less than 0.12 wt pct bulk nitrogen the ferrite is harder than the austenite and at higher than 0.12 wt pct bulk nitrogen the austenite is the harder phase The presence of residual stresses in the material can influence the results of nanoindentation measurements: indentation hardness increases if compressive stress is present and decreases in the presence of tensile stress. Thermal residual stresses in duplex stainless steels, caused by the difference in thermal expansion coefficients of the phases, are tensile in austenite and compressive in ferrite According to EBSD texture analysis, ferrite phase has a stronger texture in both F70 and F50. More strongly developed rolling texture of the ferrite phase in duplex stainless steels, in comparison to that of austenite, is widely reported Tensile properties and strain hardening of two pilot-scale lean-alloyed ferritic-austenitic stainless steels having metastable austenite phase, present at 0.50 and 0.30 volume fractions, were studied. Even a 0.30 volume fraction of austenite was efficient for achieving good elongation, close to 40%, due to the TRIP effect. According to the nanoindentation results, the austenite phase was initially the harder phase, and it experienced higher strain hardening than the ferrite phase. The intensity of the TRIP behavior was affected by the austenite volume fraction, i.e. a higher volume fraction of α′-martensite and more intense strain hardening was produced in the steel with higher austenite content. Both experimental stainless steels had almost as good elongation, regardless of their different volume fraction of the austenite phase, but ultimate tensile strength increased with the austenite volume fraction.The rate of strain hardening during tensile testing and the evolution of the α′-martensite phase, analyzed with magnetic Satmagan measurements, was found to be dependent on the loading direction: both were higher when strained in the rolling direction. This anisotropy in mechanical properties of the cold-rolled metastable ferritic-austenitic stainless steels, not reported in the former published studies, can be concluded to arise from the elongated dual-phase microstructure, fiber reinforcement effect of the harder austenite phase and the presence and interplay of rolling textures in the two phases.Evaluation of residual stress and adhesion of Ti and TiN PVD films by laser spallation techniqueThe laser spallation technique was applied for measurement of residual stress and adhesion of thin films. Two films of different properties, ductile and soft Ti, and hard and brittle TiN, were studied. The films were produced on 304 steel substrate by PVD method. The residual stress value obtained by laser spallation technique LST were compared with stress value from X-ray diffraction method. Good agreement of stress values measured by both methods was attained. Additionally, the interface strength of the films was tested by laser adhesion spallation technique LASAT with use of VISAR system. It was shown that shock wave induced by a nanosecond laser pulse adequately determines properties of PVD thin films on metal substrate.The shock waves create many unique possibilities in materials engineering although evaluation of properties of materials and layers undergoing high speed deformation is a serious experimental issue In 60-ties the high-energy laser pulse was applied as pressure load The use of short laser pulses in order to generate high-pressure shock waves create many unique possibilities in materials testing. Contrary to collision systems, wider range of pressures, speed and deformation settings may be achieved as a result of changing a shape and time duration of the laser pulse. On the basis of the laser shock waves the new diagnostic methods of dynamic behaviour of material and layer Thin films are an important component of many microelectronic, optical and micromechanical systems as well as cutting tool coatings. During their manufacture a large amount of a residual stress is induced, that has significant influence on their mechanical properties and overall efficiency. In certain conditions, the residual stress may cause layer delamination from substrate or its cracking. The most well-known practical techniques of measuring the adhesion of thin layers are scratch, peel, pull, blister or indentation test. Laser Spallation Technique LST was first introduced by Vossen In the 1990s, attempts to use the pressure wave generated by a laser pulse for testing the adhesion of thin layers, obtained by PVD and CVD methods, were made. Tensile stress at the interface of the material/layer phases, which caused separation of the layer from the surface, have been studied Based on laser spallation technique new method of residual stress measurement was proposed by Ikeda at el. The paper presents experimental results of residual stress measuring by a laser spallation technique. The technological thin films TiN and Ti, produced by PVD method on steel substrate, were studied. The residual stress value determined by the laser spallation technique were compared with stress value obtained by X-ray diffraction methods. The adhesion strength was also determined by LASAT method with use VISAR system. It was shown that shock wave induced by nanoseconds laser pulse can be suitable tool for determination of properties of technological thin films.The study of residual stress and adhesion of PVD thin films by laser spallation technique was carried out for typical commercial metals and thin films. As a substrate a stainless steel, EN X5CrNi18-10 1.4301 (304), was used. Two kinds of commercial thin films, TiN and Ti, deposited by PVD method in Surftech manufacture afterwards cleaning in alcohol and acetone activated by ultrasound, finally in vapor of tetra-chloroethyl.The PVD process consists of the following steps: vacuum generation, heating up to 450 K, ion etching, coating deposition and cooling.Nd:YAG Quantel YG 981E laser with a wavelength of 1.064 µm and pulse duration of 10 ns was applied for testing. The beam diameter was 2 mm. A diagram of the measurement system is shown in . The laser pulse (1) is directed through a glass (2) to the absorption layer (3) causing its evaporation and plasma generation. A pressure wave (4) is formed as a result of rapid expansion of a plasma plume and propagates into material (5). Graphite 5 µm thick was used as the absorption layer, while glass 1 mm thick was the inertial layer. At very short, nanosecond laser pulses, and a suitably selected type and thickness of the absorption layer, the thermal effects associated with the interaction between the beam and material are negligible Different pulse energy levels and thicknesses of substrate were applied to obtain proper conditions for delamination of technological layers. The values of pulse energy were: 0.5, 0.7, 1.0 and 1.25 J while substrate thickness had three values: 1, 0.8 and 0.5 mm. shows test parameters and presence of films delamination.In order to determine a strength of the interface a surface velocity was measured by a VISAR system. The studies were conducted at pulse energy 1.2 J for both films. Three thickness values of the steel substrate were applied. The parameters applied in the LASAT are denoted by the “∗” mark in The VISAR (Velocity Interferometer System for Any Reflector) determines the velocity of moving surface by measuring the Doppler shift of laser light reflected from the surface. It is sensitive to wavelength; therefore, it transforms changes in the wavelength to changes in the intensity of four output signals. Afterwards these intensities are converted by fast photodiodes to electrical signals recorded by an oscilloscope. Velocities can be determined in the range from m/s up to km/s and with sub-nanosecond time resolution with accuracy ±1%. The observed surface does not need to be mirror polished. Changes in its reflectivity or in the background light have no effect on derivation of velocity.The properties of the films were controlled before testing in order to confirm the producer declaration. The following properties were measured: roughness, thickness and hardness. A surface geometrical structure of the films was studied on scanning profilometer. The roughness parameters Ra, Rz were determined according to ISO 4287:1997. For selected samples the metallographic cross-sections were made perpendicularly to the surface and thickness of the films was measured on a Scanning Electron Microscope SEM. A microhardness test of the films was carried out using the Vickers method at a load of 0.2 N (20 gf). The hardness values of the films were determined based on knowledge of thickness of the films and hardness of the substrate according the method After delamination of the films by laser pulse the surface deformations were measured on a laser confocal microscope Keyence VK-X100. The diameter, d, and height, h, of the protuberance were determined based on a VK Analyzer program. The 3D views, maps and profiles of surface were generated. The height and diameter of protuberances were determined on profiles passing through the highest point of bulged area.To verify correctness of the stress measurement by the LST method the residual stress in the films were determined also by X-ray diffraction method (XRD). The studies were carried out on diffractometer Rigaku SmartLab 3 kW with use of the Cu tube and Kα radiations. The stress was calculated based on sin2ψ method.Surface topography of the steel plate before deposition process was studied. The roughness of polished steel plate prior to the deposition was Ra = 0.018 µm, Rz = 0.096 µm. After the deposition roughness increased for both tested films. The parameters were Ra = 0.39 µm, Rz = 3.14 µm for Ti film, while for TiN: Ra = 0.26 µm, Rz = 2.91 µm The main reason of high roughness is a presence of particles, visible in a shows the 3D view after Ti film deposition, whereas b presents the representative surface profile.The thickness of the films was examined on the profilometer by step method and additionally using SEM on samples for which metallographic cross section were made. It was stated that thickness of the Ti film was 3.4 ± 0.6 µm whereas 1.8 ± 0.3 µm for the TiN film. a shows the cross section of stainless steel sample with the Ti film while b presents surface of the film. Due to relatively high roughness the film thickness is not uniform.The microhardness measurement were conducted on film surface, based on knowledge of films thickness and hardness of stainless steel substrate 220 HV. Hardness of the Ti film was estimated as 640 HV and 2500 HV for the TiN films. The measured values of hardness correspond to hardness given by the manufacturer The surfaces of thin films processed by shock wave were examined on scanning profilometer. The presence of delamination was verified. Delamination of the films was observed for laser pulse energy 0.7 J and higher, and substrate thickness 0.8 mm and 0.5 mm (). For lower pulse energy and thicker substrate the shock wave was too weak to cause film delamination. shows the 3D view of surface and profile of the Ti film after film debonding caused by the shock wave at energy level 0.7 J.Small protuberance is visible on the 3D view; its altitude is comparable with the height of surface roughness peak. The profile (b) shows that delamination of the film occurred and its maximum height is 1.4 µm. At higher pulse energy the protuberances were larger, the maximum height was 13.2 µm, diameter was 2.72 mm for laser pulse energy 1 J and substrate thickness 0.5 mm. shows the map and the profile of surface after film debonding at the highest pulse energy 1.25 J.The process was repeated 3 times for each level of energy. The heights were in the range 1–13 µm, that is small when compared to diameter 2–3 mm of protuberance. For small film thickness and ratio of height to diameter of protuberance the value of residual stress can be calculated from a dimension according to relation where p - atmospheric pressure, t - thickness of film; r, h – radius and height of protuberance, respectively.Residual stress can be released by elastic deformations of the protuberance. The value of released stress can be estimated assuming the plane state of stress from Eq. where E – Young’s modulus ν – Poisson’s ratio of the film and l - diameter of protuberance, l′- total length of protuberance. In case of Ti film the parameters are: E = 110 GPa, ν=0.36Size of the protuberances was different for the same energy level but calculated value of the residual stress was very close. shows the dimensions of the protuberances and the calculated value of the residual stress for the Ti film. During the shape analysis of protuberance the problems occurred in exact determination of a radius due to absence of sharp boundary between delaminated and not delaminated parts of the film as well as relatively high surface roughness. This is probably the main reason of differences in the values of determined residual stress. Another reason is heterogeneity of the film thickness that varies from 2.8 to 4 μm. The thickness of the film affects residual stress thus the value can vary in different areas of the film. The mean value of compressive residual stress determined according to formula 1, for mean value, 3.4 µm, of film thickness was 1.01 ± 0.64 GPa. shows the map and photograph of a defect on film protuberance.Cracking was not observed, only a small collapse with irregular shape was detected. Localized instabilities were observed by Jin et al. The recorded diffraction patterns for the Ti thin film is shown in . The film was polycrystalline exhibiting reflections related to hexagonal structure. The diffraction patterns indicated strong texture. A preferred orientation was a crystallographic plane 100 parallel to the surface. The residual stress was determined by sin2ψ method, the analysis was performed based on 300 reflection. For calculations the following data was assumed: Young’s modulus E = 110 GPa, Poisson’s ratio ν = 0.36 shows the recorded XRD patterns for TiN film on steel substrate. The TiN film was polycrystalline and the reflections indicate a cubic structure. A strong texture was stated. Almost all crystallites have preferential direction and they are orientated according to 111 crystallographic plane that is parallel to surface. Such anisotropy of microstructure of film limits the ability to perform measurements and calculations of stress because it gives large error, especially for the TiN layer. Nevertheless, an attempt was made and for calculating the following data: E = 250 GPa, ν = 0.20 were assumed. Value of the residual stress was calculated based on reflection 222. Compressive residual stress was estimated: σ = −7.2 GPa, Δσ ±1.7 GPa. Due to strong texture the value is approximate.Both applied methods, LSP and XRD, give similar values of residual stress. The value of stress for the Ti film obtained by LST, is several times smaller than for the TiN film. A difference in the stress value is similar to that obtained by the XRD method.The adhesion of the films to the substrate was determined based on measurement of film velocity during delamination. a shows typical recorded signals from VISAR system made by shock waves. The signals were measured on back surface of steel samples, then the velocity profile were estimated based on them ( the signals from VISAR system for samples covered by TiN films are visible. The surface speed is lower and strong attenuation of wave pressure can be observed. This effect is caused by differences in acoustic impedance of substrate and films.a shows the signals from VISAR system for samples 0.7 mm thick covered by the Ti film for which delamination was observed, while the calculated velocity profile is shown in the data for non-delaminated film are presented.The shock wave that reaches the interface is divided into two waves: a reflected wave and a transmitted one. In case of weak shock waves (when shock stress is much lower than Young’s modulus of material) linear approximation may be used P – relative amplitude of the wave transmitted from medium 1 to medium 2;R – relative amplitude of the wave reflected from material boundaries.In case of the Ti film on steel substrate the ratio of acoustic impedances is 4.5 (for steel 47 (g/cm3·km/s). Relative amplitude of the wave reflected from material boundaries is R = 0.43 while the relative amplitude of wave transmitted from steel to film is R = 0.57. For the TiN film we obtained A = 2.4 (TiN 5.22 g/cm3, c = 3.8 km/s) weaker reflected wave from surface of substrate is visible. The delamination of film takes place during impacts of the first peak of pressure. Sharp changes in velocity profile are not visible. Relatively smooth course of velocity profile indicates on viscous failure of interface.In a model case when incident and reflected waves meets at interface the strength of interface can be estimated by simple relation where ρ – film density, c – sound speed, Δu – surface velocity changes of the films during delamination.The Δu values for the Ti film were: 25, 50, 40 and 50 m/s. For the TiN films only two proper signals from ViSAR system were registered and the average value of velocity changes during delamination was Δu = 58 m/s. The spall strength of interface, estimated from relation 4 for the TiN film, was 550 MPa and for the Ti film was 450 ± 53 MPa. The higher adhesion of the TiN film compared to the Ti film agrees with level of pulse energy that caused delamination. The delamination was observed at 0.7 J for Ti film while for the TiN film it occurred at 1.2 J.The study shows that laser spallation technique can be successfully used for estimating the value of residual stress of technological thin films deposited by PVD method. Until now there are no suitable methods to measure residual stress in thin films with poor crystallization or strong texture. This method is simple and quick. It allows obtain indicative value of compressive residual stress even for films with high roughness.The value of residual stress (−6.3 GPa) for TiN films measured by the proposed method is similar to that obtained for films of comparable thickness deposited by PVD method on steel substrate. In the work The accuracy of the LST depends on precision of measurement of size of the bulge. Several techniques can be adopted, for example scanning profilometry or confocal microscope. For technological thin films with strong adhesion to metal substrate the high level of laser pulse energy is required. The thickness of substrate is limited and should be matched to laser pulse energy.The study shows that in case of technological films with good adhesion to steel substrate the LASAT can be successfully applied. The interface strength for the Ti films was 450 MPa whereas for the TiN film it was 550 MPa that is similar to that found by Zhou et al. The presented experimental results show that shock wave induced by nanoseconds laser pulse can be suitable new tool for determination of properties of technological thin films.Supplementary data associated with this article can be found, in the online version, at 3D cohesive modeling of nanostructured metallic alloys with a Weibull random field in torsional fatigueThe cohesive finite element method together with Monte Carlo simulation for nanostructured metallic alloys with random fracture properties is developed to study the 3D fatigue crack propagation and torsional fatigue life. Three-parameter Weibull distribution is used to characterize the spatially random cohesive strength and fracture energy. The proposed model also considers the effects of thickness and different treatment of the nanograined layer (NGL) on the fatigue life. It is shown that the model can predict realistic crack patterns and reasonable fatigue life. The simulated fatigue cracks are mainly circumferential or oblique at an angle and they are in good agreement with the experimentally observed fracture patterns. Both different random fields and loads have significant effects on the crack initiation, crack pattern, and fatigue life. It is found that this layer plays a very important role in improving the fatigue life. As the layer thickness increases, the torsional fatigue life of the nanostructured metal also increases. The increase is particularly pronounced at high stress levels. We find that the major source of this increase is due to the increased probability for fatigue cracks to initiate from the interior surface of the tubular specimen and then propagate toward the exterior surface. This process has a profound beneficial effect on the fatigue life.damage variable after N cycles in damage extrapolation techniquemode-I fracture toughness of coarse-grained metalmode-I fracture toughness of nanograined layerinitial stiffness of the cohesive elementcumulative distribution function of failurecohesive traction in the normal directionpeak value of the nominal traction in normal directioncohesive traction in the first tangential directionpeak value of the nominal traction in the first shear directioncohesive traction in the second shear directionpeak value of the nominal traction in the second shear directioncrack opening displacement in the normal directioncrack opening displacement in the first shear directioncrack opening displacement in the second shear directionThe great majority of failures, including fatigue, wear, and corrosion in engineering materials, are very sensitive to microstructure and properties of the material surface. In most cases failures originate from the exterior layers of the work piece. Therefore optimization of the surface microstructure and properties can effectively improve the failure properties and service life of the materials Although there are considerable investigations on the axial fatigue of SMATed metals, studies on torsional fatigue are sparse We shall adopt the cohesive finite element method (CFEM) in this investigation. The CFEM has proven to be an effective tool in investigating the fracture process during cyclic loading of structural materials But it must be cautioned that scattering of fatigue test data is a common phenomenon, so it is desirable to introduce some probabilistic approach into the CFEM to account for such scattering. This is an inevitable outcome because of the internal defects of the specimen, unavoidable wear, processing errors, etc. In our recent experimental investigations Of course random statistical distributions have been widely used to describe the heterogeneous nature such as those occurring in microstructures and material defects. For instance, using Voronoi cells and Delaunay triangulation, Al-Ostaz et al. Our fully-reversed torsional fatigue experiments were conducted with a sinusoidal waveform under the frequency of 1 Hz . The effect of the diameter of the steel balls in the SMAT on fatigue properties has been compared. Specifically, for the 304 SS which has been SMATed by balls with diameters 2 and 3 mm, the torsional fatigue life improved remarkably, but the 3 mm series gave even better results.In this work we have developed a 3D CFEM model to study the crack initiation, propagation, and torsional fatigue life with the aid of MCS. In , the CFEM, together with the cohesive law and the quantization of the constitutive parameters, is elaborated. In , Weibull cumulative distribution function is introduced. In , 3D cohesive element modeling for the CG and SMATed specimen is developed. In , the effects of the random fields and loads on the crack initiation, crack pattern, and fatigue life of the CG specimens are investigated. In , the dependences of fatigue life on the treatment in SMAT and on the thickness of NGL are discussed. Main conclusions are drawn in The CFEM is developed to model the material separation process. Many variations have been proposed and successfully applied to predict crack propagation. The CFEM allows the damage initiation/evolution and fracture processes to be modeled explicitly. Moreover, it is an effective tool to model the spontaneous multiple crack initiation, branching, and coalescence, so it has been widely used to investigate brittle, quasi-brittle, and ductile fracture Furthermore, the CFEM has significant advantages compared to other methods including the boundary element method (BEM) and the extended finite element method (XFEM). At present, in using the BEM to model a crack, the main problem arises from the fact that two source points coincide at the same location on the cracked boundary, which leads to a mathematical degeneration of the numerical solution When the crack initiation site or propagation path is not known in advance, two approaches including the intrinsic and extrinsic CFEM are available. The former embeds cohesive elements along the boundaries of all volumetric elements The CFEM reflects the cohesion of the material by means of the traction–separation relation, which has been used to control the separation of material on both sides of the crack. Many cohesive laws, which specify the constitutive relation between traction and separation, have been developed for different conditions Here GIC, GIIC, and GIIIC represent the total areas under the traction–separation curve for individual mode. The mode-I and mode-II(III) traction–separation relations are shown in (a and b), respectively. GI, GII, and GIII denote the work done by the tractions and their conjugate relative displacement in the normal, first, and second shear directions, respectively, and given by where δn, δt, and δs are the normal and two shear displacements, respectively. Tn,Ts, and Tt represent the normal and the two shear tractions, respectively. The numerical calculations proceeded by computing Eq. for triple modes until the failure condition of Eq. is met and the cracks advance; at this point the element is considered to be no longer capable of bearing a load, and thus it fails. Note that unloading from any point C follows path CO and subsequent reloading follows OC and then CB. Part of the work expended on causing the separation in this regime is irreversible, as illustrated by the hysteresis loop OAC which implies dissipation during the softening. Correspondingly, there is a decrease in the cohesive strength. This is reflected in the elastic reloading along OC and further softening along CB.The cohesive law includes several parameters. It is reasonable to assume that only the cohesive strength and the fracture energy play key roles. Tmax is the cohesive strength, at which damage initiates. G is the fracture energy, i.e., the external work required to create and fully break a unit surface area of the cohesive element. It is obtained from GiC=KiC2(1−υ2)/E(i=I,II) and GIIIC=KIIIC2(1+υ)/E in terms of its mode-I, mode-II, and mode-III fracture toughness KIC, KIIC, and KIIIC. The Young׳s modulus E and Poisson׳s ratio υ of the CG and the NGL are taken as the same as those in Frontan et al. KIIC and KIIIC can be determined by the strain energy density factor (S) criterion proposed by Sih KIIC=3(1−2υ)2(1−υ)−υ2KIC,namely,KIIC=0.91KICFor the simulation of fatigue crack propagation, the range of the cohesive strength (Tmax) has been extensively discussed. It can be related to the yield strength (σy) of the material. Nguyen et al. In this paper Tmax is calibrated by comparing the prediction with the experimental results. In addition, the initial tensile stiffness Kn0 and shear stiffness Kt0 and Ks0 should be large enough to represent the uncracked material, but care must be exercised as too large values may cause numerical ill-conditioning Weibull distribution is widely used in the analysis of the static strength of ceramics, fibers and composite materials and fatigue life of metallic materials Our preliminary attempts show that the mean field approach for the data of heterogeneous materials could result in unrealistic crack patterns and fatigue life due to lack of the fatigue sources. These phenomena are inconsistent with experimental observations.P(σ)=1−exp[−VV0(σ−σuσ0)m]forσ>σuandP(σ)=0ifσ≤σuwhere σ0 the material parameter, m the Weibull modulus, σu the threshold stress below which the failure probability is zero, V the sample volume, and V0 the reference volume. The variance and mean of the Weibull distribution can be determined by σ0, σu, and m. If σu is taken as zero, Eq. degenerates into the two-parameter form, which has been used in the random analysis of brittle materials . In the process of generating random numbers, the Weibull modulus, which describes the degree of scatter of the material strength, ranges between 50 and 60 for steels The bulk material properties such as Young׳s modulus and Poisson׳s ratio are assumed to be constant for simplicity. The plastic property is defined as isotropic, and the specific material parameters for the CG specimen are taken from the experimental studies in Frontan et al. The hollow thin-walled tube with the thickness of 1 mm has been used in our torsional fatigue experiments (a), we find that the fatigue cracks are mainly circumferential or oblique at an angle. Therefore, a 3D CFE model is developed based on the above experimental observation in this paper, and the frontal view of the insertion process is illustrated in (b). The initial meshes consist of 6-noded wedge elements (C3D6 in , the CG specimen is discretized with ~10 k elements. Specifically, the number of the linear wedge elements (C3D6) is ~3 k, that of the 8-noded cohesive elements (COH3D8) is ~5 k, and that of the 6-noded cohesive elements (COH3D6) is ~1 k.For the SMATed specimen, in order to investigate the influence of the thickness of the NGL on the crack initiation, crack pattern, and fatigue life, we choose the NGL with the thickness of 20 µm, 40 µm, and 60 µm. The geometrical modeling methodology is the same as that of the CG CFE model. The corresponding CFE model is shown in (a–c). The SMATed specimen with the NGL thickness of 20 µm is discretized with ~20 k elements. Specifically, the number of the linear wedge elements (C3D6) is ~4 k, that of the 8-noded cohesive elements (COH3D8) ~9 k, and that of the 6-noded cohesive elements (COH3D6) ~6 k. The SMATed specimen with the NGL thickness of 40 µm is discretized with ~27 k elements. Specifically, the number of the linear wedge elements (C3D6) is ~8 k, that of the 8-noded cohesive elements (COH3D8) ~12 k, and that of the 6-noded cohesive elements (COH3D6) ~6 k. The SMATed specimen with the NGL thickness of 60 µm is discretized with ~35 k elements. Specifically, the number of the linear wedge elements (C3D6) is ~10 k, that of the 8-noded cohesive elements (COH3D8) ~15 k, and that of the 6-noded cohesive elements (COH3D6) ~8 k.The boundary conditions and loading process are consistent with experiments. Specifically, the bottom of the specimen is fixed, while the top is subject to the torque. Set up a reference point and then build a kinematic coupling between the reference point and the node set consisting of all nodes on the top of the specimen by creating coupling constraint in Interaction module of ABAQUS. After that, a torque can be directly applied at the reference point in Load module It is computationally expensive and thus intractable to perform a cycle-by-cycle simulation for a high-cycle fatigue analysis . When ΔN is less than 1000, the predicted fatigue life shows better convergence; when ΔN reaches 5000, the fatigue life diverges. Therefore, from the perspective of computational accuracy and efficiency, ΔN is selected as 200 at higher stress level and 1000 at lower stress level., in order to get the accurate relation between the cohesive strength Tmaxn and yield strength σy of the matrix material, Tmaxn=2.7σy, 3.25 σy, and 3.8 σy, the corresponding Tmaxt=Tmaxs=Tmaxn/3, are selected to study the effect of Tmax on the fatigue life under the sinusoidal torque with the amplitude 41 Nm (the corresponding shear stress amplitude is 390 MPa), 39 Nm (the corresponding shear stress amplitude is 371 MPa), and 36 Nm (the corresponding shear stress amplitude is 343 MPa). As shown in , when Tmaxn is 2.7 σy, the simulation results are lower than the experimental value, when Tmaxn is 3.8 σy, the simulation results are higher than the experimental results. Therefore, Tmaxn is calibrated as 3.25 σy. Similarly, the cohesive strength of the NGL is calibrated as twice of yield strength of the nanocrystalline materials.When Tmaxn is taken as 3.25 σy, we do a systematic mesh convergence check: (1) refining mesh in Z (height) direction, (2) refining mesh in R (radial) direction, (3) refining mesh in C (circumferential) direction, and (4) refining mesh in both C (circumferential) and Z (height) directions, by reducing the corresponding characteristic mesh size to one half of the former one. The simulated results of the fatigue life versus shear stress amplitude in different mesh refinements are illustrated in . It shows that the results obtained by the mesh that we use for the CG specimens (termed as “coarse mesh”) are fairly consistent with those obtained by several kinds of refined meshes except when the shear stress amplitude is in a very high level. This observation is consistent with the finding in Yang et al. As mentioned above, we find that when the homogeneous material model is employed, unrealistic crack pattern occurs, as shown in . Due to lack of the fatigue sources, the cohesive elements open and close at the same rate during the loading process, which leads to uniformly-distributed cracks with the same width.During the simulations where the cohesive strength and corresponding fracture energy are modeled by Weibull random distribution, three groups of torque are selected, namely, 41 Nm, 39 Nm, and 36 Nm. All of the torques change with a sinusoidal waveform under the frequency of 1 Hz and the stress ratio of –1. For each torque, five random series are generated. (a–e) illustrates five groups of the Weibull random fields of cohesive strength with a mean 912 MPa and a standard variance 71 MPa. Different random fields show various weak areas and produce various fatigue sources, which lead to the scatter of fatigue life.When the torque is 41 Nm, effects of the different random fields on the crack pattern and fatigue life are compared. The numerical results show that the random material model predicts the more reasonable and realistic crack pattern, and that cracks are mainly circumferential or oblique at 45°, 60°, or 120°. As shown in , No. 1 random field, as the cycle number increases, small cracks in the weak area gradually initiate, and a few circumferential cracks are linked with the oblique cracks and then merge into major cracks. After the main cracks form, crack propagation in other areas is suppressed, so it results in crack localization and mode-II cracks slide further. Finally, the specimen fails as the major cracks pass through multiple weak areas. This simulated crack pattern agrees well with the experimental one. In (a–d), the same torque is applied to the material but with different random fields, namely, No. 2, No. 3, No. 4, and No. 5 random field. Different crack pattern is observed. The failure modes are mainly dominated by the mode-I cracks. In general different random fields lead to various internal “defects” in the material, and they effectively simulate the scatter of the fatigue life in the experiments. illustrates the relation between the rotation and cycle number. When the specimen is in the failure stage, its rotation changes abruptly. In this case the cycle number is defined as the fatigue life. Note that due to the damage extrapolation, we can output only the rotation after each damage extrapolation (ΔN cycles) and we do not have the rotation during each damage extrapolation. This is the reason that the cyclic change of the rotation in individual cycle cannot be seen.By keeping the same random series (No. 1 random field), the effect of different load on the crack pattern and fatigue life can be studied. As shown in (a–c), different loads, namely, 41 Nm, 39 Nm, and 36 Nm, lead to various crack propagation patterns. At a higher torque, there are less small cracks initiated in the local region and thus the major cracks dominate the specimen. In this case, elements in the weak area are subject to larger force and local stress concentrates, the small cracks in other area do not propagate, and the specimen fails rapidly. On the other hand, when a lower torque is applied, some small cracks initiate on the exterior surface of the specimen. In this case, many elements around the weak area are mobilized to resist the load, which makes it possible to initiate more small cracks. Finally, the weaker areas become even weaker and the fracture paths form. illustrates the relation between the rotation and cycle number under different loads. The overall trend is that decreased torque leads to increased cycle number. As shown in , the shear stress amplitude versus fatigue life obtained from this simulation is in a good agreement with the experiments. The Weibull random fields in (a-e) deviate slightly from the ones with the same mean but a smaller standard deviation of 19 MPa. It has only small quantitative effect but no qualitative effect on the fatigue life.Based on the experimental result that the 3 mm treated series has a longer fatigue life, the flow stress of the NGL in this series is assigned a 20% increase. In the computations the material parameters are also listed in . We use linear strain hardening in the plastic constitutive relation. As shown in , the relation that the cohesive strength of the NGL is twice of the corresponding yield strength is guaranteed for the 2-mm series and the 3-mm series to figure out the effect of the flow stress on the fatigue life.The initial thickness of the NGL is taken as 20 µm. In the SMATed specimens, we refine the surface mesh and assign the properties of nanocrystalline 304 SS to the NGL. The properties of the CG 304 SS are assigned to the matrix material.Three groups of torque are selected, namely, 45 Nm (the corresponding shear stress amplitude is 428 MPa), 43 Nm (the corresponding shear stress amplitude is 410 MPa), and 41 Nm (the corresponding shear stress amplitude is 390 MPa). All of the torques change with a sinusoidal waveform under the frequency of 1 Hz and the stress ratio of −1. For each torque, five random series are generated. We use the same random series (No. 3 random field) under the fatigue load 45 Nm to compare the crack pattern and fatigue life in the specimens of 2-mm and 3-mm ball series. Numerical results show that the pattern of crack propagation in the 2-mm series is similar to that in the 3-mm series. The small cracks all initiate from the exterior surface of the specimens, and gradually propagate. The increased flow stress of the NGL has resulted in an increased fatigue life by about 24%, which is clearly demonstrated in . It implies that the increased flow stress in the 3-mm series exhibits higher resistance against fatigue crack initiation on the NGL. It is an outcome of the higher yield strength in the 3-mm series as compared to the 2-mm one. The simulated fatigue life in both series is also found to capture general trend of experimental results, as shown in . This is another remarkable effect of the NGL. Because of its contribution, the torsional fatigue life of the SMATed alloy is much superior to that made of traditional CG metals.Now the thickness of the NGL in the SMATed specimens is increased to 40 µm and 60 µm. Our objective is to uncover the effect of thickness of the NGL on the crack pattern and fatigue life. The same mesh size and material properties of the NGL (2-mm series) are used. We also apply the same torques as in the previous SMATed model.For each torque, five random series are generated. Numerical results show that when the thickness of the NGL is increased to 40 µm, the fatigue life can be improved at a higher stress. shows the mode-II crack initiation in No. 5 random field under the torque of 45 Nm. Cracks also initiate from the exterior surface of the specimen, and gradually propagate. This is the same as the failure pattern for the NGL thickness 20 µm. As crack propagates and crack tip opening displacement increases, the stress state around those mode-II small cracks becomes complicated, i.e., a multi-axial stress state exists. Therefore, mode-II fracture changes into mixed-mode fracture so that the circumferential major crack forms.We also discover that, when the thickness of the NGL increases to 60 µm, a new mechanism develops: cracks now initiate from the interior surface of the tubular specimen and then gradually propagate to the exterior surface in the cases of (i) 43 Nm with No. 2 random field and (ii) 45 Nm with No. 5 random field. shows the crack propagation in the first case. As the cycle number increases, small cracks are found to initiate from the interior surface of the tubular specimen, and later on other small cracks are seen to initiate from the exterior surface. This feature is quite different from the failure pattern when the NGL thickness is 40 µm. The similar phenomenon has also been observed in the fatigued gradient nanograined Cu where the cracks initiated from the subsurface layer and then propagated to the top surface , we find that when the cracks initiate from the interior surface, the NGL can help retard crack propagation, and fatigue life of the specimens is prolonged. illustrates the simulated fatigue life with different NGL thickness. A remarkable feature is that torsional fatigue life of the specimen is markedly higher with the increase of NGL thickness at high stress levels.A torsional fatigue model for nanostructured metallic alloys has been proposed in this study. We follow an efficient approach to insert the cohesive elements into the initial bulk elements. An irreversible CFEM combined with MCS has been employed to describe the 3D fatigue fracture. The proposed model has been verified by the experimental results. The following main conclusions can be drawnBy characterizing spatially-varying fracture properties as random fields, more reasonable crack pattern and fatigue life can be predicted, and the scatter of the fatigue life in the experiment can also be captured.For the CG specimen, cohesive strength Tmax has a significant effect on the fatigue life. For this reason, the Tmax value should be carefully calibrated in the simulation of fatigue failure. Both random field and load level also have significant influence on crack pattern and fatigue life.The NGL plays a very important role in improving the torsional fatigue life of the material. The increase of NGL thickness is an effective means to improve the fatigue life. When the thickness of the NGL reaches 60 µm from 20 or 40 µm, there is a strong probability that fatigue cracks initiate form the interior surface of the tubular specimen and then propagate to the exterior surface. This mechanism has a very beneficial effect to the improvement of torsional fatigue life for nanostructured alloys.We believe that this study has provided a new idea to use numerical simulation to study the torsional fatigue failure, and to improve the fatigue life through use of SMATed alloys. This numerical approach can also be applied to study axial fatigue, fretting fatigue, and three-point bending fatigue. The calculated results can also provide guidelines for future experimental investigation using surface treatment to enhance the fatigue life.Mitigating the impact of the static and cyclic loading on loose coastal saturated sands utilizing a waterproof and super-fast curing polymerAccording to the dramatic increase in construction near loose coastal saturated soils, stabilizing these soils due to saturation conditions has always faced challenges. The main purpose of this investigation is to assess the static and dynamic performance of saturated sand stabilized with polyvinyl acetate powder - as a newly introduced source of polymers which besides helping vegetation grow, owing to its numerous features such as anti-acid, and most importantly waterproof properties and super-fast curing, is superior to its rival, traditional liquid polyvinyl acetate. This paper Analyzes the dynamic properties of soil stabilized based on the results of tensile test crack pattern, microscopic observations of matrix texture, and elasticity modulus of hysteresis loops. Lack of significant change in the strength of samples in saturated and dry conditions indicated waterproofness of polyvinyl acetate powder and revealed a significant rise in the compressive and tensile strength of saturated specimens up to 6% of the polymer. Also, an exponential correlation of unconfined compressive strength (UCS) with direct tensile strength (DTS) was found by data fitting. Also, evaporation tests showed a 7% reduction in evaporation rate with 6% polymer, which can confirm this polymer as a suitable option for improving vegetation. Shear modulus and damping ratio also increased and decreased up to 2% of the polymer, respectively, and by increasing the polymer beyond the 2%, dynamic properties were changed due to the zigzag crack pattern and consequently more ductility of the soil matrix, reduction of elasticity modulus, and increasing the thickness of polymer membranes between soil particles. Ultimately, the research results confirmed polyvinyl acetate powder's efficiency, especially with these tiny amounts, as a potential method for controlling saturated grounds.Grounds adjacent to the sea and rivers have always been exposed to changing humidity. Some factors, such as rainfall and flooding, cause soil moisture changes, which can significantly affect the soil's mechanical properties and reduce soil durability [Soil stabilization is a technique of improving the soil's mechanical properties, including reducing permeability, increasing strength, and decreasing deformation. Apart from that, stabilization is used to enhance dynamic properties and reduce soil liquefaction potential as well as soil erosion []. Various materials such as polymers, fibers, and other complementary materials are used to stabilize the soil []. In the meantime, conventional chemical additives in soil improvement, often for environmental reasons, have decreased []. Such materials also increase soil pH (soil alkalinization) and create unfavorable and corrosive environments in the soil, limiting vegetation range because of groundwater contamination [Currently, soil stabilization using polymers has become a significant research interest in soil stabilization due to advantages, including using low percentages of polymer and at the same time, achieving high strength and environmental protection [Considering the advent of ecological polymers, the tendency to use them in order to improve the properties of soils is changing. Polyvinyl acetate is an ecological material with significant advantages, including effortless production and non-toxicity []. Therefore, utilizing liquid polyvinyl acetate, despite its favorable environmental and strength properties, has always been faced with the challenge of water exposure. Several researchers improved its water resistance by adding materials such as polypropylene fiber, melamine, urea, and formaldehyde to conventional polyvinyl acetate [] according to functional requirements, by adding buffers, monomers, protective colloids, and other auxiliary materials to polyvinyl acetate, improved mechanical properties of stabilized soil. The results showed that increasing the vinyl acetate solution could increase water conservation, erosion resistance, compressive strength, and soil durability. Also, field tests by creating vegetation and spraying polyvinyl acetate solution on the natural slope surface revealed that vinyl acetate polymer effectively improved slope resistance to erosion and protected vegetation growth, which is consistent with the achieved data of vegetation growth test by Bu et al. [According to a study by Newman and Tingle [], vinyl acetate and acrylic-based copolymers are the most popular soil stabilization products. An investigation over the effect of polyvinyl acetate on compressive strength of expansive soil showed by increasing the amount of polymer, the compressive strength after a specific content (3.75%) led to a decrease in the strength of the specimen. This reduction was attributed to high water absorption and PVA by adding PVA higher than 3.75% [] studied the effect of polyvinyl acetate slurry injection into the sandy soil and reported that by growing grout thickness, the rate of increasing elasticity modulus reduces. Other researches have been conducted to improve the behavior of soils stabilized with polyvinyl acetate []. In general, past literature shows that polyvinyl acetate efficiency due to polymer restriction in wet conditions is mostly in dry testing conditions.Another perspective of soil stabilization is the treatment of soils against the complications of earthquakes. Accordingly, determining the dynamic properties of soil is one of the essential geotechnical tasks. Geotechnical phenomena such as landslides and soil liquefaction may all play a role in earthquake disaster. In this regard, any attempt to assess the risk and prevent an accident may prevent loss of life and financial losses. Studies have shown that in places where the soil is strengthened in different ways, it can minimize damages as much as possible [Evidence reported that during powerful earthquakes, the soil might experience a high shear strain level (more than 5%) []. Therefore, due to such high strains level, the evaluation of dynamic properties (shear modulus and damping ratio) is necessary for designing structures against earthquakes.The results of a study on the dynamic properties by performing undrained cyclic triaxial tests on sand stabilized with agar biopolymer and different curing times showed that the shear modulus of samples stabilized by 2% agar and 7 days of curing time was 317% higher than the shear modulus of primary soil in the loading cycle of 50. They also observed a significant increase in the damping ratio of stabilized soil []. Using Superabsorbent polymer (high crosslinked density sodium salt polyacrylate), Wu et al. [] showed that a high amount of polymer could reduce shear modulus and increase the damping ratio of the soil matrix. Maher et al. [] researched the dynamic properties of soils stabilized with different types of grouts. The results showed that grout type and grout concentration had essential effects on the shear modulus and damping ratio of the experimental specimens. The high addition of sodium silicate grout, which produces stiff gels, improves the shear modulus of soil. Acrylate and polyurethane grout, which produce flexible gels (such as rubber), improve sand damping by increasing grout concentration. Subramaniam and Banerjee [] conducted several experiments on cement-stabilized clay to investigate the degradation behavior of shear modulus. This study showed that factors such as mix proportion and loading conditions are essential factors affecting hardness degradation. Other researches have been conducted on the dynamic properties of sandy soils injected with mortar based on cement, epoxy resin and other materials [Although several studies have reported the effect of conventional polyvinyl acetate on mechanical properties and static soil strength, its weakness against moisture has limited its use in saturated soils. Hence, in this paper, the static and dynamic properties of sandy soil stabilized using polyvinyl acetate powder as a waterproof polymer have been evaluated to in addition to filling the gap in the literature of dynamic experiments, it will end all concerns of researchers about the weakness of this polymer in saturated soils. Beyond that, to be used as a reference for continuing researchers' research as well as practical applications. The effects of polymer percentages and curing time were analyzed on the compressive and tensile strength of specimens and the effects of cyclic stress ratio and polymer percentages on the shear modulus, damping ratio, and stiffness degradation of the samples. In the end, SEM observations on the tissue of some samples were also investigated.The study area is south of Hormozgan Province, called Suru Beach, adjacent to the Persian Gulf, similar to Toyoura and Sengenyama standard sands (see ). The grain size distribution of soil is shown in . Based on the boundaries of potential for liquefaction curves [], it is observed that the potential of sand-Suru liquefaction is high. Today, construction projects, including coastal factories and recreational hotels in this area, have increased significantly. The menace of earthquakes and soil formation with specific physical and mechanical properties have put this region at significant risks [ shows the magnitude of earthquakes in the study area and surrounding areas from 1900 to 2019. shows the SEM image of used soil. Lack of coherence between particles, relatively round particles, and absence a bonding agent between the particles cause the particles to move on each other without limitation. The soil specifications tested are listed in The polymer used in this study is PVAc powder, which is a product of Bijan Foam Central Company in Iran. This powder becomes a solution after mixing with water and is prepared for consumption (). In this paper, for abbreviation, only the word “polymer” is used. Compared to the conventional liquid polyvinyl acetate, the most important innovation and benefit of this polymer are its waterproofness. Due to the lack of need for other materials to increase efficiency in saturated soil, the PVAc powder replaced the liquid polymer to prevent the polymer from dissolution upon contact with water and also its deposition in the hoses of the triaxial apparatus. Low cost, ultra-high adhesion, waterproof, fireproof, odorless, non-toxic, high viability, and pollution-free characteristics are other advantages. Other characteristics of polymer are listed in In order to accurately investigate the differences between the two polymers, extensive studies of chemistry and materials are needed, but during an FTIR analysis, the overall differences between the two polymers can be disclosed. The results of the spectrum of two liquid and powder polymers are displayed in . The main differences between the two polymers are hydroxyl (O–H), carbonyl (CO), and C–O groups. In the study of liquid polymer spectrum, 1095 cm-1 represents the C–O bond, 1640 cm-1 and 1732 cm-1 wavenumber related to the carbonyl group, 2946 cm-1 represents CH2 bonds, and wavenumber 3440 cm-1 represents hydroxyl group []. In powder polymeric spectrum, wavenumber 1152 cm-1 represents the C–O bond, wavenumbers 1549 cm-1 and 1622 cm-1 belong to the carbonyl group, 2959 cm-1 represents a methyl group and CH2, and 3366 cm-1 related to the hydroxyl bond [As can be seen in the liquid polymer, a strong peak is seen in wavenumber at 3440 cm-1, indicating free hydrophilic hydroxyl groups in the polymer structure that are ready to react with water molecules []. However, in the powder polymer, this peak has been largely destroyed; this evidence can be the result of a reduction in the interning of powder polymer with water molecules. In fact, it can be said that there are very few oxygens and hydrogen atoms in the polymer structure freely that can react with water. In other words, these atoms are more involved in self-bonding building and cannot react with water. Therefore, it can be said that during this process, this polymer has become hydrophobic.Another point is the similarity of wavenumbers at 2946 cm-1 and 2959 cm-1 in two polymers, representing the CH2 hydrocarbon bonds. The wavenumber in the powder polymer has found a slight shift to the left, which can be the overlap state of CH2 and CH3 (methyl). In other words, CH2 bonds react with the hydrogen of the free hydroxyl group in the bonding structure and become methyl, which is a hydrophobic bond [Wavenumber at 1152 cm-1 is also related to the C–O group (acetate), a strong bond, which constitutes a large part of the powder polymer. Bond strength in C–O is higher than C–N and C–C bonds.On the other hand, two peaks in wavenumbers at 1640 cm-1 and 1732 cm-1, known as Shoulder Carbonyl, are seen in liquid polymers []. This group is highly hydrophilic. This group has shown itself in powder polymer in wavenumbers at 1549 cm-1 and 1622 cm-1. The shift of the wavenumbers of this group to the right in the powder polymer indicates that the carbonyl content has been reduced. In other words, the number of oxygen and carbon molecules has been reduced. In fact, the lower the wavenumber, the lower the number of free groups in the bond structure. Therefore, during this process, the hydrophobic properties of the polymer have been increased.Finally, due to the low carbonyl and hydroxyl groups in the powder polymer structure, the potential of reaction with water decreases, and this process can quickly end the reactions between water and polymer. In this way, polymerization is done faster due to the absence of molecules for further reactions. This could mean fast curing of powdery polymer.The unconfined compressive tests were carried in accordance with ASTM ] using a standard UCS device. Static tests should continue until the failure surfaces are developed or until the axial strain is 20% or the load reached a fixed value. The compressive strength (qu) is described as the maximum stress (peak point strength) [The direct tensile test is usually considered as a reliable method for measuring tensile strength and controlling tensile cracks of soil. The tensile strength value of pure soil is considered zero []. However, chemicals materials, fibers, or a combination of these increased the tensile strength of soil matrix [ shows the schematic illustration of testing equipment, including tensile mold and tensile device. The axial displacement rate of the tensile device was 0.5 mm/min. During the experiment, the 8-shaped mold containing the sample is installed between the two clamps of the test machine, and an incremental tensile load is applied on the ends of the samples until a tensile failure occurs. Maximum load is used to determine the tensile strength. Maximum tensile strength is calculated from Eq. where σDTS is the maximum direct tensile strength (kPa), Pmax is the maximum tensile load (kN), and A is the A-A cross-section area of the sample (m2).. (see Water retention properties are aspects of ground improvement by soil stabilizers, which refers to water's relative durability in the soil. The result of this yield is sufficient retention of moisture and nutrients to plants []. This experiment aimed to understand the effect of polyvinyl acetate powder on soil water storage properties. At first, the samples were cured within a specified time for the experiment. After that, polymer solution with concentrations of 0%, 1%, 2%, 4%, and 6% on the stabilized soil matrix surface was sprayed in evaporative boxes and then weighed. After 24 h, the evaporation box's soil was weighed until the weight difference between the two consecutive measurements was no greater than 1 gr [where Ee, M0, M1, and M2 are the evaporativity of the soil (%), weight of the dried soil (gr), weight of the soil at first (gr), and soil weight after a period of time of evaporation (gr), respectively., can perform dynamic tests on cylindrical specimens of soil materials with a diameter of up to 100 mm; and the load cell of the system can apply a vertical axial load up to 20 kN. The cyclic load can be applied to the specimen in waveforms of different stresses and frequencies from 1 to 20 Hz.Shear modulus and damping ratio are the main parameters of dynamic response investigation and anti-seismic design. Different methods have been developed from cyclic loading tests for calculating dynamic properties of soils that are obtained based on the equations of elasticity theory [Usually, dynamic properties of soils are determined from symmetric hysteresis loops (SHL) before shear strain reaching 1%. However, with an increase in shear strain, hysteresis loops gradually become asymmetric. Therefore, a modified method is needed to evaluate the dynamic properties of saturated sands based on the real cycle of asymmetric hysteresis (ASHL). In this study, the reported method by Doygun and Brandes [] was used for damping ratio and the shear modulus was calculated by Kumar et al. [a, b and 8c. It should be noted that the shape of loop in a has been extracted from the actual loop in the present study in order to make these relationships more tangible with the results of this research.The first and last points of a hysteresis loop are defined as zero shear strain conditions or zero shear stress []. In this paper, a second approach has been used. Moreover, Poisson's value was considered 0.5 for saturated soil [The average single shear strain amplitude for a loading cycle is determined using Eq. where εmax and εmin are maximum axial strain in one direction and minimum axial strain in the opposite direction, respectively. Dissipated energy for a loading cycle is calculated according to Eq. whereσd,i and εa,i are applied deviator stress and axial strain at incremental data point (i), respectively. Also, n and i represent the number of data points in one hysteresis loop and computational points along the stress-strain loop, respectively.Determining soil stiffness degradation behavior under dynamic loading conditions helps solve geotechnical problems and soil-structure interaction. Soil stiffness degradation characteristics have been calculated for all specimens to promote a proper understanding of soil mass's internal stability under dynamic loading conditions. Stiffness degradation characteristics were determined by evaluating soil cyclic degradation index (δ) [, this index means the amount of stiffness degradation by increasing the number of cycles. In this study, to investigate the stiffness degradation for each specimen with a specific percentage of polymer, the shear modulus of the 10th cycle and the first cycle of each specimen were determined. The 10th loading cycle was selected based on the recommendation of Ishihara [] due to reaching a stable equilibrium state in the stress-strain graph to calculate the shear modulus.where GN and G0 are Shear modulus at Nth cycle and Shear Modulus at the 1st cycle, respectively.The amount of polymer calculated based on dry sand weight (1%, 2%, 4%, and 6% of dry sand weight) was mixed with water (10.5% of the polymer weight) and then added to the soil. It should be noted that the percentage of water used was chosen after several trials and experiments. To ensure proper uniformity and bonding, the mixture was thoroughly mixed by hand for about 5 min until the color of the mixture visually became uniform, and a homogeneous mixture was achieved. Also, The surface of each layer was scraped approximately 3 mm after each layer for the uniformity between layers. In addition, the variance of the results of UCS tests was almost insignificant, so it can be said that the mixtures were homogeneous.The prepared combination for UCS tests and dynamic tests samples in three equal parts inside the cylindrical mold with a diameter of 3.6 cm and a height of 7.5 cm and six equal parts inside the triaxial mold with a diameter of 7 cm and a height of 14 cm was compacted, respectively []. Because of the temperature fluctuation in the laboratory environment to prepare the samples in similar conditions, all specimens were kept and cured in the controlled room at 22 °C for 3, 7, and 14 days. After curing the static tests samples, each sample was placed in water one day before the experiment for 24 h until complete saturation. After the saturation process ended, the saturation degree results were satisfactory because the saturation degree increased by about 85–90%. Tamrakar et al. [] believed that the amount of water above 80% (insular saturation) was close to complete saturation because, in this case, there are a small number of inter-aggregate pores that are almost full of water resulting in a significant reduction in capillary and suction effect. It should be noted that in the case of samples that appear to have dried up after leaving the water, drying was superficial, and since suction does not significantly affect the results, it is assumed that all results refer to saturation mode [After curing the cyclic triaxial test samples, the soil specimen was placed inside the rubber membrane and fixed on the triaxial device base. A vacuum pressure of 20 kPa was utilized to make proper contact between the rubber membrane and soil specimen environmental boundary. Then, the cell was poured with airless water, applying 30 kPa cell pressure simultaneously, and vacuum pressure was removed from the specimen []. Cell pressure (CP) and back pressure (BP) were gradually increased at each stage by maintaining at the approximately constant pressure difference of 20 kPa to accelerate the saturation of specimen. After each step of extending the cell pressure, the skempton pore water pressure parameter (B = Δu/Δσ) was assesed. According to ASTM ], if the value B is equal to or greater than 95%, the sample is saturated. After achieving saturation conditions, to consolidate the specimen gradually, cell pressure was raised to the desired level. It should be noted that the waterproof polymer does not prevent soil saturation, but because the denseness of the sample (reducing permeability) and the barriers that the polymer bonds create between a series of soil particles (reducing the water absorption capacity) affect the time and degree of saturation. In fact, the polymer solution becomes only a part of the soil mass that sticks to soil particles, but still, there are many voids in the sample. Saturation of the stabilized samples required 8–10 h depending on the percentage of polymer (without using CO2).UCS and tensile strength tests were used to evaluate the maximum compressive and tensile strength of the specimens. These tests were carried out on samples with relative density of 65%. Cyclic triaxial tests were performed under consolidated-undrained conditions (CU) and stress-control with a constant value of mean principal stress closer to the actual soil conditions during an earthquake. Also, the specimens with sinusoidal waveform 1 Hz frequency at consolidation pressure of 100 kPa were tested. The selection of 100 kPa consolidation pressure is according to past earthquakes' experiences, indicating liquefaction mainly at shallow depths (limited to 10 m from the earth's surface) []. Experiments program, are summarized in Stress-strain responses of specimens through UCS test are presented in a for 3 days of curing. Three tests were repeated for each specimen to ensure that the results are exact and the variation with average value was regarded as less than 5% []. A static triaxial test was used to determine the strength parameters of pure soil. It is observed that the effect of stabilization on the maximum deviator stress and dependent strain level is considerable. As can be seen, by increasing the polymer up to 6%, the amount of compressive strength increases significantly about 1350 kPa. This trend can be attributed to the adhesion of polymer and soil particles and aggregate interlocks of the sand grains. In this case, friction between sand and polymer grain particles increases the compressive strength of the soil. More precisely, a set of mechanisms operated by polymer on the soil, including a series of reactions of the displacement of soil particle surface cations, hydrogen bonds Described in detail by Bu et al. [], creates an increasing number of strong bonds in the modified soil that are resistant to compressive loads.The rest of the results of the 7 and 14-day curing experiments are summarized in b, the results showed a significant increase in compressive strength up to the first 3 days of curing, and then there was no significant change. It is concluded that the optimum water content that is responsible for transferring polymer grains into the soil evaporates almost completely within three days and finishes the polymerization. Therefore, the optimum curing time for all experiments was considered three days.For quantitative evaluation of moisture's effect on compressive strength, qu values are provided for two curing conditions in the controlled room (3 and 7 days of curing) and additional 1 day soaking in . Compared to the curing in the controlled room (standard curing), saturation conditions reduced the strength in soil samples stabilized with 1% polymer with cured 3 and 7 days. Such a situation is attributed to a negligible effect of 1% of polymer in the soil, independent of curing time. As can be seen, the difference between the obtained other values was tiny. Therefore, the samples' behavior is independent of the saturation effect or the curing time and is controlled only by polymer.To check the durability of samples in water, samples with different percentages of polymer were placed in the washbowl of water []. Samples were regularly visited at different times up to 24 h. Several soil particles of the sample with 1% polymer were settled at the bottom of the container. This observation can be attributed to an insignificant amount of polymer. The lack of significant bonding between some soil particles that may have been separated from the outer surface of the sample resulted in the deposition of some soil particles. No effects of surface spalling, water discoloration, and deposited particle was observed in the rest of the samples. The above exciting results confirms the waterproofness of polyvinyl acetate powder under saturation conditions.The tensile test results and the diagram of the results of UCS tests with three-day curing time (optimum curing time) for samples were presented in . As can be seen, the tensile strength rises about 169 kPa by increasing the polymer percentage up to 6%. This trend can be attributed to the high-performance of polymer, which has high tensile strength and excellent adhesion properties with particles, as well as delays the micro-cracks caused by loading [Another important point is the existence of a correlation between DTS and UCS. As shown in , to estimate the direct tensile strength from the compressive strength for soil stabilized with polymer, a general relationship with the coefficient of determination of 0.9783 can be suggested. It is important to note that resizing the UCS sample may affect the compressive and tensile strength relationship. According to previous studies, increasing the height to diameter ratio of the UCS sample can decrease compressive strength [], which affects the relationship between compressive and tensile strength. Obviously, these studies require lots of time and also different sizes of samples to investigate this effect. Therefore, it is recommended for further studies in the future.The effect of polymer on the cracking pattern of samples can be observed in . The shape of the crack pattern for the D1 (see a) sample was linear-shaped crack and first began to fall from the external walls at the edges of the weakness plane until it was eventually broken. Soil particles exhumed from the sides are probably the same particles that do not participate in the polymerization process due to low amounts of polymer or have weak bonds. The D2 sample went up to rupture with an almost linear crack pattern without observing the loss of the sides (see c and d, a similar zigzag crack appeared after failure. This trend can be considered the more ductility of the soil matrix due to the polymer's increase beyond a specific limit (from 2% onwards) in the weakness plane. More precisely, this plane, which is probably filled by the thick layer of polymer, has become more ductile and prevents the rapid expansion of cracks to the end of the plane. The observed trends can be attributed to the nature of polyvinyl acetate and the membranes created in the high polymer dosses that effectively prevent the release of micro-cracks []. A similar report also described by Ref. [] that adding polyvinyl acetate to a hard composite material would increase tensile strength and reduce crack release. shows the results of the moisture retention test data. It is observed that with increasing polymer, water holding capacity increases dramatically, and the soil retains more amount of moisture. As shown, the evaporation boxes' evaporation rates are roughly the same in about 12 h. Then, after about 12 h, the variation in moisture retention characteristics increasingly emerges. It is observed that by increasing the amount of polymer during 96 h, evaporation in the soil decreases. This reduction is attributed to the creation of water evaporation resistant shields between soil particles. As reported in section , if the optimum water reaches the polymer, a large amount of polymerization process is completed within three days. After the curing, if additional water enters the sample, the polymer as shields prevents the water's evaporation. Therefore, it can verify the usage of this polymer to improve vegetation. Song et al. [] have also confirmed the positive effect of polyvinyl acetate on vegetation improvement. Therefore, spraying polymeric solution with only a small amount of 6% can reduce evaporation in the soil by up to about 7%. shows shear stress-strain diagrams for specimens with different polymer percentages under CSR = 0.5 (the most destructive ratio of selective cyclic stress in this research) in 40 loading cycles, which have subsequently been used to evaluate the dynamic properties of soil. It should be noted that due to the specimen's failure and test stoppage, R0-0.5 to 3rd cycle diagram and R4-0.5 to 17th cycle have been plotted. As the number of cycles increases, the hysteresis loops gradually spread in the strain axis in response to the reduction of the average effective stress. The width of the hysteresis loops increasingly develops, i.e. the damping ratio in the soil increases. In pure sand, as seen, the shear stress from the first cycles of the test is immediately reduced because of the large CSR applied to the specimen.It can also be seen that the deformation of samples in compressive and tensile phases is not uniform, stabilized specimens show a more significant hardness reduction in the tensile phase of the stress–strain loops. Another important point is that the trend of axial strain increase is similar for stabilized and pure samples, but this increase in stabilized samples is gradual and in the pure sample is sudden. An increase in polymer content further characterized this trend. Therefore, it can be found that soil stabilization significantly affects the stress-strain behavior of samples.The effect of polymer value on shear modulus changes in shear strain in CSR = 0.5 in 40 loading cycles is shown in . As can be seen, the shear modulus of specimens drops by increasing the shear strain. Similar results were observed for the ratio of 0.2 and 0.35 cyclic stresses. The reduction of shear modulus is mainly due to soil nonlinear properties []. Moreover, loss of hardness in the samples can be attributed to the weakening of the structure between the soil and polymer particles caused by increased shear strain. The shear stress-strain response obtained in 40 loading cycles and deviator stress diagram based on the number of loading cycles for the R2-0.5 sample in has been displayed to understand this issue better. As can be seen in a and b and when the specimen reaches failure level and considerable cyclic strain, the axial stress decreases faster, and the soil gradually reaches a near-zero stress state. Hence, shear stress can no longer be sustained by the specimen in the majority of loading cycles; and in more cycles, it shows a response proportional to the softening conditions. This trend in natural sand occurs suddenly in the initial cycles, and then the rate of its changes decreases to the point where it is fixed. Such behavior has been reported before by Xiao et al. [] in bio-cemented calcareous sand. Apart from that, a indicates that the hysteresis loops obtained in different N values are approximately symmetric between 1 and 5 cycles, whereas in cycle 5 and beyond, these loops have been highly asymmetric. Therefore, it seems that the proposed method for asymmetric loops [] is suitable to evaluate the dynamic properties of the soil. It can also be explained that the stabilized specimens have less shear strain than the natural sand, which is a reason for the apparent effect of soil stabilization and an increase in shear modulus even by using small amounts of polymer. The trends observed in this study are among the famous axioms of shear modulus and shear strain relationships and are consistent with several previous researches [For comparison between samples, it was observed that by increasing the amount of polymer up to 2%, shear modulus significantly increased. By contrast, by increasing the percentage of polymer to 4%, the shear modulus of the specimens was significantly reduced, but was still more than the pure sand shear modulus. Similar results were observed for the ratio of 0.2 and 0.35 cyclic stresses. Accordingly, G reduction by increasing the amount of polymer from 2 to 4% at first glance is unexpected. The cause could be searched exclusively in the polymer texture and modulus of the soil matrix elasticity, which is an essential parameter for judging on shear modulus. The 10th cycle of samples containing 1, 2, and 4% polymer in CSR = 0.5 is presented in . By calculating the elasticity modulus values from equations in , the decreasing trend of the elastic modulus in the R4-0.5 sample is clearly determined. Therefore, considering the direct relationship between elasticity modulus and shear modulus, it is possible to justify the reduction of shear modulus. Moreover, according to previous reports, with the increase of polyvinyl acetate beyond a specific limit, the modulus of elasticity decreases due to the nature of the polymer itself as well as the increase in latex membranes []. Therefore, by decreasing the elastic modulus, the shear modulus is reduced. Based on the evidence, due to the decreasing trend of shear modulus with 4% polymer, cyclic triaxial experiments on samples with 6% polymer were prevented. shows the development of excess pore water pressure relative to the number of cycles for pure and stabilized samples with 0, 1, 2, and 4% of polymer in CSR = 0.5. As can be seen, generating excess pore water pressure of stabilized samples varies with the pure sample. The overall response by pore water pressure generation of stabilized samples is relatively similar: a sudden increase in the initial cycles and then a slower accumulation of the excess pore water pressure. This trend indicates a delay in the generation of excess pore water pressure and thus prevents a severe and sudden reduction in effective stress between the sand grains. This trend is similar to past reports of cement-stabilized sand [The addition of polymer up to 2% increases the modulus of elasticity, adhesion, and involvement of soil particles, and as a result, soil grains suffer a more significant share of the cyclic load, which reduces the increasing rate of excess pore water pressure. In a constant CSR, the rate of generation pore water pressure rises by increasing the polymer up to 2% and decreasing by 4%. This reduction can be attributed to the decrease of shear modulus, which was examined. By decreasing soil shear modulus, the strain of samples increases. As a result, increasing strain can potentially increase the rate of generation pore water pressure []. Similar results were observed for the ratio of 0.2 and 0.35 cyclic stresses. Therefore, stabilization of sandy soil with this polymer can not only improve hardness behavior, but also improve the performance of excess pore water pressure, which leads to effective stress reduction between grains. shows the effect of polymer content on changes in damping ratio (λ)-shear strain in CSR = 0.5. As can be seen, λ increases with increasing shear strain nonlinearly. Due to the conventional trend of cyclic loading, with an increase in shear strain, the specimen should approach the state of liquefaction. The common assumption that the soil behaves like a liquid in liquefaction indicates that damping should also be somewhat similar to water. Moreover, in high strain, the stored strain energy in the specimen should be minimal, in which case the λ is increased. This trend is in line with the results obtained by Doygun and Brandes [In comparing the stabilized specimens, as can be seen, all three polymer contents decreased the λ compared to the pure soil. This trend was expected because the λ usually decreases with soil tightening []. The remarkable point was that, by increasing the amount of polymer to 4%, the λ is greater than 1 and 2% of the polymer, but it is still lower than the λ of pure sand. The cause can be attributed to the ductile texture of the polymer. Thanks to the ductile polymer membranes created with 4% polymer in the sample skeleton, the propagation pathways of stress waves in the soil decrease, and the wasted energy increases. Similar results were also observed in the ratio of 0.2 and 0.35 stresses. It should be noted that in pure soil, by applying high amounts of CSR, the shear stress level is high, so it can overcome the internal structure of the soil to generate shear strain at higher effective stresses. The studied pure sand has an incredibly weak structure due to a lack of coherence (SP soil without adhesion with round grains). Therefore, when faced with an extremely high stress level at the initial cycle, the sample quickly fails and acts like a liquid that has a high damping ratio. In fact, the studied pure soil cannot withstand the CSR>0.35. These results are consistent with previous reports on similar loose sandy soils [(a) and (b) shows the graph of shear modulus changes in the shear strain of primary specimens with 0% and 2% polymer (optimum percentage selected in this study) at different CSRs. A higher CSR value implies more deviator stress on the specimens and causes more shear strain. It is observed that in all samples, by increasing the CSR, the specimen missed its hardness and its shear modulus decreased due to declining the confined phenomenon in the sample. In fact, by increasing CSR in all specimens, more considerable shear strain occurs and leads to a drop in the shear modulus as observed trend obtained by Kumar et al. [To compare CSR's effect on stabilized and pure specimens, as can be seen in (a) and (b), by increasing the amount of polymer, CSR's impact on shear modulus decreases. This behavior can be attributed to polymerization and hardening of soil on stabilized specimens. Similar results were observed in the amount of polymer 1% and 4%. The R0-0.2 sample in the initial cycles showed significant strength to shearing. However, after the first few cycles, its shear modulus suddenly decreased, but for the R0-0.35 and R0-0.5 specimens at the beginning of the test, the shear modulus quickly reduced. This indicates that the primary sand with no polymer can only withstand cyclic loads at the stress ratio of 0.2 and only a few initial cycles. Therefore, soil stabilization with polyvinyl acetate can effectively preserve the soil during cyclic loading in different cyclic stress ratios.The cyclic degradation index (δ) was evaluated for all specimens. It should be noted that the closer δ to the value of one represents the lower hardness reduction due to loading from cycle 1 to 10. As shown in , by an increase in CSR, the δ decreases in all stabilized specimens, that offers growth in cyclic degradation because of the rise in the cycles from 1 to 10. Also, the reduction of δ from CSR = 0.2 to CSR = 0.35 is negligible in all samples. In contrast, there was a substantial decrease in δ with CSR = 0.5, which is attributed to the high power of degradation the stress ratio of 0.5.Unstabilized samples suffered from severe δ reduction in all cyclic stress ratios. This reduction was attributed to their failure before reaching cycle 10. Since the soil behaves like a liquid after a failure. The 10th cycle shear modulus had a near-zero value in unstabilized samples, so δ was significantly reduced because G10 is in the numerator of Eq. fraction. The process of lowering stiffness in different percentages of polymer is also quite evident. As can be seen, in all ratios of stresses with increasing polymer up to 2%, δ had a significant increase, but 4% of the polymer resulted in a decrease in δ, indicating a rise in stiffness degradation during loading in this additive ratio.Damping ratio changes in the shear strain of pure specimens and those with 2% polymer in different cyclic stress ratios were illustrated in (a) and (b). In general, the damping ratio rises with an increase in CSR []. By increasing the CSR, the internal structure between soil and polymer are destroyed, and the bond between the particles is weakened, therefore, the vibration waves are dispersed non-uniformly from the top to the bottom of the specimen. Comparing the effect of CSR on stabilized and pure specimens in (a) and (b) shows that increasing polymer reduces the impact of CSR on specimens, resulting in a decrease in the damping ratio. Similar results were achieved in the amount of polymer 1% and 4%. illustrate SEM photographs and schematic model of interaction between polymer particles and sand microstructure, respectively. Vinyl acetate polymer interacts directly with soil particles. Most mechanisms show that adhesion consists of 4 steps: wetting, absorbing, tightening, and mechanical locking []. When polymer chains penetrate the soil grains, soil particles will also be soaked and ready to absorb into polymer particles. In fact, water acts as a factor for transferring polymer to soil grain surfaces, and by evaporating water, the polymer works to fix soil particles to each other. This reaction creates a specific lattice coating structure. Obviously, The samples' behavior varies depending on the thickness of the polymer coating in the pores between soil particles., the dynamic properties of the samples are completely dependent on the polymer percentage. By increasing the polymer up to 2% in a, it can be observed that the soil particles are close together and are attached with a low thickness coating by polymer. In other words, the grains of sand are further compressed, and only a thin coating of polymer surrounds the sand particles. This coating with a high elastic modulus leads to an increase in soil matrix shear modulus. Vibrating energy also passes through the sample quickly due to the closeness of the grains and the interconnected structure, reducing the damping ratio. In other words, dissipated energy only increases in the event of a collapse or fracture of the polymer coating walls, and this situation only happens in high cyclic stress ratios.b, sand particles are distanced due to the high polymer amount. In this case, the seismic response is largely controlled by the polymer's lattice coating, which surrounds the sand particles. The created coating has much less elasticity modulus than the 2% polymer coating. Therefore, this ductile coating will be failure faster due to shearing and reduce the shear modulus. In previous reports also, Ajalloeian et al. [] attributed the cause of elasticity modulus changes in soil matrix to thick coating created by polyvinyl acetate. A large amount of vibrating energy is also consumed on breaking or collapsing the polymer coating walls. As a result, a lot of it is wasted and leads to an increase in the damping ratio compared to the samples with 1% and 2% polymer. Therefore, it can be concluded that polymer should only fill the gaps between particles rather than increase the distance between soil particles. It should be noted that due to the creation of a continuous structure, the damping ratio for all stabilized samples is less than the pure sand damping ratio, and the above results are merely for comparison between stabilized samples.In this study, a series of static and dynamic triaxial tests were conducted to investigate the effect of polyvinyl acetate powder on the static strength and dynamic properties of soil. The key findings of this study are:UCS and DTS tests showed that by adding polymer to the soil up to 6%, the compressive and tensile strength increased to 1350 kPa and 169 kPa, respectively, for 3 days of curing time. Due to obtaining about 90% of compressive strength during three days of curing, this time was selected as the optimum curing time.Evaluation of strength in saturated and dry conditions showed that polyvinyl acetate powder is highly waterproof. Also, evaporation tests showed a 7% reduction in evaporation rate with 6% polymer.Adding polymer up to 2% increased the shear modulus in the specimens, but with an increase of 4% polymer, the reduction of shear modulus was observed, indicating the optimum 2% of the polymer. This trend was attributed to the decreasing of the elasticity modulus of polymer coating beyond the 2% of polymer.Increasing the CSR reduced the confined phenomenon and, as a result, decreased the shear modulus in the specimens. Moreover, by increasing the CSR, the stabilized specimens will have more shear modulus than soil without polymer. It was inferred that increasing the polymer reduces the destructive effect of CSR in soil.By increasing the polymer up to 2% in weight, the damping ratio goes down, and then grows with an increase of 4% of the polymer, but it is still lower than the damping ratio of natural sand.SEM observations showed that dynamic parameters are controlled by polymer texture between soil particles, and the thicker this texture (from a certain level onwards), the more formable the sample will be, and the less elasticity modulus will be.Milad Banitalebi Dehkordi: Conceptualization, Investigation, Methodology, Formal analysis, Visualization, Preparation, Validation, Writing - original draft, Writing - review & editing, Resources. Mohammadali Rowshanzamir: Conceptualization, Validation, Writing - review & editing, Supervision, Formal analysis, Visualization. Sayyed Mahdi Hejazi: Supervision, Validation, Investigation, Resources, Review & editing. Naeim Pishehvarzad: Investigation, Resources, Review & editing. Hamid Hashemolhosseini: Supervision, Review.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.Experimental investigations on cryogenic cooling by liquid nitrogen in the end milling of hardened steel► Investigated the machinability of LN2 cooling on AISI H13 hardened tool steel. ► LN2 machining provides lower tool wear, surface roughness and cutting forces. ► Better cooling and lubrication effect through reduction in the cutting temperature. ► The reduction in the cutting temperature is substantial at a lower cutting speeds. ► Smaller serrated teeth are produced indicating that lower shearing forces.Difficult-to-machine materials, such as AISI H13 hardened steels, are widely used in extrusion dies, die casting dies, hot forging dies and plastic mould dies due to their higher resistance to thermal shock and thermal fatigue, high temperature strength, good toughness, ductility, and dimensional stability during hardening. While machining hardened steel, the contact friction between the tool–workpiece and tool–chip interfaces generates high temperatures on the cutting tool. This generated heat increases workpiece surface roughness, and decreases the tool life and the dimensional accuracy of the work material. The cutting fluid is invariably used as a coolant to reduce the heat generated and friction between the tool–workpiece and the tool–chip interfaces, and also wash away the chips from the tool. Problems with the use of conventional coolants are the potential health hazards to the operating personnel which on contact or inhalation of mist or fumes, and improper disposal of cutting fluids that cause serious environmental problems, such as water and soil pollution Researchers have investigated the use of cutting fluid with the high pressure coolant to reduce the cutting temperature and improve machining performance Recently, experiments have been conducted to study the effect of LN2 cooling on tool wear, surface roughness and dimensional consistency in the turning operation In machining, the application of LN2 into the tool–chip interfaces should provide effective cooling and lubrication without polluting the environment. However, more work is required to explore the potential of using LN2 cooling in the machining of hardened steels. Therefore, a new LN2 cooling system was developed for reducing the cutting zone temperature. In this system, the LN2 is applied to cool the cutting zone, particularly tool–chip interface by using nozzle. LN2 can easily penetrate into the tool–chip interface to reduce the cutting temperature. The objective of this research is, to experimentally investigate the influence of three machining conditions such as dry, wet and LN2 cooling on the cutting temperature, tool wear, surface roughness, and cutting force, for end milling of hardened AISI H13 tool steel under different cutting speeds and feeds.The experiments were conducted on a CNC vertical machining centre (ARIX VMC 100). The workpiece material for investigation was AISI H13 hardened tool steel of hardness 52 HRC; It had material dimensions: 150 × 100 × 50 mm. Flat bottom end mill P20 TiAlN PVD coated carbide inserts were used in this study. The cutting parameters used in this experiment are listed in . Dry machining was performed without using any coolant. The problem with dry machining is less cooling ability of air, making it ineffective for the removal of heat during machining. In general, the rate of heat removal depends on the convection heat transfer coefficient and temperature of the cutting fluid. An increase in the convection heat transfer coefficient with high pressure air (≈2000 W/m2 |
K at pressure of 4–7 bar) compared to dry machining (≈20 W/m2 |
K) . A 150 mm long slot was machined during each pass for the end milling experiments. The effects on cutting parameters under dry, wet and LN2 machining conditions were measured. shows the variations of cutting temperature for different cutting speeds under dry, wet and LN2 machining conditions. It was observed that as the cutting speed is increased, the cutting temperature increases under all the machining conditions, which may be attributed to an increase in the cutting energy dissipation rate. The higher temperature in the cutting zone leads to softening of the cutting tool, which accelerate the tool wear and its breakage. Therefore, by reducing cutting speed improves the machinability indices. It can be seen that lower temperatures are observed with LN2 machining. The cutting temperature at a cutting speed of 125 m/min and feed rate of 0.02 mm/tooth was 582 °C, 396 °C and 246 °C for dry, wet, and LN2 machining, respectively. The cutting temperature for LN2 cooling was reduced by 57% over the dry machining and 37% over the wet machining cases. This is because when LN2 is supplied onto the tool–chip interface, it evaporates quickly by absorbing the heat resulting in the reduction of the cutting temperature. As the cutting speed was increased from 75 m/min to 100 m/min, the variation in reduction of the cutting temperature due to LN2 cooling was found to be 1.93% and 3.45% compared to dry and wet machining. When the cutting speed was increased further from 100 m/min to 125 m/min, the variation in reduction of the cutting temperature due to LN2 cooling was 3.17% and 4.37% respectively. At higher cutting speeds, the cutting temperature is increased due to the nature of the chip–tool contact and heat transfer during machining shows the surface roughness (Ra) of the workpiece at different cutting speeds for the three machining conditions. It can be observed that with an increase in the cutting speed, the surface roughness decreases for all the machining conditions. In general, an increase in the cutting speed decreases the surface roughness a–c shows the effects of the cutting speed on the feed force (Fx), normal force (Fy), and axial force (Fz) under all machining conditions at a constant feed rate. In general, the cutting force decreases with increasing cutting speeds shows the SEM photographs of the worn insert edges after 30 min of machining under dry, wet, and LN2 machining conditions. In the milling process, the cyclic heating and cooling at the cutting edge results in very high stress and higher cutting temperature. As the cutting is progressed, initiates thermal cracking and edge chipping. It is hypothesized that the typical failure modes in the cutting tool inserts are thermal cracking and edge chipping. It was also observed that the chipping of the cutting edge was obtained under all three machining conditions. In dry cutting, severe chipping of the cutting edge was observed, followed by wet, and then LN2 machining. In LN2 machining, lesser chipping was found, compared to dry and wet machining. The chipping of the cutting edge was observed in wet machining due to the formation of thermal cracks near the cutting edge resulting in a fracture of the cutting edge. However, cutting inserts in LN2 machining were less seriously affected by thermal fatigue. This is due to reduced temperature in the cutting zone, which will remove the generated heat effectively and improve the tool life. shows SEM images of chip shapes for a cutting speed of 75 m/min, a feed rate of 0.02 mm/tooth, and a depth of cut of 0.5 mm under dry, wet, and LN2 machining conditions. In LN2 coolant machining, shorter chips are obtained compared to those in dry and wet machining. This may be attributed mainly due to better penetration of LN2 into the tool–chip interface, resulting in the reduction of the cutting temperature. At a lower temperature, the chip cannot promote curl due to increased chip hardness and lower ductility. Further, the colour of the chips obtained under the three machining conditions is also different. In dry cutting, the chips produced are dark blue in colour, which was caused by the extreme heat generated at the tool–chip interface that results in burnt chips. The chips obtained in the case of wet machining are black, which also indicates intense heat generated at the tool–chip interface. This is because the conventional coolant does not penetrate into the tool–chip interface resulting in an inadequate lubrication effect, whereas, the chips produced by LN2 machining were silver in colour indicating chips that were not burnt, due to the better cooling and lubrication effect. shows SEM images of the chip morphology for a cutting speed of 125 m/min, a feed rate of 0.02 mm/tooth, and a depth of cut of 0.5 mm under dry, wet, and LN2 machining conditions. In dry cutting, large serrated teeth are obtained indicating the heavy shearing action at the cutting zone. In the case of wet machining also, similar serrated teeth are produced due to the intensive shearing action. This can be attributed to the fact that conventional coolant does not provide effective cooling and lubrication at the tool–chip interface. However, smaller serrated teeth are produced under LN2 machining, indicating lower shearing forces compared to those under dry and wet machining. This is because, the penetration of LN2 into the tool–chip interface results in the formation of a nitrogen cushion, which reduces the friction.The experiments were conducted on end milling of hardened AISI H13 tool steel using LN2 coolant to investigate cutting performance and changes in cutting temperature, tool wear, surface roughness, cutting force, tool wear morphology and geometry of the chip shape. Results for application of LN2 coolant was compared to those for dry and wet machining. Based on the results of the experimental investigation, the following conclusions are drawn.LN2 machining provides lower cutting temperature, tool wear, surface roughness and cutting force compared to those under dry, wet machining conditions. This is because of the better cooling and lubrication effect through substantial reduction in the cutting zone temperature. The reduction in the cutting temperature using the LN2 coolant is substantial at a lower cutting speeds.The experimental results indicate that compared to dry and wet machining, LN2 machining reduced the cutting temperature in the range of 57–60% and 37–42%; while the tool wear decreased approximately in the range of 29–34% and 10–12%; further, the average surface roughness decreased moderately in the range of 33–40% and 25–29%.The cutting forces (Fx, Fy and Fz) in the LN2 machining was reduced in the range of 22–24%, 19–24% and 20–26% respectively compared to dry machining, while the reduction of the cutting forces range by 4–9%, 9–12% and 11–15% compared to wet machining respectively.The SEM photographs of chips showed that the shearing action in the case of LN2 machining was lower indicating that small serrations, which were relatively higher in the case of dry and wet machining. The chip curl cannot be promoted under the LN2 machining condition causing short chips are produced.The application of the LN2 coolant in the end milling of hardened AISI H13 tool steel can provide not only environmental friendliness, but also an improvement in the tool life, surface finish and a reduction in the cutting force.Effects of the thickness of Ti buffer layer on the mechanical properties of TiN coatingsIn order to improve the impact adhesion property of TiN hard coating maintaining their hardness and wear resistance, the ductile Ti buffer layer which could absorb impact energy was inserted in the middle of TiN film as well as the Ti interlayer on substrate. These TiN films were deposited using cathodic arc ion plating with various thickness of Ti buffer layers between 0.24 and 0.75 μm. The result of X-ray diffraction analyses showed that the preferred orientation of TiN is (1 1 1). The Ti interlayer grown on the substrate has the preferred orientation of (1 1 1). However, the Ti buffer layer grown on the TiN layer has a (0 0 2) plane, which establishes the epitaxial relationship with the TiN(1 1 1) plane. The elastic modulus and hardness of Ti buffer layer with 0.48 μm thickness were measured to be approximately 220 and 8.2 GPa, respectively, which were higher than values (165, 6.5 GPa) of the Ti interlayer. The results of impact adhesion test under the impact load of 2.5 kgf showed that the indentation cavity volume and circular cracks of TiN coating were greatly reduced with increasing the thickness of Ti buffer layer. This tendency can be attributed to the effective absorption of impact energy by the Ti buffer layer.Recently, hard coatings such as TiN, TiCN, TiAlN, CrN, BN and DLC are used for cutting tools and wear applications. The use of these hard coatings has greatly improved the tribological performance of tool and machine elements In this article, we propose the new type of TiN coating for which the Ti buffer layer is deposited between TiN films as well as the Ti interlayer between substrate and TiN film, as shown in , to improve impact adhesion property maintaining their hardness and wear resistance. The elastic modulus, hardness and preferred orientation of each layer composing this TiN coating were evaluated and also its mechanical properties were compared with those of the TiN coating without the Ti buffer layer.The coatings were deposited on AISI H13 steel and Si(1 1 1) wafer by the cathodic arc ion plating method. The AISI H13 steel substrate (diameter: 50 mm, thickness: 5 mm) was mirror polished (Ra=0.1 μm) and treated with ultrasonic cleaning. Before the deposition, the chamber was purged by Ar gas pumping down to 2×10−5 Torr and the surface of substrate was cleaned by bombardment of arc ion vapor generated between the substrate and Ti target (diameter: 65 mm, purity: 99.95%). This ion bombardment was carried out by applying a bias voltage of −700 V to the substrate for 2 min at an Ar pressure of 3.5×10−3 Torr. Optimum deposition conditions such as target power, substrate bias voltage, target-to-substrate distance and working pressure were determined through preliminary experiments. The detailed deposition conditions are listed in The microstructure and thickness of coatings were observed using scanning electron microscope (SEM: HITACHI S-2400). SEM observation was performed on the cross-sections of films deposited on Si(1 1 1) wafer. The depth profile of chemical composition was evaluated by Auger electron spectroscopy (AES: PHI-670). The preferred orientations of Ti interlayer, Ti buffer layer and TiN were observed by X-ray diffraction (XRD: SEIFERT 3000PTS, Cu Kα radiation) and their elastic modulus and hardness were measured by nano-indentation (Nano-indenter II, MTS). To evaluate the impact failure property of modified TiN coatings, the impact test using an AISI52100 steel ball (diameter: 6 mm, Hv=850) was carried out by impressing a normal impact load of 2.5 kgf to them 1.5×103 and 8×103 times. The impacted area was analyzed by SEM and energy dispersive X-ray (EDS) analysis. shows the cross-sectional SEM micrographs of coatings as a parameter of Ti buffer layer thickness (x value). All the films show the dense columnar structure grown perpendicular to the substrate surface, which corresponds to the Zone T (T/Tm=0.1–0.5) in the Thornton's structure zone model The depth profile of chemical compositions of coatings deposited on Si wafer was measured by AES, and its result is illustrated in . The carbon and oxygen are rarely found throughout the depth of coating, showing clearly that films are deposited without their contamination. Also this figure shows that the atomic content ratio of N to Ti in the TiN layer is 0.9–0.92 and N is not observed in both Ti layers. Therefore, it is expected that N in the TiN layer is hardly diffused into Ti layers during deposition process, and the pure Ti buffer layer is formed between TiN layers. As reported previously in Ref. The XRD patterns of coatings deposited on the AISI H13 substrate as a parameter of x value are illustrated in . In the case without Ti buffer layer (substrate/Ti interlayer (b)), the TiN peak which has the preferred orientation of (1 1 1) at 2θ=36.5° is observed but the Ti peak is not done because the thickness of Ti interlayer is too small.In the cases, for which the Ti buffer layers exist, shown in c–g, the Ti peaks appear and their preferred orientation is (0 0 2) at 2θ=38.3°. The intensity of Ti(0 0 2) peak increases with increasing thickness of Ti buffer layer, indicating that the Ti buffer layer between TiN layers has a preferred orientation of (0 0 2). shows the XRD patterns of the films at each step of processes depositing Ti interlayer, Ti buffer layer and TiN layers. From a, it is noted that the Ti interlayer has a preferred orientation of (1 1 1) at 2θ=62.8°. From these results, the deposition mechanism of TiN coatings with Ti buffer layer could be defined as follows: first, Ti ions and atoms with high energy shows the microhardness of TiN coatings. The microhardness in the case without the Ti buffer layer is approximately Hk=2850 but, when the Ti buffer layer exists, its value decreases to Hk=2300 for x=0.75 μm with increasing x value. This phenomenon can be attributed to the insertion of ductile Ti buffer layer and decrease of residual stress. The residual stress of TiN coating for x=0.75 μm decreases to approximately a half of that in the case without the Ti buffer layer, as shown in The hardness of Ti interlayer and Ti buffer layer could not be measured using the microknoop hardness tester because their thickness were very small. Therefore, the hardness and elastic modulus of Ti interlayer, Ti buffer layer and TiN layer were measured by nano-indentation tester. Their results are summarized in . The hardness and elastic modulus of Ti buffer layer for x=0.48 μm are approximately 8.2 and 220 GPa, respectively, which are larger than those (5.5 and 165 GPa) of Ti interlayer. This result can be attributed to the difference between the preferred orientations of Ti interlayer and buffer layer.The results obtained in the impact test are given in . After impacts of 1.5×103 times, the failures of TiN coatings with or without the Ti buffer layer had almost the same characteristics that a few circular cracks were observed in the peripheral zone a). The result from EDS analysis of these zones, the Fe (above 10 wt.%), which is the substrate element, was detected. This result noted that the TiN film was separated completely in these zones. In the cases of TiN coatings with the Ti buffer layer, the number of circular cracks in the peripheral zone largely decreases with increasing x value, as shown in b–d. Especially for the TiN coating of x=0.62 μm, its number is the smallest and the significant coating delaminations as observed in the TiN coating without the Ti buffer layer do not exist in the intermediate and central zones of impact cavity. shows the impact cavity volumes of specimens formed after the impact test. This parameter is used to evaluate the impact test, because the results from the failure observation are in good correlation with the indentation volume of cavities formed in the impact test , all the coatings for 1.5×103 impacts have almost the same value of indentation volume, but for 8×103 impacts the difference in indentation volume is certainly shown. The impact cavity volume of TiN films greatly reduces with increasing x value, and in the case of x=0.62 μm, the impact cavity volume decreases to approximately a half of that in the case without the Ti buffer layer. In the impact test, the coating system under the indenter is deformed plastically, so that the hard coating starts to macro-crack to reduce its internal stress and the wear at the macro-crack, increases with the number of impacts, resulting finally in delamination of coating In this work, we have proposed the TiN coatings with the Ti buffer layer as well as the Ti interlayer synthesized by cathodic arc ion plating, in order to improve the impact failure property maintaining their hardness and wear resistance properties. The properties of these coatings have been studied by evaluating the microstructure, composition, preferred orientation and impact failure resistance. The results are summarized as follows:While the Ti interlayer has the preferred orientation of (1 1 1) at 2θ=62.8°, the Ti buffer layer has the preferred orientation of (0 0 2) at 2θ=36.5°, which has the epitaxial relationship with the TiN(1 1 1) plane.The AES analysis has shown that the N-to-Ti atomic ratio in the TiN layer is 0.9–0.92 and the N is not observed in the Ti interlayer and buffer layer, indicating that N in the TiN layer hardly diffuse into Ti buffer layer and the pure Ti buffer layer is formed between the TiN layers.The hardness and elastic modulus of Ti buffer layer (x=0.48 μm) are approximately 8.2 and 220 GPa, respectively, which are higher than those (6.5 and 165 GPa) of Ti interlayer. The results can be attributed to the difference between the preferred orientations of Ti interlayer and buffer layer.The delaminations and indentation cavity volume of TiN coatings greatly reduce with increasing the thickness of Ti buffer layer. This tendency can be attributed to the effective absorption of the impact energy in the Ti buffer layer.A large-displacement CMOS micromachined thermal actuator with comb electrodes for capacitive sensingIn this paper, we present the design and characterization of a large-displacement thermal actuator fabricated in a conventional CMOS process. The thermally driven microstructure is fabricated by two dry etching steps after the completion of CMOS. The structure contains multiple layers of metal, silicon dioxide, and polysilicon. Capacitive sensing with vertical comb electrodes is used for detection of the actuator displacement. The microactuator is characterized by the static and dynamic measurements, showing a measured out-of-plane displacement of 24 μm at an applied power of 17 mW, a thermal time constant of 0.24 ms, and a mechanical resonant frequency at 16.8 kHz with a quality factor of 21. The measured minimum input-referred noise voltage of the sensing amplifier is 16.9μV/Hz, equivalent to a minimum input-referred noise displacement of 0.34nm/Hz at a displacement of 6 μm. The fabricated devices, after additional post micromachining, are intended for use as scanning cantilevers in atomic force microscopy.Thermal actuation is known for its capability in producing a large and linear displacement with respect to a heating power. The driving mechanisms include the well-known bi-morph (or multi-morph) effect Fabrication of thermal actuators in a CMOS process provides the benefits of monolithic integration and convenient signal processing for multiple signals This work presents the design and fabrication of a large-displacement CMOS-micromachined thermal actuator with vertical comb electrodes for capacitive sensing for fast surface imaging as being performed by atomic force microscopy (AFM). In a commercial AFM, the sensed signal of the tip motion due to the tip-surface interaction is provided by optical detection for the closed-loop piezo-actuator control, which constantly keeps a proper tip-sample contact force during scan. Optical detection and piezoelectric actuation are not easy to make CMOS-compatible for making a scanning probe array. Prior work in the CMOS-compatible AFM scanning probe array mainly uses piezoresistive sensing Fabrication of the devices starts with the TSMC 0.35-μm two-polysilicon four-metal (2P4M) CMOS process, followed by the post-CMOS micromachining steps similar to those described in . Our aim is to fabricate a composite microstructure that contains metal, dielectric, and polysilicon layers for the respective actuation and sensing purposes. First an anisotropic dielectric reactive-ion etch (RIE) with CHF3/O2 plasma is performed to define the structural sidewalls with the top metal layer being used as an etch-resistant mask. A 2-μm gap or less can be readily achieved in this step to define the spacing of the sensing electrodes, which is better than the method that uses stacked metal and via layers as the sacrificial materials The targeted actuator displacement is 7 μm for the scanning cantilever application. The displacement is within the detection range as limited by the thickness of the capacitive sensing electrodes defined by the post CMOS fabrication. As will be shown later in the experimental results, the thermal actuator can move more than the thickness of the sensing electrodes. For thermal actuation, the maximum heating temperature should not exceed the limit that metallization layers can tolerate while achieving a large displacement.A top view of the thermal actuator design is shown schematically in (a). The design is a cantilever structure with a polysilicon heater routed from the anchor to about one half of the beam length. The rest of the structure without the polysilicon is intended to operate at a lower temperature than that of the heated part such that it mainly provides linear amplification of the cantilever motion. To achieve a reduced out-of-plane rigidity and thus a large thermomechanical displacement, the cantilever design mainly contains three metal layers (metal-1 to metal-3) and the inter-metal dielectric layers without inclusion of the top metal-4, resulting in a total thickness close to 5 μm. We determine not to further reduce the thickness with the metal-2 or metal-1 as the top layer because a larger structural curl can occur in these cases. The beam cross section at the end of the heater is shown in (a). The sensed signal from the comb electrodes is routed by the narrow metal-1 line. In order to promote heat conduction across the beam cross-section to get a small thermal time constant, the polysilicon heater is electrically connected to its top metal layers with several vias as shown. The comb electrodes as shown in The original analysis of a thermally actuated bi-morph cantilever can be found in . The simulation of the actuated cantilever as shown in indicates that a downward displacement is produced because the coefficient of thermal expansion for metal (2.5 × 10−6 |
°C−1) is much larger than that of silicon dioxide (0.5 × 10−6 |
°C−1). A displacement of 11.5 μm is obtained for an applied power of 10 mW, averaging 1.15 μm/mW. The thermal time constant of the cantilever can be estimated by a lumped-parameter analysis using the relation τ |
= |
L2/αeffwhere h is the thickness, ρ the mass density, cp the specific heat, and k is the thermal conductivity of a film. The summation is over all the films on the cantilever. Using thermophysical properties and thicknesses for aluminum, silicon dioxide, and polysilicon layers, αeff is estimated to be 4.4 × 10−5 |
m2/s. From the values of L (75 μm) and αeff, the thermal time constant is calculated to be 0.12 ms.The vertical capacitive comb electrodes have a total of 18 rotor fingers, with an overlap of 50 μm, a gap of 2 μm, and a thickness close to 7 μm, giving a nominal sensing capacitance of 55 fF by the parallel-plate capacitor approximation. The continuous-time capacitive sensing scheme as shown in is used for detection of the cantilever motion. The single-ended signal is taken from the mid-point between the sensing capacitance Cs and the capacitance Cin at the pre-amp input. After modulation, the pre-amp signal is demodulated and low-pass filtered to obtain the baseband output signal. The applied modulation frequency is intended to be high enough in order to avoid the flicker-noise region. The dc bias at the input sensing node is provided by a transistor operated in the sub-threshold region. This bias scheme is preferred over the use of a reset transistor in order to avoid charge injection in the single-ended sensing scheme. Based on the applied gate-to-source voltage, the biasing transistor can provide a resistance value more than a few hundred megaohms in the simulation, which is large enough in comparison with the impedance of the pre-amp input capacitance at the modulation frequency. The pre-amp is a unity-gain buffer implemented by using a two-stage operational amplifier. The op-amp design uses PMOS input transistors for reduction of the flicker noise at low frequencies. The transistor sizes are designed to get a low thermal noise and an input capacitance value comparable to that of the sensing capacitance. By simulation, the op-amp achieves an open-loop gain of 69 dB, a unity-gain frequency of 12.7 MHz, a phase margin of 60°, and an input capacitance of 45 fF.The micrograph of the released thermal actuator is shown in . The sensing amplifier is covered by the top metal and moved away from the etched edges by 60 μm for etch protection. The dynamic response of the actuator in the out-of-plane motion was measured by a Laser Doppler Vibrometer (LDV) in which the actuator motion was optically detected and then converted to an electronic output. The dynamic response shown in indicates that the primary mode is 16.8 kHz in the out-of-plane direction. The main mechanism for energy dissipation is attributed to Couette damping between the sensing electrodes, which results in a measured quality factor of 21, and a damping ratio of 0.024. The measured value is in good agreement with the calculated value of 26 from the Couette damping coefficient expressed by B |
= |
ηA/g, where η is the air viscosity (77 μN s/m2), A the total overlapping area of sensing electrodes, and g is the electrode spacing. The plot also shows that the second mechanical mode occurs at 32.7 kHz. The resistance of the polysilicon heater was measured at 995 Ω, as compared to 803 Ω obtained from circuit extraction. Temperature distribution of the heated microstructure for each applied voltage was obtained by infrared measurements (InfraScope II from Quantum Focus Instruments). The whole die was pre-heated close to about 80 °C before measurement for enhancement of the measuring accuracy. As shown in , the highest temperature occurred near the end of the heating resistor and was measured around 232 °C at an applied power of 17 mW. shows the measured resistor values with respect to the heater temperature. The linear relationship indicates that the temperature coefficient of the polysilicon resistor is 0.1% K−1. The actuator displacement was measured by a Wyko NT1100 optical profiler for each applied power. The actuator has a measured radius of curvature of 4.5 mm at rest. The curve in shows that the maximum tip displacement is 24 μm toward the substrate at 17 mW, averaging 1.4 μm/mW. The result implies that the targeted 7-μm displacement requires a heating power about 5 mW.The pre-amp input capacitance was first measured by using a test circuit which had a fixed 1-pF capacitor connected to the input ac source. The frequency response of the pre-amp output over the ac input was measured by an Agilent 4395A network/spectrum analyzer, and the measured gain led to an input capacitance of 55 fF. Then the frequency response of the pre-amp with the micromachined capacitor was measured as shown in . The measured bandwidth is 12.1 MHz, close to the simulated value of 12.7 MHz. By using the previously measured input capacitance, the initial sensing capacitance is calculated at 40 fF, about 20% less than the calculated value. The first pole frequency as shown in is determined by the resistance of the biasing transistor and the total capacitance seen at the input node. The result leads to a measured resistance about 1.5 GΩ for the biasing transistor. This value is almost four orders of magnitude larger than the impedance of the MEMS capacitor at the applied modulation frequency. The pre-amp signal was modulated at 10.5 MHz in order to avoid the flicker noise, and measured by a spectrum analyzer at a 10-Hz resolution with respect to the actuated displacement. The spectrum with no applied actuation power is shown in (a) with a magnitude of 667.7 mV, and the minimum input-referred noise voltage is 16.9μV/Hz. The relationship of the sensed voltage with respect to the actuator displacement is plotted in (b). By calculation, the total sensing capacitance, Cs=∑iCs,i, is the summation of the individual sensing capacitance Cs,i contributed by each rotor electrode, which has a different rotor displacement than that occurred at the tip. The sensed voltage at each tip displacement is obtained by using the capacitive divider as shown in , and then the sensitivity is calculated using the derivative of the sensed voltage with respect to the tip displacement. shows the measured and calculated sensitivities within the sensing range, which is 7 μm of the electrode thickness. The value of the measured sensitivity is lower at each displacement because the relative motion between electrodes is not as large as expected due to thermal crosstalk to the stator as shown in . A maximum measured sensitivity of 5 × 104 |
V/m occurs at a displacement of 6 μm. This subsequently leads to a minimum input-referred noise displacement of 0.34nm/Hz.The transient response of the actuator by thermal actuation was obtained by measuring the pre-amp output when a 200-Hz square-wave heating voltage of 2.3 V was applied. illustrates the measured signal after modulation. The measured thermal time constant is 0.24 ms for the envelope to rise from the initial value to 63.2% of the steady state. The time constant is smaller than the value obtained by the lumped-parameter analysis, and is equivalent to a pole frequency of 4167 rad/s for a first-order linear system. The transient response shows no significant overshoot even though the actuator has a very lightly damped characteristic as shown in . The reason is that the mechanical resonant frequency is 25 times larger than the pole frequency due to the thermo-mechanical transduction. As the heat is produced, the thermo-mechanical force is generated at a relatively low speed so the actuator can move almost quasi-statically to the set point without causing a large oscillation.This work presents a multi-morph thermal actuator fabricated in a conventional CMOS process. To our best knowledge, this is the first reported large-displacement thermal actuator with integrated capacitive sensing. The vertical capacitive comb electrodes are adopted instead of parallel-plate capacitors because the latter is not suitable for detection of large displacements. The experimental results show that a displacement of 24 μm is achieved at 17 mW with a maximum measured temperature at 232 °C. With a sensing capacitance of 40 fF, the minimum input-referred noise displacement of the sensing pre-amp is 0.34nm/Hz. For a closed-loop control bandwidth that is determined by the thermal time constant of the actuator, the sensor noise will limit the minimum detectable signal to 8.8 nm.Many aspects in the static and dynamic performances can be further improved in the future design. For examples, the structural curl can be reduced if the top metal-4 layer is added to increase the total thickness, although a higher temperature is expected in order to get the same displacement as in the current design. The capacitive sensitivity can be enhanced by using a more advanced CMOS process that has more metal layers to define the thickness of sensing electrodes. For instance, some foundries already provide up to eight metallization layers in their CMOS processes. Another advantage by having thick electrodes is to allow the entire actuation range to be covered by capacitive detection, as the current result shows that the actuator moves more than the sensing electrode thickness.Li-Sheng Zheng received his BS degree in electrical engineering in 2003 from the Yuan Ze University, and his MS degree in electronics engineering from the National Tsing Hua University in 2005. His research interests include CMOS-compatible microsensors, microactuators, and control system design.Michael S.-C. Lu received his BS and MS degrees in power mechanical engineering from the National Tsing Hua University, Hsinchu, Taiwan, in 1991 and 1993, respectively. In 2002, he received the PhD degree in electrical engineering from the Carnegie Mellon University, where he completed the work on the parallel-plate capacitor control of a CMOS-micromachined microactuator for a MEMS-based micro disk drive. Since August 2002, he has been an assistant professor with the Department of Electrical Engineering and the Electronics Institute at National Tsing Hua University. His research interests include CMOS-compatible sensors and actuators, MEMS scanning probes, and control systems.A hybrid mode/Fourier-transform approach for estimating the vibrations of beam-stiffened plate systemsIn this paper, a hybrid Mode/Fourier-transform approach is described for estimating the vibration response of a structure such as a beam-stiffened plate with excitation applied to the beam. The beam is defined deterministically in terms of its modes, whereas the plate is treated approximately by assuming it extends to infinity. Equilibrium and continuity conditions are approximated along the interface between the beam and the plate in the wavenumber domain by a Fourier transform method. Consequently, both the dynamic response of the beam and the power transmitted to the plate can be simply estimated. Meanwhile, the dynamic interactions of the coupled system can be determined. These depend on the correlations between the modal properties of the beam and the wave motions of the plate. Expressions are given for the effective mass (density) and effective loss factor the plate applies to each mode of the beam. When a locally reacting plate approximation is incorporated into the Mode/Fourier-transform procedure, a simpler ‘locally reacting impedance method’ can be developed. The results are discussed and compared to those of fuzzy structure theory. Numerical examples are presented.Many practical engineering structures are built up from beams and plates. One such example is the machinery foundation of a ship, which is constructed from a collection of stiff beams and large flexible plates. When excited by external vibration sources, wave motions are generated in both beams and plates. Usually, the wavelengths in the stiff beams are relatively long compared to those in the plates. The differences in wavelengths may then present a number of challenges to predicting the vibrations of beam/plate built-up structures This paper concerns a simple method for approximately modelling a certain class of beam/plate built-up structures. Being broadly representative of machinery foundations, a beam-stiffened plate system, such as that shown in is considered with external excitation sources applied to the beam. The beam is assumed to be well-defined with a long-wavelength and/or a low modal density, while the plate has a relatively short-wavelength and/or a high modal density, perhaps with complex boundary conditions. Under such circumstances, therefore, the frequency–response–functions (FRFs) of the stiff beam and the power transmitted to the flexible plate are of interest.In the following section, a hybrid Mode/Fourier-transform (FT) approach is described by simply approximating the large flexible plate receiver as if it extended uniformly to infinity. It is a combination of conventional modal analysis and FT methods, and is used to predict both the FRFs of the beam and the power transmitted to the plate. The analysis concerns the dynamic correlations between the modal properties of the beam and wave motion in the plate. Then in a locally reacting plate approximation It is expected that the Mode/FT approach can provide a useful methodology for predicting the vibrations of beam/plate coupled structures, in that it is able to deal with the large dynamic mismatch between the beam and plate components and at the same time can overcome the practical difficulty in determining the exact dynamic properties of the large, flexible plate. In addition, it gives insight into the vibration and coupling of general built-up structures comprising substructures which are dynamically mismatched.It is quite common to estimate the vibration properties of a large flexible plate, especially in a frequency average sense, as if it extended uniformly to infinity. In the Mode/FT approach the vibration of a beam attached to an infinite plate is considered. Central to the Mode/FT approach is to approximately enforce the equilibrium and continuity boundary conditions along the interface between the beam and the plate in the wavenumber domain. The correlations between the modal properties of the beam and the wave motions of the plate can then be determined, and hence both the FRFs of the beam and power transmitted to the large flexible plate, as well as the dynamic interactions within the beam-stiffened plate system, can be found. shows the beam and its force loadings. The beam is assumed to be straight and uniform. xb is the local co-ordinate of the beam, and fe(xb) and fIb(xb) are the amplitudes of the external and interface forces acting on the beam, respectively. ( contains a list of symbols.) Time-dependent behaviour of the form exp(jωt) is assumed, and the explicit time dependence will henceforth be suppressed. By conventional modal analysis where φb,n is the nth natural mode of the beam when it is separated from the plate, and wb,n is the corresponding modal amplitude. For convenience, normalized mode shape functions are used in the above equation, so thatwhere Lb is the length of the beam. From where Yb,n is the nth modal receptance of the uncoupled beam, and fe,n and fI,nb are, respectively, the nth modal forces corresponding to fe(xb) and fIb(xb). These terms are given byHere mb is the mass per unit length of the beam, and ωb,n and ηb,n are the nth natural frequency and modal loss factor of the uncoupled beam, respectively. shows the plate and its force loadings along the interface, where (xp,yp) are the local co-ordinates of the plate, and (xpI,ypI) and fIp(xpI,ypI) are, respectively, the interface locations on the plate, and interface force distribution.The one- and two-dimensional FTs are, respectively, defined as It is assumed that the interface starts from the point (xpI,ypI)=(xp,yp)=(0,0) and ends at (xpI,ypI)=(xp,yp)=(Lb,0) along the line ypI=yp=0. The interface force acting on the plate (per unit) coupling area can be expressed as has a unit of N/m. The equation of motion of the plate is given by where Dp and mp are, respectively, the bending stiffness and the mass per unit area of the plate, and ∇ is a differential operator defined aswhere Wp(kx,ky) and FIp(kx) are, respectively, the FTs of wp(xp,yp) and fIp(xp,yp). The inverse FT of the plate displacement, by The plate displacement along the interface can then be expressed asBy integration over ky, the above equation can be re-written aswhere Wp(kx) is the FT of the plate displacement along the coupling line in the wavenumber domain kx, and is given byThe above equation gives the relation between the interface displacement and the interface force in the wavenumber domain. As a result, the line-impedance of the plate along the interface can be expressed asIf the damping of the plate is negligible, the above equation is such that implies that only the waves propagating in the beam faster than the wave motion in the plate can transmit energy into the plate. Hence it is reasonable to assume that energy transmitting, non-reactive interaction between a beam and an infinite plate mainly involves wavenumbers within the range |kx|<|kp|.From the above description, it is seen that the local co-ordinates of the beam and plate are related such that xpI=xp=xb=x, where 0⩽x⩽Lb. The equilibrium and continuity conditions along the interface between the beam and the plate areA new set of orthogonal functions is now defined asTaking the FT of the above equation, gives, it is seen that the plate interface force and displacement response are related, in the wavenumber domain, bywhere Wp(k) is the FT of wp(x,0), given by, the displacement of the beam may be re-written aswhere Wb(k) is the FT of wb(x), given byIt is now assumed that the displacement of the plate outside of the interface region gives a negligible contribution to the integral in is thus equivalent to assume that Wp(k) is dominated by the contribution from wp(x,0) in the range of 0⩽x⩽Lb. Substituting denotes the complex conjugate. Let both sides of and integrated over k from −∞ to +∞. If it is assumed that Zp(k) changes slowly compared to Φb,n(k) so that the cross couplings between the modes of the beam can be ignored, it follows that shows the coupling relations between the line-impedance of the plate Zp(k) and the mode shapes of the beam. Hence the interactions between the wave motion in the plate and the modal properties of the beam can be determined., the nth modal amplitude of the beam, wb,n, after coupling to the plate, can be expressed as shows that the nth modal impedance of the beam, after coupling to the plate, is increased by Zn. Hence Zn may be called the ‘plate-loaded modal impedance’, which depends on both the plate properties kp and Dp, and the beam property φb,n(x), by the relations given in it is implicitly assumed that the plate loads each beam mode independently and hence that the cross-mode loading is negligible., the beam displacements can then be expressed asThe power transmitted from the beam to the plate is given by, the transmitted power can be expressed as indicates that only the components of the mode shapes of the beam with wavelengths larger than the plate wavelength can transmit significant power to the plate. Otherwise, the components generally only cause near-field wave motions in the plate.In summary, the Mode/FT approach can be briefly divided into the following steps:(1) The beam model is defined in terms of its uncoupled natural modes (), while the plate model is described in the wavenumber domain by a line-impedance ((2) By introducing a new set of orthogonal functions in the range −∞<x<+∞ based on the beam modes φb,n in the range 0<x<Lb (), the plate interface force can then be decomposed in terms of ). As a result, a new relation between the plate interface force and displacement can be given ((3) When the plate displacement outside of the interface region is ignored (), an estimate can then be made of the relation between displacements of the plate (along the interface) and beam in the wavenumber domain (). Consequently, an approximate relation between the plate interface force and the beam displacement can be established ((4) The line-impedance of the plate is assumed to change slowly with k compared to Φb,n(k). By the orthogonality properties of φb,n and hence , the interface force and displacement relation can then be simply estimated (). Finally, the beam displacement and the power transmitted to the plate can be predicted in a simple manner. the cross-mode coupling interaction has been ignored. Such a simplification is quite reasonable if the uncoupled mode shape φb,n has a strong sinusoidal component at a given wavenumber (as it generally will for a uniform, straight beam), so that |Φb,n(k)|2 is sharply peaked in the wavenumber domain. These cross-mode coupling terms are expected to be less important for the higher modes of the beam.The dynamic interactions between the beam and the plate are given by . The modal receptance Yb,n of an uncoupled beam is given in , while the modal receptance Yb,n′ of the beam after coupling to the plate becomesThe term jωZn can be separated into real and imaginary parts so thatwhere Kn1 and Kn2 are given, respectively, as indicates that the plate in effect adds mass mn and damping ηn to each mode of the beam. The energy dissipated by the induced effective damping corresponds to the energy transmitted from the beam to the plate. It is seen from that ηn→∞ when ωb,n=0. This means that the rigid-body modes of the beam can be greatly damped by the plate. give the approximations for the effective mass and damping added to the beam by the plate. These two expressions can be further simplified under certain circumstances, which are described below. This gives insight into the coupling behaviour and allows comparisons with the locally reacting models of Suppose that the uncoupled mode shape φb,n of a uniform, straight beam has a strong sinusoidal component at a given wavenumber, e.g.,where θ represents a phase constant which is determined by the exact boundary conditions of the beam. Under such circumstances |Φb,n(k)|2 tends to be sharply peaked in the wavenumber domain around the value of but converge quickly to zero as |k|→∞. If it is assumed that the other terms in the integrands in vary slowly with k compared to |Φb,n(k)|2, Kn1 and Kn2 can, respectively, be simply approximated asAs a special case, when the beam is relatively very stiff compared to the plate such that kb,n⪡kp, the above equations become can then be estimated in a much simpler manner. Physically, In the above section, a hybrid Mode/FT approach is used to provide simple estimates of the vibrations of beam-stiffened plate systems. In this section, the limiting case where the beam-stiffened plate system has a very big dynamic mismatch will be considered, i.e., the plate is relatively very much more flexible than the beam. It then behaves as a ‘locally reacting’ model Such a plate model was then incorporated into a standard substructuring procedure to predict the vibration response of a beam-stiffened plate system by splitting the coupled structure into a beam attached to a set of independent narrow strips of the plate The above equation just corresponds to the results given by . It implies that the plate-loaded impedance (using a locally reacting plate model) for each mode of the beam is approximately constant. It depends only on the plate properties kp and mp, regardless of the beam properties, since the beam is of relatively very high impedance. Substituting , the modal amplitudes of the beam are given approximately byConsequently, the power transmitted to the plate can be simply estimated byFrom the above it is seen that the locally reacting impedance method can, under these circumstances, provide estimates of the vibration response of a beam/plate system in a much simpler manner.Similarly, the effective mass and loss factor loaded to each mode of the beam by the locally reacting plate model is given, from The above equations indicate that the effective loss factor increases with frequency but the effective mass decreases. Also the effective loss factor depends on both beam and plate properties whereas the effective mass depends on only the plate properties, regardless of the order of the beam mode., fuzzy structure theory was used to investigate the dynamic coupling relations between a large deterministic ‘master’ substructure and a continuous set of light oscillators, i.e., ‘fuzzy attachments’. It was found that the attached items act mainly to provide damping to the master structure. Moreover, the level of this damping is independent of the dissipation factor of the attachments. Similar conclusions were also given in When the plate receiver is relatively much more flexible than the source beam, the former behaves like ‘fuzzy attachments’ to the latter. By , it is seen that in this case the ratio of mn′/mb can be very small since mpλp/mb is usually very small for a fuzzy-like plate. As a result, the plate in effect only adds damping to each mode of the beam. indicates that the effective damping is independent of the internal damping of the plate itself. These conclusions are consistent with those of fuzzy structure theory. that the effective loss factor loaded to each mode of the beam by a fuzzy-like plate attachment can be simply estimated as ηn′≈mpλp/mbπ.The beam-stiffened plate system, comprising a free–free beam attached to a simply supported plate as shown in is considered in this section. The relevant dimensions and the coupling locations are given in and the material (perspex) properties are listed in are considered, corresponding to wavenumber ratios kp/kb=1.8 and 3.0, respectively. A time harmonic point force of unit amplitude acts at a distance ξ from one end of the beam. Results are shown for both the point mobility of the beam at the driving point and the power transmitted to the plate, as well as the effective mass and loss factor the thick plate adds to the first 3 modes of the beam. that the FRF-based substructuring method can provide an ‘exact’ solution for the dynamic response of a beam-stiffened plate system when the line-coupling is simulated by many discrete point couplings. These points should be spaced at most a quarter of the plate wavelength apart. For example, at the frequency thick plates are, respectively, about 0.152 and , and hence the connecting points required should be spaced at no more than 0.038 and apart at this frequency. In this section predictions made by the FRF-based substructuring method are compared to those of the Mode/FT approach and the locally reacting impedance method. The results are shown in respectively, for kp/kb=1.8 and 3.0. The first 30 modes of the beam are included for all calculations, whereas the exact solutions contain the first 1600 and 2400 modes of the 0.006 and thick plates, as well as 53 and 94 connecting points, respectively. that when the wavelengths in the beam and the plate are comparable (e.g., kp/kb=1.8), both the beam and the plate properties contribute significantly to the response of the coupled system. In this case, the Mode/FT approach, which approximates the plate receiver as if it were infinite, is too broad-brush to give accurate discrete frequency results. Nor is the locally reacting impedance method, which treats the plate as being locally reacting. However, in , where kp/kb=3.0, it is seen that the main ‘peaks’ and ‘troughs’ of the response curves are largely controlled by the modal properties of the beam, while only the small ‘wrinkles’ appearing in the response curves are sensitive to the dynamics of the plate. These observations indicate, as expected, that the exact details regarding boundary conditions, size and shapes of a very flexible receiver, tend to be less important when estimating the broad features of the coupled response of the system as the dynamic mismatch of the system increases. As a result, the Mode/FT approach can be used to provide a fairly good estimate but with much lower computational cost (e.g., about 5% and 2% of the FRF-based substructuring method when kp/kb=1.8 and kp/kb=3.0, respectively) since relatively very few degrees of freedom are needed. This advantage is more noticeable as the flexibility of the plate increases, in that a very large number of connecting points are generally required by the FRF-based substructuring method. also show that the locally reacting impedance method, being a special case of the Mode/FT approach, is most useful when the beam-stiffened plate system has a big dynamic mismatch, e.g., kp/kb>2. The computational cost is only about 2% of the Mode/FT approach. This is because the plate-loaded modal impedance Zn, in this case, can be taken as independent of the order of the beam mode.It is worth noting that although the Mode/FT approach (locally reacting impedance method) was developed based on an infinite (locally reacting) plate approximation, it can be very useful to deal with beam/plate coupled structures where the exact dynamic properties of the plate receivers may not be available, due to property and boundary uncertainties, for example. Provided the plate receiver is flexible enough so that it exhibits non-resonant behaviour in the frequency range of interest, the Mode/FT approach can be used to give quite an accurate estimate of the vibration of the beam/plate coupled structure, at least in a frequency average sense. show, respectively, the effective mass and loss factor added to the first 14 bending modes of the beam by the thick plate when it is either assumed to be infinite or modelled as locally reacting. In a dimensionless mass is used which is defined as ratio of mn/mb or mn′/mb. It is seen that there are very small differences between the two sets of results in but that the predictions are virtually identical in can estimate the effective mass and damping the plate adds to the beam in the case of kp/kb>2 in a simple manner. Meanwhile, it can also be observed from that the effective mass decreases as frequency increases so that the plate can be taken as mainly to add effective damping to the beam in the high frequency range. Since the damping effects are really only important at the beam resonances, the effective damping ηn in can be taken as (mp/mb)(λp,n/π), where λp,n corresponds to the plate wavelength at ω≈ωb,n. These values are shown in corresponding to the first 14 resonant frequencies. It indicates that the lower the order of the beam mode, the larger the effectively loaded loss factor.In this paper, a hybrid Mode/FT approach was described for estimating the vibration response of a beam-stiffened plate system. Provided the plate receiver is flexible enough so that its vibration tends to exhibit non-resonant behaviour in the frequency range of interest, this approach can give a very simple and accurate estimate for both the FRFs of the beam and the power transmitted to the plate. When the plate receiver is much more flexible than the beam (e.g., kp/kb>2), a locally reacting plate approximation was incorporated into the Mode/FT procedure to yield a locally reacting impedance method in an even simpler way. The performance of these two approximation approaches was demonstrated by numerical examples.Meanwhile, it was seen that the dynamic interaction between the beam and the plate could be interpreted as the plate adding effective mass and damping to each mode of the beam. When the plate behaves like fuzzy attachments to the beam, the plate can be taken as mainly adding damping to each mode of the beam. Moreover, the effective damping is independent of the internal damping of the plate itself. These are in good agreement with the results of fuzzy structure theory. The numerical investigations also indicated that relatively more damping is added to the lower orders of modes of the beam.Effect of degree of corrosion on the properties of reinforcing steel barsThis paper reports results of a study conducted to assess the effect of degree of corrosion of reinforcing steel bars on their mechanical properties. Reinforcing steel bars, 6 and 12 mm in diameter, that were corroded in reinforced concrete specimens were removed and tested in tension. Results indicated that the level of reinforcement corrosion does not influence the tensile strength of steel bars, calculated on the actual area of cross-section. However, when the nominal diameter is utilized in the calculation, the tensile strength is less than the ASTM A 615 requirement of 600 MPa when the degree of corrosion was 11 and 24% for 6- and 12-mm diameter steel bars, respectively. Furthermore, reinforcing steel bars with more than 12% corrosion indicates a brittle failure.The reduction in the useful service-life of reinforced concrete structures, mainly due to reinforcement corrosion, is a cause of concern to the construction industry world wide. Considerable resources are expended to repair and rehabilitate deteriorating concrete structures. It is estimated that more than $20 billion are required for the repair and rehabilitation of highway structures in the US In normal situations, concrete provides protection to the reinforcing steel. The dense and relatively impermeable structure of concrete provides the physical protection, while the high alkalinity of the pore solution provides the chemical protection. The alkaline compounds, mainly calcium and to a certain extent pottasium and sodium, in the cement contribute to the high alkalinity (pH>13.5) of the pore solution. At this high pH, steel is passivated in the presence of oxygen presumably due to the formation of a sub-microscopically thin γ-Fe2O3 film Corrosion of the reinforcing steel bars is caused either due to diffusion of the chloride ions to the steel surface or due to carbonation of concrete. Corrosion of reinforcing steel and the subsequent cracking of concrete due to the ingress of chloride ions to the steel surface is more predominant than that due to carbonation of concrete. A number of mechanisms by which chlorides break down the passive layer have been proposed, e.g. the chemical dissolution of the film The reduction in the load-carrying capacity of a reinforced concrete member due to reinforcement corrosion is attributed to the combined effect of a decrease in the bond between concrete and/or reduction in the tensile strength of the bars. While some data are available on the effect of reinforcement corrosion on the bond strength of concrete This study was conducted to evaluate the relationship between the degree of corrosion of the steel bars in concrete on their mechanical properties.Reinforcing steel bars were embedded in the concrete specimens prepared with ASTM C 150 Type V cement. Crushed limestone with a maximum size of 19 mm, specific gravity of 2.64 and water absorption of 2.3% was used as coarse aggregate, while beach sand with a specific gravity of 2.64 and water absorption of 0.56% was used as fine aggregate. A coarse to fine aggregate ratio of 1.68 and a water/cement ratio of 0.45 were kept invariant in all the concrete mixtures. Two groups of concrete specimens were prepared. The first group of specimens was prepared with 6-mm diameter steel bars while the other group was prepared with 12-mm diameter steel bars. Deformed reinforcing steel bars meeting the requirements of Grade 60 of ASTM A 615 were utilized in the concrete specimens.After casting, the concrete specimens were cured for 28 days. The corrosion of reinforcing steel was accelerated by impressing an anodic current of 2 mA/cm2. This was done through an integrated system incorporating a DC rectifier with a built-in ammeter to monitor the current and a potentiometer to control the current intensity. The concrete specimens were partially immersed in 5% sodium chloride solution in a fiberglass tank so that the reinforcing steel bars were above the solution. This type of arrangement was selected to assure that the corrosion product formed is not washed away and cracks are formed in the concrete specimens. The direction of the current was adjusted so that the reinforcing steel became an anode and a stainless steel plate placed on top of the concrete specimen served as a cathode. A schematic representation of the test set-up is shown in . In order to induce different levels of reinforcement corrosion, a calibration curve establishing the relationship between the duration of the impressed current and the corresponding degree of reinforcement corrosion was prepared prior to conducting the actual experiments. The current supplied to each concrete specimen was checked on a regular basis and a drift was corrected by adjusting the potentiometer. The desired degree of reinforcement corrosion was obtained by applying the anodic current for the time period assessed from the calibration curve.After the desired level of reinforcement, corrosion was obtained, the concrete specimens were split along the line of the steel bars. The degree of reinforcement corrosion was measured as gravimetric loss in weight of the reinforcing steel bars after cleaning them with Clark's solution according to ASTM G1. After assessing the weight loss, the steel bars were tested in tension to evaluate their mechanical properties. The mechanical properties of the steel bars were evaluated using an Instron Universal Testing machine of 250 kN capacity. A purpose-built extensometer was utilized to measure the elongation in the bar. The load and elongation data were recorded using a computerized data acquisition system at pre-determined load intervals till failure of the specimen occurred. The data so generated were utilized to plot stress–strain diagrams for each of the tested specimens. The stress–strain diagrams were utilized to determine the yield and tensile strength of the steel bars. The elongation, due to the applied load, was measured after the completion of the tensile test and it was expressed as a percentage of the original gauge length. The tensile tests were conducted on both clean and corroded reinforcing steel bars so that the influence of degree of reinforcement corrosion on the tensile properties of reinforcing steel bars could be assessed. are typical stress–strain curves for 6-mm diameter steel bars with varying degrees of corrosion. The tensile strength of both the groups of these steel bars is almost similar. However, the total elongation of the bars with 0.88% corrosion is more than that of bars with 13.9%. summarizes the tensile strength data for 6-mm diameter bars with varying degree of reinforcement corrosion. These data indicate that the actual load carried by the bars decreased with increasing level of reinforcement corrosion. However, due to a decrease in the cross-section of the bars net tensile strength is marginally affected. shows the variation of the ultimate strength of 6-mm diameter steel bars with the degree of corrosion. The ultimate strength of the clean bars and those corroded to 75% corrosion was 796 and 741 MPa, respectively. It should also be noted that even after degradation of the bars due to reinforcement corrosion their tensile strength is more than 600 MPa specified by ASTM A 615. also shows the tensile strength of bars calculated using the nominal diameter, i.e. 6 mm. Using this criteria the tensile strength of the steel bars falls below the ASTM A 615 criteria of 600 MPa when the degree of reinforcement corrosion is 11.6% and above. are typical stress–strain curves for 12-mm diameter steel bars, with 11.7 and 32.70% corrosion, respectively. In this group of specimens also, the degree of reinforcement corrosion did not affect the ultimate tensile stress. The variation of the tensile strength of 12-mm diameter steel bars, with the degree of reinforcement corrosion, is plotted in . These data indicate that the variation in the tensile strength with degree of corrosion is very insignificant. For example, the actual tensile stress is 760 MPa for the clean bars and 844 MPa for the steel bars with 80% corrosion. The data on tensile strength calculated using the actual and nominal diameter of 12-mm diameter are summarized in . The tensile strength calculated using actual area of cross-section is more than 600 MPa specified by ASTM A 615. However, the tensile strength calculated on the nominal area based on a diameter of 12 mm is less than the value specified by A 615 for reinforcement corrosion of 24% and above.The above results indicate that even at high levels of corrosion, there is no significant change in the tensile strength of bars calculated using the actual cross-section. However, when the nominal diameter of the bars is utilized to calculate the tensile strength, these values fall below the ASTM A 615 specifications of 600 MPa for reinforcement corrosion of 11.6% or more for 6-mm diameter steel bars and 24% or more for 12-mm diameter steel bars. Also, the brittleness of steel bars is affected by the degree of reinforcement corrosion as will be discussed in the latter part of this paper. Maslehuddin et al. shows the load-elongation curves for 6-mm diameter steel bars, corroded to different levels. This comparison indicates that as the degree of corrosion increases, the corresponding elongation of the bar before failure decreases. There is a systematic pattern wherein with increasing corrosion, the bars fail with decreasing amount of yield strain compared to the non-corroded bars, which show a large amount of yielding before their ultimate failure. This indicates that corrosion of reinforcing steel increases its brittleness.Reinforcing steel bars with 12.6% or more reinforcement corrosion indicate a brittle behavior. Also, the elongation of bars with 12% or more corrosion is generally less than that specified by ASTM A 615, i.e. 9%. shows the effect of increasing corrosion on the rebar configuration. It is seen that as corrosion progresses beyond 40%, relatively small lengths of rebars show thinning, thereby demonstrating the tendency for notch formation with increasing corrosion. show several severe notches for bars corroded to 75 and 80%, respectively. This preferential corrosion is characterized for high levels of chlorides or for situations where concrete is cracked or honey-combed at specific locations providing ingress to chloride ions and oxygen to the steel surface at such locations. Preferential corrosion resulting in the thinning of steel bars over small lengths would have the effect of reducing considerably the cross-sectional area of the bars locally and hence, reducing the load-carrying capacity of the bars. Preferential corrosion and notch formation also alters, as seen in , the load-deformation characteristics of the rebars. When a notch or locally thinned section of the steel bars is stretched by a tensile force, the strain would be concentrated at the notch and the overall strain of the bar will be less at failure than in an uncorroded bar. Hence, as the notch becomes deeper, the stress concentration progressively increases at the locations of notch and the rebar behavior effectively becomes more brittle.The above finding is supported by a study conducted by Almusallam et al. A marginal decrease in the tensile strength of steel bars was noted with increasing degree of reinforcement corrosion when the stress was calculated utilizing the actual area of cross-section. Also, the tensile strength calculated using the actual area of cross-section was more than 600 MPa for bars with as much as 75 to 80% corrosion. However, when the tensile strength was calculated utilizing the nominal diameter, the tensile strength was less than the ASTM A 615 requirement of 600 MPa when the level of corrosion was 12% or more in 6-mm diameter steel bars and 24% or more in the 12-mm diameter steel bars.The data on stress–strain characteristics of reinforcing steel bars corroded to varying levels of corrosion indicate a decrease in the ductility of bars with increasing level of corrosion. Furthermore, with increasing levels of corrosion bars failing at low level of yield strain compared to uncorroded steel bars that demonstrate large yielding before failure. Reinforcing steel bars with 12.6% or more reinforcement corrosion indicated a brittle behavior. Also, the elongation of bars with more than 12% corrosion was less than 9% specified by ASTM A 615.The results of this study indicated a close relationship between the failure characteristics of steel bars and slabs with corroded reinforcement in that a sudden failure of slabs in flexure was noted when the degree of reinforcement corrosion was more than 13%.Energy absorption mechanism of Al–steel bilayer sheets produced by cold roll welding during wedge tearingThe behavior of Al–steel bilayer sheets produced by cold roll welding is investigated through the wedge tearing process. It is observed that through tearing the energy absorbed by cold roll welded bilayer sheets is larger than that of non-welded ones, even though all parameters are identical. Also bilayer sheets with low bond strength have the same energy absorbed by non-welded bilayer sheets. By investigating all contributing mechanisms in tearing and mechanical properties of composite layers and developing theoretical equations, it is concluded that bending of sheets through wedge tearing plays a major role in difference of energy absorbed by welded and non-welded bilayer sheets. Moreover, there is a good correlation between experimental data and theoretical equations developed for predicting the load–displacement curves of tearing and energy absorption of Al–steel bilayer sheets.In collision of sheets by rigid bodies there are several forms of energy absorption ways such as crumpling, folding or cutting. Tearing by a wedge tool is an easy way for understanding the mechanism of energy absorption during cutting Al–steel bilayers produced by cold roll welding have had rapid growing applications in recent years Considering the above-mentioned points, it seems that the wedge tearing behavior of bilayer sheets should be investigated. In this study the work is on the well-known ones, i.e. Al–steel bilayer sheets., in which yield strength is considered as the only parameter of material properties contributing to energy absorption:where t is the material thickness, l the length of cut, σ0 the yield strength and c a constant that depends on tearing conditions such as wedge angle, sheet angle relative to wedge, mode of tearing and friction between wedge and sheet.In using these formulas for bilayer sheets, there are some problems. The first problem is the thickness of a bilayer sheet. The thickness of bilayer sheet depends on the thickness of each layer which differs according to rolling reduction and the initial thickness. The other problem is the yield stress of layers makes the yield stress of the bilayer sheet. The yield stress of a bilayer sheet is derived from mixture rule. Although some researchers reported that due to different plastic anisotropy of two layers in a welded bilayer sheet, the real yield stress deviates from mixture rule, this effect is negligible where f1 and f2 are the fractions of layers, σ01 and σ02 the yield stresses of layers. This rule indicates that two sheets act as they are unbonded and free to yield. Whereas the yield stress of bilayer follows the mixture rule, it means the two sheets act separately as they are free to yield By considering three factors contributing to tearing, the energy absorption can be estimated. shows schematic of tearing by wedge. In this figure, the parameters contributing to Eqs. such as membrane stretching and bending behind the wedge can be seen. can be written for a bilayer as follows:Ėm=0.365VRcosθσ0bt=0.365VRcosθ(σ01f1+σ02f2)t.It should be noted that t is the total thickness of the bilayer sheet.The second term that affects the amount of work carried out in tearing test is friction. For both welded and non-welded sheets this term is similar assuming that the contact is between wedge and Al side of the bilayer sheet. So this term does not contribute to difference of tearing work carried out for welded and non-welded sheets.. For calculating the plastic bending moment, it has been supposed that entire sheet deforms plastically.Using the fully plastic bending moment of welded sheets given in , the rate of bending energy is achieved as follows:where H is the function of yield stresses ratio of layers and thickness fraction of each layer defined in . Since through tearing of non-welded bilayer sheets, each layer bends individually, in order to calculate Ėb for non-welded sheets the amount of M0 is considered as the sum of fully plastic bending moment of two layers (see where P is a constant that depends on the yield stresses ratio of two layers and thickness fraction of each layer defined in Without considering the friction effect, the force for tearing (Fp) is obtained according to virtual work theory as follows By substituting the values of Ėb and Ėmin Eq. , the force is obtained. For example, the force for welded sheets is as follows:It is essential that the value R to be optimized for minimizing the amount of force. From dFp/dR=0, it is achieved, the tearing force of welded sheets without considering the friction can be written asSimilar to the welded sheets, the amount of Fp for non-welded sheets is obtained asSince there is no difference between the friction work of monolayer sheet and that of bilayer sheet, the friction term of tearing force calculated by Zheng So, the total force of tearing for welded sheets can be achieved asFw=Fp−w+Ff=0.918t1.5l0.5(Hsinθ)0.5(1+μtanθ)Therefore, the amount of energy absorbed by welded sheets is calculated as follows:Ew=∫0lFwdl=∫0l0.918σ0bt1.5l0.5(Hsinθ)0.5(1+μtanθ)dl=0.612σ0bt1.5l1.5(Hsinθ)0.5(1+μtanθ)From the similar procedure for non-welded sheets, the force and absorbed energy can be written asAs it can be seen from these relations the amount of tearing work or energy absorption for bilayer sheet depends not only on the yield stresses and thicknesses of layers but also on a constant (H or P) that is function of the ratio of yield stresses and thickness fraction of both layers.Materials used for this study were low carbon steel (St-12) and commercial pure aluminum (1050). Thicknesses of Al and steel sheets were 1.5 and 1 mm, respectively. The specimens of initial dimension 13 cm×5 cm were cut from as-received sheets. After cleaning the surfaces of two sheets by acetone they were brushed by wirebrush made from steel and then clamped together. This stage was necessary to remove oxide layers and other surface contaminants in order to weld two layers. Since in this research the effect of cold weld is investigated on the energy absorption of bilayer sheet through tearing test, some of the specimens must be non-welded. It has been shown that interfacial coefficient of friction causes difference in thickness fraction of layers in bilayer sheet Specimens for tensile test were prepared according to ASTM-E8M standard from welded sheets in the rolling direction and tested by Hounsfield tensile test machine at the cross head speed of 2 mm min−1. For example in , the individual stress–strain curves for aluminum and steel layers of non-welded bilayer sheet after 25% rolling reduction are presented. Also, in order to assess the bonds strength of specimens, the peeling tests were carried out according to ASTM-D903-93 standard.To investigate the effect of cold welding on energy absorption of the bilayer sheets during tearing, load–displacement curves for tearing of welded and non-welded bilayer sheets have been achieved. The curves are shown in . These curves comprise two main stages It has been reported that cutting process in front of the wedge occurs due to plastic flow and no fracture occurs Friction between sheet and wedge is identical for both welded and non-welded sheets because the contact surface is selected from Al side of the bilayer sheet. Thus, the friction does not cause to the difference in energy absorption of welded and non-welded bilayer sheets through tearing. two curves for welded and non-welded sheets are apart from each other. This is due to different plastic bending moment of them as mentioned in , since in non-welded sheets plastic bending moment is the sum of plastic bending moments of two layers, value of H is larger than that of P. Thus, the absorbed energy for welded sheets becomes larger than that for non-welded ones. show experimental energy absorption versus calculated one obtained from Eqs. for tearing the length of 4 cm in welded and non-welded sheets. There is a good correlation between the experimental data and calculated results. All parameters related to the bilayer sheets such as f (thickness fraction of steel layer), n (Al yield stress to steel yield stress ratio) and σ0b are given in . σ0b is obtained from uniaxial tensile test for each bilayer sheet and is the average of yield stress and ultimate tensile strength in order to consider strain hardening effect. shows the load–displacement curves for welded and non-welded bilayer sheets with 35% thickness reduction in rolling, followed by heat treatment at 500 °C for 2 h. As it can be seen, two curves are coincident approximately, so the energies absorbed by welded and non-welded sheets are identical. Thus, the plastic bending moment of welded and non-welded sheets must be identical and this happens if only two layers of welded sheet bend separately. shows the welded sample with 35% thickness reduction followed by heat treatment at 500 °C for 2 h after tearing. It can be seen that the sample is delaminated in bending region resulting two layers bent separately. In the following the reason is discussed.It has been reported that heat treatment of cold-welded bilayer Fe–Al sheets in high temperatures of over than 500 °C causes to rapid growth of intermetallic phases the result of peeling test for welded bilayer sample with 35% reduction is shown, but for heat treated one at 500 °C due to its weak bond strength no curve was achieved. In this state, the thickness of intermetallic phases exceeds 10 μm. Low bond strength between layers causes to the delamination of the layers in bending region behind the wedge tip and thus the layers bend individually where the behavior appears like non-welded sheets in tearing. In other words the heat treated sample needs the same cutting, friction and bending energies in comparison with that of the non-welded sample due to its low bond strength.From the above-mentioned descriptions, it can be noted that the welded and non-welded bilayer sheets with different bending energies due to their bond strengths show different energy absorption through tearing test.The effect of cold roll welding on the energy absorption mechanism of Al–steel bilayer sheet during tearing by the wedge has been investigated and it is concluded that:Energy absorption of cold-welded bilayer sheets is larger than that of non-welded ones, although all other parameters are identical.The energy absorption in cutting process of welded bilayer sheet is the same as that of non-welded one.A good agreement is achieved between experimental data and calculated energy absorption of both welded and non-welded bilayer sheets.The welded bilayer sheet that was heat treated at 500 °C for 2 h shows the same load–displacement curve in comparison with that for non-welded one, because of low bond strength between layers of the heat treated sheet. In other words, they have the same energy absorption.For calculating the fully plastic bending moment of a bilayer sheet it is assumed that the full thickness of bilayer undergoes yielding and the stress corresponding to this state is the average of yield stress and ultimate tensile strength to consider strain hardening effect. Sowhere σy is the yield stress and σu the ultimate tensile strength. In this paper σ0 stands for the average of yield stress and ultimate tensile strength.Considering the cross section of bilayer sheet and assuming that the thickness fraction of steel is equal to f, the plastic bending moment of bilayer sheet can be calculated.The flow stress of bilayer sheet is obtained according to mixture rulewhere n=σ02/σ01, σ01 and σ02 are the average of yield stress and ultimate tensile strength of steel and Al, respectively.Since in this study the yield stress of Al is much smaller than that of steel, the neutral axis falls on the steel side of bilayer sheet. To obtain the neutral axis, the following condition should be applied:where A is the cross sectional area of the bilayer sheet.where d is the distance of neutral axis from interface of layers as shown in . To avoid more complexity in later relations, it is assumed thatPlastic bending moment of bilayer is achieved as, rearranging σ01 and σ02 respect to σ0b and n, considering Von-Mises criterion and using Eq. , the following relationship is obtained for plastic bending moment of welded bilayer sheet (M0–w):M0−w=2(2/3)σ0bt2((1−f)2+2N2−2(1−f)N+nf2+nfN)4(1−f+nf)=2/3σ0bt2H4In the case that there is no bond or very weak bond between layers, the fully plastic bending moment is the sum of fully plastic bending moments of two layers because they act separately in bending. In this case it is obtainedM0−nw=M0−Al+M0−Steel=n23σ01(1−f)2t24+23σ01f2t24=23σ0bt24×nf2+(1−f)21−f+nf=23σ0bt24P3D printing of curved concrete surfaces using Adaptable Membrane FormworkIn this paper, we study the printing of non-developable curved panels using existing 3D concrete printing technology combined with a novel Adaptable Membrane Formwork. The Adaptable Membrane Formwork consists of a grid of threaded rods, whose heights are adjustable and covered by a membrane sheet. Using this method, we were able to 3D-print, for the first time, Saddle and Dome-shaped concrete surfaces, which are non-developable. The printed specimens had good print quality and geometric fidelity, as shown by quantitative assessment. The proposed method thus demonstrates great potential for the 3D printing of freeform, curved and architectural facades.Curvature adds possibilities to architecture that would not exist if only straight lines and linear layer surfaces make up the architect’s toolbox. The use of curvature results in richer and more expressive designs. Although the use of curvature is not new, until now it has mainly been restricted to high profile projects or iconic architecture. This is caused by the higher costs of curved buildings as result of the extra effort needed for correct measurements in drawings and on the building site, the need for unconventional construction methods on the building site, or, in case of manufacturing, the extra costs of manufacturing complex shapes in the factory.3D concrete printing has demonstrated its potential to disrupt the construction industry by printing concrete walls without conventional formworks Other pioneers of 3D concrete printing have explored Shotcrete 3D Printing so as to print freeform 3D structure with large overhangs In this paper, we investigate a method to support the printing of doubly-curved concrete surfaces, which are non-developable, on an Adaptable Membrane Formwork. The system is a temporary formwork consisting of a grid of adjustable threaded rods, covered by a flexible membrane. We used an specifically-designed algorithm to slice and generate the curved print path for 3D concrete printing. This experimental method is evaluated with regards to surface quality and geometric fidelity.The remainder of this paper is organized as follows. In Section , we review existing manufacturing techniques for curved concrete. In Section , we present in detail the proposed curved concrete printing set up. In Section , we report the results of the modeling and accuracy and precision assessment. In Section , we conclude by discussing the limitation of our current system and the direction for future work.While 3D printing in the general sense promises the possibility of free form fabrication, 3D concrete printing has largely been limited to the printing of planar structures. This is due to the low yield strength of early age concrete that has just been freshly extruded. This low yield strength prevents overhanging concrete from being printed, hence to date free standing free form curved concrete structures have not been printed.The common strategy to manufacture curved concrete is to cast concrete using static formwork. To increase the efficiency and reusability of the system, reusable mould systems have been developed. Renzo Piano first introduced the idea of a flexible formwork for the production of freely formed panels in the 1960’s, however it has proved difficult to manufacture double curved concrete panels in practices. PERI introduced a wall formwork system that uses pre-assembled panels for curved walls In 3D printing application, Costanzi et al. In this paper, we outlined the design, selection and simulation study for the Adaptable Membrane Formwork, open sourced algorithms to generate the printing path of curved structure and validation process for 3D printing of free formed curved structures. We will demonstrate 3D concrete printing of the full curved structure directly onto an Adaptable Membrane Formwork, in contrast to the work by Costanzi et al. This presents new challenges as unlike printing on a fully supported CNC-milled static mould, an adaptable mould would deform if the mould surface’s force equilibrium is not accounted for. The force analysis is conducted in Abaqus to ensure that the Membrane formwork is not overly deformed that it loses geometrical consistency to the designed shape.As the full curved structure is being printed using 3D printable concrete, as opposed to the work by Costanzi et al., there is the challenge of designing a printing path that produces smooth curved surfaces. In normal 3D concrete printing of curved structures, the curvature is digitalized. When combined with the stiff, shape retenting properties of 3D printable concrete, the printer produces a staircase effect (). This problem is not seen when casting concrete, as a self compacting concrete of good flowability can be used to allow the concrete to flow along the curve. However using self compacting concrete on a curved structure cannot guarantee that the produced curved surface is of uniform thickness. We adopted a method from curved layer fused deposition modeling in polymer 3D printing The Adaptable Membrane Formwork consists of a grid of threaded rods, whose heights are adjustable, covered by a membrane sheet. The rod grid and the membrane are further described below.: it consists of 4×4 stainless steel threaded rods of 10 mm diameter and 300 mm length. The distance between the centers of two neighboring rods is 70 mm, yielding a base surface of 210 mm × 210 mm. The heights of the rods above the surface can be manually adjusted according to the structure design, defining thereby a temporary surface on which the membrane formwork is laid. In the experiment, the individual rod heights are taken from the surface profile of the design structure and the rods rotated until the required height is reached. Alternatively, the rods could be fitted to servo motors, which would enable their heights to be automatically adjusted.The doubly curved structures we set out to model and print are a Dome and a Saddle with base area of 210 mm×210 mm, mathematically defined by the following equations (see The membrane must be able to follow the curves and contours of the desired shape, without too much sagging. shows two ways how a wrong membrane can affect the concrete panels: an overly rigid material prevents the membrane surface from being adjusted to the desired shapes, while an overly flexible material leads to uneven sagging on the surface. This sagging can be due to the weight of the cementitious material deforming the flexible membrane and causing it to lose its geometric fidelity, visually this can be observed as bumps on the printed panel.As we are printing a non-developable surface, we require that the flexible formwork material to be sufficiently elastic, such that it may be stretched to the required dimension, and still sufficiently rigid to resist excessive deformation caused by the weight of the printed concrete, we estimated that Spandex (Young’s modulus of 200 MPa and Poisson’s ratio of 0.3) is a good option. To verify this hypothesis, we conducted a Finite Element Modeling (FEM) analysis in Abaqus, reproducing the actual loading conditions, rod spacing, etc. A linear elastic model was used in the FEM analysis for a light bidirectional woven flexible membrane of 2 mm thickness, undergoing uniform loading due to the weight of the printed concrete. As the flexible member is expected to be reusable, it should not experience any plastic strain and is assumed that the deformation of the flexible membrane remains in the elastic region. The flexible membrane is meshed with a total of 44100 elements, with a mesh density of 1 mm.We then compared the results of the FEM simulation to the desired shape. For completeness, we also conducted the FEM simulation for two other materials: Wood (Young’s modulus of 15000 MPa and Poisson’s ratio of 0.35) and Rubber (Young’s modulus of 1 MPa and Poisson’s ratio 0.5) and compared to the desired shape.The membrane experiences increased loading with increasing number of concrete layer being printed on it. As such, to minimize loading, only one layer of concrete is printed on the membrane formwork. The thickness of the concrete layer can be increased by increasing the nozzle stand off distance from the membrane formwork and increasing the diameter of the extruder nozzle. If multiple layers of the concrete panel is required to be printed, the concrete is allowed to cured and gain enough yield strength before subsequently layers are printed on it. This would allow the concrete panel to bear the additional load, and avoid causing additional strain on the membrane formwork. However the subsequent layers should be printed while the prior layer is still fresh, as the bond strength at the interface degrades if the time gap between printing exceeds the printability time.The results from the FEM simulation of the three materials are intersected with 6 test planes normal to x=-60mm,0mm,60mm and y=-60mm,0mm,60mm. These planes were chosen so as to lay in-between the support nodes and thus likely to contain the greatest Z-errors ∊, due to sagging or bulging of the membrane.Next, we evaluate the print quality as follows. For each point (xFEM,yFEM,zFEM) of the FEM simulation, the Z-errors ∊ between the model defined by Eqs. and the results of the FEM are given byFor each test plane P, we select all the points (xFEM,yFEM,zFEM) located within a distance of 0.5 mm from P, and compute the mean and standard deviation of the Z-errors ∊ across those points. shows the physical printing setup, which comprises a 6-axis robotic arm, a concrete mixing and delivery system (mixer, pump, hose, nozzle), and the Adaptable Membrane Formwork. The robot is mounted on a mobile platform, which could allow the printing system to print larger structures The robotic arm has a horizontal reach of 87 cm with an accuracy and repeatability of 0.02 mm. The accuracy and repeatability of the robotic arm is a measure of the performance of the robotic arm. The robotic arm can repeatedly achieve precise positioning of the end effector when executing the same task, this makes it highly suitable for positioning the extruder nozzle of a 3D concrete printing system. A extruder nozzle is mounted to the end effector of the arm, and a hose pipe attached around the length of the arm. The pump system delivers cementitious material to the extruder nozzle for selective deposition of concrete. The printing path can be generated from a given design or CAD file and sliced into a series of tool path coordinates for the robotic extruder nozzle to follow, and build up the printed structure. Our path planning system will solve for feasible and reasonable pose for each tool coordinate Formulations used in this study consist of Ordinary Portland Cement (OPC, ASTM type I, Grade 42.5) Using the equations of the Dome and Saddle in , one can generate PLY files, which are then processed as point clouds. The point clouds are digitally orientated onto the membrane formwork. The points and normals were taken from the bottom surface of the point cloud using a normal estimation algorithm.The points and their normals of the point clouds were arranged in according to a print path strategy that starts from the lowest point to the highest point without overlaying of the path as shown in . The print path starts from blue to red. This print path strategy allows for fresh concrete to be printed on the prevailing concrete filament and hence a more stable built up of filaments. The print path is also designed to be continuous to avoid disruption and throttling of the concrete extruder pump. This ensures that the concrete undergoes a constant flow rate and will not disturb the rheological properties of the concrete caused by changes in the shear rate of the extruder pump.As the technique of printing doubly curved concrete structure is targeted at printing architectural designed structures, the concrete panel is measured for geometrical fidelity and aesthetics. Given that the concrete panel is doubly curved, and to be able to capture all the measurement in its entirety, we chose imaging techniques as our validation method. In a previous paper, researchers have used a Kinect V2 3D camera to help map out the surface shape of a fresh concrete cylinder as it undergoes deformation The printed structure is placed against a clear background, at a distance of 0.5 m normal to a Kinect V2 3D camera. The printed structure is ensured to be free from occlusion, and the bottom surface can be captured. The captured point cloud is then registered to the model point cloud using an iterative closest point (ICP) algorithm The ICP algorithm is able to handle the 6 degrees of freedom and perform rigid transformation of the captured point cloud, until the mean-square distance metric of the points in the captured point cloud is minimized against the points in the model point cloud. As the ICP algorithm described in The captured point cloud is first pre-processed by passing through a pass-through filter that removes points in the background and NaN points. This step would effectively segment the points of the printed structure from the captured point cloud. Subsequently, a statistical outlier removal filter is also used to remove all noises from the capture point cloud. The initial alignment of the captured point cloud of the printed structure is transformed manually by objectively positioning the printed structure in the same normal direction as the model point cloud. The ICP algorithm is then applied to refine the pose of the point cloud.The refined point cloud is then intersected with 6 test planes normal to x=-60mm,0mm,60mm and y=-60mm,0mm,60mm. These planes were chosen so as to lay in-between the support nodes and thus likely to contain the greatest Z-errors ∊.Next, we evaluate the print quality as follows. For each point (xprinted,yprinted,zprinted) of the point cloud, the Z-errors ∊ between the model defined by Eqs. and the printed specimen are is given by∊Saddle≔|zprinted-fSaddle(xprinted,yprinted)|,For each test plane P, we select all the points (xprinted,yprinted,zprinted) located within a distance of 0.5 mm from P, and compute the mean and standard deviation of the Z-errors ∊ across those points.Results of both simulation on selection of membrane and printing of concrete shell structures are presented in this section. shows the FEM model of the 3 different materials for the Dome and Saddle structure. In (a), (d), for model built using the rubber, there is noticeable sagging of the surface when under loading due to the weight of the concrete deposited when printing. While in (c) and (f), the center of the surface retains a distinct planar face as it resists the bending forces from the weight of the concrete. It is only in (b) and (e), that the surface is still curved after concrete printing.As such, it can be seen that it is necessary to carefully select the right material that is sufficiently flexible to be bend into shape and stiff enough to resist sagging when concrete is printed over it. shows the comparison of the different materials against the desired model at 6 test planes normal to x=-60mm,0mm,60mm and y=-60mm,0mm,60mm. a shows the surface profile of the different materials against the desired model. b shows the mean absolute Z-errors ∊of the different materials and the standard deviation of the Z-errors ∊ over the 6 test planes.It is observed that the profiles of the spandex material follows the closest to the model profile, with a mean absolute error of 2.5 mm, standard deviation of 0.45 mm and mean absolute error of 4 mm and standard deviation of 0.8 mm for the dome and saddle shape respectively. This is in comparison to the rubber with mean absolute error of 2.7 mm and 5.8 mm and the lumber with mean absolute error of 3.4 mm and 5.9 mm for the dome and saddle shape.Additionally, the rubber model shows significant sagging in the saddle model, with the weight of the concrete depressing the rubber membrane. The lumber model shows significant resistance to bending in both the dome and saddle model, as its young modulus is too high and it does not deform to fit the model. This results in higher mean absolute error for both rubber model and lumber model.The flexible mould assumes the geometry of the designed shape and must have sufficient strength required to resist bending and the loading from the concrete printing while maintain geometrical fidelity.The finite element model shows good agreement with the CAD model with mean absolute error less than 4 mm for both the Dome and Saddle structure. This demonstrate that the selected material (spandex) is capable of bearing the pressure exerted by the fresh concrete and the bending required to adhere to the curvature of the CAD model, at a rod spacing of 70 mm, in a 4 × 4 grid setup.The finite element model shows localized stress, particularly in the area where the rods are. Those areas have a higher stress state than other regions and may be areas where higher strain is likely to occur at this localized area.The printed shell structures are shown in . The structures is visually smooth, with no observable surface roughness, as it was printed with mortar grade cementitious mixture using fine aggregates. There is even color variation as the printing was done continuously using a single batch of cementitious mixture. There is no staircase effect between layers as the printing path is printed normal to the curved surface, rather than normal to the substrate print bed as in the generic 3D concrete printing setup. Using a vernier caliper and measuring along the edges, the shell thickness is roughly 10 mm.An overlay of the printed part’s point cloud and desired model’s point cloud is shown in the top right of (b), (c) shows the distribution of Z-errors ∊ of the Dome shaped part and the Saddle shaped part against an imaginary plane that intersects the printed part normal to x=-60mm,0mm,60mm and y=-60mm,0mm,60mm. Individual plots of the profile of the printed parts against designed model can be found in d to i. It is observed that the profiles of the printed part are generally close to the target surface, with mean absolute error across the 6 planes is less than 2 mm for the dome, mean absolute error of 4 mm for the saddle. The biggest standard deviation is 0.5 mm from the mean absolute error. The maximum absolute error for the 5 mm for the dome model and 9 mm for the saddle model.The high standard deviation error might be attributed to the use of the Kinect V2 camera used to capture the point cloud. Yang et al. found that at a distance of 0.5 m, the average depth accuracy of the Kinect V2 camera is around 2 mm The robotic printer shows no bias in printing along the longitudinal direction or transverse direction. It is observed that the robotic printer shows a higher average absolute error of 4 mm when printing the Saddle part as compared to 2 mm when printing the Dome part. The maximum error observed is 5 mm on the dome and 9 mm on the saddle structure. As when printing the Saddle part, it is a hyperbolic paraboloid shape which would require more support nodes to accurate reflect its shape as compared to the Dome part.When printing the Saddle part, which has a hyperbolic paraboloid shape, the printing path translate down along the x-axis and up along the y-axis. This changing of gradient of the print path when simultaneously depositing concrete may have caused the printer to deposit an excess of concrete at those points, hence there are Z-errors ∊of both positive and negative nature.As all prints were performed on a thin spandex membrane, the actuators tips were seen to impart an indention mark on the final product. We used a vernier caliper and measured along the edges of the printed part. The average shell thickness is found to be 10 mm.This paper presents a novel method for the 3D-printing of curved concrete structures. Our setup consists of a 6-axis robotic printer and an Adaptable Membrane Formwork. This affords an increase in the level of flexibility and geometry complexity for the manufacturing process of concrete architectural elements. As a case study, we printed two non-developable, doubly-curved, surfaces: a Saddle and a hemisphere Dome. We showed that our setup could 3D-print these thin (10 mm) concrete shell elements with good accuracy and surface finishing. This opens the way to flexible yet economically-sustainable schemes for manufacturing curved concrete surfaces.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.The phenomenon of dowel action as a shear transfer mechanism across cracks has long been recognized as an important component of the overall shear resistance capacity of reinforced concrete beams. In this paper, a simple analytical model for the dowel action of reinforcing bars crossing cracks is developed for analysis of reinforced concrete beams. This model is incorporated into a computer program that uses the displacement method and the initial stiffness procedure. The nonlinear behaviors of several reinforced concrete beams tested by others are analyzed. The beams are analyzed first with the dowel action neglected and then with the dowel action considered. It is found that in certain cases, the dowel action can have significant effects on the shear strength of reinforced concrete beams and that the theoretical results of the proposed model generally agree better with the experimental values when the dowel action is accounted for.Cracking in concrete beams may result in a significant reduction in their stiffness and strength. Although the flexural behavior of cracked reinforced concrete beams can generally be well predicted, accurate prediction of the shear behavior of reinforced concrete beams remains a formidable task due to the complexity of the shear transfer mechanism in the reinforced concrete. Shear resistance in reinforced concrete beams is provided by the shear transfer in the compression zone, aggregate interlock across the crack face, stirrups crossing the shear crack, and dowel action of longitudinal reinforcing bars crossing the crack in the concrete. The contributions of the compression zone, the stirrups, and the aggregate interlock are fairly well modeled in the literature, but so far the dowel action of the reinforcing bars has not been explicitly represented, despite the implicit belief in much of the current design thinking that dowel action is an important component of the shear resistance. The dowel action of reinforcing bars can play an important role if other contributions to shear transfer are relatively small as in the case of a beam with a small amount of web reinforcement or the case of a post-peak stage of the loading process. It may contribute significantly to the post-peak resistance and hence contribute to the shear ductility of concrete members.From a literature survey on finite element analysis of reinforced concrete structures covering papers published from 1985 to 1991 To incorporate the effects of the dowel action in the nonlinear analysis of reinforced concrete beams, a simplified analytical model for the dowel action is described in this paper. The model is incorporated into a computer program that employs the displacement method and the initial stiffness procedure.The analytical model used to predict the behavior of a dowel bar embedded in concrete is based upon the work presented by Timoshenko and Lessels k = stiffness of the elastic foundation (the concrete represents the flexible foundation);The solution to this differential equation is given by: y=eλx(Acosλx+Bsinλx)+e−λx(Ccosλx+Dsinλx)Es = modulus of elasticity of the steel bars;Is = moment of inertia of the bar (equal to πdb464 in which db is the diameter of the bar);A, B, C, and D = constants determined from the boundary conditions for a particular problem.Cutting the reinforcing bar at the face of the crack, the bar may be treated as a semi-infinite beam resting on an elastic foundation and subjected to concentrated dowel force Vd and moment Mo applied at its end, as shown in . For a semi-infinite beam on an elastic foundation, the constants A and B are equal to zero and Eq. y=e−λx2λ3EsIs[Vdcosλx−λMo(cosλx−sinλx)]. with respect to x gives the slope, dy/dx: dydx=e−λx2λ2EsIs[(2λMo−Vd)cosλx−Vdsinλx].Applying the solution for a semi-infinite beam on an elastic foundation to dowel bars crossing a joint in a concrete pavement, Friberg’s Assuming that an inflection point exists in the dowel at the center of the crack, the forces acting on the portion of the dowel within the crack width, z, are shown in . Substituting −(Vdz2) for Mo and setting x equal to zero, Eqs. for the slope and deflection of the dowel at the face of a crack in concrete, as shown in The stiffness of the elastic foundation (concrete surrounding the dowel bars) is an important parameter in the equations presented in this paper. Before these equations can be used, a value for the elastic foundation stiffness is needed. For the elastic foundation stiffness of the surrounding concrete, k, the following data-fitting expression proposed by Soroushian et al. fc′ = compressive strength of the concrete in N/mm2;c1 = coefficient ranging from 0.6 for a clear bar spacing of 25 mm to 1.0 for larger bar spacing.The load–deflection response for dowel bars embedded in concrete proposed by Millard and Johnson Vd = dowel force at a shear displacement Δ at a crack;When the dowel deformation is not too large and none of the materials have yielded, the dowel force–displacement relation is linearly elastic. However, when the elastic limit is exceeded, the dowel action becomes plastic. At the ultimate limit state, local crushing of the surrounding concrete and/or yielding of the dowel bar occurs. Based on experimental results, Dulacska fy = yielding strength of the dowel bar. can be assumed equal to the distance from the inflection point in the dowel at the center of the crack to the level of the bar in the concrete; therefore: Δ=2[yo+(dyodx)(z2)]=Vd2λ2EsIs[(2+λz)λ+(1+λz)(z)]. will yield the dowel force of the reinforcing bar: Vd=1.27db2(fc′)(fy){1−exp[−kVd((2+λz)λ+(1+λz)(z))2.54λ2EsIsdb2(fc′)(fy)u]}.The forces acting on the portion of the dowel within the crack width, z, are as shown in where Mo is equal to −(Vdz2). The moment produced by the dowel force, Vd, will tend to reduce the moment applied at the section where the crack intersects the reinforcing bar. The resultant moment is used in the standard section analysis to compute the strain and curvature. In the standard section analysis, the resultant moment is applied at its corresponding beam cross section. Due to the application of the moment a change in the strains and stresses will occur at the section. Two parameters, strain and stress, are used to define the strain and stress distributions. These two parameters are then obtained from the equilibrium requirements. The analysis is repeated for a number of sections. An arbitrary number of sections along the beam is chosen and incorporated in the computer program to perform the analysis. When the dowel action of the reinforcing bars is not considered, the standard section analysis is performed using the moment applied at the section and not the resultant moment above.It is worth noting that the section analysis employed in the computer program along with the displacement method and the initial stiffness procedure has an advantage over the standard finite element method. The essential feature of the analysis is that the actual deflected shape is obtained by integrating the actual strains and curvatures. In the finite element method, the deflected shape of a member is usually assumed as a function of the displacements at the nodes and equilibrium between the external and internal forces is satisfied only at the nodes.To verify the reliability of the proposed analytical model, a comparison with experimental and analytical work conducted by other researchers is carried out. The deep beams tested by Ashour . The top and bottom longitudinal reinforcement bars have yielding strengths of 500 MPa and 400 MPa, respectively. The web reinforcement was 8 mm diameter steel bars with yielding strength of 370 MPa. The compressive strengths of the concrete for the beams CDB1, CDB2 and CDB3 were 30.0 MPa, 33.1 MPa and 22.0 MPa, respectively.The load–deflection curves are plotted in . It is seen that when the dowel action is not taken into account, the predicted strengths are lower than the corresponding experimental values. However, when the dowel action is taken into account, the load–deflection responses of the beams are in better agreement with the test results. This reveals that the contribution of the dowel action has a significant effect on the behavior of the beams. The effect of the dowel action becomes evident when the applied load approaches the peak. Beyond the peak, the effect of the dowel action is even more significant especially when the aggregate interlock action along the cracks drops due to gradual increase of crack widths. The importance of the dowel action increases as the amount of web reinforcement decreases. In beam CDB1, almost all of the vertical shears are resisted by the web reinforcement and thus the contribution of the dowel action is relatively small. In beam CDB3, there is no web reinforcement and consequently the dowel action plays a more important role in resisting the applied shear force, which agrees with He and Kwan A simple analytical model for the dowel action of reinforcing bars crossing cracks in concrete is developed and incorporated into a computer program for the nonlinear analysis of reinforced concrete beams. The behavior of the dowel bar is derived based on the beam on an elastic foundation theory. Application of the dowel action model to the analysis of deep reinforced concrete beams tested by others verified that the proposed dowel action model can be used to predict the behavior of shear critical reinforced concrete members. The analytical results also showed that the dowel action could have significant effects on the behavior and ductility of the reinforced concrete beams especially when the amount of web reinforcement in the beam is small. Therefore, in the nonlinear analysis of shear critical reinforced concrete members, the dowel action should be taken into account.It is recommended to carry out a parametric study to investigate the influence of some parameters such as bar diameters and amount of reinforcement on the dowel action as a shear transfer mechanism across cracks. Comparison with other experimental results would provide more complete and satisfactory results.Further research on the bearing capacity of dowel action in concrete structures reinforced with fiber reinforced plastic (FRP) bars would provide some insight on the importance of the dowel action.Controlled formation of wrinkled diamond-like carbon (DLC) film on grooved poly(dimethylsiloxane) substrateWe report a simple method for controlled formation of highly-ordered, wrinkled diamond-like carbon (DLC) film on grooved poly(dimethylsiloxane) (PDMS) specimens. Grooved surfaces of the specimens were treated with Ar plasma prior to DLC coating, which resulted in the formation of wrinkled DLC film aligning perpendicular to the steps of the ridges. The wavelength and the amplitude of the resulting wrinkled film exhibited variation in the submicron- to micron-scale range according to the duration of Ar plasma treatment. Since surface topography at the microscale-to-nanoscale level affects cell function in almost all types of mammalian cells, the wrinkled, grooved surfaces coated with DLC film would be applicable to biomedical engineering fields.► We present a method for controlled formation of wrinkled DLC on grooved PDMS. ► Ar plasma treatment of PDMS prior to DLC coating results in the wrinkles formation. ► The size of the wrinkles can be controlled by the duration of Ar plasma treatment. ► The wrinkles exhibit variation in the submicron- to micron-scale range. ► The wrinkled, grooved DLC might be useful in the biomedical engineering field.Surface engineering plays a critical role in fabricating highly functionalized materials applicable to industrial and biomedical fields. Buckling, or wrinkling, is a phenomenon commonly observed in our daily life, and controlling surface wrinkling has recently gained increasing attention as a means to create well-defined and complex surface topographies for various applications |
Diamond-like carbon (DLC) has received considerable attention as a coating material for biomedical applications owing to its outstanding properties |
); however, increasing the film thickness resulted in a coarse surface ( |
(b) to (d)), demonstrating the difficulty in controlling the formation and evolution of wrinkled DLC film simply by increasing the film thickness. In addition, increasing the thickness of hard DLC film can lead to the formation of cracks, which will degrade the outstanding properties of DLC film. Therefore, controlling the formation and evolution of wrinkled DLC film regardless of film thickness would open up opportunities for DLC-polymer composites.In this study, we thus focused on controlling the formation and evolution of wrinkled DLC film on the grooved surfaces of PDMS substrates. We employed Ar plasma treatment to the grooved surfaces of PDMS specimens prior to DLC coating, assuming that Ar plasma treatment would form a modified layer on the top surface of the PDMS substrates and induce buckling, which could then be used to control the formation of wrinkles of DLC film subsequently deposited.Grooved PDMS substrates were fabricated by a molding method using a grooved SiO2 master on Si wafer. The master was fabricated by photolithography and a dry etching process. A silicon (100) wafer with a thermally-oxidized layer of 2 μm in thickness was first coated with negative resist (ZPN1150, ZPN Corp.). Parallel channels of equal groove and ridge with a width of approximately 5 μm were then created on the resist-coated wafer with a mask aligner (SUSS MA6 BSA, SUSS MicroTec). Thereafter, the unmasked region of SiO2 film, i.e. the developed region, was dry-etched (MUC-21, RV-APS-SE, Sumitomo Precision Products Co. Ltd.) to a depth of 1 μm. The resist mask was then removed using n-methyl-2-pyrrolidone (NMP), acetone, isopropyl alcohol (IPA), and DI water. Finally, an oxygen plasma ashing process was carried out to remove the resist completely. The feature size of the grooved surface selected here was recently shown to increase the alignment of endothelial cells |
PDMS prepolymer was prepared by a mixture of silicone elastomer base with a curing agent at a ratio of 10:1 by weight (Silpot 184, Dow Corning Toray Co., Ltd.) and the trapped air bubbles were removed in a vacuum chamber. The resulting mixture was then poured onto the master and cured at 70 °C for 120 min (MH-10, Masada Seisakusho Co. Ltd.). Thereafter, the PDMS replica was peeled off from the master and cut into specimens each with a diameter of ~ 9 mm and a thickness of ~ 6 mm for the experiments.The grooved surfaces of the PDMS specimens were treated with Ar plasma, followed by deposition of DLC film with a radio frequency (RF) plasma-enhanced chemical vapor deposition (PECVD) apparatus (Custom-built, Hirano Koh-on Co., Ltd.) with a frequency of 13.56 MHz. The Ar plasma treatment was carried out at a power of 200 W and a pressure of 26.6 Pa, and the duration varied from 1 to 7 min. The DLC film was subsequently deposited onto the surface from acetylene (C2H2) gas. The deposition was performed for 10 s at a power of 200 W and a pressure of 13.3 Pa. The film thickness was approximately 40 nm, as measured with a profilometer (Dektak3030, Veeco Instruments Inc.).Sample surfaces were observed with a scanning electron microscope (SEM; Sirion, FEI Company) operated at an accelerating voltage of 5 kV. The samples were coated with osmium (Os) prior to observation to prevent electron charging. The detailed surface topographies were analyzed by atomic force microscopy (AFM; SPM9600, Shimadzu Corp.) in dynamic mode and the analysis was performed in a 30 μm × 30 μm area. The measurement was performed at 64 different locations in the area and the results are expressed as the mean of 64 replicates and the corresponding standard deviation. Chemical composition of the sample surfaces was measured by X-ray photoelectron spectroscopy (XPS; JPS-9000MC, JEOL Ltd.) using MgKα radiation, and the photoemission angle was 55°. shows the SEM images of the sample surfaces. Wrinkles aligning perpendicular to the steps were formed on the surface of the PDMS specimens treated with Ar plasma, followed by deposition of DLC film. The orientation of the wrinkles was probably due to the difference in compressive stress parallel and perpendicular to the steps. When steps are present on the surface, the stress perpendicular to the steps is relieved, whereas that parallel to the steps remains almost unchanged |
summarizes the wavelength and the amplitude of the wrinkles on the ridges before and after DLC coating and the aspect ratio (amplitude/wavelength) of the wrinkled DLC film on the ridges as a function of the duration of Ar plasma treatment. For the samples treated only with Ar plasma, the wavelength and the amplitude increased from 880 to 2056 nm ( |
(b)), respectively, as the duration increased from 1 to 7 min. As for the samples coated with DLC film, the wavelength and the amplitude increased from 1017 to 2209 nm ( |
(b)), respectively, with increasing duration. We note that similar results were obtained for the wrinkles formed on the grooves. The aspect ratio of the wrinkled DLC film decreased from 0.13 to 0.09 with longer duration of Ar plasma treatment ( |
(c)). The result of a higher aspect ratio for a wrinkled surface with a smaller wavelength is consistent with the results reported by Ahmed et al. |
shows the chemical compositions of the sample surfaces. The ratios of carbon-to-silicon (C/Si) and oxygen-to-silicon (O/Si) for the untreated PDMS surface were 1.5 and 0.9, respectively. The values are reasonable because PDMS contains a silicon–oxygen skeleton with two methyl groups attached to the silicon atom. The slight difference from the theoretical values was probably due to surface oxidation or contamination. The ratio of O/Si increased whereas that of C/Si decreased after 1-min Ar plasma treatment, which is indicative of the surface oxidation of the PDMS specimen due to the replacement of methyl groups with oxygen by Ar plasma treatment. The ratios of O/Si and C/Si increased as the duration of Ar plasma treatment increased up to 5 min, and further increase in the duration resulted in saturated values. These results imply that the surface oxidation could be enhanced to a limited extent by increasing the duration of Ar plasma treatment. Here, we note that although |
(a) demonstrates the general tendency of the ratio of O/Si to increase with longer durations of Ar plasma treatment, it does not completely reflect the status of the surface chemistry of the samples just before DLC coating because the specimens treated with Ar plasma were removed from the chamber for XPS analysis, and in such a situation, changes in the surface composition are inevitable. |
(b) shows the elemental composition of the DLC-coated sample surfaces. The increase in the concentration of carbon was attributed to DLC film as DLC mainly consists of carbon and the oxygen detected was attributable to the surface oxidation of the film. A small amount of silicon (~ 7 at.%) was detected despite the DLC coating, which implies that small portions of the samples, such as sidewalls of the ridges, were not entirely covered with the film. However, the elemental composition for the samples coated with the film was almost identical irrespective of the duration of Ar plasma treatment.The wavelength, λ, of the wrinkles of the film can be expressed by Eq. |
This equation shows that an increase in the film thickness and/or Young's modulus lead to an increase in the wavelength. XPS analysis reveals the formation of an oxidized layer due to Ar plasma treatment ( |
(a)) and therefore, the increase in the wavelength shown in |
(a) was probably due to an increase in the thickness and/or Young's modulus of the layer. According to Eq. |
, the wavelength of wrinkles is proportional to the layer thickness and the ratio of Young's modulus between the layer and the substrate to the one-third power. Since the power index of the layer thickness is much greater than that of the modulus ratio, the layer thickness has a stronger effect than the modulus ratio in determining the wavelength. The increase in the layer thickness would presumably be the predominant factor in increasing the wavelength of the wrinkles. The wavelength only slightly increased after DLC coating, as illustrated in |
(a). This was probably because of the stability of the system after the formation of wrinkles by Ar plasma treatment. In addition, as shown in Eq. |
, the wavelength is not a function of the applied stress, or the stress in the DLC film.The amplitude, A, of the wrinkles can be given by Eq. |
, where ε and εc are the applied strain and the critical strain to induce buckling, respectively. |
Since the extent of applied strain is limited by the nature of the polymer, the amplitude of the patterns created should thus be on the order of the layer thickness |
(b) shows that further increase in the duration of Ar plasma treatment would eventually lead to a saturated value for the amplitude, which could be attributed to the limitation of the thickness of the oxidized layer. The increase in the amplitude after DLC coating could be attributed to the stress in the DLC film because the amplitude is a function of the applied strain, as shown in Eq. |
We note that although we adopted one specific feature size of the grooved surface in the present study, we were able to observe the formation of wrinkles on grooved surfaces of varying feature sizes through our preliminary study. It would be desirable to select the feature size depending on the potential applications. We also observed that the pressure of Ar plasma treatment could affect the wavelength and the amplitude of the wrinkles. In the present study, the conditions of Ar plasma treatment were selected based on the optimum conditions of DLC film deposition using the apparatus described in Materials and methods. Further detailed studies on the effects of Ar plasma treatment conditions on the wrinkles formation and the characterization of the layer formed by Ar plasma treatment would allow for more control over the size of the wrinkles.We have shown that we can fabricate ordered, wrinkled DLC film on grooved surfaces of PDMS substrates and control the wavelength and the amplitude of the wrinkles in the submicron- to micron-scale range simply by controlling the duration of Ar plasma pre-treatment. This technique, as well as the wrinkled DLC film fabricated in this study, would be applicable in the field of biomedical engineering. Further in vitro and in vivo investigations are needed to investigate the effects of the surface topographies on the behavior of endothelial cells.Interfacial characteristics and mechanical properties of duplex stainless steel bimetal composite by heat treatmentThe interfacial morphologies play a crucial role in mechanical properties of laminated/bimetal composite. This study investigates the effects of heat treatments on the interfacial characteristics, mechanical properties and fracture behaviour of a 2205 duplex stainless steel/AH36 carbon steel bimetal composite with varying interface situations fabricated by the hot-rolling and subsequent heat treatments. The bimetal composite was annealed from 850 °C to 1150 °C in steps of 100 °C with soaking 1 h. Heterogeneities of grain size and element concentration exist in the microstructural evolution of bonding zone adjacent to interface after annealing treatments, which were observed by the optical microscope and scanning electron microscope (SEM) coupled with the energy dispersive X-ray spectroscopy (EDS). It was found that the diffusion transition zone of Cr and Fe alloy elements between component 2205 and AH36 steel layers present an increasing trend with the rise of annealing temperature. The results of conventional, shear and compact tensile test indicate that the tensile strength of 2205/AH36 bimetal composite gradually decreases but the fracture elongation increases with the rising annealing temperature, the thicker alloy element diffusion zone results in the stronger interfacial shear strength and better ductility of bimetal composite, but the thick and strong interface has less positive effect than the mechanical properties of bimetal composite itself on preventing the fatigue crack growth across the interface.Bimetal and laminated metal composite with dissimilar metal layers can be used in a variety of aggressive fields, such as shipbuilding, chemical and oil production, as well as power plants and flue gas desulphurisation plants, due to their ideal combination of good mechanical properties, corrosion resistance, and adequate weldability []. In comparison with single component materials of composite, the bonding zone adjacent to the interface formed in the composite manufacturing process, shows a complex combination and gradient of microstructure with various crystal structures, morphology and diffusion of alloy elements []. The different properties of interfacial bonding zone have an important effect on the quality of bimetal composite [], so that the microstructural characteristics and mechanical properties of interfacial zone have been studied by several researchers.Some researchers focused on interfacial properties of bimetal composite after fabrication, such as explosive bonding and rolling [], without heat treatments to verify and optimise the fabrication processing. The tensile properties and micro-hardness of bonding interface for the austenitic stainless/low carbon ferritic-pearlitic steel composite were investigated by Motarjemi et al. [], and it has been found that the ultimate tensile strength and micro-hardness showed a sudden drop near the interface due to a carbon depleted zone between two component layers. The creation of interface zone was reported to change the failure type of aluminium/copper composite in the shearing process []. The bonding strength of tri-metal aluminium/stainless steel/aluminium composite was evaluated using peeling test by Akramifard et al. [], and they indicated that the bonding strength was enhanced by increasing the amount of thickness reduction. Mendes et al. [] demonstrated that the width of interface zone correlated the shear strain of aluminium/steel composite. Yang et al. [] studied the influence of thermal conductivity on bonding strength for multilayers, and indicated that the composite exhibited relative high bonding strength with low thermal conductivity.Other researchers have studied the effects of heat treatment on interfacial properties to improve the performance of laminated composites. Liu et al. [] studied the effects of heat treatment on the microstructure and mechanical properties of hot-rolled stainless steel clad plate. Macwan et al. [] discussed the correlation between post-roll annealing and interface microstructures of aluminium/magnesium/aluminium tri-layered metal composite. They indicated that the higher annealing temperatures gave rise to the thicker width of interface compounds. Bina et al. [] reported that the thickness of diffusion zone and the tensile strength were larger with the increased heat treatment time and temperature for copper/stainless steel bimetal plate and laminated zirconium/titanium plate, respectively. The effects of different annealing time at 500 °C for aluminium and stainless steel bimetal plate were studied by Hwang et al. [], who concluded that thicker intermediate layer reduced the bonding strength for over 2 h annealing time. Sheng et al. [] investigated the interface structure of aluminium/copper composite at various annealing temperatures. The former one found that the heat treatment with low temperature could improve the bonding strength of aluminium/copper bimetal composite, but high temperature and long heat treatment time caused the formation of intermetallic compound zone in the interface which reduced the bonding strength. Chen et al. [] also obtained the similar relationship between the bonding strength and annealing temperature for the aluminium/steel composite plate. Quadir et al. [] proposed that the post-rolling recrystallisation annealing process could improve the bonding toughness for adjacent aluminium strips. Although a large amount of research has been done into the interfacial characteristics and mechanical properties of various bimetal or laminated composite, there is still a lack of research into the microstructural characteristics and behaviour of bonding zone adjacent to the interface of duplex stainless steel bimetal composite under various post heat treatment conditions, and the mechanical and fracture properties of interfacial zone after high temperature treatments need also to be further studied.This study aims to investigate the interfacial characteristics and mechanical properties of duplex stainless steel bimetal composite annealed from 850 °C to 1150 °C in steps of 100 °C with soaking 1 h. A comparative study will be made on the influence of annealing temperature on interfacial characteristics, including the diffusion behaviour of different elements, the thickness of bonding zone and fracture behaviour, as well as total tensile and shear tensile performance of bimetal composite. After the introduction in Section , the details of experimental procedures will be presented in Section , the experimental results will be addressed, including optical micrographs of bimetal composite in Section , and element diffusion behaviour of interfacial zone in Section , the correlation between interfacial characteristics and conventional, shear and compact tensile behaviours was systematically discussed in Sections , respectively. The final aim of this work is to provide a reference for the optimisation of the practical fabrication processing of duplex stainless steel bimetal composite.A duplex stainless steel bimetal composite, including 2205 duplex stainless steel layer (3 mm) and AH36 carbon steel layer (8 mm), was fabricated by the hot-rolling and annealing process at 850 °C, 950 °C, 1050 °C and 1150 °C for 1 h, respectively. The chemical compositions of each steel layer are shown in Experimental samples were cut from a bimetal composite plate perpendicular and parallel to the rolling direction (). After annealing, the interfacial evolution and microstructure were investigated in the rolling direction-normal direction (RD-ND) section plane of composite specimens. The RD-ND section plane was mechanically ground followed by etching with a solution of 50 ml HCl +50 ml HNO3+50 ml H2O, and the optical microstructure of interfacial zone was investigated by the Nickon Eclipse LV100NDA optical microscope. A JSM-6490F scanning electron microscope (SEM) coupled with the energy dispersive X-ray spectroscopy (EDS) was employed to investigate the morphology and elements diffusion of the interfacial zone.In order to evaluate the effect of annealing treatment on the interfacial characteristics and mechanical properties of bimetal composite, conventional and shear tensile tests using a fatigue testing system (Instron-8801) were conducted, respectively. The conventional tensile specimen with the gauge length of 25 mm, and the thickness of 6 mm (the thickness of each layer is 3 mm) was cut based on ASTM a. The shear tensile specimen, as shown in b, was employed to evaluate the interfacial bonding strength and distinguish the fracture behaviour of bimetal composite. The compact tensile specimen based on the ASTM 647, as shown in c, was used to investigate the influence of heat treatment on the crack growth behaviour across the interface, and a micro tensile tester [] was used in this experiment. All the tests were repeated 3 times for each specimen.Hot rolling is a solid-state bonding method to join dissimilar metals with a certain pressure at elevated temperature, which generates the microstructure evolution of bonding metals, such as interfacial grain recrystallisation [ shows the microstructure of specimens after hot rolling and subsequently heat-treated at 850, 950, 1050 and 1150 °C in the RD-ND cross-section plane, respectively. The left duplex stainless steel (2205) layer has a characteristic laminated structure, composed of alternating long ribbon-like ferrite and austenite phase bands. The right low carbon steel (AH36) layer contains the polygonal ferrite grains. Generally, the interface transition zone of stainless steel bimetal composite contains an obvious decarburised zone of carbon steel substrate and a carburised zone of stainless steel [], but the carbon element transition zone between two steel layers is not clear after all heat treatments in this study. The possible reason is that the coexisting ferrite and austenite interweave with each other in 2205 steel layer, which can reduce the diffusion of carbon element from AH36 steel layer, even though the diffusion velocity and solubility of carbon element in ferrite and austenite are different, i.e., the carbon element has higher diffusion speed but lower solubility in ferrite phase compared with austenite phase []. As a result, the black carbide thin band is concentrated at the interface that constitutes a clear boundary, but no obvious interface oxides can be observed.In addition, the optical microstructure evolution of 2205 and AH36 steel layers has no obvious difference after annealing treatments. The ferrite and austenite phases of 2205 steel layer remain markedly oriented along the RD with the morphologically anisotropic structure under each state, but thicker bands of austenite and ferrite phases gradually appear in the specimens annealed at 1050 and 1150 °C. It is also interesting that the ferrite grains of AH36 steel layer near interface are coarsening after heat treatments, marked by the interface and red dashed line in , and this situation is obvious for the specimen after annealing at 850 °C. The reason was presented by Liu et al. [] that it is difficult to refine the grains of decarburised zone of carbon steel layer due to the absence of pearlite which can encourage the nucleation of ferrite grains.The diffusion behaviour of interfacial elements between component steel layers plays an important role in the bonding status and interfacial strength of bimetal composite, and a greater alloy diffusion distance often leads to the stronger interfacial shear strength []. In this study, the most difference of chemical compositions between the 2205 and AH36 steels contains C, Cr, Fe, Mo and Ni elements. The concentration difference of these elements between two steel layers causes the element diffusion during bonding and post annealing processes. The resulted element diffusion was obtained by EDS analysis. SEM morphologies and X-ray mappings of Cr and Fe elements adjacent to the interface after annealing treatments at different temperatures of 850 °C, 950 °C, 1050 °C and 1150 °C are shown in . It can be seen that an obvious drop in compositions of Cr element appears in the AH36 steel layer, whereas there is a sharp increase in compositions of Fe element. The diffusion zone of Cr and Fe elements between two steel layers is not obvious after annealing at 850 °C and 950 °C, but the gradient distribution of Cr and Fe elements can be observed after annealing at 1050 °C and 1150 °C.In order to obtain the alloy diffusion distance, the resulted profile curves of element diffusion under different states (a–d) were drawn following the scan line in . It is clear that the diffusion transition zone between two component steel layers increases with the rise of annealing temperature (] also reported this similar phenomenon. The growth of the transition zone is assumed to be parabolic law, and its thickness can be defined as [where δ is the thickness of transition zone (m), t represents the bonding or annealing time (s), and K denotes the inter-diffusion coefficient, expressed by Arrhenius equations:where K0 is the frequency factor (m2 s−1), Q is the activation energy (J mol−1) for inter-diffusion, R is the gas constant (8.3145 J mol−1K−1), and T is the absolute temperature (K)., the thickness of transition zone is expressed as:As the annealing time of all states is the same (1 h), taking logarithm of both sides of Eq. The activation energy (Q) and the frequency factor (K0) can be estimated from the slope and intercept of the relationship plot of lnδ versus1/T, respectively. Therefore, the activation energy (Q) is calculated as 124.8 KJ mol−1, and the value of K0 for the transition zone is calculated as 5.98 × 10−6 m2 s−1. The predicted thickness values of transition zone can be calculated at different temperatures of 850 °C, 950 °C, 1050 °C and 1150 °C, respectively. The predicted results in comparison with experimental values are listed in b. A good agreement between the experimental mean thickness values and the predicted thickness values was observed.Moreover, the diffusion concentration profiles of Fe and Cr elements in transition zone are different (a–d), and the diffusion profiles for Fe or Cr element in 2205 steel layer are also different from that in AH36 steel layer. The element diffusion behaviour is non-steady obeying Fick's second law, so that the element concentration across the interface between 2205 steel layer and AH36 steel layer can be quantified by the diffusion equation [where c is the concentration of element, D2205 and DAH36 are the diffusion coefficients in 2205 steel layer and AH36 steel layer, respectively, and x is the diffusion distance of element.As the thickness of transition zone is much smaller than that of entire specimen, the bonded bimetal composite can be seen as infinite diffusion couples. The initial and boundary conditions, which can be used to calculate the solution of diffusion equation, are expressed below, respectively:Initial condition:c(x,t=0)={c1(x<0)c2(x>0)Boundary condition:c(x,t)={c1(x=−∞)c2(x=+∞)where c1 and c2 represent the concentration for a particular element in 2205 steel layer and AH36 steel layer, respectively. Due to the same diffusion flux on the interface, there is an added boundary condition [c(x,t)={c1=k1+k2erf(x2D2205t)(x<0)c2=k1+k2'erf(x2DAH36t)(x>0)where k1 is the element concentration of the centre plane, and k2 and k2' are the variation amplitudes of the element concentration in 2205 steel layer and AH36 steel layer, respectively. As a result, the element concentration across interface of 2205/AH36 bimetal composite can be calculated using above relations.The tensile properties of bimetal composite are a critical evaluation index when it is applied in structural components []. The microstructure and interface morphology of composite material will be changed under different heat treatments. To investigate the effect of annealing on the mechanical properties of bimetal composite, conventional uniaxial tensile tests were first conducted. shows the true stress-strain curves, tensile strength and fracture elongation for bimetal composite at different annealing temperatures for 1 h. Tensile results show that the tensile strength gradually decreases but the fracture elongation is larger with the increase of annealing temperature. Previous study has indicated that the tensile strength of strong 2205 steel layer play a dominant role in the total tensile strength of bimetal composite [], but the coarsening grain of 2205 steel with the rise of annealing temperature leads to the decrease of total strength due to the Hall-Petch strengthening law []. Another reason is that the elimination of dislocations and residual stress in composite results in the decrease of tensile strength at higher annealing temperatures []. Meanwhile, the thicker bonding transition zone at higher annealing temperatures has less influence on the total tensile strength of bimetal composite here. The elongation is the main factor of judging plasticity, so the relatively good plasticity may coincide with the good microstructure of relatively homogeneous grain size at high annealing temperatures. In addition, the stress-strain curve has a tendency of sudden change at 1050 °C, but the difference of stress-strain curve between 1050 °C and 1150 °C is not obvious, indicating that the 1050 °C is the critical annealing temperature of significant change in microstructure and interface morphology of bimetal composite here.a and b). These phenomena are attributed to the lack of plasticity and ductility of both 2205 steel and AH36 steel layers annealed at 850 °C and 950 °C. The fracture pacing of two different layers is relatively consistent, and both damage behaviours are brittle fractures. This also explains that the tensile elongation values of specimens annealed at 850 °C and 950 °C are relatively low (In contrast, the diffuse necking and interface delamination appear in the tensile specimens annealed at 1050 °C and 1150 °C (c and d). The fracture positions and times between 2205 steel and AH36 steel layers are also not the same. As the plasticity and ductility of 2205 steel are weaker than that of AH36 steel, the fracture time of 2205 steel is early under the same imposed strain [], which can be verified by the existing small step (marked by yellow dashed lines in c and d), resulted from the further necking of AH36 steel layer, on frontal fracture section between two different steel layers. Therefore, there are two reasons for the interface delamination of tensile specimens annealed at 1050 °C and 1150 °C: (i) the discrepant localised necking of two steel layers in the thickness direction; (ii) the further deformation and localised necking of AH36 steel layer after the fracture of 2205 steel layer. In addition, the warping phenomenon has also been observed in the specimens annealed at 1050 °C and 1150 °C, in which the small curvature occurs on the frontal fracture section. It is attributed to the different elastic and plastic deformation between two steel layers of bimetal composite [], and another reason is that the further localised necking of AH36 steel layer produces a certain bending moment on 2205 steel layer, which further exacerbates the warping phenomenon.The schematic illustration of delamination in the tensile deformation process of bimetal composite was conducted to explain its tensile fracture behaviour with the delamination, as shown in . The heterogeneity in grain size, strength and stacking fault energy between two steel layers of composite annealed at 1050 °C and 1150 °C leads to the incompatible behaviour during the tensile deformation process []. The ductility of AH36 steel layer is better than that of 2205 stainless steel, resulting in the different material flow speeds and the shear stress field, as shown in b. The different flow speeds and shear stress lead to the form of intergranular tunnel cracks in the transition zone, and consequently the occurrence of tensile delamination [The shear tensile tests were conducted to evaluate the bonding interface strength of bimetal composite, which is an important consideration to make the composite be safely applied in industrial service. shows the shear load versus extension curves of specimens annealed at 850 °C, 950 °C, 1050 °C and 1150 °C. It is noted that all shear tensile curves have a fracture starting point, marked by circles in , in which the interface begins to slide and fracture. Taking the facture starting point as a boundary, all shear tensile specimens experienced two deformation stages. The shear load first increases with the rise of extension until to a sharp decrease at the fracture starting point, and then the shear load remains essentially constant until the loaded specimen is completely broken. The fracture starting point load values of specimens annealed at 850 °C and 950 °C are close, and the load values at fracture starting point increase with increasing annealing temperatures from 950 °C to 1150 °C. In addition, the shear extension increases with the increase of annealing temperature as well, and the maximum shear extension occurred in the specimen annealed at 1150 °C. Consequently, the thicker alloy element diffusion zone results in the stronger interfacial shear strength and better ductility of bimetal composite, and the element diffusion is kind of interfacial metallurgical bonding process. The similar results were reported by Wang et al. [ shows the profile, frontal shear fracture morphologies, and 3D profile images of 2205 steel layer of shear tensile specimens annealed at different temperatures. From the profile fracture morphologies (a–d), it is seen that all shear fracture positions are located at relatively weak AH36 steel layer, and the fracture and crack starting points are presented at the junction of both ends (). The crack propagation direction is almost along 45° with the bonding interface accompanying with a slight warping phenomenon on AH36 steel layer. The warping is obvious for the shear tensile specimen annealed at 1150 °C, which reveals that the interface strength has been enhanced at high annealing temperature []. The frontal fracture morphologies are not smooth (-d1), and there is a small bulge occurred on the 2205 steel layer after the shear tensile test at all states. The 3D profile images of bulge were obtained by the laser microscope (-d2), and it is noted that the peak values of bulge from 339.3 μm to 239.8 μm decrease with the increase of annealing temperature. As the higher annealing temperature leads to the stronger interface strength, a stronger bonding transition zone can experience less plastic deformation with a smaller bulge.The finite element (FE) simulation model was built to study the shear tensile process, the position of fracture starting point and the located fracture area. To simplify the FE model, the bonding interface between 2205 steel and AH36 steel layers was set as the rigid connection in this study []. The FE stress distribution of specimen annealed at 850 °C in the shear tensile test is shown in . The maximum stress occurred at the junction of both ends, which means that this area is most prone to material failure and fracture. As the 2205 steel layer is relatively stronger than the AH36 steel layer, the cracks and damage are more likely to invade and propagate to the weak material. The aforementioned experimental results and phenomenon of shear tensile specimens agree well with FE simulation results.The compact tensile tests with mode-I cracked specimens were conducted to investigate the fracture toughness and fatigue crack growth behaviour of bimetal composite after annealing treatments. The mode-I crack in strongly bonded bimetal composite often nucleates in the weaker component layer with lower yield strength as well as smaller fatigue threshold, and then propagates to the interface of stronger layer [], so that the compact tensile tests were carried out following this weak-strong transition path. shows the relationship curves of load versus tensile distance of compact specimens annealed at different temperatures. It is found that the curve shape of specimens annealed at 850 °C and 950 °C is different from that of specimens annealed at 1050 °C and 1150 °C. The former two tensile load-distance curves, shown in a, have two stages: (i) the specimen experiences elastic and plastic deformation without the crack growth, and the load value increases with the rise of tensile distance; (ii) based on the experimental observation, the crack occurs in both AH36 steel layer and 2205 steel layer at the same time after a sharp drop of load, marked in the circles, and the crack continues to propagate in 2205 steel layer until to be completely broken. In contrast, the latter two tensile load-distance curves, as shown in b, have one more stage and there are three stages: (i) the first stage is the same as the former curves with the specimen experiencing the deformation process; (ii) the crack occurs in the AH36 steel layer with a slight decrease of load at point A, marked in the circle; (iii) the crack begins to propagate across the interface with the second sharp drop of load at point B. In addition, the tearing load value of specimen annealed at 850 °C is higher than that of specimen annealed at 950 °C, and the load at 1050 °C is greater than that at 1150 °C. This trend agrees well with the influence of annealing temperature on the total tensile strength of bimetal composite. Meanwhile, it indicates that the thick and strong interface has less positive effect than the mechanical properties of bimetal composite itself on preventing the fatigue crack growth across the interface from weak layer to strong layer of bimetal composite.Crack propagation paths across the interface under different states were obtained to investigate the influence of annealing temperature on the crack growth behaviour of bimetal composite, as shown in . As mentioned before, the crack appeared in 2205 and AH36 steel layers annealed at 850 °C and 950 °C at the same time from the beginning, marked by the blue arrow in b1, and then the crack grows directly in the 2205 steel layer. In addition, the crack paths are not smooth with jagged edge, shown in b2. The reason mentioned before that the plasticity and ductility of bimetal composite have been reduced by the annealing treatments at 850 °C and 950 °C, leading to the brittle shear fracture. On the other hand, the crack propagates from the AH36 steel layer to interface (marked by the blue arrow in d1), and then to 2205 steel layer (marked by the blue arrow in and 13d3) step by step in the specimens annealed at 1050 °C and 1150 °C, respectively.The effects of heat treatments over the temperature range from 850 to 1150 °C on mechanical properties and interface characteristics of 2205/AH36 duplex stainless steel bimetal composite were investigated in this study. The main conclusions of this research are obtained as follows:There is no significant difference in optical microstructure of 2205 and AH36 steel layers under various annealing treatments. The ferrite and austenite phases of 2205 layer show markedly oriented along the RD. The AH36 steel layer contains the polygonal ferrite grains, but the ferrite grains of AH36 layer coarsen adjacent to the bonding interface.The diffusion transition zone of Cr and Fe alloy elements between two 2205 and AH36 steel layers present an increasing trend with the increase of the annealing temperature, and its experimental mean thickness and predicted thickness show a good agreement. A calculation method of alloy element concentration across interface of bimetal composite was proposed as well.The tensile strength of 2205/AH36 bimetal composite gradually decreases but the fracture elongation increases with the increase of the annealing temperature. No obvious diffuse necking and interface delamination occur in the tensile specimens annealed at 850 °C and 950 °C, but these phenomena appear in the tensile specimens annealed at 1050 °C and 1150 °C.Based the results of shear tensile tests, it is concluded that the stronger interfacial shear strength and better ductility of 2205/AH36 bimetal composite results from the thicker alloy element diffusion zone. The shear fracture positions are located at relatively weak AH36 steel layer under all heat treatments, and the fracture and crack starting points are presented at the junction of both ends of shear tensile specimen.As the relatively low plasticity and ductility of 2205/AH36 bimetal composite annealed at 850 °C and 950 °C, the crack appeared in two steel layers together from the beginning, and the compact tensile load-distance curves have two main stages. In contrast, the crack propagate from the AH36 steel layer to interface, and then gradually to 2205 steel layer, and the compact tensile load-distance curves have three stages. The thick and strong interface has less positive effect than the properties of bimetal composite itself on preventing the fatigue crack growth across the interface.Zhou Li: Conceptualization, Methodology, Investigation, Formal analysis, Writing - original draft. Jingwei Zhao: Methodology, Data curation, Supervision. Fanghui Jia: Methodology, Software, Investigation. Xiaojun Liang: Validation, Resources, Supervision. Qingfeng Zhang: Resources, Project administration. Xiangqian Yuan: Validation, Resources, Project administration. Sihai Jiao: Resources, Funding acquisition, Supervision. Zhengyi Jiang: Conceptualization, Writing - review & editing, Supervision.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.Probing the effects of thermal treatment on the electronic structure and mechanical properties of Ti-doped ITO thin filmsTitanium-doped indium tin oxide thin films were synthesized via a sol-gel spin coating process. Surface chemical bonding states and mechanical properties have been investigated as a function of titanium content (2 and 4 at%) and annealing temperature ranging from 400 to 600 °C with increments of 100 °C. Raman analysis was performed to study the phonon vibrations for the prepared samples and the results revealed the existence of ITO vibrational modes. The elemental compositions, bonding states and binding energies of the film materials were investigated using X-ray photoelectron spectroscopy (XPS) technique. The XPS results indicated that the ratio of the metallic elements (In, Sn, Ti) to the oxygen on the surface of the thin film coatings decreased due to the increase of the oxide layer on the surface of the thin films. Also, by increasing the annealing temperature up to 600 °C, the Ti 2p and Cl 2p signals were no longer detected for both 2 and 4 at% Ti contents, respectively, due to the thicker surface oxidation layer. Mechanical properties of the synthesized films were also evaluated using a nanoindentation process. Variations in the hardness (H) and the elastic modulus (E) were observed with different Ti at% and annealing temperatures. The hardness is within the range of 6.3–6.6 GPa and 6.7–6.8 GPa for 2 and 4 at% Ti content samples, respectively, while the elastic modulus is within the ranges of 137–143 and 139–143 GPa for 2 at% and 4 at% Ti contents samples, respectively. A combination of the highest H and E were achieved in the sample of 4% Ti content annealed at 600 °C. Furthermore, the H/E ratio ranges from 4.5 × 10−2 to 5.0 × 10−2 which reflects a reasonable level of wear resistance.Transparent conductive oxides (TCOs) receive widespread attention from researchers due to their unique combination of very low electrical resistivity and high optical transparency over the visible spectral region Novel ITO composites doped with 3-d and/or 4-d transition metals, such as (Ti, Ag, Cr, Mo, W, Ta and Cu), are being considered as potential candidates in a wide range of optoelectronic applications such as organic and inorganic solar cells, touch screens, organic light-emitting diodes, sensors and electro-chromic devices Hydrated indium nitrate (In(NO3)3⋅5H2O, purity 99.9%, Alfa Aesar) titanium(IV) isopropoxide (Ti[OCH(CH3)2]4, purity 99.9%, Sigma Aldrich), and tin chloride dihydrate (SnCl2⋅2H2O, purity 98%, Chem-supply) were used as received as precursors to produce Ti-doped ITO films via a sol-gel spin coating process. Absolute ethanol was used as a solvent and the ITO films were deposited onto soda-lime glass slides.ITO solutions (0.1 M) were prepared by dissolving appropriate amounts of In(NO3)3⋅5H2O and SnCl2⋅2H2O separately in absolute ethanol. The solutions were combined and stirred vigorously for 1 h. Required amounts of (Ti[OCH(CH3)2]4) were then dissolved in ethanol and added to ITO solutions in order to obtain solutions of Ti doped ITO with 2 and 4 at% Ti contents, respectively. The resultant solutions were then refluxed at 85 °C for 1 h and aged for 24 h at room temperature. Since uniformity and homogeneity of the thin films mainly depends on the cleanness of the substrates, the glass substrates with (25 × 25 mm dimensions) were first washed with soap and rinsed repeatedly in deionized water. Then, the substrates were sonicated at 60 °C for 10 min in ethanol and DI water, respectively and dried in a vacuum drying oven at 100 °C, prior to the coating process. A Polos spin coater was used to fabricate Ti-doped ITO films based on three main spin steps. Firstly, the solution was dispensed on to the substrate at 300 rpm for 15 s followed by spreading at 2500 rpm for 20 s and finally dried at 4000 rpm for 20 s. The sample was calcined on a conventional hot plate at 150 °C for 10 min. These steps were repeated until the desired coating thickness (300–400 nm) was achieved. Thermal annealing in air atmosphere was performed upon the fabricated samples at (400, 500 and 600) °C for 2 h. is the flow chart for Ti doped ITO thin films preparation via sol-gel spin coating technique.Raman analysis was performed on a Nicolet 6700 Fourier transform infrared (FT-IR) spectrophotometer attached with an NXR FT-Raman module. Raman spectra were obtained by using the following settings: Helium-Neon (He-Ne) laser beam with excitation wavelength and operation power of 1064 nm and 0.204 W, respectively, InGaAs detector with 90° detection angle, optical velocity of 0.3165, CaF2 beam splitter, gain of 1, aperture of 150, maximum peak to peak signal along with optimum focusing and side-to-side values, and 32 scans with resolution of 8 cm−1 in the range of 0–4000 cm−1. Information of elemental compositions, chemical structures and bonding states of the thin film coating surfaces were probed using a Kratos Axis Ultra-X-ray Photoelectron Spectrometer. The X-ray source was Al-Kα monochromatic radiation (hv = 1486.6 eV) with a power of 15 kV and 10 mA. The base pressure of the analysis chamber maintained at 2.9 × 10−9 Torr. The XPS survey and high resolution scans were collected before etching. Typical high resolution XPS core level spectra were focused on the regions of In3d, Sn3d, Ti2p, O1s and C1s. The deconvolution of high resolution spectra was carried by employing the CASA XPS software (version 2.3.1.5) which provides information for the analyses of chemical bonding states.The elastic modulus (E) and the hardness (H) of the coatings were measured using a nanoindentation workstation (Ultra-Micro Indentation System 2000, CSIRO, Sydney, Australia), equipped with a diamond Berkovich indenter The structural and morphological properties of the synthesized and annealed Ti-doped ITO thin film coatings were characterized via x-ray diffraction (XRD) and field emission scanning electron microscopy (FESEM) techniques and were discussed in our previous work The FESEM images of the synthesized ITO and Ti-doped ITO films as deposited (150 °C) and after being annealed at 400, 500 and 600 °C show that the surfaces of all the thin films are smooth, homogeneous, and composed of uniform coalesced clusters, and show a grain structure demonstrating nanocrystalline features. However, the as deposited thin film of 4 at% Ti shows a smoother surface and possesses larger grains compared to those of pure ITO and 2 at% Ti-doped ITO, which may be attributed to the enhancement of crystallinity with Ti ratio.Raman spectroscopy was used to study the effect of Ti contents and annealing temperature on the electronic and mechanical properties of Ti doped ITO thin films. It is well known that ITO based materials have a body centred cubic structure that belongs to Ia3 space group, similar to that of In2O3. Two types of cation are present in the ITO based structure: (1) 8 In3+ with 3 sides symmetry at b-sites and (2) 24 In3+ with 2-fold point symmetry at d-sites. Moreover, the 48 oxygen atoms in this structure occupy general e-sites with no symmetry. Thus, six possible vibration modes may be identified The Ag, Eg and Tg symmetry vibrations are Raman active and infrared (IR) inactive modes; whereas, Tu vibration modes are Raman inactive and IR active. The Au and Eu vibration modes are inactive for both Raman and IR measurements. presents the results of Raman active modes for the Ti doped ITO thin films at 2% and 4% Ti concentrations after being annealed at the temperatures of 400, 500 and 600 °C. The observed vibrational modes correspond to 106, 135, 176, 275, 367, 432, 584, 633 and 704 cm−1 which represent an unequivocal finger print for In2O3 and/or ITO cubic structure These results are in good agreement with Raman active modes observed from In2O3 and ITO based materials, refer to The elemental compositions of Ti doped ITO thin films were obtained via XPS survey scans. (a, b) shows the survey scan results for the synthesized Ti doped ITO thin films for both Ti contents. The photoelectron peaks for In3d, Sn3d, Ti2p, O1s, Cl2p and C1s in the binding energy range of 0–1200 eV were observed. The XPS survey spectra confirm the existence of the principal elements (In, Sn, Ti, Cl and O), as well as carbon, in the related sample coatings. lists the atomic compositions of the Ti doped ITO thin films at 2% and 4% Ti concentrations after being annealed at 400, 500 and 600 °C. The results imply that the surface elemental composition of the film materials was significantly affected by annealing temperature. As the annealing temperature increased, the ratio of atomic percentages of the principal elements (In, Sn and Ti) to oxygen on the surface of the thin film coatings decreased for both levels of Ti doping. At 600 °C the Ti2p and Cl2p signals were completely absent for both 2 and 4 at % Ti concentrations, respectively, indicating that surface oxidation is taking place at high temperature. As the oxygen content becomes higher at high temperatures, the surface oxidation layer should become thicker. In order to compensate for any charge shifts, the XPS energy scale was calibrated by the C1s (C-H) line at 284.60 eV (bonding energy).The XPS spectra for these elements are shown in . The surface chemical bonding states of the annealed Ti doped ITO films were characterized by de-convoluting the high resolution In3d, Sn3d, Ti2p, Cl2p and O1s photoelectron lines using the Gaussian distribution, in order to appraise analysis the possible chemical bonding states of these atoms in the composites. The parameters, derived from the analysis of the XPS spectra, are listed in and include: the photoelectron lines, bonding states and their corresponding binding energies, full width at half maximum (FWHM) values and atomic percentages of the elemental compositions present in the films after being annealed at 400, 500 and 600 °C as evaluated from XPS curve fittings.The de-convoluted curves of the high resolution XPS spectra of In3d5/2 photoelectron lines are shown in (a, b). It is clear that the de-convoluted In3d5/2 spectrum is assigned to three different bonding states in the range of 443.6–445.4eV. The lower energy peaks placed within the range 443.6–443.8 eV (labelled i) is linked to In° bonding state, precisely In-In bonds, while the mid energy peaks located in the range 444.1–444.6 eV (labelled ii) corresponds to In3+ bonding state from In2O3 displays the de-convoluted curves of high resolution XPS spectra for Sn3d5/2 photoelectron lines. Three bonding states in the range of 485.6–487.2 eV have been allocated. The first components are obtained within the range 485.6–485.8 eV (labelled ‘i’) correspond to Sn4+ in SnO2, whereas the second features (labelled ‘ii’) observed in the range 486.0–486.5 eV are related to Sn2+ from SnO. It has been reported by Fan and Goodenough that the Sn3d peak for Sn2+ in SnO was seen at a binding energy around 0.5eV higher than that for Sn4+ in SnO2The Ti2p photoelectron lines of Ti doped ITO films are presented in . The curve fitting of Ti2p core level XPS spectra assigned three components within the energy range of 457.3–458.5 eV. The lower constituent in the energy range of 457.3–457.5 eV (labelled ‘i’) corresponds to Ti3+ in Ti2O3 bonding state The de-convolution of O1s spectra exhibits three sub-peaks within the energy range of 529.3–531.8 eV as shown in . The first components in the range of 529.3–529.6 eV correspond to O-In bonds and O-Ti bonds, in In2O3 and Ti2O3. The second components within the range 530.3–530.8 eV are attributed to TiO2 and SnO2 bonding states. Finally, the other components in the range of 531.4–531.8 eV could be due to the existence of O-Sn bonds shows the results from curve fitting of high resolution XPS spectra for Cl 2p photon lines. Here also three components were obtained in the range of 197.6–199.9 eV. The first components are observed in the energy range of 197.6–198.0 eV (labelled ‘i’) related to InCl bonding state details the de-convoluting results of the XPS data of spin coated Ti doped ITO samples as a function of Ti concentrations and annealing temperature.The thickness of the TCO films prepared for this study is within the range of 300–400 nm. It has previously been reported that the indentation depth should be less than 10% of the film thickness to avoid substrate effects. Therefore, in order to determine the hardness and elastic modulus values for our Ti doped ITO thin films, the measurements were taken at a maximum indenter depth of around 13 nm, which is less than one-tenth our samples thickness. (a, b) shows the load-displacement curves determined from the nanoindentation measurements corresponding to the Ti doped ITO samples of both Ti contents and after being annealed. It was reported by Jian and co-worker that establishment of cracking in films underneath the nanoindentor resulted in a distinct discontinuity in the loading part of the loading displacement curve (a, b) confirmed that continuous loading curves were obtained for all the films, indicating that the phenomenon of cracking was absent in the Ti doped ITO films at different Ti contents and annealing temperatures. shows typical load-displacement curves of the nanoindentation measurements. Hardness and Elastic (Young's) modulus can be calculated directly from the measurements of indentation load and penetration depth for both loading and unloading process. From a typical load-penetration depth (p-h) curve, maximum load, maximum displacement and unloading stiffness (also called contact stiffness S) can be determined. The value of how resistant solid matter is to deformation under an applied force is known as the hardness which can be calculated from the following relation:where Pmax is the maximum load and A is the area of the hardness impression.Young's modulus can also be calculated from the values of unloading stiffness and contact area by the following relation:where β is a dimensionless constant taken as unity and Eeff can be defined aswhere σ and σi are the Poisson's ratio of the indenter and the thin film coating respectively. Eeff and Ei are the Young's modulus of the indenter and the thin film coating, respectively.The hardness (H) and elastic modulus (E) values of the Ti doped ITO films derived from nanoindentation experiments are shown in (a, b). A difference is observed between the trends in the hardness results of the two sets of samples. For the 2 at% samples, the hardness decreased with increasing annealing temperature, changing from 6.6 to 6.3 GPa when the annealing temperature increased from 400 to 600 °C. In contrast, for the 4 at% samples, the hardness seems to stabilise around 6.8 GPa after annealing at different temperatures, only showing a slight decrease after annealing at 500 °C. Overall, the results show that the ITO films with higher Ti concentrations have the highest average hardness. The hardness of the Ti-doped ITO thin films measured in the present study are generally consistent with those reported by Zeng et al. (6.5 ± 1.6 GPa) for 250 nm thick sputtered ITO thin films onto glass substrate using a Berkovich indenter with 6 mN load ). These results are in general agreement with those reported by Biswas and co-authors, which show that there is a relation between the hardness and the oxygen contents in the ITO film materials. They found that when the oxygen content increased from 6 to 10 wt% in the precursor solutions, the hardness of the corresponding ITO films decreased from 9.6 ± 0.9 GPa to 1.6 ± 0.1 GPa ), which, when combined with substitutions, interstitials, and/or the formation of oxygen vacancies and other point defects, may cause a hardness decrement, although this effect is not so significant in our 4 at% samples. In relation to the annealing temperature increment, the Young's modulus of Ti doped ITO films decreased for the films of 2 at% Ti, while it increased for the films of 4 at% as shown in (a and b). However, both thin films with 2 at% and 4 at% Ti contents present similar Young's modulus in the range of 137–143 GPa, which is comparable to the reported results given by Zeng et.al (120–160 GPa) Elastic modulus along with hardness of material can influence wear behaviour. The wear of a material coupled with elastic limit define the ability of this material to deform under an applied stress and regain its initial state without being deformed permanently that both the hardness and Young's modulus depends on the annealing temperature. As discussed previously, the prepared Ti doped ITO thin films were annealed in air atmosphere resulting in changes of the composition of the sample surface due to oxidation process. Thus, the decrease in the hardness of Ti doped ITO samples along with increasing annealing temperature could be attributed to increasing the oxygen contents at the surface of the film. A similar trend for Young's modulus was observed with increasing annealing temperature. Thus, it is possible to surmise that the annealing temperature exerts a negative effect on the mechanical properties of the Ti doped ITO film coatings. The H/E values in this study are in the range of 4.5 × 10−2 – 4.6 × 10−2 and 4.8 × 10−2 - 5 × 10−2, for the films of 2 at% and 4 at%, respectively. These values represent a reasonable level of wear resistance, which is even better than other metal oxide ceramics with H/E values of 3 × 10−2 - 4 × 10−2Ti-doped ITO thin films were fabricated on glass substrates using a low cost and efficient sol-gel spin coating method. The effects of Ti concentrations (i.e., 2 at% and 4 at% Ti) and annealing temperature (ranging from 400 to 600 °C) on the phonon vibrational modes, surface chemical bonding states and mechanical properties of Ti doped ITO thin films were studied using Raman spectroscopy, XPS and nanoindentation techniques. Raman analysis revealed the existence of ITO and/or In2O3 vibrational modes. By increasing the annealing temperature some peaks were inversely altered. The XPS results show that the main component atomic percentages such as In, Sn and Ti decreased as the annealing temperature increased from 400 to 600 °C, while the O atomic percentages increased. Also, at 600 °C, the Ti2p and Cl2p signals were completely absent for 2 at % and 4 at % Ti concentration, respectively, indicating that surface oxidation takes place at high temperature.The nanoindentation load-displacement curves confirmed that all the films exhibited continuous loading curves, indicating that the phenomenon of cracking was absent in the Ti doped ITO films at both Ti contents. Variations in the hardness (H) and the elastic modulus (E) were observed with different Ti at% and annealing temperature. The hardness is within the range of 6.3–6.6 GPa and 6.7–6.8 GPa for 2 at% and 4 at% Ti content samples, respectively. In most cases the hardness values are negatively affected with increasing annealing temperature, and the films with higher Ti concentration in the ITO films possess the highest average hardness. Synthesized Ti-doped ITO thin films at different Ti contents show the same Young's modulus values in the range of 137–143 GPa. A combination of the highest H and E were achieved in the sample of 4% Ti content annealed at 600 °C. All the Ti-doped ITO films appear to possess high wear resistance. Combining with optimised control over the doping and annealing processes, the results from this work are expected to help facilitate the engineering design of customizable Ti-doped ITO thin films for various industrial applications.Fire response of exterior reinforced concrete beam-column subassemblagesInvestigating the structural response of reinforced concrete beam-column sub-assemblies at elevated temperatures is the purpose of this paper. This goal was achieved by conducting the ISO-834 standard fire test on two identical one-third scaled reinforced concrete beam-column subassemblage test specimens. The test specimens, which each consisted of one reinforced concrete cantilever beam anchored at the mid-height of a reinforced concrete column, were installed together in a full scale furnace and subjected to downward and upward service loads, respectively. The fire compartment fully engulfed the cantilever beams (except the beams’ top face and the loading points), the beam-column connections and the lower columns. The fire test terminated after 74 min as soon as the tensile longitudinal steel bars of the upward-loaded cantilever beam attained the predefined critical temperature 530 °C. The lower columns exhibited partial concrete spalling and typical diagonal cracks appeared at the beam-column connections. Based on the recorded internal temperature distributions at the joint cores it was found that the material strength loss in the fire had insignificant impact on the load bearing mechanism of the joints. On the other hand, the gradual decrease in rotation capacity of the beam ends during the fire course considerably influenced the load-deflection relationship. A detailed numerical work has been carried out to simulate the response of the test specimens and will be published elsewhere.Under exposure to extreme building fires, occurrence of destructive forces within reinforced concrete beam-column connections, irrespective of the location of plastic hinges, is very likely. Thus, it is of great importance to ensure that a fire-exposed beam-column connection fulfils its primary design objective, i.e., the safe transfer of shear and moment demands between other structural elements. However, the thermo-mechanical interactions between the individual members (beams and columns) under the internal thrusts as a result of restrained thermal expansions and moment redistribution due to non-uniform heating have been less appreciated in the literature. A detailed review on previous studies in this respect is reported in Ref. a. As can be seen in the figure, the side columns provided an axial and rotational restraints at the beam ends. It was seen that during the early stage of fire the thermal expansion of the heated middle reinforced concrete beam imposed significant outward drifts on the columns such that the columns accommodated considerable deformations. The beneficial prestressing action of the generated axial thrusts within the beam incredibly increased its fire resistance. However, as the fire continued due to the progressive fire damage the beam ends at the column faces underwent severe rotation capacity loss. Meanwhile, the rapid increase in the beam mid-span deflection overtook the decreasing rotation capacity and consequently resulted in structural collapse approximately 180 min after the start of fire test.In this study to investigate the fire response of an ideal beam-column connections under no lateral thermally-induced thrust and no moment redistribution influence, the authors reduced the degree of structural indeterminacy of the test specimen in a. This was done by removing the mid-section of the reinforced concrete beam and turning it into two separate reinforced concrete cantilever beams, as shown in b. As it will be discussed in the later sections, the two cantilever beams of the test specimen were equally loaded at their free ends with opposite directions (upward loading and downward loading). The recorded thermo-mechanical responses of the two test specimens in this study revealed important features of such structures when exposed to fire. Moreover, the reported results in this paper are of great importance in developing structural macro-models for predicting the interaction between the beams, joints, and columns in redundant structures. The authors has been carried out an extensive numerical work in this respect which will be published elsewhere.To study the structural performance of an exterior beam-column subassemblage, such as those illustrated in b, the load-deflection relationship of the cantilever beams and the load-bearing mechanism of the joints in the figure at room temperature are defined in the first step. The influence of fire will be then discussed based on the recorded thermal and mechanical responses in this study.The linear response of a singly reinforced cantilever beam (before yielding either the tension longitudinal reinforcement or the flexural compression zone) comprises three flexibility components, as illustrated in . Flexural deformation δf, shear deformation δv (ignoring stirrups), and slip deformation δs, the sum of which defines the total displacement at the loading point, as expressed by Eq. Where, φ(x) is curvature (due to the load Q), Av is effective shear area, Geff is constant shear modulus of elasticity, and θ is beam end rotation at anchorage face.By assuming a uniform bond stress u¯ and a triangular tensile stress distribution along the anchorage length la in c, slip sa at the face of anchorage can be obtained by integrating the anchorage strain along length la. Thus, assuming the rotation θ occurring about the neutral axis, the rotation at the anchorage face isθ=sad−c=∫0laεsdx×1d−c=fs,max2db8Esu¯(d−c)Here, d is the distance from the extreme compression fiber to the centroid of tension bar, c is the compression zone depth, Es is modulus of elasticity of steel, db is the nominal diameter of bar, and fs,max is the tensile stress of bar at anchorage face.Regarding the influence of elevated temperatures on the flexural component in Eq. , very limited fire endurance tests on unrestraint reinforced concrete beams were carried out, of which beam tests conducted by Lin et al. Under service load shear demands in beam-column joints are expected to generate shear stresses below allowable levels stated in seismic design codes. However, as it was mentioned earlier, under fire-induced axial thrust actions joints could undergo excessive shear forces. The disposition of transmitted forces and moments at room temperature from adjacent members around and within a typical beam-column connection is simplified in . Note that it is assumed that beam member is cantilever, thereby no axial force would emerge due to Poisson effect and/or thermal expansion in fire.In a linear response and at onset of joint cracking, the horizontal joint shear Vjh can be calculated as the subtraction of steel bar tensile force Ts,b at the column face from the upper column shear force Vc1. Thus, the average horizontal shear stress vjh can be estimated asSimilarly, the average axial joint stress pj can be derived by dividing the acting axial force P by the joint area Aj. Thus, at onset of diagonal cracking of the joint panel by equating the nominal principle tensile stress and concrete tensile strength ft, the joint shear vj can be derived as concrete tensile strength ft at the beam-column joint panel can be approximated as the root of concrete compressive strength multiplied by 0.33 For the purpose of this research, two identical test specimens, as schematically illustrated in , were designed and constructed. The test specimens consisted of two 1250×250×250 mm reinforced concrete columns (representing as upper and lower story columns) and two 1000×200×250 mm reinforced concrete cantilever beams. It should be noted that the geometry of the test specimens were determined so as to use the available installation space of a 6500×2000×1000 mm full scale furnace. As the furnace in this study is primarily used for beam tests, the designed test specimens could represent a 1/3–1/2 reduced scale of the actual structure in practice. Steel bars type D19 for beam and D16 for columns were used as the longitudinal reinforcements and 21 MPa nominal compressive strength for concrete was considered in design. 40 mm cover concrete to the centre of the longitudinal reinforcements was considered to meet 60-min fire rating. Considering the ACI stress block, the yielding moment capacity of the beam and columns were 43.3 and 52.0 kN m, respectively. A vertical load of 17.3 kN was calculated as the acting load in accordance with the allowable stress design method of Japan. This method considers one-third of concrete compressive strength and 215 MPa allowable stress for longitudinal steel bars. The loads were applied to the free ends of the cantilever beams at a distance of 800 mm from the column faces. Regarding the lateral reinforcements, ribbed bar type D9 (80 mm spacing) and D6 (70 mm spacing) were considered for the beam and columns, respectively. The longitudinal reinforcements of the cantilever beams were extended to the joints hooked with 90° bent extension of the bars. Similar anchorage pattern was repeated at the free end of the beams. The ultimate shear capacity of the joint Vj,u, which can be calculated as in Eq. Normal weight concrete with siliceous aggregate (max. size 20 mm) was used. The concrete mixture and mechanical properties of the cast concrete are shown in . Mechanical properties of steel reinforcements are listed in as well. Note that each mechanical properties of steel and concrete materials in the tables below are the average values of at least three mechanical tests.The two test specimens were assembled into one test frame by installing two 2400 mm span H-shape steel beams (250×250×9×14 mm) at the top and bottom ends of the columns. To provide sufficient rigidity at the corner joints between the steel beams and the reinforced concrete columns, the steel beams were tightened to the columns with four post-tensioned steel rods (post-tensioning force=141 kN). The top faces of the cantilever beams were covered with 100 mm thick lightweight concrete blocks as slab. b shows the bending moment diagram of the test frame.The first stories of the test specimens - the two lower columns, joints, cantilever beams (except the top faces) - and the bottom steel beam were installed inside the furnace. The fire compartments were built by installing ALC panels around each test specimen such that the lower columns, the joints and 550 mm of the cantilever beams (except the top face) from the column faces were thoroughly engulfed. The bottom steel beam was thermally insulated with several layers of fire resistive sheets and gypsum paste. a shows a photo of the upward loaded (UL) test specimen installed in the furnace. The loading points at 800 mm from the column faces were kept outside the furnace. The fire nozzles inside the fire compartments injected the prescribed heat flux and the produced smoke was transmitted out through the smoke ducts located at the bottom corner of the furnace.To measure the internal temperature distributions of the test specimens during and after the test, several cross-sections in the test specimens (shown as “thermal cross-section” in a) were instrumented with φ0.65 JIS Class II thermocouple. In addition to that, to ensure that the furnace temperature increased in accordance with the prescribed temperature scenario the air temperature of each fire compartment was measured by beam-type thermocouples at locations close to the surface of test specimen as shown in a. These beam-type thermocouples are visible in the photos in . The structural responses of the test specimens (rotations at the beam ends and joints as well as columns’ axial expansions) were measured by the displacement transducers, which were mounted outside the furnace. A series of temperature resistive strain gauges were installed on the reinforcing bars at the thermal cross-sections. However, apparently the strain gauges did not exhibit good performance and failed to capture useful data.Roughly 60 min before commencing the fire test, the cantilever beams were gradually loaded to the design load level. After checking the safety of the test setup and measuring instruments the initial cracks were inspected. Minor beam flexural cracks as small as 0.08 mm wide were observed at the cantilever beam ends. Note that the cracking moment of the cantilever beams was 7.96 kN m, which was less than the applied moment at the beam ends (13.48 kN m). Afterwards, the fire compartments were closed thermally sealed. Next the furnace heated the test specimens in accordance with ISO-834 standard fire curve for 74 min when the bottom tensile reinforcements of the upward loaded cantilever beam exceeded the prescribed temperature 530 °C in this study. This limiting temperature was determined so as to prevent the occurrence of reinforcement yielding at the beam ends. shows the degradation ratio of mechanical properties of concrete and steel materials. As can be understood from in this table, at 530 °C the reinforcing bar could lose roughly 50% of its room temperature yielding strength. Above this temperature the rapid deflection of the cantilever beams could damage the test facilities. The test specimens remained inside the furnace for 60 min and gradually cooled (furnace cooling) before its removal from the furnace for in-place damage inspection.The visible damage pattern of the two specimens after cooling is illustrated in . Some of the damages such as the 2.0 mm wide vertical crack in b along the corner longitudinal reinforcement of the lower column was clearly visible. The crack formed 15 min after the start of heating. This crack is shown in b on the face C of the lower column. A similar crack formed at face D of the lower column, which later during the furnace cooling spalled the cover concrete off. The cantilever beams exhibited large flexural cracks especially at the beam ends, whereas in the beam-column joints the diagonal shear cracks were noticeable. Compared to the pre-fire initial crack width, the flexural crack openings at the beam ends considerably increased (roughly 20 times) and farther extended into the initially compressed zones. It seems that the decrease in the mechanical properties of the hot tensile reinforcements shifted the neutral axes farther to equilibrate the forces and moments at the cross-sections.The internal temperature distributions of the cantilever beams at the target locations (beam end and 240 mm from the column face) are plotted in a and b, respectively. For the sake of better comparison, only the temperature records at the core concrete, the bottom and the top main reinforcements are plotted in the figures. As can be seen in the figures, the beam end cross-sections apparently attained relatively cooler temperatures than the cross-sections closer to the beam tips. This thermal discrepancy is largely attributed to the thermal diffusivity effect of the adjacent unheated top columns. The formation of temperature plateau within the center of core concrete of all the thermal cross-sections is noteworthy. Such phenomenon happens as a result of transmission of free water content of fire-exposed outer concrete layers into the cooler inner core layers. As soon as the free water content of core concrete was completely lost the thermocouples recorded sharp temperature rise. The temperature difference between the thermocouples No. 5 in the figures at the bottom longitudinal reinforcements drew the authors’ attention to the influence of crack on the internal thermal profiles of the cracked cross-sections c shows the internal temperature distributions of the joint cross-sections. The cross-sections were aligned with the centroidal axis of the corresponding cantilever beams. The corner longitudinal bars due to the double-face heating attained relatively higher temperatures than the bars located elsewhere in the cross-sections. The thermal diffusivity effect of the upper cold columns was expected to impose large thermal gradients on the joints, especially the cover concrete. This thermal difference can be better pictured by analyzing the temperature profiles of the lower columns at the top cross-sections in d. The thermal profiles of the columns’ mid-height and bottom cross-sections were almost similar to those plotted for column's top cross-sections and thus, not presented here.The structural response of the test specimens was basically investigated based on the readings from displacement transducers of the beams and upper columns. In the following the fire resistance of the members are discussed.a and b show the relative deflection at the loading points and rotation at the beam ends versus heating and cooling process, respectively. The term relative deflection here is defined as the subtraction of the recorded deflections at the loading points from those of the beam ends. It should be noted that in 67 min from the start of fire tests, the two cantilever beams were unloaded to 10 kN and fully reloaded again to examine the residual stiffness of the elements. As a result, in the graphs below at this time a jump can be seen. The distinct deflection difference in a is mainly attributed to the higher temperatures attained by the bottom tensile reinforcements of the UL's cantilever beam. At the end of heating, when the temperatures of the tensile reinforcements of the UL and downward-loaded (DL) cantilever beams peaked at 530 and 250 °C, respectively, the beams could experience roughly 40% and 15% yielding strength losses, respectively. That is to say, by ignoring the compressive strength loss of cover concrete, the moment capacity of the two cantilever beams could decrease from pre-fire 41 kN m to 34.85 and 24.6 kN m, respectively. During the fire test, the anchorages of UL and DL test specimens attained average temperatures 250 and 150°C, respectively. The influence of such temperature rise on the slip flexibility of the cantilever beams can be interpreted by looking at the beam end rotation in Eq. . By neglecting the changes in the bar diameter db and rotation arm d-c, it can be argued that the degradation of Young's modulus of steel and the reduction in bond strength could increase the rotation at the columns’ faces and thereby the flexibility.The temperature profiles of the joints revealed that the damage to the effective cross-sectional area of joints in b was insignificant. Moreover, the joint cores attained relatively low temperatures (below 200°C in average), which could imply minor damage to the mechanical properties of the cast concrete (see ) and thereby preserving the shear capacities at the joints. In the absence of beam thrust action on the columns, the average joint shear stress in Eq. was 0.71 MPa, which is smaller than the concrete tensile strength in Eq. , 1.51 MPa. Unlike the cantilever beams, the direct displacement reading of the lower columns (except their internal temperatures) was not feasible. As an alternative, the readings at the upper columns’ bases, plotted in b, were used. The distinct rotational behavior of the UL test specimen in the figure is noteworthy. While the DL test specimen exhibited a steady increasing beam-column connection rotation, the TL test specimen underwent a sharp rotation during the first 30 min, following a gradual reverse rotation. This different rotational behavior is attributed to the greater loss of mechanical properties of the tensile reinforcements at UL cantilever beam end, which apparently decreased its rotation capacity. Regarding the axial expansion of the columns, it can be seen in the figure that the two lower columns steadily expanded during the fire test. The greater axial expansion of the UL column is in line with expectation as this column was basically in tension (see The results of a fire test on two RC beam-column subassemblages were presented and discussed in the paper. The following conclusions can be drawn:The two exterior beam-column subassemblies designed based on the conventional seismic design code in Japan exhibited satisfactory fire resistance.The standard 90° hoop anchorage together with the adequate lateral confinement by lateral hoops could sustain well the integrity of the joints.It was observed that the thermal diffusivity effect of the upper columns outside the furnace remarkably contributed to cooler joint cores, thereby causing less significant strength loss.The fire damage to the beam ends, especially the upward-loaded beam, decreased the structural stiffness of the beam and damaged the integrity between the beam ends and the column faces, which consequently decreased the rotation capacity of the beam-column connections.To predict the mechanical behavior of the test specimens at elevated temperatures, the interaction between the cantilever beams and the side columns should be correctly modelled. A detailed numerical model in this regard has been developed by the authors and will be published elsewhere.Temperature and strain-rate dependence of the elevated temperature ductility of Inconel 718 prepared by selective laser meltingThe elevated temperature tensile properties of SLM IN718 were measured as a function of strain rate and test temperature to better understand the time-dependent and thermal aspects of environmental sensitivity. SLM and wrought materials were solution treated, aged, and tested over the range of 550–750 °C and 10−3 to 10−6 s−1. The SLM material tested across all conditions had inferior strength and ductility compared to wrought material of the same heat treatment because of environmental sensitivity in the form of dynamic embrittlement. SLM samples show evidence of brittle intergranular fracture, crack growth, and oxidized NbC particles on the fracture surface, which all contribute to the observed poor ductility. These features, and subsequent embrittlement, are intensified with decreasing strain rate and increasing temperature. Higher strain rates and lower temperatures are shown to improve the ductility in SLM IN718 but despite this recovery it remains susceptible to environmental attack even in the extreme cases of the current study. The prevalence of NbC at grain boundaries in the SLM material is the principal source of dynamic embrittlement and environmental sensitivity.Inconel 718 (IN718) is a precipitation-hardened nickel-based superalloy that has proved popular for additive manufacturing (AM) due to its excellent weldability and widespread use in the aerospace industry. Many studies have investigated the processing-structure-property relationships for selective laser melted (SLM) IN718. These have included the effects of process parameter variation on as-built microstructures []. While there is an extensive literature for the as-built and post-processed microstructures as well as mechanical properties at ambient conditions, there is still room for exploration into the detailed elevated temperature properties of this SLM alloy. This is especially true for IN718, where despite being originally designed for operation in high-temperature environments, the elevated temperature tensile response has received relatively little attention compared to room temperature tests [Recently it has been shown that room temperature behavior may not reveal some of the shortcomings of the current state of SLM IN718. McLouth et al. [] demonstrated an almost 650% difference in creep rupture elongation at 650 °C between wrought and SLM material despite similar tensile behavior at room temperature. The difference in ductility is attributed to the SLM material's increased sensitivity to environmental attack. In a similar vein, Witkin et al. [] noted a complete lack of notch ductility in SLM processed IN718 when tested as combination stress rupture (CSR) test bars at 650 °C. Where wrought samples could pass a standard quality acceptance test that required 23 h of sustained load on the notched section of 690 MPa with a minimum of 4% smooth section elongation, SLM samples always exhibited brittle notch failures with no elongation, often at less than 23 h. The sensitivity was attributed to the triaxial state of stress and lack of grain boundary compliance due to limited δ phase precipitation. The multi-axial state of stress can induce large stresses on unfavorably oriented grains and result in cavity nucleation []. Comparison of the notched stress rupture results of Witkin et al. [] to those of the creep rupture of McLouth et al. [] shows that tests conducted in lab air are consistent with an embrittling mechanism of IN718 called dynamic embrittlement.Dynamic embrittlement is a type of gas phase embrittlement that results from an embrittling species (oxygen for IN718) diffusing into grain boundaries and producing local decohesions []. This phenomenon is known to occur in Ni-based alloys at temperatures above 500 °C []. Dynamic embrittlement is promoted in the presence of a stress concentration, which introduces an extra driving force for the oxygen diffusion to occur given by is the diffusive flux within the grain boundary, D is the grain boundary diffusivity of the embrittling element, C is its concentration in the boundary, k is the Boltzmann constant, Ω is the atomic volume, T is the temperature, and ∇σ is the stress gradient resulting from a stress acting on the boundary. Once oxygen has entered the boundary, it creates a local decohesion of adjacent boundaries at the crack tip, facilitating crack extension []. This mechanism has been observed for traditionally manufactured IN718, and increases in severity with temperature [. The oxidation of Nb-rich carbides has also been shown to have a deleterious effect that can exacerbate the embrittlement during oxygen diffusion []. XPS studies have shown that the formation of Nb2O5 as a result of the oxidation of NbC is a plausible mechanism to enhance intergranular fracture in IN718 The majority of the current literature on elevated temperature tensile properties reports strength and elongation values taken from tests at relatively fast strain rates, on the order of 10–3 s-1 []. At these rates, dynamic embrittlement is less likely to occur as there is not enough time for diffusion of embrittling species to influence the ductility. As a result, these samples were shown to have similar ductility, albeit slightly lower, and strength in comparison to those of their wrought counterparts. Other studies have either not reported the strain rate of testing [], or focused their results only on metrics of strength in lieu of reporting ductility values [] recently reported elevated temperature tensile properties at various strain rates and temperatures, and observe degraded ductility in SLM material similar to what has been observed in the aforementioned studies at slow strain rates. However, they focus their discussion mostly on the nucleation and growth of cavities to explain the embrittled behavior, without a thorough analysis of potential environmentally driven mechanisms. DE is ruled out in their study by reasoning that oxygen pickup during production would render samples already embrittled. This interpretation is inaccurate, since DE is caused by oxygen diffusion into the sample from the test environment, and subsequent embrittlement is driven by a stress concentration during loading—occurring dynamically. Further study of the strain rate and temperature dependence of the environmental susceptibility of SLM material is necessary.The current study analyzes the elevated temperature tensile behavior of SLM IN718 through variations in strain rate and temperature. These variables address the temporal and thermal effects on mechanical properties to better understand what factors may control elevated temperature behavior. For comparative purposes, wrought samples were tested under identical conditions. Results will be analyzed in the context of the DE phenomenon to distinguish between SLM and wrought material and the degree to which each form of the alloy is prone to DE.IN718 cylinders were fabricated in the Z-orientation in a Concept Laser M2 Cusing from pre-alloyed powder. Tensile dogbones were then machined in accordance with ASTM ], with a gauge length of 31.75 mm, a gauge diameter of 6.35 mm, and 12.7 mm grip ends. All parts were made with a laser power of 180 W, scanning speed of 600 mm/s, a 5 × 5 mm island scanning strategy, and a layer thickness of 30 μm. Samples used in the current work were made in a similar fashion to those from a previous study [], and it should be noted that much of the analysis to be presented here builds upon that work.12.7 mm diameter hot-rolled wrought bar was purchased in the mill-annealed form and machined after heat treatment for direct comparison to SLM material. The chemical composition of the pre-alloyed powder, bulk SLM material, wrought material, and the acceptable range as specified in AMS 5663 [Hot isostatic pressing (HIP) and heat treatment (HT) were used for post-processing of samples. A HIP cycle at 1163 ± 12 °C and 103 ± 2 MPa in argon for 3 h was performed on SLM samples, and then both SLM and wrought material were heat treated together in accordance with AMS 5663. The first step was a 954 ± 14 °C solution treatment for 1 h and a water quench. This was followed by a dual aging cycle that started at 718 ± 8 °C for 8 h and was then furnace cooled to 621 ± 8 °C and held until a total aging cycle time of 18 h was reached, after which the samples were air cooled.Dogbones were tested at an elevated temperature in accordance with ASTM ]. Two samples were tested for each condition in this study. Tests were conducted on an Instron Model 5989 universal testing machine within a SF-16-2230 type clamshell furnace with three heating zones. An Epsilon 3448-0100-050 axial furnace extensometer was used to monitor strain during testing. Crosshead movement was displacement controlled to achieve strain rates of 8.33 * 10−4, 8.33 * 10−5, or 8.33 * 10−7 mm/mm/s. These rates were chosen to reflect common strain rates observed in typical mechanical testing while also providing a range over which patterns in the material behavior could be observed. The middle condition, 8.33 * 10−5 s−1, is called for in ASTM for the determination of tensile properties []. On the slow end, 8.33 * 10−7 s−1 is near the calculated minimum rate observed during previous creep testing [], while on the fast end, 8.33 * 10−4 s−1 was chosen to evaluate tensile properties for which time-dependent behavior is less likely. For simplicity, these rates will be referred to as 10−3, 10−4, and 10−6 s−1 for the remainder of the paper. For these tests the temperature was a constant 650 °C, verified by a Type K thermocouple in direct contact with the specimen. This temperature was chosen for all variable strain rate testing as this is the most common test temperature for acceptance testing in the aerospace industry []. A second set of tests was conducted at a strain rate of 10−4 s−1 while test temperature was set to 550 °C, 650 °C, or 750 °C. For all tests, the samples equilibrated at the test temperature for 30 min prior to testing.Sample microstructures were characterized by scanning electron microscopy (SEM) after sectioning parallel to the build/loading direction followed by standard metallographic preparation techniques. After the final polishing step with 0.3 μm alumina, samples were etched with Kalling's Reagent #2. A JEOL JSM 7600F field emission SEM operated at 20 kV and a JEOL JSM 6460 SEM operated at 15 kV were both used for imaging. Quantitative analyses of particle distributions and sizes were made using thresholding techniques and particle counting capabilities in the ImageJ software. Scanning transmission electron microscopy was performed on an aberration-corrected FEI Titan TEM at 300 kV. High Angle Annular Dark Field (HAADF) and bright field detectors were used to create Z-contrast images. Samples for TEM were prepared by a focused ion beam (FIB) lift-out method on an FEI Strata 400 dual-beam FIB.The microstructures of the SLM and wrought material used in the current study are shown in . Clear differences exist between them: grain size, grain morphology, NbC volume fraction, and δ phase. These microstructural characteristics and precipitates have been identified through previous work using a combination of electron backscatter diffraction (EBSD), transmission kikuchi diffraction (TKD), and energy dispersive spectroscopy (EDS) []. Qualitatively, the SLM material contains many small blocky NbC particles (white arrows) scattered throughout the microstructure. Their formation and orientation are governed by solidification behavior during production []. Wrought material has larger and more widely spaced NbC particles. The δ phase (red arrows) in SLM material is found parallel to the grain boundaries and incorporates the GB morphology, while that of wrought material is more acicular, extending from the grain boundaries towards the grain interiors. This has the effect of increasing the precipitate-free zone around grain boundaries in wrought material, providing more local plasticity that can improve local ductility [b and d, γ’’ sizes for SLM and wrought material have been determined to be 63 and 31 nm, respectively [Phase populations were quantified based on ImageJ analysis of SEM images for both structures. NbC particle measurements of SLM samples were performed on the as-HIP condition to avoid bias from inclusion of the δ phase, and δ phase analysis was performed on the heat-treated condition for both material types. The NbC population is stable below the initial HIP temperature and is not altered by the current heat treatment temperatures, so the as-HIP value is representative of the fully heat treated value []. The δ phase accounts for roughly 0.9% of the area in SLM samples and 9.2% in wrought samples. NbC particles are observed to be smaller in the SLM condition relative to the wrought condition, with average diameters of 0.56 μm and 4.7 μm, respectively. However, the interparticle spacing of NbC for SLM is roughly 6.4 μm, while for wrought samples it is 66 μm. The area % of NbC in SLM and wrought are 1.4% and 0.47%, respectively. This represents a significant difference in the amount of NbC that forms based on the manufacturing process.Stress-strain curves for strain rate variation testing at 650 °C are shown in and tabulated values of key tensile properties are presented in . Values of wrought strength are similar to those reported by Booker and Booker, who studied variations in tensile properties of wrought Inconel 718 at different strain rates and temperatures []. Minimum property values for acceptance of commercial wrought material as outlined by AMS 5663 [] are provided for comparison to the standard 10−4 s−1 rate.The wrought strengths exceed those of their SLM counterparts at all three strain rates with differences of 7.5%, 10.4%, and 2.5%, at 10−3, 10−4, and 10−6 s−1, respectively. These differences in strength are attributed to the smaller γ’’ size in wrought material, similar to what was previously observed for RTT []. Because the primary deformation mechanism in IN718 is massive planar slip, obstructions to dislocation movement introduced by the γ’’ precipitates are essential in determining strength []. Dislocations cannot cross-slip in IN718 due to the low stacking fault energy in the γ matrix, and so they must either cut through particles or loop around them []. The smaller particles of the wrought sample promote particle shearing, a more tortuous route for dislocations as they must travel in pairs through the particles [], whereas the larger particles of the SLM material may facilitate bowing out between or looping around precipitates, lowering the overall strength. The dependence of material strength on the strain rate is likely based on particle coarsening behavior, but a discussion of this is outside the scope of the current study.Compared to the strength values, the ductility metrics offer a more significant separation of properties between SLM and wrought material. In descending strain rate order, the elongations drop by 49%, 84%, and 78.3%, respectively. These are more significant differences relative to the ~10% differences observed for yield and ultimate strengths. The SLM ductility is far more sensitive to changes in the strain rate than their wrought counterparts, with a decrease in elongation of 75% going from 10−3 s−1 to 10−4 s−1. In comparison, the wrought material only drops by 20% between these same strain rates. The slight decrease in wrought elongation from 10−4 s−1 to 10−6 s−1 is likely related to the onset of time-dependent strains occurring during slow strain rate testing, as well as particle coarsening [Fractography of the tested samples is highly informative as to the difference in the failure mechanisms and resulting ductility differences between wrought and SLM samples. Optical images of the SLM and wrought fracture surfaces at each strain rate can be seen in . While the SLM samples show a variation of color across the fracture surfaces (marked by dotted red lines), the wrought samples from each test appear as a single color. The gradient color change in these marked areas is related to the thickness of the oxide that forms upon exposure to the lab air at elevated temperature. Due to gradual crack progression, different areas of the fracture surface are exposed to air for different amounts of time and the thickness of the oxide—and resulting color—will change as the crack propagates. The SLM fracture surface appearance indicates progressive crack growth during testing. The 10−6 s−1 sample does not have as distinct of a color change due to the sample remaining in the furnace for a prolonged period after testing was complete. With decreasing strain rate, the size of the affected area grows larger.Detailed SEM images of the fracture surfaces for the 10−4 s−1 SLM and wrought samples are shown in . The oxidized areas in SLM samples are shown to be comprised of intergranular features while the center has a ductile overload type of transgranular failure. The wrought sample has a characteristically ductile cup-and-cone type of failure, where large dimples are observed throughout the center of the sample and near the edges a shear lip forms. There is no evidence of intergranular cracking or environmental damage in the wrought samples. In addition to the intergranular fracture surface in SLM materials, oxidized NbC particles similar to those observed on the fracture surfaces of previously studied creep samples are seen on the surface (]. These particles have a similar feathery appearance as observed in the literature [] conducted XPS studies on oxidized NbC particles and found that they readily form Nb2O5 and suggest that the oxidation and subsequent decomposition of NbC may promote intergranular failure in IN718. Sjoberg and Ingesten et al. [] found that upon oxidation, NbC particles will swell considerably and this volume increase will promote intergranular crack growth through local stress risers. NbC was observed as one of the primary differences between the wrought and SLM microstructures and is a source of embrittlement when exposed to oxygen.The small interparticle spacing of NbC in SLM samples combined with their placement along the grain boundaries contributes to the enhanced environmental susceptibility of SLM samples compared to the wrought. The SLM samples have an average NbC interparticle spacing of 8 μm and average grain size of 50.9 μm, which means that numerous NbC particles will be found within the same grain or grain boundary. Wrought samples have an interparticle spacing of 66 μm and an average grain size of 21.9 μm, excluding them from adjacent grains or grain boundaries []. The close spacing in SLM samples along grain boundaries reduces diffusion lengths for oxygen atoms that react with the particles, pointing towards a mechanism in which crack propagation is enhanced relative to wrought material via oxidation of particles within grain boundaries. Both factors increase SLM material's susceptibility to environmental attack. Their appearance along the fracture surface is further evidence of their negative role on elevated temperature properties.It was proposed that environmental damage during creep rupture testing in SLM IN718 at strain rates around 10−8 s−1 occurs upon the propagation of a microcrack to a free surface in a previous study []. This mechanism is driven by the presence of a stress concentration, which promotes the inward diffusion of oxygen as presented in Eqn. . Oxygen causes local decohesion of GBs in the material and reacts with NbC on the GBs or within the matrix to exacerbate the damage.SEM and EDS analysis of sectioned fracture surfaces for the SLM and wrought material tested at 650 °C and 10−4 s−1 is presented in to demonstrate oxidation damage. A secondary crack that has propagated into the microstructure from the surface is shown in each of the tested samples with dramatic differences in morphology between the two. The SLM crack is oriented perpendicular to the loading direction and extends ~1 mm into the surface, while the wrought crack has been effectively blunted to be oriented more parallel to the load and only extends 50 μm into the surface. EDS maps of the two emphasized regions are provided to show the chemical differences that exist. In , a clear enrichment of Nb, Cr, and O on the cracked surface is observed. This represents Cr2O3, a beneficial oxide found in superalloys, and Nb2O5, a harmful oxide that forms when oxygen reacts with Nb that can lead to grain boundary embrittlement []. Two sources of Nb exist in the SLM material, the large amount of Nb found in NbC at the grain boundaries, but also GB segregated Nb, a common phenomenon in SLM material []. These Nb sources can have deleterious effects on environmental resistance and exacerbate the intergranular crack growth. In the wrought sample only O and Cr are enriched within the crack's fracture surface presenting no evidence of Nb2O5. These chemical differences observed in the secondary cracks in tested materials provide evidence that SLM IN718 is far more susceptible to environmental damage than wrought material. The crack growth susceptibility in the SLM material stems from environmental damage propagated by the oxidation of NbC particles and Nb segregated at the grain boundaries.Intergranular crack propagation is observed in to initiate near the free surfaces of the sample and propagate inward. Near these propagating cracks, there will be an increased diffusive flux due to the stress concentration as shown in Eqn. . The presence of continuous strings of NbC will enhance the growth of these cracks through selective oxidation and volume expansion of particles near grain boundaries. The primary difference between wrought and SLM, then, is not in the deformation mechanisms within the sample bulk as much as it is in the failure mechanism and the amount of strain that can be accommodated prior to onset of failure.The accumulation of environmental damage on the fracture surface is only shown in the SLM materials in the current study and supports the DE mechanism. With a decreasing strain rate there is an increase in the time over which environmental damage can occur. Dynamic embrittlement typically occurs in the presence of a stress concentration, such as a notch or crack, and an oxygen-exposed stress concentration does not exist for these samples until a microcrack connects to the surface. Once this occurs local decohesion and oxidation of NbC particles will drive further crack growth, resulting in decreased overall plasticity; crack propagation will begin to dominate overall deformation with limited strain throughout the rest of the gauge length. The presence of δ phase along grain boundaries and large spacing of the NbC particles in wrought material mitigate these effects. Local plasticity from the δ phase stems from the formation of a γ’’-free zone due to the local depletion of Nb []. This creates areas of the more compliant γ-matrix near grain boundaries, increasing the local plasticity and toughness, and allowing for the absorption of more strain energy. Therefore, the increased δ phase population in wrought material improves its resistance to crack propagation relative to SLM material, which does not benefit from increased localized plasticity.To further study the limited ductility of SLM material at elevated temperatures, samples of an identical dogbone geometry were tested at 550 °C, 650 °C, and 750 °C at a constant strain rate of 10−4 s−1. The stress-strain curves of these tests are presented in . The material properties for both SLM and wrought material show a decreasing strength with increasing temperature, and a ductility dip around 650 °C. Strength dependence on temperature in this range is a known phenomenon for IN718, as previously observed in the literature [The ductility of samples is shown to reach a minimum for both processing conditions at 650 °C. On the lower temperature end at 550 °C, the material is not as susceptible to cracking as it is at 650 °C, leading to improved ductility. On the higher end at 750 °C, coarsening of the γ’’ particles occurs, lowering overall strength and facilitating dislocation movement to improve ductility []. The SLM and wrought material both display this behavior but on different scales. The initial drop in ductility from 550 °C to 650 °C is quite pronounced in both SLM and wrought, dropping by 52% and 30%, respectively. However, the recovery of ductility is quite different from 650 °C to 750 °C between SLM and wrought where increases in elongation of 17.2% and 57%, respectively, are seen. The SLM samples, which are prone to oxidation-enhanced crack growth do not recover as much ductility at 750 °C because this temperature also promotes the diffusion of oxygen along grain boundaries. Wrought material, which does not show signs of dynamic embrittlement has a large recovery of ductility from 650 °C to 750 °C, in line with the common “ductility dip” phenomenon observed for Ni-based superalloys [Sensitivity to the testing temperature has been demonstrated for the dynamic embrittlement mechanism that is discussed here via the temperature-dependent diffusion constant <I>D</I> in Equation ; furthermore, oxygen diffusion rates in Ni have been shown to follow an Arrhenius relationship, increasing in diffusivity with temperature [] observed brittle intergranular failure in IN718 at 800 °C, citing the formation of brittle oxides due to diffusion of oxygen as the culprit. They observed increased oxidation and limited tensile ductility at 800 °C when compared to 600 °C, similar to the current results. Wei et al. [] demonstrated a faster crack growth rate in IN718 with increased temperature for this same reason; their XPS analysis of fracture surfaces confirm the presence of oxidized Nb-rich carbides along the grain boundaries.The fracture surfaces from temperature variation tests revealed similar behavior to those of the strain rate samples, as seen in . With increasing temperature, the area of environmental attack and depth of penetration is increased. Both 550 °C and 650 °C conditions show multiple starter sites and corresponding short intergranular crack growth, but the 750 °C shows only a single region of this growth. The depths of penetration measured on the fracture surfaces for the 550 °C, 650 °C, and 750 °C samples are 0.4 mm, 1.1 mm, and 4.0 mm.] in a study of the temperature dependence of intergranular cracking on ALLVAC 718PLUS, a γ′-strengthened alloy which behaves similarly to IN718. After tensile testing smooth and v-notched bars pulled rapidly to failure after a specified dwell time, he observed a similar intergranular cracking mechanism that increased in fracture surface area with increasing temperature. By using the extent of intergranular failure to identify the depth of penetration <i>x</i> of the embrittling species and a hold time of <i>t</i>, he calculated the activation energy and concluded that susceptibility to intergranular fracture was related to the testing environment. Taking a similar approach with the current samples, the activation energy for grain boundary fracture was calculated to be 170.0 kJ/mol, a result very similar to the 177.0 kJ/mol calculated for ALLVAC 718PLUS in laboratory air. The results are compared in , where it is shown that increasing oxygen content of the environment decreases the activation energy. Reactions of intergranular precipitates with grain boundary diffusing oxygen—and hydrogen in high-moisture environments—was the embrittling mechanism in ALLVAC 718PLUS. Based on the calculated activation energy of 170 kJ/mol for IN718, a similar mechanism exists in the present study.Other literature that has investigated the activation energy of crack growth has found similar values for IN718: 197 kJ/mol in air [] further related the grain boundary diffusion in Monel of 171 kJ/mol to their own experiments on Inconel 718. These results cite environmental attack as an embrittling mechanism in IN718, with oxygen being the primary culprit. Valerio et al. [] elaborates on the potential mechanisms, saying that the enrichment of Nb at grain boundaries and the decomposition of NbC as it is oxidized are responsible for environmental susceptibility. In their study, the activation energy for crack growth is calculated as 287 kJ/mol in pure oxygen, while it is 191 kJ/mol in moist argon. The decrease in activation energy suggests an additional contribution of hydrogen to the embrittlement of IN718. Gao et al. [] found that the activation energy of oxidizing NbC was 266 kJ/mol, a result in line with the 287 kJ/mol activation energy for crack growth, suggesting this as the rate-controlling process for environmentally driven crack growth in IN718.Elevated temperature tensile testing of SLM IN718 shows a susceptibility to environmental attack that leads to limited ductility and premature failure. At all strain rates and temperatures tested in the present study, the SLM ductility was lower than that of wrought material. The lack of ductility was ultimately determined to be linked to dynamic embrittlement. The degree of environmental attack, evidenced by the intergranular fractures and reduced ductility in the SLM samples, has been shown to be both time- and temperature-dependent. The enhanced inward diffusion of an embrittling species due to longer hold times or higher temperatures facilitates the oxidation of NbC within the SLM samples and drives brittle intergranular crack growth. The root of this behavior stems from the susceptibility of the microstructural constituents to environmental attack and brittle behavior. Both an excess of NbC and a lack of grain boundary δ phase contribute to the embrittlement seen in SLM material and explains why its environmental sensitivity is elevated relative to wrought IN718 alloy. Evidence of excess oxidation and the presence of elevated Nb concentrations on secondary crack features in the SLM material is consistent with the abundance of oxidized NbC particles on intergranular fracture surfaces. This was not observed in wrought material, where NbC particles are far less frequent and much larger, leading to much less surface area prone to oxidation throughout the material volume.These observations indicate that the unique distribution of fine, abundant NbC particles in SLM-processed material plays a significant, even primary role in elevated temperature deformation of SLM IN718. It also suggests that elevated tensile ductility could be achieved through the development of heat treatments that reduce the NbC particle density and promote local plasticity through GB δ phase formation.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.Tait D. McLouth: Conceptualization, Methodology, Resources, Investigation, Formal analysis, Data curation, Writing – original draft, Writing – review & editing. David B. Witkin: Conceptualization, Methodology, Resources, Investigation, Writing – review & editing. Julian R. Lohser: Conceptualization, Methodology, Investigation, Formal analysis, Writing – review & editing. Scott D. Sitzman: Methodology, Resources, Formal analysis, Visualization, Writing – review & editing. Paul M. Adams: Methodology, Resources, Formal analysis, Visualization, Writing – review & editing. Zachary R. Lingley: Methodology, Resources, Investigation, Formal analysis. Glenn E. Bean: Conceptualization, Resources, Writing – review & editing. Jenn-Ming Yang: Supervision, Project administration, Funding acquisition. Rafael J. Zaldivar: Conceptualization, 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.The strength of acrylic bone cement cured under thumb pressureIn this investigation, the static tensile strength of bone cement was quantified after mixing it in an open bowl or in a commercially available vacuum mixer and molding it under pressures consistent with values obtained by finger/digital application, as it is used in surgery. Pressure, held for a brief time span on cement in its lower viscosity state, has been demonstrated to increase penetration of the cement into bone. Clinically, bone cement is pressurized by digital pressure, specialized instruments, or by implant design.Specimens were cured under constant pressures of up to 100 kPa, which is in the range reported for thumb pressurization of plugged proximal femurs and instrumented pressurization of acetabular sockets. The results showed that application of constant pressure during the polymerization of open bowl mixed bone cement significantly improved its mechanical properties. Application of 100 kPa constant pressure to the open bowl mixed bone cement while it cured increased its ultimate strength to a value similar to vacuum mixed cement. Curing under pressure showed no significant effect on the tensile properties of vacuum mixed cement. Curing under pressure did not significantly reduce the size of the largest pores in the tensile specimens.Acrylic bone cement is formed from a two-part mixture of liquid and powder. A chemical reaction is initiated when the two parts are combined resulting in a solid, load bearing material when the MMA liquid polymerizes in a matrix surrounding soluble, prepolymerized polymer beads and an insoluble radiopacifier. Bone cement has been used for a variety of orthopedic applications with great clinical success, credited with excellent clinical results and tremendous growth of THR in the late 1960s through the early 1970s When comparing different brands of cements or different mixing techniques, a number of authors have reported a wide range of strengths resulting from uniaxial tensile tests on the same bone cement material. For example, the tensile strength reported in the literature shows over 100% variation in tensile strength for Surgical Simpex® P bone cement (22–52 MPa) and similar ranges of strength for two other widely used bone cements, Palacos R, and CMW 1 Pressurization of cement is performed clinically by use of thumb/digital pressure or by various devices designed to efficiently seal and apply force to the cement, forming interdigitation with the surrounding bone. Reported values from these techniques range from 45 to 90 kPa for continuous pressurization with peak pressures up to 300 kPa Static tensile properties were measured because these are associated with cement fracture and static uniaxial tensile testing is a necessary precurser to uniaxial tensile fatigue testing. With regard to other mechanical tests, differences in compressive strength may not be clinically relevant and differences in bending strength are difficult to interpret since that test involves both tensile and compressive stresses.Testing was performed in order to address the questions of whether the application of pressure throughout the cement cure affects its strength and whether it has similar effects on cement mixed under vacuum and cement mixed in an open bowl.All samples were made from a single lot of Surgical Simpex® P cement (Stryker Howmedica Osteonics). Full sized doses (40 g of powder) were mixed to mold the specimens in sets of three per dose. The cement was either vacuum mixed in an ACM (Stryker Instruments) or hand mixed in an open bowl. The mixed cement was injected into individual molds using a surgical cement gun. Each mold yielded an ASTM D638 type IV tensile specimen. The cement was injected into the mold and pressurized through the upper grip of the tensile specimen (). Rectangular plungers were designed to keep the cement pressurized, starting from a time of 5 min after initiation of mixing and continuing for a minimum of 25 min, until the cement was hardened. For each dose of cement mixed, the cement was cured with either no plunger, or with plunger weights resulting in 50 kPa or 100 kPa of pressure on the cement.Six test conditions were examined in the experiment: (open bowl and vacuum mixing methods)×(0, 50, and 100 kPa curing pressures). Fifteen specimens were molded for each test condition, resulting in a total of 90 specimens.Specimens were X-rayed at 32 kV for 1 min. The X-rays were examined for evidence of porosity in the gage region. The diameter of the largest pore in the gage region of the test specimens was measured using calipers and recorded. Test specimens with a maximum void size greater than 2 mm in diameter were excluded from the experiment.The molded specimens were allowed to cure for a minimum of 7 days in phosphate buffered saline at 37°C. Each specimen's cross sectional area was measured in the middle of the gage region. Testing was performed using an Instron load frame and strain was measured using an Instron strain gage with 25.4 mm gage length. Specimens were uniaxially loaded to failure at a constant displacement rate of 5 mm/min. Specimens that failed outside of the gage region were excluded from the experiment.Load and strain were recorded throughout the test for each specimen. Stress was calculated by dividing the measured load by the cross sectional area. Failure stress was calculated using the maximum load and dividing it by the cross sectional area. Elastic modulus was calculated in the linear region of the stress/strain curve.Following testing, fracture surfaces were examined using light and electron microscopy.The effect of pressure on the static tensile properties was analyzed for specimens produced by each mixing condition. Failure stress and strain to failure for open bowl mixed and vacuum mixed cement were compared at each pressure using Students t-tests (Statgraphics version 5.0-Manugistics, Inc. 9715 Key West Avenue, Rockville, MD 20850).The ultimate tensile strength of the open bowl mixed specimens was related to the applied pressure (p<0.01) (). Specimens cured under 50 and 100 kPa pressure were 7% and 11% stronger than specimens cured with no applied pressure, respectively. The failure stress of the vacuum mixed specimens, however, was independent of applied pressure (p=0.69). When comparing the vacuum mixed specimens to the open bowl mixed specimens, there was a statistically significant increase in failure stress of 18% under no pressure and 12% under 50 kPa pressure. There was no significant difference in failure stress of the vacuum mixed and the open bowl mixed specimens cured at 100 kPa pressures (p=0.16).Results for strain to failure corresponded with the failure stress (). For open bowl mixed specimens, strain to failure was related to the applied pressure (p<0.01). Specimens cured under pressure had significantly greater strain to failure than specimens cured with no applied pressure. When comparing the vacuum mixed specimens to the open bowl mixed specimens, all differences were statistically significant (p<0.01). There was a 45% increase in strain to failure under no pressure, a 38% increase in strain to failure under 50 kPa pressure, and a 19% increase in strain to failure under 100 kPa pressure.The elastic modulus for all test specimens in this study was 2.83±0.18 GPa. An ANOVA demonstrated that the elastic modulus was insensitive to pressure or mixing atmosphere.Examination of the fracture surface by light microscopy demonstrated a difference in the texture of the fracture surface for the vacuum mixed and open bowl mixed groups (A significant difference in porosity was seen between the vacuum mixed and open bowl mixed groups when examined via X-ray (p⪡0.01). The average size of the largest pore in the vacuum mixed group was 0.31±0.58 mm and the average size of the largest pore in the open bowl mixed group was 1.33±0.34 mm. Maximum pore diameter was not significantly affected by pressure (p=0.69). Within the resolution of the X-ray, no pores were visible in the gage region of 77% of the vacuum mixed samples while all open bowl mixed samples had pores visible in the gage region.The results of this study demonstrated that continuous pressurization throughout curing was beneficial to the strength of the open bowl mixed samples despite the continued presence of porosity in the specimens. Under static tensile failure conditions, pressurization of the open bowl mixed cement to 100 kPa resulted in similar material strength to vacuum mixing. Both pressurization and vacuum mixing would be expected to strengthen the polymerizing material as opposed to the pre-polymerized or insoluble powder material. Since both effects strengthen the same polymerizing region of the final product, specimens produced by vacuum mixing are not significantly affected by pressure.Vacuum mixing produced stronger specimens with fewer voids than open bowl mixing. These results were consistent with other studies that have also demonstrated that vacuum mixing increases cement strength by elimination of voids It was expected that curing the tensile specimens under pressure would reduce their porosity. In this experiment, the total porosity was not measured, rather the diameter of the largest pore in the gage region was measured, as this would be expected to affect the tensile properties of the material. The strengthening of the polymerized matrix may be a result of reduction in micro-porosity at the interface with the insoluble, micron sized barium sulfate or the soluble pre-polymerized beads. The strengthening may also reflect a change in residual stress within the polymerized matrix.X-radiography represented a non-destructive method to measure porosity in the tensile specimens prior to testing. The method provided a measure of porosity over the entire gage region of every specimen tested. Other methods like cutting and polishing cross sections for light and scanning microscopy may have a higher resolution, but these methods are destructive and only quantify porosity in discrete areas of selected specimens with unknown mechanical strength.This study indicated the importance of including the effect of pressurization when studying the mechanical properties of acrylic cements. Fully quantifying the effects of the specimen preparation and curing environment on one cement is very important prior to focusing on a more difficult question regarding the relative strength of multiple cements in clinical situations. A study to accurately evaluate the strength of multiple cements would involve an array of tests as well as careful attention to specimen preparation, since multiple factors play a role in the resultant strength of bone cement.There has been clinical precedence for maintaining pressure on curing cement. The literature describes maintaining finger pressure on the curing cement in order to enhance the quality of the cement/bone interface Under the conditions of this study, curing bone cement under pressures consistent with thumb or digital pressurization of the cement resulted in an increase in the strength of open bowl mixed cement to values comparable to vacuum mixing. This increase in mechanical properties occurred despite the fact that pressure did not eliminate porosity from the open bowl mixed tensile specimens in a manner comparable to vacuum mixed cement. Curing bone cement under pressure had no significant effect on the strength of cement prepared by vacuum mixing.Quasistatic and dynamic deformation of tungsten reinforced Zr57Nb5Al10Cu15.4Ni12.6 bulk metallic glass matrix compositesQuasistatic and dynamic deformation behavior of composites of Zr57Nb5Al10Cu15.4Ni12.6 metallic glass reinforced with tungsten is studied. The plastic deformation of the metallic glass was increased under quasistatic compression in composites. Localized shear band failure of these composites results in self-sharpening behavior during ballistic impact.The development of bulk metallic glass matrix composites opens new opportunities for application of metallic glass. Monolithic bulk metallic glasses possess high strength but fail catastrophically along narrow shear bands when loaded in tension or compression. Recent research illustrates the feasibility of processing metallic glass composites that can undergo substantial plastic deformation in compression Metallic glass reinforced with ductile metallic fibers or particulates show inhibited shear band formation when tested in quasistatic compression, resulting in the generation of multiple shear bands and substantial plastic deformation. The shear bands typically form at ±45° to the loading axis. At high strain rates (106 s−1), multiple shear band formation is suppressed, and failure occurs along a single adiabatic shear band, just as in the monolithic metallic glass The adiabatic shear band failure mechanism of tungsten-reinforced metallic glass composites at high strain rates suggests that it may be used in kinetic energy penetrator applications. The two primary families of materials are currently used for kinetic energy penetrators: tungsten-based alloys and depleted uranium (DU). Unlike tungsten, DU fails by adiabatic shear when loaded in dynamic compression. As a result, when a DU projectile penetrates armor its tip remains sharp and about the same diameter as the rest of the projectile, and the sheared material is sloughed off. The kinetic energy is thus focused over a smaller area of the target and the penetration depth is enhanced. This behavior is known as “self-sharpening”. The tip of a tungsten-based penetrator expands to form a large mushroomed head, leaving a cavity of increasing diameter with deeper penetration. Self-sharpening is the widely accepted reason that DU exhibits penetration performance superior to tungsten. Some materials, such as certain tungsten heavy alloys (WHAs), exhibited a limited self-sharpening.In this paper the quasistatic and dynamic deformation behavior of composites of Zr57Nb5Al10Cu15.4Ni12.6 metallic glass reinforced with 80%Vf tungsten wires, 50%Vf tungsten particles, and 50%Vf of mixed tungsten/rhenium particles is presented and discussed. The plastic deformation of the metallic glass was increased under quasistatic compression in all wire or particle reinforced composites. This improvement occurs because the ductile reinforcement restricts shear band propagation and promotes the generation of multiple shear bands. The high strain rate deformation behavior of tungsten-wire or particle-reinforced metallic glass composites is studied in ballistic penetration experiments. Ballistic penetration tests were performed firing metallic glass composite rods into 6061 T651 aluminum and 4130 steel targets. Localized shear band failure of these composites results in self-sharpening behavior during ballistic impact. The outstanding feature of the composite kinetic energy penetrators is their self-sharpening behavior; this allows them to penetrate significantly deeper than the WHA penetrator, which mushrooms on impact.Ingots of Zr57Nb5Al10Cu15.4Ni12.6 were made by arc melting a mixture of the elemental metals (purity 99.5% or greater). Tungsten wires with a nominal diameter of 254 μm, were straightened and cut to 5 cm lengths. Tungsten powders with an average diameter of 100 μm and mixed tungsten/rhenium (with a mass ratio of 6.25% rhenium) powders, with an average diameter of 50 μm (W) and 10 μm (Re) were also used as reinforcement. Composite specimens were cast in a resistive furnace by melting the ingots in an evacuated 7-mm ID 304 stainless steel tube packed with wire or particle reinforcement, applying 687 kPa argon pressure and infiltrating for 20 min, followed by quenching in water. Complete details of the casting process may be found in Ref. (a) is an SEM micrograph of Zr57Nb5Al10Cu15.4Ni12.6 metallic glass reinforced with 80Vf tungsten wires that shows the interfacial region between tungsten wires (light gray) and the amorphous matrix (dark gray). The matrix appears uniform. (b) shows W particles distributed uniformly in the metallic glass matrix. The matrix phase appears free of heterogeneity. However, multiple phases can be seen in the matrix of the composite reinforced with W/Re particles, ((c)). Microprobe analysis reveals that the rhenium reacts with the matrix components and forms a gray appearing phase (number 1) that contains 12% Re. The black areas (number 2) consist mainly of matrix elements with a small amount (<1 at.%) W and Re.Compression tests were performed on monolithic Zr57Nb5Al10Cu15.4Ni12.6 metallic glass and composites containing W wires, W particles, and mixed W/Re particles (). The unreinforced metallic glass has only 0.5% plastic deformation in quasistatic compression. The samples reinforced with 50%Vf mixed W/Re particles sustained plastic deformation of 8%. The tungsten particle reinforced composites deformed in the same way. The tungsten wire reinforced composites showed 16.2% compressive strain to failure. The compressive strength of the wire reinforced composite increased from ∼1800 MPa (monolithic Zr57Nb5Al10Cu15.4Ni12.6) to ∼2150 MPa (80%Vf W wires), and the elastic modulus jumped from 85 to 320 GPa. This increase is within 8% of the elastic modulus calculated using the rule-of-mixtures model, and suggests that the wires are tightly bonded to the matrix. The elastic modulus and the ultimate strength of the particulate composites are approximately equal to unreinforced Zr57Nb5Al10Cu15.4Ni12.6.The quasistatic compressive fracture of unreinforced Zr57Nb5Al10Cu15.4Ni12.6 (Vit106) and the particulate composites take place along the plane of maximum shear stress, which is oriented at 45° to the axial load ((a)). A proposed mechanism for the adiabatic shear failure of metallic glass is that a fluid layer forms in the shear plane (a) reveals the extensive flow of metallic glass over the particles, implying that the metallic glass has reduced viscosity in the shear band. The compressive fracture surface of the composites reinforced with 80%Vf W wires is shown in (b). The failure mode changed from shear bands to fiber splitting, localized tilting and buckling. The tungsten fibers are tightly bound to the matrix because the thermal expansion coefficient for the metallic glass (8.6×10−6 K−1) is almost twice that of the tungsten (4×10−6 K−1), resulting in high compressive radial stress at the fiber/matrix interface. This effect is heightened when the sample is compressed because the Poisson ratio of the matrix is higher than that of the reinforcement (0.35 versus 0.28), causing the matrix to “squeeze” the wires even more tightly when the composite is loaded. The tensile matrix hoop stress guides the fracture path toward and through the tungsten wires. It is proposed that the wires first yield, followed by axial shear cracking, making the wires unstable and unable to prevent buckling in the composite.(a) is a photograph of an aluminum target after impact with an 80%Vf W wire composite rod traveling at a velocity of 785 m s−1. The impact surface is at the top in the photograph. The penetrator tip, which began as a right circular cylinder, is chiseled to a sharp point (arrow 1). Asymmetric forces caused the penetrator to rotate and travel off axis during the penetration event (arrow 2), reducing the total penetration depth in this sample. (b) shows a 50%Vf W/Re particle/Vf Zr57Nb5Al10Cu15.4Ni12.6 composite rod fired at a velocity of 998 m s−1. As in (a), the penetrator tip formed a sharp point (arrow 3). Arrow 4 points out the trailing end of the penetrator.Penetrators fired at the steel target are illustrated in (a) shows an 80%Vf W wire composite penetrator fired at 1197 m s−1 embedded in the steel target. The tip of this penetrator has expanded about 1.5 times its initial diameter (arrow 1). It has not been deformed extensively into a “mushroom” like shape, although the tip is not as clearly self-sharpening as observed after firing the same material into an aluminum target. Broken tungsten wires fill the hole next to and behind the penetrator (arrow 2). (b) shows a 50%Vf W/Re particle/Zr57Nb5Al10Cu15.4Ni12.6 fired at 944 m s−1 composite embedded in the steel target. The penetration tunnel formed in the steel targets by the particulate composite penetrators was both larger in diameter and shallower than that of the wire-reinforced composites.Penetration depth versus velocity is plotted in (a) and (b) for the aluminum and steel targets, respectively. The W/Re projectiles showed the greatest penetration depth in the aluminum targets. Results from a tungsten heavy alloy penetrator (X-27C) and W wire/Zr41.2Ti13.8Cu12.5Ni10Be22.5 (Vit1) have been included in Particulate composites consisting of a Zr57Nb5Al10Cu15.4Ni12.6 metallic glass matrix reinforced with 50%Vf mixture of W/Re particles exhibited 8% plastic elongation when tested in quasistatic compression. Quasistatic compressive strain to failure of an 80%Vf W wire/Zr57Nb5Al10Cu15.4Ni12.6 metallic glass composite, with the wires aligned with the loading axis, exceeded 16%, more than 6 times higher than monolithic Zr57Nb5Al10Cu15.4Ni12.6. Young's modulus of the tungsten wire composite was four times greater than the unreinforced matrix material and is in good agreement with the rule-of-mixtures prediction. Compressive strength of the wire composite is 20% higher than the unreinforced matrix. The failure mode of the 80%Vf W wire composite shifts from localized 45° shear bands to wire splitting, buckling and tilting. At high strain rates (∼106 s−1), the failure mode of the composite rods reverts to localized adiabatic shear banding, indicating that shear is the preferred failure mechanism at the highest strain rates. The penetration performance of the composite materials was 10–20% better than that of tungsten heavy alloy penetrators of comparable aspect ratio.Behaviour of stainless steel plain channel section columnsIn this paper, the structural stability of cold-formed stainless steel plain channel columns under axial compression is investigated. Reliable finite element models for channel section columns are first developed and validated against experiments conducted on stainless steel lipped channel specimens. This is followed by a parametric study in which columns made of austenitic, ferritic and duplex stainless steel are assessed. The considered cross-section classes and column lengths cover the entire range of global slenderness. The effects of material and geometrical nonlinearity are considered in the numerical analysis. The numerically generated data are then employed to evaluate the accuracy of the current European and Australian design codes EN 1993-1-4 and AS/NZS 4673 respectively, for predicting the flexural and flexural-torsional column buckling resistance. The results show a necessity to improve the current buckling curve used to predict the flexural buckling resistance of plain channel section columns, currently adopted in EN 1993-1-4, whose use may lead to unsafe predictions, especially for the austenitic grade.Regarding overall buckling, the FTB mode is a characteristic of open cross-sections for which the centroid and shear centre do not coincide, hence decreasing the torsional rigidity of the section. For plain channel sections, this eccentricity only exists in the direction of the major principal axis; therefore the buckling in the symmetry plane is essentially independent of torsion []. It has also been shown that, for plain channel section columns of the same length, as a consequence of the shift of the centroid of the effective cross-section, columns with fixed-ends exhibit greater overall capacity than columns with pinned-end conditions []. Another influential parameter is the member slenderness: for the same cross-sectional geometry, increasing the members’ unrestrained length increases the chances to get minor axis FB.The present paper studies cold-formed stainless steel (CFSS) plain channel section columns. Stainless steel is a chromium based alloy characterised by pronounced corrosion resistance and appealing surface finishes. According to their metallurgical microstructure, grades of stainless steel can be classified into essentially five main families: austenitic, ferritic, duplex (austenitic-ferritic), martensitic and precipitation hardening. Today, austenitic, ferritic and duplex families have been relatively often used as structural materials. Thin-walled sheets of austenitic grades, owing to the attractiveness of their surface finishes, have predominantly been used as cladding in buildings, while duplex grades, thanks to their enhanced mechanical properties combined with good corrosion resistance, have mostly been used in thicker structural load-bearing elements in corrosive environment. As structural material, ferritic grades are usually utilized in protected environment exposed to mild atmospheric conditions [Stainless steels exhibit clear differences in their mechanical properties compared to carbon steel. They are characterised by a distinct nonlinear stress-strain relationship compared to the elastic, perfectly-plastic material model for ordinary carbon steel, leading to a different treatment in most design standards. Nonlinear behaviour of stainless steel commences at low stress levels and the stress-strain curve is characterised by extended strain-hardening and the absence of yield plateau, which requires the equivalent yield stress, conventionally adopted as the 0.2% proof stress, to be used in the structural design []. For CFSS plain channel section, the significant drop in strength in the intermediate cross-section slenderness range is not only caused by the element interaction but also by the inherent material nonlinearity [The aim of this research is to assess the suitability of the current design models provided in the European and Australian standards for FB and FTB of cold-formed stainless steel (CFSS) plain channel columns. The finite element (FE) model presently used is firstly described. The models were calibrated and validated against experiments performed on CFSS lipped channels taken from previous studies. A parametric study is subsequently performed to generate reliable data over a wider range of members’ non-dimensional slenderness and for three different stainless steel families. The current codified design models are then evaluated through the assessment of the safety factor γM1 and resistance factors φc.The theoretical and experimental observations on carbon steel channel columns serve as important benchmarks for a better understanding of the structural behaviour of stainless steel channel columns. Out of research conducted in the past concerning the behaviour of CFS plain channel sections, the following deserves to be mentioned here. The first published one from Mulligan et al. [], involved experimental research conducted on 11 stub columns. The purpose of the research was to analyse the local buckling interaction between the cross-section walls. The authors report that the Effective Width Approach is applicable to the thin-walled plain channel stub columns considered in the paper. Ye et al. [] performed experiments on 9 pinned-ended columns, investigating the interaction between local and FB. It was shown that the current design procedures proposed in EN 1993-1-3 [], where interaction between local and overall buckling is accounted for, provide conservative predictions for CFS plain channel columns. The accuracy of the strength predictions is significantly increased if the method proposed in Annex E of EN 1993-1-5 [], where the effective cross-section properties are based on the actual stress level instead of the yield strength, is used. Young and Rasmussen [], explored the behaviour of press-braked members under compression, analysing the influence of different boundary conditions on the overall column behaviour. The material used was carbon steel G450 and a total of 22 specimens (14 fixed-ended and 8 pinned-ended) were tested. It was found that, for columns with the same effective length, fixed-ended column strengths were greater when the ultimate load exceeded the local buckling one. This is because fixed-ended conditions prevent additional bending to occur when the line of action of the internal force shifts due to local buckling. Moreover, it was concluded that local buckling shows the greatest impact on the strength of plain channel columns in the short and intermediate range of length. Moldovan [] conducted tests on 16 stub columns and 19 columns, with the purpose of investigating the interaction of local, FB and FTB modes. The test results were found to be in good agreement with the theoretical predictions. To the best knowledge of the authors, the aforementioned researches constitute a summary of the currently available experimental research relevant to axially compressed carbon steel plain channels.Tests and models of compressed stainless steel members conducted so far concerned, in majority, cold-formed hollow sections. The scientific literature on the behaviour of various types of open stainless steel cross-sections is today relatively scarce. Concerning the latter, the greatest part addresses the behaviour of lipped channel sections, and only a few of those concerned plain channel sections. In Ref. [], Becque et al. conducted experiments on 29 pin-ended lipped channel stainless steel columns with the aim to analyse the interaction of local and overall flexural buckling. Three stainless steel alloys were considered: EN1.4301, EN1.4016 and EN1.4003. In Ref. [], Rossi et al. examined the combination of distortional and overall flexural-torsional buckling on cold-formed stainless steel lipped channel columns. A total of 21 columns made of EN1.4003 were tested. In Refs. [], Lecce and Rasmussen investigated the effects of distortional buckling on cold-formed stainless steel lipped channels. A total of 19 tests were performed including 11 simple lipped channel columns and 8 lipped channel columns with intermediate stiffeners, made of EN1.4301, EN1.4016 and EN1.4003 grades. The results of [] are used to calibrate the FE model which is presented in this paper.Regarding plain channels, in essence two studies should be mentioned here: Dobrić et al. [], who performed experiments on plain channel columns made of the austenitic grade EN1.4301, with a total of 4 stub column specimens with fixed-end conditions; and Kuwamura [] who, among other types of cross-sections, performed experiments on 11 cold-formed stainless steel stub column specimens comprising plain channels made of austenitic EN1.4301 and EN1.4318 grades. None of these researches however covered overall (FB or FTB) buckling tests of slender stainless steel plain channel section columns.Based on the content of the presented literature, it can be concluded that, the structural behaviour of CFSS is generally similar to the one of CFS equivalents. The major difference comes from the fact that stainless steel exhibits material non-linearity. On the one hand, the stress-strain behaviour characterised by gradual yielding leads to a reduction of the buckling strength of CFSS columns in the intermediate slenderness domain. On the other hand, the pronounced work-hardening associated with cold forming operations during manufacture positively affects the structural response of CFSS columns and increases the buckling strength in the low slenderness domain. In the high slenderness domain, CFSS and CFS columns exhibit quite similar behaviour, considering their approximately equal values of modulus of elasticity.Although not directly related to the topic of this paper, the following provides a broader view on what has been done in the past on the behaviour of both stainless and carbon steel channel sections subject to either compression, bending or a combination of both. Experiments and numerical analyses of built-up stainless steel channel section columns and beams are reported in Refs. [] respectively. With regard to single lipped and plain laser-welded channel members in bending, considerable results were obtained by Theofanous et al. in Ref. []. The combined effect of compression and minor axis bending on laser-welded stainless steel channels was analysed by Liang et al. in Refs. [] carried out experiments on full-scale floor trusses fabricated from cold-formed steel channel sections tested under four point bending. It is also worth mentioning the following investigations on channels with perforated webs: in Ref. [], Zhao et al. performed four point bending tests on cold-formed steel specimens; in Ref. [], Yousefi et al. investigated the web crippling strength of cold-formed stainless steel plain channels.In this section, the European and Australian design codes for the design of stainless steel thin-walled members are summarised and the bases for assessing the behaviour of plain channel section columns are outlined. The common codes which are applicable to the design of stainless steel thin-walled structures are Eurocode 3: EN1993-1-4 [These codes request that the design strength of thin-walled sections, parts of which are susceptible to local buckling, should be determined on the basis of the Effective Width Approach. This approach accounts for local instability of parts of the cross-section in a manner which deems some parts ineffective and omits them from the calculation of the cross-sectional properties. The width of the plate elements comprised in the cross-section is reduced by introducing a reduction factor, which depends on the support conditions of the walls, loading conditions, yield strength of the material and width-to-thickness ratio of the walls. According to EN1993-1-4 [], Clause 5.2.3, this reduction factor can be obtained as follows:ρ=1λ‾p−0.188λp2‾≤1ρ=0.772λ‾p−0.079λ‾p2≤1ρ=1λ‾p−0.188λ‾p2≤1Please update Ref. [39].λ‾p≥0.748ρ=0.772λ‾p−0.079λ‾p2≤1for internal elements with λ‾p≥0.651, b‾ is the notional widths of plane cross-section parts allowing for corner radius [], t is the plate thickness, ε = [(235/fy)·(E/210000)]0.5 is the material parameter and kσ is the plate buckling coefficient, taken as 0.43 for outstand elements and 4.0 for internal elements in uniform compression.Clause 5.4 provides a procedure to determine the design buckling resistance of compression members, which is described by the following equations:Where χ is the non-dimensional buckling reduction factor, A is the gross area of the cross-section, Aeff is the effective area of the cross-section and γM1 is the partial safety factor.For members with non-symmetric Class 4 cross-sections, allowance shall be made for the additional moment due to the eccentricity of the centroid of the effective cross-section with respect to the centroid of the gross cross-section.The reduction factor χ is based upon the Perry-Robertson curve and can be obtained using Equation where ϕ is the operational parameter which can be calculated using Equation where Ncr is the elastic critical force for the relevant buckling mode, obtained based on gross cross-sectional properties.The parameter ϕ is obtained in the following manner:where λ‾0 is the limiting non-dimensional slenderness and α is the factor which accounts for the imperfections.The parameters α and λ‾0 depend only on the buckling mode and production process, they equal respectively 0.49 and 0.4 for FB of cold-formed open cross-sections, while for torsional and FTB, they equal 0.34 and 0.2, respectively. However, research performed over the last years has led to the conclusion that the current EN 1993-1-4 buckling curves for cold-formed stainless steel sections may be optimistic and that there exists enough differences between the stainless steel families to afford a specific treatment in the design standard []. This fact was accounted for in the 4th edition of the Design Manual for Structural Stainless Steel [] for some types of cross-sections, but for CFSS channel columns made of austenitic, ferritic and duplex stainless steel, the parameters α and λ‾0 respectively equal 0.76 and 0.2, irrespective of the alloy. But it has not been studied extensively and not yet been introduced in the current edition of EN 1993-1-4. It is the goal of the present paper to completely respond to the question for stainless steel plain channel section columns.Local buckling of slender monosymmetric cross-section causes a shift of the centroid of the effective cross-section which consequently introduces secondary bending moment. Therefore, an initially centrically compressed column becomes a beam-column. This is however not the case for fixed-ended channel columns for which the shift in the line of action of the internal force is balanced by the shift in the line of action of the external force []. The effective width approach for local-overall interaction account for effective section properties in the calculation of the beam-column buckling stress. For stainless steel column with Class 4 cross-sections, the following equations from Clause 5.5 of EN 1993-1-4, take into account interaction effects between compressive axial load and uniaxial bending moment induced by the shift of the effective centroid.For preventing premature buckling about the major axis:For preventing premature buckling about the minor axis (for members subject to lateral-torsional buckling):For preventing premature buckling about the minor axis:In the above expressions, NEd is the applied design value of the axial compression load; eNy and eNz are the shifts of the centroidal axes when the cross-section is subject to uniform compression; (Nb,Rd)min is the smallest value of the design buckling load Nb,Rd for the following four buckling modes: flexural buckling about the y axis, flexural buckling about the z axis, torsional buckling and torsional-flexural buckling; (Nb,Rd)min1 is the smallest value of Nb,Rd for the following three buckling modes: flexural buckling about the z axis, torsional buckling and torsional-flexural buckling and Mb,Rd is the design lateral-torsional buckling resistance. The interaction factors ky and kLT can be obtained as follows:ky=1.0+2(λ‾y−0.5)NEdNb,Rd,ybut1.2≤ky≤1.2+2NEdNb,Rd,yFor cold-formed cross-sections, according to EN 1993-1-3 [] an alternative interaction formula may be used:in which MEd includes the effects of shifts of neutral axis, if relevant.], for uniformly compressed members, the effective width of the cross-section shall be determined in accordance with Clause 2.2.1.2, where the effective widths are obtained using the following equations:where λ‾p is the slenderness ratio of the plate element and can be obtained via equation According to Clause 3.4.1 of AS/NZS 4673:2001 [], the design compressive axial force shall be calculated as a product of φc and Nc, where φc is the strength reduction factor for members in compression and Nc is defined as follows:where Ae is the effective area calculated at buckling stress fn, which is the least of the flexural, torsional and flexural-torsional buckling stress.In order to account for the non-linear material law of stainless steel, the AS/NZS Specification proposes an iterative design procedure employing the tangent-modulus approach.For sections not subject to torsional or FTB, the FB stress is defined in as:where Et is the tangent modulus in compression corresponding to the buckling stress, k is the effective length factor, l is the unbraced length of the member and r is the radius of gyration of the gross cross-section. A rather similar expression is provided in ASCE 8–02 [], Clause 3.4.1, except that foc is regarded as fn, which seems more sensible in terms of nomenclature and avoids possible confusion.As an alternative to the iterative method, an explicit design procedure is also proposed. In this procedure, the following expression for the FB stress fn is given:which is in essence the same as in the European code except that the slenderness is here expressed in terms of the buckling length kl and the radius of gyration r rather than the critical load Ncr as in equation For austenitic, ferritic and duplex grades, the parameters α, β, λ0 and λ1 are given in . These generic equations are based on []. Note that the parameters included in equation do not bear the same significations as the ones in equation . The parameter η in the Australian code should be compared to α(λ‾−λ‾0) in the European one, where λ0 is the plateau length. In the next sections of this paper, the parameters provided in will be denoted with the subscript AUS: αAUS and λ0, AUS.For sections subject to torsional buckling, fn is defined as follows:where A is the gross cross-sectional area, r0 is the polar radius of gyration about the shear centre, G0 is the initial shear modulus, J is the torsional constant, E0 is the initial elastic modulus, Cw is the warping constant, kt is the effective length factor for twisting and lt is the unbraced length for twisting.For sections subject to FTB, fn shall be adopted as the lesser of fn calculated according to Eq. and the critical FB stress obtained in accordance with Clause 3.4.2 of AS/NZS 4673:2001 [where σey is the flexural major-axis buckling critical stress, while the meaning of the factor β is essentially the same as in EN1993-1-3 [It should be emphasized that there is a discrepancy between Eq. and the expression for the critical FTB stress provided in ASCE 8–02 [], Clause 3.4.3, which has the following form:There has probably been a typing error and Eq. should be adequately corrected by putting the second term 4βσeyσt under the square root, as in Eq. According to Clause 3.5 of AS/NZS 4673:2001 [], the design axial compressive load N∗ and the design bending moments My∗ and Mz∗ , y and z being the major and the minor principal axes, respectively, shall satisfy the following equations:N∗φcNc+CmyMy∗φbMbyαny+CmzMz∗φbMbzαnz≤1,0Where Nc is the nominal member capacity of the member in compression, Mby and Mbz are the nominal member moment capacities about the major and the minor principal axes, respectively, Ns is the nominal section capacity in compression, αny and αnz are the moment amplification factors obtained as 1−(N∗/Ne), where Ne is the elastic buckling load about the minor (Nez) and the major (Ney) axis, Cmy and Cmz are the coefficients for unequal end moments, ϕc and ϕb are the strength reduction factors for compression and bending, respectively.This Section describes the numerical procedures employed to develop reliable FE models and to generate a large series of numerical data in order to assess the appropriateness of the existing codified procedures for the design of CFSS channel columns.In the absence of experimental data on the overall buckling behaviour of slender CFSS single channel columns, the experiments on CFSS lipped channel columns with fixed ends from Rossi and Rasmussen [], were used to validate the model. The papers include details of the experimental approach, the observed structural behaviour and measured data such as the experimentally obtained ultimate buckling loads. The numerical simulations of the mentioned experiments are described in Ref. []. ABAQUS FE software package was used []. Linear Buckling Analysis (LBA) was employed to predict the critical buckling mode shapes used to model the distributions of the initial geometric imperfection and allow for a realistic incremental non-linear procedure. The geometrically and materially non-linear analysis (GMNIA) was carried out as quasi-static with the dynamic explicit solver.Numerical results were generated and compared against the ten experiments of Rossi and Rasmussen [] and the four experiments of Lecce and Rasmussen []. In order to model the experiment of [The same approach was used to model the specimens' boundary conditions in Ref. [] with contact conditions between the column's end cross-sections and the end plates defined via tie constraints at the joining surfaces, although there was no additional plate preventing warping of the end cross-sections.Two reference points were defined at the centroid of the top and bottom bearing plates, coinciding with the centroids of the specimens’ end cross-sections. Displacement controlled analysis was used and a nodal displacement of one reference point was prescribed. Typical geometry, boundary conditions and mesh are shown in The base material of all specimens in Refs. [The inputted geometric imperfections are linear combinations of sine wave functions which reflect the eigenmode shapes obtained via LBA. Four shape distributions of geometric imperfections were considered: a sine wave (bow) imperfection in the plane perpendicular to the minor principal axis, a twist imperfection, a local imperfection and a distortional geometric imperfection. The imperfection amplitudes matched the measured ones. Considering that a number of investigations such as [], indicate that residual stresses due to cold working insignificantly impact the overall behaviour of stainless steel thin-walled compressed members, the residual stresses induced by the manufacturing process were not included in the FE models.The accuracy of the FE models was assessed by comparing the key results to the experimental ones i.e. ultimate buckling loads and full load-deflection curves. The numerical failure modes including distortional buckling and minor axis FB for low and intermediate column slenderness and flexural-torsional mode for high column slenderness match the experimental ones [ gives a qualitative comparison of the distortional buckling mode occurring in the specimen with a length of 900 mm against the FE prediction.Excellent matching is achieved for the ultimate buckling load Nb,u for all experiments. The average value of the FEM-to-experiments ultimate load ratio Nb,u,FEM/Nb,u,exp equals 1.01 and the coefficient of variation (CoV) is 1.81%, as shown in compares the experimental load versus end-shortening curves for a range of four selected columns with the equivalent curves obtained through FE modelling.As for the previous experimental programme, the average value of the FEM-to-experimental ultimate load ratio for the experiments included in Ref. [ compares the FE load versus end-shortening curves with the corresponding experimental ones. The numerical failure modes show inward or outward distortional buckling and correspond to the experimental ones (see In general, quite good agreement is achieved in terms of overall shape, initial stiffness, deformation capacity and ultimate resistance.In the formulation of design criteria of structures for which initial imperfection effects can be significant, the permissible fabrication and erection tolerances prescribed in the appropriate codes should be used as the basis of stability checks. To assess the sensitivity of the column's compressive capacity to several combinations of imperfection modes and amplitudes, the following imperfection sensitivity study was performed. Four different imperfections were considered: flexural (bow), local, distortional and twist deviations. The magnitude of the imperfection, based on LBA corresponding to the eigenmode shape, was successively chosen equal to ω0 = ±t, for a leading distortional imperfection in agreement with []; ω0 = ±d/100 for a leading local imperfection, in accordance with the cross-section tolerance given in EN 1090–2 []; ω0 = ±d/50 for a leading twist imperfection, based on Annex C of EN 1993-1-5 [] and δ0 = ± L/1000 for flexural imperfection that corresponds to 80% of the fabrication tolerances given in EN 1090–2 []. Following the clause C.5.(5) of EN 1993-1-5 [], one of the cross-section imperfections was taken as the leading imperfection and the others were taken as the accompanying imperfections whose amplitudes were reduced by a factor 0.7. It was found that the pattern using a leading local imperfection with an amplitude of d/100 in the low slenderness domain, a distortional imperfection of t in the intermediate slenderness domain, and a twist imperfection of d/50 in the high slenderness domain, led to the best agreement with the experimental results.An extensive FE parametric study was conducted including a wide range of overall and cross-section slenderness to meet different performance levels and to establish a calculation model for the design buckling resistance Nb,Rd of CFSS plain channel columns. In total 14 different plain channel cross-sections dimensions were selected providing both slender and non-slender cross-sectional behaviour. The geometrical proportions of the cross-section walls satisfy the conditions of Table 5.1 of EN 1993-1-3 []. The wall thicknesses range between 2 and 6 mm, as provided in , with the used dimensional code for the cross-section geometry as shown in . Pinned-ended columns were studied addressing their FB capacity about their minor and major principal axes and their FTB capacity.Shell elements S4R with a size equal to 1.5t, where t is the cross-section thickness, were used to discretise the cross-section and the same size of shell elements was selected along the length of the columns. Reference points were set at the centroids of the columns’ end cross-sections and kinematically constrained to the end cross-section surfaces. Displacement control was used to apply the compressive displacement to the reference point in the loading zone. The geometry, mesh and boundary conditions of one typical FE model are presented in Four stainless steel material models were presently considered: austenitic grade in cold-rolled condition, austenitic grade in hot-rolled condition, ferritic grade and duplex grade. The key material properties are based on Dobrić’s tests (EN 1.4301) [] and Saliba and Gardner's tests (EN 1.4162) []. Strength enhancement due to work hardening in the corner regions was considered according to Rossi's predictive model []. The Modified Ramberg-Osgood material model [] was used to model the stress-strain curves. Superposition of the initial geometric imperfections in the form of buckling mode shapes was introduced in each FE model. The pattern including local imperfection with an amplitude of d/100 and twist imperfection with an amplitude of d/50 together with a flexural imperfection with a magnitude of L/1000 was used in the parametric study. Depending on the slenderness domain, one of the cross-section imperfections was used as the leading and the other was reduced by a factor equalling 0.7. Because the distortional instability is not a critical mode of plain channel cross-section, the distortional imperfection was presently not considered.FB about the major principal axis is not a dominant failure mode for CFSS channel columns. In order to prevent the FB about the minor principal axis and FTB, and to force buckling to occur about the major axis, lateral restraints were introduced along the column length in the model. It is worth pointing that no such restraints were added to study minor axis FB or FTB.GMNIA was performed to obtain the ultimate loads and failure modes using the quasi-static analysis via dynamic explicit solver in the ABAQUS software package [The numerical results were carefully analysed to clearly identify the failure modes. The numerical failure mode which consisted of FB about the minor principal axis or FTB was selected to evaluate the corresponding theoretical failure load. In general, the observed overall instability modes were accompanied by cross-section local buckling. Additionally, in numerous cases, the FTB mode found in the FE investigations was not pure but coupled with FB about the minor principal axis.As already mentioned, major axis FB is not a dominant failure mode for CFSS channel columns with pin-ended supports. Therefore, this failure mode could only be obtained using appropriate boundary conditions along the column length and did not necessitate further identification. present typical minor axis FB, major axis FB and FTB responses of selected FE models, respectively.The generated numerical data were used to assess the appropriateness of the currently available design methods i.e. according to Eurocode 3 EN 1993-1-4 [], and the Australian code AS/NZS 4673:2001 []. For the design according to EN 1993-1-4 [], two values of the imperfection factor α = 0.49 (buckling curve c) and α = 0.76 (buckling curve d) in conjunction with a limiting non-dimensional slenderness λ‾0 = 0.2 were considered to predict FB loads about the minor and major principal axes, respectively. The buckling curve b (α = 0.34 and λ‾0 = 0.2) was used to predict FTB loads. Note that the change of imperfection factor in the calculation of the column FB resistances affects the calculation of the FTB resistances.The effective areas of Class 4 cross-sections were obtained following the procedure described in Clause 4.4 of EN 1993-1-5 [] considering the reduction factors provided in Ref. [], the minor axis column buckling strengths were calculated using the explicit approach that accounts for material nonlinearities by introducing the parameters α, β, λ0 and λ1 (as provided in ). To evaluate the influence of the shift of the centroid when considering the effective cross-section, the data points related to slender cross-sections (Class 4) were selected and reassessed based on the EN1993-1-4 interaction formulae. The direction of the predicted shift in plain channel section leads to a secondary minor axis bending moment Mz,pred = Nu,predeNz with no secondary major axis bending moment. A shift of the effective centroid towards the web causes bending towards the web.For reason of clarity, graphical comparisons between the predicted design resistances i.e. the buckling curves c and d, in conjunction with a limiting non-dimensional slenderness λ‾0 = 0.2, and the normalised FE compressive resistances for CFSS channel columns, including both non-slender and slender sections, are provided in for FB about the minor principal axis and in for FB about the major principal axis. In these two graphs, a different label was selected for each family of stainless steel. To be complete, the EN 1993-1-4 [] buckling curve for cold-formed open sections, employing the imperfection factor α = 0.49 and limiting slenderness λ‾0 = 0.4 is also depicted in compares the normalised FE compressive resistances related to FB about minor principal axis to the AS/NZS buckling curves based on the explicit approach (AS/NZS 4673:2001 []), which is applicable to cold-formed sections only, for each of the stainless steel grades. Experimental data for channel section resistances from Refs. [The FE ultimate loads are normalised by the squash load for each stainless steel family and are plotted against the non-dimensional column slenderness ratio. The normalised FE results are based on the enhanced average yield strength of the cross-section [], i.e. including the corner strength enhancement., for slenderness values lower than the plateau length, it was decided to use the formulation proposed in Ref. [] where strain-hardening effects are accounted for. Therefore, instead of using the classical horizontal yield limit proposed in conventional approaches, a compression level equal to fu (the tensile strength) is assumed to be attained as the slenderness approaches zero. Thus, the maximum reduction factor χ equals fu /fy, which improves the comparison between the design and numerical strengths.The points, representing pairs of corresponding FE data (Nb,u,FEM) and design data (Nb,u,pred), relate to minor axis FB (firstly compared to EN 1993-1-4 then to AS/NZS 4673 design predictions), FB about major axis and FTB are plotted in , including both slender and non-slender cross-sections and all analysed stainless steel grades.(a) FE data versus design data EN 1993-1-4 (buckling curve α = 0.49 λ‾0 = 0.2) /FB minor axis.(b) FE data versus design data AS/NZS 4673 /FB minor axis.(c) FE data versus design data EN 1993-1-4 (buckling curve α = 0.34 λ‾0 = 0.2) /FTB.(d) FE data versus design data EN 1993-1-4 (buckling curve α = 0.49 λ‾0 = 0.2) /FB major axis.In order to provide an indication of how the design procedures predict the strength, provides the numerical-to-predicted ratios per grade and per cross-section Class.Following to the results of the comparative analysis, the following conclusions can be drawn:(1) The buckling curve provided in EN 1993-1-4 [) leads to a significant number of unsafe predictions for CFSS channel columns considering FB about either the minor or the major principal axis. Hence, we shall emphasize the necessity for a lower buckling curve or a partial safety factor greater than the current value of γM1 = 1.10.(2) For minor axis FB of columns made of austenitic grades, the limiting non-dimensional slenderness appears to be closer to 0.2 while this does not seem to be the case for duplex and ferritic grades. At low slenderness, i.e. in the plateau region with λ‾z < 0.2, a number of experimental data, especially from Refs. [] exceed the squash load. This is due to the beneficial influence of strain hardening caused by cold working on the cross-section capacity.(3) The comparison between the FE data for minor axis FB and the codified ones based on buckling curves c and d in conjunction with a limiting slenderness of 0.2 reveals considerably unsafe predictions too in the low and, partially, in the intermediate slenderness range when λ‾z ≈ 0.2–1.0. The same can be concluded for major axis buckling however in a minor extent. This is quite clear in especially for austenitic grades. In these cases, a cross-section instability followed by shifting of the neutral axis in conjunction with a curved stress-strain curve prior the yield strength result in significant flexural strength degradation.In the intermediate slenderness range, the varying nonlinear stress-strain material law leads to different compressive capacity for columns made of different stainless steel grades. At high slenderness however, when the column behaviour is governed by elastic FB, the difference is not significant. In this slenderness range, the FE data are well represented by the codified curves, especially for non-slender sections.(4) The predictive curve c is in good agreement with FE data for duplex and ferritic grade considering non-slender channel sections. However, buckling curve d seems more appropriate for austenitic grades (see ). When the EN 1993-1-4 interaction formula (eq. ) is used in conjunction with the suitable buckling curve, safe but conservative results with higher scatter are obtained for all stainless steel families. Again, the buckling curve c provides acceptable agreement for the duplex and ferritic families with slender sections while the buckling curve d offers safer design predictions for the austenitic family. that buckling curve c (and d) in conjunction with a limiting slenderness of 0.2 may be suitable to predict major axis FB for non-slender cross-sections made of duplex and ferritic stainless steel grades (and austenitic grade). Note that the same can be stated for slender cross-sections when they are used in conjunction with the interaction formula for major axis flexural buckling and secondary minor axis bending moment.(6) The explicit approach of AS/NZS 4673:2001 [] provides considerably precise and reliable predictions of the strength of non-slender CFSS plain channel columns for minor axis FB (see ) with a lower scatter compared to the Eurocode predictions. In addition, similar conclusion can be drawn when Eq. is used for slender cross-section, when secondary minor axis bending moment should be considered.(7) The scatter of the data is significantly higher for the FTB mode, also when interaction between the axial force and the secondary minor axis bending moment is considered. A higher level of conservativeness of the codified predictions is also obtained.In order to evaluate the level of reliability of the European and Australian codified buckling curves for stainless steel plain channel section columns, which were found to be rather unsatisfactory for FB about the minor or major principal axis or for FTB, the values of the partial factors for member resistance γM1 [], are calculated based on a statistical analysis. The provisions given in Annex D of EN 1990 [] and the methodology described in Ref. [ was used to obtain the parameter d, instead of the equation provided in Ref. [The design buckling resistances Nb,Rd,1 and Nb,Rd,2 in Eq. are calculated taking into account a slight increase of the gross cross-sectional area A. Additionally, the parameter Vrt is adopted in accordance with Equation As for the coefficients of variation, the ones proposed in Ref. [] for fy, which are based on thorough statistical evaluation, were used. They equal 0.06, 0.045 and 0.03 for austenitic, ferritic and duplex grades respectively. The coefficient of variation for the geometric properties is considered equal to 0.05, which is the value employed in the development of the AISC stainless steel design guide []. In the analyses, the material over-strength factors were taken as 1.3 for the austenitic, 1.1 for the duplex and 1.2 for the ferritic grade.The numerical data from the parametric study performed in Section were used in the present statistical analyses. In compliance with EN 1990, Annex D, Clause D8.2.2.5 [], the total population of the test was divided into sub-sets, depending on the group of data being considered, respectively for minor or major axis FB or FTB and their interaction with uniaxial minor axis moment, cross-section slenderness (non-slender Class 3 and slender Class 4) and stainless steel family. In this case, the methodology allows to use the total number of data points in the original series to assess the fractile factor which avoids large safety factors due to a smaller number of data points in each sub-set. Herein, it is worth pointing that the number of data points in each sub-set eventually remained high.A summary of the key results of the reliability analysis is presented in . The parameters of interest useful for a better understanding of the results are as follows: n which is the total number of data points; b which is the average ratio of experimental (here FE)-to-model resistance, which is based on the least squares fit of the slope of the rei versus rti plot for each set of data, see Eq. ; the coefficient of variation Vδwhich is a measure of the variability of the FE-to-model resistance; and γM1 is the partial safety factor for the buckling resistance.Based on the results of the reliability analysis, the following comments can be drawn:(1) For FB about both principal axes and for non-slender sections, the assessment confirms that the Eurocode buckling curve c (α = 0.49, λ‾0 = 0.2) provides reliable predictions for both the duplex and ferritic grades and that, conversely, for the austenitic grade, the buckling curve d seems more appropriate.(2) The CFSS duplex and ferritic channel columns subject to interaction of minor/major axis FB and minor axis bending should also be calculated using the buckling curve c, see . It should be emphasized that this does not comply to the proposal of the Design Manual for Structural Stainless Steel [], where the more conservative buckling curve d is adopted. However, for austenitic grades, a difference should be made between interaction between minor axis buckling or major axis buckling with the secondary bending moment. In the first case (minor axis FB and minor axis bending), both curves c and d provide unsatisfactory results. In the second (major axis FB and minor axis bending), the buckling curve d appears to be adequate.(3) For minor axis FB (non-slender channel sections), the reliability study shows that the partial safety factors for the current AS/NZS 4673 explicit approach are 0.84, 1.07 and 0.96 for the austenitic, duplex and ferritic stainless steel grades respectively. In addition, the Australian codified procedure covering interaction of axial compression and uniaxial minor axis moment (for slender cross-sections) provides reliable results with the partial safety factors equal to 0.83, 1.07 and 0.99 for austenitic, duplex and ferritic stainless steel grades respectively; meaning that this approach seems more suitable for channel column design in comparison with the traditional Eurocode approach.(4) For the FTB mode, the theoretical predictions are rather unsatisfactory leading to safety factors ranging between 0.98 and 1.17. However, it should be noted that the buckling curve b leads to safe while rather conservative design predictions.The appropriate resistance factor φc to be used in conjunction with the rules of AS/NZS 4673 has been calculated on the basis of the statistics shown in , and the LRFD (Load and Resistance Factor Design) framework, see Section K2.1.1 of the North American Specification []. The resistance factor, taking into account the dead and live load combination, is obtained from Eq. where Cφ = 1.52 is the calibration coefficient; Mm = 1.1 and Fm = 1.0 are the mean values of the Material (M) and Fabrication (F) factors for concentrically loaded compression members, respectively; VM = 0.1 and VF = 0.05 are the coefficients of variation of the aforementioned factors; βo is the target reliability index for LRFD, which amounts to 2.5 for structural members; Pm and VP are the mean value and the coefficient of variation of the Professional factor (P), expressed as the test-to-design strength ratio; VQ is the coefficient of variation of load effect, which is equal to 0.21 for LRFD, and CP is the correction factor calculated in the following manner:where m = n - 1 represents the degrees of freedom and n represents the number of tests., the resistance factors φc for CFSS channels are presented both for pure compression (non-slender sections) and when interaction between compression and minor axis bending moment should be considered. Considering all of the available numerical data, the resistance factor φc is always greater than 0.9, which is the value for column design as per AS/NZS 4673 []. This is firstly due to the particular shape of the buckling curve, which is able to follow the behaviour in the low and intermedium slenderness range quite well, combined with, the scaling of the curve depending on the stainless steel family.In the present paper, a comprehensive FE assessment of the structural behaviour of cold-formed stainless steel plain channel columns under pure compression was carried out. Minor and major axis buckling as well as flexural-torsional buckling are carefully addressed. The derived FE model is then used to perform a parametric study in which austenitic, duplex and ferritic grades are studied over the whole column slenderness range, for non-slender and slender (Class 4) cross-sections. The generated data are then compared to the current European EN1993-1-4 [] and Australian design methods AS/NZS 4673 []. The appropriateness of the different codified buckling curves (considering the shift of the centroid for Class 4 cross-sections) is assessed through reliability analyses according to the methodologies proposed in EN1990:2002 Annex D [] and in the North American Specification [The parameters α and λ‾0 which are respectively equal to 0.49 and 0.4 in the existing EN1993-1-4 should be revised for the design of cold-formed stainless steel plain channel columns.For minor axis flexural buckling of plain channel section columns, the buckling curve c in conjunction with the non-dimensional limiting slenderness λ‾0 = 0.2 may be used for ferritic and duplex grades for all cross-section classes. Whereas, the buckling curve d together with λ‾0 = 0.2 is more suitable for cold-formed austenitic channel columns with nonetheless the exception of slender cross-sections (i.e. when minor axis FB interacts with minor axis moment).The buckling curve c in conjunction with the non-dimensional limiting slenderness λ‾0 = 0.2 appears to be more appropriate to predict major-axis flexural buckling of cold-formed channel columns for duplex and ferritic grades, while the buckling curve d may be proposed for the austenitic grade again.The use of buckling curve b in conjunction with λ‾0 = 0.2 to predict the flexural-torsional buckling leads to safe but quite conservative results characterised by significantly higher scatter.Very good agreement was found when the AS/NZS 4673 explicit approach is used. It is therefore proposed that the factor η=α(λ‾−λ‾0) in , Clause 5.4.2 of EN 1993-1-4, shall be replaced by Equation with the values of α, β, λ‾0 and λ‾1 as in . In this case, the safety factors γM1 as per EN1990:2002 Annex D, would be lower than 1.10 for all stainless steel alloys and all cross-section classes.Jelena Dobrić: Software, Investigation, Formal analysis, Writing - review & editing, Visualization, Resources. Jovana Ivanović: Software, Formal analysis, Writing - review & editing, Visualization. Barbara Rossi: Conceptualization, Methodology, Formal analysis, Validation, Writing - original draft, Writing - review & editing, Supervision, Resources.The following is the Supplementary data to this article:Supplementary data to this article can be found online at Tailoring tensile ductility of thin film by grain size graded substratesExtensive experiments have shown that thin metal or metallic glass films usually rupture under a small tensile strain, which is extremely unfavorable for their engineering applications. The introduction of a highly deformable substrate with homogeneous microstructures can enhance the ductility of the films. However, the strong mechanical contrast between the substrate and the film usually induces interface debonding and premature cracks at the interface. Another disadvantage of the above film/substrate system is its significantly reduced strength due to the low strength of the homogeneous substrate. Recently, experiments have shown that a heterogeneous substrate with a grain size graded microstructure is able to provide an exceptional strength-ductility synergy in the film/substrate system. However, why does the graded substrate render such outstanding properties remains unsolved due to its complex microstructure. In order to answer this question, here a dislocation density-based constitutive model was incorporated into a finite element scheme to investigate the deformation of a thin film attached to a graded substrate. The deformation of the film on a normal substrate with a homogeneous grain microstructure was also analyzed for comparison. A V-shaped notch was adopted in the film to model its necking behavior based on a necking criterion. The necking strain is adopted as the tensile ductility. The results show that three typical deformation behaviors can be triggered by tailoring the microstructure of the graded substrate including the grain size of the topmost surface layer and the thickness of the grain size graded region. The three modes correspond to very different necking strains. Interestingly, the graded substrate with an optimal microstructure can provide the film with much higher necking strain than the homogeneous coarse-grained substrate could although the former itself is less ductile than the latter. In addition, the film/graded-substrate system possesses much better strength-ductility synergy than the film/homogeneous-substrate system. The enhancement of the tensile ductility results from the strong strain delocalization effect induced by the graded substrate. The predicted stress-strain responses are also compared with available experimental measurements.Freestanding thin films (metal or metallic glass) have been reported to possess very limited tensile ductility (). This is mainly caused by the incapacity of metal film to retard strain localization, e.g., necking, due to the small thickness (), or the catastrophic failure due to formation of a single run-away shear band in metallic glass (). In order to elevate the rupture strain of the metal film, substrates with high deformability have been used as confinement to suppress the strain localization in the films (). For example, a Cu film deposited on a polyimide substrate can achieve a tensile strain of 100% without cracking (). Another example is that the strain localization in a freestanding nanocrystalline Ni film can be effectively retarded by a coarse-grained (CG) Cu substrate ( reported a Ni-P amorphous thin film resting on a CG Ni substrate that can deform homogeneously under tension without shear bands when the film thickness is sufficiently small. Note that the microstructures of all the above substrates, e.g., the distribution of molecules in elastomer or grain boundaries in metal (), are homogeneous. That means the substrate has isotropic mechanical properties such as elastic modulus or yield strength if the anisotropy induced by grain orientation is ignored.On the other hand, extensive investigations have shown that heterogeneously structured materials like gradient nano-structured metals possess much more attractive mechanical properties than their homogeneous counterparts, such as high strength and high ductility (). The gradient metals are characterized by a gradient distribution of the microstructures (e.g., grain size or twin thickness and spacing) from the surface to the interior, which renders them very promising engineering properties. For example, the gradient interstitial-free (IF) steel produced by surface mechanical attrition treatment exhibits a tensile ductility comparable to the homogeneous counterpart, while its yield strength is 2.6 times higher than that of the CG sample (). Also, the twinning-induced plasticity steel with a gradient nanotwinned structure produced by pre-torsion has doubled yield strength as compared with its homogeneous counterpart with no loss in ductility (). Even bulk metallic glass can become more ductile by introducing a gradient amorphous microstructure. For instance, a gradient bulk metallic glass prepared by can achieve a tensile elongation of nearly 2% under room temperature while maintaining a fracture strength of 2 GPa. As for friction and fatigue performance, the gradient AISI 316 L stainless steels produced by surface mechanical rolling treatment enables a fatigue limit of 420 MPa, which is a significant enhancement as compared with that of its homogeneous coarse-grained counterpart, i.e., 180 MPa (). Moreover, the friction coefficient of a gradient nano-grained Cu-Ag alloy is reduced by nearly 50% as compared with that of the coarse-grained sample (Considering the better performance of the heterogeneous materials as compared with their homogeneous counterparts, a natural question arises, i.e., is it still better for the former than the latter to confine a thin film to increase its ductility? Indeed, showed that a nano-grained Cu layer in a gradient structure can gain a local strain that exceeds 100% without cracking. Another example is a Ni-P metallic glass film on a gradient nano-grained Ni substrate that has a tensile uniform elongation as high as 12% by forming multiple shear bands (). The above value is exceptional because bulk metallic glass at room temperature usually fails catastrophically through shear bands at very small strain (generally less than 1%) ( found that the grain coarsening process of the surface nano-grained layer in a gradient Cu rod under tension is uniform and homogeneous rather than abnormal that is usually the case of the freestanding nanograined layer.The above experiments suggest a promising role of the gradient structures in improving the ductility of thin metal or metallic glass films. However, due to the complexity of the gradient microstructure with grain size spanning over four orders of magnitude, there are only a few experimental investigations and there is also a lack of theoretical modeling and simulation work. Therefore, a mechanism-based theoretical analysis could enable a comprehensive understanding of the deformation of the thin film on a gradient substrate. Here we extend our dislocation density-based model on a gradient IF steel () to consider the effect of the gradient substrate on the tensile behavior of a thin film. The thin film considered here is focused on metal and is modelled to be an elastic-perfectly plastic solid that is characterized by low tensile ductility. The model is also applicable to metallic glass film due to its mechanical properties (high strength-low ductility) similar to metal film as suggested by ). The interface between the film and the substrate is modeled by a cohesive law. The above model is then incorporated into a finite element (FE) scheme. The tensile ductility of the thin film is represented by its necking strain based on a necking criterion. Through the FE simulations, three necking modes have been identified. By tailoring the gradient microstructure, the tensile ductility of the films can be optimized to be much higher than that of the films on CG substrates. Moreover, the film/gradient-substrate system has much better strength-ductility synergy than the film/homogeneous-substrate system.The computational model is schematically illustrated in . The total length of the model L, the thickness of the film hf and the thickness of the substrate hs are adopted to be 160 µm, 5 µm, and 400 µm, respectively. The gradient substrate is modeled as a composite structure consisting of a CG phase and a grain size gradient surface layer (GSL) that has n homogeneous phases with different grain sizes. The thickness of the GSL and the CG phase are denoted as hg and hc, respectively. A V-shaped notch with 2 µm wide and 0.1 µm deep is set at the center of the film's upper surface to induce non-uniform deformation. The film/substrate system is stretched in x-direction under plane strain condition. Considering the symmetry of the model, only the right half is calculated to reduce the computation time.The plastic deformation of the gradient substrate can be modeled by a dislocation density-based theoretical model established by ). We employed the J2 flow theory for the CG phase and all the phases in the gradient region, i.e.,where ɛ˙p and σ′ are the plastic strain rate tensor and the deviatoric stress tensor, respectively, and η=3ε˙p/2σ is a factor that can be determined from uniaxial tensile tests, in which ε˙p=2ε˙p:ε˙p/3 and σ=3σ′:σ′/2 are respectively the equivalent von Mises plastic strain rate and stress. The equivalent von Mises stress σ in each phase can be determined as:where σ0, M, α, µ, b, and ρs are the lattice friction stress, Taylor factor, Taylor constant, shear modulus, the magnitude of the Burgers vector, and the statistically stored dislocation density, respectively. The last term on the right hand side of denotes the flow stress arising from the Hall–Petch strengthening due to the existence of grain boundaries (), which can be expressed as σGB=kHP/d, where kHP is the Hall–Petch slope and d is the grain size of each phase. This term is introduced to account for the grain size dependent yield strength of IF steel. The Hall-Petch strengthening results from the presence of grain boundaries (GBs) that serve as obstacles for dislocation motion. The dislocations tend to pile-up at the GBs, which generates stress concentration at the tip of the pile-up to activate dislocation sources within adjacent grains. Smaller grains can pile up less dislocations and have smaller stress concentration, thus requiring a larger applied stress to initiate dislocation sources (i.e., yielding) in neighboring grains.The evolution of ρs with respect to the plastic strain εp can be determined by modifying the original Kocks–Mecking model (), which incorporates a grain size dependent dynamic recovery:where k=k3/(bd), k1=ψ/b, k2=k20(ε˙p/ε˙0)−1/n0, ψ is a proportionality factor, k20 and ε˙0 are material constants, k3 is a geometric factor related to the grain shape and the portion of dislocations arriving at the grain boundaries, ke=(de/d)2 is an additional dynamic recovery factor and n0 is inversely proportional to temperature. The first term on the right-hand side of the equation is associated with the athermal storage of dislocations by incorporating the influence of grain size ddue to the presence of high density of grain boundaries that act as geometric obstacles to dislocation glide (). The second one is another dislocation storage term that is a result of dislocation-dislocation interactions. The third and fourth terms are related to the annihilation of dislocation during dynamic recovery, in which the ke term is introduced to describe the grain size dependent dynamic recovery as indicated by experiments (). The incorporation of d (k=k3/(bd) and ke=(de/d)2) is to describe the dependence of the flow stress on grain size after yielding (i.e., strain hardening) by considering that grain size significantly affects the storage and annihilation of the dislocations during plastic deformation.Although the original Kocks-Mecking model is mainly developed for face centered cubic (FCC) metals (), there are quite a few studies that have successfully employed and extended Kocks-Mecking model to investigate the plastic deformation of various body centered cubic (BCC) metals such as IF steel and dual phase steel (). We know that the deformation mechanism of BCC metals is different from that of FCC metals due to their higher number of slip systems and lower coordination number. As a consequence, BCC metals have more frequent cross-slip events but lower possibility for dislocation interaction. As a result, BCC metals have less capability to store dislocations but stronger capability to annihilate dislocations. To address this difference in the original Kocks-Mecking equation, i.e., dρdεp=M(k+k1ρ−k2ρ), we can adopt smaller k1 and larger k2 for BCC metals, in which the former term k1ρ represents the dislocation storage and the latter one (− k2ρ) denotes the dislocation annihilation (dynamic recovery). The modified model has four adjustable parameters, i.e., k3, ψ, k20 and de; and all can be determined by fitting with experimental data. The adopted parameter values for IF steels in the present study have been given in our recent paper (). Indeed, IF steels has smaller ψ (thus k1) but larger k20 (thus k2) than Cu as obtained in . For example, ψ = 0.019 and k20 = 21 were obtained for nano and ultrafine-grained IF steel (BCC structure), whereas ψ = 0.025 and k20= 13.4 were determined for corresponding Cu (FCC structure). if the applied plastic strain is zero, i.e., εp = 0, and the initial dislocation density is zero, we have ρ = 0, thus no contribution to the flow stress (here is the yield strength at εp = 0) comes from the dislocation density. Now the yield strength is σy = σ0 + σGB, in which the frictional stress σ0 is independent on grain size. Hence if we further eliminate the term σGB, we have σy = σ0, which is unable to describe the grain size effect in yield strength. Therefore, in order to describe the grain size dependence of yield strength, the grain size must be introduced in the expression of the flow stress, i.e., . The predicted yield strengths for IF steels with grain size varying from 96 nm to 35 µm by , which agree well with the experimental data (). The yield strengths without considering the σGB term are much smaller than the experimental data and are independent on the grain size. The variation results from the change of σ0.a presents the evolution of the dislocation density with respect to the plastic strain obtained by using for grain sizes ranging from 100 nm to 35 µm. The results for the case that eliminates the effect of the grain size, i.e., the first and the fourth term in the right-hand side of , have also been shown for comparison. The results show that grain size has significant influence on the dislocation density evolution. That is, for larger grain size (d = 35 µm and 5 µm), ρ increases strongly with the plastic strain, whereas for smaller grain size (d = 100 nm, 500 nm, 1 µm and 2 µm), the ρ firstly increases with the plastic strain but later it reaches almost a plateau. This finding indicates that the materials with smaller grain sizes have less stored dislocations and have less capability to strain hardening thus smaller tensile ductility than those with larger ones. The predicted uniform elongations are also in good agreement with experimental data as shown in the strength-elongation combination map (The distribution of the grain size d along the thickness direction in GSL is assumed to follow the exponential relation according to experimental measurements (where ag and bg are two constants determined by the grain sizes (d1) of the topmost phase in GSL and the CG phase (dc), and h is the vertical distance from the top surface of the substrate. The material used for the present simulation is IF steel, and the values of all the material parameters are extracted from The thin film is modeled as an ideal elastic-plastic solid for both the metal and the metallic glass, which is adopted by ), to represent its very small tensile ductility as observed in experiments (). Thus the equivalent von Mises stress–strain response of the thin film can be written as:where Efilm and σYfilm are Young's modulus and the yield strength of the film, respectively. To simulate a film with high stiffness and high strength, its Efilm and σYfilm are set to be 160 GPa and 1.1 GPa, respectively. The Poisson's ratio of the film is 0.3.The film/substrate interface is described by a cohesive zone model with a bilinear traction-separation relation (), which has been successfully used to simulate the interfaces of various composite materials (). The damage of the interface occurs as the maximum stress approaches the interfacial strength σn,s0 that corresponds to a critical interfacial displacement δn,s0. The subscripts n and s designate the normal and shear directions, respectively. The interface is fully broken if the maximum displacement reaches δn,smax. The fracture energy release rate, i.e., the work needed to create a unit area of new surface, can be evaluated by calculating the area under the curve in the traction-separation plot (the green area in ). It is denoted as Γn,s, which depends on the values of interfacial strength σn,s0 and maximum interfacial δn,smax. The effect of Γn,s can be represented by that of σn,s0 and δn,smax.The coupling of mode I and mode II loadings was considered by a quadratic nominal stress criterion to characterize the damage initiation:where ⟨σn⟩=σn if σn≥0 and ⟨σn⟩=0 if σn<0; σn and σs are the stresses on the normal and shear directions of the interface, respectively. After the damage initiation, the evolution of σn,s can be expressed as:where δn,s is the relative displacement on the normal and shear directions of the interface and D is a damage variable defined as:where δemax is the maximum value of the effective displacement attained during the loading history with effective displacement δe defined as δe=(δn)2+(δs)2; δe0 and δef are the effective displacement at the damage initiation and complete failure of the interface, respectively. Here we assume δef=δn,smax, that is, the effective displacement at the fully damage state under mixed-mode loading is equal to the maximum interfacial displacement under pure mode I or mode II loading.For simplicity, identical interfacial properties are used for both the normal and the shear directions, i.e., δn0=δs0 and σn0=σs0. A dimensionless number σn,s0/σYfilm is adopted to represent the interface strength. The value of σn,s0/σYfilm varies from 0.2 to 10, while those of δn,s0 and δn,smax are set to be 1% and 2% of the film thickness, respectively. In order to avoid interpenetration between the film and the substrate, non-friction contact behavior is enabled in the simulation.Moreover, we ignored the effect of geometrically necessary dislocation induced back stress strengthening in the present model due to the small difference in strength between the substrate surface and the film. According to , the generation of geometrically necessary dislocations is a result of the strain partitioning between the film and the substrate due to their strength difference. To get a significant back stress strengthening in a composite, strong strain partitioning must be stimulated between the phases. However, in the present study, the introduction of the gradient substrate has significantly reduced the strength contrast between the film and the substrate surface. As a result, the strength of the substrate surface is very close to that of the film, thus leading to a small difference in strength between the film and substrate. For example, the strength of the substrate surface with d1 = 26nm and 40 nm are 1.36 GPa and 1.13 GPa, respectively, which are comparable to that of the film, i.e., σYfilm=1.1GPa, which results in a very small strain partitioning and ultimately negligible back stress in the gradient-substrate/film composite.The finite element software ABAQUS was used for simulations. The geometrical model was established through a python script. The film and the substrate were meshed by four-node bilinear plane strain quadrilateral elements (CPE4), which can eliminate the risk of plastic locking because of the adopted reduced integration on the volumetric terms. The interface was meshed by four-node two-dimensional cohesive elements (COH2D4). A sufficiently dense mesh with 75 elements along the thickness direction was used in the film near the notch in order to model the necking behavior of the system (). The thickness of each phase in GSL was set to be sufficiently small, i.e., Δh = 0.83 µm, to ensure that the grain size changes continuously in the gradient region. The tensile ductility, i.e., the necking strain, of the film is defined as the critical applied strain at which the thickness of the thinnest place in the film becomes one-fifth of the original film thickness, which is similar to the criteria used in ). This definition enabled us to investigate the delocalization behavior in the film/gradient-substrate system. In contrast, we are unable to observe the effect of the gradient substrate on the strain delocalization if we use the Considère criterion that only considers uniform deformation throughout the sample. Most importantly, the parameter value in the defined necking criterion is determined by comparing the predicted value for tensile uniform elongation and the experimental data. For example, the predicted tensile ductility of the coarse-grained IF steel is 24.9%, which is comparable to the experimental measurement for uniform elongation, i.e., 26.6%. The above value is also very close to that obtained by Considère criterion, i.e., 25.9%. The yield strength was adopted to be the 0.2% offset stress. The values of some key parameters used in the simulations are listed in unless otherwise stated. The equivalent stress-plastic strain data as obtained from the dislocation density based constitutive model for all the phases for a typical gradient substrate are shown in . These data serve as direct input to ABAQUS for modeling the deformation of gradient substrate.Three typical deformation modes, i.e., types A, B, and C, have been observed in the film/gradient-substrate system by tailoring the grain size of the topmost phase in GSL (d1) and the GSL thickness (hg) (). Here the interfacial strength is adopted to be identical to the yield strength of the film, i.e., σn,s0=σYfilm=1.1GPa. b, d and f correspond to the deformation of the samples as the necking criterion is met. In the case of type A mode, a neck is formed right at the site where the V-shaped notch is placed (b). This deformation behavior is similar to that of the film with a homogeneous elastomer substrate as shown in . The deformation of the film on a CG substrate also belongs to this mode (g and h). Type A mode usually leads to very small necking strain, e.g., εN = 0.078, at hg = 300 µm, d1 = 112nm, because of the strain localization in the necking region.In order to quantify the necking behavior in the film/gradient-substrate system, we defined a localization parameter ξ by ξ=Δh/lN, in which Δh = (hU − hN) with hN and hU respectively the film thicknesses in the necked and uniformly deformed regions, while lN is the width of the necked region (a, c and e). Here Δh represents the height difference between the necked and un-necked region. The width of the necked region (lN) is incorporated because narrower necking area denotes stronger localization of defomration. Therefore, the parameter represents the degree of deformation localization in the sample. From the definition we can see that larger Δh and smaller lN, thus bigger ξ, generate stronger necking or strain localization. If we consider the extreme case, i.e., Δh = 0, we have ξ = 0, which means that the strain localization is entirely suppressed in the thin film. presents the evolution of ξ during tension for the three deformation modes as given in . The results show that, for type A, ξ increases sharply with the applied strain and reaches a value as high as 1.08 under a strain of 0.078 at which the necking criterion is satisfied. In contrast, the parameter for types B and C increases slowly with the strain and then decreases sharply to a very small value that is close to zero due to the strong strain delocalization effect induced by the gradient substrate (see the two arrows in ). For example, the ξ value for type B reaches a maximum of 0.32 at a strain of 0.09. However, ξ is then reduced significantly to a value below 0.05 until the interface is broken. The above value is more than one magnitude of order lower than that in type A. The findings show that the gradient substrate in type B and C significantly suppresses the deformation localization and thus leads to much higher tensile ductility in the gradient-substrate/film composite. For example, the resultant ductility is 0.22 for the case of hg = 50 µm, d1 = 26 nm (type B in c), which is much higher than that obtained in type A behavior, e.g., 0.078 at hg = 300 µm, d1 = 112 nm (a). The type C mode (e.g., the case of hg = 100 µm, d1 = 14nm) has similar ξ as type B. The only difference is that the necking in the former occurs in the notch zone (f), whereas the necking in the latter appears in the right side of the notch ( presents a map for the three deformation modes. The map shows the type B and C deformation modes occur as d1≤28nm (see the horizontal arrow), i.e., the yield strength of the top surface layer of the substrate is close to or higher than that of the thin film. The boundary between the types B and C is hg = 80 µm (see the vertical arrow). In contrast, the type A mode occurs at d1>28nm. These findings indicate the advantage of the gradient substrate over the homogeneous substrate for the following reasons. First, the gradient substrate can enable a strength in the surface that can be comparable or even higher than the ultra-strong thin film, which cannot be achieved in the homogeneous CG substrate. Second, even though some nano-grained substrates with homogeneous microstructures can gain a very high strength, their ductility will be drastically reduced due to the refined grains, which will lose its role in retarding or suppressing the necking of the thin film. presents the variation of the neck strain εN with respect to the topmost surface layer grain size d1. Four hg values are considered, i.e., hg = 50 µm, 100 µm, 200 µm and 380 µm. The necking strain of the film with a CG substrate is also shown for comparison (see the red dashed line). The results show that as d1 increases, the εN value first increases up to a maximum and then decreases. For all the hg cases, the maximum occurs at around d1 = 28 nm, which is the boundary between the type A and the other two deformation modes. It is important to note that the maximum εN of the film on the gradient substrate is larger than that of the film on the CG substrate as hg < 200 µm. For example, at hg = 100 µm, εN of the film with the gradient substrate is higher than that of the film with the CG substrate within the range of d1∈[16nm,32nm]. The corresponding maximum εN of the film on the gradient substrate can achieve as high as 0.23, which is 21% higher than that of the film on the CG substrate. Moreover, the cases in which the film on the gradient substrate has improved tensile ductility as compared with the film on the CG substrate are marked by a black dashed line in . Interestingly, all these cases appear at the transition area between the three necking modes. presents the GSL thickness dependence of the necking strain of the film/gradient system for five d1 values, i.e. d1 = 20 nm, 28nm, 40 nm, 64nm, and 144nm. The results show that when d1 is larger than 40nm, i.e., the strength of the gradient surface layer is relatively small, εN decreases monotonically with hg. This trend originates from the ductility reduction of the gradient substrate with an increasing hg for large d1 (). The above cases correspond to the type A necking mode. However, if the value of d1 is small, e.g., d1 = 20nm and 28nm, εN shows a trend of first increase and then decrease, which is caused by the transition of the deformation modes, i.e., from type B to type C, as hg increases (). The advantage of the gradient substrate in enhancing the ductility of the thin films over the CG substrate can also be seen in . For instance, when d1 is 28 nm and hg is less than 200 µm, the necking strain of the film with the gradient substrate is higher than that with the CG one, achieving as high as 0.256 at hg = 80 µm. shows the necking strain of the film εN as a function of the ratio of the yield strength of the film σYfilm to the that of the substrate surface σY1 for three σYfilm values, i.e., σYfilm=850MPa, 900MPa and 1100MPa. Here the gradient layer thickness (hg) of the substrate is set to be 100 µm, while d1 varies from 16 nm to 204 nm, which results in a strength ratio of σYfilm/σY1∈[0.65,1.35]. For all the three cases of σYfilm, εN first increases to a maximum at around σYfilm/σY1=0.85, and then decreases with respect to the strength ratio. The maximum εN value is resulted from the transition of the necking mode of the films, i.e., from type C to type A. The results are consistent with the deformation map with hg = 100 µm (Extensive studies have shown that interfacial strength plays a very important role in debonding and crack growth behaviors in the interface between the film and the substrate (). Therefore, in this section, the effect of the interfacial strength on the tensile ductility of the film is investigated. In experiments of , where metallic glass films are electrolessly deposited on metal substrates, there is no delamination between the film and the substrate even after the fracture of the film, which indicates that the interfacial strength of the film/metal substrate is very high and might be even higher than the strength of the film itself. Although there is no measured interfacial strength for the present film/gradient substrate system, we can predict how high the tensile ductility of the thin film can reach if we assume a very high interfacial strength. Hence, we adopted in the calculations a normalized interfacial strength that spans over two orders of magnitude, i.e., σn,s0/σYfilm∈[0.2,10]. The resultant εN values are shown in a, in which four cases of hg and d1 are considered, i.e., hg = 40 µm, d1 = 24nm; hg = 50 µm, d1 = 24nm; hg = 100 µm, d1 = 24nm and hg = 100 µm, d1 = 144nm. The results for the CG substrate are also shown for comparison. The results show that for the samples with large d1 or large hg, e.g., hg = 100 µm and d1 = 144nm, εN first rises as the interfacial strength increases and then remains almost unchanged after σn,s0/σYfilm≈1. The CG case has a similar variation trend. For the samples with small d1 and hg, e.g., hg = 50 µm and d1 = 24nm, there appears an abrupt εN increase, i.e., from 0.22 to 0.32, as σn,s0/σYfilm≥2.5. This tensile ductility is 1.6 times of that of the film on a CG substrate. This exceptional enhancement of the tensile ductility results from the full suppression of the debonding between the film and the substrate at the above interfacial strength, in which case the film can deform along with the substrate and finally gains a higher rupture strain ( shows the variation of the necking strain with respect to the ratio δn,smax/δn,s0 for three gradient substrates. The results show that the necking strain varies slightly or even remains unchanged as δn,smax/δn,s0increases from 2 to 11, which means that the reatio δn,smax/δn,s0 has negligible effect on the necking strain.In addition to the tensile ductility, the yield strength of the film/gradient-substrate system is also calculated to obtain a strength-ductility map for the film/gradient-substrate system (). Five values of the gradient layer thickness are considered, i.e., hg = 30 µm, 100 µm, 200 µm, 300 µm and 380 µm. For each hg, the topmost phase grain size (d1) varies from 16 nm to 144 nm. And the interfacial strength is set to be σn,s0/σYfilm=1. The results for the film on a series of homogeneous substrates with different grain sizes (from 100 nm to 34 µm) are also included for comparison. The results show that for each hg, there exists a peak that corresponds to the optimal strength-ductility synergy in the gradient system, which is in contrast to the strength-ductility tradeoff as observed in the cases of the homogeneous substrates. Note that all the peaks are located outside the shaded region, which means that by tailoring the gradient microstructure, the strength-ductility synergy of the gradient system can be always better than that of the homogeneous cases. And the higher the hg value is, the larger the distance of the location of the peak from the shaded area is. For example, the tensile ductility of the film/gradient-substrate at hg = 380 µm can reach as high as 0.165 with a strength of 600 MPa, whereas that of the homogeneous case is only 0.072 for the same strength. This shows that the gradient substrates can enable exceptional strength-ductility balance in the films, which cannot be achieved by a homogeneous substrate.a presents the simulated engineering stress–strain curve for a typical thin film/gradient IF steel substrate system with hf = 40 µm, hg = 180 µm and d1 = 40nm. The corresponding curves for the freestanding film and the gradient substrate itself are also included for comparison. The symbol ‘X’ denotes the point where the thickness of the film reduces to 60% of the original one. The results show that the freestanding film has a very small tensile ductility, i.e., 0.04, which is a typical value for thin metal or metallic glass film (). The softening after yielding results from the necking of the thin film, in which the necked region is strain-localized, whereas the uniform area is unloaded. Therefore, the stress and strain in the un-necked region are much smaller than those in the necked area. This results in a decreased force that can be sustained by the thin film, thus leading to a softening in the film. However, the introduction of the gradient substrate renders the film a tensile ductility as high as 0.16, which is increased by 0.12 as compared with the case without the gradient substrate. This extraordinary enhancement results from the significant delocalization of the deformation in the film as posed by the gradient substrate. The delocalization then promotes uniform deformation in the thin film. Most importantly, the magnitude of the improvement agrees well with the recent experimental measurements for a Ni-P amorphous film on a gradient Ni substrate as shown in b, in which the tensile uniform elongation of the Ni-P film has been increased by 0.11 due to the gradient substrate (In this paper, a numerical study was conducted to analyze the role of the gradient nanostructured substrate in modulating the tensile ductility of the thin film. A dislocation density-based constitutive law is incorporated into a finite element scheme to model the gradient substrate. The results show that the ductility of the thin film can be considerably enhanced by the gradient nanostructured substrate, which is consistent with the experimental findings. Three deformation modes have been identified in the film/gradient-substrate system by tailoring the microstructures of the gradient substrate, i.e., the thickness of the GSL hg and the grain size of the topmost phase in the GSL d1. The strain localization of the film can be effectively retarded by the gradient substrate with optimal hg and d1, resulting in significantly enhanced tensile ductility as compared with the homogeneous case. Moreover, the film/gradient-substrate system can gain outstanding strength-ductility balance by evading the strength-ductility tradeoff as commonly observed in the homogeneous system.The wave propagation model investigated herein is based on the known fact that material discontinuities affect the propagation of elastic waves in solids. The change in certain material characteristics, such as a local change in stiffness or inertia caused by a crack or the presence of material damage, will affect the propagation of transmitted elastic waves and will modify the received signal. Wave frequencies associated with the highest detection sensitivity depend, among other things, on the type of structure, the type of material, and the type of damage. This paper presents a method of wave propagation, which can be further used to detect small delaminations in beam-like structures. The considered beam is modelled by spectral finite elements.In recent years, investigations have been based on analysing anomalies in elastic wave propagation through the monitored part. Damage detection systems are based on the known fact that material discontinuities affect the propagation of elastic waves in solids. Wave frequencies that are most sensitive to damage depend on the type of structure, the type of material, and the type of damage. Elastic waves are generated and sensed by an array of transducers either embedded in, or bonded to, the surface of the structure.The main objective of the theoretical portion of this problem is to develop a model that will determine the relationship between the power of a transducer, the frequency of a generated signal, the type of monitored solid and the range of effective signal transmission. The frequencies used in this technique are much higher than those typically used in modal analysis based methods but lower than in ultrasonic testing. At such high frequencies, the response is dominated by the local mode and the wavelength of the excitation is small enough to detect incipient-type damage.Interest in various non-destructive damage detection methods has considerably increased over the past 20 years. During this time many methods founded on modal analysis techniques have been developed (Adams and Cawley This paper presents a method of wave propagation, which can be further used to detect small delaminations in beam-like structures. The beam considered is modelled by spectral finite elements.The approach is similar in style to that of the finite element method but has the very significant difference that the element stiffness matrix is established in the frequency domain. As a consequence, these spectrally formulated elements describe exactly the wave propagation dynamics and in contrast to the conventional element this means that elements can span all the way from one point to another without losing fidelity. is a schematic of a conceptual damage model of a Timoshenko beam. The beam considered is divided into four parts with lengths L1, L2=L3, and L4. The length of the beam is L, width b, and height h. The delamination is situated between parts 2 and 3. Its length is L2=L3.In this analysis the displacement field for axial and transverse motion is based on first order shear deformation theory (FSDT) so axial displacement u0(x,y,t) and transverse displacement w0(x,y,t) can be written in the following form:where, φj(x,t) denotes independent rotation along the xj axis, and wj(x,t) is the transverse displacement along the xj axis.Using Hamilton’s principle for the Timoshenko beam the following equations of motion can be obtained (Doyle, where, Fj denotes cross-section, E Young’s modulus, G Kirchhoff modulus, ρ density. In Eq. the adjustable parameters K1 and K2 have been introduced, Doyle Since there are two independent variables wj and φj the following solutions are assumed:where, k denotes a wave number, ω a frequency.The characteristic equation is quadratic in k2 and has the same form as that for a Timoshenko beam (Doyle There are four roots (two sets of mode pairs).Transverse spectral displacements for the first part of the beam have the following form:where, i.e., kn1 denotes the wave number calculated as follows,and where, ρ is the density of the beam material, F1 is the area of the first element cross-section, E denotes Young’s modulus, I1 denotes the geometrical moment of inertia of the beam cross-section, and ωn is a natural frequency. Rn,j denotes the amplitude ratios given by Doyle The unknown coefficients Ai (i=1 to 16) can be calculated as a function of the nodal spectral displacements, taking into account the boundary conditions at the tips of the delamination. At the left end of the beam (x1=0) the nodal spectral displacements are defined as follows:At the right end of the beam (x4=L4) the nodal spectral displacements have the form,, in order to satisfy the compatibility of displacements and the equilibrium of forces at the junctions between the integral and delamination regions, we define the conditions as follows:where, Pi denotes axial forces in parts 2 and 3 of the beam under consideration (). The forces Pi are not known a priori as they depend upon the extent of stretching of the delaminated layers 2 and 3 (see Majumdaar and Suryanarayan denote midplane axial displacements in parts 1 to 3, The total axial extension/contraction of the midplane of parts 2 and 3 can be described as,where, i=2, 3. Taking into account Eqs. where, Pd=|P2|=|P3|, (see Majumdaar and Suryanarayan The continuity of transverse displacements, normal slopes, shear forces, and bending moments at the second tip location give similar expressions as above. By using Eqs. we obtain a set of 17 simultaneous linear homogeneous algebraic equations with 17 unknown constants: Ai, (i=1 to 16), and Pd. The equations can be written in matrix form,where, i.e., a1,1=1, a1,2=1, a7,2=−EI1kn3exp(−knL1), a8,5=E(I2+I3)kn2,The coefficients Ai, (i=1 to 16), and Pd can be related to the nodal spectral displacements by the relations,The element has two nodes and two degrees of freedom per node (transverse displacement and independent rotation). The nodal spectral forces can be determined by differentiating the spectral displacements with respect to x. The nodal spectral forces for the left hand side of the beam (x1=0) are formulated as follows:and the nodal spectral forces for the right hand side of the beam (x4=L4) are formulated as follows,Taking into account that the column matrix, which appears after the square matrix in has only four non-zero elements, relation where, four columns of the rectangular matrix are selected from the square matrix depicted in . Certainly the selection depends on the placement of the non-zero elements the frequency dependent dynamic stiffness matrix for the beam spectral finite element with delamination can be calculated, and relation is then obtained and finally it is reconstructed in the time domain by use of the inverse fast Fourier transform (FFT).Numerical calculations were carried out for a cantilever beam of length equal to L=2 m. The area of the beam cross-section was A1=A4=0.0008 m2 (b=0.02 m, h=0.04 m). The beam was made of aluminium with Young’s modulus E=72.7 GPa Poisson ratio ν=0.33, and density ρ=2700 kg/m3.The beam was excited by a transverse triangular force impulse (with value peak to peak 1 N) modulated by a harmonic function (). The frequencies used in this technique are much higher than those typically used in modal analysis based methods but are lower than the frequencies used for ultrasonic testing. In our case the excited frequencies lies in the range between 200 and 1200 kHz, with dominant one about 700 kHz. At such high frequencies, the response is dominated by the local mode and the wavelength of the excitation is small enough to detect incipient or potentially significant damage.The accelerations were calculated at the point excitation (the free end of the cantilever beam). The results of the numerical calculations are presented in shows two signals, namely the excitation and the reflected signal. illustrates an additional signal (see the arrow), which appears for a delamination located at a distance of L1=0.99 m. The length of the delamination is L2=0.02 m, meaning that the defect size is 1% of the total length of the beam. show delaminations located at distances L1=0.95 and 0.90 m, respectively. The defect sizes in these instances are 5%, and 10%, respectively. depict additional signals (see the arrows) which appear for delaminations located at distances of L1=0.85 and 0.80 m, respectively. The lengths of these delaminations in these cases are L2=0.30 and 0.40 m, respectively. This means that the failures are 15% and 20% of the total length of the beam. The first arrow shows the first tip of the delamination, the second arrow indicates to the end of the delamination. present results for delaminations located at the midplane of the beam. illustrates an additional signal (see the arrow), which appears for a delamination located at a distance of L1=0.95 m. The length of the delamination is L2=0.10 m, meaning that the failure is 5% of the total length of the beam. The delamination is located out of the midplane and is defined by the ratio h1/h=0.1 (see present a delamination located at the distance L1=0.90 m. The failures are 10% of the total length of the beam. The delamination is located out of the midplane and is defined by the ratio h1/h=0.1. The first arrow shows the first tip of the delamination, the second arrow is pointing to the end of the delamination. illustrate additional signals which appear for delaminations located at distances of L1=1.40 and 1.35 m, respectively. The lengths of the delaminations are L2=0.10 and 0.20 m meaning that the failures are 5% and 10% of the total length of the beam. The delaminations are located out of the midplane and are defined by the ratio h1/h=0.1. illustrate additional signals which appear for delaminations located at distances of L1=0.50 and 0.45 m, respectively. The lengths of the delaminations are L2=0.10 and 0.20 m meaning that the failures are 5% and 10% of the total length of the beam. The delaminations are located out of the midplane and are defined by the ratio h1/h=0.1.From these figures it is apparent that the analysis of the differences between the signals can directly be used to establish the location and length of the delamination within the structure. These differences can easily be used for damage detection methodologies within structures.A new model of a beam spectral finite element with a delamination has been investigated. Using this model an analysis of the influence of delamination upon elastic wave propagation in a Timoshenko cantilever beam was performed. Taking into account the results of the numerical calculations the following conclusions can be made:the delamination produces additional peaks in the signal which describe the reflection of waves from the tips,the wave reflected from the fixed end has a smaller amplitude for a delaminated beam compared to one without this sort of damage,the difference between signals received from a non-damaged and a damaged beam allow one to establish the location and size of a failure case,the differences mentioned above depend on the excitation impulse,if a higher frequency excitation impulse is used smaller delaminations can be detected.The proposed model can be easily used to detect delaminations in more complicated situations, e.g., multiple delaminations located in different places. Future investigations will attempt to extend this approach to structures with more complex geometry, i.e., to cases of planar and spatial frames.It is important to underline that when we know the velocity of wave propagation it is very easy to locate the single delamination placed along midplane of the beam, and even prognoses about location their edges in case of longer one (see for example). It means that it is possible to define magnitude of the longer, single delamination located along midplane of the beam. Much more complicated situation we have when the delamination is located out of midplane of the beam in this case we can only define that the damage is present in the structure, but it is impossible to define precisely the location and magnitude of it. The similar situation is probably observed in the case of multiple delaminations––it is possible only prognose about the presence of the damage in the structure.Future work should be devoted to the interpretation of the results in order to develop efficient tool for damage detection. We are going to use a genetic algorithm or/and neural networks for determining the location and magnitude of a delamination in beam structures. Obviously these methods are generally very useful when inverse problems are investigated, but sometimes do not guarantee proper solution. For this reason maybe additional damage indicators (not only reflections of the propagating waves) should be analysed. These techniques can be used for the analysis of a structure in order to determine the failures accurately. Such a method could provide a basis for an overall health monitoring system, and to this end the authors of this paper have already published several articles on this topic Influence of bacterial incorporation on mechanical properties of engineered cementitious composites (ECC)Incorporation of bacterial technology in concrete has attracted the attention of many researchers in the past decades. While much of the attention was focused on crack self-healing in concrete, it was also observed that such incorporation sometimes alters the mechanical properties of concrete significantly. There are very few studies related to the material performance of fiber reinforced concrete containing bacteria. In this paper, the bacteria were incorporated into engineered cementitious composites (ECC), and its mechanical properties were investigated systematically. At composite performance level, it was found that both compressive and tensile strength increased in bacteria-ECC, meanwhile the ECC with bacteria of higher activity presented more pronounced effect. Furthermore, crack pattern of ECC was also improved due to the addition of bacteria as smaller crack width was observed. In contrast, tensile strain capacity of bacteria-ECC reduced as compared with normal ECC, but still retained at high level. At microscale level, fracture toughness of matrix containing bacteria was higher than that of control mix. Additionally, matrix/fiber interface properties were altered in bacteria-ECC with lower chemical bond and higher frictional bond strength. The findings at microscale well explain the change in composite performance of ECCs based on micromechanics theory.Concrete is the most consumed construction material worldwide and contributes greatly to the modern civil infrastructures in the past century. Nevertheless, due to its inherent brittleness and low tensile strength, cracking in concrete is inevitable during the service lifetime of concrete infrastructures. Normally, steel rebars are provided to reinforce the concrete in structures, therefore, the crack usually will not cause the collapse of structure directly. Nevertheless, it will accelerate the degradation of concrete by providing preferable aisle for aggressive chemicals to enter inside and corrode the steel rebar, which will endanger safety of concrete structures. Hence, maintenance and repair works are needed to seal cracks in concrete to prolong the service life of civil infrastructures. However, current repair techniques are often expensive and ineffective which need cycles of repair. To address this issue of unsustainable cycles of repair, concrete enabled with self-healing capacity stands out as a promising approach for sustainable infrastructure development which potentially requires much less repair and maintenance work.To realize the self-healing capacity in concrete, as an alternative strategy to continuous hydration based self-healing Considering the harsh environment inside concrete, a protective carrier is preferable to encapsulate or immobilize bacteria to improve its viability in concrete. It has been proved that crack with millimeter size can be healed this way. Wang et al. used the diatomaceous earth to immobilize bacteria, and found that cracks with width of 0.17 mm could be healed completely In contrast to its benefits on self-healing, incorporation of bacterial carrier into concrete is likely to decrease the compressive and flexural strength of concrete in most instances, which is unacceptable in the practical application Unlike normal concrete where crack width could be very wide and difficult to control reliably even with steel reinforcements, engineered cementitious composites (ECC) is a kind of high performance fiber reinforced cementitious composites (HPFRCC), with unique characteristics of high tensile ductility and self-controlled tight crack width ECC was initially developed by Li, Leung and coworkers at 1990s based on micro-mechanics theory with feature of high strain capacity at range of 3–5% More interestingly, with such tiny crack width, micro-crack in ECC has the capacity to heal itself autogenously through continuous hydration of unreacted cementitious materials and precipitation of CaCO3 within crack space As discussed before, this study is focused on the effect of bacterial incorporation on the mechanical properties of ECC. The effect of bacteria on self-healing behaviour of ECC is not included in this paper, and it will be reported in the future. In the following sections, a brief introduction on ECC material design theory is presented first. This would be helpful for readers to understand the discussion in the later sections. The composite performance of ECCs including compressive strength, tensile behavior, and crack pattern are then reported. Finally, alteration of bacteria on the matrix toughness and fiber/matrix interface are also discussed at the microscale level.The cornerstone of high ductile ECC lays in two criteria which are necessary to be satisfied for attaining strain-hardening behaviour Energybasedcriterion:Jtip≤σ0δ0-∫0δ0σ(δ)dδ≡Jb′where σ0 is the maximum bridging stress corresponding to the crack opening δ0; σcs is the strength of initiating crack in matrix under tension; Jtip is the energy needed for the propagation of crack in matrix; J′b is the complementary energy. expresses the crack tip toughness Jtip needs to be less than the complementary energy J′b calculated from the fiber bridging stress versus crack opening (σ-δ) curve. This is the concept of energy balance during crack extension, that is, it should have adequate energy left for a crack to propagate (forming new surfaces of the same crack) in steady state fashion after subtracting the energy consumed by opening initial crack from zero to δ0 from the energy input provided by external loads. The satisfaction in energy-based criterion ensures the occurrence of steady state cracking which is necessary for multiple cracking behaviour of ECC. Eq. states that the cracking strength of matrix (σcs) must not exceed the maximum fiber bridging stress (σ0). This criterion ensures subsequent cracks can be triggered before reaching peak fiber bridging stress, hence resulting in a multiple cracking pattern. Failure to satisfy either of the above two criterions will lead to tension-softening behaviour commonly observed in normal FRC, which is characterized by one localized fracture crack.In ECC design theory, larger margins between J′b and Jtip as well as σ0 and σcs are preferred. An abundant energy left for crack propagation indicates better chance for cracks to experience steady state propagation instead of Griffith type crack. Normally, the pseudo strain hardening (PSH) index (=J′b/Jtip) was used to quantitatively characterize the margin between J′b and Jtip. It is suggested that an increase in J′b or lower Jtip is desirable to obtain higher PSH index, thus gaining highly ductile ECC. As is known, the Jtip is associated with matrix toughness Km, while J′b has a very close relation with the matrix/fiber interface properties. For similar discussion on σ0 and σcs readers are referred to Wang et al There are two bacterial strains: Bacillus halodurans DSM 497 (wild type from DSMZ, Germany) and the mutant one based on Bacillus halodurans DSM 497, which is obtained by transposon mutagenesis method as described in Ding et al.’s previous work 100 ml overnight cultures (the wild type and the mutant) were mixed with 100 ml 0.5 M CaCl2 for incubation and CaCO3 precipitation;Precipitated CaCO3 was filtered by filter paper;Obtained CaCO3 were dried in 60 °C oven for 3 h;Luria-Bertani (LB) was used in this study as typical medium for bacterial growth. For 1 L of LB broth medium, 25 g Luria-Bertani powder was added into 1000 g of distilled water (Approximate Formula for LB medium Per Liter: 10.0 g of Tryptone; 5.0 g of Yeast Extract; 10.0 g of Sodium Chloride). Then pH value of the medium was adjusted to 9.7 by addition of saturated Na2CO3 solution.After LB medium was prepared, the bacteria were grown in it aerobically at 37 °C (1:100 inoculation).Compared with the wild type, the mutant strain showed a relatively high growth rate, which is reflected by very steep slope of optical density at 600 nm versus time curve (see a). Under the same condition of overnight growth (37 °C, 200 rpm), the mutant culture seemed quite turbid (suggesting higher bacterial concentration), as opposed to transparent look of the wild type group, which appeared quite similar to nutrition only (see b). The stationary phase bacterial cultures (Optical Density at 600 nm (OD600) of 0.01–0.2 equivalent to around 107–108 cells/ml) were used in preparation of ECC mixtures. The OD600 was tested under UV-1280 UV–VIS Spectrophotometer (Shimadzu). In biological study, one specific OD600 value represented one specific bacterial concentration (confirmed by colony forming unit [CFU] counting using drop-plate method), of which higher OD600 suggests higher bacterial concentration The ingredients in ECC include cement with strength grade of CEM 42.5, fly ash, fly ash cenosphere (FAC), mixing liquid (water and bacterial cultures), superplasticizer (SP), and Kuraray PVA fiber. To achieve high ductility in ECC, FAC is used to replace silica sand usually adopted in ECCs by equal volume. This is because the FAC in ECC has been proved to be beneficial to ductility by lowering matrix toughness and improving fiber/matrix interface properties . All mixture proportions are the same except for the type of liquid. For the bacteria-ECCs, bacterial culture is mixed with the solid ingredients by replacing water. In W-ECC and M-ECC, considering some nutrient substances in the liquid, the weight of liquid is slightly higher than water in control-ECC to keep water content constant for the three mixtures.All three mixtures in this study were mixed using a shear-type Hobart mixer. All dry solid ingredients were mixed for 3 min at low speed. Then mixing liquid together with superplasticizer was added into the dry mixtures and mixed for another 3 min. Afterwards, the PVA fiber were added into the mortar and mixed for 5 min. After mixing, the fresh ECC material was cast into the moulds, and covered with plastic sheet before demolding. Due to influence of nutrient substances on hydration kinetics of cement, hardening time of paste was prolonged This paper focuses on the mechanical performance of ECC with incorporation of bacteria. The compressive strength and tensile properties, including tensile strength, tensile strain capacity and crack pattern, of ECCs are investigated at composite level. At microscale, effects of bacteria on the matrix toughness and matrix/fiber interface are also studied via three-point bending test and single fiber pull-out test, respectively.Uniaxial compressive test was employed in accordance with ASTM to measure compressive strength of ECCs with specimen dimension of 50.8 × 50.8 × 50.8 mm Tensile performance of all ECC mixtures was characterized via uniaxial tensile test. The test set-up was illustrated in . Dog-bone shaped specimen was adopted and mechanically interlocked with fixtures instead of coupon specimen being gripped by hydraulic wedge clamps. This could avoid premature fracture in specimen because of stress concentration caused by clamping force. The dimensions of specimen in the gauge length zone are 120 mm (length) × 35 mm (width) × 15 mm (thickness). The quasi-static loading rate is 0.5 mm/min. Two external Linear Variable Differential Transformers (LVDTs) were attached to the tested specimen, thereby allowing deformation of the specimen to be recorded for the calculation of tensile strain. The tensile test was ended when one of the micro-cracks localized, which is accompanied by tension-softening curve. After the test, the crack information including number of cracks and crack width in ECC specimen within gauge length was recorded under unloaded condition.ECC matrix toughness was measured on a notched beam specimen by three-point bending test according to ASTM Sample preparation for single fiber pull-out test is schematically illustrated in . Long fibers were placed across rectangular prism mold and then fresh ECC matrix paste (without fibers) was cast into the mold. The prism sample with multiple long fibers was then cut into small pieces with thickness around 1 mm using a precision saw before testing at 28 curing days. Adoption of very thin sample in the test is to ensure successful capture of debonding process during pull-out process before fiber breakage. The detailed test set-up and procedures could be found in Ref. presents compressive strength of ECC mixtures at 7 and 28 curing days. It could be seen that bacteria-ECCs, including W-ECC and M-ECC exhibited increased compressive strength at both curing ages, although their hardening process was delayed at early age by bacterial culture, as reflected by longer duration needed for demolding. Compressive strength of control-ECC, W-ECC, and M-ECC reached 34.4 MPa, 41.1 MPa and 43.3 MPa respectively at 28 curing days. Incorporation of wild type and mutant bacteria led to 19% and 26% increment in compressive strength, respectively. Additionally, M-ECC with higher activity of bacteria shows the highest compressive strength among the three ECC mixtures. displays scanning electron microscope (SEM) observed morphology on the fracture cross-section of W-ECC and M-ECC after tensile test. It shows that massive calcite-like pieces distributed inside W-ECC and M-ECC while none of them could be found in Control-ECC. This is most likely the resulting products of biochemical reactions by bacteria. The chemical constitutions of the small pieces detected by Energy dispersive spectroscopy system (EDS) are listed in . It could be concluded that the small pieces in (a) and (b) is largely calcite by observing the atom ratio of Ca:C:O. It has been reported that the formation of CaCO3 have positive impact on the compressive strength of concrete shows tensile stress-strain curves of ECC mixtures. The first cracking strength associated with matrix property, tensile strength and tensile strain capacity of ECC mixtures are derived from these curves. They are defined as the tensile stress at the end of initial elastic stage, ultimate tensile stress and the corresponding tensile strain, respectively. All these properties are summarized as bar graph in It could be seen from the tensile test results that all ECC mixtures demonstrate pronounced tensile strain-hardening behavior, as reflected by their high tensile strain capacity. This denotes that the unique characteristic of ECC, high ductility, is retained for ECC after incorporation of bacteria. shows that, similar to the trend on compressive strength, addition of bacterial culture also enhances the first cracking strength and tensile strength of both ECCs with bacteria, between which the effect on ECC with mutant bacteria is more pronounced. Tensile strength of W-ECC and M-ECC is 4.97 MPa and 5.45 MPa, which is increased by 9.9% and 20.6%, respectively, when compared with 4.52 MPa of Control-ECC. On the other hand, due to the addition of bacterial culture, tensile strain capacity shows a slight decrease as compared with Control-ECC, especially for M-ECC. Nevertheless, its strain capacity is still more than 3.8% which could satisfy the requirement of almost all practical applications.The crack width in ECC is also considered a very important material property as it governs many transport properties of concrete under cracking status, therefore impacts on durability directly. shows crack width distribution in ECCs. With representative ECC specimen of each mixture, the crack width is recorded after unloading using light microscope with the accuracy of 10 μm. As shown in , the maximum crack width in bacteria-ECC decreases while the number of narrow cracks increases, when compared with Control-ECC. This observation is plausible to suggest that a lower water permeability and aggressive ion penetration coefficient may be derived from cracked ECC with bacteria, thereby resulting in better durability.Average crack width and total number of cracks in ECC are listed in . It can be seen that more cracks are initiated in bacteria-ECCs, whereas the average crack width is reduced. As mentioned previously, crack width is a key factor for the occurrence of self-healing phenomena in concrete. Due to the addition of bacterial culture into ECC, more cracks within 50 μm appear in W-ECC and M-ECC as illustrated in . This indicates that more cracks could be healed autogenously by taking advantage of continuous reaction of cementitious materials. The rest cracks that are wider than 50 μm are expected to be sealed/healed via bacterially induced calcium carbonate precipitation.To sum up the above discussions, incorporation of bacterial culture in ECC leads to improvement in most mechanical properties and crack pattern which are favorable for the strength and durability of structural members. Although the tensile strain capacity reduces in bacteria ECCs in comparison with that of Control-ECC, it is still retained at high level. Overall, it can be concluded that incorporation of bacteria in ECC contributes positively to the overall mechanical performance provided adequate tensile strain capacity can be maintained.Based on ECC design theory, bacteria induced composite properties alteration can be further explained from the micro-mechanics described in . Matrix fracture toughness of ECC mixtures is shown in . As expected, the matrix fracture toughness (Km) increases with the addition of bacterial culture, among which the mixture with mutant bacteria presents the highest value presumably due to its higher activity. This trend explains the enhancement of the first cracking strength in W-ECC and M-ECC. The crack tip toughness Jtip (=Km2/Em) calculated based on Km and stiffness (Em) of matrix also shows very similar trend with that of matrix fracture toughness. The stiffness of matrix is from the slope of initial linear elastic stage in tensile stress-strain curves as shown in . Albeit rather gentle, the increase of Jtip is undesirable for achieving higher PSH (=J′b/Jtip) index and ductility of ECC.Besides the crack tip toughness (Jtip), the interface parameters which have decisive impact on complementary energy (J′b) are also critical to the PSH index. The matrix/fiber interface parameters including chemical bond (Gd), frictional bond strength (τ0), and slip-hardening coefficient (β) are displayed in . Very interestingly, the chemical bond (Gd) and slip-hardening coefficient (β) drop with the addition of bacterial culture under the same mixture proportion. The average Gd values for W-ECC and M-ECC are 0.44 J/m2 and 0.16 J/m2, respectively, and are considered rather low for PVA fiber The reduction of chemical bond is probably caused by some of the bacterial metabolic products that are attached to the surface of PVA fiber. To validate this hypothesis, the surface of PVA fiber in ECC was observed by fluorescence microscopy. To facilitate for this observation, PVA fibers were obtained from the fractured cross-section of ECC specimen after tensile test, and then stained by 4′6-diamidino-2-phenylindole (DAPI) for 15 min under dark condition. After that, the stained fibers were transferred into Zeiss Axio Observer Z1-Inverted epifluorescence laser system (Carl Zeiss AG, Germany) for observation using 40 x lenses with wavelength of 405 nm. As shown in (b), the biofilm formation and bacterial aggregation (green colour) were attached to the surface of fiber from M-ECC specimen, which was not the case for fiber from control ECC specimen ((a)). It seemed plausible that in addition to the oil-coating, biofilm formation on the PVA fiber further reduced the Al3+ and Ca2+ concentration at the matrix/fiber interface. As these two ions are critical for the development of strong interfacial thin layer between PVA bulk polymers and surrounding hydration products, their reduced concentration will lower the chemical bond (Gd) The frictional bond strength (τ0) shows a reverse trend with Gd and β. It indicates that the bio-coating on the fiber surface doesn’t play the lubrication role as that induced by oil-coating and concentrated carbon particle from bottom ash . As the frictional bond is closely related to the stiffness and packing density of the interfacial transition zone (ITZ), the higher τ0 may be contributed by higher stiffness/compactness of ITZ caused by bacterial induced calcite., theoretical fiber bridging stress-crack opening displacement relationship is derived based on the interface parameters using micro- mechanics theory (zoom in), and should shift the curve towards lower right, therefore increase the J′b value , incorporation of bacterial culture increased crack tip toughness Jtip. Considering the trends of J′b and Jtip due to incorporation of bacteria, the PSH index (J′b/Jtip) will surely decrease which is not conducive to high ductility of ECC. compares the trend of PSH index and tensile strain capacity of ECCs. It shows that the strain capacity of ECC mixtures decreases along with PSH index when the mixture varies from Control-ECC to W-ECC and M-ECC. This observation again suggests that the PSH index can be a robust indicator for tensile strain capacity. On the other hand, the up left shift of the σ-δ curves denotes the growth of maximum fiber bridging stress, which explains the increase of tensile strength in bacteria-ECC specimens.Overall, friction bond strength increasing prevails over chemical bond decreasing on their effect to J′b, resulting in the decrease of PSH index. However, it should be pointed out that the reduction of Gd value due to simple bacterial treatment has very significant impact as it provide an alternative approach for fiber surface treatment and tailoring for potential high performance ductile cementitious composites. After all, the Gd value was reduced through relatively costly oil coating process during the manufacturing in the development history of PVA-ECC.In this paper, the impact of directly adding vegetative Bacillus halodurans and its mutant cells into ECC material was investigated. The mechanical performance of ECC including compressive strength and tensile properties were highly influenced after incorporation of bacteria. At macroscale level, the compressive strength and tensile strength of bacteria-ECC increased as compared with Control-ECC due to bacterial metabolism in ECC. On the other hand, the tensile strain capacity shows a reverse trend in bacteria-ECCs, but is still maintained at high level. At microscale level, similar to the strength enhancement, the matrix fracture toughness was also increased in bacteria-ECCs. For the matrix/fiber interface properties associated with fiber bridging performance, lower chemical bond (Gd) and slip-hardening coefficient (β) were observed in bacteria-ECCs, yet the increased frictional bond strength (τ0) prevailed over decreased chemical bond which in turn leads to the reduction of complementary energy (J′b). It is interestingly noted that a kind of biofilm and bacterial aggregation was attached to the fiber surface, thereby changing the interface properties.The authors declare no conflict of interest.Fracture energy and tensile strength depending on stress triaxiality along a running crack front in three-dimensional cohesive modelingIt is known that the critical fracture energy value decreases with specimen thickness, whereas the local tensile strength of the material increases with the stress triaxiality. In the present work, the critical fracture energy and the tensile strength depending on stress triaxiality are experimentally investigated and identified with the help of finite element computations. It is found that the fracture energy distributes in a running crack front very differently from that in a straight through-crack. The maximum crack driving force appears near the free surface in the plane stress state, whereas the maximum tensile stress is in the specimen middle. The local fracture energy is monotonically decreasing in the form of an exponential function, while the local tensile strength linearly increases with the stress triaxiality.Local critical J value at crack propagationDimensionless J value normalized by that of the mid-planeReference tensile strength for the plane strain stateThe upper bound of the cohesive strengthMaximum decrement of the cohesive strength from the plane strain stateLocal fracture energy depending on stress triaxialityFracture toughness for plane strain stateReference stress triaxiality of plane strain statestress-triaxiality-dependent cohesive zone modelingThe tensile strength is the capacity of a material or structure to withstand loads tending to elongate. The classical tensile strength is defined as the ultimate tensile stress measured from uniaxial tensile tests and denotes actually the lower limit of the material strength. From material testing it is known that the material strength increases with stress triaxiality defined as the ratio of the hydrostatic stress and the Mises stress, η=σh/σe, as described in the Gurson-Tvergaard-Needleman (GTN) model The influence of the stress state to cracks was extensively discussed as constraint effects in the fracture mechanics community in the 1990’s. The constraint can be divided into in-plane constraint, which is directly influenced by non-singular stresses within the loading plane, such as bending and tension loading configurations, and the out-of-plane constraint, which is related to the stresses along the crack front, such as the specimen thickness For three-dimensional crack characterization, the out-of-plane constraint is of significance when the plastic zone size is obvious but smaller than the specimen thickness Numerous parameters were proposed for three-dimensional crack fields to quantify the out-of-plane constraint effects, which are mainly related to the thickness of the 3D crack body. Guo et al. Fracture parameters describe the loading intensity and cannot directly lead to crack propagation. The fracture criterion depending on the constraint has to be determined with the help of fracture tests, which is a difficult task. An alternative way to describe crack propagation was started several decades ago, based on fracture mechanics methodology but with damage mechanics consideration, i.e. the cohesive zone modeling (CZM) The in-plane constraint in cohesive zone modeling was focused on tension versus bending loading configurations, as reported in It was found based on continuum damage mechanics analysis that both cohesive strength and cohesive energy are influenced by the stress triaxiality where Tup denotes the upper bound of the cohesive strength, whereas Ttrans represents variations of the cohesive strength depending on η. a0 and a1 are dimensionless model parameters. Correspondingly, the cohesive energy from the GTN model can be approximated aswith Γlow=γlowσ0D as the lower limit of the cohesive energy and γtrans for the transition behavior with η. b0<0 and b1>0 are dimensionless model parameters. indicate the dependence of the cohesive traction as well as the cohesive energy on the stress triaxiality. The correlation was conducted based on GTN modeling in plane strain computations and derived from the high stress triaxiality state, which means much more details for the lower stress triaxiality state, especially experimental tests with a thinner thickness should be performed to further identify the relationship between the stress triaxiality and the cohesive zone modeling parameters. In fact, it is a difficult task to identify the material-specific interdependence among Γ0,Tmax and η.Based on systematic experiments and computations, Li and Yuan In the present paper, the critical fracture energy and tensile strength depending on the local stress triaxiality are experimentally tested and identified with the help of finite element computations. Numerical computations are performed based on the real crack profiles with corresponding critical loads to find the correlation between critical fracture energy and critical fracture strength along running crack fronts with varying local stress triaxiality. The results from computations with experimental verification should provide new knowledge about material resistance against crack propagation in 3D specimens.The material tested in the present work is 7150-T651 aluminium alloy with higher yield stress and lower fracture toughness, in comparison with other aluminium alloys. The stress-strain curve is illustrated in (a) with Young’s modulus E=77 GPa, Poisson’ ratio ν=0.3, yield stress σ0=398 MPa, ultimate tensile stress σu=677 MPa, strength coefficient K=822 MPa and strain hardening exponent n=12. The material property was measured from uniaxial tensile specimens.The compact tension (CT) specimens fabricated in accordance with ASTM 399 (b). The width of CT specimens, W, is equal to 50 mm. The thickness-to-width ratio is B/W=0.5 as well as B/W=0.24, respectively. The initial crack front is straight with a/W about 0.4 for all specimens.To study the characterization of the crack front, four CT specimens with B/W=0.5, named as CT25, and two CT specimens with B/W=0.24, termed as CT12, were investigated experimentally. Crack propagation tests were performed to generate real crack fronts in different thick specimens and to study crack propagation processes. The experiments should generate different running crack fronts as a function of the applied loads for computational analysis of crack front fields. The experiments revealed similar fracture process, which implies that the fracture process in the specimens is representative. In the following section one of the CT25 specimens with three marked crack front curves and one of the CT12 specimens with two tagged crack front curves are investigated systematically in the following experimental discussions and finite element computations. Scattering of specimens is small and secondary for the present work.(b) illustrates the fracture surface of a CT specimen of B/W=0.5, termed as CT25. The testing procedures included pre-cracking, monotonic crack propagation and finally marking crack fronts under fatigue loading. After pre-cracking, the crack propagation tests were conducted in displacement-control with the rate of 0.002 mm/s. The corresponding load-displacement curves are illustrated in (a). It can be observed in the figure that the load fluctuates as the applied load reaches a high level, which actually implied crack propagation. Due to discontinuous crack propagation process in the CT specimen the load-displacement curve becomes instable in a small range under displacement control. Crack growth decreases the specimen stiffness and reduces the reaction force of the specimen, so that the load drops. With increasing further displacement, the load grows gradually to the next critical load, till the new crack propagation occurs. To mark the running crack front, the specimen was unloaded to a low level and vibrated with high frequency, as shown in 2(a).In the fracture surface, three crack fronts with different crack growth amounts can be clearly found in 2(b). The average crack propagations for the present computational investigation are 8.34 mm, 11.77 mm and 14.69 mm, with corresponding critical loads 15.98 kN, 15.1 kN and 12.61 kN, respectively. The crack fronts are termed as C1, C2 and C3 in sequence. All crack fronts contain deep tunneling effects, which increase with crack growth. There is a shear lip zone about 0.5 mm thick near free surfaces.(b), two stable crack fronts of the CT specimen with B/W=0.24, CT12, are studied in the present work, with the average crack extensions of 5.73 mm and 7.18 mm, respectively. The corresponding critical loads are 11.33kN and 12.18kN. The crack fronts are termed as C1 and C2 for the first and second crack length. It is known that the crack speed in the CT specimen middle is much higher than that in the specimen surface, due to the surface effect. The crack tunneled in the specimen. The curvature of the specimen increases with crack propagation. If the specimen can be assumed to be displacement controlled overall, the fracture energy in the specimen middle (near plane strain state) must be much lower than that in the specimen surface, near the plane stress state. Near the CT12 specimen free surface, there is a shear lip zone about 1 mm thick, which implies that the fracture energy for the plane stress is even higher than the shear fracture under mode III. In the specimen CT12, the fracture process is coupled with different mechanisms.To study the local stress field around the curved crack front, the finite element mesh consistent with the crack fronts is generated. The finite element mesh in the in-plane is illustrated in (a), with very fine elements around the crack front, with the in-plane element size of circa 10-3 mm. (b) demonstrates the corresponding computational meshes of the CT12 specimen varying with the crack fronts. Besides the shear lips, the whole crack front was modelled accurately in the computations. The elements near the surface are refined dramatically to catch the stress and strain variations. But the crack surface was assumed to be planar so that the shear failure is not studied.It is known that tunneling effect leads to the convex crack front in cracked specimens, which can be explained by the variations of stress state in 3D specimens. In the present CT25 specimens of aluminum alloy, however, the slight concave crack fronts were observed, as shown in (a). The was induced by the inhomogeneous material property in the aluminum plate. Investigation of the material micro-structure reveals that the grain size in the middle of the thick plate is slightly larger than that near the surfaces, that is, the material in the middle region could possess a higher fracture toughness. This phenomenon was found in all other CT25 specimens and the critical loads were in the same level. The effects become even more obvious with increasing plate thickness. For the thinner specimen the crack front is usual ((b)). To have symmetric crack propagation, the whole plate thickness was taken to fabricate the specimens and the small discrepancy of the concave crack front was removed, as illustrated in (a). In computations, the crack profiles of CT25 near the center plane were modified to straight crack fronts. depicts crack extension along the thickness direction, where the dash lines denote the modified crack fronts of the CT25 specimen, while the solid lines represent the crack profiles from the fracture surface.The J2 incremental plasticity is used for computations, based on the true tress-strain curve measured for the aluminum. Without considering unloading and reloading, the crack field is less affected by the plasticity model. The J-integral stands for the crack driving force and characterizes the crack state. To find the J-integral distribution along the specimen thickness, three-dimensional elastoplastic finite element analysis (FEA) is performed for the crack propagation tests. For each considered CT configuration, a separate finite element mesh is generated and a quarter of the specimen is modeled due to the symmetry. All the computation cases share the same planar meshes depicted in (a). The nodes along the crack fronts in both CT25 (with three crack fronts) and CT12 (with two crack fronts) specimens are illustrated in . The size of the inner element ring toward crack tip decreases exponentially with the radial distance from the tip. The thickness of the element layer decreases exponentially towards the specimen free surface to catch drastic variations of the stress distribution. Twenty nodes hexahedral element are used for computing the three-dimensional crack front fields.In conventional fracture toughness tests, the J-integral as the crack driving force is calculated based on the average crack length of the actual crack profile, which means the running crack front is assumed to be a straight line. To study distributions of the crack driving force, the three equivalent straight through-cracks of the CT25 specimen are analyzed under the actual critical tensile loads. Additionally, the CT specimen under increasing load amplitudes is calculated to study the correlation between the J-integral distribution and the applied load.The J-integral distributions along the thickness direction of the three straight through-cracks in the CT25 specimen are shown in (a). The value of the J-integral is the crack driving force plotted against the normalized specimen thickness, 2z/B, which increases from 0 to 1 representing the location from the center plane to the free surface. It can be observed that the J-integral decreases along the crack front, which is known and can be found in many 3D crack field computations in published works. It is recognized that, with increasing loads, the stress state in a 3D specimen transforms from plane strain toward plane stress along the specimen thickness direction, as discussed in Computations of the straight through-crack specimen with the CT25-C3 equivalent crack length are documented in (b) under increasing loads, in which J is normalized by its maximum. The dimensionless J-integral, defined as the ratio of the J-integral along the thickness direction and the mid-plane, Je=J/Jmid, as the unity crack driving force is plotted against the normalized specimen thickness, 2z/B. The figure confirms that the unity driving force decreases with increasing applied load, especially near the free surface, indicating that the decreasing stress intensity depending on the applied load. Actually, as the load increases, the out-of-plane constraint is more obvious, as the plastic zone grows, which results in increasing plane stress features. For a given applied load, the stress intensity factor for a plane stress crack is much smaller than that for plane strain. By giving displacements, the plane stress crack possesses significantly smaller stress intensity factor than the plane strain crack. The decreasing crack driving force in the 3D specimen is caused by growing plane stress features with a straight through crack. In other words, the J-integral alone cannot describe the stress and strain state at the crack tip in a 3D specimen uniquely. It is necessary to find other physical solid fracture parameters to characterize the out-of-plane constraint, which should be independent of specimen dimensions.The difference of the driving force in the thickness direction results in tunneling crack fronts in the monotonic crack propagation tests. Moreover, the values of the J-integral in the middle plane of the equivalent three straight through-cracks are not at the same level and the J value in the middle plane increases with the growth of the equivalent crack length, which implies that the straight through-crack computations cannot reflect the true stress state in three-dimensional crack propagation along the thickness direction. The distribution of the J-integral was taken to explain the tunneling effect in the CT specimens, which has to be reconsidered for real crack fronts.In a straight crack specimen, the J distribution representing the crack driving force is artificial and not characteristic for crack propagation. In a real 3D cracked specimens with a stable running crack, the J value along the crack front reaches a critical state, especially if the crack front becomes self-similar. In this case, the J is characteristic for the material and should stand for the fracture energy for crack propagation. In the present computations forty contours within each element layer along the crack front were used to evaluate the J integral. In this sense, the present J value should just describe the crack propagation in the element layer, not the normal to the crack front tangent. In fact, discussions of the crack growth on the 3D specimen free surface cannot consider the normal direction.(a) plots the local critical J-integral distributions, JC, along the three different crack fronts of CT25 under corresponding critical loads measured from the tests. The J values from the figure denote the resistance of the material against cracking. Interesting is that the J distributions from the real running cracks are totally different from the known J distribution in a three-dimensional straight crack ((a)). As predicted from the GTN model, the fracture energy in the specimen middle, i.e. under plane strain condition, must be much smaller than that of plane stress state, which matches the results in (a). In the region 2z/B⩽0.8, the stress field is essentially plane strain and the fracture energy is hardly affected by crack growth. Towards the free surface, the stress field contains more and more plane stress features and JC grows. Variations of JC become different in the shear lip zone near the free surface. Computational results for CT12 are similar to CT25, as shown in (b), only the grey zone is larger. Both specimens provide consistent computational results.The crack front zone near the free surface was modeled as mode I failure and did not considered the combined mode I and III damage mechanism. In the present work fracture energy for mode I and tensile strength are discussed, the complex failure mechanism in combined mode I and III is beyond the scope of the present work. That is, the grey zone near the free surface contains large variations in the J values, which implies different fracture mechanisms, not for the J-integral concept. How to build a meaningful FEM model for the shear ip zone is an open issue.To study the influence of crack models in the grey zone numerically, three additional crack front forms were considered. They represent angle cracks with 30° (MC1), 0° (MC2) and −30° (MC3) to the surface normal vector. The legend ”Origin” denotes the projected crack from the lip zone on the crack surface. The local FE mesh was modified correspondingly, as depicted in (a). The J-integral distributions in the shear lip zone are illustrated in (b). As expected, the local modifications of the crack front near the free surface did not affect the J distribution outside the grey zone.Discussions above reveal that the critical J-integral, that is, the fracture energy JC along the crack front is an increasing function of the thickness coordinate and the maximum is located near the free surface, which is totally different from the crack driving force distribution for known straight through-cracked specimens. Both results are not contradictory and represent two different physical parameters in the cracked specimen. describes the distribution of the crack driving force under applied load in the specimen thickness, while JC along the crack front in represents the material resistance against cracking as a function the local stress state, i.e. under different constraint conditions.The tensile strength of the material, Tmax, is not unique and depends on the stress state, as known from damage mechanics The local tensile stress distribution ahead of a running critical crack front of the CT specimens is plotted in (a). In the figure, the stress in different element layers is normalized by the material yield stress, whereas the horizontal axis is non-dimensionalized by the local J-integral value, J/σ0. r denotes the distance to the current crack tip. If the stress distribution satisfies the HRR field (a) confirm the unique stress singularity of the HRR field for r→0 in all element layers and, however, the stress values decrease as the element layer approaches the free surface (2z/B→1). The latter is the 3D effect from the plane strain in the specimen middle to the plane stress in the free surface.To quantify effects of the tensile stress distribution along the crack front, the tensile strength for the crack is defined to equal σ22 at r/(J/σ0)=1 and plotted in (b) as a function of the thickness location. Note that r/(J/σ0)=1 represents the specific distance to the crack tip for the blunting region or the plastic zone The local tensile stress σ22 at r/(J/σ0)=1 , i.e. the tensile strength Tmax, decreases from the mid-plane to the free surface, which in fact reflects the material strength at a running crack front affected by the local stress state. For a given CT specimen, the plane strain state can be found in the specimen middle region and possesses significantly higher material strength than the plane stress state, which is consistent with the results in The stress triaxiality defined as the ratio of the hydrostatic stress and the Mises stress, η=σh/σe, has been confirmed to be a meaningful parameter to characterize the out-of-plane constraint The plane strain crack field in the CT specimen reveals that the stress triaxiality distribution depends on the distance to the crack tip, while the plane stress field shows a stable low η value. The stress triaxiality under plane strain seems to be constant only in the finite strain zone r/(J/σ0)<0.1. In the J dominate zone the η distributions are independent of the applied load intensity, as shown in (b), where the η value at r/(J/σ0)=1 is plotted as a function of the applied load J/σ0. The load-independent η value in (b) implies the characteristic feature of the stress triaxiality to the crack tip field and is an effective parameter to characterize the out-of-plane constraint. It is generally recognized that the plane strain state describes the highest possible out-of-plane constraint state, whereas the plane stress state represents the lower limit. The progressive change from the plane strain state to the plane stress state is just the variation of the out-of-plane constraint.In a three-dimensional crack front field, the stress triaxiality is more complicated, as demonstrated in (a) shows distributions of the stress triaxiality ahead of the crack front in the CT specimen with B/W=0.24. In the figure, the stress triaxiality decreases with distance to the crack front in the whole thickness. All curves share a similar feature, but the specimen middle region possesses significantly higher stress triaxiality than the free surface, as expected. η near the free surface reaches the plane stress level shown in (a), although the distribution is decreasing slightly. In fact, the stress triaxiality drastically changes near the free surface due to free surface effects, as illustrated in (b), in which the stress triaxiality η at r/(J/σ0)=1 is plotted against the dimensionless thickness for both specimens CT25 and CT12 with the different real fronts.The stress triaxiality decreases along the thickness direction in all cases and reflects the variation of the stress state from plane strain to plane stress. The plane strain state produces significantly higher stress triaxiality than the plane stress state. From plane strain state to plane stress state, the stress triaxiality gradually decreases with the thickness in all cases, reflecting the variation of the out-of-plane constraint. The small differences of the stress triaxiality near the center plane between CT25 and CT12 specimen may be attributed to the effect of the modified straight crack front in the CT25 specimen. The distributions of η along the crack fronts in both specimens display that the stress triaxiality around a running crack front is stable, but affected by the specimen geometry.Summarizing the computational results of the stress triaxiality above, the stress triaxiality in a real running crack front is characteristic for three-dimensional crack fields. The plane strain state represents the highest out-of-plane constraint and produces the highest stress triaxiality, whereas the plane stress state characterizes the lower limit. The stress triaxiality is a decreasing function of the specimen thickness, which reflects variations of the stress state along the thickness direction. Furthermore, the absolute value of the stress triaxiality under the plane strain state at r/(J/σ0)=1 is invariable regardless of the crack extension length and the specimen thickness. In other words, for a given CT configuration, the stress triaxiality is a suitable parameter to characterize the stress state in the thickness direction, which covers the changes of the applied load, crack length and specimen thickness.Discussions of experimental and computational results on running crack fronts of the tested CT specimens confirm that the critical fracture energy is a decreasing function of stress triaxiality, with the maximum at the free surface, whereas the material tensile strength increases with η. Both critical fracture energy and stress triaxiality around a running crack front are affected by elastoplastic crack propagation and form a stable correlation during crack propagation. Effects of elastic unloading is not included by calculating the fracture energy for each individual cracks. Interactions between elastic unloading and crack growth are neglected in the present study. The results are obtained from finite element computations aided by experimental observations and did not introduce any additional postulate. Since the stress state around a running crack front is not constant, the stable distributions of JC and η build the intrinsic correlation between the fracture energy and the stress triaxiality.(a) illustrates the fracture energy Γ against the stress triaxiality η for both CT25 and CT12 specimens. It can be observed that Γ decreases as η increases, which means the local fracture energy is a monotonic decreasing function of the stress triaxiality, aswhere η and Γ represent the stress triaxiality at r/(J/σ0)=1 ahead of the crack front and the local fracture energy, respectively. Correspondingly, Γlow is the fracture toughness and ηIC characterizes the reference stress triaxiality for the plane strain state. The coefficient A is a dimensionless model constant, which actually characterizes the capacity of the out-of-plane constraint. These fracture parameters need to be identified with the help of finite element computations based on fracture mechanics tests. In the present work, Γlow=12 kJ/m2 and ηIC=2.35 correspond to the plane strain state. The value of A is about 1.5. It should be pointed out that the unique function is independent of the crack extension length and specimen thickness for a determined specimen configuration, as shown in (a). Note that the shear lips near the free surface are not taken into account, where crack propagation behavior is mainly under mode III and no longer applicable to characterize by the J-integral.The local tensile stress at the running crack front represents the tensile strength of the material, Tmax, depending on the stress triaxiality. The relationship between the local tensile strength and stress triaxiality can be identified from (b). It can be found that the local tensile stress at running crack tip increases with η, which indicates that the material strength is an increasing function of stress triaxiality, aswith T0 as the plane strain tensile strength of the material, and Ttrans characterizes the decremental diviation due to the stress triaxiality to Tmax. It is noteworthy that the linear function is coincident with the results of Comparing the present results with Eqs. are determined. Since the GTN model is only suitable for the near plane strain state, the high η results should be more reasonable. The results from both models are summarized in The correlations for the fracture energy from both models possess the same form, but the identified values for the model parameters are very different. Significant differences can be found in the near plane stress state. The present work shows significantly higher fracture energy for the plane stress than the prediction from In the present paper, the critical fracture energy and material strength depending on stress triaxiality were experimentally tested and identified with the help of finite element computations. Systematic full-field elastoplastic computations of three-dimensional CT specimens were performed with the different crack profiles and corresponding critical loads identified from the experiments. From the discussions above the conclusions can be drawn as follows.A method to identify the quantitative correlation between fracture energy and tensile strength to the stress triaxiality is suggested and verified based on extensive fracture tests and computations. The results are consistent with the known consensuses in the fracture mechanics community. If the plastic zone becomes too large, effects of elastic unloading has to be considered additionally.The local fracture energy in the three-dimensional CT specimens increases in the thickness coordinate and reaches the maximum value in the free surface, which is totally different from the known decreasing crack driving force for a straight through-crack specimen. The critical fracture energy in the middle specimen is much smaller than the surface fracture energy and tends to maintain constant in a large portion of the specimen.The local tensile strength of the material decreases with the thickness coordinate and appears to keep a steady value in crack propagation in CT specimens. From the CT specimens the material tensile strength increases with the stress triaxiality linearly and takes the plane strain strength as the upper limit.As an effective parameter to characterize the out-of-plane constraint, the stress triaxiality η at r/(J/σ0)=1 decreases along the crack front in the thickness direction, which represents the variation of the stress state from plane strain to plane stress. For a given CT configuration, the stress triaxiality seems to be invariant in the crack propagation process.The local fracture energy is a monotonic decreasing function of the stress triaxiality, while the local tensile strength increases linearly with η, as given in Eqs. , which are independent of crack extension and specimen thickness.There are no conflicts of interests with respect to the present paper.Supplementary data associated with this article can be found, in the online version, at The following are the Supplementary data to this article:Influences of the dynamic strain aging on the J–R fracture characteristics of the ferritic steels for reactor coolant piping systemThe leak-before-break (LBB) design of the piping system for nuclear power plants has been based on the premise that the leakage due to the through-wall crack can be detected by using leak detection systems before a catastrophic break. The piping materials are required to have excellent J–R fracture characteristics. However, where ferritic steels for reactor coolant piping systems operate at the temperatures where dynamic strain aging (DSA) could occur, the fracture resistance could be reduced with the influence of DSA under dynamic loading. Therefore, in order to apply the LBB design concept to the piping system under seismic loading, both static and dynamic J–R characteristics must be evaluated.Materials used in this study are SA516 Gr.70 for the elbow pipe and SA508 Cl.1a for the main pipe and their welding joints. The crack extension during the dynamic and the static J–R tests was measured by the direct current potential drop (DCPD) and the compliance method, respectively. This paper describes the influences of the dynamic strain aging on the J–R fracture characteristics with the loading rate of the pipe materials and their welding joints.The design of the primary and the secondary piping for Korean Standard Nuclear Power Plants is applied on the LBB concept. The piping materials applied to the LBB concept should have excellent fracture toughness in order to prevent the unstable fracture due to the large through-wall crack. Therefore, to verify the integrity of the piping materials, it is required to perform tensile tests and the fracture toughness tests (J–R test). The tensile test should be carried out for use in the determination of the detectable leakage crack length and the elastic-plastic FEM analysis for the piping with the through-wall crack. The J–R test should be carried out for use in the crack stability evaluation of the piping under the normal operation loads and the safe shutdown earthquake loads.In the case of the fracture toughness tests, the static and the dynamic J–R tests were performed for the reactor coolant piping system made of carbon steel. The dynamic J–R test is required to verify the integrity against the instability fracture due to a sudden drop of fracture toughness under the seismic loading. In this paper, as a research for applying the LBB concept to the reactor coolant piping system of Ulchin 5 and 6, the influences of dynamic strain aging on the J–R fracture characteristics with the loading rate of the pipe materials and their welding joints were studied.The static J–R tests were performed by the unloading compliance method in accordance with ASTM E813-89 and ASTM E1152-87. Dynamic J–R tests were performed by the DCPD method in accordance with ASTM E1737-96 A5 due to the rapid loading speed. The fracture toughness test conditions of the coolant piping system are summarized in . Three J–R tests at the design temperature of 316 °C were performed for each selected heat of the base metal and the weld metal. In the case of the dynamic J–R test, additional J–R tests at the hot standby temperature of 177 °C and room temperature were performed in order to investigate their temperature dependency.The machine used for this test is a servo-hydraulic universal test machine with a chamber for high temperature testing and a loading capacity of 25 t. The test apparatus was calibrated in accordance with ASTM E4 and confirmed within ±1% of the working range. In the tensile test, strain was measured by using the high temperature extensometer, and in the J–R test, load line displacement was measured by using the high temperature crack opening displacement gage (Capecitec Model P-COD Gage).The design of the Ulchin 5 and 6 plant employs a two-loop reactor coolant piping system. Each loop contains one steam generator and two reactor coolant pumps as shown in . Each hot leg is a 42 in. inner diameter pipe of SA508 Cl.1a material with 3.5 in. nominal thickness. The cold leg is 30 in. inner diameter pipes of SA508 Cl.1a material with 3 in. nominal thickness wall. The elbow material is SA516 Gr.70. The straight pipe and the elbow are welded by submerged arc welding (SAW) and shielded metal arc welding (SMAW). The test block for elbow base metal was taken from the plate before hot rolling. In order to simulate the thermal effect of hot rolling, a simulation heat treatment on the test block was carried out based on the variation of temperature at hot rolling. After the heat treatment, compact tension (CT) specimens were taken and tested. Weld deposits for the weld metal test specimens were prepared by using the same welding procedure and the same heat of weld material used in the production weld. indicates the fracture toughness test specimen matrix. show the detailed welding conditions and the chemical compositions of each material, respectively.Tensile tests were performed on the round specimens with orientation in L direction, and fracture toughness tests were performed on the 1 in. CT specimen with orientation in L-C direction. For dynamic J–R test specimens, current input wires were mechanically fastened to both sides of the specimen with screws at the points A and B in , and voltage measurement wires with a diameter of 0.7 mm are welded by spot welding at the points C and D in Tensile tests were performed in accordance with ASTM E21. Yield strength was determined by the 0.2% offset method. From the load–displacement curve obtained through the test, the true stress–true strain curve was obtained, and then material constants α, n were obtained by fitting the true stress–true strain data with the normalized Ramberg–Osgood relation as follow (where ε0 is the strain at yield point, σ0 is the true yield strength, α is the Ramberg–Osgood material constant and n is the strain hardening exponent. The Ramberg–Osgood material constants α, n are required in LBB analysis software such as PICEP (Static J–R tests were performed by the unloading compliance method in accordance with ASTM E813-89 and ASTM E1152-87. At first, the CT specimens were precracked by cyclical loading until crack length was about 0.6W. Then, the CT specimen was side grooved to ensure a straight crack front, where the depth of side groove is 10% of on each side of specimen thickness. Prior to the start of the test, the specimen was held at test temperature for 1 h in order to obtain uniform heat distribution over the specimen, and was tested by the unloading compliance method. After the test, the specimen was broken at subzero temperature to compare the measured crack extension length with the calculated crack extension length.The specimen crack length of the dynamic J–R test was measured by the DCPD. Test speed was determined by the natural frequency method proposed at Battelle (where Di is the load line displacement at crack initiation of the static J–R test. The first mode natural frequency of the piping system was 10 Hz, and the test speed of 1000 mm/min was applied to the all materials.The schematic drawing of the dynamic J–R test apparatus is shown in . The specimen was isolated from the load frame by inserting Bakelite plates which are strong and provide isolation between the test jig and the machine frame, and 100 A constant current was supplied to the specimen by using the power supply in order to measure crack growth length during the test. For high-speed data acquisition, HP3852A DAS system was used. The modules are a HP44704A high speed voltmeter and a HP44711A high speed FET multiplexer. By using the acquisition system, the variation of load, COD value and output voltage were acquired digitally during the test.The test procedure is as follows; first, the specimen was precracked by cyclical loading and side-grooved. After attaching the current input wires at the W/2 position and the voltage measurement wires on the front face of the specimen as shown in , the specimen was installed in the testing machine. Dynamic J–R tests were performed on the specimen at 1000 mm/min under stroke control with the 100 A current on. For the high temperature test, to compensate for the thermal effect, the DCPD output voltage was obtained by subtracting the voltage measurements taken with the current off from the measurements made with the current on. In analysis, the variation of crack length was calculated from Johnson’s equation for all data after crack initiation point (where U is the electric potential signal, U0 is the electric potential signal at crack initiation, a is the crack length, a0 is the initial crack length, W is the specimen width, and 2y is the initial spacing of the potential probes.In the early experiment for the J–R test of high ductile materials for the primary piping, the apparent crack backup shown in ) and the data scatter occurred. These resulted from a contact between the pin and the edge of the grip hole. When the CT specimen is loaded, the pin is rotated by angle of θ shown in due to specimen deformation. By rotation of the pin on the loading surface of the grip hole, the pin moves to the left-hand side in in order to have a sufficient gap between both sides of the specimen and the clevis grip. The J–R curves for high energy piping materials could be obtained accurately through the improvement of the grip configuration. shows static J–R curves for reactor coolant piping. The excellent static J–R properties were obtained in the SA516 Gr.70 steel for the elbow and SMAW weld deposit. J–R curves of SAW metal were worse than those of SMAW metal due to the higher welding heat input as indicated in . In comparison between hot leg pipe and cold leg pipe, the J–R curves of cold leg pipe are slightly better than those of hot leg pipe. These might result from the forging effect.No materials satisfied the size condition as valid JIC value due to the high JQ values. Meanwhile, when J–TR curve is obtained from J–R curve, the condition for satisfying J-controlled crack growth is as In this test result, crack extension length, 0.3b0 satisfies the condition of ω>1 for all materials, therefore, J–TR curve is valid until crack extension length is 0.3b0. shows tensile properties tested at 316 °C and described at Certified Material Test Report (CMTR) at room temperature.First, in order to confirm the test speed of 1000 mm/min, actual speed was measured from time versus COD displacement relationship and its accuracy was within 5% of input speed. represents COD value versus output voltage curve for five materials. Pulse drop signals for all test materials appeared at initial loading region as shown in . It is known that this phenomenon occurs due to the ferromagnetic effect (). Namely, when the structure of the ferromagnetic substance is rapidly changed, a magnetic field arises in the material and an electric potential difference is induced. Accordingly, it was difficult to measure the crack length because of a rapid loading voltage pulse superimposed on the dc electric potential signal. In particular, it was difficult to find the crack initiation point due to the pulse drop phenomenon. In this paper, in order to coincide the calculated crack length using the Johnson equation () with the measured final crack length, the crack initial points were tracked back from the final crack lengths that were physically measured on the fracture surfaces of the broken specimens (). For the DCPD signals corresponding to the blunting behavior before the crack initiation point, the DCPD signals caused by the crack tip configuration were nearly screened by the ferromagnetic signal. Therefore, the blunting behaviors were assumed according to the standard blunting relationship. represents the variation of J–R curves according to the temperature with respect to each material. It shows that the J–R curve decreases with the increasing test temperature. shows the dynamic J–R curves for reactor coolant piping. In order to compare the dynamic J–R curve with the static J–R curve, the fracture toughness at 0.1 in. crack extension, J0.1 in. values were obtained from the J–R curves, and the variation of J0.1 in. value with loading rate at operating temperature, 316 °C is shown in . The J0.1 in. value at 1000 mm/min is lower than that at 1 mm/min for the elbow material (SA516 Gr.70 steel), but the J0.1 in. value at 1000 mm/min is higher than that at 1 mm/min for SAW metal. The J0.1 in. values of the other materials were similar regardless of the loading rate.According to Kim’s report, fracture toughness at crack initiation, JI has the minimum value in dynamic strain aging (DSA) temperature region for given loading rate, and the temperature corresponding to the minimum JI value gets higher with increasing loading rate (). This tendency can be explained as the dynamic strain aging effect. In general, when the strain rate increases, the dislocation movement becomes faster and when the temperature increases, the diffusion rate increases. Therefore, when the strain rate increases, the DSA temperature region is higher because DSA occurs by interaction between the solute atoms and the dislocations. By the DSA effect, the dislocation density increases and fracture toughness decrease, so when the strain rate increases, the temperature corresponding to the minimum JI value increases. shows the dependence of fracture toughness on temperature and loading rate in the DSA region. The temperature corresponding to minimum J0.1 in. value gets higher with the strain rate. This might be closely related to the dynamic strain aging effect. Namely, the elbow material and the SAW metal correspond to the type A and the type B material in , respectively, although the temperature corresponding to the minimum JI value at loading rate of 1000 mm/min can not be known. From the fracture toughness with the loading rate, it seems that the elbow material (SA516 Gr.70 steel) and the SAW metal (US-40N7PFH-55SN) are susceptible to the dynamic strain aging at 316 °C.In order to apply the leak-before-break design concept to piping systems, the static and the dynamic J–R tests were performed by the compliance method and the direct current potential method, respectively. The following conclusions were drawn from the results:For the elbow base metal (SA516 Gr.70 steel) and the SMAW metal, excellent static J–R properties are shown. On the other hand, J–R curves for the SAW metal are the lowest among five materials.The J0.1 in. value at 316 °C of the SA516 Gr.70 steel at loading rate of 1000 mm/min is lower than that at 1 mm/min, however, the J0.1 in. values of the SAW metal are contrary to each other. It is likely that the elbow material (SA516 Gr.70 steel) and the SAW metal (US-40N7PFH-55SN) are influenced by the dynamic strain aging at 316 °C.Microstructure and properties of novel CoCrFeNiTax eutectic high-entropy alloysEutectic high-entropy alloys are potential replacements of structural alloys, due to their microstructure and properties. In this work, CoCrFeNiTax (x = 0.1, 0.2, 0.3, 0.395, 0.4 and 0.5, x value in molar ratio) eutectic high-entropy alloys were produced by arc melting technique. Two phases, FCC solid solution and Laves phase, are identified in the alloys. The alloys are transformed from hypoeutectic to hypereutectic solidification by increasing Ta content. CoCrFeNiTa0.395 eutectic high-entropy alloy exhibits an ultrahigh yield strength of 1.4 GPa, while CoCrFeNiTa0.3 hypoeutectic high-entropy alloy shows a compressive strength of 2.5 GPa and a considerable fracture strain of 44%. Such remarkable strengthening effects are shown to result from the ideal combination among the second-phase, solid solution, and boundary strengthening.Being widespread concerned, high-entropy alloys (HEAs) which are designed as multi-element metallic system, break the shackles of traditional design theory of alloys. As they were reported for the first time in 2004 The CoCrFeNiTax (x = 0.1, 0.2, 0.3, 0.395, 0.4 and 0.5 in molar ratio) HEAs were produced by arc melting by high-purity elements (Co ≥ 99.95, Cr ≥ 99.99, Fe ≥ 99.99, Ni ≥ 99.99 and Ta ≥99.99 wt%) in a Ti-gettered high-purity argon atmosphere. The ingot was flipped and remelted for five times to eliminate the inhomogeneity. Crystal structure was studied by a D8 Discover X-ray diffraction (XRD) with Cu Kα radiation, operated at a voltage of 40 kV and a current of 30 mA. Microstructure was examined by a Quanta 3D FEG field emission scanning electron microscope (FE-SEM) with an X-ray energy dispersive spectrometer (EDS) operating at 25 kV and backscattered electron (BSE) mode. It was also examined by a JEM-2100F field emission transmission electron microscopy (FE-TEM). The thin foil sample for TEM observation was cut from the EHEA, mechanically polished to a thickness of 50 μm, and then ion-beam thinned at a cold station of 100 K. The microhardness was measured by a 300 g load applied for 15s via an FM-700 automatic microhardness tester. The alloys were electrode-discharge machined to cylinders with the size of Φ 5 × 8 mm, and the compressive properties were evaluated by a CMT 5305 universal electronic testing machine with a strain rate of 1 × 10−3 s−1 at room temperature.The XRD patterns of CoCrFeNiTax EHEAs are shown in . FCC solid solution and Laves phase, two phases were detected in the CoCrFeNiTax EHEAs. With the increase of Ta content, the diffraction peaks of Laves phase became more obviously. And the (200) peak of the FCC solid solution of the EHEAs are shown in b. The diffraction peaks shifted toward lower 2θ with increasing Ta content. It could be due to the lattice distortion induced by adding Ta into the solid solution. shows the microstructures of CoCrFeNiTax EHEAs obtained under BSE mode. The typical hypoeutectic microstructures were obtained in CoCrFeNiTa0.1, CoCrFeNiTa0.2 and CoCrFeNiTa0.3 EHEAs, while the hypereutectic ones were obtained in CoCrFeNiTa0.4 and CoCrFeNiTa0.5 EHEAs. With the increase of x value of CoCrFeNiTax hypoeutectic HEAs, the volume fraction of eutectic structures became greater obviously. And with the increase of x value of CoCrFeNiTax hypereutectic HEAs, the more proeutectic Laves phase was obtained. In , regions A and B represented the FCC solid solution and the Laves phase, respectively. EDS results of regions A and B in the EHEAs are listed as . In addition, bright components in BSE image are believed to contain heavy elements. According to , the bright regions are thus made of Laves phase. In light of this observation, the eutectic microstructure comprises of a mixture of the Laves phase and the FCC solid solution. During the eutectic reaction, Laves phase and FCC solid solution grow coupling with each other to generate lamellar structures. The final microstructures are composed of proeutectic phase and the eutectic mixture of Laves phase and FCC solid solution. show that the FCC solid solution is depleted in Ta and enriched in Cr and Fe while the Laves phase is enriched in Ta and depleted in Cr and Fe. The values of ΔHmixAB are calculated by Miedema model also shows the atomic sizes of the elements. Ta has the largest atomic size in CoCrFeNiTax EHEA system and quite negative mixing enthalpies with Ni and Co. It is unfavorable to the solution of Ta into the FCC solid solutions. Co, Cr, Fe and Ni have similar atomic sizes as well as similar mixing enthalpies with the result that it enhances the tendency to form the disordered solid solution. Some tantalum is into the lattice of FCC solid solution and it is consistent with From the microstructure, CoCrFeNiTa0.4 alloy seems to have the close-eutectic compositions. To further research the EHEAs, CoCrFeNiTa0.395 alloy was prepared and characterized. shows the microstructure of CoCrFeNiTa0.395 EHEA obtained under BSE mode. The EHEA is characterized by fine fully lamellar microstructure. The microstructure consists of equiaxed eutectic cells with an average size of 10–30 μm. It can be seen from the highly magnified image that bright Laves phase and dark FCC solid solution lamellas exhibit a radial pattern in the eutectic cells, as shown in TEM provides detailed information on microstructure. By viewing eutectic microstructures at high magnification, the fine phases are identified by combining TEM bright-field (BF) imaging, high-resolution TEM (HRTEM) and fast Fourier transform (FFT) of ‘A’, as seen in a that some fine-sized Laves phase with a typical width of ∼150 nm exist between FCC solid solutions. Thus, the strength of the EHEA can be improved by precipitation strengthening of the fine hard Laves phase. The HRTEM image in b and FFT patterns confirm the orientation relationship of Laves phase and FCC solid solution. HRTEM suggests the following crystallographic orientation for the C14 Laves phase and FCC solid solution in the EHEA:Similar orientation was reported earlier At the interfaces, {0001}Laves phase are matched by {111}FCC that are inclined against the interface plane by 19°. This enables δ = 0.079. The quantitative illustration of misfit at the Laves phase-FCC interface is shown in c. In fact, the microstructure is typical of binary eutectic crystallization from a melt, requiring cooperative nucleation and growth of Laves phase and FCC solid solution. Lamellar eutectics minimize the interface energy by maximizing the area of low-energy facets ΔHmix (mixing enthalpy), δ (atomic size difference) and ΔSmix (mixing entropy) have been proposed by Zhang et al. ΔHmix=∑i=1i≠jnΩijcicj=4∑i=1i≠jnΔHijmixcicjwhere ci is the atomic percent of the ith element, ΔHijmix is the mixing enthalpy between the ith and jth elements, ri is the Goldschmidt atomic size of the ith element, and R is the gas constant and equivalent to 8.314 J·K−1·mol−1. The tendency of forming stable intermetallic is reflected by ΔHmix, the degree of the atomic size mismatch is characterized by δ, and the entropy of mixing of the HEA system is characterized by ΔSmix. Based on limited experimental work on HEAs performed so far, ΔHmix, δ and ΔSmix were found to play dominant roles in controlling the phase selection in HEAs. Zhang et al. ΔHmix, δ and ΔSmix of CoCrFeNiTax EHEAs are calculated and shown in . It can be seen that the ΔHmix of CoCrFeNiTax EHEAs are about −5.35 to −10.37 kJ·mol−1, δ are from 2.28% to 4.56%, and ΔSmix are between 12.20 and 13.15 J·K−1·mol−1. They all meet the criteria for formation of HEAs where Tm[=∑i=1nci(Tm)i] is the average value of the melting temperature. The melting temperature of Co, Cr, Fe, Ni and Ta are 1768, 2180, 1811, 1728 and 3290 K, respectively. The Tm and Ω of CoCrFeNiTax EHEAs are calculated and shown in . It is concluded that the criteria for forming fully single solid solutions are Ω ≥ 1.1 and δ< 6.6% where Xi is the Pauling electro-negativity of the ith element, X¯(=∑i=1nciXi) is the average value of the Pauling electro-negativity, and (Md)i is the d-orbital energy level of the ith element in the M-element centered cluster in the i-M binary solid solution alloy, in which i is a solvent and M is a solute. The values of Pauling electronegativity of Co, Cr, Fe, Ni and Ta are 1.88, 1.66, 1.83, 1.91 and 1.50, respectively It summarized that TCP phases can be stable at ΔX> 0.133 except for some kinds of HEAs containing a great deal of Al On the other hand, calculated enthalpies of formation of the lowest energy structures of binary compounds relative to phase separation into pure elements have been suggested by Troparevsky et al. a shows the microhardness of the CoCrFeNiTax EHEAs, which the value of the hardest one is 583 HV. It is found that the microhardness has an approximately linear increase with increasing Ta content, which can be roughly expressed as yHV = 900.9x + 124.43, where yHV is the microhardness, and x is the Ta content. As described above, it is obvious that in the EHEAs the volume fraction of Laves phase increases with the increasing of Ta content. There is no doubt that, the increase of volume fraction of the harder Laves phase will lead to the increase of microhardness of the EHEAs. In addition, the Ta atoms occupied the positions in the FCC matrix also lead to a strong lattice distortion and make contributions to the microhardness of the EHEAs.The compressive stress-strain curves are shown in b. CoCrFeNiTa0.1 and CoCrFeNiTa0.2 EHEAs exhibited excellent compressive ductility, and did not fracture. CoCrFeNiTa0.3 EHEA exhibits high compressive strength and fracture strain of 2515 MPa and 44%, respectively. CoCrFeNiTa0.395 EHEA exhibits high compressive strength and fracture strain of 2432 MPa and 27%, respectively. The fracture strength and fracture strain of CoCrFeNiTa0.5 hypereutectic HEA both go down. The compressive strength and fracture strain of CoCrFeNiTa0.3 EHEA are particularly noteworthy since. We can further estimate the strength and ductility of the HEAs and compare it with that of other CoCrFeNi-based HEAs c. It clearly indicates that CoCrFeNiTa0.3 EHEA outperform the other CoCrFeNi-based HEAs.The outstanding compressive properties of the HEAs are attributed to the second-phase hardening and solid-solution strengthening. The hardening is from the Ta-rich Laves phase and the strengthening is from the atoms which into the FCC lattice. The Ta-rich Laves phase resists destructive action, and the FCC solid solution is with a great ductility. However, the properties of CoCrFeNiTa0.5 alloy are worse than the one of CoCrFeNiTa0.395 EHEA due to the formation of a large number of Laves-phase patches. The excessive addition of Ta is detrimental to the strength and ductility of the EHEAs. CoCrFeNiTa0.3 alloy is into the plastic deformation stage much earlier than CoCrFeNiTa0.395 EHEA, it is due to the fact that reticular-like microstructure is deformed more easily than lamellar microstructure. The compression fracture morphologies of CoCrFeNiTa0.5 hypereutectic HEA are shown in . The microcracks originate first at the coarse primary Laves phase and then propagate to the nearby fine eutectic structures. The presence of microcracks causes the EHEA to fracture early before reaching high strength and strain. shows the relationship between the volume fraction of the Laves phase and the yield strength. The volume fractions of the Laves phase were measured upon a number of SEM images by software. Interestingly, the EHEA, CoCrFeNiTa0.395, shows the highest yield strength. For lamellar eutectics, the strengthening mechanism includes the second-phase, solid solution and boundary strengthening σEHEA=VLavesphaseσLavesphase+(1−VLavesphase)σFCCwhere an isostrain assumption is made, VLavesphase is the volume fraction of Laves phase, σLavesphase is the stress of Laves phase at a specific value of strain, and σFCC is the stress of FCC solid solution at this level of strain. Eq. reveals a significant enhancement effect on the EHEA by the second-phase strengthening. Furthermore, alloying has always been attempted as a means of strengthening the lamellar reinforcing-phase as well as the matrix, as it provides obvious solid solution strengthening to the eutectic alloys. Notably, HEAs are an unusual kind of alloys, and with a strong alloying. There is almost no solvent in the HEAs. Every element can be seen as the solute. It makes lattice-distortion severe and leads to a strong solid solution strengthening.Lamellar eutectics have been shown to be strengthened as the interlamellar spacing is reduced where σ∗ is a frictional stress, k is a constant, and λ is the lamellar spacing. Eutectoid steel, consisting of lamellae of ferrite and cementite, has also been found in 1966 In this work, the microstructure and properties of the novel CoCrFeNiTax eutectic high-entropy alloys were characterized and evaluated. It was found that the eutectic high-entropy alloys are transformed from hypoeutectic to hypereutectic solidification by increasing Ta content. The increase of Ta content promotes the formation of Laves phase. The phase formation criteria, ΔΗf, appear to be suitable for predicting the phase formation in this alloy system. The eutectic high-entropy alloy, CoCrFeNiTa0.395, which with fine fully lamellar microstructure shows the ideal combination among the second-phase, solid solution and boundary strengthening. It could exhibit high compressive strength and yield strength, while hypoeutectic high-entropy alloy could show a higher ductility.Biaxially loaded high-strength concrete-filled steel tubular slender beam-columns, Part I: Multiscale simulationThe steel tube walls of a biaxially loaded thin-walled rectangular concrete-filled steel tubular (CFST) slender beam-column may be subjected to compressive stress gradients. Local buckling of the steel tube walls under stress gradients, which significantly reduces the stiffness and strength of a CFST beam-column, needs to be considered in the inelastic analysis of the slender beam-column. Existing numerical models that do not consider local buckling effects may overestimate the ultimate strengths of thin-walled CFST slender beam-columns under biaxial loads. This paper presents a new multiscale numerical model for simulating the structural performance of biaxially loaded high-strength rectangular CFST slender beam-columns accounting for progressive local buckling, initial geometric imperfections, high strength materials and second order effects. The inelastic behavior of column cross-sections is modeled at the mesoscale level using the accurate fiber element method. Macroscale models are developed to simulate the load-deflection responses and strength envelopes of thin-walled CFST slender beam-columns. New computational algorithms based on the Müller's method are developed to iteratively adjust the depth and orientation of the neutral axis and the curvature at the column's ends to obtain nonlinear solutions. Steel and concrete contribution ratios and strength reduction factor are proposed for evaluating the performance of CFST slender beam-columns. Computational algorithms developed are shown to be an accurate and efficient computer simulation and design tool for biaxially loaded high-strength thin-walled CFST slender beam-columns. The verification of the multiscale numerical model and parametric study are presented in a companion paper.► A new multiscale model for biaxially loaded CFST slender beam-columns is presented. ► The model accounts for the effects of local buckling and high strength materials. ► Computer algorithms are developed to simulate mesoscale and macroscale behavior. ► Steel and concrete contribution ratios and strength reduction factor are proposed.High strength thin-walled rectangular concrete-filled steel tubular (CFST) slender beam-columns in composite frames may be subjected to axial load and biaxial bending. Biaxially loaded thin-walled CFST slender beam-columns with large depth-to-thickness ratios are vulnerable to local and global buckling. No numerical models have been developed for the multiscale inelastic stability analysis of biaxially loaded high strength thin-walled CFST slender beam-columns accounting for the effects of progressive local buckling of the steel tube walls under stress gradients. The difficulty is caused by the interaction between local and global buckling and biaxial bending. However, it is important to accurately predict the ultimate strength of a thin-walled CFST slender beam-column under biaxial loads because this strength is needed in the practical design. This paper addresses the important issue of multiscale simulation of high strength thin-walled rectangular CFST slender beam-columns under combined axial load and biaxial bending.Extensive experimental investigations have been undertaken to determine the ultimate strengths of short and slender CFST columns under axial load or combined axial load and uniaxial bending Although the performance of CFST columns could be determined by experiments, they are highly expensive and time consuming. To overcome this limitation, nonlinear analysis techniques have been developed by researchers for composite columns under axial load or combined axial load and uniaxial bending This paper extends the numerical models developed by Liang The mesoscale model is developed by utilizing the accurate fiber element method . Each fiber element can be assigned either steel or concrete material properties. Fiber stresses are calculated from fiber strains using the material uniaxial stress–strain relationships.It is assumed that plane section remains plane under deformation. This results in a linear strain distribution throughout the depth of the section. In the numerical model, the compressive strain is taken as positive while the tensile strain is taken as negative. Fiber strains in biaxial bending depend on the depth (dn) and orientation (θ) of the neutral axis of the section as illustrated in . For 0° |
≤ |
θ |
< 90°, concrete and steel fiber strains can be calculated by the following equations proposed by Laing εi={ϕyi−yn,icosθfor yi≥yn,i−ϕyi−yn,icosθfor yi<yn,iin which B and D are the width and depth of the rectangular column section respectively, xi and yi are the coordinates of fiber i and εi is the strain at the ith fiber element and yn, |
i is the distance from the centroid of each fiber to the neutral axis.When θ |
= 90°, the beam-column is subjected to uniaxial bending and fiber strains can be calculated by the following equations given by Liang εi={ϕxi−B2−dnfor xi≥xn,i−ϕxi−B2−dnfor xi<xn,iwhere xn, |
i is the distance from the centroid of each fiber element to the neutral axis.Stresses in concrete fibers are calculated from the uniaxial stress–strain relationship of concrete. A general stress–strain curve for concrete in rectangular CFST columns is shown in . The stress–strain curve accounts for the effect of confinement provided by the steel tube, which improves the ductility of the concrete core in a rectangular CFST column. The concrete stress from O to A in the stress–strain curve is calculated based on the equations given by Mander et al. in which σc stands for the compressive concrete stress, f′cc represents the effective compressive strength of concrete, εc denotes the compressive concrete strain, ε′cc is the strain at f′cc and is between 0.002 and 0.003 depending on the effective compressive strength of concrete where Dc is taken as the larger of (B |
− 2t) and (D |
− 2t) for a rectangular cross-section, and t is the thickness of the steel tube wall as shown in The parts AB, BC and CD of the stress–strain curve for concrete shown in are defined by the following equations proposed by Liang σc={f′ccfor ε′cc<εc≤0.005βcf′cc+1000.015−εcf′cc−βcf′ccfor 0.005<εc≤0.015βcf′ccfor εc>0.015βc={1.0for Bst≤241.5−148Bstfor 24<Bst≤480.5for Bst>48where Bs is taken as the larger of B and D for a rectangular cross-section.The stress–strain curve for concrete in tension is shown in . The constitutive model assumes that the concrete tensile stress increases linearly with the tensile strain up to concrete cracking. After concrete cracking, the tensile stress of concrete decreases linearly to zero as the concrete softens. The concrete tensile stress is considered to be zero at the ultimate tensile strain which is taken as 10 times of the strain at concrete cracking. The tensile strength of concrete is taken as 0.6f′cc.Stresses in steel fibers are calculated from uniaxial stress–strain relationship of steel material. Steel tubes used in CFST cross-sections are normally made from three types of structural steels such as high strength structural steels, cold-formed steels and mild structural steels, which are considered in the numerical model. shows the stress–strain relationship for three types of steels. The steel material generally follows the same stress–strain relationship under the compression and tension. The rounded part of the stress–strain curve can be defined by the equation proposed by Liang Local buckling significantly reduces the strength and stiffness of thin-walled CFST beam-columns with large depth-to-thickness ratios. Therefore, it is important to account for local buckling effects in the inelastic analysis of high strength CFST slender beam-columns. However, most of existing numerical models for thin-walled CFST beam-columns have not considered local buckling effects. This may be attributed to the complexity of the local instability problem as addressed by Liang et al. . Due to the presence of initial geometric imperfections, no bifurcation point can be observed on the load-deflection curves for real thin steel plates. The classical elastic local buckling theory The effective width concept is commonly used to describe the post-local buckling behavior of a thin steel plate as illustrated in be1b={0.2777+0.01019bt−1.972×10−4bt2+9.605×10−7bt3for αs>0.00.4186−0.002047bt+5.355×10−5bt2−4.685×10−7bt3forαs=0.0 are taken as zero after the maximum edge stress σ1 reaches the initial local buckling stress σ1c for a steel plate with a b/t ratio greater than 30. If the total effective width of a plate (be1 |
+ |
be2) is greater than its width (b), the effective strength formulas proposed by Liang et al. The internal axial force and bending moments acting on a CFST beam-column section under axial load and biaxial bending are determined as stress resultants in the section as follows:in which P stands for the axial force, Mx and My are the bending moments about the x and y axes, σs, |
i denotes the stress of steel fiber i, As, |
i represents the area of steel fiber i, σc, |
j is the stress of concrete fiber j, Ac, |
j is the area of concrete fiber j, xi and yi are the coordinates of steel element i, xj and yj stand for the coordinates of concrete element j, ns is the total number of steel fiber elements and nc is the total number of concrete fiber elements.The inelastic moment-curvature responses of a CFST beam-column section can be obtained by incrementally increasing the curvature and solving for the corresponding moment value for a given axial load (Pn) applied at a fixed load angle (α). For each curvature increment, the depth of the neutral axis is iteratively adjusted for an initial orientation of the neutral axis (θ) until the force equilibrium condition is satisfied. The moments of Mx and My are then computed and the equilibrium condition of tan |
α |
= |
My/Mx is checked. If this condition is not satisfied, the orientation of the neutral axis is adjusted and the above process is repeated until both equilibrium conditions are met. The effects of local buckling are taken into account in the calculation of the stress resultants. The depth and orientation of the neutral axis of the section can be adjusted by using the secant method algorithms developed by Liang . A detailed computational procedure for predicting the inelastic moment-curvature responses of composite sections was given by Liang The pin-ended beam-column model is schematically depicted in . It is assumed that the deflected shape of the slender beam-column is part of a sine wave. The lateral deflection of the beam-column can be described by the following displacement function:where L stands for the effective length of the beam-column and um is the lateral deflection at the mid-height of the beam-column.The curvature at the mid-height of the beam-column can be obtained asFor a beam-column subjected to an axial load at an eccentricity of e as depicted in and an initial geometric imperfection uo at the mid-height of the beam-column, the external moment at the mid-height of the beam-column can be calculated byTo capture the complete load-deflection curve for a CFST slender beam-column under biaxial loads, the deflection control method is used in the numerical model. In the analysis, the deflection at the mid-height um of the slender beam-column is gradually increased. The curvature ϕm at the mid-height of the beam-column can be calculated from the deflection um. For this curvature, the neutral axis depth and orientation are adjusted to achieve the moment equilibrium at the mid-height of the beam-column. The equilibrium state for biaxial bending requires that the following equations must be satisfied:in which Mmi is the resultant internal moment which is calculated as Mmi=Mx2+My2.The macroscale model incorporating the mesoscale model is implemented by a computational procedure. A computer flowchart is shown in to implicitly demonstrate the computational procedure for load-deflection responses. The main steps of the computational procedure are described as follows:Discretize the composite section into fine fiber elements.Initialize the mid-height deflection of the beam-column um |
= |
Δum.Calculate the curvature ϕm at the mid-height of the beam-column.Adjust the depth of the neutral axis (dn) using the Müller's method.Compute stress resultants P and Mmi considering local buckling.Compute the residual moment rma |
= |
Mme |
− |
Mmi.Adjust the orientation of the neutral axis (θ) using the Müller's method.Calculate the residual moment rmb=tanα−MyMx .Increase the deflection at the mid-height of the beam-column by um |
= |
um |
+ |
Δum.Repeat Steps (4)–(13) until the ultimate axial load Pn is obtained or the deflection limit is reached.In the above procedure, εk is the convergence tolerance and taken as 10− 4 in the numerical analysis.In design practice, it is required to check for the design capacities of CFST slender beam-columns under design actions such as the design axial force and bending moments, which have been determined from structural analysis. For this design purpose, the axial load-moment strength interaction curves (strength envelopes) need to be developed for the beam-columns. For a given axial load applied (Pn) at a fixed load angle (α), the ultimate bending strength of a slender beam-column is determined as the maximum moment that can be applied to the column ends. The moment equilibrium is maintained at the mid-height of the beam-column. The external moment at the mid-height of the slender beam-column is given byin which Me is the moment at the column ends. The deflection at the mid-height of the slender beam-column can be calculated from the curvature asTo generate the strength envelope, the curvature (ϕm) at the mid-height of the beam-column is gradually increased. For each curvature increment, the corresponding internal moment capacity (Mmi) is computed by the inelastic moment-curvature responses discussed in . The curvature at the column ends (ϕe) is adjusted and the corresponding moment at the column ends is calculated until the maximum moment at the column ends is obtained. The axial load is increased and the strength envelope can be generated by repeating the above process. For a CFST slender beam-column under combined axial load and bending, the following equilibrium equations must be satisfied: shows a computer flowchart that implicitly illustrates the computational procedure for developing the strength envelope. The main steps of the computational procedure are described as follows:Discretize the composite section into fine fiber elements.The load-deflection analysis procedure is used to compute the ultimate axial load Poa of the axially loaded slender beam-column with local buckling effects.Initialize the applied axial load Pn |
= 0.Initialize the curvature at the mid-height of the beam-column ϕm |
= |
Δϕm.Compute the mid-height deflection um from the curvature ϕm.Adjust the depth of the neutral axis (dn) using the Müller's method.Calculate resultant force P considering local buckling.Compute the residual force rmc |
= |
Pn |
− |
P.Adjust the orientation of the neutral axis (θ) using the Müller's method.Calculate the residual moment rmb=tanα−MyMx.Compute the internal resultant moment Mmi.Adjust the curvature at the column end ϕe using the Müller's method.Compute the moment Me at the column ends accounting for local buckling effects.Repeat Steps (16)–(18) until |rma| < |
εk.Increase the curvature at the mid-height of the beam-column by ϕm |
= |
ϕm |
+ |
Δϕm.Repeat Steps (6)–(20) until the ultimate bending strength Mn(= |
Me |
max) at the column ends is obtained.Increase the axial load by Pn |
= |
Pn |
+ |
ΔPn, where ΔPn |
= |
Poa/10.Repeat Steps (5)–(22) until the maximum load increment is reached.Plot the axial load-moment interaction diagram.As discussed in the preceding sections, the depth and orientation of the neutral axis and the curvature at the column ends need to be iteratively adjusted to satisfy the force and moment equilibrium conditions in the inelastic analysis of a slender beam-column. For this purpose, computational algorithms based on the secant method have been developed by Liang In general, the depth (dn) and orientation (θ) of the neutral axis and the curvature (ϕe) at the column ends of a slender beam-column are design variables which are denoted herein by ω. The Müller's method requires three starting values of the design variables ω1, ω2, and ω3. The corresponding force or moment functions rm, 1, rm, 2 and rm, 3 are calculated based on the three initial design variables. The new design variable ω4 that approaches the true value is determined by the following equations:am=ω2−ω3rm,1−rm,3−ω1−ω3rm,2−rm,3ω1−ω2ω1−ω3ω2−ω3bm=ω1−ω32rm,2−rm,3−ω2−ω32rm,1−rm,3ω1−ω2ω1−ω3ω2−ω3When adjusting the neutral axis depth and orientation, the sign of the square root term in the denominator of Eq. is taken to be the same as that of bm. However, this sign is taken as positive when adjusting the curvature at the column ends. In order to obtain converged solutions, the values of ω1, ω2 and ω3 and corresponding residual forces or moments rm, 1, rm, 2 and rm, 3 need to be exchanged as discussed by Patel et al. and the exchange of design variables and force or moment functions are executed iteratively until the convergence criterion of |rm| < |
εk is satisfied.In the numerical model, three initial values of the neutral axis depth dn, 1, dn, 3 and dn, 2 are taken as D/4, D and (dn, 1 |
+ |
dn, 3)/2 respectively; the orientations of the neutral axis θ1, θ3 and θ2 are initialized to α/4, α and (θ1 |
+ |
θ3)/2 respectively; and the curvature at the column ends ϕe, 1, ϕe, 3 and ϕe, 2 are initialized to 10− 10, 10− 6 and (ϕe, 1 |
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