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θ), where V0 is the driving voltage amplitude and θ is the temporal driving phase difference (all the four PZTs were excited with same voltage amplitude). shows the FEA results of the vibrational displacement amplitude distribution in the z direction in the channel at 273 kHz when changing the driving phase difference between two pairs of transducers θ from 0° to 240°. The vibrational amplitudes were normalized by the maximum value at each phase difference. Each dotted line L indicates one of the vibrational nodal lines. When changing the phase difference of the input voltage to the transducers, the positions of nodal lines in the y direction gradually moved to the +x direction across the cross-point of the channels (from x |
= 11 mm to x |
= 16 mm). The reverse-phase mode was generated at θ |
= 180° in which the nodal line was at x |
= 15 mm. In the FEA, only the boundary conditions for the electric excitation on the PZT electrodes were applied, while other electric elements were not taken into account. shows the sound pressure amplitude distributions and the vector flow of acoustic radiation force acting on a small rigid sphere The prototype of the ultrasonic manipulator was fabricated based on the FEA results. shows the vibrational distribution at the bottom of the channel measured by a laser Doppler vibrometer (LDV; NLV-2500, PI Polytec, Waldbronn, Germany). By applying an in-phase input voltage Vpp of 75 V to the four transducers, the flexural vibration mode—which is the same vibration mode as the FEA result shown in —was excited on the chip at 225 kHz, and the flexural vibration with a wavelength of ∼13 mm was generated along the channel. The difference in the resonance frequencies between the FEA and experimental results is attributed mainly to the uncertainty of the elastic properties (Young’s modulus and Poisson ratio) of the glass substrate used in the FEA. In addition, the asymmetric vibrational distribution was caused by the contact condition and the individual differences between the transducers. The flexural vibration shifted in the x direction when the driving phase difference θ changed, as predicted by the FEA. Focusing on the P points in —each of which are one of the vibrational nodal points—we compare the movement distances of the flexural vibration in the x direction between the experimental and FEA results, as shown in . These results agree well. The vibration nodal points change little around θ |
= 0° and move drastically around θ |
= 180°. The step motion of 1 mm in the FEA result is attributed to the mesh size of the FEA model in the x–y plane. shows the relationships between the driving phase difference, the movement distance of the nodal point, and the standing wave ratio (SWR). The SWR can be expressed as a ratio of the amplitude at the antinode to that at the node of the standing wave, and an SWR of 1 means that a pure traveling wave propagates. As shown in , the vibrational nodal points moved drastically with the smaller SWR when the vibration mode was switched from a standing wave to a traveling wave, or from a traveling wave to a standing wave around θ |
= 150–210°. These results mean that the positions of the flexural vibration and the acoustic field in the channel can be controlled parallel to the channel by changing the driving phase difference between the transducers, which enables noncontact transportation of the microparticles in the liquid. The decrease of the SWR suggests that the standing wave components decreased and the traveling wave was generated in the x-direction because a part of elastic energy of the flexural wave was absorbed by the transducers as electrical energy shows the change in the average vibrational amplitude in the channel when changing the driving phase difference. As the phase difference approached 180°, the average vibration amplitude decreased because the vibration mode changed to the reversed-phase mode. This fact implies that the acoustic radiation force to the particles will decrease because the acoustic radiation is expressed as a function of sound pressure.We examined the one-dimensional manipulation of microparticles in the channel on the chip. To do this, we immersed silicon carbide microparticles with an average diameter of 50 μm in the channel. The microparticles gradually settled to the bottom of the channel in ethanol. By exciting the transducers electrically, the acoustic standing wave was generated in the channel by the flexural vibration, and the microparticles could be trapped along the nodal lines of the standing wave every half the wavelength. Cavitation bubbles trapped on the antinodal lines of the acoustic standing wave in the channel were observed if non-degassed water was used. We observed the motion of the microparticles in the channels from above (z direction) with an optical microscope (LT-9000, Keyence, Osaka, Japan) by changing the driving phase difference. shows the trajectory of the microparticle transported in the +x direction at the cross-point of the channels when the driving phase difference was changed; superimposed are photographs of the transported particle taken every phase difference of 2°. By changing the phase difference, the microparticle was transported in the +x direction with the movement of the flexural vibration. Note that the transportation trajectory of the particle was not straight perfectly because the acoustic radiation force in the direction vertical to the standing wave (the y direction in ) was smaller than that in the direction of the sound axis (the x direction) will disturb the acoustic field in the channel and affect the transportation trajectory. shows the relationship between the phase difference and the movement distance of microparticle in the x direction. The movement distance of the particle could be controlled by the phase difference, and the particles were transported over a distance of ∼2.6 mm when the phase difference was changed from 160° to 200°. The gradient of the transportation characteristics in was not constant and decreased near θ |
= 180° slightly because the vibrational nodal position of the substrate moved significantly when the traveling-wave mode and the standing-wave mode were switched, as predicted in We also performed two-dimensional manipulation on the chip. By switching the combination of the two pairs of transducers, we changed the transport direction of microparticles at the channels’ cross-point. shows the motion of a microparticle manipulated in the x and y directions at the cross-point. As mentioned in the previous section, combining PZTs 1 and 3 and PZTs 2 and 4 produced one-dimensional manipulation in the x direction. If the combination of the four transducers changes when the particles are at the cross-point, the transport direction can change; the particles can be transported in the y direction by combining PZTs 1 and 2 and PZTs 3 and 4 (see ). By controlling the combination of the four transducers and the driving conditions, the microparticle can be transported in any direction. In this way, the particles can be separated by using the difference in the acoustic characteristics of the particles and the steady flow in the channel. It should be noted that the ultrasound frequency we used in the experiments was somewhat lower than that commonly used in cell manipulation techniques. In future research, ultrasound frequency should be increased by downsizing the chip since cavitation bubbles will not be generated in non-degassed water and the acoustic radiation force for micrometer-sized cells will increase.We investigated a technique for noncontact manipulation of microparticles by using the flexural vibration of a chip. The configuration of the glass substrate, transducers, and channel were designed by FEA, and the vibration mode and transportation characteristics were predicted. By controlling the combination and the electric driving conditions of the four transducers, we shifted the flexural vibration mode of the glass substrate and the acoustic standing-wave field in the channel, and we manipulated the motion of trapped microparticles along the channel.Linear friction welding of AISI 316L stainless steel▶ Linear friction welding is a feasible process for joining AISI316L. ▶ Most welds had tensile strengths superior to the parent material. ▶ Welding parameters had a significant impact on weld microstructure. ▶ Control of microstructure by controlling welding parameters is a process benefit.Linear friction welding is a solid state joining process established as a niche technology for the joining of aeroengine bladed disks. However, the process is not limited to this application, and therefore the feasibility of joining a common engineering austenitic steel, AISI 316L, has been explored. It was found that mechanically sound linear friction welds could be produced in 316L, with tensile properties in most welds exceeding those of the parent material. The mechanical properties of the welds were also found to be insensitive to relatively large changes in welding parameters. Texture was investigated in one weld using high energy synchrotron X-ray diffraction. Results showed a strong {1 1 1}〈 1 1 2 〉 type texture at the centre of the weld, which is a typical shear texture in face centre cubic materials. Variations in welding parameters were seen to have a significant impact on the microstructures of welds. This was particularly evident in the variation of the fraction of delta ferrite, in the thermo-mechanically affected zone of the welds, with different process parameters. Analysis of the variation in delta ferrite, with different welding parameters, has produced some interesting insights into heat generation and dissipation during the process. It is hoped that a greater understanding of the process could help to make the parameter optimisation process, when welding 316L as well as other materials, more efficient.Linear friction welding (LFW) is a solid state joining process, which is established as a niche technology for the fabrication of integrally bladed disk (blisk) assemblies in aeroengines Practically all published literature on the subject has concentrated on the joining of materials that are used for aeroengine applications (i.e. titanium and nickel alloys, e.g. Austenitic stainless steels are readily welded by a number of different welding processes, and welds with good mechanical properties have been produced with the more conventional arc welding processes (e.g. As all common welding methods can be used to join austenitic stainless steels, process selection is a complex issue and will be determined by the intricacies of the particular application. However, there are a number of advantages to using friction welding, over other processes, which could make it viable for certain purposes. Key among these is the fact that the processes are solid state and therefore solidification problems (e.g. hot cracking, porosity, segregation, etc.) are avoided. Solidification problems have been encountered in arc welding of austenitic stainless steel (e.g. The major disadvantage of friction welding processes is the high capital cost of the equipment, and this is especially the case for LFW, although the capital costs are reducing as the design of the machines develop. This high cost is likely to mean that the LFW processes will not attain widespread use for joining stainless steels in the short term, although it could be viable for certain high value added niche applications. Process selection between the friction welding family of processes is simpler as the different processes are normally used for different part geometries. Friction stir welding is generally used for butt welds in thin sheet, rotary and inertia friction welding are suitable for tubes and cylinders, whilst LFW is usually used for non axi-symmetric blocks.Although the LFW process brings about many advantages over fusion welding processes, a particular feature of the process when welding austenitic stainless steels (γ phase, face centre cubic crystal structure) may be the formation of delta (δ)-ferrite and sigma (σ)-phase in the heat affected or thermo-mechanically affected zones of the weld. The high temperature δ-ferrite phase, which has a body centred cubic (BCC) crystal structure, forms in fusion welds of 300 series austenitic stainless steels (for example The intermetallic σ phase is detrimental to weld properties because of its low fracture toughness and its tendency to deplete the adjacent austenite of chromium, thus making the material susceptible to corrosion As both large increases in δ-ferrite and the formation of σ phase can be detrimental to weld properties, it is preferred that no σ phase is produced as a result of the LFW process and the amount of δ-ferrite within the microstructure is kept at a similar level to that in the parent material. Consequently an attempt has been made to optimise welding parameters for minimising the generation of δ-ferrite.As δ-ferrite is a high temperature phase, the welding temperature will have a large impact on the amount of the phase left in the microstructure after welding. There have been a few studies into the effects of welding parameters, during the LFW of different titanium alloys, on welding temperature There are a number of possible reasons for the discrepancies between different studies. These include differences in the welded material, parameters used (full disclosure of parameters was not given in There has been a relatively small amount of research into crystallographic texture development in linear friction welds, even though the material near the weld line is exposed to severe deformation during the joining process. To date textures have been studied in Ti-64 linear friction welds, and a very strong transverse α texture, {101¯0}〈112¯0〉, and a {1 1 1} fibre β texture has been reported close to the weld line As there is no publicly available information on textures in austenitic stainless steel linear friction welds it is difficult to predict the type of textures that would be expected. However, there has been some work on rolling textures in these materials and textures in linear friction welds may be similar. When rolling 316L different texture components were prevalent depending on the deformation conditions The material used for producing small scale linear friction welds in AISI 316L (Cr 17.3, Ni 9.8, Mo 2, Mn 1.9, Si 0.5, Fe balance, all in wt%; determined from experimental analysis of the base material) was supplied as 20 mm × 20 mm square drawn bar, which was saw cut into 75 mm lengths to produce weld samples.Samples were welded on an electromechanical LFW machine (a rotating crankshaft is attached to two cranks which provide the linear reciprocation; an alternative would be to use hydraulic systems to generate reciprocation) at TWI Ltd, Cambridge, UK. Preparation of the sawn ends, which would form the faying surfaces (welding faces), was limited to degreasing with acetone just prior to welding.There are a number of key parameters involved in LFW ), which can have a significant impact on the joint properties. These parameters include:frequency of oscillation: in this study it is defined as the number of sinusoidal oscillations (of the reciprocating part) completed in a secondamplitude of oscillation: defined as the maximum displacement of the oscillating sample from its equilibrium position (equilibrium position is when the displacement between the oscillating and stationary sample is zero, i.e. samples are aligned)friction pressure: the pressure that is applied, perpendicular to the weld interface, during the rubbing, or frictional, phase of the process. Pressure is calculated by using the nominal area of contact at zero amplitudeforge pressure: the pressure, which is usually higher than the pressure during the frictional phase, that is applied at the end of the process (after oscillation has stopped), for a set period of time, to consolidate the jointburn-off distance: the distance that the parts are allowed to shorten (shortening is caused by the removal of plasticised material from the weld) before the amplitude is decayed and the forge pressure is appliedIn this study four parameters (friction pressure, frequency, amplitude and burn-off distance) were varied to produce 22 different parameter combinations and 66 welds (3 welds at each parameter setting). In each weld a forge pressure that was the same as the friction pressure was applied for a period of 5 s. For each of the parameters that were varied, a minimum, mid and maximum value was determined from experience at TWI of friction welding materials similar to 316L. Each parameter was varied between its minimum and maximum value whilst keeping all other parameters constant at the mid value (8 different force settings, 4 frequency settings, 4 amplitude settings and 3 burn-off settings were used, in all cases whilst keeping other, non-variable, parameters at the mid level). In addition, welds were fabricated with all values at the minimum, mid and maximum values (giving 3 additional parameter settings). However, it was not always possible to use all of the extreme parameters in combination due to either limitations in the capability of the machine or Insufficient heating at the particular parameters; less extreme values for certain parameters were chosen in these cases. The different levels for the four parameters that were varied, along with parameters for the all high and all low welds, are shown in The burn-off (displacement in the direction of applied force) and the applied force were monitored during welding. Data was gathered at 10 Hz during the welding process. From this data the burn-off rate (rate of material expulsion) and the duration of the frictional phase (friction time) were determined. The burn-off rate was determined by fitting a straight line to the burn-off data during a period in which the process is operating at steady state (). The fit was conducted using the least squares method, and the gradient of this line of best fit was taken to be the burn-off rate. The friction time was determined to be the period from the first contact of specimens until the oscillation had stopped (A selection of welds were sectioned for metallographic examination by cutting parallel to the reciprocating direction (). These sections were then mounted in Bakelite, ground and polished. Polished specimens were subsequently electrolytically etched in 60% HNO3 for a general analysis of the microstructure, or electrolytically etched in KOH for a quantitative analysis of the weld line delta ferrite fraction. The delta ferrite fraction was determined by image analysis using Image J software A texture analysis was completed on one weld, using high energy synchrotron X-ray diffraction at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France. The analysis procedure followed that of Romero et al. ); this thickness was sufficient to allow diffraction images to be taken in transmission. A monochromatic beam of wavelength 0.142 Å (88keV) and 200 μm × 200 μm in size was used to record diffraction patterns at locations along a line going across the weld line at mid-width. A step size of 100 μm was applied, which resulted in overlapping diffracting gauge volumes. A high resolution Pixium 4700 area detector, placed 646 mm away from the sample, was used to collect complete Debye Scherrer diffraction rings. With the given energy/sample–detector distance it was possible to obtain a full representation of the austenite texture by using a single diffraction image.In order to fully represent texture an orientation distribution function (ODF) is needed, in which the coordinate system of the crystal and the sample are aligned through the use of three angles (φ1, Φ, φ2 in Bunge notation) The sample-to-detector distance, the centre of the diffraction image and the tilt of the detector were calibrated through the measurement of diffraction patterns of an aluminium powder of known lattice spacing. The calibration was carried out using the ESRF software package Fit2d Each diffraction image was sliced around 5° angles to produce 72 different sections, using Fit2d The peak intensities from the diffraction spectra, in each 5° slice, were extracted using the Le Bail method a–c), which has not been observed when LFW titanium alloys, where a single wing like structure is formed Welds that were representative of the different parameter sets were sectioned for detailed metallographic characterisation. Although most of the sectioned samples showed a complete bond line with no visible defects (as in a), there were a limited number of welds with defects caused by a lack of bonding. An incomplete bond was found when applying a low pressure (80 MPa) during welding, with bonding taking place at the centre of the weld interface, but not towards the edges (b). A lack of bonding across much of the weld line was found in the weld produced with all parameters set to the low level (c). In both of these cases the defects are thought to be because of the poor consolidation of welds, demonstrating that there is a low parameter threshold, or minimum energy level, for obtaining structurally integral linear friction welds in austenitic steel. A similar energy threshold was previously observed when LFW Ti-64 A number of welds were tensile tested, and in most cases cross weld tensile test failure occurred within the parent material region of the gauge length. This indicates that the weld region had a higher ultimate tensile strength than the parent material. This was the case in all welds apart from the poorly consolidated welds (i.e. applied pressure of ≤80 MPa and all low parameters) and a weld made at a high frequency of oscillation. A summary of the tensile test results is shown in The general microstructure of six 316L linear friction welds were examined. Fine grains were seen close to the weld line in most of the welds (see for a typical microstructure). The area of grain refinement was quite large, spanning between 500 and 750 μm in the different welds. A considerable amount of δ-ferrite (in the form of black stringers in ) could also be seen close to the weld line in some welds (effects of welding parameters on δ-ferrite formation is discussed further in Section ). Further away from the weld line there was a region spanning between 180 and 450 μm (on either side of the grain refined region), in the different welds, where the microstructure had been deformed slightly but a large amount of grain refinement had not taken place. The areas of grain refinement and deformation are, collectively, commonly termed the thermo-mechanically affected zone (TMAZ) Although this general description of the microstructure was accurate for most of the welds, one of the welds studied had a very different microstructure. The weld zone of S20 (see shows the texture variation induced by the LFW process for the high pressure weld S17 (see for welding parameters). Measurements from the weld line showed a strong {1 1 1}〈 1 1 2 〉 type texture at the weld line (a), in which grains were predominantly orientated in the {111}〈12¯1〉 and {111}〈1¯1¯2〉 orientations (rotation of about 60° around the axial direction (φ1); d). There were slight deviations from these predominant orientations with small rotations around the transverse and axial directions (φ1), as shown in The same type of texture, but of reducing strength, was seen until just beyond the boundary between the grain refined and deformed regions (). Beyond this boundary the texture was still predominantly of the {1 1 1}〈 1 1 2 〉 type, but there seemed to be a greater amount of rotation around the axial direction, than at the weld line (b). A similar amount of rotation occurred around the transverse direction. This type of texture continued to be present, but gradually reduced in strength, until a close to random texture was seen at a distance of about 3.3 mm from the weld line (As mentioned previously, in some welds a significant increase in δ-ferrite could be seen close to the weld line. However, on analysis of a number of different welds (S11 to S24) large differences in the fraction of δ-ferrite close to the weld line were observed. The parent material contains about 1–2% δ-ferrite, and this was maintained in the welds made with all parameters set to a low level (S23 and S24) and in the low frequency welds (S12 and S13, ). In contrast, the welds made at low pressures contained about 8% δ-ferrite (≤80 MPa, S20 and S21, b). The fact that the microstructure and δ-ferrite fraction of linear friction welds in 316L can be controlled by controlling welding parameters may make the LFW process advantageous for certain applications (e.g. applications involving long term high temperature exposure, where there is a susceptibility of δ-ferrite decomposition to σ phase).A total of 14 welds were studied for weld line δ-ferrite fractions and shows that there is a linear relationship, in the studied range, between δ-ferrite fraction and burn-off rate. confirms that the short time at high temperature experienced by high burn-off rate welds has a significant effect on the δ-ferrite fractions present in the weld region. The welds that did not fit the pattern were those produced with low level welding parameters (circular data points), which were also of poor quality, and those produced with a low oscillation amplitude (triangular data point).There were three welds that did not fit into a linear relationship between burn-off rate and δ-ferrite fraction at the weld line, and these welds will be discussed in this section. Another possible mechanism for low δ-ferrite formation would be a low welding temperature, and this appears to be the case for the welds produced with all parameters set to the low level (S23 and S24). A comparative assessment of the maximum power input, Pm, can be obtained by multiplying the maximum sliding velocity, vm, by the applied force, F (Eq. where f is the frequency and α the amplitude.Through this calculation it can be seen that the power inputs in S23 and S24 were significantly lower than in the other welds (). This suggests that a particularly low welding temperature was achieved in these welds. Furthermore, the low heat input and welding temperatures were not sufficient to produce welds of high structural integrity, as seen from the very poor mechanical properties in (S23 and S24 were made at the same parameters as S10). is S15 (produced at the same welding parameters as S5, ), which was produced with a low oscillation amplitude. A moderately large pressure was applied to produce this weld, together with a relatively low power input. Hence two factors resulting in a cool weld (high material ejection rate and low power input) were applied simultaneously resulting in an exceptionally low fraction of δ-ferrite. is useful for explaining the behaviour of the anomalous welds in , it is difficult to use it to determine trends, between δ-ferrite and power input, across the whole of the parameter space. This is largely because the power input and burn-off rate are interdependent but tend to give opposite effects on the final δ-ferrite fraction. For example, if the welding pressure is increased the power input increases encouraging higher temperatures. However, the burn-off rate also increases with welding pressure (as discussed further in Section ) encouraging greater heat ejection and lower temperatures. It is therefore hard to predict the results from these competing influences without using a computer program to model the process, which, although would be very useful, is beyond the scope of this work.As mentioned earlier, σ phase formation has been observed in some regions of friction stir welded 304 austenitic stainless steel ). A number of welds (S13, S17, S19) were also tested for sigma phase by using optical microscopy, in accordance with test method A of ASTM A923-08, with no sigma phase detected in any of the welds. These welds were chosen because they covered a range of burn-off rates (from 1.4 to 4.3 mm/s; see ) and weld line δ-ferrite fractions (from 2% to 6%), whilst also exhibiting no microstructural defects.The variation of burn-off rate with different process parameters is explored in more detail in this section, as the burn-off rate has been demonstrated to have a significant impact on the microstructure of the weld. It was seen that burn-off rates increased almost linearly with welding pressure (). The relationship with frequency and amplitude, however, was very different, and there seemed to be a peak in burn-off rates at mid range frequencies and amplitudes (b and c). This relationship is similar to that seen with different rotation speeds during rotary friction welding The relationship between the pressure and the burn-off rate is not unexpected since applying high weld pressures will expel material more easily and at an increased rate. However, there does appear to be a limit as to how high burn-off rates can increase with increasing pressures. This is evident in the slight curvature of the burn-off rate/pressure curve in a, but is much clearer from an analysis of friction times (The effects of frequency and amplitude on burn-off rate may be a result of the differences in contact conditions, at the interface, with different welding conditions. At low frequencies and amplitudes the burn-off rate would be expected to be low because the low heat input would create a small amount of plasticised material and therefore produce a low burn-off rate when it is removed . In contrast, large layers of plasticised material can be removed from the joint almost as soon as they are formed at mid-range frequencies and amplitudes. This gives high burn-off rates as well as very short times at high temperatures, which limit δ-ferrite formation (Frequency and amplitude will both act in a similar way in increasing heat input, and therefore have similar impacts on burn-off rate, as both parameters affect the sliding velocity of the oscillating part (the sliding velocity along with the applied pressure being the key factors in producing heat input). highlights this point by again showing a peaked curve when plotting burn-off rate against maximum sliding velocity. However, there appears to be a slight dip in the curve at mid range sliding velocities (at about 400 mm/s). This indicates a slightly more complex relationship, and suggests certain combinations of amplitudes and frequencies are more effective at removing material than others, even if the amplitudes and frequencies combine to give the same sliding velocity.As mentioned previously, studies on the effects of welding parameters, especially applied pressure, on welding temperature have produced some contradictory results ) at the weld line. If different applied pressures were causing material to be expelled at different temperatures a similar level of δ-ferrite would be expected in welds made at the same pressure. This is because the sliding velocity is not likely to have a large effect on the temperature at which material is expelled. This reasoning leads to the suggestion that a time at temperature effect is the dominant factor in producing variations in microstructures with different applied pressures.The results of the present study also suggest that a change in burn-off distance has no effect on the maximum welding temperature. The variation of burn-off distance effectively allows a change in solely the welding time without the need to change other more significant parameters, e.g. applied pressure, frequency, etc., that can influence the power input and output. When comparing S16 and S11 (Sound linear friction welds, with cross weld tensile test failure in the parent material, could be produced in AISI 316L. The process, with regard to welding parameters, was demonstrated to be quite robust and fairly large changes in welding parameters did not, in most cases, affect the tensile strength, ductility or defect levels of the weld.A strong {1 1 1}〈 1 1 2 〉 type texture was seen at the weld line of a 316L linear friction weld. This is a typical shear texture in face centre cubic materials. Large variations in the fraction of δ-ferrite close to the weld line have been observed in welds produced by using different welding parameters. The control of δ-ferrite fraction by just varying welding parameters may make the LFW process advantageous for certain applications. A number of general conclusions were drawn from studying the effects of welding parameters on the welding process and on the final δ-ferrite fraction.The highest burn-off rates occur when applying a high welding pressure in combination with mid-range amplitudes and frequencies (about 30 Hz and 1.5 mm amplitude in 316L).A sole change in welding time, achieved through variation of burn-off distance, does not appear to have a significant effect on producing different microstructures with different welding parameters.Although these general conclusions were drawn from studying linear friction welded 316L, they should be applicable, possibly with some small to moderate variations, when welding other engineering alloys, such as typical aeroengine materials.where P is the power input, Ff is the maximum force parallel to the oscillation (i.e. in the reciprocating direction), and ω is the angular frequency, 2πf, where f is the frequency.The maximum value that the cos(ωt) term in Eq. can achieve is 1, which results in an equation for the maximum power input, Pm (Eq. The force in the reciprocating direction can be related to the applied force, F, through a friction coefficient, μ (Eq. If we assume that the friction coefficient, μ, is equal to 1 then Eq. results. As the friction coefficients, for the different welds produced in this study, should be very similar, Eq. should allow an adequate comparison of power inputs into the different welds. This should be true even though the assumption that μ is equal to 1 is not.Thermal bowing on steel columns embedded on walls under fire conditionsThe contact of steel columns with building walls is responsible for huge thermal gradients within its cross-section during fire. Current regulatory codes for fire design of steel members provide a formulation to assess the load-bearing capacity of these members assuming uniform temperature through the cross-section; however, this is not what happens in the major part of the cases in real structures where the columns are embedded on walls. The walls on one hand will provide a temperature reduction on the columns, which is somehow favourable in terms of its fire resistance, on the other hand the differential heating on the columns cross-section may lead to unfavourable stresses (bending moments) responsible for instability (thermal bowing). Considering that the structural behaviour of columns is strongly dependent of the second order effects this is an important phenomenon which may lead to a significant reduction on its fire resistance. This paper presents the results of a numerical study to assess the influence of the differential heating on the fire design of steel columns. New interaction axial force–bending moment diagrams for non-uniformly heated H steel columns are proposed.reduction factors of the effective yield strength for different temperaturesdesign value of the plastic bending momentThe contact of steel columns with the building walls is responsible for huge thermal gradients within its cross-section developed during fire Culver was maybe the first one to study the behaviour of steel columns under thermal gradients. In 1972, he presented a numerical study about the influence of the boundary conditions and distribution of temperatures along the length column on its behaviour in fire In 2010, another work on this issue was presented by Knobloch et al. In the sequence of the previous studies and taking into account the importance of the thermal bowing on the fire design of steel beam columns, the authors of the present paper decided to perform a study to develop new interaction axial force–bending moment (N–M) diagrams for non-uniformly heated H steel columns A large series of bare steel columns and steel columns embedded on walls was tested under fire conditions in the Laboratory of Testing Materials and Structures of the University of Coimbra The thermal action was applied by a gas-fired furnace, one side of the model, for the case of steel columns embedded on walls (a) and by an electric furnace, engulfing the element, for the case of bare steel columns (b). The standard ISO 834 fire curve was programed however not reached in the first five minutes on the electric furnace.The walls were perfectly connected to the columns using steel connectors. This way, a possible disconnection of the walls from the columns during the fire test was prevented. However, the walls did not contribute to the prevention of the lateral deflection of the steel member and it was assumed that the walls did not resist any out-of-plane forces.The results of these fire resistance tests were then used to calibrate a numerical model using a finite element analysis performed with Abaqus presents a scheme of the specimens used in the fire resistance tests on steel columns embedded on walls (a) and bare steel columns (b) with the location of the thermocouples. describe the cases studied numerically and the ones studied experimentally and used for comparison with the firsts.The specimens were made of HEA160 and HEA200 profiles, 3 m height, with end steel plates of dimensions 450 mm×450 mm×30 mm, all of steel grade S355. intend to represent the two possible orientations of the column in relation to the wall, parallel and perpendicular. Two different thicknesses of the walls were used to provide different insulation of the column to fire exposure. The two different H sections, intend to provide two different values of the slenderness of the columns.The reference “Exx” indicates the tests carried out on steel columns embedded on walls while the reference “Iyy” indicates the tests carried out on isolated bare steel columns. Walls with a thickness nearly the same or smaller than the columns width were considered. The walls thicknesses were chosen according to the commercial dimensions of the bricks. Two different orientations of the steel profile in relation to the wall surface were considered: web parallel and perpendicular to the wall surface. The reason for this choice is that a different behaviour was expected, since in the two cases, bending occurred around minor or major axis of the cross sections.The values of the slenderness λ were determined using the following formula:L0 is the buckling length of the columns calculated by: indicates the relevant axis, around which buckling of the columns occurs. Considering that the walls prevent the buckling on its plane the relevant buckling axis, when the profile is oriented with the web perpendicular to the wall is y–y, while when the web is parallel to the wall is z–z. intends to show the performance of the gas furnace, used for testing the columns embedded on walls, and the electrical furnace used for testing steel bare columns. The temperatures in the gas furnace and steel profile for a HEA160 steel column with the web perpendicular to a thin wall (b) are depicted. The gas temperatures in the gas-fired furnace follow very closely the ISO 834 fire curve while in the electric furnace present a slight delay up to 7 min of test and then follow closely this curve.A numerical model was built with solid elements from the Abaqus library of finite elements (a and b). A sequential analysis has been used in the numerical simulations to solve the thermo-mechanical problem. For each increment of time a thermal analysis was performed first. Then, the resulting temperature field was used as boundary condition for a subsequent mechanical analysis to obtain the thermal stresses and strains for the same increment. The two problems are uncoupled in the sense that the mechanical deformations do not generate any heat that affects the temperature field.The elements chosen for the columns were the C3D20RT while for the rest of the surrounding structure were the C3D8RT. The C3D8RT is an 8-node while the C3D20RT is a 20 node linear finite element with reduced integration, an hourglass control solid element and a first-order (linear) interpolation. These elements have one integration point, three degrees-of-freedom per node corresponding to translations and six stress components in each element output.The finite element mesh was generated automatically by the Abaqus programme and the side of the finite elements was 30 mm in the specimen, walls and upper beams of the 3D restraining frame and 100 mm in the columns of the 3D restraining frame (Imperfections were considered as an eccentricity equal to L/1000. For this particular topic no detailed sensitivity analysis was conducted. However, results of the column with and without bow imperfection were compared, and no significant differences were encountered. So, the value of L/1000, recommended in the literature was adopted, in particular in clause 4.3.3(7) of EN 1993-1-2.Concerning the interaction between the steel member and the walls, a “tie-constraint” of type master-slave was adopted. This interaction was proved to reproduce with accuracy the temperatures and behaviour observed experimentally, both in the column and walls. The boundary condition between the walls and the steel columns was considered as fully-constrained, due to the fact that connectors were welded in the column in the walls interface, and no slip was observed in the tests. The walls provided a restraint concerning the deflection in their plane but no other boundary condition or artificial restraint was introduced. The only restraint in the plane of the walls is the mechanical deformation of the wall.The thermal and mechanical properties at high temperatures of the concrete were defined according to EN1992-1-2(2004) The thermal boundary condition on the specimen was defined in Abaqus by two types of surface, namely, “film condition” and “radiation to ambient”, corresponding respectively to heat transfer by convection and radiation. On the unexposed side, a convection coefficient of 4 Wm2/°C and emissivity coefficients of 0.7 for the concrete and 0.8 for the steel, and on the exposed side a convection coefficient of 25 Wm2/°C and an emissivity of 0.7 were used for both materials. The values of the emissivity were determined by a sensitivity analysis, performed in the early stage of this work, to calibrate the model. Several values of this parameter were tested for concrete and steel, ranging from 0.6 to 0.8, and the adopted values were the ones with a better agreement with the temperatures in the steel surface, between experimental and numerical results. Lastly, a conduction coefficient of 200 W/m2K was adopted in the contact between the steel profile and the concrete.a–d present a view cut of the FE mesh of the numerical models studied of steel columns embedded on walls.The present section intends to show that there is a good agreement between experiments and numerical simulations to give credibility to the models and show their validation. In the following figures temperatures as well as restraining forces are depicted for a column embedded on walls and a bare steel column.a, mean temperatures for several cross-sections of a bare steel HEA 160 column are depicted, and in b, mean temperatures in the whole column for two HEA 200 columns embedded on walls, (with the web parallel and perpendicular to the wall) are depicted with time.As it may be observed in these graphs, a quite good agreement was obtained between numerical and experimental results, especially in terms of temperatures, but also in terms of restraining forces. In restraining forces in function of the time are depicted for a HEA 160 bare steel column with a stiffness of the surrounding structure of 125 kN/mm and a load level of 30% (a) and two HEA 200 columns embedded on walls with a stiffness of the surrounding structure of 45 kN/mm and a load level of 50% ( presents the evolution of the restraining forces for HEA200 (b), bare and embedded on walls steel columns, in function of time. The values are adimensional refered to the initial applied load. The fire resistance (critical time) is here defined as the instant when the restraining forces reach again the initial applied load.Considering that the colapse occurs when the restraining forces after increasing up to a maximum decays and reaches the initial applied load, it can be clearly observed in (a and b) that steel columns embedded on walls attained higher fire resistances than isolated bare steel columns. The fire protection of the walls to the columns that reduces the steel temperatures plays here a higher influence than the fire-induced bending moments resulting from the diferential heating. As explained before the mechanical interaction between the walls and the columns, only prevented deflection in the plane of the walls. In the other direction, the walls deflected along with the column. The fire-induced bending moments were solely developed in the steel material. Also, it is observed that the variation of restraining forces was lower than in bare steel columns.It is interesting to observe that the phenomenon of thermal bowing overlaps the expected behaviour due to the values of slenderness. It was expected that a column with higher value of slenderness present a worst fire behaviour, but this is not the case. In fact, colums with the web perpendicular to the wall surface (lower slenderness) presented lower fire resistance. For example, comparing test E08 (λ=42.2) column with the web parallel to the wall surface with test E09 (λ=25.4) column with the web perpendicular to the wall surface (a), it is observed that test E08 presents a higher fire resistance than test E09, despite of the higher value of slenderness. The same conclusion is observed comparing test E03 with test E04 (b) where higher fire resistances are observed in cases with higher slenderness.For HEA200 steel columns, the embedding on walls, increasing the fire resistance. The fire resistance for the steel column embeded on walls (test E03) was 21.4 min while for the isolated bare steel column (test I20) was 8.3 min. Also, it is observed that the increasing of restraining forces can be as low as 0.4% for test E04 instead of 4% for the isolated bare steel column (test I20), i.e., 10%. (For the HEA160 steel columns, a fire resistance of around 20 min was achieved for tests E05 and E06 for columns embedded on walls. In terms of restraining forces, the lowest value observed is 1% for test E06 (b). This result was expected because in test E06 the steel profile was completely embedded on the walls.Tests E11, E06, E09 and E04 on columns embedded on walls and with the web perpendicular to the wall surface provided lower restraining forces.Tests E03, E04, E05 and E06, where columns were completely embedded on walls, presented higher fire resistance, showing the beneficial effect of the walls on protecting the columns.The buckling of steel columns embeded on walls with the web paralel to the wall surface (tests E05, E03, E08 and E10) is more abrupt than in the ones with the web perpendicular to the wall surface (tests E04, E09, E06 and E11).The analysis of these graphs lead to the conclusion that the failure of isolated bare steel columns is significantly different form the failure of steel columns embedded on walls because the firsts can be abrupt when comparing with the seconds. it is observed that the axial displacements and lateral deflections were very similar in tests E04 and E09 (HEA200), however the firsts were smaller than the seconds in each test. The axial displacements on the bare steel columns (I20) were higher than in the columns embeded on walls (E04 and E09) while the lateral deflections were similar. The higher axial displacements on the bare steel columns are explained by the higher surface of fire exposure compared to the ones embeded on walls.(a and b) the behaviour of a steel column embedded on walls is represented. In the beginning, the displacement is towards the side of the furnace, i.e., the side of the thermal action, after which there is an inversion causing the column to move to the opposite side. Also, rotations on top and bottom of the columns suffer the corresponding inversion. This figure shows the deformed shape of an H steel column with the web parallel to the wall surface submitted to a fire on the left side. a is referred to the beginning of the test, in which the column will deflect towards the hot side, and b is referred to the end of the test, in which the column will deflect to the cold side. This phenomenon known as “thermal bowing” was already described in the introduction section of this paper. The inversion of bending moments, accompanied with the inversion of deflections is typical of heated columns with restrained thermal elongation submitted to differential heating. represents the behaviour of an H steel column with a thermal gradient in the direction of the web (b). In this figure the yy and zz axis are according to the ones considered in EN 1993-1-1 (2005) b depicts the inversion of bending moments along the column length during the time of the test.a–c shows the behaviour of an HEA160 steel column embeded in a thin wall (test E11) and with the web perpendicular to the wall surface.These curves were derived from the aproximated formula from EN 1993-1-1 (2005) which may be arranged in the following mannerwhere ky,θ is the reduction factor (relative to fy) for effective yield strength at elevated temperature given in EN 1993-1-2 (2005) These curves were derived from the EN 1993-1-1 (2005) which may be arranged in the following manner, for different uniform temperatures:, the curves of the axial force–bending moments diagrams of the Eurocode 3 formulation are compared with the real resistance of the cross-section, considering the reduction of the strength in the heated portion of the steel profile for the case of the web parallel to the wall surface. it may be observed that the continuous lines representing the real resistance of the cross-section are always outside the envelope defined by the EN 1993-1-1 (2005) The major outcomes of this paper are the proposals of new axial force–bending moment diagrams, for the design of steel columns unevenly heated, and to give insights to explain the phenomenon of thermal bowing in restrained steel H columns embedded on walls. But the purpose of the work was to evidence that considering uniform temperature within the cross-section may be very un-economical, if the temperature in the exposed part of the profile is adopted. Other approach would be to consider a mean temperature within the cross-section, but in this case, the thermal gradients should be assessed. A geometrical material non-linear analysis of the behaviour of columns under the ISO 834 standard fire was carried-out to ascertain whether the phenomenon of thermal bowing in steel H columns embedded on walls is beneficial or detrimental for the columns. It was concluded that the contact with the walls is responsible for a great reduction in the temperatures of the cross-section, leading to higher fire resistances than the ones observed in isolated steel columns.One of the conclusions of this work is that the thermal bowing, provoked by the differential heating, is responsible for a change in the usual fire resistance of columns. In fact, it was observed that columns with a higher slenderness presented higher fire resistance than others with lower slenderness, due to this phenomenon. Columns with higher values of slenderness, in the plane perpendicular to the wall surface, presented higher fire resistance.The detailed analysis of the finite element study allowed the understanding of the stress-strain state experimented by the several parts of the H steel profile during the fire. Using a specific case of a column embedded on walls, it was possible to observe the inversion of bending moments and collapse mechanism with the formation of plastic hinges on bottom, top and mid-height of the column.The first conclusion was that the failure of steel columns embedded on walls is significantly different from the failure of isolated steel columns. The criterion of considering the colapse as the instant when the axial force after increasing up to a maximum decays and reaches the initial value seems to be inadequate to the columns embedded on walls, due to the fact that in these cases failure is not so abrupt, and a great resistance is observed for a long period of time. It was observed that these columns behave much more like beam-columns failing by bending, provoqued by “thermal bowing”, instead of failing by buckling. The inversion of bending moments and consequent lateral deflections from one side to the other, as well as the formation of plastic hinges, due to the plastification of several sections of the column, bottom, top and mid-height, leads to the conclusion that the failure of the columns occurs by bending. The typical behaviour of columns failing by a phenomenon of instability caused by an increase of the internal efforts due to the deformed shape of the column was not observed.The main conclusion of this work is that the use of EN 1993-1-1 (2005) for the design of steel-beam columns using plastic interaction diagrams axial force–bending moment with uniform temperature equal to the temperature attained in the exposed part of the steel profile is always very conservative.Effect of Ta on glass formation, thermal stability and mechanical properties of a Zr52.25Cu28.5Ni4.75Al9.5Ta5 bulk metallic glassThe effect of Ta on glass-forming ability, crystallization behavior and mechanical properties of Zr52.25Cu28.5Ni4.75Al9.5Ta5 bulk metallic glass (BMG) is investigated. The solubility of Ta in the Zr-base BMG alloy depends on the arc melting conditions. 3.2 at.% Ta dissolve in the alloy inducing an increase of about 20 K in both glass transition temperature and crystallization temperature of the BMG. However, Ta does not significantly change the extension of the supercooled liquid region. The remaining Ta particles in the master alloy may induce a composition-segregation layer around the particles upon subsequent casting. This further induces the crystallization of Zr2Cu that deteriorates the ductility of the samples. The compressive strength and ductility of the as-cast 3 mm diameter Zr52.25Cu28.5Ni4.75Al9.5Ta5 samples are improved in comparison with the Zr55Cu30Ni5Al10 BMG alloy. The fracture plane of the present alloy has an angle of 31–33° with respect to the stress axis, which remarkably deviates from the maximum shear stress plane. The improvement of the mechanical properties and the peculiar fracture feature for the Zr52.25Cu28.5Ni4.75Al9.5Ta5 BMG alloy can be attributed to the effect of dispersed Ta particles.As shown in recent comprehensive studies on bulk metallic glasses (BMGs), the glass-forming ability, stability, phase transformations, microstructure, deformation mechanisms and mechanical properties for Zr-base BMGs are quite well understood An alloy with nominal composition of Zr52.25Cu28.5Ni4.75Al9.5Ta5 was designed by adding 5 at.% Ta into a well known Zr55Cu30Ni5Al10 alloy, which was reported to exhibit large glass forming ability Due to its much higher melting temperature, Ta is difficult to mix with the Zr-base BMG alloy. For getting a homogeneous master alloy, different arc melting procedures are applied for the present study. One is directly arc melting the mixture of pure Zr, Cu, Ni, Al and Ta, and the other one is arc melting pure Zr and Ta in a first step to produce a supersaturated intermediate binary Zr-Ta alloy, followed by arc melting the mixture of the intermediate alloy and the other pure metals. We have compared the master alloys prepared by the different procedures and found no difference in Ta distribution. However, repeated arc melting significantly affects the size and the distribution of the remaining Ta particles in the master alloys. shows the size and the distribution of Ta (white particles, as confirmed by electron microprobe analysis) in the master alloy. After three times arc melting, Ta particles with a size of about 5~20 μm are visible (). After five times arc melting, the Ta particle size is reduced to about 0.5~1 μm (). Some larger Ta particles can be observed in the bottom of the ingot near the water-cooled copper hearth (). This inhomogeneous Ta-distribution can be avoided by cutting the button into pieces between each arc melting procedure. Once the Ta particles remain in the master alloy, their size and distribution keeps unchanged in melt-spun ribbons or cast bulk samples because the subsequent induction melting cannot re-melt the Ta particles.The master alloy used for producing the melt-spun ribbons was determined to contain 3.2 at.% Ta dissolved in the matrix. The remaining Ta exists in form of particles (micrograph not shown) in the as-quenched ribbons, which is indexed in the XRD pattern shown in . DSC analysis indicates that the glass transition occurs at about 705 K, and crystallization starts at about 785 K for the as-quenched ribbon, thus ΔTx=80 K ((a)). Compared to the Zr55Cu30Ni5Al10 BMG ), dissolution of 3.2 at.% Ta in the glass does not change ΔTx. Ta, however, causes a shift of Tg and Tx to higher temperatures. After heating the ribbons up to 798 and 873 K, respectively, Zr2Cu precipitates predominately at 798 K as indexed in (b). The stable crystalline phases consist of Zr2Cu, Zr2Ni and Zr3Al after complete crystallization at 873 K as shown in The size and the distribution of the Ta particles depend on the procedure used for preparation of the master alloy, and the diameter of the cast rods only affects the as-solidified matrix. This was confirmed for as-cast 3 and 5 mm rods. XRD analysis indicates that the microstructure contains a glassy phase and intermetallic Zr2Cu besides Ta particles, as shown in . Comparing the main peaks of Zr2Cu for the different samples reveal that the volume fraction of Zr2Cu in the 3 mm diameter rod is smaller than in the 5 mm diameter rod. It is reasonable to assume that large samples (lower cooling rate during solidification) exhibit more crystalline precipitates in the glassy matrix. Because of the different volume fractions of crystalline phase formed in the matrix, the residual glass has a different composition in the 3 and 5 mm rods. This can be further represented in the DSC curves shown in . The exothermic DSC peak at 786 K for the 3 mm rod shifts by about 7 K from the peak temperature of 793 K determined for the ribbon. The exothermic DSC peak for the 5 mm rod decreases even by about 9 K from the peak temperature of the ribbon, because more Zr2Cu precipitates in 5 mm rod compared to the 3 mm rod. The characteristic transition temperatures for the differently prepared Zr52.25Cu28.5Ni4.75Al9.5Ta5 alloys are summarized in shows the as-cast microstructure of the Zr52.25Cu28.5Ni4.75Al9.5Ta5 5 mm rod. The white Ta particles dispersed in the matrix originate from the master alloy. Since the Zr2Cu precipitates are very fine shows a magnified image where a Ta particle, the area around the Ta particle and the matrix are marked by A, B and C. Electron microprobe analysis indicates that A is pure Ta, the average composition is Zr51.6Cu27.6Ni3.0Al15.8Ta2.0 for the area B, and Zr54.8Cu28Ni5Al9Ta3.2 for the matrix C. The Ta particles in master alloy seem to cause the formation of area B during solidification. Upon further heating the sample up to 973 K and holding there for 10 min, the Ta particles and their surrounding area on the micrograph remain unchanged (), but a crystallization occurs in the glassy matrix ( shows the room temperature compressive stress-strain curves of the Zr52.25Cu28.5Ni4.75Al9.5Ta5 samples with 3 and 5 mm diameter at a strain rate of 1×10−4s−1. For comparison, the stress-strain curve of Zr55Cu30Ni5Al10 metallic glass sample taken from reference SEM observations show that the fracture of the present alloy under uniaxial compressive loading always occurs in a shear mode, as seen in . The compressive fracture surface is inclined under an angle θ to the stress axis and can be measured as marked in the figures. The fracture angles θ between the stress axis and the fracture surface are equal to 31 and 33° for the two specimens with 3 mm diameter. However, the samples with 5 mm in diameter fracture to several parts after compressive test. As shown in . This observation further proves that the Ta particles in the compressive sample are homogeneously dispersed in the matrix.For most metallic glasses, it was reported that the fracture angle θ is basically along the maximum shear stress plane with an angle of 45° to the stress axis Further observations show that the typical feature on the fracture surfaces is a vein-like structure, as shown in . This vein-like structure is consistent with the observations in most metallic glasses , which is similar to the fractography of the (nanocrystalline+glass)/dendritic crystalline composites (d). Meanwhile, there are many regions with severe plastic deformation induced by the Ta particles, as shown in . This indicates that the Ta particles can effectively block the shear deformation of the metallic glassy matrix, and furthermore may improve the strength and possibly the ductility of the samples.The melt-spun Zr52.25Cu28.5Ni4.75Al9.5Ta5 ribbon exhibits a glass transition temperature of 705 K and a crystallization temperature of 785 K at heating rate of 20 K/min. Both characteristic temperatures are about 20 K higher than those of Zr55Cu30Ni5Al10 metallic glass. About 3.2 at.% Ta causes a significant increase in stability of the glassy phase. The effect of Ta on the stability for this alloy is consistent with that of Zr59Cu18Ni8Al10Ta5For the bulk cast rods, in the case of partially precipitating intermetallic Zr2Cu compound in the glassy matrix due to inadequate cooling rate or inhomogeneous nucleation induced by the existing crystalline particles, both the crystallization temperature, Tx, and the extension of the supercooled liquid region tend to decrease with increasing volume fraction of Zr2Cu crystals. The lower Tx corresponds to a lower thermal stability of the glassy matrix against crystallization. This can be attributed to the changes of the composition of the glassy phase and the Zr2Cu precipitates that may act as nucleation site to induce heterogeneous nucleation.It seems that the solubility of Ta in Zr-base BMG alloys is very different for various combinations of constituents in the alloys. Xing et al. On the other hand, our results show obvious evidence that Ta particles can induce a composition-segregation around the particles during solidification. In contrast to W and ceramic particles The deformation and fracture mechanisms of BMGs have been widely investigated in the past decades . However, for the present BMG composite, the fracture angle (31–33°) is obviously smaller than the common value of 42–43°, as shown in . This indicates that the fracture mechanism of the present BMG composite should be different from single-phase metallic glasses due to the interactions among the micrometer-sized Ta particles, fine Zr2Cu precipitates and the glassy matrix. To understand the special fracture features of such composites, the normal stress has been considered as important contribution for the deviation of the fracture angle from the maximum shear stress plane. Considering the critical shear fracture stress τC on the plane under a normal compressive stress σ, one can generally write Here, μ is a constant of the material. For a uniaxial compressive specimen, the normal and shear stresses σθ and τθ on any plane under the uniaxial compressive loading can be easily calculated from the following equations:Here, σ is the uniaxial compressive stress. By substituting σθ and τθ into , one can get the critical fracture condition as below:It is apparent that the fracture stresses, σF, depends on the shear angle θ. There is a minimum value of the fracture stresses at different shear angles. On the other hand, the specimens should preferentially fracture along a favorable shear plane at the minimum applied stresses. Therefore, the minimum applied fracture stresses, σF, must correspond to the measured fracture angles (as illustrated by ). Thus, the following equation can be obtained:From the experiments, θ=42∘ for the single-phase BMGs (as in ), and θ=32∘ for present samples. Therefore, from , the two constants μmg and μcp for a single-phase BMGs and the present BMG composite can be calculated as follows:μcp (=0.49) is obviously larger than μmg (=0.11), therefore, the deviation of the fracture angle from 45° is more pronounced for the composite (θcp=32°) than for the metallic glass (θmg=42°). This indicates that the normal compressive stress should play a more remarkable role in the fracture process of the present composite than the fully glassy specimen. Therefore, we can consider the two constants μcp and μmg as the structure factors of the normal stress on the shear fracture of the two materials. On the other hand, as shown in , the interactions among Ta particles, Zr2Cu precipitates and the glassy matrix have been observed during shear fracture of the present composite. These interactions should contribute to the effect of the normal stress on the fracture processes of the specimen. Therefore, from the viewpoint of the microstructure, the constant μcp can be regarded as an external reflection of the interactions among Ta particles, Zr2Cu precipitates and the glassy matrix during deformation. In turn, those interactions will affect the deformation mechanism of the metallic glass composite, furthermore improving its mechanical properties, such as strength and ductility. lists the strength data for different Zr-based BMGs available so far In the present work, the effect of Ta on the phase transformation and mechanical properties of the Zr-based BMG can be illustrated as in . The volume fraction and the grain size of the Zr2Cu precipitates can be controlled by the cooling conditions. In addition, the volume and the size of the Ta particles can also be adjusted by the control of composition and the melting conditions, as discussed in the sections above. When the specimens of the composite are subjected to the uniaxial compressive loading, the interactions among Ta particles, Zr2Cu precipitates and the glassy matrix will affect the deformation and fracture mechanism in comparison with the fully glassy alloy. show some direct interactions among the Ta particles, Zr2Cu precipitates and the glassy matrix, and the consequent change in the fracture mode can be seen in . This indicates that these interactions have changed the constant μ of the composite and, furthermore, affect the mechanical properties. In essence, the change in fracture mode reflects the change in the microstructure of the composite, which was induced by the dissolved Ta and the Ta particles during cooling. From the present work and the results of Hirano et al. Refractory Ta is hard to dissolve into Zr-base BMGs. The solubility of Ta depends on arc melting conditions when the Ta-content is below about 5 at.%. To improve the dissolution of Ta and its homogeneity in the Zr-base BMG, a long arc melting time is needed. The size and the volume fraction of Ta particles present in the master alloy can be controlled by using appropriate arc melting conditions. These Ta particles can be withheld upon subsequent casting and act as a strengthening phase in Zr-base BMGs.About 3.2 at.% Ta dissolved in the alloy increase Tg and Tx by about 20 K. The Tg/Tm and ΔTx values of the Zr-base BMG alloy, however, do not change significantly. 3.2 at.% Ta only improve the thermal stability of the Zr-base BMG matrix, but do not change its glass forming ability significantly.With increasing diameter of as-cast samples, the volume fraction of Zr2Cu precipitated during solidification increases, which deteriorates the ductility of the samples. The precipitation of Zr2Cu partially depends on the decrease in cooling rate during casting with increasing the sample diameter. The existing Ta particles can induce a composition-segregation layer around the particles, which may further lead to the crystallization of Zr2Cu during solidification.Uniaxial compression tests show that Young’s modulus increases from 70 GPa (Zr55Cu30Ni5Al10) to 90 GPa (3 mm diameter rod) and 103 GPa (5 mm diameter rod) for the present alloy. The specimen with 3 mm diameter clearly displays strain hardening behavior and the plastic strain before failure reaches about 1.2%, which is higher than that of single-phase Zr55Cu30Ni5Al10 BMG. Meanwhile, the fracture plane of the Zr52.25Cu28.5Ni4.75Al9.5Ta5 alloy has an angle of only 31–33° with respect to the stress axis, which is significantly lower than the typical value of 42–43° observed for single-phase BMGs. The difference in the mechanical properties and the fracture mechanisms between BMGs and the present BMG composite can be explained by the interactions among Ta particles, Zr2Cu precipitates and the metallic glassy matrix.Neural networks applications in concrete structuresThis paper presents and discusses the applications of neural networks in concrete structures. It aims at introducing neural networks applications in structural design. The paper covers two applications of neural networks in concrete structures. Backpropagation networks are chosen for the proposed network, which is written using the programming package MAT-LAB. The overall results are compared and observed for the performance of the networks. Based on the applications it was found that neural networks are comparatively effective for a number of reasons, which include the amount of CPU memory consumed by neural networks is less than that consumed by conventional methods and their ease of use and implementation, neural networks provide both the users and the developers more flexibility to cope with different kinds of problems.The design of structures is an iterative process where the designers assume a design then go through the analysis process. Next the designer needs to use the design rules of the adopted design standard to design the structure. Next the designer needs to compare the assumed and the calculated designs. Ideally the two designs should be the same. In reality they are seldom the same, hence the designer needs to take the new design and go through the process of analysis and design again. The iterations should continue until the difference between the assumed design at the beginning of the step and the output from the same step is negligible. This lengthy process has led to the adoption of optimisation techniques. These techniques have been implemented successfully in many structural systems. These optimisation techniques are usually lengthy and complicated to implement, hence putting more burden on the designer.One of the techniques to reduce the resources and the time required for the design process is to store many optimum designs and train a neural network for the design. Thus, the neural network will come up with a design based on its training rather than conducting a full design from scratch. In this paper, the optimum design of simply supported reinforced concrete beams is introduced in simple equations form. Next, these equations are used to calculate the optimum design of beams under different loading and configurations. These optimum designs are used to train a neural network, which is established specifically for the optimum design of beams.As a second application, the design of fibre reinforced concrete beams is presented and a neural network is developed for the optimum design of fibre reinforced concrete beams. Examples are solved and compared with conventional designs.The cost function of a beam typically includes the costs of concrete, the cost of reinforcement and the cost of formworks as illustrated in For simply supported beams it is sufficient to base the design only on the section at mid-span, which produces maximum bending moment, and near a support which produces maximum shear force, because most designs determine the maximum bending moment and maximum shear. The amount of longitudinal reinforcement governed by mid-span flexural considerations may be reduced towards the supports by curtailing some of the reinforcing bars as the bending moment envelope may allow. On the other hand, the spacing of stirrups may be adjusted to the requirements of shear force envelope. Finally, the reinforcement details will be subject to the requirement of the design standard AS3600 In this problem, the objective function is the cost unit length of a reinforced concrete beam, which is given as the following relationship:where Cc is the cost of concrete per unit volume; Cs is the cost of steel per unit volume; Cf is the cost of formwork per unit peripheral area; b is the width of the beam; d is the effective depth of the beam; d1 is the cover to the centroid of tensile reinforcement and As is the cross-sectional area of tensile reinforcement.The constraints for the optimisation problem are the flexural strength, which can be represented aswhere fc′ is the compressive strength of concrete; fy is the tensile strength of steel; p is the steel ratio, given by p=As/bd; φ is the strength reduction factor, AS3600 recommends φ=0.8 for flexural and Mu is required moment capacity.The constraints on the lower and upper limits of steel ratio, respectively, can be written aswhere pmax and pmin are, respectively, the maximum and minimum allowable reinforcement in a cross-section. The side constraint that is incorporated with the means of limit value of maximum depth hm of the beam is written asThe optimisation problem is to minimize equation . The problem can be solved by the Lagrange multipliers technique Using Lagrange multipliers technique the following expressions are obtained:The above equations are used to build a database for the different designs for the beams and then they are used to train the neural network.Concrete usually presents low tensile strength and insufficient ductile behaviour. Because of these deficiencies prestressing has been applied in concrete members. However, the cost of production and equipment as well as the cost of labour for prestressing are comparatively high. Alternatively, addition of steel fibres into concrete has been found to increase tensile strength and improve ductile behaviour of concrete members with relatively low cost. Steel fibre reinforced concrete (SFRC) is a concrete made of hydraulic cement with aggregates and is reinforced with discontinuous discrete steel fibres. In typical applications, ductile steel fibre is randomly dispersed throughout the brittle low strength concrete to improve tensile strength, ductility and fracture toughness of reinforced concrete.In late 1960’s and early 1970’s steel fibre concrete had been extensively studied and tested for the improvement of concrete strength as well as to reduce sizes and weight of concrete members. The early use of steel fibrous concrete includes building slabs, road and airfield pavements. However, it had very little distribution to structural design and construction at its early use. This fact is mainly due to the lack of its analysis and design methods as well as the relatively low amount of study on steel fibre Since 1980’s, there have been several vast developments on steel fibre concrete. Besides the improvement of tensile strength and ductility, a number of recent investigations have shown that steel fibres also have the ability to increase the flexural strength, bending moment capacity, impact resistance, energy absorption, and shear strength to reinforced concrete beams. Swamy and Al-Ta’an This section presents the optimisation of reinforced fibrous concrete beams in accordance with AS3600.The basic design assumptions of rectangular reinforced fibered concrete is represented in The nominal flexural strength of fibrous concrete simply supported beam is given as the following relationship where Mn is the nominal bending moment of cross-section, As is the area of steel reinforcement, a is the depth of rectangular stress block, σt is the tensile stress in fibrous concrete, b is the beam width, d is the distance from the top fibre to the centroid of the steel bar, h is the height of the beam, and β1 is the factor of 0.65–0.85, depending on the concrete compressive strength The ductility requirement specifies that the reinforcing bar area, As, should be less than 0.75Asb, where Asb=pb(bd) and pb is the steel ratio at balance condition. The maximum reinforcement is given byThe effective tensile strength of fibrous concrete (MPa) can be aswhere Fbe is the bond efficiency of fibres varies from 1.0 to 1.2 The ultimate shear strength of a fibre reinforced concrete beam with web reinforcement can be expressed aswhere Vn is the nominal shear stress of fibre reinforced concrete section, Vf is the shear stress of fibrous concrete, Vs is the shear stress due to web reinforcement, and f′t is the tensile strength of concrete based on splitting cylinder test.The objective function Z for steel reinforced fibrous concrete beams subjected to bending and shear can be formulated aswhere Cc is the unit cost of concrete, Cs is the unit cost of reinforcing bar, Cf is the unit cost of steel fibres, Cu is the unit cost of labour, is the applied moment, S is the centre-to-centre spacing of shear reinforcement.For a given problem, values of f′c, fy, the width and the maximum height of concrete section are known. After the completion of the optimisation process, the optimum value of area of steel, depth of steel, beam width, area of stirrups, spacing of stirrups, moment capacity, resisted shear and minimum value of total cost are obtained.The developed database for the optimum design of beams, which are based on the equations above, were used to train a neural network. The design input to the problem includes: applied moment, ; concrete strength, f′c; yield strength of steel reinforcement, fy; beam width, b; maximum depth of beams, hm; unit cost of concrete, Cs; unit cost of steel reinforcement, Cs; and unit cost of formwork, Cf. The design output includes: optimum steel ratio poptimum; optimum area of reinforcement, As(optimum); optimum effective depth of beams, doptimum; and optimum unit cost of beams Coptimum.Two alterative networks were considered. In the first case, the cost of concrete, cost of steel and cost of formwork are not parts of inputs for a network. They are taken as fixed values, which are specified by the user. The neural network is presented in The network parameters are: number of training samples is 550, number of input layer neurons is 5, number of hidden layer neurons is 10, number of output layer neurons is 4, type of backpropagation is Levenberg–Marquardt backpropagation, activation function is Sigmoidal function, learning rate is 0.01, number of epochs is 3874 and sum-square error achieved is 0.0001.The network was tested with 50 samples. It has an average error of 2.71%. The actual outputs and the outputs from the networks of each sample are graphically represented in and the decrease in sum-square error is presented in In the second alternative, the cost of concrete, cost of steel and cost of formwork were the considered inputs. Unit cost of concrete and the unit cost of steel reinforcement is $129/m3 and $1075/t Network parameters used are as follows. The number of training samples is 550; number of input layer neurons is 8; number of hidden layer neurons is 10; number of output layer neurons is 4; type of backpropagation is Levenberg–Marquardt backpropagation; activation function is sigmoidal function; learning rate; 0.01; number of epochs is 3000; sum-square error achieved is 0.08. The neural network is presented in The network had been tested with 50 samples and yielded the average error of 6.1%. The results are presented in and the decrease in sum-square error is presented in In order to minimise tensile reinforcement, shear reinforcement, depth and total cost of steel fibrous reinforced concrete beams, a neural network is constructed. Simply supported rectangular beams design are implemented in accordance with AS3600.The 14 input variables are: applied moment , N; concrete strength (f′c), MPa; yield strength of steel reinforcement (fy), MPa; initial guessed area of tensile reinforcement (As), mm2; length of steel fiber (lf), mm; diameter of steel fiber (df), mm; percent by volume of steel fibre to concrete (pf); minimum depth of beams (dmin), mm; maximum depth of beams (dmax), mm; minimum width of beams (bmin), mm; maximum width of beams (bmax), mm; maximum reinforcing index by volume of steel fibre (RImin); and minimum reinforcing index by volume of steel fibre (RImax).It is assumed in the design that a minimum of shear reinforcement is required. The algorithms will search for the minimum of objective function in the space of six design variables (outputs). These are: optimal area of tensile reinforcement (As), mm; optimal width of beams (b), mm; optimal depth of beams (d), mm; optimal spacing of stirrup (S), mm; ultimate flexural strength of beams (Mu), kN m; and total cost of beams, $/m.The network has 14 input neurons, 8 hidden neurons and 6 output neurons. The network parameters are: number of training samples is 604; number of input layer neurons is 14; number of hidden layer neurons is 8; number of output layer neurons is 6; type of backpropagation is: Levenberg–Marquardt backpropagation; activation function is Sigmoidal function; learning rate is 0.01; number of epochs is 450; and sum-square error achieved is 0.001.The network used in this application had been tested with 100 samples and yields an average error of 6.68%. present comparison between conventional design and designs obtained from the neural network.Five different learning algorithms of backpropagation are considered in this study. Each of these algorithms has been tested with the problems in this study. Pure backpropagation is found to be extremely slow in learning. Backpropagation with momentum and with adaptive learning can be said to be the solution to a slow network. However, pure backpropagation with small learning rate shows a low possibility of oscillation. Backpropagation with momentum and with adaptive learning tend to oscillate after a large learning set is used. Backpropagation with Levenberg–Marquardt updating rule and fast learning backpropagation were found to have capability to solve all the problems. The distinction of backpropagation with Levenberg–Marquardt updating rule to other algorithms is that backpropagation with Levenberg–Marquardt updating rule consumes a significantly large amount of memory. In most cases, it was found that backpropagation Levenberg–Marquardt updating rule spent fewer epochs and less time to converge. For example, when the first application was tested with fast backpropagation, the network took 50,000 epochs to converge with an error of 0.02 and consumed 7 h. When Levenberg–Marquardt updating rule was used, the network took 800 epochs to reach 0.025 of error with 5 h of time consumed in the same platform. According to Demuth and Beale The backpropagation simulator in this study is restricted to two hidden layers, which yields a total of four layers. Therefore, the observation of the effect of the number of hidden layers of networks on their performance is restricted to two layers. From this study, each problem was tested with both one hidden layer and two hidden layers and it did not show any significant difference in terms of accuracy but it did show the difference in terms of time required for learning. For example in the optimisation of SFRC, there are 14 neurons at the input layer, eight neurons at the hidden layer and six neurons at the output layer. It is found that when one hidden layer was added, the time consumed increased from 6 to 17 h to reach an error of 0.001. Therefore, all optimal networks in this study consist of one hidden layer.The number of samples is another important factor that determines how well a network learns. A large number of samples usually provides a network more necessary features to capture because there are more cases available for a network to differentiate. The number of samples usually depends on the characteristics of a problem. In some cases, a large amount of samples does not guarantee that a network can learn better than with smaller samples. This situation was found in the first application. Initially, 1000 samples were used to train a network. Then 100, 200, 300, 400, 500, 700, 800, 1000 and 1400 of sample were tested and the results show that the average of percent error of the network that was tested by 200, 500 and 1000 were not much different. This study assumes that the major reason for this situation is because the necessary features of that application are easy to be captured by the learning algorithm, even though the network architecture is relatively complex.However, for applications that have more complex network architectures, such as the second application, the number of samples did affect the performance of the network itself. The test started by using 100, 200, 400, 500, 550 with fixed number of epochs and the result show that the number of samples of 100 did not lead the network to converge. When the number of samples was increased, the network had the ability to reach a lower error goal. It was also found that training a network with fewer samples often led to early convergence. This is because the goal error had reached but some features were not captured. When that network was tested, it gave inaccurate output. Apart from increasing the number of training samples, decreasing error goal and increasing the number of epochs can be done to obtain more accuracy.It is found that there is a trade off between the performance of a network and time consumed. The performances of a network are found to increase with the suitable increase of the number of samples, learning time and the number of hidden layer neurons. Meanwhile, the increase of these parameters also increases consumed time.This paper studies and discusses new forms of computing, neural networks, which are increasingly used in various areas including science and technology, education, business and military. In civil engineering fields alone, neural networks are extensively investigated because they show some special features to extract significant information from a massive set of data and the ability to cope with ill-defined problems, which are common problems in civil engineering applications.Beam structures are chosen for this study and the area involved is concrete beam design and cost optimisation. Beam design aims to estimate the best dimensions, depth and width of its cross-section, and the cross-sectional area of reinforcement based on the Australian Standard AS3600. Cost optimisation of concrete beam is to minimise the cost of material such as concrete, reinforcement and formwork, by optimising the beam’s dimensions and its area of reinforcement, while satisfying all the requirements, namely strength and serviceability. The second application is the optimum design of fibre reinforced concrete beams.Several problems were encountered during training the network. The most significant problem was found to be the uncertainty of outputs due to the great difference in values between output variables. Obviously, this problem occurs in the second application for which the range of one output is significantly small while the range of another output is extremely large. This situation causes the output with the greatest range to have the highest effect on the sum-square error. Therefore, the outputs with greatest ranges from the network are close to the output from conventional method, while the outputs with smallest range from the network behave differently. The effect of this problem is usually diminished by increasing the network’s learning time, adjusting learning rate and reducing error goal.From this study, neural networks are found to be superior to existing conventional methods in many ways. It was found that neural networks reduce the overall time required for implementations by a significant amount when compared with existing conventional methods. One of the major reasons that contribute to this advantage is that each network requires the solution of relatively simple set of equations to solve all kinds of problems while conventional methods may use more elaborate set of equations. Moreover, the performance of each proposed network includes the accuracy of outputs and the ease of use is satisfactory. With careful implementations, neural networks will be proficient to solve a vast number of structural engineering problems.Relationship between texture and low temperature superplasticity in an extruded AZ31 Mg alloy processed by ECAPThe development of low temperature superplasticity and texture is examined in an AZ31 Mg alloy after extrusion and processing by equal-channel angular pressing (ECAP). It is demonstrated that an elongation of ∼460% may be attained at a temperature of 150 °C, equivalent to 0.46 Tm where Tm is the absolute melting temperature. This result demonstrates the potential for achieving low temperature superplasticity. The experimental results show that the mechanical properties of the alloy are influenced by the different textures present after extrusion and after extrusion and subsequent processing by ECAP.The increasing shortage of natural resources, together with the world-wide implementation of stricter environmental regulations, is making it necessary to produce and utilize a range of light-weight metallic alloys for the transportation industry. Magnesium is currently the lightest metal in use for structural applications. However, whereas there has been a steady growth in the use of magnesium in the electronics industry, due primarily to the need for light-weight parts for lap-top computers and consumer electronic products Equal-channel angular pressing (ECAP) was used to process a magnesium alloy where this procedure was selected for three reasons. First, ECAP is a processing technique involving the application of severe plastic deformation (SPD) and it is well established that SPD techniques are capable of producing fully-dense bulk solids having ultrafine grain sizes There have been limited reports of high ductilities achieved in Mg alloys using ECAP, as summarized in where ε˙ is the strain rate and ɛ is the elongation to failure An AZ31 alloy with a composition, in wt.%, of Mg-3% Al-1% Zn-0.3% Mn was obtained from the CDN Company, Delta, BC, Canada. The as-received alloy was produced through semi-continuous casting and provided in the form of an extruded billet measuring 178 mm in diameter and 300 mm in length. The grain size in the cast condition was ∼75 μm.The as-received billets were initially extruded at 300 °C using an extrusion ratio of 42:1 to give rods with diameters of 10 mm. Henceforth, these bars are termed the extruded condition. Some of the extruded rods were then processed by ECAP at 200 °C for eight passes using a die with an internal angle of 110° between the two channels and an angle of 20° at the outer arc of curvature where the two channels intersect. Processing was performed using route BcTensile tests were conducted at constant cross-head speeds using an Instron 5582 universal testing machine equipped with a three-zone furnace. The temperature was controlled to within ±2 °C and the tests were conducted within the temperature range from 150 to 250 °C using initial strain rates from 10−4 to 10−2 |
s−1. The tensile specimens had gauge lengths and diameters of 8.3 and 4.0 mm, respectively, and the specimens were machined so that the loading directions were parallel to the extrusion or pressing directions.The grain structures were examined by optical microscopy (OM) and transmission electron microscopy (TEM). X-ray diffraction (XRD) and electron back-scatter diffraction (EBSD) were used to examine the transverse cross-sectional planes of the as-received billets and samples in the extruded and ECAP conditions. The areas examined by XRD and EBSD were approximately 10 mm × 10 mm and 600 μm2, respectively. Several separate areas were selected for the construction of EBSD pole figures in order to ensure good reproducibility. shows the grain structures of the AZ31 alloy in (a) the extruded and (b) the ECAP conditions, respectively. Both conditions yielded arrays of essentially equiaxed grains and the grain sizes measured using the linear intercept method were ∼2.5 and ∼0.7 μm for these two conditions, respectively, these results are given in the top row of The thermal stability of the grains was examined by heating samples at temperatures up to 350 °C and statically annealing for a period of 1 h: the results from the static annealing are shown in . It is apparent that reasonable grain stability is maintained up to 200 °C for the ECAP condition but with pronounced grain growth at higher temperatures, whereas the extruded condition shows reasonable grain stability up to a temperature of 300 °C.Typical stress–strain curves are shown in for tests conducted at room temperature at an initial strain rate of 1.0 × 10−3 |
s−1 using samples in the as-received, extruded and ECAP conditions: the values of the tensile yield stress (YS), the ultimate tensile stress (UTS) and the elongation to failure are summarized for these three conditions in . Although the grain size is smallest in the ECAP condition, it is important to note that the YS and UTS are lower in the ECAP condition than in the extruded condition although the ECAP condition yields values of YS and UTS, which are significantly higher than in the as-received billet. shows typical plots of true stress versus true strain for tests conducted on the ECAP material at 150 °C, equivalent to ∼0.46 Tm. The highest elongation achieved under these conditions was ∼460% at a strain rate of 1.0 × 10−4 |
s−1 for a specimen showing a region of extensive strain hardening. A full summary of all of the tensile elongations is given in where the results are plotted against the testing strain rate at three different testing temperatures for (a) the extruded condition and (b) the ECAP condition. In (a) for the extruded condition, reasonably high elongations occur only at a testing temperature of 250 °C. By contrast, it is apparent from (b) that superplasticity is achieved in the ECAP condition at the lowest strain rate when testing at a temperature of 150 °C. It is apparent from inspection of (b) for the ECAP condition at 250 °C are a direct consequence of the extensive grain growth occurring at this temperature so that the submicrometer grain size is removed. Thus, measurements showed that the average grain sizes in the gauge sections of the ECAP specimens strained to failure at a strain rate of 1.0 × 10−4 |
s−1 at 150, 200 and 250 °C were ∼1, ∼3 and ∼8 μm, respectively. shows the X-ray diffraction pattern simulated by computer for random Mg powders and (b) and (c) show the patterns taken from the transverse cross-sectional planes of samples in the extruded and ECAP conditions, respectively. It is apparent by inspection that the {101¯0} planes for the extruded specimens show a strong tendency to lie perpendicular to the extrusion axis but this trend has been lost in the ECAP condition. The X-ray (0 0 0 2), (101¯0) and (101¯1) pole figures are given in the three rows in for the extruded condition (on left) and the ECAP condition (on right): it should be noted that, in order to protect the X-ray detector, only the poles within 0–80° were constructed. It is apparent from , in confirmation with the X-ray diffraction patterns shown in , that most of the {101¯0} planes in the extruded condition lie perpendicular to the extrusion axis and it follows therefore that the (0 0 0 2) planes generally lie parallel to the extrusion axis. By contrast, the (0 0 0 2) basal planes in the ECAP condition lie primarily within an angular range from 40° to 50° with respect to the pressing direction (or with respect to the normal direction, ND, assigned in the pole figures). Since ECAP processing was undertaken in this investigation using a die with a channel angle of 110°, it is reasonable to anticipate that the basal planes in the majority of grains will rearrange during processing to become close to the theoretical shearing plane as the billet passes through the die.Parallel pole figures were also constructed by EBSD for some local regions on the transverse cross-sectional planes in the extruded and ECAP conditions and these are shown in the two columns in . These EBSD results are generally consistent with the X-ray pole figures and the diffraction patterns, thereby providing additional confirmation of the overall conclusions.These experiments confirm the potential for achieving LTSP in the AZ31 alloy through processing using a combination of extrusion and ECAP. This two-step procedure of extrusion and ECAP, designated earlier as EX-ECAP , the present result compares favorably with the report of an elongation of 391% for a Mg-10% Li-1% Zn alloy also tested under the same conditions of temperature and strain rate Based on the texture characterization, the nature of the microstructures for the extruded and ECAP conditions may be illustrated schematically by depicting the predominant grain orientations for these two conditions, as shown in where the arrows at right indicate the tensile axes for the subsequent the tensile testing. The results for the extruded condition are consistent with earlier reports demonstrating an alignment of the basal planes into the extrusion direction in various Mg alloys where the preferred orientation of the basal planes in the ECAP condition, and the consequent easier slip in tensile testing, leads to lower values of the YS and the UTS by comparison with the extruded condition despite the presence of a smaller grain size after ECAP.It is possible to check this conclusion quantitatively using the stereographic projections for pure Mg. Thus, it follows that <101¯0>//ED and <2¯5¯76>//ED correspond to the extruded and ECAP conditions, respectively, where ED is the extrusion direction. Considering the three primary slip systems in hexagonal structures, namely (i) the basal {0 0 0 1}<112¯0>, (ii) the prismatic {101¯0}<112¯0> and (iii) the pyramidal {101¯1¯}<112¯0> slip systems, it follows that the average Schmid factors may be calculated for each system as summarized in . These calculations confirm there is a high Schmid factor of 0.27 for basal {0 0 0 1}<112¯0> slip in the ECAP condition whereas the Schmid factor is zero for the extruded condition. The calculations are therefore consistent with the lower YS and higher elongation observed for the ECAP condition at room temperature and 150 °C when dislocation slip is the rate-controlling deformation process. By contrast, at the higher temperature of 250 °C, as documented in , the influence of this more favorable texture is lost in the ECAP condition because of the occurrence of significant grain growth.The grain size of the AZ31 alloy was reduced from ∼75 μm in the as-received condition to ∼2.5 μm by a single-pass extrusion at 300 °C and to ∼0.7 μm through additionally processing by ECAP for 8 passes at 200 °C. Following extrusion and ECAP, the AZ31 alloy exhibited low temperature superplasticity (LTSP) with a maximum elongation of ∼460% when using a strain rate of 1.0 × 10−4 |
s−1 at 150 °C, equivalent to a homologous temperature of 0.46 Tm.A detailed investigation revealed different textures in the extruded and ECAP conditions. These dominant textures were characteristic of <101¯0>//ED in the extruded condition and <2¯5¯76>//ED in the ECAP condition, where ED is the extrusion direction. The results show that the basal planes tend to lie parallel to the extrusion axis in the extruded condition but there is a rearrangement during ECAP and the basal planes become reasonably aligned with the theoretical shearing plane.Using the measured textures and the calculated Schmid factors, it is anticipated that the ECAP specimens will exhibit lower yield stresses and higher elongations to failure at room temperature when dislocation slip is the dominant rate-controlling process. This is consistent with the experimental observations.Mechanically strong double network photocrosslinked hydrogels from N,N-dimethylacrylamide and glycidyl methacrylated hyaluronanHyaluronan (HA) is a natural polysaccharide abundant in biological tissues and it can be modified to prepare biomaterials. In this work, HA modified with glycidyl methacrylate was photocrosslinked to form the first network (PHA), and then a series of highly porous PHA/N,N-dimethylacrylamide (DAAm) hydrogels (PHA/DAAm) with high mechanical strength were obtained by incorporating a second network of photocrosslinked DAAm into PHA network. Due to the synergistic effect produced by double network (DN) structure, despite containing 90% of water, the resulting PHA/DAAm hydrogel showed a compressive modulus and a fracture stress over 0.5 MPa and 5.2 MPa, respectively. Compared to the photocrosslinked hyaluronan single network hydrogel, which is generally very brittle and fractures easily, the PHA/DAAm hydrogels are ductile. Mouse dermal fibroblast was used as a model cell line to validate in vitro non-cytotoxicity of the PHA/DAAm hydrogels. Cells deposited extracellular matrix on the surface of these hydrogels and this was confirmed by positive staining of Type I collagen by Sirius Red. The PHA/DAAm hydrogels were also resistant to biodegradation and largely retained their excellent mechanical properties even after 2 months of co-culturing with fibroblasts.Tissue engineering technology has shown great promises in producing functional replacements for diseased tissues and organs including skin Hyaluronan (HA), a natural glycosaminoglycan, composed of β-1,4-linked units of β-1,3-linked glucuronic acid and N-acetyl--glucosamine, is an abundant component in connective, epithelial, and neural tissues Although the photocrosslinked MeHA hydrogel is highly biocompatible, it is brittle. This lack of structural integrity largely limits its potential in many fields where good mechanical properties are required. Integrating a synthetic polymer into the MeHA hydrogel matrix is one possible strategy to enhance its mechanical properties. Due to its exceptional biocompatibility, the hydrophilic synthetic polymer poly (N,N-dimethylacrylamide) (PDMAAm) has been widely utilized in the biomedical fields In this study, we reported the synthesis of hydrogels composed of interpenetrating double networks (DN) by combining HA with PDMAAm. Methyacrylate groups were first introduced onto HA chains and photocrosslinked to prepare the first hydrogel network (photocrosslinked hyaluronan, PHA). The second network PDMAAm subsequently formed by photocrosslinking of N,N-dimethylacrylamide in the presence of the first formed HA network (i.e., PHA/DAAM). This DN structure resulted in a series of hydrogels with exceptional mechanical performance. Structure and physical properties of the resulting hydrogels were investigated by SEM, swelling and compression tests. Mouse dermal fibroblast was used as an in vitro model to evaluate the initial non-cytotoxicity of these hydrogels; deposition of ECM on the three-dimensional network was also assessed. The results showed that the hydrogels were both mechanically strong and non-cytotoxic, and thus have many potential biomedical applications including implantables designed for load bearing.Sodium hyaluronan (Mw, 1.5 × 106) was provided by Engelhard, Inc. (now, BASF) (Stony Brook, NY). Glycidyl methacrylate (GMA), N,N-dimethylacrylamide (DAAm), N,N′-methylene bisacrylamide (MBAAm) triethylamine (TEA), tetrabutylammonium bromide (TBAB), α-ketoglutaric acid, and Sirius Red were purchased from Sigma–Aldrich Company (St Louis, MO).Cell culture inserts (polycarbonate, 6.5 mm diameter, 0.2 μm pore size) were obtained from NUNC (Rochester, NY, USA). M. DUNNI (clone III8C) murine dermal fibroblast CRL-2017 and McCoy's 5A medium were obtained from ATCC (Manassas, VA, USA). Fetal Bovine Serum (FBS) was acquired from Hyclone (Logan, UT, USA) and Penicillin–Streptomycin (Pen–Strep) solution was obtained from Gibco (Grand Island, NY, USA). MTS assay kit (CellTiter 96s) was purchased from Promega (Madison, WI). All other chemicals were of reagent grade and deionized distilled water was used.Photocrosslinkable HA was synthesized by derivatizing HA with methacrylate following a method described previously NaCl followed by water. The final photocrosslinkable HA was recovered after lyophilization. The substitution degree of HA was determined by 1H NMR (Varian Unity-500, CA, USA).The PHA hydrogel was prepared by irradiating a 2% (w/v) GMA derivatized HA solution with UV light at 365 nm (Fisher company, Hampton, NH, USA) for 2 h in the presence of a photo-initiator 2-oxo-ketoglutaric acid, at a concentration of 0.1 mol%.A series of PHA/DAAM hydrogels with incremental properties were prepared. For a typical preparation, a previously formed PHA hydrogel was first immersed in a DAAm solution at ambient temperature, where the concentrations of DAAm monomers used were 1, 2, 3, 4, and 5 mol/L. Moreover, these DAAm solutions contained various amounts of MBAAm crosslinker (0, 0.01, 0.05, 0.1, 0.5, 1, and 2 mol% with respect to the DAAm monomer concentration) as well as a photo-initiator at 0.1 mol%. Upon equilibrating of the PHA hydrogel with the DAAm monomers solution, a second network was formed in the presence of the first network by irradiating the DAAm equilibrated PHA hydrogel for 2 h under UV light at 365 nm. The hydrogel formed was referred as PHA/D-x-y (x is the monomer concentration, whereas, y is the crosslinker concentration). For example, a hydrogel prepared from a PHA network combined with a second network formed with 3 mol/L DAAm, 0.01 mol% MBAAm and 0.1 mol% 2-oxoglutaric acid, was coded as PHA/D-3-0.01.The PHA/DAAM hydrogels were snap frozen using liquid nitrogen followed by lyophilization. Fractured pieces with dimensions ∼5 mm × 2 mm × 3 mm were mounted onto an aluminum board with copper tape and sputter-coated with gold. The surface and cross-sections were examined with a field-emission scanning electron microscope (SFEG Leo 1550, AMO GmbH, Aachen, Germany) at 20 kV.Equilibrium swelling studies were performed on PHA/DAAM hydrogels. Lyophilized hydrogels were first weighed (Wd) and immersed in 0.01 |
PBS at 37 °C. After 5 days of equilibration, the hydrogels were removed from the PBS solution, blotted with tissue for removal of excess water, and weighed (Ws) again. The equilibrium water content (EWC) was calculated through the following equation:For comparison, the equilibrium water uptake studies were also performed on both single network PHA and PDAAm hydrogels, respectively.Mechanical properties of the swollen hydrogels before and after 2 months of incubation with cell culture were performed with a screw-driven desktop loading frame (Model 1K-16 Universal Materials Tester, Interactive Instruments, USA). A cylindrical hydrogel specimen (diameter: 8 mm, height: 5 mm) was set on the lower plate and compressed by the upper plate connected to a load cell, with an applied strain rate set at 0.1% per min at ambient temperature. The initial compressive modulus was determined by the average slope in a range of 0–10% strain from the stress–strain curve. The fracture stress was determined from the peak of the stress–strain curve. To evaluate the changes in mechanical properties of the hydrogels subject to cell degradation, co-culture was performed using as a model cell line M. DUNNI mouse dermal fibroblast CRL-2017 cells cultured in McCoy's 5A medium containing 10% FBS and 1% Pen–Strep solution maintained at 37 °C under a humidified atmosphere of 5% CO2. Briefly, hydrogel cylinders (diameter: 8 mm, height: 5 mm) were deposited in 24-well plates, and 1 × 106 |
cells were then seeded in each well. The medium was changed every other day. After 2 months of cell culture, the hydrogel cylinders were retrieved and fixed with 70% ethanol, followed by rinsing three times with PBS, and maintained in PBS for mechanical testing.Cell toxicity assay was carried out with the same cell line on representative hydrogels (PHA, PHA/D-3-0.01, PHA/D-3-0.05, and PHA/D-3-2) in 96-well plates (1 × 105 |
cells/mL). To avoid the error caused by removing the hydrogel pieces each time while performing the assay, a non-contact methodology was employed to evaluate the cytotoxicity of the PHA/DAAM hydrogels. Briefly, sterilized PHA and PHA/DAAM hydrogel pieces, tailored to 5 mm × 2 mm × 2 mm, were first deposited in culture inserts and immersed in cell-seeded culture wells (n |
= 3 per group). Cell viability was determined by MTS assay on day 0, 3, 7, 10 and 14. For each time point, 20 μL MTS solution were added to the culture medium, and monolayer cultured cells were used as controls. After incubating at 37 °C for 1 h, the absorbance of solutions was determined at 490 nm.Long-term cell culture was performed on the PHA/DAAM hydrogels in 48-well plates to determine the changes in hydrogel morphology and ECM deposition on the surface of the hydrogel. A piece of hydrogel (approximate dimension: 6 mm × 6 mm × 1 mm) was deposited in each well, 1 × 105 |
cells were then seeded directly. The medium was changed every other day. To observe cell morphology on the surface of PHA/DAAM hydrogels, images of cells were acquired in situ with a QCapture 5 imaging software (Surrey, Canada). After cultured with mouse fibroblast in a direct contact mode for 1 month, the PHA/DAAM hydrogels were retrieved and fixed with 70% ethanol for 30 min, rinsed gently with PBS followed by distilled water. To evaluate the extracellular matrix (ECM) deposition on the surface of the hydrogels, the collagen secreted was detected with Picrosirius Red (0.1% Sirius Red in saturated picric acid) staining Statistical analysis was performed using a Student's t-test with a q |
< 0.05 for statistical significance. All values are reported as the mean and standard error of mean.Introducing methyacrylate groups onto HA is a facile technique to produce a photocrosslinkable MeHA macromer. In this work, the reaction condition of HA derivatization with GMA was chosen according to Schmidt's report shows the 1H NMR spectra of modified HA and native HA as control. Compared to native HA, modified HA showed two new peaks at ∼5.6 and ∼6.1 ppm attributable to the presence of acrylate groups on HA, confirming grafting of methyacrylate groups on HA chain, which was consistent with the published results In the presence of a photo-initiator, the methyacrylate HA macromer, when exposed to UV light, undergoes a free radical polymerization to form a three-dimensional crosslinked hydrogel (PHA). The PHA hydrogel formed was then immersed in an aqueous DAAm solution containing various amounts and combinations of crosslinker and photo-initiator until equilibrium was reached, respectively. This was followed by subsequent exposure to UV for polymerization of the DAAm entrapped in the swollen PHA hydrogel, leading to formation of a double network hydrogel. depicts representative SEM images of the cross-section for lyophilized PHA (A), PHA/D-3-0.01 (B), PHA/D-3-0.05 (C), and PHA/D-3-2 (D) hydrogels. All hydrogels were highly porous throughout the cross-section. Pure PHA hydrogel exhibited the largest pore size (average: 50 μm) among the four hydrogel formulations. Due to the presence of the second PDAAm network, which increased the relative crosslinking density of the hydrogel structure, the other three hydrogels PHA/D-3-0.01, PHA/D-3-0.05, and PHA/D-3-2 appeared to have more compact porous structures with an average pore size ranging from 10 to 20 μm. Evidently, due to the higher crosslinking density, the pore partitions of PHA/D-3-2 hydrogel were the thickest.A and B depict the relationship between EWCs of PHA/DAAm hydrogels and concentrations of monomer and crosslinkers used, respectively. All hydrogels exhibited EWCs value greater than 80%. In A, the EWC of pure PHA hydrogel, as a control (i.e., DAAm monomer concentration = 0 mol/L), was approximately 98%. Upon introducing the second network, the EWC values of the PHA/DAAm hydrogel formulations decreased from 98% to 88%, attributable to an increase in the crosslinking density, with a corresponding increase of the DAAm monomer concentration from 0 mol/L to 5 mol/L, while maintaining the crosslinker concentration at 0.1 mol%. These results were in a good agreement with those reported previously B. A decrease in EWC was observed with an increase in the concentration of crosslinker in the second network. For example, when the concentration of DAAm monomer was kept at 3 |
, an increase in MBAAm concentration from 0.01 mol% to 2 mol% reduced the EWC from 94% to 83%. Higher crosslinker concentration created a denser polymer network and thus rendered the polymeric chains to move in closer proximity to each other, which enabled stronger hydrophobic interactions leading to lower EWC depicts the stress–strain behavior of PHA, PHA/D-3-0.05, and D-3-0.05 hydrogels under uniaxial compression. Pure PHA and D-3-0.05 single network hydrogels fractured at stresses 0.29 MPa and 0.04 MPa, respectively, while the PHA/D-3-0.05 possessed a fracture stress of over 5.25 MPa. The fracture strain of PHA/D-3-0.05 hydrogel was 87.1%, which was considerably higher than that of either the PHA (56.1%) hydrogel or the D-3-0.05 (78.4%) hydrogel. The mechanical effect produced by a DN structure The initial compressive moduli of hydrogels were deduced from the stress–strain profiles. All PHA/DAAm hydrogels showed similar initial compressive moduli of order 0.1 MPa. Representative results of the initial compressive moduli of PHA, PHA/D-3-0.01, PHA/D-3-0.05, and PHA/D-3-2 hydrogels are summarized in . With the exception of the PHA hydrogel possessing a relatively low compressive modulus at 0.045 MPa, the other three hydrogels exhibited comparable moduli in the range of 0.3–0.6 MPa, indicating a higher crosslinking for PHA/DAAm hydrogel . Fibroblast secretes a myriad of hydrolases, including hyaluronidase , the fracture stresses varied considerably among the hydrogels. A shows the effect of varying DAAm monomer concentration on the fracture stress of the PHA/DAAm hydrogels. Increasing the DAAm concentration from 0 mol/L to 3 mol/L resulted in a gradual enhancement of the fracture stress of the hydrogels from 0.29 MPa to 4.12 MPa; a further increase in DAAm concentration led to a gradual decline in the fracture stress of hydrogels. In particular, a double network system, containing one stiff but brittle first network and one soft but ductile second network, typically exhibit excellent overall mechanical properties in both strength and toughness B). Due to the DN structure, the fracture stress attained a maximum value of 5.25 MPa at a crosslinker concentration of 0.05 mol%. For the PHA/D-3-0.05 hydrogel, the abrupt increase in the mechanical strength likely did not result from an increase in chemical crosslinkage or physical entanglement since the second network was loosely crosslinked. DN effect suggests that the highly crosslinked first network has a relatively higher modulus but rather brittle (see ). Under compression, stress could easily develop locally inside the network, leading to formation of cracks. However, the presence of the soft but loosely crosslinked second network could effectively dissipate the stress imposed during compression by deforming the network conformation and/or sliding the physical entanglement points along the polymer chains B, increasing the crosslinker concentration from 0.05 mol% to 2 mol% resulted in a progressive decrease of fracture stress of the hydrogels. This increase in the crosslinker concentration resulted in substantial increase in the crosslinking density and thus, formation of a stiffer network with very limited capacity to dissipate stress imposed during compression, leading to the reversal of the DN effect.B, the water content of the PHA/DAAm hydrogel prepared from 3 mol/L of DAAm with a 0.05 mol% crosslinker concentration was greater than 93%. In general, when hydrogels are fully swollen, their compressive fracture stresses are lowered due to the softer network. Remarkably, the fully swollen PHA/D-3-0.05 hydrogel still possessed a high fracture stress at 5.25 MPa, implying that the DN structure could greatly improve the mechanical strength of the swollen hydrogels. Moreover, these hydrogels composed of double networks all exhibited one definitive fracture line when broke (see a); this pattern was distinctively different from hydrogels composed of a single network or interpenetrating polymer networks without the DN effect; they tended to fracture into multiple fragments under compression (For comparison, the fracture tests were also performed on the PHA/DAAm hydrogels after 2 months of incubation in cell culture. There was no noticeable change on shape of these hydrogel specimens when compared to their pristine counterparts by gross observation. As shown in (circles), all PHA/DAAm hydrogels consistently displayed decreased failure stress after co-cultured with cells. The fracture stress of PHA single network hydrogel decreased drastically from 0.29 MPa to 0.019 MPa (A), whereas the fracture stress of PHA/DAAm hydrogels were moderately reduced by cell-mediated degradation. Furthermore, the peak value (i.e., the DN effect) was maintained at an MBAAm concentration of 0.05 mol% (B). The result was consistent with the resistance of DAAm networks to biodegradation. Hydrogels with higher DAAm or MBAAm concentrations exhibited less decrease in failure stress.The cytotoxicity potential of PHA/DAAm hydrogels was evaluated by co-culturing dermal fibroblasts for 2 weeks utilizing an indirect contact method; cell viabilities were determined by MTS assay at 3, 7, 10 and 14 days. The hydrogels were deposited in cell culture inserts to avoid the disturbance of cells anchored to the culture wells during their removal for assay.Both the morphology and the amount of cells seeded in all wells, during the entire culture span, did not show noticeable difference (data not shown). depicted the results of MTS assay for PHA/D-3-0.01 (Gel 1), PHA/D-3-0.05 (Gel 2), PHA/D-3-2 (Gel 3), and PHA (Gel 4). After 3 days of incubation, the absorbance of all samples increased considerably with no significant difference among all groups. The presence of hydrogels did not affect cell growth and thus, validating the hydrogels' lack of cytotoxicity. In general, the media's absorbance increased steadily from 0 to 14 days with values comparable to those of their corresponding controls indicating that the presence of PHA/DAAm hydrogels did not affect cell proliferation. Varying the concentration of either DAAm monomer (from 0 mol/L to 3 mol/L) or the crosslinker (from 0.01 mol% to 2 mol%) for hydrogel preparation did not show any noticeable effect on cell growth. Moreover, as mentioned previously, after prolonged co-culturing with cells, the hydrogel did not exhibit drastic change in their shapes or mechanical properties, suggesting that they were not easily degraded by cells. This could be attributed to the facts that the stable bonds formed by free radical polymerization were highly resistant to biodegradation, and the poly (N,N-dimethylacrylamide) hydrogel is a non-biodegradable material.The morphology of cells deposited directly on hydrogels was monitored continuously for 1 month. depicted representative images of the fibroblasts on the surface and on the en face side of PHA/D-3-0.01 (A, B) and PHA/D-3-0.05 (C, D) hydrogels. Cells assumed round morphology initially and tended to cluster (marked with “”) suggesting that the surfaces of pristine PHA/DAAm hydrogels were not conducive to cell attachment (A and C). Similar cellular behavior was previously reported on the interaction of fibroblast cells and polymer surface by Tamada and Ikada B and D) and formed cluster similar to that on the hydrogel surface. An increase in the surface roughness of polymer could enhance the cell adhesion strength C). It could be postulated that fibroblasts began to secret ECM once deposited on the PHA/DAAm hydrogel surface creating an environment conducive to their attachment.Cells are known to deposit ECM on biomaterial surfaces and ECM is essential in regulating cellular behavior shows the surface of PHA/D-3-0.01 (A, B) and PHA/D-3-0.05 (C, D) hydrogels after staining. They were observed with both conventional and polarized light under bright field; under conventional light, besides collagen, depositions of other ECM ingredients showed up. Stained and observed under a polarized light, portions of collagen fibers showed the characteristic birefringence (B and D). It is reported that Type I collagen appeared as reddish-yellow, and Type III collagen appeared to be greenish under polarized light showed the representative morphology of the fibroblasts underneath the PHA/D-3-0.05 hydrogels after 1 week (B was captured in the presence of an intact piece of hydrogel (right side). There was no morphological difference between the fibroblasts residing underneath the hydrogel or on the culture dish (left side, B), suggesting that the hydrogel does not have adverse effect on the fibroblasts. Cell underneath the hydrogel continued to proliferate (C) after 2 weeks, which further demonstrated the lack of cytotoxicity of the hydrogels.Hydrogels co-cultured with fibroblasts were lyophilized and examined under SEM to corroborate with the ECM staining results obtained. Representative SEM images of the PHA/D-3-0.05 hydrogels were shown in A) on the pristine hydrogel surface (i.e., never co-cultured with cells), which was generally ridden with multi-holes or crumples (A). After 1 month of co-culturing with fibroblasts, ECM appeared to have accumulated on the surface of the hydrogel (B, the hydrogel surface was almost completely masked by ECM with a partially covered area where the porous hydrogel structure remained visible. The uncovered part of surfaces maintained similar morphology as their pristine counterparts as shown in Double network hydrogels based on HA and poly (N,N-dimethylacrylamide) have been prepared by a two-step photocrosslinking process. The hydrogels exhibit porous internal structures with good swelling properties. Their mechanical properties are related to both the DAAm monomer concentration and the crosslinker concentration of the second network. Due to the synergistic effect of DN structure, the new hydrogels possess greatly enhanced mechanical properties as compared to the single network PHA hydrogel; the loosely crosslinked second network dissipates stress during compression contributing to the high mechanical strength of the double network hydrogel. Even though the PHA/DAAm hydrogel contains more than 90% water, its fracture stress is as high as 5.2 MPa. The PHA/DAAm hydrogels are non-cytotoxic but highly resistant to biodegradation and they largely retain their excellent mechanical properties even after 2 months of co-culturing with fibroblasts. The results of long-term cell culture reveals that fibroblasts secrete ECM (mostly Type I collagen) to modify the surface of the hydrogels. The collective performance profile of the PHA/DAAm hydrogels strongly suggests that this class of material has great potential for biomedical applications, particularly those designed for load bearing; future investigation will direct at exploring its potential as spinal disc substitutes. Trans. Nonferrous Met. Soc. China 22(2012) 2066−2071 Hot deformation behavior of AZ91 magnesium alloy in temperature ranging from 350 °C to 425 °C G. R. EBRAHIMI 1 , A. R. MALDAR 1 , H. MONAJATI 2 , M. HAGHSHENAS 3 1. Department of Materials and Polymer Engineering, Faculty of Engineering, Hakim Sabzevari University, Sabzevar, Iran; 2. Materials Engineering Department, Islamic Azad University, Najafabad Branch, Isfahan, Iran; 3. Department of Mechanical and Materials Engineering, Western University, London, Canada Received 17 November 2011; accepted 1 February 2012 Abstract: The flow behavior and microstructure evolution of AZ91 magnesium alloy during a thermomechanical process, hot compression test， was investigated. The specimens were hot compressed at a temperature ranging from 350 °C to 425 °C and at strain rate of 0.1 s −1 to the strains of 0.3, 0.5 and peak. Microstructural evolutions were studied using optical and scanning electron microscopes. The results show that during the compression process, the recrystallized grains nucleate along the pre-existing grain boundaries. The amount of dynamically recrystallized grains is increased with strain in a sigmoid scheme followed by Avrami equation. The size of dynamically recrystallized grains also increases at the beginning and decreases after reaching the maximum value. Key words: AZ91 alloy; hot compression; microstructure evolution; recrystallization; peak strain 1 Introduction Owing to their low density, high specific strength and good thermal and electrical conductivities, magnesium alloys have been used for a wide variety of applications [1−3]. Improving the fuel efficiency of vehicles and reducing CO 2 emissions due to their high specific strength and stiffness have nominated them as a great alternative for steel and aluminum alloys in the transportation industries [2,4−6]. Also, magnesium alloys can potentially be used instead of plastics in the electronic and computer industries [7]. However, these alloys have not been used for high performance applications due to their low mechanical properties at room and elevated temperatures [8]. The poor formability of magnesium and its alloys at room temperature has limited their applications [8−12]. The restricted formability is due to the lack of independent slip systems at room and ambient temperatures (200−450 °C) [4,12]. Among cast Mg alloys, AZ91 alloy is the most widely used alloy due to its good combination of high strength at room temperature, good cast ability and excellent corrosion resistance [13,14]. However, as it is a cast alloy, there are limited studies on the microstructure evolution and hot deformation behaviour of AZ91 alloys [13,15]. During the hot deformation of Mg alloys, according to the stacking fault energy (SFE) in Mg (γ SF =125 mJ/m 2 ) [11], dynamic recovery (DRV) is expected to be the dominant softening mechanism [12]. However, it has been shown that the main restoration phenomenon is dynamic recrystallization (DRX) due to the lack of easy and active slip system [16,17]. The operation of DRX is of particular importance as it reduces the flow stress and grain size. As there is little data considering the relation between DRX grain size and thermomechanical behaviour of cast Mg alloys [4,12], the present study was designed to investigate the evolution of microstructure during the hot deformation process of AZ91 alloy. To this aim, hot compression tests were carried out over the temperature range of 350−425 °C and DRX features in the resulting microstructures were studied using optical and scanning electron microscopes. 2 Experimental The experimental material used in the present study was as-cast AZ91 magnesium alloy (Mg−9.2%Al− Corresponding author: M. HAGHSHENAS; Tel: +1- 519-702-2049; Fax: +1- 519-661-3020; E-mail: [email protected] DOI: 10.1016/S1003-6326(11)61429-5 G. R. EBRAHIMI, et al/Trans. Nonferrous Met. Soc. China 22(2012) 2066−2071 2067 0.8%Zn−0.22%Mn). Homogenization heat treatment was conducted at 420 °C for 24 h followed by water quenching. The hot compression specimens were prepared in the form of cylinders with 15 mm in height and a height to diameter ratio of 1.5. The hot compression tests were done as follows. 1) The specimens were heated up to test temperatures in the range of 350−425 °C. 2) The specimens were soaked for 3 min to be homogenized. 3) Hot compression tests were performed under strain rate of 0.1 s −1 and two separate true strains: i) ε=0.3, ii) ε=0.5. 4) The specimens were water quenched for less than 5 s to preserve as-deformed microstructure. The tests were done using a Zwick/Roll 25-Ton machine equipped with an electrical resistance furnace, which can maintain temperature variation of ±5 K. Teflon tape was also used to protect samples from oxidation. Deformed specimens were conducted by standard sample preparation techniques followed by immersion etching in an acetic-picric solution. Scanning electron microscope (SEM) and optical microscope (OM) equipped with an image analyzer were employed for microstructure examination. 3 Results and discussion 3.1 Initial microstructure Figure 1(a) shows that the initial microstructure of Fig. 1 SEM images showing microstructures of as-cast ingot (a) and homogenized specimen (b) the alloy consisted of supersaturated α-Mg as main phase and eutectic α+β as minor constitution. The latter was observed at inter-dendritic arms. In order to dissolve β(Mg 17 Al 12 ) precipitates, the samples were homogenized at 420 °C for 24 h and then water quenched. Figure 1(b) shows the microstructure after homogenization process, containing coarse equiaxed grains with mean diameter of ~200 µm with fine β precipitates at distributed boundaries. The dendritic structure has also disappeared. 3.2 Stress—strain curves True stress— strain curves obtained during hot compression tests at 350, 400 and 425 °C and strain rate of 0.1 s −1 are presented in Fig. 2. At the initial stage, the stress increases rapidly due to work hardening resulting from the continuous accumulation of dislocation. By increasing the strain, flow stress increases up to a maximum value and thereafter decreases to a steady state. Such flow softening behavior is observed after a critical strain and is generally attributed to the dynamic recrystallization (DRX) phenomenon as well as the nucleation and coarsening of β precipitates [16,18,19]. This behavior is dependent on the deformation temperature. Fig. 2 True stress—strain curves of deformed samples at strain rate of 0.1 s −1 and different temperatures The peak points of the curves shift to the lower stresses and strains by increasing the deformation temperature, as shown in Figs. 3(a) and (b), respectively. It is well documented that increasing the deformation temperature of Mg alloys leads to decreasing critical resolved shear stresses (CRSS) for slip systems, pyramid and prismatic planes [18]. Consequently, these result in more mobility of dislocations on the slip planes, which are manifested by decreased peak stress. Nucleation of newly recrystallized grains, on the other hand, is effective in decreasing the peak stress by decreasing the dislocations density [19]. G. R. EBRAHIMI, et al/Trans. Nonferrous Met. Soc. China 22(2012) 2066−2071 2068 3.3 Evolution of microstructures The evolution of microstructures at three points of the flow curve, i.e., peak strain, strains of 0.3 and 0.5, is depicted in Fig. 4. At peak strain, dynamically recrystallized grains nucleate at original grain boundaries, forming a necklace grain structure at all tested temperatures. However, the size of recrystallized grains increases and their volume fraction decreases by increasing testing temperature from 350 to 425 °C. Increasing the strain to 0.3 is accompanied by increasing the volume fraction of DRX and finer grains are developed at lower temperatures. This can be observed more clearly in Fig. 5, where the dependence of average grain size is plotted vs strain. It may be seen that at a constant strain, the average grain size of DRX increases with increasing the deformation temperature due to the increase in the restoration rate [16]. Recrystallized grains at the peak point start to grow by increasing strain and the rate of increase of the grain size from peak strain up to 0.3 is relatively equal in all testing temperatures. Increasing strain beyond 0.3, up to 0.5, develops the volume fraction of DRX toward full recrystallization. However, even at the strain of 0.5, there are still some unrecrystallized regions in the microstructure. Fig. 3 Dependence of peak stress (a) and peak strain (b) to deformation temperature in hot compression experiments Fig. 4 Microstructure evolution of AZ91 during hot compression tests at temperatures of 350 °C, 400 °C and, 425 °C and strains: (a1), (a2), (a3) Peak strain; (b1), (b2), (b3) ε=0.3; (c1), (c2), (c3) ε=0.5 G. R. EBRAHIMI, et al/Trans. Nonferrous Met. Soc. China 22(2012) 2066−2071 2069 Fig. 5 Evolution of dynamic alloy recrystallized grain size with true strain at a strain rate of 0.1 s −1 Figure 5 shows the changes in the recrystallized grain size against strain in tested temperatures. The average recrystallized grain size does not follow the same rate of increase as before, and it shows an even decreasing trend at 350 °C. This is a very interesting finding because straining beyond the peak point has been able to continuously decrease DRX grain size. Hot compression flow curves at 400 and 425 °C (Fig. 2) show that the strain of 0.3 is approximately the beginning point of steady state region. Therefore, it is expected to see no noticeable change in DRX grain size by more straining, which is in agreement with the measurements of average grain diameters shown in Fig. 5. However, at 350 °C the steady state is not attained even at the strain of 0.5 and the average size of dynamically recrystallized grains still continues to decrease. 3.4 Volume fraction of recrystallization Figure 6 shows the volume fraction of dynamically recrystallized grains vs strain at three deformation temperatures which was measured using image analysis technique. It is seen that the general trend of increasing volume fraction follows a well-known S-type growth rate. Moreover, the recrystallization volume fraction is increased by raising the deformation temperature. In general, dynamically recrystallized fraction can be well described by the Avrami equation [16]: ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠⎞ ⎜ ⎜ âŽ� ⎛ − −−= ′m X p c DRX 3.0exp1 ε εε (1) where ε c is the critical strain; ε p is the peak strain; m' is a material constant [20] which indicates the recrystallization kinetics and depends on the deformation temperature. It is well known that the driving force of DRX decreases as the deformation temperature increases, leading to a hindrance effect on DRX. This leads to a decrease in the value of m'. Raising the deformation temperature increases the rate of restoration phenomena. In the present study, the amount of m' was found to be 1.4 using linear regression method. The amount of m' for AZ31 alloy was previously reported to be 1.2 [21−24] which is lower than the current value for AZ91. In AZ91 alloy, Al atoms play a pining role on dislocation motion while fine precipitates act as nucleation sites for newly recrystallized nuclei [25,26]. These cause an increasing rate of DRX. Moreover, it has been shown that differences in the initial texture and orientation of basal and prismatic planes during deformation, lead to a change in DRX kinetics [26,27]. Fig. 6 Evolution of dynamically recrystallized fraction with true strain at strain rate of 0.1 s −1 3.5 Recrystallization mechanism and comparison between the present work and other results As AZ91 is a cast alloy, little study has been performed on its hot deformation behavior. In the present work, our findings on AZ91 were compared with previously published data on AZ31. Microstructures in the peak strain at the temperatures of 350, 400 and 425 °C (Fig. 4) indicate the formation of newly recrystallized grain at the primary boundaries which clearly shows the occurrence of dynamic recrystallization (DRX). The formation of recrystallization grains can be done with different mechanisms [28]. In magnesium alloys, different mechanisms have been proposed, among which the most common mechanism is discontinuous recrystallization (DDRX). Other mechanisms, including continuous dynamic recrystallization (CDRX), twin induced recrystallization and particle stimulated recrystallization, are also discussed. As seen in Fig. 7, grain boundaries are not smooth, in which a serrated-wavy nature of boundaries is clear and boundaries are about to bulge. In the DDRX nucleation theory, by increasing the strain upon the critical strain, grain boundaries become wavy and eventually bulge out. Grain boundary bulging creates G. R. EBRAHIMI, et al/Trans. Nonferrous Met. Soc. China 22(2012) 2066−2071 2070 new fine grains along pre-existing boundary during straining. At the peak strain, bulges are separated from primary boundaries and form new grains. A more magnified part of Fig. 7 shows a bulge that is separated from the boundary and has formed a new grain. By increasing the strain, more DRX grains form and an extensive evidence for the formation of the first layer of necklace structure (along the pre-existing grain boundaries) through the bulging mechanism is observed (Fig. 8). At the strain close to steady state, the necklace structure is completed. In addition, when the steady state of strain is realized, new grain gradually grows towards the inside of primary grains as a result of full dynamic recrystallization. Based on hot compression flow curves (Fig. 2) and the microstructures at different strains, it can be deducted that continuous dynamic recrystallization is predominant at all deformation conditions in the present study. The Fig. 7 SEM micrographs obtained after hot compression at 400 o C and 0.1 s −1 at peak strain Fig. 8 Necklace microstructure obtained after hot deformation under strain rate of 0.1 s −1 and temperature of 325 o C at peak strain stress— strain curve of DDRX shows a clear and prominent peak due to the reduced density of dislocations caused by grain boundary migration. This will lead to the lower rate of the work hardening. Other parameters like texture, primary grain size, alloying elements, and precipitates can affect recrystallization phenomenon as well. Studies by TAN and TAN [27], SITDIKOV et al [29], GALIYEV et al [30,31] on AZ31, AZ61 and ZK60 showed the occurrence of CDRX that is due to the formation of new grains caused by misorientation of subgrain boundaries. At temperatures ranging from 200 to 350 °C, dynamic recovery is dominant, which results in creation of new grains [28]. As seen in Fig. 7, β precipitates, in white color, are present inside the grains and also grain boundaries while new grains are formed independent of the precipitates. The results of other researchers [21,25] on the other AZ series of magnesium alloys at temperatures above 350°C indicated that the occurrence of dynamic recrystallization is discontinuous. According to these studies and the present study, it can be concluded that the mechanism of recrystallization in the Mg alloys containing aluminum and zinc is mainly a function of the deformation temperature. Parameters such as texture, initial grain size and applied stress state only alter the kinetics of recrystallization and grain size while the only parameter affecting the mechanism of recrystallization is temperature. 4 Conclusions 1) At all tested temperatures, by increasing strain, the number of recrystallized grains first increases and they reaches a maximum value and decreases. 2) The fraction of recrystallized grains increases exponentially with increasing the strain and follows Avrami equation (m'=1.4). 3) Wavy/serrated grain boundary at peak strain shows inconsistent recrystallization behavior. 4) Recrystallization mechanism in AZ91 Mg alloy at the temperature ranging from 350 to 425 °C follows a necklace mechanism. References [1] AVEDESIAN M, BAKERT H. ASM specialty handbook: Magnesium and magnesium alloys [M]. New York: ASM International, 1999. [2] ÄŒÃ�ŽEK L, GREGER M, DOBRZANSKI L A, JURICKA I, KOCICH R, PAWLICA L, TAŃSKI T. Mechanical properties of magnesium alloy AZ91 at elevated temperatures [J]. Achievements in Materials and Manufacturing Engineering, 2006, 18: 203−206. [3] KAINER K U. Magnesium alloys and technology [M]. Weinheim: Wiley-VCH, 2003. [4] XU S W, KAMADO S, MATSUMOTO N, HONMA Y, KOJIMA T. Recrystallization mechanism of as-cast AZ91 magnesium alloy G. R. EBRAHIMI, et al/Trans. Nonferrous Met. Soc. China 22(2012) 2066−2071 2071 during hot compressive deformation [J]. Materials Science and Engineering A, 2009, 527: 52−60. [5] GREGER M, KOCICH R, ÄŒÃ�ŽEK L. Superplastic properties of magnesium alloys [J]. Achievements in Materials and Manufacturing Engineering, 2007, 22: 83−86. [6] PEREZ-PRADO M T, del VALLE J A, CONTRERAS J M, RUANO O A. Microstructural evolution during large strain hot rolling of an AM60 Mg alloy [J]. Scripta Materialia, 2004, 50: 661−665. [7] FARAJI G, DASTANI O, AKBARI MOUSAVI S A A. Microstructures and mechanical properties of Al 2 O 3 /AZ91 surface nanocomposite layer produced by friction stir processing [J]. Journal of Engineering Manufacture, 2011, 225: 1331−1345. [8] FARAJI G, MASHHADI M M, KIM H S. Microstructure inhomogeneity in ultra-fine grained bulk AZ91 produced by accumulative back extrusion (ABE) [J]. Materials Science and Engineering A, 2011, 528: 4312−4317. [9] M´ATHIS K, GUBICZA J, NAM N H. Microstructure and mechanical behavior of AZ91 Mg alloy processed by equal channel angular pressing [J]. Journal of Alloys and Compounds, 2005, 394: 194−199. [10] DAHLE K A, LEE Z C, NAVE M D, SCHAFFER P L, JOHNSON D H. Development of the as-cast microstructure in magnesium- aluminium alloys [J]. Light Metals, 2001(1): 61−73. [11] KUMAR N V R, BLANDIN J J, DESRAYAUD C, MONTHEILLET F, SUERY M. Grain refinement in AZ91 magnesium alloy during thermomechanical processing [J]. Materials Science and Engineering A, 2003, 359: 150−157. [12] EBRAHIMI G R, MALDAR A R, EBRAHIMI R, DAVOODI A. The effect of homogenization on microstructure and hot ductility behaviour of AZ91 magnesium alloy [J]. Kovove Mater, 2010, 48: 277−284. [13] WANG L, KIM Y M, LEE J, YOU B S. Improvement in rollability of AZ91 magnesium alloy by carbon addition [J]. Materials Science and Engineering A, 2011, 528: 943−949. [14] KHOSRO AGHAYANI M, NIROUMAND B. Effects of ultrasonic treatment on microstructure and tensile strength of AZ91 magnesium alloy [J]. Journal of Alloys and Compounds, 2011, 509: 114−122. [15] KIM W J, PARK J D, KIM W Y. Effect of differential speed rolling on microstructure and mechanical properties of an AZ91 magnesium alloy [J]. Journal of Alloys and Compounds, 2008, 460: 289−293. [16] ION S E, HUMPHREYS F J, WHITE S H. Dynamic recrystallisation and the development of microstructure during the high temperature deformation of magnesium [J]. Acta Metall, 1982, 30: 1909−1919. [17] FLYN P W, MOTE J, DORN J E. On the thermally activated mechanism of prismatic slip in magnesium single crystals [J]. Trans the Metall Society of AIME, 1961, 221: 1149−1154. [18] MAKSOUD I A, AHMED H, RODEL J. Investigation of the effect of strain rate and temperature on the deformability and microstructure evolution of AZ31 magnesium alloy. [J]. Materials Science and Engineering A, 2009, 504: 40−44. [19] MA Li-qiang, LIU Zhen-yu, JIAO Si-hai, YUAN Xiang-qian, WU Di. Dynamic recrystallization behaviour of Nb−Ti microalloyed steels [J]. Wuhan University of Technology: Materials Science, 2008, 23(4): 551−557. [20] LIU L, DING H. Study of the plastic flow behaviors of AZ91 magnesium alloy during thermomechanical processes [J]. Journal of Alloys and Compounds, 2009, 484: 949−956. [21] XU S W, MATSUMOTO N, KAMADO S, HONMA T, KOJIMA Y. Dynamic microstructural changes in Mg−9Al−1Zn alloy during hot compression [J]. Scr Mat, 2009, 3: 61. [22] BEER A G, BARNETT M R. Influence of initial microstructure on the hot working flow stress of Mg−3Al−1Zn [J]. Materials Science and Engineering A, 2006, 423: 292−299. [23] BEER A G, BARNETT M R. Microstructural development during hot working of Mg−3Al−1Zn [J]. Metallurgical and Materials Transactions A, 2007, 38: 1856−1867. [24] BARNETT M R. Influence of deformation conditions on the high temperature flow stress of magnesium AZ31 [J]. Light Metals, 2001(1): 167−177. [25] DING H, LIU L, KAMADO S, DING W, KOJIMA Y. Evolution of microstructure and texture of AZ91 alloy during hot compression [J]. Materials Science and Engineering A, 2007, 452−453: 503−507. [26] FATEMI-VARZANEH S M, ZAREI-HANZAKI A, HAGHSHENAS M. A study on the effect of thermo-mechanical parameters on the deformation behavior of Mg−3Al−1Zn [J]. Materials Science and Engineering A, 2008, 249: 438−444. [27] TAN J C, TAN M J. Dynamic continuous recrystallization characteristics in two stage deformation of Mg−3Al−1Zn alloy sheet [J]. Materials Science and Engineering A, 2003, 339: 124−132. [28] HUMPHREYS F J, HATHERLY M. Recrystallization and related annealing phenomena [M]. 2nd ed. UK: Elsevier, 2004. [29] SITDIKOV O, KAIBYSHEV K, SAKAI T. Dynamic recrystallization based on twinning in coarse-grained magnesium [J]. Mater Sci Forum, 2003, 419−422: 521−526. [30] GALIYEV A, KAIBYSHEV K, SAKAI T. Continuous dynamic recrystallization in magnesium alloy [J]. Mater Sci Forum, 2003, 419−422: 509−514. [31] GALIYEV A, KAIBYSHEV R, GOTTSTEIN G. Correlation of plastic deformation and dynamic recrystallization in magnesium alloy ZK60 [J]. Acta Mater, 2001, 49: 1199−1207. AZ91é•�å�ˆé‡‘çš„çƒåŠ›è¡Œä¸ºå’Œæ˜¾å¾®ç»„织演化 G. R. EBRAHIMI 1 , A. R. MALDAR 2 , H. MONAJATI 3 , M. HAGHSHENAS 4 1. Department of Materials Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran; 2. Department of Materials Engineering, Sabzevar Tarbiat Moallem University, Sabzevar, Iran; 3. Department of Materials Engineering, Islamic Azad University, Najafabad Branch, Isfahan, Iran; 4. Department of Mechanical and Materials Engineering, Western University, London, Canada 摘 è¦�ï¼šç ”ç©¶AZ91é•�å�ˆé‡‘在çƒåŽ‹ç¼©è¿‡ç¨‹ä¸çš„æµ�å�˜è¡Œä¸ºå’Œæ˜¾å¾®ç»„织演化。在350~425 °Cå¯¹è¯•æ ·è¿›è¡ŒçƒåŽ‹ç¼©å�˜å½¢ã€‚ 在应å�˜é€ŸçŽ‡ä¸º0.1 s −1 时，应å�˜åˆ†åˆ«ä¸ºå³°åº”å�˜ã€�0.3å’Œ0.5。使用光å¦å’Œæ‰«æ��电å�æ˜¾å¾®é•œç ”ç©¶æ˜¾å¾®ç»„ç»‡çš„æ¼”åŒ–ã€‚ç»“æžœ 表明, 在压缩过程ä¸å†�结晶晶粒沿预先å˜åœ¨çš„æ™¶ç•Œå½¢æ ¸ï¼›åŠ¨æ€�å†�结晶晶粒的数é‡�éš�ç�€åº”å�˜çš„å¢žå¤§å‘ˆæŒ‡æ•°å¢žåŠ ï¼Œ 且æœ�从Avrami方程；动æ€�å†�结晶晶粒的尺寸在开始时增大，达到最大值å�Žå¼€å§‹å‡�少。 关键è¯�：AZ91é•�å�ˆé‡‘ï¼›çƒåŽ‹ç¼©ï¼›æ˜¾å¾®ç»„织演化；å†�结晶；峰应å�˜ (Edited by YANG Hua) 2008, 460: 289−293. [16] ION S E, HUMPHREYS F J, WHITE S H. Dynamic recrystallisation and the development of microstructure during the high temperature deformation of magnesium [J]. Acta Metall, 1982, 30: 1909−1919. [17] FLYN P W, MOTE J, DORN J E. On the thermally activated mechanism of prismatic slip in magnesium single crystals [J]. Trans the Metall Society of AIME, 1961, 221: 1149−1154. [18] MAKSOUD I A, AHMED H, RODEL J. Investigation of the effect of strain rate and temperature on the deformability and microstructure evolution of AZ31 magnesium alloy. [J]. Materials Science and Engineering A, 2009, 504: 40−44. [19] MA Li-qiang, LIU Zhen-yu, JIAO Si-hai, YUAN Xiang-qianHot deformation behavior of AZ91 magnesium alloy in temperature ranging from 350°C to 425°CThe flow behavior and microstructure evolution of AZ91 magnesium alloy during a thermomechanical process, hot compression test, was investigated. The specimens were hot compressed at a temperature ranging from 350°C to 425°C and at strain rate of 0.1 s−1 to the strains of 0.3, 0.5 and peak. Microstructural evolutions were studied using optical and scanning electron microscopes. The results show that during the compression process, the recrystallized grains nucleate along the pre-existing grain boundaries. The amount of dynamically recrystallized grains is increased with strain in a sigmoid scheme followed by Avrami equation. The size of dynamically recrystallized grains also increases at the beginning and decreases after reaching the maximum value.Effect of hybrid gelator systems of beeswax-carrageenan-xanthan on rheological properties and printability of litchi inks for 3D food printingHybrid gelators can be used for improving textural and rheological properties of foods, have more potential for 3D printing. This paper studied the rheological, microstructural and 3D printing characteristics of litchi pulp with hybrid gelators of beeswax, κ-carrageenan and xanthan gum. The rheological results showed that, in the extrusion stage of 3D printing process, the yield stress of the hybrid gelator ink (HGI) was 623.27 ± 4.38 Pa, the K and n value were 2.92 × 105 Pa·sn and 0.12 ± 0.01, respectively. In recovery stage, the time of shear viscosity returned to a stable was 30 s and the gelation time was 124.52 s for HGI. In self-supporting stage, the G′ of HGI was almost 10 times that of hydrogelator ink (HI). These results indicate that HGI has good shear-thinning, recovery and mechanical properties. Differential scanning calorimeter and X-ray diffractometer revealed that this rheological property was caused by the beeswax in the hybrid gelators after incubation (45 °C) that produced more orthorhombic structure and consumed the energy in the ink. The microstructure indicated that the HGI was a hybrid gelator systems filled with beeswax, which increased the printability of the material during the printing process. The product printed with HGI has high precision, and could withstand an inclination angle of 53.5° and a layer height of 85 layers. These hybrid gelator systems play a guiding role in improving the stability, precision and formability of 3D printed products.Three-dimensional (3D) food printing is an innovative fabrication method that has the advantages of customized food designs, personalized nutrition, simplification of the supply chain and broadening of the available food material (). This technique has the potential to produce a variety of foods in the future (). However, in recent years, 3D printing technology has also faced many difficulties. Most of these problems are closely related to the rheological properties of the materials in the printing system, which can make moulding of the product difficult and lead to poor stability, low-precision printing, and low printing efficiency (). Therefore, the development of specific food gel systems suitable for 3D printing based on a regulation of the material properties is the main subject of current food 3D printing research.Hydrocolloid is a hydrogelator, with the characteristics of thickening and gelling water-based solutions, which can improve the rheology of food materials and make the materials suitable for 3D printing ( reported that hydrocolloids (xanthan gum, gelatin, and agar etc.) could enhance the printability and texture. used hydrocolloids to improve the rheology and printability of multi-component gel systems of carrageenan-xanthan-starch. However, the use of hydrocolloids has the disadvantage of poor stability of the printed products, such that they cannot support higher printing layers. While organogelators have high hardness and thermal stability. Researches show that hybrid gelator (hydro and organo) systems usually impart good rheological properties and mechanical properties (A. J. ). The properties are mainly manifested as an enhanced thermal stability and recovery, a smooth texture, a higher viscosity and a greater yield stress. The hybrid gelator systems are a potential 3D printing material.). Beeswax is a hard and dystectic material with high thermal conductivity and thermal reversibility (). One of the necessary conditions for materials suitable for 3D printing is thermal reversibility. In addition, the high hardness of beeswax is conducive to the self-support of printing materials. It is speculated that addition of beeswax-carrageenan-xanthan hybrid gelators to the litchi inks can improve the moulding performance of printed products.In this study, litchi and carrageenan-xanthan were used to form a hydrogelator ink (HI), and then adding beeswax was used to form hybrid gelator ink (HGI) at a particular temperature by high-speed mixing. Both groups of ink were used as a material for 3D printing. After incubating at a certain temperature, the two inks were squeezed and printed. The rheological properties, thermal properties and crystal structure of the hybrid gelator ink formed by adding beeswax were compared and analysed. The forming mechanism of HGI was evaluated by 3D printing, and the printed product was evaluated.Dried “Nuomici” litchi (water 240.00 mg/g, total sugar 618.00 mg/g, fiber 83.00 mg/g, pectin 51.00 mg/g, protein 6.00 mg/g, other 2.00 mg/g) was supplied by Guangzhou Jiali Dried and Fresh Fruit Food Co. Ltd (Guangzhou, China). Decolorized beeswax (molecular mass 677.20, melting point 56–65 °C, acid value 5–8, ester value 80–95, total volatile matter max 1.00%), xanthan gum (average molecular weight of 2000.00 kDa) and κ-carrageenan (average molecular weight of 277.60 kDa) were purchased from Sigma-Aldrich (Zwijndrecht, Netherlands).Dried litchi was soaked in distilled water (w/v, 1:1) for 30 min, and then homogenized by colloid grinder for 10 min. The moisture content of above-mentioned homogenate was condensed to 9.00% by freeze dryer. Hydrocolloid (κ-carrageenan and xanthan gum, w/w, 1:1) were dispersed in distilled water, and then completely dissolved at 100 °C for 10 min.Two groups of ink were prepared for 3D printing. (1) hydrogelator ink (HI): composed of litchi homogenate (69.80 g), carrageenan (0.75 g), xanthan gum (0.75 g), and distilled water (28.70 g). (2) hybrid gelator ink (HGI): composed of litchi homogenate (53.30 g), carrageenan (0.75 g), xanthan gum (0.75 g), beeswax (15.00 g), and distilled water (30.20 g). The moisture remained at 35.00%. Then, to remove the air bubbles which was introduced by stirring, the vacuum oven (25 °C, −0.08 Mpa) was used for the mixtures incubation and continued for 30 min.The moulding stability of the inks was assessed by syringe type extrusion-based 3D printer (SCXNNOVE-E1, Changxing Shiyin Technology Co. Ltd, China). A 3D model (squirrel, bottom layer thickness was 1.0 mm, layer height was 0.8 mm, the wall thickness was 1.6 mm and the fill density were 100%) was established, and then inks were printed after incubating at 45 °C for 30 min. The nozzle length, diameter, printing speed and printing temperature were 2.0 cm, 0.8 mm, 22.0 mm s−1 and 45 °C, respectively. The rated extrusion force is 71.0 N. Stability evaluation: the height and tilt angle of the squirrel model is used to evaluate the stability of the ink.The rheometer (MCR520, Anton Paar, Austria), which equipped with Peltier heating system, was used to characterize the rheological properties of inks. This system contained parallel plate geometry (25 mm diameter, 1 mm gap). The rheological behavior was determined according to the method of with some modifications. In order to make samples steady, equilibration treatment was carried out at initial temperature (45 °C) for 1 min. During the extrusion process, temperature ramp tests (the temperature was heated from 25 °C to 65 °C), yield stress and shear-thinning behavior were carried out. Recovery period was consisted of shear recovery and temperature recovery (temperature recovery was applied to characterize the complex modulus (G*, G* = (G′2 + G″2)0.5, indicating the overall resistance to deformation) in connection to time dependence when temperature changed from printing temperature 45 °C to room temperature 25 °C). Self-supporting stage, A dynamic frequency sweep was performed, from 0.1 Hz to 10.0 Hz, at a constant strain of 1 × 10−3 (within the linear viscoelastic range).The differential scanning calorimeter (DSC3 STAR, Mettler Toledo, Switzerland) testing was carried out according to previous reported method with some modifications (Artur J. ). The heating and cooling scanning temperature range was 25 °C–50 °C with a rate of 5 °C min−1. Integrations of DSC peaks were done using a line baseline, and it represents the corresponding enthalpy value. Characterize the change in the heat of the ink during the 3D printing process.The crystal structure of the samples was characterized using an X-ray diffractometer (XRD-6000, Shimadzu, Japan). Cu (Kα) radiation (wavelength = 1.5418) as the incident X-ray source, operating at 50 mA and 40 kV, performing 2θ scans from 3° to 50° at a rate of 2° min−1 (). The crystalline index (%cryst) was determined by the method from the The samples were freeze-dried for experiment. The sample was firstly tested at 25 °C, and then placed it in an incubator (MIR-154, SANYO Electric Co. Ltd, China) at 45 °C for 30 min, and finally tested again at 25 °C. Simulate the effect of temperature on the crystal structure of the inks during the 3D printing process.Scanning electron microscope (ZEISS Gemini SEM series, Germany) was used to observe the microstructure of the freeze-dried samples. The sample was placed and observed in a SEM chamber, the parameters of which were 5.0 kV and 400 X.Each sample was measured in triplicate for average data and then plotted the curves. SPSS (version 13.0 for Windows) and Origin (version 9.0 for Windows), as statistical tools, were used for follow-up analysis, diagramming and linear fitting.During extrusion-based 3D printing, the following conditions are required for the ink: (1) it must be able to be squeezed smoothly, (2) the viscosity and mechanical strength must be recovered quickly after being extruded, (3) there must be a sufficient mechanical strength for non-deformability after it is deposited (). Therefore, extrusion-based printing contains three stages: extrusion, recovery and self-support.The first phase is extrusion. During this process, the viscosity, yield stress and shear-thinning behavior of the ink determine its extrudability. A presents changes in the viscosity as a function of the temperature for HI and HGI during a temperature sweep of 6 °C min−1. Both groups of ink exhibited similar profiles in that the viscosity decreased during the temperature sweep. Specifically, at low temperatures (25–56 °C), the viscosity of HGI was higher than that of HI, but at high temperatures (56–60 °C), the opposite was true. Notably, the distinct boundary was 56 °C, which suggested that the changes in viscosity were related to the melting point of the beeswax. Beeswax is a combination of polymorphs with a high melting point (56–65 °C) (). It crystallizes rapidly into a solid state when placed below the melting temperature. reported that the presence of solid particles increases friction in the continuous hydrogel phase. Therefore, the addition of beeswax increases the viscosity in the ink under the melting point. When the ink was heated and reached a certain temperature (56 °C), the beeswax melted, and Brownian motion of the organic molecules in the beeswax was enhanced (). The hydrophobic force induced organic molecules in the beeswax to connect, which led to a separation of the interface in the hydrogel system. The resistance in HGI changed from mixed friction to liquid friction. reported that the viscosity of organic molecules in beeswax is only 0.1 mPa·s. Therefore, the viscosity decreased rapidly in HGI. Based on the characteristics of 3D printing, a lower viscosity of ink is necessary to avoid nozzle clogging by the ink, but an excessively low viscosity can lead to shaping difficult after extrusion. As a result, the ink needs a suitable viscosity during the printing process. The viscosity of HGI decrease rapidly as the temperature exceeded 56 °C, which is not conducive to product shaping. Therefore, the printing temperature should be appropriately lower than this temperature (56 °C), so we choose 45 °C for subsequent experiments.The yield stress and viscoelastic modulus (G′) reflect the mechanical strength of the ink, as it supports subsequent stacking layers during post-printing conditions. Moreover, an appropriate yield stress is essential for extrudability since it is strongly linked to the minimum force required to initiate the flow of an ink (). The yield stress of an ink is defined as the intersection of G′ and G′′ (viscous modulus) (B shows the variations in G′ and G″ for the HI and HGI as a function of shear stress at 45 °C. The G′ and G″ of HGI were significantly higher than those of the HI. For clarity, the yield stress of the inks is illustrated in . The yield stresses of HI and HGI were 460.02 and 623.27 Pa, respectively. This result indicated that HGI had a higher mechanical strength and yield stress, which enabled the ink to exist in a solid-like form after extrusion. In HGI, the solid beeswax particles increased the hardness of the system because the particles were stiffer than the matrix ( reported that at shear rate from 1 to 100 s−1, the shear action increased the frequency of collisions and contact time between particles, and the collision and aggregation of wax particles resulted in the formation of a large network of crystals. In the current study, the rigidity of HGI increased when the shear rate up to 2 s−1. Hence, HGI had a greater viscoelastic modulus and yield stress than the HI. The extrusion was discontinuous during the printing, which means that the extrusion process would repeatedly start and stop; therefore, a low yield stress was needed during the extrusion and subsequent printing processes. The minimum pressure required to start a flow for the ink with a yield stress is described by Pmin = (4L/D) τyield (), where Pmin, L, D and τyield represent the minimum pressure required, the nozzle length, the nozzle diameter, and the yield stress of the ink, respectively. The rated extrusion force of the 3D printer was 71.0 N. Through calculations, the rated yield stress of the 3D printer was 1413.27 Pa, which is significantly greater than the yield stress of HGI (623.27 Pa).After overcoming the yield stress, the required pressure that keeps inks fluid depends on their viscosity and the shear-thinning property (C, HI and HGI exhibited shear-thinning characteristics at 45 °C, and the viscosity decreased and the shear stress increased as the shear rate increased. Significantly, the shear stress and viscosity of HGI decreased rapidly when the shear rate exceeded 10.0 s−1. reported that a shear rate exceeding 10 s−1 would destroy the crystal network of beeswax. Therefore, when the shear rate was lower than 10.0 s−1, beeswax still exists in complete solid form at 45 °C, and then the viscosity decreased and the shear stress increased as the shear rate increased ( reported that the alkane crystals of beeswax melt at 45 °C. At the shear rate exceeds 10 s−1, the melted alkane crystals in beeswax to be exposed to the ink herein. In hybrid gelator systems, when the concentration of the oil phase increased, the viscosity of the system significantly decreased (). As a result, the liquid friction between HGI components reduced the shear stress rapidly. The model that is frequently used for shear-thinning fluids is the Power Law (η = Kγ(n−1)) (). For n < 1, the fluids have the characteristics of shear thinning, and a smaller n indicates an increase of shear-thinning behavior (, the K values of HI and HGI were 2.21 and 2.92 × 105 Pa·sn, respectively, which are consistent with our previous results ( B). Moreover, the n values of HI and HGI were 0.21 and 0.12, respectively. As the incompatibility between the two-phase system led to a weakening of the interaction forces between the hybrid gelators, the cross-linked carrageenan-xanthan molecules in HGI were more likely to break (). During the shearing process, the carrageenan-xanthan molecules in hybrid gelator systems were so prone to orientation movement that the value of n decreased. The HGI exhibited increased shear thinning. In the extrusion stage, the melting of the orthorhombic structure in beeswax is beneficial to reduce the viscosity and shear stress of HGI. At the same time, the incompatibility between the hybrid gelators promotes the low n value of HGI. This facilitated the smooth extrusion of HGI.The second stage is recovery. During this process, inks extruded from the nozzle tip experienced shear force and temperature changes. Thus, the recovery of the properties of the ink was determined by the viscosity recovery and temperature recovery characteristics. A shows the shear recovery characteristics of ink during high and low cyclic shearing rates at 45 °C. To simulate the shear conditions during extrusion, the ink was first treated with a shear rate of 2 s−1. Then, the shear rate increased to 10 s−1. Finally, the shear rate was set to 2 s−1 again. Both groups of ink viscosity significantly decreased at a high shear rate and recovered rapidly at a low shear rate. For HGI, the viscosity sharply declined from 3.28 × 105 Pa·sn at 2 s−1 to 0.33 × 105 Pa·sn at 10 s−1, then quickly became stable within 30 s and remained steady even over an extended amount of time, indicating that the ink returned to a stable state. However, the viscosity of HI decreased from 2.85 × 105 Pa·sn at 2 s−1 to 0.45 × 105 Pa·sn at 10 s−1 and recovered sequentially, and the viscosity could not be restored to the stable state. These results revealed that HGI had a better shear recovery performance. reported that shear action generates considerable frictional heat in high-viscosity media systems. As explained earlier in C, HGI experienced liquid friction behavior at 45 °C, which generated less heat than the HI. Less heat enables the material to return to a stable state. During the shear recovery period, the viscosity of HGI recovered its stability easier in a short time. reported that HGI with rapid shear recovery is suitable for 3D printing because they can be quickly recovered and provide a sufficient mechanical strength, which is essential to support the next extruded layer.A temperature cycle test was executed to investigate the gelation kinetics of the inks (B). Tgel stands for the time needed to reach the G* plateau (). As the temperature decreased, the value of G* in both groups of ink increased significantly, but HGI had a higher G* value. By linear fitting, the Tgel of HGI and HI were 124.52 and 150.45 s, respectively. A short Tgel enables rapid gelation of inks so they can obtain a sufficient resistance to deformation and then self-support (). This result indicated that HGI had a more rapid gelation and a higher overall deformation resistance. When the temperature decreased below 45 °C, the alkane crystals in the beeswax re-accumulated, and the thermodynamically stable phase was transformed into a solid, which significantly increased the hardness of the beeswax particles ( reported that the stiffness of a fat-filled hybrid gelator systems increases when the fat hardness increases. Simultaneously, the aggregate particles in the beeswax increased the stiffness in HGI during the shearing process (). The hardness of the material is linearly related to the overall deformation resistance, and the modulus of the hybrid gelator systems ink increased significantly as the temperature decreased (). In addition, the thermal conductivity of beeswax is 0.25 W/mK, so it is a good thermal storage material (). It is presumed that a part of the heat was absorbed and accumulated by the beeswax under the same incubation conditions (45 °C, 30 min) in the HGI. Compared with the amount of heat in HI, HGI contained less heat and was more prone to gelation in a short time during the cooling process (). In the process of 3D printing, HGI, which demonstrated a rapid gelation and high resistance to deformation, ensured the high precision and stability of the printed products.The last part indicated that it was self-supporting. The self-supporting behavior of the ink was evaluated by a frequency sweep test (). The G′ of the two groups of ink were obviously higher than G″. The two groups of ink exhibited certain solid rheological properties. Moreover, G′ in HGI was almost 10 times that of the HI. G′ reflects the stiffness of a printed material, which indicates its ability to support subsequent deposited layers after the printing process (). A high G′ is favourable for the stability of the ink. These results show that HGI has a stronger self-supporting ability, which is conducive to the self-supporting ability of the ink after printing. The addition of beeswax significantly improved the stiffness of the hybrid gelator ink, consistenting with the results in DSC measurements are used to measure the thermodynamic and kinetic parameters of materials. demonstrates the normalized non-isothermal DSC curves obtained for each component during a cycle of cooling-heating between 20 and 50 °C at a rate of 5 °C min−1. The variation in the heat flow as a function of the temperature presents a different transition (peak) from 31 to 43 °C in HGI (A). This result indicated that the beeswax is a major cause of thermal distortion of the inks. According to B, the endothermic and exothermic peaks from HGI were observed at 39.25 °C and 38.17 °C, respectively. This peak corresponded to the solid-solid transition of the int-(CH2) peak from the orthorhombic alkane transition from the orthorhombic to rotator phase ( also reported that the temperature change of the orthorhombic endothermic peak transition is from 33.9 to 42.4 °C, and the temperature corresponding to the exothermic peak is from 31.5 to 41.5 °C. Interestingly, the energy of endothermic enthalpy (1.73 J/g) and exothermic enthalpy (0.75 J/g) of HGI is not conserved by fitting the area under the peak. This suggested that the orthorhombic structure consumed energy during the phase transition (). Therefore, under the same processing conditions, part of the energy of HGI was consumed by the orthorhombic structure in the beeswax, resulting in a lower heat in HGI than HI. HGI can quickly undergo gelation and is more suitable for 3D printing, confirming the speculation in XRD measurements are used to investigate the molecular arrangements of structures forming crystals. The characteristic peaks of the crystalline structure of the samples during incubation (45 °C) and room temperature (25 °C) are presented in . Obviously, the diffractograms of HGI (B) have four typical diffraction peaks, which located at 2θ = 4.42° (weak), 6.66° (very weak), 21.28° and 23.62°. According to Bragg's law (2dsinθ = nλ), their interplanar spacings were calculated to be 2.00, 1.33, 0.42 and 0.30 nm. This indicated that these diffraction peaks were caused by the beeswax (). However, this difference from the results by , who observed nine peaks. This difference may be attributed to part of the peaks being obscured by non-crystalline regions. Moreover, the crystallization index (%Cryst) of HGI treated with different conditions is shown in . When HGI was incubated at 45 °C, the monoclinic crystal index for the peaks at 2θ = 4.42 and 6.6° was reduced from 0.63 to 0.46 and 0.21 to 0, respectively, which may have been caused by the chemical reaction of the diesters in the beeswax. Conversely, the crystal index of orthorhombic peaks at 2θ = 21.28 and 23.62° increased from 5.26 to 5.83 and 1.74 to 1.95, respectively, which was caused by the increase in hydrocarbons/monoesters in the beeswax at 45 °C (). Noticeably, the results in DSC show that the energy absorbed and released by HGI was not conserved, which illustrated that the orthorhombic content in the beeswax affected the heat absorption and exothermic process of the energy change of HGI. The decomposition of diesters into hydrocarbons/monoesters requires the absorption of large amounts of energy (H. ). Therefore, it may be that the diesters in the beeswax underwent a substitution reaction at 45 °C, which absorbed a large amount of heat in HGI and generated additional hydrocarbons/monoesters. During the cooling process, hydrocarbons/monoesters restacked to form orthorhombic structures. The orthorhombic structure had a high hardness, which significantly improved the deformation resistance of HGI (). Advantageously, during the 3D printing process, the low heat in HGI promoted rapid gelation of the ink, and the high deformation resistance of the ink remarkably improved the shape preservation of the printed product.SEM has been used to show complex composite morphologies. Typical SEM images for HI and HGI are shown in . Obviously, HGI (B) showed a rough characteristic surface with a particle distribution compared that for HI (A). Beeswax exists as a solid at room temperature and fills in HGI. Moreover, these beeswax particles are distributed relatively evenly. Litchi homogenate contains many fibres, polysaccharides, proteins and other substances, which increase the binding sites for carrageenan-xanthan and their interactions (). A high viscosity system was formed, and the beeswax particles were dispersed in the system uniformly. Thus, HGI was a hybrid gelator systems filled with beeswax. Furthermore, during the extrusion process of the 3D printer, the dispersed beeswax particles in HGI facilitated the smooth passage of the nozzle, which ensured the formability and accuracy of the printed product.A squirrel without support on the hand was printed to investigate the ability of HI and HGI to fabricate complex 3D structures (). First of all, both groups of ink could be continuously and smoothly extruded. However, the squirrel printed by HGI maintained its shape even under the load of many successive layers (85 layers), which was challenging for the HI. Comparatively, the shape of the squirrel fabricated by HI lacked stability and disintegrated during the same treatment as HGI. To characterize the self-supporting ability of HGI, the angle of inclination of the squirrel without support on the hand was used to evaluate the ability of the ink to manufacture complex 3D structures. The angle of the squirrel arm printed with HGI reached 53.5°. HGI exhibited excellent 3D printing behavior. The following factors can explain this finding. Firstly, during the extrusion stage, the orthorhombic crystals in the beeswax were melted at an incubation temperature of 45 °C, simultaneously, the shearing action exposes the melted orthorhombic organic molecules to the HGI system. The viscosity of the HGI decreases rapidly and the ink can be extruded smoothly. Secondly, during recovery stage, the shear stress and temperature disappear and decrease, respectively. HGI realizes gelation in a short time, and the beeswax solidifies rapidly, which improves the mechanical strength of the system. Finally, during self-support stage, the solidified beeswax particles and carrageenan-xanthan gel provide sufficient mechanical strength of the system to ensure that the printed product is not deformed. Thus, HGI can significantly improve the 3D printing of complex food systems when beeswax-carrageenan-xanthan work together during the printing process.In conclusion, edible litchi inks containing hybrid gelator (hydro and organo) systems, which were produced with a mixture of beeswax, carrageenan, xanthan and litchi, exhibited improved rheological behavior and mechanical strength. In the hybrid gelator systems, the orthorhombic structure of beeswax melted and more hydrocarbon/monoester compounds were formed during the incubation (45 °C) which led to increase the shear-thinning effect of HGI. Simultaneously, during the formation of hydrocarbon/monoester compounds, it consumes energy and shortens the Tgel. Once hydrocarbon/monoester compounds formed, it re-stacks to form more orthorhombic structures during self-support stage, which increase the mechanical strength. These hybrid gelator systems have the advantages of smooth extrusion, fast gelation, and high deformation resistance during the 3D printing process, and could improve the accuracy, shape retention and stability of 3D printed food materials.The authors declare no competing financial interest.Han Tian: Methodology, Data curation, Writing - original draft, Investigation, Software, Formal analysis. Kai Wang: Validation, Supervision, Writing - review & editing. Haibo Lan: Formal analysis, Writing - review & editing. Yao Wang: Formal analysis. Zhuoyan Hu: Supervision, Writing - review & editing, Resources, Funding acquisition. Lei Zhao: Conceptualization, Methodology, Supervision, Writing - review & editing, Resources, Funding acquisition.Damage-based strength reduction factor for nonlinear structures subjected to sequence-type ground motionsThis paper investigates the strength reduction factor of single-degree-of-freedom (SDOF) system subjected to the mainshock–aftershock sequence-type ground motions. Both displacement ductility and cumulative damage are considered in the reduction factor. Records of mainshock-aftershock earthquakes were collected and classified according to site properties. The aftershock ground motions in sequence are scaled to five relative intensity levels. Based on the nonlinear time-history analysis of inelastic SDOF systems, the effects of natural period, ductility factor, damage index and aftershock have been studied statistically. The results indicate that the aftershock ground motion has significant influences on strength reduction factors, and the damage-based strength reduction factor is about 0.6–0.9 times of the ductility-based strength reduction factor. Finally, an empirical expression for strength reduction factor was established by regression analysis.According to statistics, about 88% of strong earthquakes are accompanied by aftershocks. An aftershock is defined as a smaller earthquake following the mainshock, which is the largest earthquake in the sequence. Structural damage caused by the mainshock is further aggravated under aftershocks and can even lead to structural collapse. The 2010 New Zealand Current seismic design principles include analysis of a structure's elastic-plastic behavior under moderate/rare earthquakes. Since the design strength of most structures is generally much lower than the minimum strength required to maintain the elastic stage under strong earthquakes, a reduction factor is often used to reduce the elastic strength demand and thereby obtain the elastic-plastic strength demand of a structure. Theoretical analysis and experimental studies of strength reduction factors have demonstrated that the structure ductility has a significant effect on the strength reduction factor. The displacement ductility factor helps to assess the extent of structural damage where Fy(μ=1) is the yield strength required to maintain the structure in elastic stage; Fy(μ=μi) is the yield strength required to maintain the ductility demand of the structure equal to a given target ductility value as μi.Moreover, the cumulative damage of nonlinear hysteresis cycles also plays a significant role in determining the damage level of a structure. Some studies suggest that cumulative damage can be accounted for by modifying the ductility capacity, such as the equivalent ductility method where Fy,D is the inelastic strength demand to limit the inelastic response of the structure to a specified damage level Dj for a given ductility capacity μi. In this study, the performance levels of a structure are defined using a damage index to take the cumulative damage of the structure into consideration.As mentioned above that the aftershock will aggravate structural damage, current damage-based strength reduction factor, however, does not reflect the influence of aftershock ground motions. In this regard, the current study explores this issue through extensive numerical calculations on a nonlinear SDOF system subjected to sequence-type ground motions. collects real mainshock and aftershock ground motion records that are essential to investigate RD. The collected records are then divided into different categories according to the site condition. defines the performance level and computational parameters to be used in the calculation of RD. In , extensive elastic-plastic time history analysis of a nonlinear SDOF system with various parameters are then carried out to determine the RD for two cases, i.e., mainshock only and mainshock plus one aftershock. The influence of ductility factor, damage index and some other parameters on RD are explored in through parametric studies. Finally, an empirical formula for damage-based strength reduction factor is proposed in A sequence-type ground motion record usually consists of one mainshock event and one or multiple aftershock events, which are called as one earthquake (mainshock only), a sequence of two earthquakes (mainshock plus one aftershock), a sequence of three earthquakes (mainshock plus two aftershocks), and so on. Scenario of mainshock plus one aftershock was commonly considered in previous studies To build up a ground motion of two earthquake events, one can connect two artificial ground motions In total, we constructed 342 sequence-type ground motion records for site classes B and C as listed in . The number of qualified records for site classes A and D are too small to conduct any meaningful statistical analysis. For further analysis, the PGA of mainshock of all the selected sequence-type ground motion records were scaled to an identical value of 0.2g.The relative peak ground acceleration of aftershock ground motion γ is defined as:where PGAas is the PGA of aftershock ground motion, PGAms is the PGA of mainshock ground motion. The parameter γ was introduced to represent the relative intensity level of aftershock with respect to the mainshock. The intensity of aftershock is usually smaller than that of mainshock. However, the aftershock ground motions with greater intensity with respect to that of mainshock ground motions do exist in real earthquake records. Thus, to study the effect of relative intensity of aftershock on the strength reduction factor, five levels of γ are considered in this study, there are γ=0.5, 0.8, 1.0, 1.2 and 1.5.Peak displacement or storey drift are common parameters used in performance levels in performance-based structural design and evaluation. However, structural damage takes on various forms under an earthquake, and the extent of the structural damage may not be fully reflected by maximum deformation or storey drift only where D is the damage index, μm is the ductility factor when the structure reaches the maximum elastic-plastic deformation under earthquake ground motion, μu is the ductility factor when the structure fails under monotonic loading, Fy is the yield strength, xy is the yield displacement, Eh is the cumulative hysteretic energy dissipation under earthquake ground motion, β is a constant parameter that represents the ratio of cumulative damage caused by hysteretic energy. Negro To associate the performance levels with the damage index resulting from modified Park-Ang model, performance levels and the range of the damage index should be determined firstly. Four performance levels, namely Operational, Immediate Occupancy, Life Safety and Collapse Prevention, are proposed by FEMA-356 , show that D=(0.2–0.5) is the boundary of repairable damage and unrepairable damage while the D approaching 0 represents elasticity without damage. Thus, an additional performance level named Damage Control was suggested between Immediate Occupancy and Life SafetyThe dynamic equilibrium equation of a nonlinear SDOF system subjected to an earthquake is given by:where c is the damping coefficient; fs is the restoring force of the structure; x is the relative displacement, and xg is the ground displacement.According to the definition of the strength reduction factor in Eq. , it is able to calculate the RD spectra by Eq. when the period, damping ratio and restoring force model of the SDOF system are given. shows the computation flowchart for determining RD spectra. For any ground motion input, the RD is calculated by gradually reducing the strength ΔF from the corresponding elastic strength Fe under given ductility until the specified D is achieved within a tolerance of 1%. Then, a series of strength reduction factors RD for SDOF system in different ductility factors μi and damage indexes Dj can be obtained by calculating different periods and ground motions, which constitute the RD spectra.For a comprehensive study of the RD factor under single earthquakes and sequence-type earthquakes, a series of SDOF systems are employed in the calculation. The hysteretic model used in this study is elastic-perfectly plastic model because of its simple constitutive relationship. The natural period of the SDOF system varied from 0.1 to 3.0 s with an interval of 0.1 s and its viscous damping ratio was assumed to be 5%. Five ductility factors μ=2, 4, 6, 8 and 10 are selected to consider the different ductility performance, and five damage indices D=0.1, 0.2, 0.5, 0.8 and 1.0 are selected to consider the different damage level.Using the procedure just described, a total of 513,000 strength reduction factors are computed, corresponding to the SDOF systems with 30 periods undergoing five different levels of ductility and five levels of damage index when subjected to 342 mainshock ground motions and corresponding 342 main-aftershock ground motions. Results are analyzed statistically according to the period, the ductility, the damage index of the system and the site condition where the motion is recorded. For example, shows all the calculated RD curves and pseudo spectral accelerations (PSA) curves for μ=6, D=1.0 and site class C for mainshock and seismic sequence, respectively. Their mean spectra are also plotted in thick solid lines. Due to space limited, just the representative results are shown in the following sections, while other cases having the similar results are not shown.The mean RD spectra of the SDOF systems of different ductility classes and damage indices for the two site classes subjected to mainshock ground motions and mainshock-aftershock ground motions with γ=0.5 are shown in . As shown in the figures, the RD factor shows the same trend regardless of ductility, damage index, site condition and type of ground motions. The RD factor increases with increasing period of systems, the variation is dramatical in short period region (0–1.0 s). In the long period region (1.0–3.0 s), the RD factor is approximately period independent and approach to a constant value based on ductility and damage index.For a given damage index, the mean RD increases with the increase of ductility factor. That is to say, the strength demand of the structures with high ductility is smaller than that of the structures with poor ductility. It indicates that structures with sufficient ductility can withstand a certain degree of damage caused by earthquake. The ductility has significant effect on the RD. For example, the average difference between the mean RD of μ=2 and 4 is about 34% for the structures with D=1.0 on site class B subjected to sequence-type ground motions.For a given ductility factor, the mean RD increases with the increase of target damage index. It indicates that the damage of the structure with high strength is lighter than that of the structure with low strength subjected to same ground motion. The effect of damage index is considerable. For example, the average difference between the mean RD of D=0.2 and 0.5 is about 31% for the structures with μ=6 on site class B subjected to sequence-type ground motions.To reflect the degree of dispersion of the strength reduction factor spectra, the coefficients of variation (COV) of the corresponding mean RD spectra are calculated, the COVs of RD spectra subjected to sequence-type ground motions with γ=0.5 are shown in . The COV is defined as the ratio of the standard deviation to the mean.The COVs are independent of the period, and COVs on different site class present the approximate trend. However, for a given period, the COVs change rapidly with the variation of damage index and ductility factor. The maximum coefficient of variation of the mean strength reduction factor calculated under each group site condition does not exceed 45%, which reflects the randomness and discreteness of the ground motion in a certain extent.In order to study the influence of the cumulative damage on the strength reduction factor, the assessment of structural damage parameters using displacement and modified Park-Ang damage index respectively are compared, and the difference of the ductility-based strength factor Rμ and the damage-based strength factor RD is calculated under the same sequence-type ground motions, as shown in . When the damage index and the ductility factor are same, Rμ and RD changing with period of structure are mainly the same. Because of the damage contribution in terms of energy, the displacement demand of RD is less than that of Rμ, so the RD value is always less than the Rμ value. Under sequence-type ground motions, the ratio between the RD and Rμ is 0.8–0.9 for low ductility factor (μ=2), and the ratio is 0.6–0.9 for high ductility factor (μ=6).In the short period region, the mean RD/Rμ for sequence-type ground motions with γ=0.5 decreases drastically with the period increases, indicating that the effect of energy item accounts in damage index is changed rapidly. Because the yield strength of system is large when period is close to zero, the hysteretic energy dissipation is small relatively, thus the difference of RD and Rμ is small. The yield strength of system decreases and the hysteretic energy dissipation increases when period increases, so the changing of RD is more greatly than Rμ and the RD/Rμ decreases drastically.In the long period region, the mean RD/Rμ for sequence-type ground motions with γ=0.5 decreases slightly with the period increases. The yield strength and yield displacement decrease weakly and the energy item accounts in damage index increases slightly with the period increases.To evaluate the effect of aftershock on the RD factors, the value of RD, seq/RD, ms, which represents the ratio between RD of sequence-type ground motions (denoted as RD, seq) and corresponding RD of mainshock ground motions (RD, ms), are employed. The mean RD, seq/RD, ms is calculated with the structures of different ductility factors and damage indices subjected to different intensity of aftershock, part of the results are shown in shows the mean RD, seq/RD, ms for sequence-type ground motions with γ=0.5 and μ=6 (b and d). The mean RD, seq/RD, ms are within [0.94, 0.98] Ce within [0.93, 0.99] on site class C. The difference between RD, seq and RD, ms is less than 10%, so the aftershock ground motions with γ=0.5 can be ignored in evaluating the RD factor.When γ increase to 1.0, the mean RD, seq/RD, ms for the ductility factor equal to 6 constantly or the damage index equal to 1.0 constantly is shown in . The mean RD, seq/RD, ms are within [0.82, 0.96] on site class B, while the mean RD, seq/RD, ms are within [0.81, 0.96] on site class C. The aftershock ground motions with γ=1.0 would decrease the RD factor at a level of <20%. The RD subjected to sequence-type ground motions is always less than that of mainshock ground motions, indicating that the strength demand of sequence-type ground motions is greater than that of mainshock ground motions. The effect of aftershock is significant in this case.For the same damage index, the mean RD, seq/RD, ms is insensitive to ductility factor. It indicates that the aftershock ground motion has similar effects on the RD for different ductility factors. For the same ductility factor, the values of RD, seq/RD, ms have little difference for various damage index except for D=0.1. The value of the mean RD, seq/RD, ms for D=1 is quite larger than other values of D. This is because the systems remains in elastic region when D=0.1, and the cumulative damage is so small that can be ignored. In this case, the RD is mainly depending on the historical maximal displacement, so the difference between RD, seq and RD, ms is subtle, as shown in To study the influences of the intensity of sequence-type ground motions, the mean RD, seq/RD, ms with different values of γ are analyzed. The mean RD, seq/RD, ms of SDOF systems with μ=6 and D=1.0 subjected to sequence-type ground motions are shown in . It is obviously indicate that the mean RD, seq/RD, ms decrease with the increase of γ. The effect of aftershock ground motion on the systems in short period region is greater than that on the systems in medium-long period region. Take mean RD, seq/RD, ms of sequence-type ground motions with γ=1.5 as the example, the values of mean RD, seq/RD, ms is smaller than 0.7 in the short period region while the values of mean RD, seq/RD, ms is larger than 0.8 in the medium-long period region; That is to say, the RD factor decrease by more than 30% in the short period region and less than 20% in the medium-long period region when the systems subjected to the aftershock ground motions with γ=1.5.From the discussion above, the influence of aftershock on the RD factor are related to the period of the system, the damage index and the intensity of aftershock. Besides, the damage of structures subjected to sequence-type ground motions is severer than that of structures subjected to mainshock ground motions due to the cumulative damage caused by aftershock. Therefore, the yield strength demand of sequence-type ground motions is greater. And the higher the intensity of aftershock is, the greater the yield strength demand is needed.The influence of site conditions on RD spectra can be seen in where mean RD spectra are plotted for system subjected to sequence-type ground motions recorded on site class B and site class C. As shown in these figures, the RD spectra on the two site condition have the similar tendency in all period range.For the convenience of comparison, the ratio between the RD spectra for site class B and the RD spectra for site class C are calculated and the results are plotted in . It is shown that site class B exhibits lower RD values in the short period (<1.0 s), while exhibiting higher RD values in the long period (1.0–3.0 s). This phenomenon implies that the neglecting of site condition effect will lead to a certain overestimation of inelastic strength demand in the short period (<1.0 s). The RD spectra on site class C exhibit an opposite trend. However, the errors are within 10% for different ductility levels and damage indices. Thus, the influence of site condition on the RD spectra can be neglected. The RD is just a reduction factor from elastic spectra to inelastic spectra. Besides, the effect of site condition on the RD spectra does not reflect its effect on elastic spectra and inelastic spectra.To study the influence of post-yield stiffness ratio H on RD factor, two levels (5% and 10%) of post-yield stiffness ratio are selected to compare the influence. For the convenience of comparison, the ratio between the RD spectra of different post-yield stiffness ratio and the RD spectra of elastic-perfectly plastic are computed and the results are listed in . The RD factor of elastic-perfectly plastic is 0.9–1.0 times of the RD factor of 5% post-yield stiffness ratio, while the RD factor of 5% post-yield stiffness ratio is 0.95–1.0 times of the RD factor of 10% post-yield stiffness ratio. The results indicate that the increase of this ratio leads to a slightly increase of RD factor, but not the major influence factor.To study the effect of damping, the RD of systems with damping ratio ζ=0.02 and ζ=0.10 is calculated. The RD of structures with damping ratio ζ=0.02 and ζ=0.10 is normalized by the RD of structures with ζ=0.05 for sequence-type ground motions with γ=0.5, as shown in It is evident that the decrease of damping ratio always results to increase of RD factor by various extents. For elastic structures, the input energy is dissipated by the structural damping; for inelastic structures, the input energy is dissipated by the structural damping and hysteretic energy. The damping has a significant influence on the elastic structures and a less effect on the inelastic structures. Thus, the RD factor decreases with the increase of structural damping.Take the RD of ζ=0.05 as the benchmark, the influence of damping is commonly within 20% and 15% for ζ=0.02 and ζ=0.10 respectively. With the decrease of damage index, the corresponding RD of ζ=0.02 or ζ=0.10 is approaching to the RD of ζ=0.05.For practical purpose, the overall mean RD curves are desired to using a unified expression because of the similarity shape of mean RD for different grouping of parameters. Modification coefficients can be employed to incorporate for special condition. Based on the observations above, three factors, which have a significant effect on RD spectra, are considered to conduct regression analysis. Then, the simplified expression of RD is the function of period T, damage index D and ductility μu, that isFurthermore, the simplified expression of RD must satisfy the following boundary limits:When the period of structure is close to zero, the corresponding yield displacement tends to zero and a small reduction of elastic strength leads to very large ductility. Thus very stiff structures should be design as elastic system:For a structure, the damage index D=0 means that the structure subjected to ground motions suffers no damage, so the structure will stay elastic stage without reduction of the strength:For a structure, the ductility μu=1 means that the structure will stay elastic stage without reduction of the strength:In large period range, RD will close to a constant value, denoted as R̃D, which is a function of damage index and ductility.Based on all the above assumptions, the following equation for the mean RD spectra is obtained by regression analysis:RD=1+D(μ−1)(a0T+a1T2)(μ+a2)(1+a3T+a4T2)⋅10.87+0.08eγwhere a0, a1, a2, a3 and a4 are regression parameters depending on the site class, post-yield stiffness, the values of the parameters are listed in are compared with the actual mean spectra with the statistical results and the sequence ground motions with γ=0.5, as shown in . A good match is observed for all damage indices and ductility classes.As mentioned before, the previous relationships Rμ-μ-T represents that the ductility-based strength reduction factor is related to ductility and period with the ultimate limit state. The damage-based strength reduction factor is related to period, ductility and damage index, donated as Rμ-μ-D-T relationship. In order to compare the difference between the Rμ and the RD, the RD spectra with the ultimate limit state D=1.0 and the Rμ spectra are draw in . Generally, the RD spectra and the Rμ spectra exhibit similar trends. The RD spectra are always lower than the Rμ spectra at same ductility and soil condition. Meanwhile, when the ductility factor is small, the difference between the two is not obvious, but with the increase of the ductility factor, the difference becomes obvious. Comparing the strength reduction factor of sequence-type ground motion and aftershock ground motion, the difference is significant, indicating that the influence of aftershock cannot be ignored.The primary purpose of this paper is to investigate the damage-based strength reduction factor RD for sequence-type ground motions. The construction of RD spectra for various damage index and ductility levels ensure a more rational determination of strength demand of inelastic systems, taking into account the cumulative damage with multiple performance targets. For the purpose, a statistical study of RD factor was conducted. The RD factors are computed for a series of elastic-plastic SDOF systems undergoing different levels of damage index and ductility factor subjected to a large number of sequence-type ground motions recorded on different site conditions. The influence of aftershock on RD is specially studied. The following conclusion can be drawn from this study.The RD factor is strongly dependent on the period of system in short period and approximately independent on the long period.The difference between damage-based strength reduction factor RD and damage-based strength reduction factor Rμ is significant, and the latter is 40% higher than the former in the long period for sequence-type ground motions. That is, the strength demand determined by RD factor is greater than that determined by Rμ factor.The influence of aftershock ground motion on RD factor increases with the increase of intensity of the aftershock. The effect of aftershock ground motion with γ=0.5 on RD factor can be negligible, while the aftershock ground motion with γ=1.5 can decrease the RD with short period at a level of more than 25%. The effect of aftershock ground motion on RD factor depend on the period, ductility factor, damage index and the intensity of the aftershock ground motion.The proposed expression of the RD is proposed as a function of period, damage index and ductility factor. The regression parameters are dependent on the site condition, post-yield stiffness ratio and the intensity of aftershock ground motion. The expression of the RD can be used to easily determine the strength demand of inelastic systems in seismic design.Synthesis and characterization of the mechanical properties of Ti3SiC2/Mg and Cr2AlC/Mg alloy compositesHerein we report on the fabrication and characterization of Mg and Mg-alloy metal matrix composites (MMCs) reinforced with the MAX phases, Ti3SiC2 and Cr2AlC. Pure Mg and Al-containing Mg-alloys with varying Al content (AZ31, AZ61 & AZ91), were pressureless melt infiltrated into 55±1 vol% porous MAX preforms. The resulting microstructures and mechanical properties were characterized by X-ray diffraction, scanning electron microscopy, microhardness and uniaxial compression tests. Similar to Ti2AlC/Mg composites increasing the Al content in the matrix enhanced the mechanical properties of the Mg/Ti3SiC2 composites, but had little effect on the properties of the Mg/Cr2AlC composite system. The latter were inferior to those reinforced with the other MAX phases. The Ti3SiC2/AZ91 composite achieved the highest Vickers hardness (1.9±0.1 GPa), yield strength (346±4 MPa) and ultimate compressive strength (617±10 MPa) obtained in this study. All composites exhibited fully and spontaneously reversible hysteresis loops, evidence of energy dissipation, during compression cycling. Having an elastic modulus of ≈ 160 GPa, the Ti3SiC2/AZ91 composite may be suited for high specific strength, high damping applications.Magnesium, Mg, alloys have attracted a great deal of interest over the past decades in the aerospace, automotive and electronics industries mostly due to their lightweight, high specific strengths, damping capacity and superior machinability The MAX phases, possessing a unique combination of metallic- and ceramic-like properties, have the potential to be used as reinforcements in metal matrix composites, MMCs One of the main motivations of fabricating MAX/Mg composites has been the fact that both Mg and the MAX phases are kinking non-linear elastic, KNE, solids The purpose of this work was to determine if the aforementioned mechanical property trends can be repeated, and/or improved upon in the same Mg alloy matrices used previously, but with other MAX phases, specifically, starting with Ti3SiC2 or Cr2AlC powders.The following composites: Ti3SiC2/Mg, Ti3SiC2/AZ31, Ti3SiC2/AZ61, Ti3SiC2/AZ91, Cr2AlC/Mg, Cr2AlC/AZ31, Cr2AlC/AZ61, and Cr2AlC/AZ91 were fabricated. In most cases the reinforcement loading was ~ 55±1 vol%.Pure Mg (99.8% pure), AZ31B (3 wt% Al, 1 wt% Zn) both purchased from Alfa Aesar (Ward Hill, MA) and AZ61L (6 wt% Al, 1 wt% Zn, low Mn) and AZ91D (9 wt% Al, 1 wt% Zn) both supplied by Thixomat (Livonia, MI) were used. The Ti3SiC2 powder used is commercially available (−325 mesh, Kanthal, Sweden). Approximately 500 g of the as-received Ti3SiC2 powder was placed into a 500 mL plastic bottle (US Plastic, Lima, OH) along with ≈25 (10 mm in diameter) zirconia milling balls (Inframat® Advanced Materials, Manchester, CT) which in turn was placed on a ball mill rotating at 60 rpm for ≈ 24 h. The milled powders were subsequently passed through a − 400 mesh sieve. Thus all Ti3SiC2 powders herein were − 400 mesh.In synthesizing Cr2AlC powders, it is important to keep the heating rate low. A fast heating rate can cause a self-propagating high temperature reaction – i.e. the powders ignite. The heating rates also depended on the amount of reacted material. For 450 g, 600 g and 700 g batches of elemental Cr:Al:C powders the heating rates were: 300, 125 and 100 °C/h, respectively. Powder bed heights, corresponding to the three batches of elemental powders, were ~ 67, 90, and 105 mm, respectively.The bricks of lightly sintered, high purity Cr2AlC were milled into a fine powder using a semi-automated milling machine (Bridgeport Machines Inc., Brigdeport, CT). The milled powder was then subject to the same ball milling and sieving procedure described above. This process was repeated until ~ 400 g of − 400 mesh powder – sufficient to synthesize all Cr2AlC reinforced MMCs used in this work – was obtained.Porous Ti3SiC2 (54 ± 1 vol% dense) and Cr2AlC (55 ± 1 vol% dense) preforms were synthesized using the same procedure. A cylindrical graphite die ~ 170 mm high, ~ 114 mm wide and 38 mm in diameter was used to make the preforms. Approximately 60 g of the sieved – 400 mesh MAX phase powders was poured into the graphite die bore in 10 g batches. After every 10 g addition, the die was gently tapped (manually) on the workstation table a few times to decrease the chances of having large voids in the powder pack. The die was, however, not tapped too much as to orient the MAX powders, as a random orientation of particles was desired. Once the die was prepped, it was placed in the HP.To synthesize the Ti3SiC2 preforms, the HP was heated to 1100 °C, at a rate of 500 °C/h, and held at 1100 °C for 1 h. A loading rate, corresponding to ~ 70 MPa/h, began when the furnace reached 900 °C. The maximum pressure of 13.8 MPa was sustained while the furnace was at its maximum temperature. The application of pressure was necessary to produce green-bodies with strengths that were good enough to prevent fracture during MI. This method produced 18 mm high and 38 mm in diameter porous (54 ± 1 vol% dense) Ti3SiC2 cylinders. The density of the sintered preforms was calculated from their mass and dimensions. Four preforms of each MAX phase powder were made.To synthesize Cr2AlC preforms, the HP was heated to 900 °C at a rate of 500 °C/h and held at 900 °C for 1 h. This procedure produced 55±1 vol% Cr2AlC cylinders, ~ 18 mm high and 38 mm in diameter. No pressure was applied in this case and the resulting preforms were more fragile.Both HP programs were operated under ~10 Pa vacuum, and had a cooling rate of ≈ 500 °C/h. A controlled and relatively slow cooling rate from the peak temperature is important to avoid thermal shock of the sintered green-body preforms.Any extra Mg was ground off (Struers Rotopol-22, Struers Rotoforce-4, Cleveland, OH) using 80 grit sandpaper (Allied High Tech, Compton, CA) in the presence of water. The sample was then vacuum heat dried for one hour at ~ 140 °C. Archimedes' principle was used to confirm that the samples' densities were 95% dense or higher.Each MMC was cross-sectioned (Struers Accutom-5, Cleveland, OH.) using a diamond wafering blade (Allied High Tech products, #60–20080, Compton, CA), hot mounted (Struers LuboPress-3 Cleveland, OH) in epoxy (Allied High Tech products, #150–10105, Compton, CA), and subsequently polished down to a 1 µm surface using a diamond slurry (Allied High Tech, Compton, CA). Polished surfaces were imaged in a scanning electron microscope, SEM (Zeiss Supra 50VP, Germany) equipped with an energy dispersive spectroscope (Oxford Inca X-Sight, Oxfordshire, UK).X-ray diffraction, XRD, patterns of the composite samples were obtained using a diffractometer (Rikagu Smartlab, Japan) with step scans of 0.02° in the 5° to 80° 2-theta range and a step time of 1 s, with a 10 mm2 window slit. Cu Kα radiation (40 kV and 30 mA) was used.XRD was also performed on the synthesized − 400 mesh Cr2AlC powder. A small addition of silicon (~ 5 wt%) was added as an internal standard. Jade XRD pattern recognition software (Materials Data, Inc., Livermore, CA.) was used to analyze the XRD results.Vickers microhardness measurements were made using a Vickers microhardness indenter (LECO Corp., St. Joseph, MI) using a 10 N force with a 10 s dwell time. Ten indentations were made on each MMC composition. These measurements were averaged and their standard deviations determined.The composites made herein were readily machinable, as previously reported for MAX phase MMC composites The cubes were loaded until fracture on an electromechanical testing machine (Instron 5600, Norwood, MA). Each EDM cylinder was cyclically loaded in compression in order to determine yield strengths and effective moduli. An extensometer (2620-603 Instron, 10 mm gauge length with a 10% full range) was attached directly to the cylinder to measure strain. For the cyclic loading, each cylinder was loaded to a maximum stress followed by subsequent cycles in decrements of 50 MPa down to 100 MPa. The maximum stress was approximately 65% of the maximum UCS for each composite as determined from the cubes. This was done to guarantee that the cyclic compression samples would not be destroyed.The cyclic stress-strain tests showed reversible non-linear behavior, in the form of closed hysteric loops. Thus, it is non-trivial to determine their true Young's moduli. To circumvent this problem, a linear regression of the closed hysteric loops - obtained when the maximum stress was 100 MPa – was used to estimate what we refer to as the modulus at 100 MPa or E100. Another metric used to quantify the stiffnesses of these composites is the effective elastic modulus, Eeff(avg), which is obtained by least squares fitting of the entire data set and gives an overall effective "average" modulus An additional Ti3SiC2 composite sample was fabricated with AZ31 using 3 vol% more MAX phase reinforcement and was then mechanically tested. This was done in hopes to better understand the sensitivity of mechanical properties in regards to a composite with a slightly higher percentage of MAX phase reinforced composition. Furthermore, an additional Cr2AlC composite was made by jet-milling the synthesized powder. As the commercially produced Ti3SiC2 powders are jet milled, and were found to have significant deformation, the possible repercussions on the interfacial strength between the matrix and the reinforcement were preliminarily investigated.B) for the Cr2AlC powders synthesized herein, found them to predominantly single phase. Small peaks, corresponding to ~ 1 wt% of Cr23C6 were found to exist.Typical, back-scattered electron SEM images of the Ti3SiC2 (54 ± 1 vol%)/Mg, Cr2AlC (55 ± 1 vol%)/Mg and jet-milled Cr2AlC (53±1 vol%)/Mg composite samples are shown in A, B, and C, respectively. In these images, the MAX phase constituents appear as light gray and the Mg-matrices appear as dark areas around the former. For the Ti3SiC2 based MMCs, the matrix appears intact (A). However, for the Cr2AlC-based MMCs there was clear evidence of particle pullouts that most likely occurred during polishing (B). Comparison of these micrographs also makes it clear that the Ti3SiC2 particles were much more deformed and delaminated than their Cr2AlC counterparts. The latter were more circular and less deformed (compare A and B). However, jet-milling the Cr2AlC powders produced a morphology more similar to the commercially obtained Ti3SiC2 (compare A and C). As discussed below, this morphology could have influenced the mechanical properties.A compares the Vickers microhardness, VH, results obtained herein to those of previous work on the Ti2AlC/Mg-alloy compositions as a function of Al-content in the Mg alloys A it is also clear that while the VH values for the Ti2AlC and Ti3SiC2 MMCs increased monotonically with increasing Al-content, the VH values of their Cr2AlC counterparts were more or less independent of Al-content. The VH of the composite made from jet-milled Cr2AlC was found to increase slightly with the presence of 9 wt% Al.The UCSs were also compared with previous work B). The Ti2AlC/AZ31, Ti3SiC2/AZ91 and Cr2AlC/AZ91 composites were found to have a maximum UCS of 773±7, 617±10, and 545±35 MPa, respectively. The Ti3SiC2 reinforced MMCs generally show an increasing trend in UCSs with Al wt% in the matrix. On the other hand, the UCSs of the Cr2AlC reinforced MMC’s mimic those of the VH (compare C). For both the Ti2AlC and Ti3SiC2 MMCs, YSs were generally observed to increase with Al content in the matrix. The YSs of Cr2AlC MMCs were, again, relatively independent of Al content.The E100 values for the Ti3SiC2 and Cr2AlC based composites were also compared with previous work D). The maximum E100 values for the Ti2AlC, Ti3SiC2, and Cr2AlC based MMCs were found to be 136 ± 6, 159 ± 3 and 133 ± 1 GPa, respectively. Similar to the YS, E100 dropped slightly at 3 at% Al, before rising again modestly (When the MMCs tested in this work were loaded to a maximum stress of 350 MPa followed by loading to lower stresses, they exhibited fully reversible non-linear behavior in the form of closed hysteresis loops (Mechanical testing results from the Ti3SiC2/AZ31 and Ti3SiC2/AZ91 (both with 54 ± 1 vol% Ti3SiC2) MMCs were compared with the Ti3SiC2 (58 vol%)/AZ31 composite’s testing results (). The E100, Eeff(avg), YS, UCS and VH results for the Ti3SiC2 (54 vol%)/AZ31 and Ti3SiC2 (58 vol%)/AZ31 are compared in . The 3% increase in carbide preform density (from 54 to 58 vol%) resulted in 7%, 10% and 13% increases in UCS, VH and YS, respectively.), it is clear that, for the most part, the general property trends of the Ti3SiC2/Mg-alloys MMCs mimic those of the Ti2AlC/Mg based composites reported by Anasori et al. One of the main conclusions of our previous work A, B and C, indirectly confirm this important conclusion since it is obvious that the properties of the Ti2AlC/Mg based composites are higher than their Ti3SiC2-reinforced counterparts. This conclusion becomes even more compelling when it appreciated that the Young's modulus of Ti3SiC2 (≈ 340 GPa) is higher than that of Ti2AlC (≈ 280 GPa) D, show that at the lower Al contents, the E100 results of the Ti3SiC2- and Ti2AlC-based MMCs are comparable. However, at about 160 GPa, the E100 of the Ti3SiC2/AZ91 composite samples is, as far as we are aware, the highest ever reported for a readily machinable Mg-based composite. We previously reported on TiC-AZ91 composites with E100 of 184 ± 5 GPa We now turn our attention to the Cr2AlC-based MMCs. Referring to , it is clear that all the properties plotted exhibit a minimum at ≈ 3 wt% Al, before increasing again. The fact that in all cases, and in sharp contradistinction to the other two MAX reinforcements, the properties of the 3 wt% Al are lower than those of the pure Mg MMCs is important and strongly suggests that one of the constituents of the AZ series alloys has a deleterious effect on the matrix-reinforcement interface bonding in the case of Cr2AlC.In general, when the increases in mechanical properties of the composites are compared to the AZ series of the Mg alloys without reinforcements (not shown), the rates of increase are comparable. For example, the increase in VH of the Ti3SiC2 and Cr2AlC composites is ~ 0.5 GPa going from 0 to 9 wt% Al (A). The corresponding increase in VH of the pure alloy matrices is ~ 0.3 GPa , to the presence of the Al in the Mg matrices. Said otherwise, the reason the mechanical properties of the composites increase with Al-content is because the matrices themselves get stronger as a result of solid solution hardening Interfacial reaction/bonding with Al in the matrix should account for the remaining improvement in properties. It follows that a decrease in properties in the case of Cr2AlC may be attributed to the only other major alloying element, viz. Zn, that for whatever reason, segregates at the interface and weakens it. Under this hypothesis, at low Al concentrations, there may not be enough reaction/bonding between Cr2AlC and the matrix to overcome the deleterious effects of the Zn. However, at higher Al concentrations more reaction/bonding can occur and some interfacial strength is regained. These comments notwithstanding it is hereby acknowledged that more work is needed to understand the degradation in properties observed in the case of Cr2AlC.As noted above, the Ti3SiC2/AZ91 composite was found to have the highest mechanical strengths. The Al’s affinity to wet Ti3SiC2, coupled with Mg’s ability to infiltrate between the micro- and nano-fissures of the kinked and delaminated MAX particles (A) can explain the good mechanical/elastic properties of the Ti3SiC2/Mg-alloy composites.SEM micrographs of the starting Cr2AlC grains showed them to be rather smooth with few kinks and/or delaminations. This provides two strong points of argument for the reduced mechanical properties observed for the Cr2AlC/Mg-alloy composite system: 1) the Mg or Mg-alloys did not have opportunity to penetrate between the Cr2AlC particles' microcracks and nanofissures to create the strong mechanical interlocking witnessed in the Ti2AlC- and Ti3SiC2-based composite systems, 2) Cr2AlC is not in thermodynamic equilibrium with Al at 800 °C To test the first conjecture we jet milled some of our Cr2AlC powders. The Vickers hardness value of the Cr2AlC/AZ91 composite made with the jet milled powders was slightly higher than those made with the regular powder (open blue circles in A). And while these results suggest that deforming the particles may enhance the mechanical properties, the effect is small and possibly within statistical error. Thus, it is likely the interfacial reaction products and/or lack of wetting have the largest effect on mechanical properties.Upon cyclic compression testing, fully reversible hysteretic stress-strain loops were observed for all MMCs fabricated herein. These results are similar to the previous work on single phase Ti3SiC2 and Ti2AlC-Mg composites Porous Cr2AlC and Ti3SiC2 preforms were pressurelessly melt infiltrated with Mg and Mg-alloys to produce Mg-composites reinforced with 55±1 and 54±1 vol% Cr2AlC and Ti3SiC2, respectively. From an examination of the microstructural and mechanical properties of these composites we conclude that:Al-containing Mg-alloys reinforced with Ti3SiC2 have better mechanical properties than pure Mg. Specifically, the AZ91-based composite displayed the highest mechanical and elastic properties in this work. Notably, at 160 GPa, the E100 of this composite is one of the highest ever reported for a Mg-based composite.For composites reinforced with Cr2AlC, on the other hand, the effect of Al-content in the Mg-alloys had a small effect on the VH, UCS, Eeff(avg), E100, or YSs.Closed and fully reversible hysteresis loops were observed for every sample fabricated in this work. These loops are representative of the damping capability of Mg-alloys and consistent with the formation of ripplocations in the MAX phases.Microstructural characterization by SEM has made it clear that the Ti3SiC2 reinforcement phase is severely kinked and delaminated with an elongated rectangular morphology. As-synthesized, the Cr2AlC grains are more or less spherical. However, after jet milling, their morphology were more similar to the commercial Ti3SiC2 powders that are also jet milled.The lower mechanical strengths of the Cr2AlC-reinforced composites are likely due to reduced interfacial reaction/bonding, as little improvement in hardness was found after jet milling. Further work is needed to understand the interplay of the MAX phases with Zn in the Mg alloys, and with the reaction products that form due to the thermodynamic instability of MAX phases with Al.The difference in mechanical properties between the two Ti3SiC2/AZ31 composites stemming from the vol% density of the porous Ti3SiC2 sintered preforms is considerable. The effect of a small increase in preform density (+3%) shows a considerable increase in mechanical properties. Although there was only a 3% increase in the effective modulus at 100 MPa, there are appreciable increases in the VH, YS and UCS. Therefore it is suggested that future work composites with higher MAX phase loadings should be investigated; especially for the Ti2AlC/AZ91 and TiC/AZ91 composites.A continuous crystallographic approach to generate cubic lattices and its effect on relative stiffness of architectured materialsThis original work proposes to investigate the transposition of crystallography rules to cubic lattice architectured materials to generate new 3D porous structures. The application of symmetry operations provides a complete and convenient way to configure the lattice architecture with only two parameters. New lattice structures were created by slipping from the conventional Bravais lattice toward non-compact complex structures. The resulting stiffness of the porous materials was thoroughly evaluated for all the combinations of architecture parameters. This exhaustive study revealed attractive structures having high specific stiffness, up to twice as large as the usual octet-truss for a given relative density. It results in a relationship between effective Young modulus and relative density for any lattice structure. It also revealed the opportunity to generate auxetic structures at will, with a controlled Poisson ratio. The collection of the elastic properties for all the cubic structures into 3D maps provides a convenient tool for lattice materials design, for research, and for mechanical engineering. The resulting mechanical properties are highly variable according to architecture, and can be easily tailored for specific applications using the simple yet powerful formalism developed in this work.The important development of Additive Manufacturing (AM) processes and the potential capabilities that it offers for industrial applications, allows producing more complex three-dimensional parts. These opportunities highlight new ways to design optimal functional and lightweight structural parts. The use of lattice structures is also motivated by the requirements to reduce the costs inherent to the AM processes by decreasing material consumption and building time. The development of architectured porous materials is the ultimate step to achieve mass reduction on mechanical parts. Basically, this reduction consists in removing the fraction of the material that has a limited effect if any on the mechanical resistance. Hence, only the load-bearing material fraction is kept. To achieve this mass-reduction, two main strategies are emerging. The first approach relies on a topological optimization [] aimed at removing the needless part of the material (.1). This first strategy is efficient, but depends widely on the initial geometry of the considered part. In addition, topological optimization may result in multiple solutions, with numerical issues on the selection of the proper optimal structure. The second strategy aims at developing mesostructured metamaterials having controlled properties, which can fit a large range of application requirements []. Since the last decade, this strategy has been successfully explored by Ashby and Bréchet []. They developed hybrid multifunctional materials with appropriate properties providing an extension of the Ashby selection map compared to the initial properties of the bulk materials.The lattice architecture is especially attractive for its capability to produce Functionally Graded Materials (FGM) with variable stiffness. Again, there are two main strategies: either the lattice density is modified, or the architecture is altered. These two distinct concepts are illustrated on .2 and .3: metal lattices were obtained by selective laser melting by using TA6V powder, with a laser power of 175W and a scanning rate of 775 mm/s. If the density is affected (.2), the part weight may become sub optimized. On the other hand, to adjust the stiffness gradient while preserving mass minimization (.3), it is necessary to produce architectures at will with a continuous procedure. It is also necessary to capture accurately the effective contribution of architecture to stiffness, independently of the density. As far as we know, up to now, there has not been any method reported in the literature for the continuous generation of lattice architectures. Information concerning the dependence of stiffness on density in a large cluster of continuous structures is also a missing piece of information. It would be very relevant and groundbreaking to set a method for the generation of architectures using crystallographic rules, and to compare them by evaluating the mechanical behavior. This paper proposes a continuous generation of cubic architectures and the investigation of the relationship between stiffness and density.Periodic-cell and architectured structures have been extensively studied due to straightforward mathematical description []. The octet-truss lattice is an example of a structure which is commonly investigated. Fuller initially proposed this structure in 1961 []. Nayfeh focused on its elastic properties [], while its plastic behavior has been studied by Deshpande et al. []. It is worth noticing that the octet-truss lattice is especially attractive because it fulfills the Maxwell criterion [where b is the number of struts, j is the number of joints, s and m are the number of states of self-stress and mechanisms. The octet-truss is therefore able to bear mechanical loading even in the case of frictionless rotation at joints []. The octet-truss symmetry corresponds to a face-centered cubic structure []. Many other structures with cubic symmetry have also been analyzed []. However, some of these cubic lattices were considered of lesser interest since they do not satisfy the Maxwell criterion. Indeed, they are assumed to exhibit significant stress level at nodes inducing an early collapse of the structure.Nevertheless, any cubic lattice could possibly be attractive regardless of Maxwell’s criterion. For instance, the primitive cubic structure [] does not satisfy the Maxwell criterion, but is commonly adopted for simple mechanical structures. In itself, any lattice structure could be interesting due to specific elastic properties [This study aims at exploring large numbers of geometrical configurations based on cubic lattices with crystallographic symmetry. First, the study will propose a continuous description of the architecture with reduced parameters. Next, the third section is devoted to the estimation of elastic properties using finite elements computations. Numerical results are then illustrated as performance surfaces by exploring the whole space of the architectural parameters. In the fourth section, the effect of the lattice architecture on the overall specific moduli is analyzed leading to the formulation of an explicit relationship. The latter clearly expresses the impact of relative density on elastic properties. The end of this section is dedicated to the Poisson ratio of cubic structures yielding to the identification of original auxetic structures for specific architectures and density ranges. The paper ends with some concluding remarks and provides some ideas for a future work.At first sight, the mathematical description of lattices is complex since each beam location requires three position coordinates and three Euler angles. The description is made easier by considering only the joint nodes, having three coordinates only. It is common sense in crystallography to reduce further the mathematical description of nodes positions using symmetries. The minimal number of nodes to generate a 3D lattice can be reduced to a couple of points by proper use of all the isometric operations of a given space group. This approach using symmetries is innovative because it breaks with the habit of considering lattices as a huge complicated beams cluster. This new approach focuses on the minimalist architectural information of the lattice network. Any alteration of this information would lead to great modifications by moving continuously and slightly a single structural parameter. Such a method is ideal for mechanical engineering due to its simplicity and its versatility. The question arising at this point is: what is the minimal information required to properly describe cubic lattices?In materials science, the three most common crystal structures are primitive cubic (Pm3¯m), face centered (Fm3¯m) and body centered (Im3¯m). If the atoms in a crystal are replaced with vertices in the lattice, and chemical bonds are beams, then crystalline architectures can be directly applied to build porous materials. These three usual cubic structures have a common point: they share the samem3¯m point group. However, this m3¯m group contains only 10 well-known space groups, leading to 10 lattice structures already reported in literature. This panel would be very limited for producing FGM. To generate a larger number of structures, it is necessary to break the rules given by Bravais lattices, while preserving the symmetries of the point group. To distance ourselves from these rules, let us first consider the Bravais structures more closely. The Bravais cubic lattices are defined by two sets of nodes positions:One at the origin, defined by the vertex of the primitive cube,One located in the middle of the faces (FCC), or in the middle of the cube (BCC).The first set of nodes must be preserved as is, because it is a mandatory condition for cubic structures. The second set of nodes is more interesting, because it is defined by changing geometric coordinates. If one considers the unit cube length to be equal to one, then the secondary point has the following coordinates:For a primitive cube, it does not exist at all. Still, one can attribute coordinates (0, 0, 0.5) to this node, and the resulting lattice will be equivalent to the primitive cube. The structure is actually a perovskite (ABX3)-related structure with an empty A site []. If the structure is made of beams only, then the architecture can be considered as primitive-like.For a face-centered cube, the structure is set with a node at position (0, 0.5, 0.5)For a body-centered cube, the structure is set with a node at position (0.5, 0.5, 0.5)By generalization, it is possible to set a continuous description of cubic structures for Pm3¯m,Fm3¯m and Im3¯mspace groups by modifying the position of this secondary node. If the coordinates of the node are within the range (0 ≤ x ≤ 0.5), (0 ≤ y ≤ 0.5), z = 0.5, then the location is limited to the blue triangle shown on . This specific position necessarily generates continuous 3D space structures once symmetry operations are applied. In case the node does not belong to the triangle, the lattice network is usually broken due to some missing bindings, and the lattice is not relevant for mechanical engineering applications. The couple of (x,y) parameters within the range [0; 0.5] is a necessary and sufficient set to describe continuously a large family of cubic lattices within the m3¯m point group. This parameters set is to be considered as some kind of DNA of the architecture. Its continuous modification progressively drives the structure away from well-known crystal lattices to new configurations that have not been investigated until now.The lattices diverging from the usual space groups are no longer compact. Beams are no longer in agreement with the concept of chemical bonds in crystallography because the beams length may differ from the minimal distance between nodes. Only the primitive, face-centered and body-centered structures correspond to existing structures in crystallography. Other structures are correct in terms of symmetry, but have no equivalent in crystallography. details the building procedure of a FCC structure from two points A and B, by successive application of the isometries of the Fm3¯m space group. First, a beam produced from the two parent nodes is declared. Then, a (110) mirror creates a new node on the bottom face of the cube. Because the distances between the three nodes are equal, this results into a triangle. Then, the application of (101) forms a tetrahedron, which is the elementary basis of FCC structure, and represents tetrahedral sites of FCC. The (101) mirror propagates it to the other side of the cube, and successive operations finally fill the entire space with tetrahedrons, resulting in the well-known FCC octet-truss.. All the different software and scripts were handled by a main script managing the sequence of calculation steps. It allows to run large sets of calculations over wide parameters ranges in an automatic way, with barely no manual operations from the user.Finite Elements Model (FEM) was used to evaluate the mechanical behavior of the lattice structures. The finite element model is based on linear elasticity, and its setting does not constitute a scientific goal in itself, because the procedure is already very well-known. It is considered only as a convenient tool to determine the stiffness of the structures. The scientific challenge rather lies in the capability to process a large cluster of structures and to compare them with relevant and systematic post-processing of the FEM data. In particular, significant efforts were dedicated to extract information on the exact contribution of architecture independently of the relative density.The mechanical loading is compression: it is very common for testing foams and lattices, and it is easy to set up both experimentally and numerically. Compression is applied on a face of the cube, resulting in a macroscopic strain of ε=1%. For this range of low deformation, non-linear behavior was not detected, and buckling did not occur. The opposite face and two perpendicular faces were set as symmetry planes (blue faces on ). It implies a frictionless sliding on these planes. Therefore, the effective volume tested is 8 times larger than the computed volume, and corresponds to a cube with 2 cells width. The representative volume selected is a cube with a size of 1 arbitrary unit length. The model is insensitive to the repetition number of cubic cells if there are at least 8 cells. Due to symmetry planes, this condition is fulfilled and the model is robust with regard to the representative volume. The complete model was computed into the V6.13-2 Abaqus (Dassault Systèmes) finite element calculation software. A general static step has been considered to load lattices. The lattice was meshed with C3D4 linear tetrahedron continuous and isoparametric finite elements. The average number of elements is within the range 30000-250000 depending on the lattice beam density.The models were run for three different homogeneous materials, with isotropic elastic properties indicated in . Three decades of Young modulus are explored to evaluate the sensitivity of the model to the elastic properties of the bulk material. The first material typically has an elastic modulus close to the common ABS polymer used in 3D printers. The second material is typical of thermoset polymers and of some composites or natural materials. Finally, the third material is close to the properties of Ti-6Al–4 V alloy used for additive manufacturing by SLM or EBM. Poisson ratio is set constant at 0.4 for all materials, to capture only the effect of Young modulus on stiffness.The overall lattice stiffness (noted E) strongly depends on the relative density ρ and the elastic modulus of the material E0. Therefore, the relative Young modulus E/E0 is used to compare the architectures with one another. Moreover, the relative density ρ=V/V0 is computed, with V the volume of the lattice, and V0 the volume of a bulk elementary cube. The relative density is a direct measurement of the filling rate, or the porosity fraction. ρ=1corresponds to a bulk cube, and ρ=0 to an empty cube. The relative modulus E/E0 is discussed as a function of ρ to deduce the elastic performances of lattices.Six values of radii are explored: r = 0.05, 0.075, 0.1, 0.125, 0.2, 0.3; resulting in six different values of ρ for each lattice structure. In addition, x and y architectural parameters are explored within the range [0; 0.5] with a step of 0.05. The study requires 1188 calculations to entirely cover the 4-dimensions space of (x, y, r, E0) parameters.The usual Bravais lattices can be built-up from this new formalism by setting the parameters x and y to bound values. The primitive cube is obtained for x = 0 y = 0, FCC is obtained for x = 0 y = 0.5, and BCC for x = 0.5 y = 0.5. The intermediate structures for some x and y are more interesting and quite unexpected for a couple of them. illustrates the progressive change in structure with growing x and y. If y is increased from 0 to 0.2, then the beams are split in two V-shaped segments (b and e). If x and y vary together with the same value, the beams are not split in two, but get the V-shape, and the structure becomes the hexatruss well-known in literature [c and f). These structures with V-shaped branches are expected to have auxetic properties, with a negative Poisson ratio []. A special case occurs for x = 0.25 y = 0.25 (d): in addition to the V-shaped segments, new beams suddenly appear under this condition, because the distance between nodes n°2 (marked in red) is the same as the distance between nodes n°1 and 2. These beams are marked by red arrows, and correspond to new chemical bonds. The structure gains in density and may have different properties. If the x and y parameters increase together until their bound value set at 0.5, the V-shaped branches of the hexatruss structure join each other, and it results in a BCC structure.The relative lattice Young’s modulus was found to be completely independent from the bulk Young Modulus E0. The E/E0 ratio varies less than 0.01%, while E0 varies in the range 1 to 100. The E/E0 ratio can be safely considered as material-independent. Therefore, the conclusions thereafter can be considered valid for any kind of elastic isotropic material for small deformations.The relative Young’s modulus E/E0 is deduced from the set of calculations for different values of (x, y) and with variable density ρ. The overall results are displayed by black dots on . The dots are contained in a narrow area on the plot, and the overall trend is weakly affected by the change in architectures. This means the architecture has a second order effect, behind the density. The trend can be approached by a power law:This equation properly describes the bounds: if E = E0 then ρ = 1. In addition, parameter m is a much relevant indicator of the elastic behavior of a structure. In an ideal case, if m=1, then the architecture behavior follows the well-known rule of mixtures: stiffness is linearly correlated with density. According to Ashby et al. [], if m > 1 then there is a synergy effect: the material gets the best of porosities for mass reduction, and the best of bulk material for stiffness increase. If m < 1, then the result is the “weaker link scenario”, with limited mass reduction and a rapid decrease in stiffness. illustrates the power law in the specific case of octet-truss architecture, with x = 0 and y = 0.5. The relation is properly linear, and the slope is the coefficient m. The y offset is set to 0, because the modulus at ρ = 1 must match with the bulk Young modulus. The results are in good agreement with the experimental data obtained on octet-truss by Bonatti et al. [The global m coefficient is obtained by a least square regression of the power law. The average value of m is μ = 2.21, and the standard deviation is σ = 0.358. The red line on represents the average curve computed with the power law and the mean value μ. Blue dashed lines correspond to m = μ ± σ. Most cubic architectures have an m factor within this range. The cubic lattice structure benefits more from the weakening due to open porosities than from the reinforcement due to the beams. The trend is clear and the variation is limited despite the wide variety of structures. It can be deduced that this trend is likely to be common for many lattice structures, and only secondary order changes in stiffness are to be expected. also illustrates the relative modulus of two structures with the same density set at ρ = 0.5. The x = 0.005 y = 0.1 structure is 68% stiffer than the structure x = 0.25 y = 0.4. While the global trend is similar for all the lattices, significant variations of stiffness can result from small changes on m parameter. To conclude, changing the architecture results in noticeable improvement of properties while decreasing density, but it seems difficult to escape from the so-called “weaker link scenario” (m > 1).The resulting relative modulus E/E0 is illustrated on It is to be noticed that for a given radius, the structures with a maximal stiffness are not conventional Bravais lattices (PC, FCC, BCC), but rather correspond to non-trivial combinations of x and y parameters. The generation of complex cubic structures involves a larger number of beams by unit volume and provides in the end higher mechanical performances. For instance, the structure x = 0.15 y = 0.35 provides a density twice larger than octet-truss, and an apparent modulus three times larger for r = 0.1. The gathering of architectures properties into color maps is a powerful tool for the mechanical design of lightweight multifunctional parts.In the specific case of the research for a lightweight stiff material, the best architecture would be the one having the higher E/E0 without requiring an increase in ρ. In terms of m factor, this corresponds to the smaller values. illustrates the variation of m with x and y on a color map. The lowest value possible is reached for the primitive cubic structure, with m = 1.3. This means the primitive structure is the one requiring less matter for a given stiffness in uniaxial compression. This is not very surprising, given that the beams are mostly oriented in the direction of the loading axis, and pure compression is dominant in this structure. On the other hand, octet-truss has a higher m = 1.9, because beams are mostly oriented at 45° from the loading axis, and flexion is predominant. The m value reaches extremely high values for BCC structure, because exactly all the beams are oriented at 54.7° from the loading axis and there are no beams hindering flexion. The highest value is m = 2.9 for x = 0.35 and y = 0.4: this structure is the one losing its elastic stiffness the most rapidly when ρ drops. One may wonder over the interest for such structures with poor elastic properties. It is actually as interesting as stiff structures. It constitutes the ideal case for the development of low Young modulus biomaterials for bone substitution. The lower the stiffness, the lower the stress-shielding effect, and the higher the bio-integration of an implant made with this structure []. Therefore, both extremes of m are promising: minimal m is ideal for mass reduction, while maximal m is expected to be ideal for biomaterial applications.The variations of m are complex and depend on the overall structure, as well as on more local features such as the geometric configuration of nodes, or the beams length and orientation. Despite this apparent complexity, the global behavior is mostly predominated by beam orientation, and other structural parameters play a second-order effect on stiffness. The orientation of each beam in relation to the loading axis is evaluated by an angle φ as illustrated on . If pure compression is applied on the top face of the lattice, the beam will undergo forces including compression and flexion together. The fraction of compression in global loading is related to cos(φ). If the value cos(φ) = 1, then the loading in the beams is compression only and the system corresponds to the Voigt upper bound. For lower cos(φ), flexion predominates and m decreases, while the system evolves progressively toward the Reuss lower bound. For each structure, a mean value cos(φ)¯ is calculated over all the beams set. The m factor is linearly correlated to cos(φ)¯, and can be deduced with a reasonable accuracy from the linear Eq. This equation may be used as a first approach for an unknown cubic lattice, and would provide a rather correct evaluation of m, and consequently of the apparent modulus as a function of beams radius. To conclude, the main factor affecting the m value is the beams orientations. Other architectural factors (e.g. nodes density, beams length) have a second-order effect on m.The Poisson ratio defines the radial expansion of the matter compared to the main loading axis. On a cubic specimen made of lattice structures, the Poisson ratio is the deformation in transverse directions normal to faces, normalized by the compression strain. The transverse deformation is determined by the displacement of outer faces from the central axis of the specimen.Ifux→ is the position vector of a mesh node on the outer surface of the cube along the principal εx = dux/uxtransverse direction X, then the expansion due to Poisson ratio is measured byFor each lattice model, the average Poisson ratio is calculated over all the mesh nodes of outer lateral faces of the cubic specimen. The resulting Poisson ratios are summarized on for r = 0.05. The Poisson ratio varies in a large range from −0.1 to 0.4. Lower values are met for low x and y combinations close to zero, and Poisson decreases until it becomes negative. Such structures with ν < 0 are called “auxetic” [], and have a deformation behavior unmet for common bulk materials. On the other hand, Poisson ratio increases for large x, y values. The maximum is obtained for x > 0.4 and y > 0.4, and ν reaches a value up to 0.4 identical to the property of the bulk material.The Poisson ratio is severely affected by the beams radius. With an increase in lattice density, ν rises progressively, and converges to the bulk value set to ν = 0.4. illustrates the x and y conditions to obtain an auxetic structure with ν < 0 (red line). The auxetic area spreads from 0 to 0.2 for x and y values if the radius is as low as 0.05 mm. When the radius increases, this auxetic area vanishes rapidly: for r = 0.075 mm there are only a couple of conditions around x = 0.2 y = 0.05 having auxetic properties. For larger radii, there are no more auxetic structures and the deformation behavior becomes more conventional.The above estimations of Poisson ratio are based upon average displacements of mesh nodes on outer faces. However, one may wonder if the transverse deformation is homogeneous on a lateral face. The answer is no, and it becomes more tedious to find a proper definition of Poisson ratio if the transverse deformation fluctuates. Therefore, a second definition, more local, of the Poisson ratio is proposed. The nodes on external faces are defined in cylindrical coordinates, with an angle θ and a radial vector u→. The mesh node undergoes a displacementdu→ due to the elastic compression. Only a fraction of this displacement dur→ contributes to the lateral expansion specific to Poisson effect. The displacement duθ→ corresponds to the rotation of a rigid body. The Poisson ratio within the material slice at an angle θ from a principal transverse direction is given by ν = dur/u. This value is calculated as a function of the angle θ, and the plot is illustrated on The structure x = 0.05 y = 0.2 is a lattice architecture with a very low Poisson ratio, for a large range of radii, as shown on . The local Poisson ratio would be expected to be invariably negative along outer faces. However, it is not the case on for r = 0.05. There are large ranges of θ angles where Poisson is rather close to 0, meaning that beams are neither reentering inside the structure nor moving outside, but stay still at their initial position. For some other ranges of θ the Poisson ratio drops to values as low as −0.4, meaning that a large number of mesh nodes of outer faces move toward the inner direction. This is especially the case for angles near 0, 45, and 90°. At 0 and 90°, nodes are located in the middle of V-shaped portions of beams, and the movement to the inside is larger. For θ = 45°, the edges of the cube are involved. The occurrence of vertical V-shaped beams at this location explains this sudden decrease in Poisson ratio.As a conclusion, there is much evidence of the auxetic nature of some cubic lattices, but this becomes less accurate at the scale of a beam. The Poisson ratio properly describes macroscopic behavior, but becomes less meaningful at smaller scales. The local Poisson ratio is a useful approach to understand the heterogeneous deformation of outer faces and to visualize the radial deformation of the beam network. illustrates the fraction of beams in cubic lattices having a tilt angle φ > 55°, resulting in some possible printing issues. This map indicates the areas for possible issues due to overhanging. The architecture parameters with possible difficulties is limited to (x + y) < 0.35. For these structures, specific supports may be required, and difficulties or impossibility to remove all of these are expected.This issue is resolved by tilting the part compared to the building plate []. For instance, the Primitive Cubic lattice (x = 0 y = 0) is expected to be difficult to produce according to . When the 〈111〉 direction is oriented parallel to the normal vector of the building plate, all the beams have a tilt angle φ = 55° and supports may become unnecessary.Additional difficulties may occur with the hexatruss structures. For instance, the point 2 on the structures 2 and 3 of are lower points and it will be disconnected from the rest of the part if the printing is conducted along the {100} planes. For instance, the structure (x = 0 y = 0.2) was printed by Fused Deposition Modeling (FDM), resulting in collapse at this specific location. On the other hand, these collapse effect with SLM technique was significantly reduced, due to the mechanical support provided by the powder bed. Other structures with such low points were printed successfully by SLM technique [Manufacture can result in some other difficulties, like beam radius deviation []. This phenomenon can be considered in the present work by correcting the input parameter depending on the orientation of each beam.), three values of Young Modulus were tested over three orders of magnitude, and the results were found to be identical in the three cases. Using the color maps, it is possible to estimate m factor and E/E0. The data set of calculated E module is illustrated on over an Ashby map, for ABS with E0 = 1 GPa, and for TA6 V titanium alloy with E0 = 100 GPa. As a result, one can predict any apparent Young modulus for any material and then give new upper and lower bond (red dashed line in ). These bonds gave us an Ashby map which takes into account bulky materials and associated cubic lattices structures.In the case of polymer-based cubic lattices, the apparent modulus of the structures varies between 1 MPa and 1 GPa. For densities as low as ρ < 102 kg m−3, the elastic properties are very similar to polymer foams. It may meet specific applications for thermal and acoustic insulation, or vibrations damping applications, or for structural flexible parts. With metallic lattices made of TA6V, the modulus also decreases with density. The metallic lattice has properties similar to composites, then polymers, then natural materials as density gradually decreases. One may wonder why choosing an expensive metallic lattice while polymers constitute such a cheap and efficient option. Choosing a metallic lattice can be attractive due to higher creep properties compared with a bulk polymer. The electric and thermal conductivity, friction resistance, physical properties and biocompatibility are some examples of additional functions available with metallic TA6V lattice, which would be difficult to obtain with commercial polymers. Therefore, lattice architecture materials show the best of their potential for applications combining mechanical design with other physical properties within a multifunctionLattices with a cubic symmetry were investigated using finite elements modeling. A new parameterization technique based on crystallography using the m3¯m point group was proposed. This technique requires only two parameters, corresponding to the position of initial atoms, and provides a large panel of different structures.The lattice can build up on its own due to symmetries, and its generation is completely automated by scripts. This procedure does not require the use of close-loop algorithms, contrary to topological optimization. It is straightforward and more versatile for mechanical engineering, as it does not depend on the geometry of the parts considered. This procedure also gives us the possibility to make architecturally graded materials.The global trend for modulus variation with density is a power law, with an exponent m representative of the elastic behavior. The m factor is independent from beams sections and from material, and properly illustrates the contribution of architecture to the apparent lattice modulus. In addition, the Poisson ratio was determined for all the structures, and was shown to vary widely, from its bulk value down to negative values for some specific auxetic architectures.The elastic behavior was simulated and summarized on color maps. These abacuses are powerful tools for mechanical design, and provide predictions of the resulting modulus at a glance. The continuous generation of a large panel of cubic lattices allows for the selection of optimal structures to reach a target stiffness value, without necessarily affecting the density.It makes it possible to adjust within a suitable range the Young modulus while preserving a minimal density. However, the severe dependence of stiffness on density, and the limited variation of specific Young modulus are two main limitations to this method. Some stiffness ranges remain beyond reach with cubic lattices, and it would be necessary to modify either the density or the bulk material properties to achieve it.This paper is dedicated to the generation of lattices, and the methodology was extensively detailed. In the future work, an experimental procedure will be established to confirm the material independence of effective elastic properties. In addition, the use of different additive manufacturing processes will provide information on process-dependence.Opto-mechanical characterization of hydrogen storage properties of Mg–Ni thin film composition spreadsThin film composition spreads of Mg–Ni were deposited by co-sputtering on micromachined Si-cantilevers. The investigated compositions range from about Mg60Ni40 to about Mg80Ni20. Structural properties as well as mechanical stress before and after hydrogenation were measured with X-ray diffraction (XRD) and laser profilometry, respectively. The composition spreads were hydrogenated in a special pressure vessel, which allows measuring optically the hydrogen-induced deflection (stress-change) of 16 cantilevers as a function of hydrogen pressure and/or temperature. It was found that the hydrogen-induced stress is correlated with the composition and microstructure of the films. Highest hydrogen-induced stress changes were found for compositions close to the crystalline Mg2Ni phase.The search for new hydrogen storage materials which fulfill the difficult requirements of mobile applications illustrates the development of stresses in thin film/substrate combinations due to hydrogenation and de-hydrogenation. A stress-free initial state of the thin film and substrate combination is shown in a. Hydrogen entering the lattice of the thin film induces a volume change (b). This leads to compressive stress in the hydrogenated thin film (c), as long as the film is adhering to the substrate, e.g. Si, which does not absorb hydrogen. If the hydrogen-induced stress is higher than the yield strength of the hydrogenated thin film, compressive plastic deformation can occur (d). When hydrogen is released from the thin film, the elastic compressive stresses are reduced. However, the plastic deformation should lead to tensile stress in the dehydrogenated thin film/substrate combination (Mg-based hydrogen storage materials are intensively studied as promising candidates for application as light-weight storage materials in a future hydrogen economy: MgH2 has a hydrogen storage capacity of 7.6 wt.% Thin film Mg–Ni composition spreads were prepared in a seven-cathode ultra-high-vacuum dc/rf magnetron co-sputtering system (base pressure 10−7 |
Pa) at RT on micromachined Si-cantilevers (gradient direction perpendicular to the long axis of the cantilevers, inset), and additionally on glass substrates. The fabrication of the cantilevers has been described elsewhere The chemical composition of the thin films was analyzed by energy-dispersive X-ray analysis (EDX) in a scanning electron microscope (SEM, LEO). The investigated compositions ranged from about Mg60Ni40 to about Mg80Ni20. X-ray diffraction (XRD) (Bruker, Panalytical) was used to determine the microstructure of the films. Residual stress measurements were performed by curvature measurements of the thin film substrate combinations using a laser profilometer (FRT).Hydrogenation was carried out in a special gas phase apparatus equipped with a 50 mm window for optical observations Spectrophotometric measurements were performed with a fibre optic dispersive spectrometer (Ocean Optics) in the 1.2 eV < |
E |
< 3.1 eV energy range. The reflectance and transmittance probes were mounted on an X–Y stage to screen all compositions cNi of the Mg–Ni spreads deposited on 70 mm × 5 mm glass substrates.The variation of film thickness over a cantilever array, and the variation of composition over the cantilevers are depicted in for the fabricated Mg–Ni composition spreads. On the Mg-rich side the films have a thickness >200 nm, whereas the Ni-rich side is thinner, about 180 nm. The inset shows a cantilever array, indicating the area, which is optically accessible during hydrogenation experiments (16 measurable cantilevers). shows 3D plots of the observed XRD spectra for the as-deposited Mg–Ni composition spreads 2 and 3. The observed peaks in as-deposited Mg–Ni composition spreads are (0 0 3) and (0 0 6) reflections of the Mg2Ni phase. The intensities of (0 0 3) and (0 0 6) peaks increase with the Ni-content towards the composition of the Mg2Ni phase. For Ni contents higher than 36%, the intensity decreases again. This shows that the co-deposition process – without any intentional heating – can lead to crystalline materials. The intensity of the measured peaks, i.e., the crystallinity of the material, is highest for compositions close to the stoichiometric phase. After the hydrogenation cycles, (0 0 3) and (0 0 6) reflections of the Mg2Ni phase are still present (not shown). show the hydrogen-induced stress changes of different Mg–Ni thin film/cantilever combinations upon the first hydrogenation at 0.1 MPa and RT as a function of time for two as-deposited Mg–Ni composition spreads. The stress changes are not corrected for the hydrogen-induced stress contributed from the Pd cap layer. All the films are under compressive stresses upon hydrogenation. However, the magnitude of the hydrogen-induced stress changes as well as the shape of the measured curves varies with composition. The highest stresses are measured for the compositions close to the crystalline Mg2Ni phase.In the first minutes of hydrogenation of Mg–Ni composition spreads (), it can be observed that the hydrogen-induced stress increases rapidly upon exposure to the hydrogen pressure of 0.1 MPa. For most observed compositions the stress goes through a maximum and relaxes within several seconds to lower values. The highest stress within composition spread 1 is about −1.39 GPa for the composition Mg68Ni32. For composition spread 3 the highest stress is about −1.37 GPa for the same composition Mg68Ni32. For lower and higher Ni-contents the hydrogen-induced stress is lower ( illustrates the development of the hydrogen-induced stress for longer hydrogenation times and upon dehydrogenation for composition spread 3. A different behaviour can be distinguished for films with cNi |
≤ 23% and cNi |
≥ 27%. The films with lower cNi show an increase of stress with hydrogenation time, whereas the films with higher content show a relatively constant (cNi |
= 27–28%) or decreasing stress with time. The films with lower cNi show a maximum stress upon hydrogenation at 0.1 MPa and 150 min of about −0.46 GPa, which is probably mainly due to Pd hydrogenation. When pH2 is set to zero the stress is reduced very quickly to a certain level. This level of about −0.18 GPa is very similar for the films with lower cNi, but quite different for films with cNi |
≥ 27%. However the immediate stress change upon the start of dehydrogenation is similar for all compositions. Again this could be attributed to the Pd cap layer.The residual stresses for as-deposited films were found to be either slightly compressive or tensile depending on the Ni-content. After the hydrogenation cycles, the residual stress was significantly increased and in the tensile stress region for the measured composition spreads, as can be expected ( shows the measured hydrogen-induced stress changes as a function of Ni content for composition spread 1 within the first minutes of hydrogenation (highest observed stress changes). The highest stress changes are found for the composition close to Mg2Ni. This is in agreement with the optical measurement of a hydrogenated Mg–Ni spread shown in : the minimum in reflectance is also around the Mg2Ni composition, indicating that most of the insulating Mg2NiH4 phase is formed around the stoichiometric composition.The results show that thin film composition spreads deposited on micromachined-Si cantilever libraries can be used for the investigation of hydrogenation and dehydrogenation properties of thin films by measuring the hydrogen-induced stress. This stress is correlated with the amount of hydrogen taken up by the respective thin film. Highest stresses in the investigated Mg–Ni system are found in proximity of the stoichiometric compound Mg2Ni. As the hydrogen induced compressive stresses are very large, plastic deformation in the thin films occurs, which leads to tensile residual stresses.Workability Studies in Forming of Sintered Fe-0. 35C Powder Metallurgy Preform During Cold UpsettingAn experimental investigation on the workability behaviour of sintered Fe-0. 35C steel preforms under cold upsetting, have been studied in order to understand the influence of aspect ratio and lubrication condition on the workability process. The above mentioned powder metallurgy sintered preform with constant initial theoretical density of 84% of different aspect ratios, namely, 0.4 and 0.6 respectively were prepared using a suitable die-set assembly on a 1 MN capacity hydraulic press and sintered for 90 min at 1200 °C. Each sintered preform was cold upset under nil/no and graphite frictional constraint, respectively. Under the condition of triaxial stress densification state, axial stress, hoop stress, hydrostatic stress, effective stress and formability stress index against axial strain relationship was established and presented in this work. Further more, attained density was considered to establish formability stress index and various stress ratio parameters behaviour.Biography: S Narayan(1980-), Male, Assistant LecturerThermorheological properties of a Carbopol gel under shear► The thermorheological properties of a Carbopol gel are studied experimentally. ► An anomalous thermorheological behavior is found. ► A qualitative explanation of this behavior may be provided by the Eyring theory. ► A jamming concentration of the Carbopol network is identified.An experimental investigation of the thermo-rheological properties of aqueous solutions of a commercial polyacrylic acid (Carbopol®) at various concentrations is presented. The rheological parameters of the solutions are assessed by performing increasing/decreasing controlled stress stepped ramps and interpreting the results within the framework of a recent model which can correctly describe the irreversibility of deformation states in a range of low deformation rates, Putz and Burghelea Physical and/or chemical gels which are a particular class of viscoplastic materials have found during the past several decades an increasing number of applications relevant to various key industrial sectors which include cosmetics, food processing, pharmaceutical, oil field engineering etc. Of particular interest are the applications related to targeted drug delivery where gel capsules made off various types of carbomer microparticles (commercialized under the generic trade name Carbopol®) are used as vectors to dispense low molecular weight chemical compounds, Hoare and Kohane The relevance of the thermo-rheological investigations of physical gels is twofold. From a practical point of view, non-isothermal flows of such materials are often encountered in industries such as food industry, polymer processing etc. In addition, the characterization of non-isothermal flows of physical gels may also shed light on various geophysical flows e.g. magma flows. From a fundamental standpoint, a systematic study of the temperature correlation of the rheological properties of viscoplastic materials is of paramount importance for the characterization of non-isothermal flows of viscoplastic materials.Carbopol® resins are synthetic polymers of acrylic acid initially introduced in 1950s (B.F. Goodrich Co.). They are cross-linked with various chemical compounds such as divinyl-glycol, allyl-sucrose, and polyalkenyl polyether. In an anhydrous form, the average size of the polymer molecules is of the order of hundreds of nanometers. In the absence of crosslinks, the polymer particle can be viewed as a collection of linear chains intertwined (in a coiled state) but not chemically bonded. The Carbopol® particles are soluble in polar solvents and, upon solvation, each individual polymer molecule hydrates, partially uncoils, and swells about 1000 times. Addition of a neutralizing agent, such as sodium hydroxide (NaOH), leads to the creation of negative charges all along the polymer backbone due to ionization of the carboxylic acid groups. Consequently, swollen polymer molecules crosslink, forming a system of microgel particles. The microgel system can sustain finite deformations (behaving like an elastic solid) prior to damage. When local deformations exceed a certain threshold, the gel network breaks apart and the material starts to flow which is the commonly accepted microscopic scale origin of the macroscopic yielding of the material.During the past two decades Carbopol® gels have been considered as “model yield stress fluids” by the rheologists interested in viscoplasticity, the fluid dynamicists interested in the flow properties of such materials and the applied mathematicians interested in modeling industrially relevant flows.Within this “ideal” picture it has been often considered that, unlike their thyixotropic counterpart (e.g. bentonite gels, foams), the Carbopol® gels exhibit little or no hysteresis of the deformation states upon an increase/decrease of the applied stresses and can be accurately described by the Herschel–Bulkley model, Balmforth and Frigaard It has only recently been found that within this framework, one cannot properly describe some of the “simplest” fluid dynamics phenomena such as the flow pattern in the wake of a spherical object uniformly moving through a Carbopol® gel Putz et al. A minimalistic model (i.e. not formulated from first principles) able to account for these rheological features has recently been proposed, Putz and Burghelea Whereas a clear progress towards understanding the isothermal deformation of viscoplastic materials has been made, there exists a limited number of studies dealing with temperature dependent viscometric and non-viscometric flows of Carbopol® solutions. An experimental study of the heat transfer in the transitional pipe flow of a Carbopol® solution is presented in Peixinho et al. A linear stability analysis of the Rayleigh–Bènard Poiseuille flow of thermodependent viscoplastic fluids has been recently presented in Métivier and Nouar There exist however only qualitative experimental investigations of the Rayleigh–Bènard stability problem, Balmforth and Rust The previous studies regarding the thermorheology of Carbopol® gels may be divided in two classes.A first class of previous rheological studies found a “normal” temperature correlation of the rheological properties that can be modeled by the Arrhenius law, Islam et al. Islam and coworkers found an Arrhenius scaling of the viscosity of the Carbopol® gel with temperature which gave rather low values of the activation energy, ΔEa consistent with a low temperature sensitivity Islam et al. Peixinho et al. found no temperature dependence of the power law index and yield stress and an Arrhenius type decay of the consistency, Peixinho et al. It is worth noting that the maximum temperature investigated in Peixinho et al. There exists a second class of previous rheological studies which observe an anomalous temperature–viscosity correlation (an increase of the viscosity with the temperature), Owen et al. Barry and coworkers were among the first to provide a very complete description of the rheological properties of Carbopol® at various temperatures by combined shear measurements, creep measurements and small amplitude oscillatory measurements, Barry and Meyer By using a Brookfield Model DV-III Digital Rheometer (Brookfield Engineering Laboratories Inc., Stoughton, MA, USA) and a cone and plate configuration, Owen and coworkers observed an anomalous temperature viscosity correlation for two neutralized polyacrylic acid derivatives used in contraception under the trade names “Advantage-S” and “KY- Plus”, Owen et al. By using a falling needle viscometer, Park and Irvine observe in Park and Irvine Both classes of previous works briefly discussed above have, most probably, a limited number of things in common which makes a pertinent comparison quite difficult. Although they use a variety of rheometric equipment (note that these studies span the last four decades during which the rheometric devices have significantly evolved) it is, in our opinion, unlikely that the differences in the observed temperature correlations are due to this. This idea corroborates with the fact that sometimes, within the same study (thus using the same device and rheological method) both a “normal” and “anomalous” behavior are found, depending on grade of Carbopol® used, Owen et al. At a second analysis of the bibliography given above, one can find however other significant differences between these studies: the physico-chemical properties of the gels. Thus, various studies used various grades of Carbopol (934, 940, Ultrez 10 etc.) or even custom gel formulations, Owen et al. To conclude this part, a pertinent comparison and analysis of the existing body of literature on the thermorheological properties of Carbopol® is difficult to make based on the published results. This is due in our opinion to an incomplete understanding and control of the physico-chemical interactions that govern the cross linking, ionization, swelling and jamming dynamics of the individual molecules. Each of these molecular scale physico-chemical processes are temperature dependent (and they are characterized by their own chemical activation energies which are largely unknown) and the overall temperature dependence observed in a macroscopic rheological experiment is the result of a highly non trivial “average” of these microscopic dependencies.The paper is organized as follows. The experimental techniques and methods are presented in Section . The preparation of the fluid samples is detailed in Section . The experimental validation/calibration of the thermorheological measurements is discussed Section . Thermo-rheological properties of Carbopol® solutions with various concentrations are presented Section . The temperature dependence of the rheological parameters is presented and discussed in Section . A possible interpretation of the temperature dependence of the yield stress is proposed in Section . The concentration dependence of the temperature invariant parameters is presented in Section . The paper closes with a summary of the main findings and their impact on future studies, the remaining difficulties concerning the thermo-rheology of Carbopol® gels, Section As working fluids we have used aqueous solutions of Carbopol®-980 at three concentrations (by weight): 0.1%, 0.15% and 0.2%.The same procedure for the preparation of each fluid batch has been used, as follows. First, the right amount of anhydrous Carbopol® 980 has been gently dissolved in water while continuing stirring the mixture with a commercial magnetic stirring device. The stirring process was carried on until the entire amount of polymer was homogeneously dissolved. A particular attention has been paid to the homogeneity of the final mixture, which has been assessed visually by monitoring refractive index contrast. Next, the pH of the mixture (initially around 3, due to the dissociation of the polyacrylic acid in water) has been brought to a neutral value by addition of about 140 parts per million (ppm) of sodium hydroxide (NaOH). The final value of the pH has been carefully monitored using a commercial pH-meter. Upon the ionization and the neutralization of the carboxylic groups of the polyacrylic acid, the Carbopol particles swell dramatically forming a percolated micro-gel, Piau The rheological properties of the solutions were investigated using a AR-G2 rheometer (from TA Instruments) equipped with a Peltier system able to control the temperature with an accuracy better than 0.1 °C. To check the reproducibility of the results, part of the measurements have been repeated in the same conditions but on a different rheometer, Mars III (from Thermofischer).A first major concern for the rheological measurements was the emergence of the wall slip phenomenon at the contact with the measuring geometry, which has been previously recognized as a major source of experimental artifacts when Carbopol® gels are used, Piau The radius of the parallel plates is R |
= 40 mm and the gap measured by the rheometer (see the details in ) is d |
= 1 mm. The cleats have an equal height H |
= 600 μm and are disposed in a rectangular grid over each plate. Several advantages of cleated geometries over other methods of preventing the wall slip effect (such as using a sand blasted geometry or a vane tool) have been recently demonstrated experimentally, Nickerson and Kornfield The flow between neighboring cleats is restricted and stops over a finite distance Δ (the flow penetration length) along the vertical axis (see ) and thus, two parallel no-slip surfaces are formed at an effective distance de=d+2Δ. Consequently, the stress measurements should be corrected according to σ=σaded, where σa is the apparent stress value provided by the rheometer.A second concern was related to the possible artifacts introduced by fluid evaporation during long experimental runs. In order to prevent this, a solvent trap has been placed around the free fluid meniscus. The sealing of the solvent trap on the base plate of the rheometer has been insured by a thin layer of vacuum grease. After each experimental run it has been carefully checked (by visual inspection) that no significant changes in the shape of the meniscus occurred. Additionally, we have checked at the end of each run that one can reproduce the viscosity measured during the pre-shear step which indicated us that the evaporation effects were either minimal or absent.A third concern is related to the temperature gradient which develops within the space between the parallel plates of the measuring geometry. To monitor and account for this effect, two temperature probes have been embedded in each of the parallel plates of the geometry. The temperature of each plate (Tt,Tb) has been measured as a function of the temperature set to the Peltier plate of the rheometer (Tpp) in the range 5–55 °C. Beyond this range of temperatures, we have found that the measurements are not reproducible (a scatter of nearly 75% over several subsequent runs with fresh samples was observed) and, consequently unreliable. During these measurements, a Carbopol® sample was loaded but the top plate of the rheometer was held static. The transient temperature signals have been monitored using a digital oscilloscope and each temperature reading has been made only after the temperature of each plate has reached a steady state. Calibration measurements of the temperature at the top and bottom plate of the rheometer as a function of the temperature set to the Peltier plate are presented in As the temperature set to the Peltier plate, Tpp, departs the room temperature, a linear increase of temperature difference between the top and the bottom plates is observed. By measuring the temperature difference between the plates at a fixed temperature of the Peltier plate for various values of the distance d between the plates, it has been checked that the temperature varies linearly within the gap. This allowed us to define an effective temperature of the sample as an arithmetic mean of the temperatures of the top and the bottom plates of the rheometer, T=(Tt+Tb)/2.The reliability of the stress and temperature corrections described above has been assessed by comparative thermo-rheological measurements performed on a calibrated silicon using both the cleated geometry described above (together with the stress and the temperature corrections) and a standard cone and plate geometry.The result of this comparison is presented in . The viscosity measurements performed on the two geometries come into a perfect agreement which indicates that both the stress correction related to the cleated geometry and the temperature correction related to the temperature gradient between the parallel plates are reliable and can be safely employed in the thermo-rheological measurements concerning the Carbopol® gel.Each of the thermo-rheological measurements performed with Carbopol® gels followed the procedure described below. After loading the sample, we have waited about 30 min for the material to reach a thermal equilibrium state.In order remove any memory effects and to insure the reproducibility of our measurements, prior to each experiment the sample has been pre-sheared at a constant stress (usually the largest stress applied during the test) for 300 s. After performing the pre-shear we have waited another 300 s for the sample to equilibrate.The rheological procedure was similar to that described in Putz and Burghelea ) for both increasing and decreasing values of the applied stress,The data averaging time per stress value, t0 (referred to as the characteristic time of forcing, Putz and Burghelea Prior to discussing the thermal dependence of the rheological properties of a Carbopol® we focus on the solid–fluid transition which we have investigated in detail in Putz and Burghelea For this purpose, we monitor the rheological response of a Carbopol® sample during a stepped stress ramp performed at a constant temperature, The results of such measurements are presented in . The choice of representing the data in the coordinates γ˙=γ˙(σ) is motivated by the fact that this representation allows a more accurate identification of the various deformation regimes and a rigorous assessment of the reversibility of the deformation states, Putz and Burghelea ) the measured rate of deformation is constant for both branches (increasing/decreasing) of the stress ramp and, consequently, the strain γ is a linear function of the applied stresses. Bearing in mind that the stress ramp is linear in time, one can conclude that the material deforms as an elastic solid within this regime, G=σ/γ=ct. Within this regime, the deformation states are not reversible upon increasing/decreasing applied stresses: Gu>Gd. Here the indices denote the increasing/decreasing stress ramps, respectively.For large values of the applied stresses (σ⩾65Pa) a reversible fluid regime is observed. Quite remarkably, the transition from a solid like deformation regime to a fluid one is not direct, but mediated by an intermediate deformation regime which cannot be associated with neither a solid like behavior nor a fluid one.The irreversibility of the deformation states observed within the solid and the intermediate deformation regimes by Putz and Burghelea We note that, during each of the rheological measurements reported in the manuscript, the Reynolds number was smaller than unity, therefore the experimentally observed irreversibility of the deformation states illustrated in should not be associated with inertial effects.A simple model able to describe the irreversibility of deformation states observed in has been recently proposed, Putz and Burghelea As previously suggested by several authors where S, F denote the solid and fluid phases, respectively, Φ=[S] is the concentration of the solid phase, σ is the forcing parameter, Rd=-Kd1+tanhσ-σywΦ is the rate of destruction of solid units and Rr=Kr1-tanhσ-σyw(1-Φ) is the rate of fluid recombination of fluid elements into a gelled structure, Putz and Burghelea As a constitutive equation we use a thixo-elastic Maxwell (TEM) type model:where the viscosity of the fluid phase is given by a regularized Herschel–Bulkley model, η(γ˙)=K|γ˙|n-1+σy1-exp(-m|γ˙|)|γ˙|. Here G is the static elastic modulus, K the consistency, n the power law index and m is the regularization parameter (which we fix at 500).The choice of this constitutive equation is motivated by the presence of elastic effects in the intermediate deformation regime (see the cusp in decreasing stress branch in and the corresponding discussion). We note that in the limit Φ→1 Eq. reduces to Hooke’s law, σ=Gγ (which describes the solid deformation regime), and in the limit Φ→0 it reduces to a regularized Herschel–Bulkley model (which describes the viscous regime).In order to find the best set of parameters so we can accurately fit the controlled stress ramps data we constructed a nested function program in MATLAB® (see the full lines in ). The main function uses the built in function lsqnonlin in MATLAB® which solves nonlinear leas-squares data fitting problems using a trust-region-reflective algorithm. As inputs we provide an initial guess for the parameters vector, the target data and a function which first solves for Φ using the built in function ode15s in MATLAB® and then solves () for γ˙ using the built in function fzero in MATLAB®. The outputs of the main function are the vector with the optimal parameter values, Φ and γ˙. It is worth noting that we fitted the up ramp and down ramp separately in order to get the correct values for Gu and Gd.By performing controlled stress ramps at various temperatures and Carbopol® concentration and analyzing the data within the framework of the model above, one can assess the temperature and the concentration dependence of the model parameters. To this we dedicate the next section.We focus in the following on the influence of the temperature on the rheological behavior of the Carbopol® gels. For this purpose, controlled stress ramps similar to that presented in for several temperatures ranging in between 284.95 K and 310.85 K have been performed.To test the accuracy and the reproducibility of the results, for each value of the temperature the rheological measurements have been repeated at least three times (sometimes even five times).The temperature dependence of the elastic moduli Gu,Gd measured from the values of the shear rate plateau observed in the solid deformation regime (see . For each value of the Carbopol® concentration investigated and within the accuracy of the measurements no temperature dependence of the elastic moduli GuGd is observed. Thus, the solid-like deformation observed in a range of low applied stresses is inconsistent with a rubber-like behavior, which typically manifests through a proportional increase of the elastic modulus with the temperature, Larson The temperature dependencies of the consistency K and the power law index n for several concentrations of Carbopol® are presented in As for the elastic moduli, no temperature dependence of the consistency is observed, a. This result does not agree with observations by Peixinho and coworkers which indicate an exponential decay of the consistency with the temperature, Peixinho et al. )b, in agreement with the findings reported in Peixinho et al. Within a Herschel–Bulkley framework (which is applicable right above the solid–fluid transition, see ), the temperature invariance of both the consistency K and the power law index n indicate that the temperature dependencies of the yield stress σy and the viscosity measured at a fixed rate of shear above the yield point are qualitatively similar.The temperature dependence of the yield stress σy illustrated in reveals a rather unexpected behavior: corresponding to a critical temperature Tc a local minimum of the dependence is observed. This unexpected behavior has been observed for each value of the Carbopol® concentration and the non-monotone trend of the curves clearly falls beyond the error bars of the measurements.The critical temperature Tc marks the transition from a Arrhenius like behavior described by σy=σy0eΔEaRT (the full lines in )) to a anomalous non Arrhenius one and decreases with increasing Carbopol® concentration. Here ΔEa and R stand for the activation energy and the universal gas constant, respectively.As we have found the observation of an anomalous temperature dependence of the yield stress (and implicitly of the viscosity measured at a given applied stress, because the consistency and the power law index are temperature invariant, ) quite unexpected and intriguing (particularly the increase of σy for T>Tc), we have repeated several times the calibration measurements presented in and subsequently reproduce this result. As we have employed exactly the same stress calibration and temperature correction for all the measurements performed on the various Carbopol® gels as in the case of the calibration measurements, we have ruled out the possibility that the anomalous temperature dependence observed in is the result of an experimental artifact.Attempting to qualitatively understand the temperature dependence of the yield stress above the critical temperature within the classical framework of the Arrhenius law would quickly lead to an unphysical conclusion, that is a negative activation energy which apparently violates the second law of thermodynamics. This prompted us to seek an explanation for the experimentally observed anomalous behavior beyond the “classical” Arrhenius framework. To this discussion we dedicate the next subsection.The Arrhenius law of viscosity is probably the most popular scaling law rheologists use to describe the temperature dependence of the viscosity of materials. Remarkably, the Arrhenius law is applicable for an impressive number of structurally different materials such as Newtonian fluids, aqueous solutions of linear polymers, suspensions, and polymer melts and deviations from it were only observed in the vicinity of either glass transitions (for supercooled fluids) or the melting point (for polymer melts). Owing to this nearly universal applicability, the Arrhenius law has somewhat gained the status of an axiom and very few modern textbooks present its derivation, Larson The Arrhenius viscosity–temperature correlation emerges as a particular case from the theory developed by Henry Eyring which described the fluid flow as an activation process, Eyring Similarly to the excitation of atoms from their ground state to various energetic levels, Eyring has interpreted the motion of a “flow unit” (which is the term originally employed in Eyring In the absence of a shear force, the energy barrier associated to the displacement of the neighboring material layers along the x direction is symmetric and, consequently, the probabilities of hopping (or hopping rates) along and opposite to the x direction are equal, ν+=ν-=ν0e-ΔEaRT. Here ν0 is the equilibrium hopping frequency, ΔEa the activation energy per mol of material and R the universal gas constant.When an external shear force f+ is applied onto the material layers along the direction x, the symmetry of the activation energy barrier is broken, ΔE-,+=ΔEa±f+DNA where NA stands for the Avogadro’s number and D is a characteristic space scale (measured along the shearing direction, “+”) associated to the gel network.Consequently, the hopping rates along and opposite to the direction of the shearing force ν+,ν- are no longer equal and an effective hopping rate along the direction of the imposed shear can be calculated by the difference:Denoting by A the characteristic shearing area between two neighboring gel elements and interpreting the effective hopping rate as a microscopic rate of shear ν=γ˙, one can invert Eq. where V★=A·D stands for a characteristic volume of the gel network. In the case of a Carbopol® gel, we expect that V★ is a non trivial function of the molar mass of the polyacrylic acid, the polymer concentration and the pH which controls the degree of swelling of individual molecules, Gutowski et al. For simple fluids it is often assumed that: reduces to the well known Arrhenius lawTo test the applicability of the simplifying condition given by the inequality for the case of a Carbopol® gel, one can consider as a typical space scale related to the gel network D≈1μm,A≈1μm2 (which are of the same order of magnitude with the values assessed via diffusion measurements reported in Refs. Oppong et al. If one assumes that V★ is temperature invariant, it can readily be shown that there exists a critical temperature Tc corresponding to which the viscosity given by Eq. passes through a local minimum. By solving numerically the equation ∂η(γ˙,T)∂T=0 it can be readily shown that the critical temperature Tc which marks the transition from a thermo-rheologically simple (Arrhenius like) behavior to a anomalous one is a decreasing function of γ˙ν0 at a fixed value of the activation energy ΔEa.We emphasize once more that the Eyring model does not directly refer to the temperature dependence of the yield stress but to that of the viscosity. However, within a Herschel–Bulkley framework and due to the temperature invariance of both the consistency and the power law index (see the data presented in ), the yield stress σy at a given temperature T is a linear function of the viscosity measured at the same temperature and a fixed rate of shear, σy=η(γ˙,T)γ˙-Kγ˙n.Thus, one can conclude that the Eyring theory may qualitatively describe the anomalous temperature dependence of the yield stress illustrated in We propose in the following a simplistic phenomenological interpretation for the existence of a critical temperature Tc beyond which an anomalous temperature correlation is observed. The microstructure of a polyacrylic microgel system statistically described by the characteristic volume V∗ is the result of two competing effects: swelling of individual microgel particles and osmotic de-swelling.Here Πe stands for the elastic pressure exerted upon the microgel particles and Πin,out stand for the osmotic pressures due to the mobile ions inside and outside the microgel particles. The osmotic pressures are related to the concentrations of Cin,out via Πin,out=RTCin,out. Assuming that all ions are contained within the micro-gel particles (which is reasonable provided that no salt is added to the system) Eq. reduces to Πin=Πe. The concentration of ions trapped into the micro-gel particles may be written as Cin=αc0zQ-1 where c0 is the average concentration of polyacrylic acid inside the microgel particles, α is the degree of ionization, z the molar fraction of the acidic groups and Q=V∗/V0 is the swelling ratio (V0 is the characteristic volume of the un-swollen microgel particles). Because the macroscopic elastic modulus reflects the microscopic scale elasticity of the microgel structure, the temperature invariance illustrated in indicates that the elastic pressure of the gel network Πe is temperature invariant. With these considerations, a simple algebraic manipulation of Eq. would lead to the conclusion that the swelling ratio is proportional to the temperature or, equivalently V∗∝T.Thus, within this regime, the pre-factor in Eq. is practically temperature independent which explains why the temperature dependence of yield stress (viscosity) can be fairly well described by an Arrhenius type correlation, see the full lines in The osmotic de-swelling occurs when counter-ions may escape from the core of microgel particles into the solution by penetrating the outer shell of the particles where the local electro-neutrality condition is not fulfilled. The fraction Γ of these counter-ions is proportional to the Debye length, Γ∝λD, Cloitre et al. A dynamical equilibrium between the swelling and the osmotic de-swelling may be achieved when the concentration of ions trapped within the microgel particles becomes comparable to that of the counter-ions that leave the microgel particles, Cin≈Cout. This critical condition together with Eqs. and with the square root temperature scaling of Γ indicate the existence of a critical temperature Tc and a critical characteristic volume defied implicitly via Γc=1-Φc. Beyond this critical temperature Tc, the osmotic de-swelling wins over the swelling and a further increase of the characteristic volume V∗ with the temperature is no longer possible. Consequently, the pre-factor in Eq. is proportional to the temperature which translates into the anomalous behavior observed in . For high polymer concentration, the range of temperatures within which individual molecules can freely swell upon an increase of the temperature becomes narrower and the critical condition will be fulfilled at a lower temperature Tc. As a consequence, within this phenomenological picture, one should expect a decrease of the critical temperature Tc with increasing Carbopol® concentration. This trend is apparent in A quantitative description of the data presented in by the Eyring model could not be obtained. The reason behind this might be that Eq. considered a single (plastic) “flow unit” characterized by a single specific volume V★ related to the average size of the percolated gel network. A more realistic model should account for the presence of the Newtonian solvent (in our case the water trapped into the swollen polymer network) and a realistic statistical distribution of V★. Such a statistical distribution is difficult to predict theoretically from first principles and, most probably should be tackled experimentally by direct visualization of the polymer network, as very recently performed in Gutowski et al. In the following we focus on the concentration dependence of the thermo-dependent rheological parameters discussed in Section . The dependencies of the elastic moduli Gu,Gd obtained as an average of the measurements presented in Within the limited accuracy of the measurements, both data sets linearly extrapolate to zero corresponding to a critical value of the Carbopol® concentration, c★≈0.08 which agrees with the measurements by Ketz and his coworkers, Ketz et al. Bearing in mind that the elastic moduli Gu,Gd are a signature of an elastic solid behavior prior to the yielding of the gel, Putz and Burghelea The dependencies of the consistency K and the power law index n obtained as an average of the measurements presented in a. We observe a linear increase of the consistency K with the Carbopol® concentration which intercepts the Newtonian solvent viscosity (ηs=1mPas) at a critical value of the polymer concentration c★≈0.08. This result is consistent with the behavior of the elastic moduli illustrated in . The decrease of the power law index n with the Carbopol® concentration is consistent with the recent findings of Gutowski and coworkers for Carbopol® Ultrez 10 at pH=7 but opposite to the behavior found for Carbopol® ETD 2050 at pH=8 by the same authors. This clearly indicates that, in spite an apparently similar rheological behavior, different grades of Carbopol® (that is of different degrees of ionization and most importantly different cross-linking agents) do behave differently which corroborates with the conclusions of Pérez-Marcos et al. The dependencies of the pre-factor σy0 and the activation energy ΔEa obtained by fitting the yield stress data () by the Arrhenius law below the critical temperature Tc are presented in b. Consistently with the concentration dependence of the elastic moduli presented in , the yield stress pre-factor σy0 depends linearly on the Carbopol® concentration and extrapolates to zero corresponding to the overlap concentration c★≈0.08.For each value of the Carbopol® concentration we have investigated, the activation energy is significantly smaller than the activation energy of the aqueous solvent (roughly about an order of magnitude) and decreases with increasing polymer concentration. The small values of the activation energy makes a systematic temperature dependence of the yield stress hardly detectable, which may explain why other authors concluded that the yield stress is temperature invariant, Peixinho et al. The decrease of the activation energy with the polymer concentration may be understood in terms of a drastic reduction of the micro structural entropy induced by an increasingly stronger interaction between jammed polymer molecules, Alain and Bardet We note that, although somewhat counterintuitive, a decrease of the activation energy with the concentration has been observed Barry and his coworkers for Carbopol® 941 and quite the opposite trend for Carbopol® 940 (see Table 3 in page 10 of Barry and Meyer A systematic investigation of the thermo-rheological properties of Carbopol® gels was presented. Gels of various concentration are tested via increasing/decreasing controlled stress ramps. As previous experimental studies revealed little or no sensitivity of the rheological parameters of Carbopol® gels on the temperature, a particular care to increase the accuracy of the measurements has been devoted: a cleated geometry has been used and a temperature calibration procedure has been employed in order to minimize the impact of the inherent temperature gradients. In addition, each rheological test has been repeated at least three times and the results have been averaged over multiple runs, which allowed us to provide error bars for each data set. The rheological measurements have been evaluated within the framework of a recent model proposed by Putz and Burghelea The elastic moduli measured from the rate of shear plateau observed at low applied stresses (. This invariance indicates a non rubber-like elasticity of the gel in a solid regime. A similar temperature invariant behavior is observed for the consistency K and the power law index n. These results come into a good agreement with the conclusions of Barry and Meyer . Although quite surprising, this result was reproducible in subsequent runs (for each temperature and each concentration, the measurements have been repeated at least three times) and several Carbopol® concentrations.As an attempt to interpret an increase of viscosity with increasing temperature within the classical Arrhenius framework would lead to an unphysical conclusion, i.e. a negative activation energy, we have turned our attention to the more general theory of flow as an activated process due to Eyring can qualitatively describe the anomalous temperature dependence observed in our experiments. It has to be noted, however, that although Eq. can reliably predict the value of the critical temperature Tc, it does not qualitatively describe the measurements presented in . Thus, the main deficiency of this approach that needs to be corrected in future developments is related to the constant (over the volume of the gel) characteristic volume V★. The scanning electro microscopy (SEM) micrographs of a Carbopol® network presented in Piau , one should consider a realistic probability distribution of the flow units. Although some progress in obtaining a microscopic description of physical gels under shear has recently been made An et al. Measurements of the concentration dependence of the temperature invariant rheological parameters (the elastic moduli Gu,Gd, the consistency K and the power law index) consistently indicate the existence of a concentration onset c★ beyond which a plastic behavior is observed, a. We interpret this as an onset of jamming of swollen Carbopol® molecules which induce an elastic behavior within a range of small applied deformations.The overall conclusion of the study is that, in spite of their usually claimed “simplicity” and nearly “ideal” viscoplastic behavior, Carbopol® gels are in fact quite complicated rheological systems and a complete picture of the coupling between an externally imposed forcing (deformation field), microstructure (physico-chemical properties of the microscopic gel network) and temperature remains elusive.To our best understanding, such a overall picture can be decoupled into two parts.First, it is already quite clear that when a “slow” deformation field is imposed (with a finite characteristic time of forcing t0, see ) onto a Carbopol® sample held at a constant temperature, the transition from a solid deformation regime to a fully yielded one is not direct, but mediated by an intermediate solid–fluid coexistence regime which is irreversible upon increasing/decreasing forcing, Putz and Burghelea The second part of the picture concerning the temperature dependence of the rheological parameters appears to us, however, even more puzzling and challenging than the first one. The disagreement of our results on the observation of an anomalous temperature correlation of the viscosity with some previous results and the partial agreement with some other previous results highlighted in second part of Section indicates that, the thermorheology of Carbopol® gels strongly depends on the physico-chemical interactions within the gel micro-structure which are set by a number of parameters such as the chemical nature of the solvent, the chemical nature of the cross-linking agent (and, consequently, the degree of cross-linking) and the pH which controls the degree of ionization. Thus, for a better understanding of the second part of the picture, future experimental investigations should combine, in our opinion, the methods of macro and micro rheology with a better understanding of the physico-chemistry of the Carbopol® gels.A complete understanding of this picture may open new avenues towards designing smart materials with a rheological behavior (and consequently flow properties) that can be controlled in a complex manner by variations of the temperature (around Tc), pH (around the neutral value) and ionic content which may find various applications in the pharmaceutical and polymer processing industries.First-principles study of structural, mechanical, and electronic properties of typical iron-containing phases in Al-Cu alloys under different pressuresThe structural, mechanical, and electronic properties of typical iron-containing phases, Al3Fe, Al6Fe, and Al7Cu2Fe, in Al-Cu alloys were determined using first-principles calculations. The calculated lattice constants were in good agreement with experimental values. Al3Fe exhibited the highest structural stability and most superior alloying ability. Al6Fe had the worst alloying ability and required a high cooling rate for its formation during solidification. Al7Cu2Fe was the easiest to dissolve into the Al matrix because it has the lowest negative cohesion energy. Mechanical properties improved with increasing pressure. Al3Fe exhibited the highest stiffness and strongest resistance to volume change and shear deformation. Al6Fe had better ductility owing to the high bulk-to-shear modulus ratio and Poisson's ratio; however, it had the lowest hardness and highest anisotropy, leading to a strong tendency for crack initiation. Density of states data showed that no structural variation or phase transformation occurs for any of the phases under applied pressure; moreover, they indicated covalent bonding in Al3Fe, accounting for the relatively high structural stability. Finally, all iron-containing phases were confirmed to be paramagnetic.Al-Cu cast alloys are increasingly being used in the aerospace and automobile industries because of their excellent mechanical properties and high heat resistance. Precipitation is the main strengthening process in these alloys; it was first studied by Alfred Wilm in 1911 [] and have since been investigated by several other researchers in recent years []. Al2Cu plays the important role of being the main strengthening phase in Al-Cu alloys by dissolving into the matrix during solution heat treatment [Iron, as an indispensable element in recycled Al alloys, has a great influence on the properties of Al-Cu alloys. Owing to its quite low solid solubility, iron usually precipitates as iron-containing intermetallics, such as Al3Fe, Al6Fe, and Al7Cu2Fe, which adversely affect mechanical properties []. At a relatively high concentration of 0.5 wt% Fe, platelet-like Al3Fe is the major iron-containing equilibrium phase in the early stage of solidification [], while the metastable Al6Fe phase with Chinese-script morphology is formed with increasing solidification cooling rate []. The formation of needle-like Al7Cu2Fe, the main harmful phase in Al-Cu alloys, causes stress concentration in the matrix, rendering the alloy more susceptible to cracking. Further, owing to the high formation temperature of iron-containing phases, interdendritic feeding can be blocked during solidification, which will result in hot tearing []. Thus, iron-containing phases can lower the plasticity and strength of Al-Cu alloys. However, because iron-containing phases have excellent high-temperature stability, adding the appropriate amount of Fe in a few special alloys can significantly improve high-temperature mechanical properties. Thus, the optimization of alloy compositions is a problem that researchers have always been concerned about.Recently, first-principles calculations based on density functional theory (DFT) have been widely used to calculate fundamental characteristics. For example, previous investigations of the structural, mechanical, and electronic properties of Al2Cu at various pressures showed that pressure changes the mechanical properties but not the phase []. Further, the influence of doping elements on Al2Cu [] and solute segregation at the Al/Al2Cu interface of Al-Cu alloys have also been analyzed []. However, to the best of our knowledge, there has been no first-principles study on the fundamental properties of the iron-containing phases, Al3Fe, Al6Fe, and Al7Cu2Fe, in Al-Cu alloys.In this work, the structural, mechanical, and electronic properties of Al3Fe, Al6Fe, and Al7Cu2Fe were determined at different pressures to analyze their effect on Al-Cu alloys. The theoretical calculations are expected to serve as a guide to component design and process control during the solidification of Al-Cu alloys.DFT calculations employing the projector augmented wave method were performed using the Vienna Ab initio Simulation Package []. The Perdew-Burke-Ernzerhof generalized gradient approximation was adopted as the exchange-correlation energy []. The electron configurations were Al (3s24s1), Fe (3d74s1), and Cu (3d104p1). The geometry optimization of all phase structure is performed by full relaxation by considering both the crystal volume and atomic position. A total energy tolerance of 1 × 10−5 eV and Hellmann-Feynman force of less than 10−2 eV/Å on the atoms were used for the geometry optimization. The energy cutoff was set to 500 eV for all structures, and 5 × 9 × 7, 7 × 7 × 7, and 11 × 11 × 5 k-points were employed for Al3Fe, Al6Fe, and Al7Cu2Fe, respectively, to generate Γ-centered Monkhorst-Pack mesh grids []. These settings were verified to cause an energy error of less than 1 × 10−5 eV/cell. The Methfessel-Paxton smearing method [] was applied to achieve the most accurate structure, while the tetrahedron method with Blöchl correction [] was used to determine the final static energy.The experimentally determined structures of the iron-containing phases are as follows: Al3Fe has 102 atoms and a complex monoclinic structure with the C2/m space group (No. 12) []; Al6Fe, 28 atoms and orthorhombic structure with the Cmcm space group (No. 63); and Al7Cu2Fe, 40 atoms and tetragonal structure with the P4/mnc space group (No. 128) []. The specific crystal structures are shown in . Pressure was applied to the crystals by setting the hydrostatic pressure to the desired value in the initial conditions.The lattice parameters of Al3Fe, Al6Fe, and Al7Cu2Fe after geometry optimization are listed in , as well as the corresponding experimental values. The calculated lattice constants are highly consistent with experimental values; the maximum allowable deviation (1%) is obtained for c of Al3Fe because of its complex atomic occupancy and its symmetry doesn't change.Generally, the structural stability of a phase is evaluated on the basis of the cohesive energy (Ecoh), which characterizes the bond strength between atoms and stability of the crystal structure against decomposition to single atoms. A more negative binding energy indicates that greater energy is required to decompose the crystal; thus, crystals with lower negative cohesive energy are easier to dissolve in the matrix [Ecoh=Etot−NAEatomA−NBEatomB−NcEatomCNA+NB+NCwhere Etot is the total energy of the unit cell; EatomA, EatomB, and EatomC denote the total energies of single A, B, and C atoms in the free state; and NA, NB, and NC represent the number of A, B, and C atoms. shows that the Ecoh of Al3Fe, Al6Fe, and Al7Cu2Fe are all negative, which indicates all these phases are stable. Further, the maximum absolute value is obtained for Al3Fe followed by Al6Fe and Al7Cu2Fe, which implies that Al3Fe has the most stable binding energy. These results demonstrate that Al3Fe has the most stable structure and is the most difficult to dissolve into the Al matrix. On the other hand, Al7Cu2Fe is the least stable and easiest to dissolve.The crystal formation enthalpy (ΔH), which is the energy of formation of compounds from the pure elements, was also calculated to quantify the alloying ability. This energy can be used as a basis for assessing the thermodynamic stability of a compound in equilibrium with the Al matrix [ΔH=Etot−NAEsolidA−NBEsolidB−NCEsolidCNA+NB+NCwhere EsolidA, EsolidB, and EsolidC are the total energies of the pure elements in their ground states. The results are also listed in . All ΔH values are negative, which implies that all three phases have strong alloying ability. Specifically, Al3Fe has the highest absolute value, followed by Al7Cu2Fe; thus, Al3Fe has the strongest alloying ability and is the most easily formed phase during alloy solidification. In contrast, the metastable phase, Al6Fe, has the worst alloying ability because a higher cooling rate is required for its formation [The pressure-volume curve shows the variation of volume with pressure and can be acquired by fitting data to the Birch-Murnaghan equation [P=32B0((VV0)−7/3−(VV0)−5/3)(1+34(B'−4)((VV0)−2/3−1))where B0 is the bulk modulus with derivative B′, P is the hydrostatic pressure, and V0 and V are the volumes at zero and applied pressure conditions, respectively.To analyze the specific influence of hydrostatic pressure on structural parameters, the variation of relative lattice constants with pressure in the range of 0–30 GPa was determined, and the results are shown in . For Al6Fe, a and c change to a greater extent than b, while for Al7Cu2Fe, c changes to a greater extent than a. In contrast, the lattice constants of Al3Fe at different pressures show insignificant differences. In general, the greater the change in the lattice constant, the higher the compressibility along the axis.Despite the adverse effect of iron-containing phases on the mechanical properties of Al-Cu alloys, research on this area is scarce. Therefore, it is essential to determine the elastic constant (Cij) of iron-containing phases, which is difficult to accomplish through experiments, to understand their elastic properties.The monoclinic crystals of Al3Fe, orthorhombic crystals of Al6Fe, and tetragonal crystals of Al7Cu2Fe have 13 (C11, C22, C33, C44, C55, C66, C12, C13, C23,C15, C25, C35, and C46), 9 (C11, C22, C33, C44, C55, C66, C12, C13, and C23), and 6 (C11, C33, C44, C66, C12, and C13) independent elastic constants, respectively. These phases have excellent mechanical stability, which can be determined according to the criteria presented by Wu [The calculated Cij at different pressures are shown in . The results show that C11, C22, and C33 are sensitive to pressure, while the others vary only slightly. The calculated C11 of Al7Cu2Fe is larger than the other constants, indicating that compression along the x-axis is the most difficult. For Al6Fe, C22 is the largest, indicating incompressibility along the y-axis. The C11, C22, and C33 of Al3Fe are not much different from each other, which shows that the compression capacities along the three axes are similar. These results agree with the observed pressure dependence of the relative lattice parameters discussed above. C11-C22 is an important parameter for evaluating the mechanical properties of materials []. The smaller the value is, the better the plasticity of the material. Therefore, Al6Fe has the best plasticity because it has the largest C11-C22.Elastic properties can be deduced from B, shear modulus (G), Young's modulus (E), and Poisson's ratio (ν) according to the formula presented by Wu []. B and G values at various pressures were calculated from the second-order elastic constants using the Voigt-Reuss-Hill approximation [E can be used to describe the stiffness of a material; the smaller the E, the better the plasticity of the material. ν reflects the stability of the crystal against shear stress, that is, a large ν indicates good plasticity. E and ν can be derived from B and G using, B, G, and E increase with pressure. These values are the largest for Al3Fe, indicating that this phase has the highest stiffness and resistance to volume change and shear deformation.] introduced a general rule to predict the ductility and plastic behavior of materials: the B/G ratio should be greater than 1.75. ν is also used to judge the ductility of a material; when this parameter is larger than 0.26, the material is ductile. As can be seen in , all B/G ratios and ν values increase with pressure except in the case of Al6Fe, although this phase has good ductility because its B/G ratio is always larger than 1.75 and its ν, larger than 0.26. In contrast, Al3Fe, and Al7Cu2Fe are both brittle because their B/G ratios and ν are lower than 1.75 and 0.26, respectively. Therefore, Al6Fe contributes more than Al3Fe and Al7Cu2Fe to the improvement of mechanical properties, consistent with experimental results [H, which is the ability to resist plastic and elastic properties, can be determined from the elastic modulus. There are a few semi-empirical models used to estimate the hardness of a material, as expressed below [{HG=0.1769G−2.899HE=0.0608EHV=2(G3/B2)0.585−3 shows that phase hardness increases with increasing pressure except the Hv of Al3Fe; further, the H values of Al6Fe almost remain unchanged. Al6Fe has the lowest H in all three models, while the H values of Al3Fe and Al7Cu2Fe show slight differences.Microcracks easily occur in materials owing to significant elastic anisotropy []. A precipitation phase with severe anisotropy easily becomes the crack initiation point when the alloy is deformed. Recently, Ranganathan and Ostoja-Starzewski used the pervasive anisotropic factor (AU) to measure the anisotropy of crystals using the following equation [If AU is zero, crystals are isotropic, while increasing deviation from zero indicates increasing anisotropy. According to , Al6Fe has the highest anisotropy, which decreases from 0 to 10 GPa, after which tends to change slowly. Further, pressure has a minor effect on the anisotropy of the other two phases. Therefore, Al6Fe is the most likely crack initiation point.The total density of states (TDOS) and partial density of states (PDOS) of Al3Fe, Al6Fe, and Al7Cu2Fe were studied to examine the electronic properties and stability of the structures. The TDOS curves depicted in show only a slight change with an increase in pressure, illustrating that no structural variation or phase transformation occurs under applied pressure. Moreover, all three phases have nonzero DOS at the Fermi level, which indicates that they exhibit metallic behavior. In , the main bonding peaks of Al3Fe and Al6Fe appear from −5 to 0 eV, originating mainly from the hybridized d orbitals of Fe and p orbitals of Al. For Al7Cu2Fe, the main bonding peaks are distributed between −7.5 and 0 eV; the peaks due to the hybridized d orbitals of Cu and p orbitals of Al appear from −7.5 to −2.5 eV, while those due to the hybridized d orbitals of Fe and p orbitals of Al appear from −2.5 to 0 eV. There is an evident pseudo-gap at the Fermi level of Al3Fe, which indicates covalent bonding; in contrast, only a small pseudo-gap exists near the Fermi level of Al6Fe, while the PDOS curve of Al7Cu2Fe at the Fermi level is smoother than those of Al3Fe and Al6Fe. Covalent bonding increases the strength of the material and improves the structural stability relative to the case with metallic bonding. Further, the DOS of Al3Fe at the Fermi level is significantly larger than those of the other two phases, implying that Al3Fe is more stable.The magnetic properties of the iron-containing phases under different pressures were also calculated. The calculated atomic and total magnetic moments of these three phases were always zero regardless of the pressure, from which it can be concluded that all phases are paramagnetic. Paramagnetism is a well-known behavior of intermetallics in most Al-rich alloys [The pressure dependence of the structural, mechanical, and electronic properties of the iron-containing phases, Al3Fe, Al6Fe, and Al7Cu2Fe, in Al-Cu alloys was systematically investigated using first-principles calculations. The main findings are summarized as follows:Al3Fe has the highest structural stability and alloying ability. Al6Fe has the worst alloying ability and requires a high cooling rate for formation during solidification. The Ecoh of Al7Cu2Fe is the least stable, accounting for its easy dissolution into the Al matrix.All three phases are mechanically stable. Mechanical properties improve with increasing pressure. Al3Fe has the highest stiffness and resistance to volume change and shear deformation. Al6Fe has better ductility owing to the high B/G ratio and ν; however, it has the lowest hardness and highest anisotropy, which result in a strong tendency for crack initiation in this phase.No structural variation or phase transformation occurs under applied pressure, according to the TDOS curves. Al3Fe has the highest structural stability because of covalent bonding. All three phases are paramagnetic, as expected of intermetallics in most Al-rich alloys.Our results are expected to enable further research relevant to the applications of Al-Cu cast alloys, including the reduction of the alloying ability of iron-containing phases due to the introduction of a doping element, reduction of hot cracking tendency, and improvement of the mechanical properties of the alloy.Experimental testing of joints for seismic design of lightweight structures. Part 2: Bolted joints in strapsAn experimental testing campaign on tensile bolted joints between straps is reported. Two dominant failure modes are identified: (1) tilting, bearing and tearing of the sheets (TS) and (2) tilting, bearing and net-section failure (NSF). The analysis in terms of ductility and strength shows that bolted connections are less adequate than screwed connections (reported in Part 1 of this paper) for the seismic design of X-braced shear walls in lightweight structures. NSF joints are more ductile than TS joints in the sense that they undergo larger displacements before failure. However, if washers are not used, both types of connections fail before energy dissipation through yielding of the diagonal straps can occur. Some design recommendations to improve the seismic performance of bolted joints, including the use of washers, are given. The accuracy of Eurocode 3 formulas to predict the ultimate load is also analyzed.A growth in the application of lightweight steel technologies in residential construction has taken place in recent years, together with the development of a significant amount of investigations on the issue, mainly focused on structural questions concerning cold-formed steel members. The main current lines of research in this field can be seen in This research has allowed improving the existing design guides and standards, which are already giving solutions for the most common problems encountered in the project and construction of lightweight steel buildings. Questions such as materials for cold-formed steel construction, instability of compressed and bent members or connections and fasteners have been largely investigated, and they have already been included in codes for design. However, there are still some specific issues that clearly deserve more research. As pointed out in the first part of this paper Actually, the paper shows a part of a rather extensive experimental and numerical The investigation is focused on connections. The main objectives are, on the one side, to gain knowledge about their ductility and their behavior under cyclic loads; and, on the other side, to identify which type of joints are most suitable for seismic actions, i.e., to know which are the joints that have enough strength to allow the dissipative yielding of diagonal straps.The initial steps of the investigation were presented in a previous paper In view of this result, it seems that reliable equations to predict the mode of failure of a joint are needed to tackle the design of X-braced frames. That is the reason why part of the first paper is also devoted to verify de accuracy of the current Eurocode 3 Part 1-3 proposals for the calculation of joint resistance. It should be pointed out that the Eurocode 3 formulas for the net-section mode of failure showed to work satisfactory, while the bearing formulas gave rather conservative predictions for some of the screwed joints.The second part of the investigation, presented in this paper, is focused on bolted connections subjected to shear loading. The analysis of the joint behavior is based on the results of a testing campaign performed in the framework of the RFCS research project “Seismic design of Light Gauge Steel Framed Buildings”. Lap joints between two straps connected by means of two rows of bolts are tested under monotonic and cyclic load, see The objectives and the scheme of the paper are similar to what was done for screwed connections. The goals of the experiments are: Obtain parameters such as the initial stiffness, yielding load, ultimate load and maximum displacement.Obtain complete force–displacement (F–d) curves, needed for the finite element modeling of X-braced frames After that, we analyze the experimental results in order to:Classify the various failure modes in terms of their seismic suitability (strength and ductility).Determine the relation between parameters in joint design (steel grade, strap thicknesses, number and diameter of bolts, etc.) and failure mode.Compare experimental ultimate loads of the joints to the strengths calculated by means of the Eurocode 3 Part 1.3 design formulas.It will also be very interesting to compare the behavior of screwed and bolted connections.An outline of paper follows. The laboratory experiments are described in (test specimens) and 3 (test procedure), and the results are summarized in (monotonic tensile tests) and 5 (load–unload tensile tests). Three main features are studied: the modes of failure, the force–displacement curves, and the ductility and stiffness of the connections. The remainder of the paper is devoted to the analysis of the results. The seismic suitability of the joints is discussed in , the ultimate loads are compared to the values predicted by the Eurocode. Recommendations for design and the concluding remarks of The bolt joints tested are similar to the screw joints of the investigation reported in the first part of the paper (. It should be noticed that the experimental fyt and fut are rather higher than the nominal fy and fu.Bolts of two different diameters are used to connect the straps: 8 and 10 mm. The heads of these bolts are hexagonal and the shafts are threaded all along their length. All the straps of steel grade S 350 GD+Z are connected with washers, while washers are only used in 4 out of the 38 S 250 GD+Z straps. When used, washers of 20 mm Φ are placed under the bolt head and nut.The torque applied to the bolts is not measured. Bolts are tightened by hand using standard tools, so the torque should be small.The nominal length of the straps is either 350 mm, when connected by means of one column of bolts, or 375 mm, when connected by means of two columns. Their thickness ranges from 0.85 to 1.5 mm, and their width is always the same, 100 mm. The tolerance of the bolt holes drilled in the straps is 1 mm. shows the position of the bolts: the spacing and the longitudinal and transverse edge distances. The joint lay out is identical for all the specimens. together with their main dimensions and test results. The first column of the table shows the joint notation, whose meaning is explained in the following example:where t1 is the thickness of the first strap (t1=1mm), t2 the thickness of the second strap (t2=1mm), Φ the diameter of the bolt (Φ=10mm), nc the number of bolt columns (nc=2), sg the steel grade (S250 GD+Z), l: letter used when there are two or more identical joints (E), (W) denotes that washers are used.Tests are performed applying the same procedure as the one previously followed in the experimental campaign of screw connections The first operation is to measure the actual dimensions of the joint components (see some of the measured values in and the full collection of measurements in A 250 kN universal testing machine is used to load the joints. Tests are displacement-controlled and the load is applied at a rate of 0.01 mm/s when the elongation of the joint is lower than 2 mm; and at a rate of 0.02 mm/s when the elongation is higher.Every 0.04 mm, the applied force (F) and the length increment of the joint (d) are measured and stored in a computer. On the basis of these data, F–d curves, such as the ones shown in , are drawn. It can be seen that the specimens are loaded until they fail and the measured load is almost zero.In the course of an earthquake, displacements change their sign and, as a consequence, joints are subject to reversing movements. For this reason, apart from monotonic tensile tests, load–unload tests are also performed. In these tests, it is particularly important to capture the unloading branch of the cyclic axial load response.The cyclic tests are carried out unloading four times to a near zero load (see ). Only tension forces are applied to the diagonal straps, because they do not have compression strength. The experimental procedure followed is similar to the one explained above. The only difference is that the unloading process is load-controlled to ensure that the specimens are always in tension and do not become compressed.The specimens show various phenomena during the tests Tilting and bearing are observed in all the joints. Tilting is more evident when the joint connects two straps of the same thickness, while joints connecting two specimens of different thickness are more prone to bearing.Depending on the final mode of failure, joints can be classified into two groups: joints that fail due to the bearing and tearing phenomena (T+B+TS), and joints that are subjected to NSF (T+B+NSF) (Those joints that fail T+B+NSF show tilting and bearing from the first steps of the loading process (). Afterwards, the failure begins from the center of the original bolt holes, and it propagates perpendicularly to the direction of loading until it reaches the lateral edge of the strap (). Necking of the sheet width in the zone of failure and a small out-of-plane deformation are also observed.In relation to the bearing failure (T+B+TS), two types of joints may be distinguished (see ). This type of bearing failure is mainly observed in joints connecting straps of different thickness. On the other hand, when both straps have the same thickness, tears originate near the center of the bolt holes, in a similar way as in the NSF mode. In this case, however, tears propagate diagonally and the straps experience considerable curling (The number and diameter of bolts and the thickness of the straps are the parameters that determine the modes of failure of the specimens. All the joints with one column of bolts fail bearing (T+B+TS), while the mode of failure of the joints with two columns depends on the diameter of the bolt and the thickness of the straps. NSF (T+B+NSF) is observed in joints with two columns of 10 mm diameter bolts and joints with two columns 8 mm diameter bolts connecting straps of different thickness. Joints connecting straps of the same thickness by means of two columns of 8 mm diameter bolts fail T+B+TS.The force–displacement curves of T+B+NSF joints are different from the curves of T+B+TS joints. show the F–d curves of two joints that fail T+B+NSF. Both have two initial elastic branches, with different stiffness, separated by a small irregular horizontal branch that corresponds to the slipping of the straps. Subsequently, the joint yields and the curve either shows a small drop, if one of the straps is thin, 0.85 mm (), or it goes directly to the hardening branch (). The maximum load is achieved at the end of this hardening branch, which is followed by a sudden failure.The Agtfyt line plotted in these figures corresponds to the yielding load of the strap. This value will be used afterwards, when the seismic suitability of the joints is discussed.Joints connecting two straps by means of one column of bolts, which always fail T+B+TS, show F–d curves such as the ones of . As in the T+B+NSF curves, the slipping and the two initial elastic branches can be seen. These curves also have a well-defined first drop after yielding, that is followed by a hardening branch with one or more load peaks. The maximum load is achieved just before the first drop () or, afterwards, in the hardening interval (When a T+B+TS joint connects two straps by means of two columns of bolts, the F–d curve may be different. See, for instance, the curve of , where neither the first drop nor the hardening branch are well defined.The ductility of the connections is studied by means of the displacement ductility ratio rd=du/dy, where du is the displacement corresponding to the maximum load (or to the last load peak, in curves such as the one shown in ), and dy is the displacement at yielding. All the calculated rd ratios are above 2, as shown in , so the joints can be considered ductile. From , which depict the values of the ductility ratios and the values of displacement at failure, respectively, it can also be concluded that T+B+NSF joints are more ductile than T+B+TS joints.In relation to ductility, it was also investigated whether the two types of T+B+TS failure mentioned in show different rd values. The conclusion of this study is that both modes of failure give similar ductility ratios and similar F–d curves.Apart from the ductility ratios, the stiffness of the two initial elastic branches is included in , where k1 and k2 are the values measured before and after slipping, respectively.The effect of different parameters on these stiffnesses has been investigated. It is possible to see that both k1 and k2 increase with the number of bolt columns. No other clear correlation between k1 and other parameters can be found from the results of the tests performed. On the contrary, it is verified that k2 also depends on the thickness of the sheets and the diameter of the bolts. The higher the values of these parameters, the higher the stiffness.Similar results are obtained in two other investigations on stiffness where d is the diameter of the bolt, t1, t2 the measured thickness of the straps (from ), n=5 for joints in tension where the position of the shear plane is in the threaded part of the bolt shaft (see These formulas have been applied here to predict the stiffness of the connections tested. The values obtained with both equations are similar, and many of them above the experimental results (where k2t is the experimental stiffness, k2 the calculated stiffness. was defined to overestimate the value of k2No formula has been found in the literature to predict the value of k1. In fact, in ), and that, if a connection is designed without slipping Joints 1-1-10-2-S250 and 1-1-10-1-S250 were tested with and without washers. Comparing the results of the tests, it can be seen that washers increase the strength of connections. The resistance of joint 1-1-10-2-S250, which fails T-B-TS, is 8.6% higher when washers are used. The increase in strength of joint 1-1-10-S250, which fails T+B+NSF, is even higher, close to 17%.Washers also increase the ductility of the T+B+NSF joint. This can be clearly seen in , where the F–d curves of the joint with and without washers are compared. The corresponding values of displacement ratio also allow to detect this gain in ductility: rd=7.40 and rdw=14.97 (mean values).On the contrary, washers almost do not change the ductility of joint 1-1-10-1-S250, that fails T+B+TS. Its displacement ratio only increases from rd=4.62 to rdw=5.83. also shows that the F–d curves are not considerably affected. It can only be observed an increase in ultimate load, but not an increase in ultimate displacement.However, washers modify the behavior of T+B+TS joints in one sense. They change the mode of failure of those joints where the tears provoked by bearing originate near the center of the bolt holes. When washers are used, these joints fail in pure bearing, showing tears initiated at the edge of the zone affected by bearing (see show, plotted in the same graph, curves of monotonic and load–unload tests.It can also be seen that the unloading paths are similar to the reloading paths, and that no stiffness degradation occurs.A force ductility ratio is defined as rf=Put/(Agtfyt), where Put is the experimental ultimate load of the joint, and (Agtfyt) is the yielding load of the strap, calculated from the measured gross cross section area, Agt=attt (), and the measured yield stress of the steel, fyt (). This ratio allows to know if a joint is suitable for seismic design shows the rf values calculated for all the specimens connected without washers. The ratios of the T+B+TS joints are rather low, ranging from 0.4 to about 0.8. Ratios of T+B+NSF joints are better, but most of them are also below 1. Therefore, it can be concluded from these results that, although bolted connections are ductile, as discussed in , they are not suitable for seismic design. They do not allow the dissipative action of diagonal straps in X-braced frames.When washers are used, the strength of T+B+TS connections increases, but their ductility does not change considerably (). On the contrary, the effect of washers on T+B+NSF joints is more significant (). They exhibit longer hardening branches and failure loads higher than the yielding loads of the straps. This results in good rf values (rf >1), as shown in The F–d curves included in this paper are plotted together with the calculated yielding load of the straps, so that it can be directly evaluated whether a joint is suitable for seismic design. It should be noticed that all the F–d curves of T+B+NSF joints with washers cross the line of yielding load; but almost none of the joints without washers cross it. See of specimens 1-1-10-2-S350-A and 1-1-10-2-S250, respectively.The force ductility ratios of T+B+NSF bolt joints are compared in to the ratios of T+NSF joints obtained in the previous investigation on screws In this section, the connection maximum load carrying capacities obtained in the tests are compared to those that result from design calculations.The Eurocode 3 Part 1.3 is applied to predict the strength of specimens. According to this code, there are three possible modes of failure when loading a joint in shear: bearing (includes end-tearing), NSF and shear failure of the screws. This last mode is not considered in this paper, because it is not observed in the tests.The strength of the connections is calculated as follows:where αb is the smallest of 1.0 or e1/(3d); e1the end distance from the center of the bolt to the adjacent end of the connected part, in the direction of load transfer; d the nominal diameter of the bolt; for 0.75mm⩽t⩽1.25mm, kt=1.0 for t>1.25mm; where t is the thickness of the thinner connected strap; fu the ultimate tensile strength of the strap (fut in Pn,Rd=(1+3r(d0/u-0.3))Anfu/γM2butPn,Rd⩽Anfu/γM2,where r is the (number of bolts at the cross-section)/(total number of bolts in the connection); d0 the nominal diameter of the hole; u=2e2 but u⩽p2; e2 the edge distance from the center of the bolt to the adjacent edge of the connected part, in the direction perpendicular to the direction of load transfer; p2 the spacing center-to-center of bolts in the direction perpendicular to the direction of load transfer; An the net cross-sectional area of the strap; fu the ultimate tensile strength of the strap (fut in The strength calculations are carried out taking γM2 equal to 1 and using the core thickness of the strap: tcor=tt−tcoating=tt–0.04 mm, where tt is the measured thickness of the thinner steel sheet (The results obtained applying the above formulas can be observed in , where the third and fourth columns include the net-section and the bearing resistance, respectively. The mode of failure of the joints is predicted on the basis of these calculated strengths. The critical mode is the one that gives the lowest ultimate load. In view of the values of the mentioned columns and the sixth column of , it can be concluded that good predictions of the failure mode are obtained by means of Eqs. . The Eurocode 3 equations fail in only four specimens, most of which show calculated bearing strengths similar to calculated net-section strengths (see values of specimens 0.85-0.85-8-2-S250, 1-1-8-2-S250-A and 1-1-8-2-S250-B). gives acceptable predictions of the T+B+NSF failure load, although they are slightly conservative. The Put/Pn,Rd ratios of MeanvalueofPut/Pn,Rd:γumean=1.14,StandarddeviationofPut/Pn,Rd:sg=0.05. is too conservative, and that the NSF ultimate load can be determined without any reduction factor:This may be true when straps are connected with washers, as in the mentioned works. In fact, shows that predictions are better when the reduction factor is not applied to connections with washers. However, when Eq. is applied to joints without washers, strengths are overestimated. See in the Put/Pn,Rd ratios obtained here for the joints tested without washers. The mean value isMeanvalueofPut/Pn,Rd:γumean=0.96,StandarddeviationofPut/Pn,Rd:sγ=0.06.The Eurocode 3 strengths obtained for the bearing mode of failure are not as acceptable as the strengths obtained for the net-section mode (The mean value of the Put/Pb,Rd ratio is good, but the dispersion is too high (see also ). There can be seen values of strength clearly underestimated for joints with washers and joints with 10 mm Φ bolts. The worst results, however, are those obtained for some 8 mm Φ joints, whose bearing strength is overestimated:jointswithwashers:γumean=1.23;sγ=0.16,10mmΦjoints:γumean=1.12;sγ=0.15,8mmΦjoints:γumean=0.97;sγ=0.14.In relation to this, it was noticed that some of 8 mm diameter joints showed a bearing failure mode slightly different from the mode of failure of 10 mm diameter joints. A clear tearing out failure was observed when 10 mm Φ bolts were used (), while for 8 mm Φ bolts the tearing was mixed with a sort of punching or pull-out phenomenon similar to that of screwed connections (see , where Put/Pn,Rd ratios of joints without washers are plotted against d/t ratios. This figure shows that the higher the d/t ratio, the more conservative the strength prediction. In view of this result, it is believed that one way of improving the predictions of Eq. may be by using a gradated bearing factor, which would depend on d/t. Gradated bearing factors have been successfully applied in other investigations Finally, it is pointed out that the Eurocode 3 bearing formula was established on the basis experimental load values that corresponded to 3 mm of displacement (Pb,Rd) are also compared to the 3 mm loads (Pu3 mm). As it can be seen in , the Pu3 mm load of the joints tested are lower than the predicted values.It should be noted that for many of the joints the Pu3 mm load is not the maximum load measured in the test. Maximum loads are usually achieved in the range of 6–11 mm. The same happened in the tests of screw connections.Recommendations are given in this section for the design of bolted joints between straps of cold formed steel structures. These recommendations, which are mainly related to the geometric layout of the connection, can be classified in two groups:Recommendations for increasing the ductility of the joint.Recommendations for improving the seismic performance of the joint.(a) Recommendations for increasing the ductility of the joint: The experimental tests prove that the T+B+NSF mode of failure is rather more ductile than T+B+TS mode. Therefore, it is recommended to design joints that fail NSF, i.e., to design joints whose bearing strength is higher than the net-section strength (Fb,Rd>Fn,Rd).From the design point of view and according to the Eurocode 3 calculation formulas: The bearing strength does not increase linearly with the thickness of the sheet includes the factor kt, which gives values below 1 when the thickness of the sheet is lower than 1.25 mm. Therefore, if a high value of Fb,Rd is wanted, so that Fb,Rd>Fn,Rd, sheet thickness above 1.25 mm are recommended.The bearing formula was defined for the bearing failure and also for the end-tearing failure. The effect of tearing on strength is considered by means of the αb factor in Eq. (3) A ductile failure (Fb,Rd>Fn,Rd) does not guarantee that the joint will be suitable for seismic design. Other requirements should be accomplished, as it is explained in the following point (see also (b) Recommendations for improving the seismic performance of the joint: The objective is to design joints whose strength is higher than the yielding load of the gross cross-section (Fn,Rd>Agtfy), i.e., joints with rf>1, so that the dissipative action of the straps can develop., it has been shown that bolted connections without washers do not satisfy this condition. On the one hand, bolt joints failing T+B+TS exhibit very low values of rf ratio and, consequently, they will never be suitable for seismic design. On the other hand, T+B+NSF joints show higher rf ratios, but most of them are lower than 1. The main problem with these joints is that the diameter of the bolts is high, and it is not easy to keep the net-section area large enough to allow the dissipative yielding of the straps.However, the behavior of the T+B+NSF connections improves when washers are used, their rf ratios become higher than 1. This is observed for all the joints tested with washers. Therefore, the main recommendation is that bolt joints should be used with washers and designed to fail NSF.Other recommendations may be given in order to increase the rf values:Choose the steel with the highest fu/fy ratio, which will directly increase the Fn,Rd/Agfy ratio.Use only a row of bolts, which increases the net-section area.Drill the minimum feasible bolt diameter, so that the maximum net-section area is available.Enlarge the width of the straps in the perforated section to avoid the NSF.Place the bolts so that e2>1.66d, which avoids any reduction of the net-section area (see the net-section strength formula When the rf ratios of T+B+NSF bolted connections with washers are compared to the ratios of T+NSF screwed connections ). Consequently, it is also recommended to use screws instead of bolts in dissipative straps of cold-formed structures.Nevertheless, it is believed that more investigations should be devoted to the seismic suitability of T+B+NSF bolted joints with washers. In the present paper, from the results of a few tests, it has been possible to show the relevance of washers in the seismic behavior of joints. More tests should be performed to confirm this point and to improve the design of connections with washers. For instance, it can be investigated whether the use of washers in joints of only one row of bolts results in acceptable dissipative intervals.Finally, it should be pointed out that the problem of the net-section area reduction due to the bolt holes may be solved following the fourth recommendation mentioned above. For example, straps of non constant width can be used. However, this solution is difficult from the manufacturing point of view.The present investigation on bolted connections between straps has given results that, in some senses, are similar to the ones obtained in the previous investigation on screwed connections. For instance, here two modes of failure are also observed, the T+B+TS and the T+B+NSF modes, which show different ductility. Both modes are ductile, their displacement ductility ratios are above 2 (rd>2), but the ductility of the joints that undergo the NSF (T+B+NSF) is higher than the ductility of the joints that fail bearing (T+B+TS). Therefore, regarding the ductility of the joint itself, the T+B+NSF type of joint is preferred.The main difference with screw joints is that none of the mentioned types of bolted connections are suitable for seismic design. When the failure mode is T+B+NSF, the ultimate load is close to the yielding load of the strap, but most of the times below it. As a consequence, these connections would not allow the development of the dissipative action of the strap in an X-braced frame. When the failure is T+B+TS, the strength of the connection is even far lower than the yielding load of the strap.However, the situation improves when washers are used and, consequently, the strength of the connection increases. This is very important for T+B+NSF joints, because this increase in strength is high enough to allow the dissipative yielding of the bracings. Therefore, the use of washers becomes relevant from both the resistance point of view, and the seismic point of view in the case of T+B+NSF bolt joints.Apart from the ductility of the joints, other questions have been investigated. For example, the measurement of the stiffness of the connections has allowed to conclude that, if an accurate model of the behavior of the joint is wanted, it should be taken into account that the value of k before slipping is considerably higher than its value after slipping.The effectiveness of the Eurocode 3 Part 1-3 in predicting the strength of the joints has also been evaluated. One of the results of this study is that the Eurocode 3 formulas give good predictions of the joint mode of failure. This is very useful in design because, as it has been shown, the mode of failure of joints is a determining factor in relation to performance of dissipative frames. When it comes to the accuracy of the equations prescribed by this code, it should be pointed out that the predictions of the ultimate loads of NSF joints are acceptable, although slightly conservative. The results of the bearing equation are not so good, mainly when applied to joints connected by means of 8 mm Φ bolts.When designing, one way to know whether the use of washers in a particular joint is effective is by means of a calculation formula. Nowadays, there are not specific formulas for bolted connections with washers in Eurocode 3. Due to the relevance of washers in the seismic behavior of joints, it may be interesting to modify the net-section strength equation to take into account their effect. For instance, it can be investigated whether good predictions of the ultimate load of joints with washers are obtained if the reduction factor is removed from the current version of this equation.Finally, the last section of the paper contains a list of recommendations for designing bolted joints suitable for seismic construction. In fact, from the results of the tests performed, it can be concluded that it is better to use screws than bolts to connect the straps of a dissipative X-braced frame. However, it is also shown that bolted joints with washers, designed to fail NSF and to keep the maximum available net-section area, allow the dissipative yielding of the strap. The problem is that in the present investigation only a small group of joints are tested with washers, and it is not known whether this type of connections may be good enough for seismic design. Further tests should be carried out to give light to this question.Experience on mixed carbide fuels with high ‘Pu’ content for Indian fast breeder reactor – An overviewHyperstoichiometric Plutonium rich (70%) mixed Uranium Plutonium carbide fuel was proposed as the driver fuel for Indian Fast Breeder Test Reactor (FBTR) after some deliberations. The issues of mixed carbide fuel and of plutonium rich (70%) carbide fuel, in particular, are: presence of ‘O’ impurity, clad carburization, lower solidus temperature, lower thermal conductivity and pyrophorocity. The paper highlights the extensive research and development carried out to address the above issues. The modification incorporated in the different process steps of fabrication flow sheet is also presented. The performance of the fuel has been assessed by periodic Post Irradiation Examination (PIE) of the fuel sub-assemblies for extension of life. Till date the fuel has seen a burn up of 155 Gwd/t without any pin failure.The Fast Breeder Reactor Programme in India was initiated in the early eighties with the construction of an experimental breeder test reactor of 40 MWth (13.2 MWe) capacity. The small core size warranted high fissile inventory which, probably could be met with the use of Plutonium rich (76%) mixed Urania–Plutonia oxide fuels. However, this was not considered as reported literature FBTR has been in operation since 1985 and seen a burn-up of 155 GWd/t. Initially it was made critical with a small core of 23 sub-assemblies (MKI) followed by use of additional fuel subassemblies of MKI and MKII (55% PuC). Periodic PIE was carried out for extension of the life of the fuel pin.Mixed carbide fuels have many advantages Apart from this, ‘C’ stoichiometry plays a very important role in determining the extent of Fuel–Clad Chemical Interaction (FCCI) and Fuel–Clad Mechanical Interaction (FCMI). A hyperstoichiometric fuel is preferred as the metal phase M (Pu + U) present in hypostoichoimetric fuel causes formation of low melting eutectic with ‘Fe’ and ‘Ni’ of SS316 cladding. Moreover, carbon to metal ratio decreases with burn-up and in extreme case may lead to metal phase formation at fuel–clad interface; bonding the fuel to the clad resulting severe FCMI. Agarwal and Venugopal The experience gained over the years in the operation of FBTR helped in relaxing the fuel specification which was rather conservative. Introduction of some novel processing techniques, optimization of process parameters, modified end plug design and use of pulsed TIG welding have resulted in higher yield. The present investigation highlights the research and development work carried out from the inception of this fuel till date, to get an insight into the fuel behaviour and add to the confidence level of fuel designer to extend the fuel burn up without encountering any failure.The process flow sheet for fabrication of mixed carbide fuel pellets has been described in Ref. The performance of the fuel up to a burn up of 155 GWd/t without failure helped in reviewing fuel specification with respect to ‘O’ and ‘N’ content, classification of pellets into Class ‘A’ and ‘B’ based on M2C3 content and surface defects. The end plug weld acceptance specification was also moderated to accept criteria of minimum leak path (MLP) in the weld region instead of defect free weld. Repair of top end plug welds was also introduced. Further, earlier classification of pins as Class ‘A’ and ‘B’ is no more practiced instead all pins are allowed to have 70 mm (maximum) of fuel column with class ‘B’ pellets in the bottom side. These changes led to higher acceptance of both fuel pellets and pins. Also, the loading of fuel sub assemblies in the core has become simpler.A high energy stirred ball mill ‘Attritor’ was introduced in place of planetary ball mill to reduce processing time from powder to pellet thus increasing productivity and lowering energy consumption There are two types of pellet rejects namely physically defective and chemically unacceptable. Sintered pellets rejected due to non-conformation of chemical specification (‘O’, ‘N’, ‘C’ and M2C3) are crushed into powder followed by controlled oxidation to obtain oxide powder with (O/M) ratio of 2.17–2.20 Some of the important thermo physical properties like solidus temperature, thermal expansion, thermal conductivity and thermal toughness (hot hardness) were measured in house. These properties play a very important role in predicting the in-pile fuel performance. briefly presents the data generated on the properties of MKI and MKII fuels and that of conventional uranium rich mixed carbide fuel.Solidus temperature was estimated from the heating/cooling curve or by measuring linear thermal expansion in a dilatometer. For MKI, it was estimated from the cooling curve. This was supported by metallographic examination. For MKII it was obtained by dilatometric studies where an abrupt shrinkage of the pellet at a particular temperature indicates the solidus temperature. The details of the measurement procedures and the apparatus used are given in Ref. Thermal expansion was measured using a dilatometer. The average value of the coefficient of linear thermal expansion for MKI and MKII fuel between 300 and 1800 K were 13.8 × 10−6Hot hardness data can predict the FCMI behaviour of fuels. Carbide being more closed packed, swells more than the oxide and retains more fission gases. Swelling of carbide occurs by creep resulting in fuel–clad gap closure. Further swelling results in development of back stress which help in restrained swelling i.e. creeping of the fuel within the available pores. Generation of creep data for ‘Pu’ bearing fuel is a very elaborate and expensive proposition requiring number of samples and battery of creep machines under different time, temperature and stress conditions. Alternately, this can be determined qualitatively by hot hardness data which is much simpler needing small sample size.Hot hardness of MK I and II fuels were measured using a high temperature micro hardness tester with Vickers pyramid indenters Fuel–Clad Chemical interaction is a key issue limiting the life of a fuel pin in a reactor. For carbide fuel this occurs by clad carburization by solid state (direct contact) ‘C’ transfer or gas phase carburization by CO. The extent of clad carburization depends on the ‘Carbon Potential’ of the fuel and partial pressure Pco generated by the reaction of dissolved ‘O’ with MC. However, ‘Pu’ rich carbide has some advantages over its uranium rich counter parts. First, PuC and Pu rich MC have some range of carbon stoichiometry, unlike UC and ‘U’ rich MC which are line compounds The results of out-of-pile experiments carried out are summarized Assessment of fuel and core structural material behaviour were carried out after bum ups of 25 GWd/t, 50 GWd/t, 100 GWd/t and 155 GWd/t ) revealed a distinct zone with no porosity near the periphery due to creep of the fuel. Fuel–clad gap closure and circumferential cracking at the centre as well as at the end of the fuel column indicates that the fuel column is under the restrained swelling regime. Swelling and porosity exhaustion in the fuel, high void swelling of the cladding, loss of tensile strength, ductility and dilation of the wrapper tube and its impact on the fuel handling operations will be the limiting factors in increasing the burn-up beyond 155 GWd/t.Indian Fast Breeder Reactor Program started on a very conservative but distinctive note with the commissioning of its first ever tried Plutonium rich (70%) mixed uranium plutonium carbide fuelled fast breeder test reactor (FBTR) in the year 1985. The unique feature of this fuel prompted extensive out-of-pile studies both by experimental measurements and theoretical calculations to understand fuel behavior and address various issues. The experience gained on the performance of this fuel over the years helped in optimizing the fuel specifications in terms of ‘O’, ‘N’ and M2C3 content. Reduction of milling time with the use of ‘attritor’ and recycling the physically defective pellets resulted in increasing productivity. PIE of the fuel at different stages of burn up played a key role in deciding the life of the fuel. As of now the fuel has seen a burn up of 155 GWd/t without any problem.Materially and geometrically non-linear woven composite micro-mechanical model with failure for finite element simulationsA computational micro-mechanical material model of woven fabric composite material is developed to simulate failure. The material model is based on repeated unit cell approach. The fiber reorientation is accounted for in the effective stiffness calculation. Material non-linearity due to the shear stresses in the impregnated yarns and the matrix material is included in the model. Micro-mechanical failure criteria determine the stiffness degradation for the constituent materials. The developed material model with failure is programmed as user-defined sub-routine in the LS-DYNA finite element code with explicit time integration. The code is used to simulate the failure behavior of woven composite structures. The results of finite element simulations are compared with available test results. The model shows good agreement with the experimental results and good computational efficiency required for finite element simulations of woven composite structures.Woven composite materials are being used as primary structural components in many applications. Failure analysis of such structures is an essential part of the structure design. Along with their advantages, however, the complex architecture of the woven fabric composites makes the analysis and the simulation of their failure behavior very difficult. Tremendous amount of works dedicated to the modeling of woven composites intends to predict the elastic properties of the materials and only few of them consider the failure behavior. The reason for this is the complex phenomena affecting the progressive failure behavior of woven fabric composites. These phenomena are the material non-linearity of the matrix material combined with the geometrical non-linearity of the fiber reorientation and the damage accumulation with stress concentration in the interacting constituents.The unit cell approach is employed in the analysis of the most material models of woven composite structures. The composite structure is divided into repeated cells, representing the properties and the behavior of the whole lamina. The classical 1-D models of Ishikawa and Chou The material models of woven fabric composites described above are suitable for non-linear finite element failure analysis of composite structures, but because of the high degree of RVC discretization, they are computationally inefficient to be applied in explicit finite element codes. The non-linear finite element codes with explicit time integration are very powerful for large-scale simulations but because of the inherent small time step for stable solution they require high computational efficiency of the material models. This characteristic is an obstacle for complicated micro-mechanical models to be implemented in the explicit codes. The authors developed a computationally efficient and simplified micro-mechanical model of woven fabric composite materials The micro-mechanical material model and the homogenization procedure determining the elastic properties of woven fabric composite material employed in this work are described in The architecture of the woven fabric material is modeled by two over-crossed straight broken strands in elastic media ( The strands represent the fill and the warp yarns, respectively, and the elastic media represents the matrix material. The orientation of the yarns is described by two angles: the braid angle θ and the undulation angle β ( The RVC is divided in four sub-cells: two anti-symmetric sub-cells consisting the fill yarn and two anti-symmetric sub-cells consisting the warp yarn.The homogenization procedure for elastic properties begins with the stiffness matrix of each constituent material in each sub-cell. A degradation of the elastic moduli is applied for each constituent in the different sub-cells depending on the attained stress of the constituent. When failure is detected the degradation is applied only on the elastic moduli by multiplying them with a discount factor di∈(0,1] (i designates the elastic modulus to which it is applied). Degradation is not applied on the Poisson's ratios. In order to obey the following relation:the yarn material is considered as orthotropic with the following stiffness matrix , are the discount factors for yarn material, initially all of them equal unity, , are the elastic moduli and Poisson's ratios of the yarn material, respectively. The resin material has a simpler stiffness matrix as follows:The Young's modulus, E, and shear modulus, G, are degraded independently by different discount factors dE and dG, both initially equal unity (The elastic material properties of yarn and matrix materials are homogenized for each sub-cell and the stiffness matrix in direction of the material axes () is obtained for each sub-cell at the first level of the homogenization procedure. The homogenization procedure is based on mixed, iso-strain and iso-stress, boundary conditions. The stiffness matrix of each sub-cell is transformed to the RVC coordinate system (x,y,z in ), using the current directional braid and undulation angles of the yarns. The effective stiffness matrix of the RVC is obtained after applying the second level of the homogenization procedure. Note that because of the different stresses in the constituents of the different sub-cells, the degradation is different and the anti-symmetry of the sub-cells cannot be exploited.Having the effective stiffness matrix of the RVC, , we can calculate the stress response of the material model at each time step n for non-linear explicit finite element code: are the stress and strain increments in the composite material, respectively. In order to obtain the stress and strain in constituents one can use formulae twice, once to obtain the stress and strain increments in the four sub-cells from the stress and strain increments of RVC and then again for each sub-cell to determine the stress and strain increments in the yarn and in the matrix material from the stress and strain increments of the sub-cell. For the first calculation the following equations are applied:where k denotes the sub-cell (k=f,w,F,W) and the adopted contracted notation for stress and strain components is 1≅11,2≅22,3≅33,4≅12,5≅23,6≅31. After applying the iso-strain components (denoted by n) and the iso-stress components (denoted by s) of the strain and stress increment in each sub-cell, k, in the coordinate system of the RVC are obtained. Therefore, the full strain increment vector, {dε′}, and the full stress increment vector, {dσ′}, are constructed for each sub-cell. These increment vectors are in the RVC coordinate system and they are transformed to the material coordinate system by means of the transformation matrix [T] as reported in The full strain and the full stress increment vectors of each sub-cell are divided into iso-strain and iso-stress parts in order to obtain the stress and strain increments in constituent materials. The assumed iso-strain and iso-stress boundary conditions for the homogenization of the yarn and the matrix materials are as follows:where k now denotes the constituent materials of the sub-cell (k=y,m). Applying again, all components of the strain and stress increments in the constituent materials are obtained and the full stress increment vectors in the yarn and the matrix materials can be constructed as follows:The total stress in the constituent materials is accumulated at each time step, n, for each sub-cell and it is kept as historical variableThe orientation of the fill and the warp yarns is determined in the coordinate system of RVC by the braid and the undulation angles. They are denoted by subscript f or w for the fill and the warp yarn, respectively. We can construct directional vectors for each of the yarns in order to rotate them to the new position at each time step, n, to obtain the updated braid and undulation angles The directional vectors are rotated and then normalized by means of the approximate deformation gradient tensor, [F]:The new orientation angles of the yarns are determined from the updated directional vectors:Initially, βf=βw=β0,θf=45°,θw=−45°. Note that in this technique the orientation of the yarns depends on the global strain increment of the RVC, not on the strain increment of the sub-cells.The shear material non-linearity of composite materials is recognized by many authors where G0 is the initial shear modulus, S is the ultimate shear strength, and p is a shape parameter which can be determined by a curve-fit to experimental shear stress–strain data.In the incremental solution of the non-linear finite element method, the tangential shear modulus is used in the constitutive equations relating the stress and strain increments as follows:where Gt=dτ/dγ is the tangential shear modulus. The tangential shear modulus can be obtained as a function of the shear strain, Gt≡Gt(γ), by differentiating . In the presented material model of woven fabric composite materials, the total stress components of the constituent materials are calculated only for failure analysis and they are kept as history variables for further accumulation and analysis. The total shear strain components are missing, so that the tangential shear modulus as a function of the shear stress, Gt≡Gt(τ), has to be derived. The inverse function, γ≡γ(τ), can be easily found from and then the tangential shear modulus can be obtainedThe shear material non-linearity can be introduced in the material model as discount factors for the shear moduli from The instantaneous discount factors for the shear material non-linearity of the yarn material, and ds6, are calculated from the stress components and σ6y, respectively, by the following formulae:where py is the shape parameter of Romberg–Osgood equation and Sl and St are the longitudinal and transverse shear strength of the yarn material, respectively. Similarly, the instantaneous shear discount factor for the matrix material, dsG, is calculated from the octahedral shear stress, τ0where pm is the shape parameter for the matrix material, S is the shear strength and the octahedral shear stress is calculated from the stress components of the matrix material by using the following formula:Note that when explicit time integration is utilized the material stiffness matrix is updated with relatively high frequency and consequently the material non-linearity is properly captured.The failure criteria and stiffness degradation scheme is adopted almost entirely from Blackketter et al. where Xm is the tensile strength of the matrix material and dE,dfG are the discount factors. The failure criteria and the degradation scheme for the yarn material are given in The failure in the axial direction of the yarn leads to fiber breakage. This kind of failure is considered as an ultimate failure of the composite material.Note that the stress component in the longitudinal direction of the yarn is multiplied by stress concentration factors, ct and cc for tension and compression respectively (see ). The stress distribution in the yarn constituent is investigated in The stress concentration factor affects the ultimate failure point in the stress–strain diagram for tension or compression in 0/90° loading. If there is no failure of transverse yarns in 0/90° loading the ultimate failure point is at about the ultimate longitudinal strain of the yarn material for stress concentration factor equals unity. Test results of woven fabric composite materials in the mentioned loading condition show that the ultimate strain in the direction of loading is quite lower than the ultimate longitudinal strain of the yarn material. This is because the failure of the undulated yarns happens earlier than that of the straight yarns in longitudinal tension. The stress concentration in the undulated yarns and the combination of tension with bending of the undulated yarns, which are like a curve beam in an elastic foundation (the matrix material), lead to the lower ultimate strain.The behavior of woven fabric composite materials under shear for 0/90° loading (or +45/−45° tension/compression) is governed by the matrix material non-linearity. The ultimate failure occurs as a result of high strain and the lost of integrity of the composite material. In order to predict that failure mode, an integrity failure criterion is introduced in the failure model. The total strain of the RVC is accumulated at each time step and it is kept as a history variable. The maximum principle strain and the maximum shear strain of the RVC are calculated and examined at each time step. If one of them exceeds the ultimate strain for the integrity, Eu, an ultimate failure is assumed in the material model and the material is considered totally failed.The described micro-mechanical material model of woven fabric composite materials is programmed first in the MATLAB software. The adopted incremental approach for non-linear solution was similar to the one described in The elastic properties and the strength of the matrix material are:The total volume fraction of the fibers in the composite material is 60% and since the yarns fiber volume fraction is 70%, the volume fraction of the impregnated yarn material in the material model is considered 85.7%. The initial undulation angle of the yarns is 1° and the initial braid angle is 45°. The stress concentration factor is taken to be 1.6 for the yarns. The ultimate strain for the integrity failure is assumed to be 6%.The material model programmed in MATLAB calculates the stress response of the woven fabric composite due to steady strain loading with a constant strain increment in tension and in pure shear. The result is compared to the experimental data from The stress response to the pure shear loading is shown in The material model has slightly softer behavior in shear than the experimental result similar to all other material models presented. The stress response of the material model in tension almost coincides with the experimental result.The developed micro-mechanical material model of woven fabric composite materials is also programmed as a user defined subroutine in the LS-DYNA commercial finite element code with explicit time integration. The material model can be used for shell as well as for solid elements. Trying to justify the model in various and more complicated loadings, we found experimental data for 5-harness satin IM7/8551 7A Graphite/Epoxy in tension, compression and bending The test specimen of the composite material is modeled by means of shell elements. The elastic properties of the yarns and their strength are as follows:The elastic properties and the strength of the resin epoxy are:The stress–strain curve obtained in the finite element simulation for 0/90° tension is compared to the experimental curve and they are shown in The tensile stress versus transverse strain is given on the left side of the figure and the tensile stress versus longitudinal strain is on the right side. The stress–strain curve of the simulation in +45/−45° tension is very close to the experimental curve as depicted in ( The stress concentration factor for compression is considered to be 2.98. The stress–strain curves for 0/90° compression loading are given in The results for +45/−45° compression are shown in Using the adjusted in tension and compression parameters for the material model, four point bending of a specimen in 0/90 and in +45/−45° orientations are simulated and compared to the experimental data. The results are given in respectively. The results of the simulations are in very good agreement with the experimental results.A micro-mechanical material model of woven fabric composite materials with failure is developed. The model is computationally efficient and its implementation in the LS-DYNA non-linear finite element code shows the potential of the model to be used in large-scale simulations of composite structures. The material model is augmented by geometrical non-linearity of fiber reorientation and by shear material non-linearity. These non-linearities with the adopted failure criteria and stiffness degradation scheme make the model suitable for finite element simulations of composites in various and complex loadings. The material model stress prediction and failure are in very good agreement with the experimental data of woven fabric composite materials under different loadings.Effects of irradiation of 290 MeV U-ions in GaN epi-layersIn the present work, the resistivity, mobility and the carrier density at either room temperature or 77 K in 3-μm-thick n-GaN epi-layers irradiated with 290 MeV 238U32+ |
ions were tested with Hall measurements. It is found that the carrier mobility at 77 K is lower than that at room temperature in the specimens irradiated to fluences of the 1 × 109 and 1 × 1010 |
ions/cm2, showing a behavior different from the pristine specimen. The carrier density increases with ion fluence, and is above the dopant concentration when the ion fluence reaches 5 × 1010 |
ions/cm2. Moreover, the ionized impurity scattering plays a dominant role in the Hall effect after irradiation. A decrease of the ionized impurities due to the recombination of Ga vacancies (VGa-3) and the Ga interstitials (Ga(I)) was observed. The irradiation to the fluence of 5 × 1010 |
ions/cm2 produced N vacancies, which act as a kind of donor making the carrier density increase. The Raman spectra show that the E2 (high) mode shifts to a higher frequency meanwhile the FWTH increases after the irradiation, indicating there is an increase of strain in the irradiated GaN epi-layers. A consistency between the Raman spectra and the HRXRD spectra was found.Because of the attractive merits such as high thermal conductivity, high break down voltage, high carrier saturation mobility and wide direct band gap of gallium nitride (GaN), GaN-based electronic device are expected to work in harsh environments of high temperature and irradiation. The irradiation with energetic particles can produce N vacancy . Previous study of Kumar et al. shows that the irradiation with heavy ions can produce VN−N(I) Frenkel pairs and result in loss of nitrogen In the present work, the resistivity, the density and the mobility of carriers as well as strain were investigated in GaN epi-layers irradiated with heavier ions (290 MeV U-ions, which has a higher electronic energy loss (about 41.9 keV/nm) in materials than Si ions with 70 MeV used in the previous work The n-type GaN epi-layer film about 3 μm in thickness grown on c-plane of a sapphire substrate by the metal–organic chemical vapor deposition (MOCVD) method was supplied by CREE company. The dopant concentration is 2 × 1018 |
cm−3. Before the ohmic contact fabrication, the specimens was cleaned by acetone ultrasonic cleaning firstly, ethanol ultrasonic cleaning secondly, rinsing in deionized water thirdly, diluent HCl ultrasonic cleaning to remove the oxidation layer fourthly and rinsing in deionized water finally. After the cleaning procedures, the Ti/Al/Ni/Au ohmic contact was fabricated on the GaN and annealed at 650 °C for 55 s at N2 atmosphere. The irradiation of the specimens with 290 MeV 238U32+ |
ions (1.22 MeV/u) was performed in a terminal chamber of the Sector Focused Cyclotron (SFC) in the National Laboratory of Heavy-ion Accelerators in Lanzhou. Fluences of ions were in the range from 1 × 109 to 5 × 1011 |
cm−2. The vacuum in the chamber was around 5 × 10−5 |
Pa, while the temperature of the specimens was at ambient temperature (about 300 K) during ion irradiation.The Van der Pauw configuration was used in Hall measurements to test the carrier mobility and the carrier density of the specimens at liquid N2 (about 77 K) and at room temperature (about 300 K), respectively. Raman scattering measurements were also carried out. The Raman spectra were taken at room temperature on a HR-800 spectrometer using the 622.8 nm line of He–Ne laser as the excitation source with a power of 10 mW. The laser beam was focused on the specimen with a spot diameter of 2 μm. The spectral resolution was about 0.65 cm−1. The experiment was conducted in a backscattering configuration with the z direction oriented along the film c-axis. In addition, a D8 Discover high resolution XRD was used to perform exact θ−2θ scans at (0 0 0 2) peak. The electronic and nuclear stopping powers and the projected ion ranges in GaN were calculated with SRIM 2003 code.According to the SRIM 2003 code, the electronic energy loss (Se) is 41.92 keV/nm and the nuclear energy loss (Sn) is 0.3527 keV/nm in the case of 290 MeV 238U32+ |
ions passing through GaN. The project range of the 290 MeV 238U32+ |
ions is 13.6 μm in GaN, indicating that no U ions rest in the GaN epi-layer. The ion fluence, the displacement per atom (dpa) via nuclear collision and the electronic energy loss in unit volume in GaN are given in . Values of the resistivity of the irradiated specimens tested at 77 K and 300 K, respectively, are shown in (a). The value of the resistivity measured at 77 K is higher than that at 300 K. And the resistivity increases sharply around the fluence of 5 × 1010 |
ions cm−2. (b) shows the Hall mobility of the irradiated specimens tested at 77 K and 300 K, respectively. The value of the mobility tested at 77 K is higher than that at 300 K in the pristine specimen. However, the value of the mobility tested at 77 K is lower than that at 300 K in the ion-irradiated specimens.There are three major scattering mechanisms in GaN epi-layer (c) shows that the carrier density of the irradiated specimen tested at 77 K is lower than that tested at 300 K. The negative sign means that the majority-carrier of the GaN epi-layer is electron. From (c), we can see the electron density increases sharply at the ion fluence of 5 × 1010 |
cm−2 at 300 K. The carrier density is 1.5 × 1018 |
cm−3 in the pristine specimen, lower than the impurity density 2 × 1018 |
cm−3 in the pristine GaN epi-layer, possibly because of the compensation effect from the VGa3- which is a triple acceptor. In the specimen irradiated to ion fluence of 5 × 1010 |
ion cm−2, the carrier density increases to 3.75 × 1018 |
cm−3, higher than the impurity density 2 × 1018 |
cm−3 in the pristine specimen. It is indicated that the recombination of the Ga(I) and the VGa3- (which reduces the compensation effect) occurred, while the ion irradiation produced more VN (which is a donor and according to our recent DLTS result which will be presented in a later papers) and SiGa (which is another kind of donor in the GaN), when the ion fluence reaches 5 × 1010 |
ions cm−2.We notice that a similar behavior i.e. the decrease of the scattering centers after irradiation was reported in the work of Look’s in a HVPE GaN irradiated with 1 MeV electrons . Meanwhile more deposited energy produces more defects such as VN, SiGa and SiN (also confirmed by our recent DLTS measurement). shows the E2 (high) mode of the Raman spectra irradiated with 290 MeV U ions to different fluences. For the fluence of 5 × 1010 |
cm−2, the E2 (high) shifts to higher frequency due to the increase of the compressive stress, meanwhile the FWTH increases after the irradiation , where the (0 0 0 2) peak (which intensity has been normalized) shifts toward lower angles. According to 2dsinθ=nλ, such a shift is related to the expansion of the crystal lattice and the increase of the compressive stress along the c-plane , where B is the Bulk modulus, ν is the Poisson ratio. The linear relation between biaxial stress σa and the Raman shifts Δω is proposed as that meet εc=1.735±0.389×10-4cmΔω which is different from εc=3.8±0.4×10-4cmΔω showed in Ref. , where the sign ‘−’ means the compressive stress. The stress and the strain from the XRD and the Raman spectra are shown in , which gives an estimate of the lattice expansion after the irradiation. The compressive stress increases along the c-plane, because of the formation of Frenkel pairs of VN and N(I) which have a low formation energy of 10.8 eV In GaN epi-layers irradiated with 290 MeV 238U32+ |
ions, the resistivity and the carrier density increase because of the production of VN which act as donor emerged during irradiation. The Hall effect measurements show that the carrier mobility increases with the increase of temperature in the irradiated specimens, while the carrier mobility decreases with the increase of temperature in the pristine specimen. The ionized impurity scattering plays a dominant role in the irradiated GaN because of the irradiation-induced recombination of the Ga(I) and the VGa3-. Raman spectra show that the E2 (high) mode shifts to a higher frequency meanwhile the FWTH of the E2 peak increases after the irradiation, suggesting an increase of compressive strain in the irradiated GaN epi-layers. The compressive strain is related to the expansion of the crystal lattice.Mussel-inspired modification of carbon fiber via polyethyleneimine/polydopamine co-deposition for the improved interfacial adhesionA polyethyleneimine/polydopamine (PEI/PDA) hybrid layer was spontaneously co-deposited onto carbon fiber (CF) surface by oxidative co-polymerization through a facile one-step dip-coating approach. The microstructure and chemical characteristics of CF surface before and after modification were investigated and the results manifested that PEI/PDA functionalization could afford abundant amine groups and obviously increase the CF surface energy by 70.5%, which were advantageous to promote the fiber-matrix interfacial interaction and wettability. An enhanced macro-performance was realized by incorporating the functionalized CF (PEI-PDA-CF) into polyurethane (PU) matrix. The prepared PU/PEI-PDA-CF composite exhibited excellent tensile and dynamic mechanical properties. The satisfactory bulk performance was mainly attributed to the superior interfacial adhesion achieved by the hydrogen bonding and π-π* stacking interactions between PEI/PDA coating on CF and PU matrix, which was confirmed by the fracture morphology observations and a 45.7% rise in apparent activation energy value.Carbon fiber (CF), as an ideal reinforcement for both thermoset and thermoplastic composite materials, has been widely used in aerospace, sports and automobile industries, due to its high specific strength, specific modulus, lower density and outstanding thermo-physical properties Various surface modification techniques, including microwave radiation Recently, the mussel-inspired surface chemistry has been particularly preferred for its simplicity, versatility and wide applicability. Dopamine (DA) or its derivatives can self-polymerize under extremely mild conditions and generate adhesive polydopamine (PDA) onto almost all types of substrates In the past, many amine-containing molecules, like hexamethylene diamine, hexamethylenetetramine and poly (amido amine) dendrimer, have been used to introduce active groups onto CF. Among, Polyethyleneimine (PEI) with rich amino groups and flexible chains is an excellent candidate to functionalize CF. Some researchers have grafted PEI onto CF through supercritical fluids or conventional grafting methods, which required sophisticated equipment, multistep operations and sacrificed mechanical properties of fibers As is well known, PDA can undergo versatile reactions with molecules containing thiol or amine groups via Michael addition and/or Schiff base reactions PU pellets (AVALON 85 AE, Huntsman, USA) and CF (T700SC 12 K, Toray, Japan) were used as the polymer matrix and the reinforcing material. Dopamine hydrochloride was supplied by Sigma Aldrich. Branched polyethyleneimine (PEI, Mw = 600) and Tris (hydroxylmethyl) aminomethane (Tris) were purchased from Aladdin.Prior to use, the commercial CF bundles were ultrasonic dispersed into monofilament fibers in acetone for 20 min and dried at 50 °C. The buffer solution was prepared with 10 mM Tris and its pH was adjusted to 8.5 with 1 M hydrochloric acid. The dried fibers were then immersed into a buffer solution of PEI (4 mg/mL) and DA (2 mg/mL) with a mass ratio of 2:1 at room temperature for 24 h. The other group of CFs were dipped in a buffer solution containing only 2 mg/mL DA under the same condition for comparison. After modification, the samples were taken out, rinsed thoroughly with deionized water and dried in a vacuum oven at 50 °C overnight. The obtained fibers were referred to as PEI-PDA-CF and PDA-CF for short.Before composite preparation, CF, PDA-CF and PEI-PDA-CF were chopped into an average length of 10 mm, and then dried in an oven at 70 °C for 12 h together with PU pellets. The melt blending of fibers (10 wt%) with PU were carried out for 10 min by an internal mixer (Thermo Haake PolyDrive, USA). The rotor speed and temperature were set at 50 rpm and 190 °C. The compounds were then compression moulded into sheets of size 10 cm × 10 cm × 1 mm using a Platen Press Machine (LP-S-50, Labtech, Germany) at 200 °C under a 15 MPa pressure. The sheets were cut into dumbbell-shaped or rectangular specimens for mechanical properties testing. The resulting composites were denoted as PU/CF, PU/PDA-CF and PU/PEI-PDA-CF.The polymerization process was tracked by UV-vis spectra on UV-1800 spectrophotometer (Shimadzu, Japan). The light source wavelength was 340 nm and scan range was 200 nm–600 nm. The morphologies of fiber surface as well as fracture regions of PU composites were studied through a Scanning Electron Microscopy SEM (Nova NanoSEM 450, FEI, USA). The fracture surfaces were sputter-coated with gold (Q150TS, Quorum, UK) before observation to avoid charging. The fiber surface morphologies and roughness were also examined by Atomic Force Microscope AFM (Nanoscope Шa Multimode, Digital Instruments, USA) height images using tapping mode. The chemical composition and functional groups on CF surface were characterized by X-ray Photoelectron Spectroscopy XPS (AXIS Ultra DLD, Shimadzu, Japan) equipped with a monochromatic source of Al Kα (1486.6 eV). The binding energy peaks were calibrated with C1s at 284.8 eV as reference. The C1s and N1s spectra were fitted with CasaXPS software by Gaussian-Lorentzian function (peak shape ratio of 30). The peak positions and FWHM (full widths at half maximum) were kept relatively constant . Tensile tests of PU composites were conducted by a Universal Testing Machine (Criterion 43, MTS, USA) at a crosshead speed of 20.0 mm/min and a gauge length of 50 mm in accordance with ASTM . The dynamic mechanical performance were obtained using a Dynamic Mechanical Analyser (DMA 242C, NETZSCH, Germany). Rectangular samples of 20 mm × 5 mm × 1 mm size were tested in tension mode, heating rate of 3 °C/min, maximum amplitude of 120 μm and maximum dynamic force of 2 N at different frequencies of 1 Hz, 10 Hz, 50 Hz and 100 Hz, within a temperature range of −100 °C–100 °C.In this study, pristine CFs were simply immersed into a weak alkaline PEI/DA solution or pure DA solution and mildly stirred at room temperature. Through Schiff base reaction and/or Michael addition between PEI and DA, as well as the oxidative self-polymerization of DA, CF surface could be facilely covered by PEI/PDA co-deposition coating or pure PDA coating, as schematically illustrated in The aforementioned processes were monitored using UV-vis spectroscopy. As shown in a, b, the sharp absorption peaks at 280 nm (catechol group) and shoulder peaks at 300 nm (dehydro-dopamine) were observed to enhance gradually over time, which suggested the existence of various intermediates during the self-polymerization of DA and its co-polymerization with PEI. The weak absorption peaks at around 400 nm of DA solution (o-quinone) were replaced by the new strong peaks at 365 nm of PEI/DA solution (C=C-C=N and C=C-C=O), which verified the cross-linking reaction between DA and PEI molecules c, d. In addition, black precipitates were noticed in DA solution, while PEI/DA solution kept homogeneous.The surface microstructures of pristine CF, PDA-CF and PEI-PDA-CF were observed using SEM and AFM. The pristine CF surface was perfectly smooth and neat (). After PDA deposition, the fiber surface was uniformly covered by a thin layer (b1) and the coating layer became thicker with the addition of PEI molecules (c1). The three-dimensional and two-dimensional AFM images gave more precise information about the layers at a smaller scale. Nano-sized PDA aggregates were deposited onto the pristine CF and led to a particle-like morphology, which altered the surface average roughness (Ra) from 35 nm to 47 nm. While, PEI-PDA-CF presented a relatively smoother surface with a lower roughness (Ra = 32 nm). The low-molecular-weight PEI with rather flexible chains was taken as a cross-linking component to promote the uniform co-deposition of PEI/PDA without PDA self-aggregation, which was in good agreement with the above-described phenomenon (c, d). Theoretically, the increase in surface roughness would produce larger surface area and thus enhance the mechanical interlocking between the fiber and matrix. However, the slight variation in the surface roughness might be too negligible to influence the interfacial interaction.XPS was utilized to investigate the chemical compositions of CF surfaces. shows the XPS wide scan, C1s and N1s spectra of CF, PDA-CF and PEI-PDA-CF. The surface element compositions and functional components obtained from the deconvolution of C1s and N1s peaks are listed in , and the used peak-fitting parameters are shown in From the XPS survey spectra, the N1s atom percentage ranged from 0.8% of pristine CF to 2.1% of PDA-CF, attributed to the nitrogen element of the PDA layer. The N1s content in the case of PEI-PDA-CF dramatically reached up to 4.1%, which revealed the successful incorporation of nitrogen-rich PEI. Moreover, the C1s spectra were peak-fitted to four or five components, assigned to C-C (284.7 eV), C-N (285.4 eV), C-O (286.2 eV), O=C-O (289.0 eV) or π-π* (290.9 eV), respectively. The C-N percentage of PDA-CF was largely increased from 1.4% to 6.7%, compared with pristine CF. Besides, PDA-CF showed a new binding energy peak at 290.9 eV, which corresponded to the π–π* shake-up peak, due to the conjugated aromatic structure of PDA polymer. The C-N concentration on PEI-PDA-CF surface was sharply as high as 18.9%, mainly offered by the co-deposited PEI molecules. While, the π-π* peak disappeared in the case of PEI-PDA-CF, which may be explained that the conjugation effect was weakened by the flexible PEI chains. In the N1s spectra, the appearance of two additional binding energy peaks at 399.8 eV and 402.0 eV were ascribed to the -C-NH- and -C-NH2 functional groups generated onto CF surface Raman spectroscopy was adopted to further analyze the ordered/disordered structure of the near-surface region of carbonaceous materials. As shown in , the first-order Raman spectra exhibited two broad and seriously overlapped peaks, which were curve-fitted into four main characteristic bands . The D peak at 1350-1360 cm−1 is correlated with structural defects or disorders. The shoulder peak at 1180-1200 cm−1 known as D″ band arises from the C-C and C=C stretching vibrations of olefin-like skeleton. The A band at around 1500 cm−1 is usually observed in some lower-ordered carbon-based materials and related to the amorphous carbonaceous structures, hetero atoms or functional groups. The G band at 1590-1600 cm−1 is intrinsic of ordered graphitic structure, corresponding to a well-defined sp2-bonded carbon type. Generally, the integral area ratios of D band to G band (ID/IG), A band to G band (IA/IG) and D″ band to G band (ID”/IG) are conveniently used to assess the degree of graphitization, the relative amount of amorphous carbon atoms or functional groups and the proportion of olefin structure, respectively, which are summarized in The locations of D and G bands were found nearly unchanged, implying that impregnation process did not affect the entity structure of pristine CF. The slight increase of ID/IG values may be caused by the sonication treatment to eliminate residual DA monomer before measurement. The IA/IG ratio increased from 0.23 of pristine CF to 0.38 of PDA-CF, and reached up to 0.65 of PEI-PDA-CF. Therefore, the highest IA/IG value manifested the deposition of amorphous carbonaceous structures as well as some oxygen- and nitrogen-containing functional groups onto the PEI-PDA-CF surface. The D″ band only occurred in PEI-PDA-CF spectrum further ascertained the presence of PEI with olefin chain structures.In addition to the interfacial bonding, the interfacial wettability between the fibers and the resin matrix also has a vital impact on the interfacial interaction of fiber reinforced composites. It is well known that a higher surface energy is beneficial to the subsequent wettability during melt-blending especially for polar matrix and could greatly enhance the interfacial properties. The surface energies γS of CFs were calculated via the dynamic contact angles between testing liquids and single fibers by Wilhelmy plate method, which is composed of two components, the dispersive component γSd dominated by the topography of fibers and the polar component γSp relevant to the active chemical groups on the fibers Firstly, downward trends of contact angles from pristine CF to treated CF were observed for both polar water and non-polar diiodomethane in a. Nextly, the calculated surface free energy γS showed an obvious rise from 23.4 mJ/m2 to 29.8 mJ/m2 after PDA modification. In the case of PEI-PDA-CF, the γS was as high as 39.9 mJ/m2, a 70.5% increment against pure CF. The polar component γSp was increased by the same order, from 13.0 mJ/m2 to 19.9 mJ/m2 and then up to 28.9 mJ/m2 of PEI-PDA-CF, more than twice of neat CF. The larger increment of polar component could be interpreted with the introduction of amino-rich PEI. Whereas, the dispersive component γSd showed little change before and after functionalization. This result was reasonable since the surface roughness was only slightly altered after treatment, due to the uniform distribution of polymer layer on the fiber surface, as previously mentioned in . Namely, the enhanced surface energy was mainly contributed by a sharp increase of the polar component, which was from the massive functional groups supplied by PEI/PDA hybrid coating. The increased surface energy and high content of polar component of the fiber reinforcement indicated a great potential for excellent wettability by viscous resin and an improvement of the fiber-matrix interaction was expected to achieve.As discussed above, the coated PEI-PDA layer introduced substantial amine functional groups onto CF surface and supplied more reactive sites for interfacial adhesion. Furthermore, the hybrid coating increased the surface energy and the polarity of PEI-PDA-CF and made the surface easier to be wetted by polar resin. The desirable modification results are favorable to enhance the fiber-matrix interfacial interaction and thus promote the macro-performance of CF reinforced composites. Subsequently, the effectiveness of PEI-PDA functionalization was investigated by testing the ultimate mechanical properties of as-prepared materials through melt blending and hot-press molding.Representative tensile stress-strain plots of different PU composites (reinforced by 10 wt% fibers) are given in a. The Young's modulus, depicted as the slope of the linear portion of the curve and the tensile strength, i.e., the maximum stress, were remarkably increased with the incorporation of modified CF. On the other hand, the area under the stress-strain curve is usually identified as the toughness of materials. The average properties are shown in b and c. Compared with PU/CF, the tensile strength of PU/PDA-CF composite was increased from 19.6 MPa to 21.7 MPa by only 10.7%, and the tensile modulus was increased from 149.9 MPa to 201.2 MPa by 34.2%. Disappointingly, the improvement of pure PDA coating on the mechanical properties was limited. The reason could be that it was hard to form strong interaction between fibers and resin for the lack of sufficient functional groups, taken together with that the coating tended to be stiff and short of ductility because of the massive aromatic structures of PDA. As expected, PU/PEI-PDA-CF presented the most outstanding mechanical performance. The PEI-PDA hybrid layer gave rise to a 38.8% enhancement in tensile strength (from 19.6 MPa to 27.2 MPa) and a 59.3% increment in tensile modulus (from 149.9 MPa to 238.8 MPa), in reference to PU/CF. The improvement on mechanical performance afforded by this novel PEI and PDA treatment was more significant than that through traditional methods in Y.A. El-Shekeil's report Dynamic mechanical properties based on the characteristic viscoelasticity of polymers were also analysed in our work, which was one of the effective ways to evaluate the interface of fiber reinforced composites The dynamic mechanical analysis (DMA) curves of PU composites are presented in . The storage modulus E' is approximately similar to the elastic modulus or the rigidity of materials. It was observed that the incorporation of 10 wt% PDA-CF into PU remarkably increased the E' of PU/CF composites and the E' of PU/PEI-PDA-CF was further remarkably improved in a. This result was in consistency with the above static tensile testing and indicated the stiffening effect of the CFs on the matrix. Moreover, the better of the interfacial adhesion, the more enhancement was achieved, as well as the higher E' values. As seen in b, the loss modulus E” indicating the material's viscosity also increased with the addition of PDA-CF within the temperature range. Similarly, PU/PEI-PDA-CF showed the highest E”. The stronger interaction between fibers and matrix restricted the PU molecular movement, thus leading to a higher viscosity. c presents the temperature dependence of tan δ. The damping in the glass transition region represented the energy dissipated for the deformation or irreversible intermolecular movement inside the materials. It was noteworthy that the tan δmax for PU/PEI-PDA-CF declined to a lower value (0.236), compared to that of PU/CF (0.300). This indicated that the molecular mobility in the PU/PEI-PDA-CF system was the most difficult and thus the least energy would be consumed to overcome the inter-friction between molecular chains. This may attribute to the strongest interfacial bonding between PEI-PDA-CF and PU matrix. As a consequence, DMA data was in good agreement with the aforementioned mechanical properties and once again proved the improvement effect of the PEI-PDA coating for the PU composites.We believed that a fascinating interphase was formed between the PEI-PDA-CF reinforcement and PU matrix so as to gain the superb static and dynamic mechanical behaviors, which was also confirmed by the following SEM observation. The fracture surface morphologies of PU composites are shown in a), many holes were remained on the fracture surface due to the pull-out of fibers from the matrix under external loading. CF surface was rough and partly adhered by PU resin. Additionally, the gaps at the fiber/matrix boundary were clearly visible (marked with red circle), indicating that the fibers were debonded with PU matrix. Owing to the poor interfacial adhesion between pristine CFs and PU, the failure and de-bonding firstly occurred in the weak interfacial region. When PU matrix was reinforced by PDA-CF (b), the number of holes and de-bonded fibers decreased. The gaps between fiber and matrix disappeared and the pulled-out CF presented a comparatively rougher surface with more remaining PU fragments. These indicated that the interfacial bonding behavior was improved to some extent. While, the fracture region of PU/PEI-PDA-CF (c) showed a sharply bright contrast, implying the property at the interface has been remarkably changed. On one hand, it was clear that most fibers were deeply embedded in the PU matrix and hardly pulled out, thus, the holes almost disappeared. On the other hand, fibers outside were uniformly wrapped with PU resin layer and the fiber/matrix boundary was hard to distinguish, which was an evidence of strong bonding. In addition, most of fibers were well dispersed as individual ones in the matrix, which further proved the improved compatibility between PEI-PDA-CFs and PU resin. Such an enhanced interfacial adhesion would definitely lead to a superior mechanical performance described above.The strong interfacial interaction in the interface phase achieved by the binary PEI/PDA coating available on the CF surface was schemed in . The ductile PEI component endowed the layer certain polarity and the pendant primary or secondary amine groups could form hydrogen bonding with the ester groups of PU backbone structure. The rigid PDA component served to adhere onto the CF surface tightly for PEI was soluble in water and its aromatic structures could develop π-π* stacking interaction with the hard segment of PU matrix. The above non-covalent forces became much stronger when they cooperatively combined together to strengthen the interface between fibers and matrix. In addition, the increased interfacial compatibility rendered by the intermolecular chain entanglement between PEI flexible chain and soft segment of PU also contributed to the enhanced interfacial adhesion. Hence, an appropriate interphase was generated to bind the fiber and matrix together, which could transfer stress from resin to fibers steadily and efficiently, leading to the macro-performance improvement.In summary, the enhancement on mechanical behaviors was perceived to be brought by the improved interfacial properties, which was largely achieved via the formation of hydrogen bonding and π-π* stacking interactions between PEI/PDA layer on CF and the PU matrix. The interfacial interactions was quantitatively characterized by dynamic mechanical tests carried out at different frequencies (1 Hz, 10 Hz, 50 Hz, 100 Hz) in . The apparent activation energy ΔE determines the amount of energy required to develop molecular mobility in polymer chains including segmental motion and indirectly reflects the molecular interaction. Strong intermolecular force reduces the molecular mobility and more energy is needed to realize the movement d. ΔE could be calculated from the slope of the regression line. The Tg at varying frequency tests and the ΔE values were given in . Tg value gradually increased with the increase of test frequency. Anyway, PU/PEI-PDA-CF displayed the highest Tg under the same frequency. For example, the Tg of the three composites at 1 Hz were −19.4 °C, −16.2 °C and −9.4 °C, respectively. The higher Tg signified that the free motion among the molecules was to completed at a higher temperature.It was apparent that the trend of the ΔE values agreed with the conclusions of the above mechanical tests. The restriction of movement is usually linked to a higher activation energy. The ΔE of the PU/CF composites was calculated to be 199 kJ/mol, which implied that the relaxation required less energy because of the weak restricting effect caused by the poor fiber-matrix interfacial bonding. As expected, the highest ΔE (290 kJ/mol) belonged to PU/PEI-PDA-CF, which further testified the strong interaction existed between PEI/PDA layer and matrix.In this work, a uniform bio-inspired PEI/PDA layer was successfully coated onto CF surface through a facile one-step impregnation method. The attachment of PEI-PDA was clearly verified to bring about more active functional groups onto CF surface and also increased the wettability and CF surface free energy. As a consequence, PU/PEI-PDA-CF composite simultaneously achieved great advancement in macroscopic tensile strength and toughness. The ultimate tensile strength, modulus and toughness were increased by 38.8%, 59.3% and 28.2% respectively. Meanwhile, dynamic mechanical properties of PU/PEI-PDA-CF also showed notable improvement compared with neat PU/CF. SEM observations of fracture morphology and the dramatically increased apparent activation energy ΔE (from 199 kJ/mol to 290 kJ/mol) revealed the impressive interfacial adhesion between fibers and matrix. The greatly strengthened interfacial properties were largely due to the existence of PEI/PDA intermediate layer between the fiber and resin, which could bridge with PU in matrix through hydrogen bonding and π-π* stacking interaction, thus contributing to the significantly increased bulk performance. We believe that using the co-polymerization of DA and PEI to modify CF surface was a promising and effective way to improve the interfacial strength of CF reinforced various composites and adaptable to all high-performance fibers.The following is the supplementary data related to this article:Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.compscitech.2017.08.008Aggregates characterizations of the ultra-fine coal particles induced by nanobubblesParticle aggregates induced by nanobubble (NB) bridging has been recognized as one of the main contributors to improve the flotation performance of minerals in NBs-associated flotation. Despite the numerous investigations in particle-NB interaction, scarce research on revealing the properties of aggregates induced by NBs has been conducted, severally limiting the further understanding of the NB-assisted mineral flotation. In this study, NBs were first produced based on the principle of hydrodynamic cavitation. The aggregates of ultra-fine coal particles with different hydrophobicity induced by these tiny bubbles was investigated, with the size distribution, structure, and strength features of the aggregates systematically explained accordingly. In this study, NBs remained stable in the aqueous solution for more than one hour, and the size of these bubbles expanded from 240 to 650 nm within this period. The aggregates of coal particles was significantly enhanced, especially for the more hydrophobic ones, which could be well reflected by the right-shifted particle-size distribution curve, the newly formed chain-structure aggregates, and larger apparent viscosity and shear yield stress of the coal pulp. Moreover, the flotation performance (both flotation recovery and flotation kinetics) of ultra-fine coal particles was remarkedly improved in the presence of NBs, confirming that NBs did benefit the ultra-fine coal aggregates.Froth flotation is an efficient and cost-effective method for separating coal and other valuable minerals from gangue minerals Referring to tiny bubbles of less than 1 μm in size Although NB-induced particle aggregates are crucial to the final flotation performance, previous studies have focused on the relationship between particle aggregates behavior and final flotation performance. In contrast, less research has been conducted to reveal the aggregate behaviors of fine and ultra-fine particles with different hydrophobicity triggered by NBs. Some pioneering works on fine and ultra-fine particle aggregates induced by NBs have been done recently In this study, NB solutions were prepared and characterized using the fast and reliable dynamic light scattering (DLS) technique to uncover the characteristics of particle aggregates induced by NBs. The aggregate behaviors of ultra-fine coal particles induced by NBs were then multidimensionally explored using particle-size distribution measurement, microscope imaging, and rheology tests. Additionally, the effect of NBs in the flotation of ultra-fine coal with different hydrophobicity was discussed. We hope our findings can provide some support for a better understanding of the role of NBs in enhancing ultra-fine coal particle aggregat.This study’s raw coal samples were acquired from a mine located in Taixi, Ningxia Province, China. The preparation procedure, particle size distribution analysis, and proximate and ultimate analyses of the tested coal samples were described and presented in our previous study Two kinds of water samples, deionized water (DI water) and NB water, were prepared. The DI water was made using a deionizer (FDY2002-UV, Fullerene Technology Ltd., China) with a resistivity of 18.2 MΩ•cm, whereas the NB water was prepared by processing DI water through an NBs generator (YY7122, Sanwei Micro Motor Ltd, China) on the principle of HC. As water passed through the NBs generator, a milky liquid flow out (). After 2 min of standing, some micron-sized bubbles disappeared, forming the NB solution. Afterward, the prepared NB solution was immediately transferred to a) a DLS detector (BI-200SM, Brookhaven instrument Ltd., USA) to measure the tiny bubbles’ size distribution, b) a ZetaPlus instrument (BI-200SM, Brookhaven instrument Ltd., USA) for the zeta potential measurement of NBs, or c) a flotation machine for flotation tests.In this study, the zeta potential of NBs was measured in triplicate using a ZetaPlus instrument (BI-200SM, Brookhaven instrument Ltd., USA). In all experiments, 0.01 M KCl was used as the background electrolyte, and NaOH and HCl were used to adjust the pH value to a specific value between 2 and 12. The zeta potential of NBs under different pH values was measured. Once the NB solutions were prepared, they were immediately taken to perform the zeta potential measurements at room temperature (25 °C).The size distribution of coal particles in DI/NBs water was determined using a laser particle-size analyzer (LS13320, Beckman Coulter, USA) to characterize the size of the aggregates formed in the presence of NBs. First, the coal samples were added to the DI/NBs water to prepare 10 wt% of coal slurry, subsequently stirring using a magnetic agitator at 1000 rpm for 2 min. No ultrasonic treatment was applied to avoid destroying the structure of the aggregates. Then, appropriate samples were taken into the sample tank until the shading degree reached 40% to start the detection. All the operations were conducted carefully at room temperature (25 °C).Microscope observation tests were performed under various conditions to unveil the structure characteristics of the coal aggregates induced by NBs. First, 0.3 g coal samples were added into 100 mL of DI/NB water to prepare six mineral suspensions. After mixing for 2 min under 700 rpm, a drop of the mixed mineral suspensions was sampled for observation using an optical microscope (BX53M, Olympus Corporation Ltd., Japan). Afterward, the morphological information for the coal aggregates in the representative images was obtained using Image-Pro Plus software.In flotation, the pulp rheology measurement is a valid indicator of the state of coal particle interactions. The pulp’s apparent viscosity and yield stress help characterize particle aggregates and dispersion behavior Two kinds of flotation tests with different coal samples, conventional flotation (with DI water) and flotation assisted by NBs, were recorded in an XFG-II 100 mL laboratory flotation machine. The detailed process is as follows. First, each coal-water (10 wt%) slurry was agitated at a rate of 2100 rpm for 3 min in DI/NB water, and the air flow rate is 0.17 m3/h. Then, five concentrates were collected after a cumulative time of 0.5, 1, 2, 3, and 5 min, after which the samples were filtered and dried. Based on the recovery of each period, the cumulative recovery was subsequently calculated.The milky gas–liquid solution generated after NB generator processing contains numerous micro and nanoscale bubbles The size distribution of these tiny/ultra-fine bubbles produced by HC is primarily in the range of tens to thousands of nanometers (b depicts the effect of the standing time on the NB size distribution. The Ed of the tested bubbles decreases during 10 min of standing due to the relatively poor stability of the large-scale bubbles in the early survival period. In contrast, the size distribution curve begins to shift to the right after standing for 10 min. However, nanoscale bubbles can still be detected within 1 h, ranging from 100 to 800 nm, which confirms that these ultra-fine bubbles have superstability, supporting previous research results associated with atomic force microscopy tests We further explored the zeta potentials of NBs (c), finding that NBs are negatively charged in alkaline, neutral, and weak acidic environments, meaning more OH− is absorbed on the surface of NBs than H+As it is analyzed above, the introduction of NBs into the coal slurry benefits the particle aggregates in general. The size distribution of coal particles in DI/NBs water was tested to explore the aggregate behavior of ultra-fine coal with varying hydrophobicity caused by NBs. illustrates that the size distribution shifts to the right as the coal’s hydrophobicity increases in the same solution, illustrating the hydrophobic coal aggregates more significantly. For particles in various water types, the D90 of HHC and MHC in NBs water is greater than that in DI water, probably due to NB capillary bridging Aggregate morphology changes are visually presented using representative microphotographs () and their statistical aggregates parameters () under DI/NBs water conditions to clarify the aggregates of ultra-fine coal particles more intuitively. The more hydrophobic coal is, the more easily coal aggregates. For example, greater and more compact coal aggregates were observed in HHC (For the same coal particle in different water solutions, NBs lead to relatively larger aggregates for HHC and MHC (i.e., a larger average area and diameter in ), whereas little effect is observed on LHC, reconfirming that NBs can enhance the aggregates of hydrophobic coal particles. More importantly, some chain-structure aggregates appear in the pulp in the presence of NBs (e.g., a and c), which is considered one of the most important characteristics of aggregates induced by NB bridging The strong hydrophobic interaction caused by the bridging of NBs makes more coal particles aggregate Furthermore, the rheological properties of three kinds of coal samples in DI/NB water were evaluated concerning apparent viscosity (b) to explore the properties of aggregates of coal particles induced by NBs. The rheological curves were fitted using the Herschel Buckley model where τ is the shear stress (Pa),τHB, the Hershel Buckley yield stress (Pa) is the intercept of the curve-fitting yield stress region, ηHB is the aggregate consistency index (Pa·s), γ is the shear stress (s−1), and p is the flow index. Based on the fitting data, the τHB of the slurry under different conditions can be calculated, which is closely related to the aggregate strength are more than 0.9900, indicating that the Herschel Buckley model applies to rheological fitting regardless of the NBs.In the same water solution, more hydrophobic coal particles constantly lead to larger values of apparent viscosity and shear yield stress to the more intensive aggregates of coal particles caused the hydrophobic attraction The above results fully demonstrate that the presence of NBs can promote the aggregates of ultra-fine coal particles, resulting in larger aggregate size, more chain-structure aggregates, and higher aggregate strength. Because aggregates properties are closely related to the flotation behavior of ultra-fine coal In final, flotation experiments on ultra-fine coal particles assisted by NBs were conducted () to visualize the effect of NBs on flotation behavior better, using the classical first-order model (one of the most commonly used fitting models in the mineral flotation field) where ε is the flotation recovery, ε∞ denotes the theoretical maximum flotation recovery, k represents the flotation rate constant, and t is the flotation time. All values of R2 are more than 0.99000, indicating that the flotation of ultra-fine coal particles can be fitted well using the classical first-order model regardless of NBs.For the same water sample, the cumulative recovery and flotation rate constant of hydrophobic coal is higher than that of the less hydrophobic sample after 5 min of flotation, which can be easily attributed to the natural difference in hydrophobicity of the tested coal particles. As for the same coal in various aqueous solutions, the cumulative recoveries and flotation rate constant of HHC and MHC in NB water are higher than those in DI water, whereas the corresponding LHC values are maintained at almost the same level using both DI and NBs water. In our previously study In this investigation, the NBs-induced aggregate behaviors of ultra-fine coal particles with different hydrophobicity was investigated. The following conclusions can be drawn based on the results. First, NBs, with an effective diameter of several hundred nanometers, have superstability. Once generated, the lifetime of NBs can be stable for hours. Second, the aggregates of ultra-fine coal particles were significantly improved in the presence of NBs, especially to hydrophobic ones, reflected multi-dimensionally by the right-shifted particle-size distribution curve, newly formed chain-structure aggregates, and larger apparent viscosity and shear yield stress values of the corresponding coal pulp. Third, the introduction of NBs into the pulp in the conditioning stage leads to greater flotation recovery and kinetics of hydrophobic ultra-fine coal particles, and NBs promoting the aggregates of hydrophobic ultra-fine coal sample is one of the contributions to the improvement of coal flotation.Liming Liu, Weiguang Zhou and Li Weng conceived of and designed the experiments; Liming Liu, Weiguang Zhou and Shunxuan Hu prepared the samples and performed the experiments; Liming Liu, Weiguang Zhou and Changning Wu analyzed the data; Ke Liu funded this study; Liming Liu and Weiguang Zhou contributed to the writing and revising of this manuscript.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.Hydro-mechanical behavior of undisturbed collapsible loessial soils under different stress state conditionsA conventional triaxial test device was modified to characterize the hydro-mechanical behavior of a loessial soil during isotropic and shear loadings. This device is capable of precise and continuous measurements of water outflow during the application of loading. The tests were performed on “undisturbed” cylindrical specimens, which were taken from loessial deposits in Gorgan, a city in the northeast of Iran. Experimental measurements indicate that the hydro-mechanical behavior of loess is highly affected by the extent of applied mean net stress and the level of suction. During both isotropic and shearing stages of loading, the tested specimens may exhibit collapse, abrupt decrease in volume or sudden positive volumetric strain, upon wetting or applied loading. However, the magnitude and extent of collapse are different depending on the applied state of the stress and the hydro-mechanical loading path. The results of the experiments reveal that the peak shear strength of the soil increases, as the applied mean net stress during isotropic loading or the applied matric suction increases. The shearing test results are also used to investigate the efficiency of suction stress in describing the state of stress for unsaturated loessial soils. The outcome indicated a unique critical state line for unsaturated specimens under different stress paths and loading conditions. Furthermore, considering the effective stress concept, a hardening constitutive law is presented in this study to demonstrate the hardening/softening behavior of the collapsible loessial soils.Fitting parameters of the hardening modelIncrement of plastic change in void ratioIncrement of change of effective saturationEffective saturation at the matric suction of zeroThe Caspian lowland of northern Iran is part of the Eurasian loess belt extending from northwest Europe to central Asia and China, with the most complete loess sequences located in the area between the Gorgan and Atrek rivers in Golestan province and on the northern foothills of the Alborz Mountains (). The loess sequences in these regions are mostly silt-rich sediments with particles loosely arranged in a soil void structure, an open, metastable soil fabric and weak inter-particle bonding forces (). These types of Aeolian deposits are known for their high potential of collapse behavior. Due to the rapid urban developments in this region, major projects are facing increasing problems related to the presence of unsaturated loessial deposits, leading to foundation settlements in residential buildings or water conveying canals, instability in the slopes supporting the structures, lifeline damage, and failure occurrence in the side walls of the dam reservoirs (e.g., Nomal dam). The need for construction and development in the area has reverted to using a large number of pile foundations in the design and construction of structures or increasing the rigidity and strength of the super structures; without a comprehensive attention to the deformation behavior of the highly collapsible loessial soil which is the real cause of in admissible settlements. It is believed that a thorough and comprehensive study on the hydro-mechanical behavior of this problematic loessial soil, will lead to better understanding of the response of collapsible soils to different loading conditions.In this study, a series of suction-controlled triaxial tests are performed on “undisturbed” specimens taken from the loessial soil of the “Hezar-pich” hills in the city of Gorgan to observe and characterize the behavior of this soil under hydro-mechanical loadings. The experimental approach incorporates the axis translation technique () for suction control, two independent digitized volume change measurement devices for the precise measurement of water volume change from the cell and specimen, a strain control electronic jack for imposing the shear stress, and three electronic pressure regulators and submersible pressure sensors to control the applied pressures separately during testing. In this study, specimens are initially subjected to isotropic loading and after reaching an equilibrium state, the shear stress is applied to measure the shear stress-deformation and collapse behavior of the loessial soil. During isotropic loading, two possible mechanisms of pore structure collapse are considered: isotropic compression collapse under constant matric suction, and wetting-induced pore collapse under a constant mean net stress.The shearing test results are then used to measure the suction stress of collapsible loessial soils introduced by to describe the state of stress in unsaturated soils. The suction stress, ps, which depends on capillary inter particle and van der Waals attraction forces, electrical double-layer repulsion, and ionic bonds formed between the soil particles is considered as a material characteristic (). Due to the collapse potential of the loess, and its complicated deformation behavior, it is quite difficult to define trends between suction stress and the soil suction for this type of soil and a soil-specific experimental testing approach may be useful to examine the available choices of relationships for ps for loessial collapsible soils.Improvements in experimental unsaturated soil mechanics have led to a better understanding of the behavior of loessial soils. Early experimental works on the behavior of unsaturated loessial soils focused on their stress-deformation characteristics during an isotropic compression collapse at a constant matric suction, or a wetting-induced collapse at a constant mean net stress (e.g., utilized a modified suction-controlled triaxial test setup to perform a series of wetting-induced collapse tests on compacted clayey specimens. Results showed a great impact of matric suction, ψ, and applied mean net stress, pn, on the deformation behavior of collapsible soils, and three distinct phases of volume reduction were observed as suction was decreased from its initial value to zero. Specimens initially experienced a small volumetric strain at higher suction levels. Changes in soil volume happened at higher values of mean net stress when the suction was reduced to lower levels. After reaching the air expulsion suction, due to negligible changes in the degree of saturation of the soil specimen, the volumetric strain became very small or even negative (swelling). The specimens subjected to higher values of pn were observed to experience larger deformation due to pore collapse during wetting ( utilized a modified suction-controlled triaxial test device to perform a series of unsaturated drained shearing tests to study the behavior of a reconstituted collapsible silty soil during shear. The tests were performed by applying mean net stresses ranging from 10 to 310 kPa and matric suctions varying between 80 kPa and 600 kPa. At small values of pn, the shear stress–axial strain curves followed an increasing path during shear, tending toward a plateau at an axial strain between 12% and 20%. The volumetric strain–axial strain curves approached a constant value as the tested soil reached its critical state at large strains. At high values of mean net stress, the shearing test results indicated no significant change in the shear behavior when matric suction was increased in the specimens. applied the concepts of yielding and critical state originally developed for saturated clays to examine the influence of suction on the stress-deformation behavior of unsaturated collapsible silty soils. Results showed different critical state lines for the tested material at different applied matric suctions. Similar results were reported by other researchers (e.g., A challenge encountered in the characterization of the behavior of natural loess is a non-homogenous distribution of macro- or micro-pores which results in the presence of void spaces with different degrees of collapse potential in the soil matrix. Due to this unique characteristic, the collapse phenomenon in natural loess is mostly a continuous-stepwise reduction in volume rather than a sudden drop as water enters the voids. revealed that this continuous variation in volume will change the internal capillaries which could dramatically disturb the suction equilibrium inside the soil mass and also pressures applied to the system, complicating the pressure control when testing an undisturbed specimen of a natural loess under strain control conditions. This observation shows the need for using an unsaturated testing approach for natural loessial soils which is capable of making precise and continuous measurements of volume change and water outflow during both isotropic and shear loadings.Undisturbed samples were taken from the natural loessial deposit of the “Hezar-pich” hills, in Gorgan, northeast of Iran. The monolithic samples, with an approximate size of 30 cm × 30 cm × 30 cm, were taken from a depth of 1.0 m at different locations in this wide Aeolian land. The sample cubes were carefully transported to the laboratory, and then a special specimen sampler, including a 100-kN pushing jack and a supporting steel frame, was utilized to extract “undisturbed” cylindrical test specimens with a diameter of 5 cm and a height of 10 cm. More details about the sampling procedure are presented in . Almost all particles in the soil samples fall in the silt range with very little fine sand and 20% to 35% clay sized particles. As shown in , each of the soil specimens is classified as a yellowish brown Silt (ML), in accordance with the Unified Soil Classification System (The tested specimens have average initial values of void ratio, moisture content and dry unit weight of 0.77, 7.1%, and 15.07 kN/m3, respectively. The plasticity index for the soil is approximately 6.5% and the representative specific gravity of soil particles taken from 10 triaxial specimens yielded an average value of 2.72. Initial measurements using the filter paper technique () showed an average initial suction value of 750 kPa for the specimens ( provides some index properties of the soil.A modified suction-controlled triaxial test device () was used to investigate the impact of unsaturated stress states, mean net stress and matric suction, on the stress-deformation behavior of highly collapsible loessial soils. In this test device, the axis translation technique () was implemented to control suction in the specimen using a high air-entry (HAE) ceramic disc, with an air-entry suction value of 1500 kPa. To ensure a uniform distribution of water to the HAE ceramic disk and prevent stress concentrations beneath the disc, a 0.2 cm deep spiral-shaped groove was created in the bottom platen of the triaxial setup.Water outflow from the specimen and the chamber of the cell during the application of subsequent increments of mean net stress and matric suction was measured using two automatic volume change apparatuses connected to the water drainage lines from the bottom of the specimen and the triaxial cell, respectively. Measurements from these systems are used to obtain changes in the degree of saturation and the volume of the specimen during loading. These volume measurements were then calibrated using results of a series of careful calibration tests performed to measure possible expansion/contraction response of different parts of the test unit under different pressure levels. During the tests, frequent flushing (twice a week for specimens tested under suctions above 300 kPa and once a week for low suction testing) was performed through a flushing path beneath the bottom platen of the test unit to avoid any possible air bubble entrapment during the desaturation process. Compared to conventional methods of water outflow measurement (e.g., the visual observation of the water level in a graduated burette connected to the water drainage/entry line), the approach implemented in this study provides a more continuous and accurate quantification of the water flow behavior while collapse is happening within the soil specimen.Three on-board digitized bias pressure regulators in conjunction with two air/water bladder systems were utilized to perform simultaneous control of the air and water pressures necessary for each test. Three digital submersible pore pressure sensors incorporated into a pressure-feedback control loop were connected to the cell and pressure supply lines of the specimen to allow for accurate measurements of pore water, pore air and cell pressures during each test. The pressure-feedback control loop provides the required pressure equilibrium in the system in case of any change in pressure due to pore structure collapse under changing mean net stress or matric suction conditions.A triaxial load frame appropriate for performing constant strain rate shear test was used to apply axial loads to the triaxial cell piston. Although a constant displacement rate was used, the axial displacement during shearing was also measured using an LVDT mounted on top of the cell. A load cell was used to record axial loads applied to the specimen during shearing. More details about the testing system can be found in The testing procedure used with the modified triaxial test device consists of two stages: an isotropic loading stage, and a shear loading stage. To investigate the effect of stress conditions on the deformation and hydraulic characteristics of loessial specimens, two possible mechanisms of pore structure collapse were examined during the isotropic loading stage: pore collapse induced by an increase in mean net stresses under a constant matric suction, defined as isotropic compression collapse (), and pore collapse induced by a decrease in matric suction under a constant mean net stress, defined as wetting-induced collapse (b). A total of 18 undisturbed specimens (I1 to I10 subjected to isotropic compression collapse tests and W1 to W8 experiencing wetting-induced collapse) were sheared with the stress state conditions at the beginning of the shear loading stage as presented in For the specimens experiencing isotropic compression collapse during the isotropic loading stage, a given test specimen was first subjected to a sufficiently low value of seating pressure, (pn |
= 10 kPa) to avoid any significant compression or collapse of the soil specimens. At a constant back-pressure of 50 kPa, the air and cell pressures were increased equally to the respective target values. The specimen was then allowed to come to equilibrium under the applied stresses. According to , when the rate of changes in water volume reached a value of 0.14 cm3/day or less for this soil, the process is terminated. Experimental observations by indicate that at this rate of water volume change, the rate of changes in volume of the soil specimen would be less than 0.01 cm3/day. This criterion could be taken practically as the equilibrium condition. At the end of the equalization stage, isotropic compression was implemented by increasing the cell pressure in steps to achieve the desired mean net stresses. Water outflow from the specimen and the cell during testing was measured continuously, and sufficient time was permitted for hydraulic equilibrium to be reached throughout the height of the specimen. The shear loading stage was then started by imposing a constant axial displacement rate of 0.002 mm/min to the specimen. This rate of axial displacement proved slow enough to ensure fully drained and constant suction conditions for the tested specimens (For the soil specimens that experienced wetting-induced collapse before shearing, an isotropic confining pressure of 10 kPa was first applied to the soil specimen as the seating load. Based on the initial degree of saturation of the soil specimens () and the SWRC of the undisturbed soil samples (), an initial matric suction of 750 kPa was introduced to the boundaries of the specimen by applying an air pressure of 800 kPa to the top and a constant water pressure of 50 kPa to the bottom of the specimen. This applied boundary suction was then permitted to reach equilibrium throughout the specimen. The soil specimens were then isotropically loaded to the desired mean net stress. After reaching an equilibrium state at the desired pn value, the wetting-induced collapse was initiated by maintaining a constant air pressure at the top of the specimen, while increasing the water pressure at the bottom of the specimen. For each suction level, sufficient time was permitted to reach hydraulic equilibrium. After the equalization stage, the shear loading stage was initiated by applying displacement at a rate of 0.002 mm/min until reaching either a steady state condition or an axial strain of 20%.The isotropic compression collapse test results at various constant matric suction values are presented in (a) shows volumetric strain, εv, as a function of the applied mean net stress, pn, and (b) illustrates changes in degree of saturation, Sr, with pn. The isotropic compression test consists of two stages: the suction-equilibrium stage (dashed lines), and the isotropic compression stage (solid lines). As shown in a and b, for each suction level of 100 kPa or 400 kPa, three different target levels of mean net stress were considered in this study.During the suction-equilibrium stage (about 10 days), specimens experienced a reduction in mean effective stress as matric suction was decreased from its initial value. As a result, most specimens experienced a small amount of swelling during the early stages of the suction equilibrium. In addition to elastic rebound, this could be attributed to swelling associated with water absorption by clay particles, which bridge between the soil particles and form interparticle bonds. However, at lower values of matric suction (e.g., ψ |
= 0, and 50 kPa), pore collapse was exhibited in the specimens in a rate higher than swelling associated with water repulsion of the clay minerals and elastic rebound, which resulted in considerable reduction in the soil volume from the very early stages of loading (a). At these levels of suction, a considerable amount of water was absorbed by the soil specimen and the degree of saturation increased significantly. During the isotropic compression collapse stage of testing, the collapse of voids in the pore space resulted in a decrease in volume due to the increase in pn for all the specimens. Smaller changes in volume were measured in specimens subjected to higher levels of suction. Also, as shown in , during compression, the soil specimens experienced a relative decrease in volume and increase in water volume (to keep the internal suction constant as volume decreases) that resulted in an increase in the corresponding degree of saturation (The results from the wetting-induced collapse tests, conducted at various mean net stresses are presented in (c) and (d). As presented in these figures, for each mean net stress level of 50 kPa or 200 kPa, three different target suction values were considered for testing, while for mean net stress level of 400 kPa, two different target levels of suction were chosen. During wetting, considerable collapse deformation was observed in all specimens as suction decreased from its initial value to the desired matric suction (c). The rate of change in volume decreased as ψ reached values of 10 kPa or smaller ((d), during the wetting process, the degree of saturation of all specimens increased with negligible impact of the applied pn. During wetting-induced collapse, the soil specimens that were subjected to higher levels of pn experienced larger collapse deformation with a decrease in matric suction. present variation of shear stress, volumetric strain and degree of saturation with axial strain, εx, for various mean net stresses, pno (the mean net stress at the beginning of the shear loading stage), at different matric suction levels, for specimens experiencing different mechanisms of isotropic compression collapse or wetting-induced collapse mechanisms before shearing. As observed in , regardless of the experienced pore collapse mechanism, any increase in the applied ψ or pn results in an increase in the absolute value of the deviator stress. However, depending on the magnitude of the applied mean net stress and suction values, two different shearing behaviors were observed in the post-peak range.The specimens that experienced considerable collapse during the isotropic loading stage exhibited mostly a ductile behavior during shearing. In these specimens, the deviator stress-axial strain curves initially followed an increasing path toward a maximum value, after which the deviator stress approached a constant value with further shearing (). During shearing, the volumetric strain-axial strain curves followed a decreasing path toward a constant steady-state value as presented in , the variation of the degree of saturation of the specimens during shearing shows different trends. This originates from the combined variation in the water content and the volume of the specimens.The specimens that were subjected to high values of pn and ψ, experienced small changes in volume during the isotropic loading stage, (e.g., specimens I7, I10 and W6). In these specimens, the deviator stress-axial strain curves mostly showed brittle behavior during shear characterized by high peak strengths at approximately 5–7% axial strain, followed by softening to lower values at large-strains (post-peak strength). The variations of volumetric strain during shear confirm the dilating nature of the soil behavior in the post-peak range of the shear stress curve, similar to a behavior that is more common for dense or over-consolidated material. Based on the results presented in , the effect of change in matric suction on the strength and magnitude of volumetric strain was lower for the specimens tested at lower levels of pn. In general, these results were consistent with those reported by other researchers (e.g., In accordance with the results presented in , collapses may occur during both isotropic and shear loading stages. However, depending on the applied mean net stress, level of suction and/or shear load, the magnitude of collapse may vary during each stage of loading. At higher matric suctions, very little or no collapse may be observed during each stage. However, some combinations of hydro-mechanical loading may lead to considerable decrease in volume during both stages of loadings. From the results of this study, it is concluded that any increase in the magnitude of mechanical stresses (confining net stress or shear stress) or degree of saturation (wetting process) results in an increase in the magnitude of collapse.The SWRCs of loessial soil specimens in terms of effective saturation, Se, under different paths of loading and applied mean net stresses are presented in . Se is a scaled term of degree of saturation which is described as follows:where Sr and Sr,res are the values of degree of saturation at current and residual conditions, respectively. also includes the wetting path of the SWRC measured using the filter paper technique under zero mean net stress condition for comparison purposes.As presented in this figure, the stress path and the magnitude of mechanical load may have significant effect on the SWRC measurements of the tested specimens. For the same values of mean net stress, the effective saturation of specimens subjected to isotropic compression mode of collapse are often greater than those subjected to wetting-induced collapse. The effect of stress path seems to be less pronounced at lower levels of mean net stress (e.g., pn |
= 50 kPa).As shown in this figure, the variations of effective saturation with the mean net stress for the specimens experiencing wetting induced collapse are almost negligible and consequently, the SWRC curves associated with different mean net stresses lie almost on the same path. However, the effective saturation in the specimens experiencing isotropic compression is significantly affected by the magnitude of mechanical load, and is higher at higher levels of the mean net stress.An approach for studying the behavior of unsaturated collapsible soils and examining the influence of changes in degree of saturation and matric suction on the stress–strain behavior of unsaturated loessial soils is the use of independent stress state variables concept proposed by . The motivation for the use of this approach for this particular soil is based on two major hypotheses: first, according to , the collapse deformation processes that occur during wetting in collapsible soils could not be predicted using the effective stress approach proposed by . Such a statement is not valid because the effective stress approach as proposed by was defined only in stress state with no reference to volume change. The nature of volume change in soils depends mostly on the internal structure of the soil and in less extent, on the external stress and loading. And second, the implementation of the effective stress parameter for collapsible soils was found to be challenging and there were some uncertainties in its uniqueness under changing matric suction and mean net stress conditions.However, later interpretations of experimental results warranted reassessment of the use of the effective stress approach for unsaturated loessial soils ( developed an effective stress definition for unsaturated soils as an extension of Bishop's effective stress by modifying the matric suction contribution to the effective stress as follows:where p′ is the mean effective stress and pn is the mean net stress. ps is the “suction stress”, which is also described as mean effective stress under the conditions of no external stress ( used a working hypothesis formed on the basis of experimental observations and thermo dynamic justifications to develop a closed-form equation for the suction stress as follows:where Se is the “effective saturation” as described in Eq. . The proposed equation for suction stress was then validated against published shear failure data for different types of soils. If the variations of the suction stress, ps, are plotted against the matric suction, ψ, then the “Suction Stress Characteristic Curves” (SSCC) is created.Even though results presented a good agreement between the measured “Suction Stress Characteristic Curves” (SSCC) and those predicted using Eq. , it should be noted that in derivation of Eq. for the soil suction, dependency of “Soil Water Retention Curves” (SWRC) on the stress path and the extent of loading was ignored and the validation process was performed using published SWRC data measured mostly under the condition of zero external. However, as presented in , the hydro-mechanical behavior of loessial soils is considerably stress and stress path dependent. Accordingly, the authors of this paper believe that it is necessary to consider the extent of both mechanical loading and wetting when defining the state of stress in loessial soils. describes the variations of deviator stress, volumetric strain, and degree of saturation of the soil specimens at different loading conditions during shear. The results are presented for three specimens of I8, I7 and I1 (a) which were subjected to isotropic induced collapse loading with initial mean net stresses of 50, 200 and 400 kPa, while subjected to constant suction values of 400, 300 and 0 kPa, respectively, and three other specimens of W3, W6 and W7 (b) which were subjected to the wetting-induced collapse with suction values of 400, 300 and 0 kPa under constant mean net stresses of 50, 200 and 400 kPa, respectively, during their isotropic loading stages, before shearing., it is evident that the shear behavior of collapsible soils is tightly linked to its behavior during the isotropic loading stage. As described by , three distinct phases of deformation can be considered for an unsaturated collapsible soil subjected to different values of mean net stress and matric suction during the isotropic loading stage especially in the case of wetting induced collapse (c): (1) “pre-collapse”, which is typically associated with low elastic deformations that almost happens at high levels of suction (I8 and W3 specimens in ), (2) “main collapse”, with large non-recoverable deformations happening at intermediate suctions (I7 and W6 specimens in ), and (3) “post-collapse”, which is associated with negligible deformations during shear after experiencing the main collapse during Isotropic loadings (I1 and W7 specimens in For the specimens with the “pre-collapse” or “post-collapse” phases of deformation in the isotropic loading stage, the effect of stress path on the hydro-mechanical behavior of collapsible soils during shear is relatively negligible. The specimens I8 and W3 are both in pre-collapse region and are subjected to high matric suctions and relatively low mean net stresses during isotropic loading stage with no or very little experience of collapse before shearing. Since they are consolidated and sheared under applying low values of initial mean effective stresses (p′o |
= 167.2 kPa for I8, and p′o |
= 151.3 kPa for W3 referring to ), their shear strength are relatively low and no considerable collapsible deformation has happened during their isotropic loading stage as well as their shearing stage. Moreover, their shear behavior is strain hardening as no collapse is probable under such a loading condition. Referring to , the degrees of saturation at the start of shearing for I8 and W3 are 0.328 and 0.291, and the initial mean effective stress, p′o, for these two specimens are 167 kPa and 151 kPa, respectively. The combination of these two initial conditions of the specimens before shear resulted in almost identical stress–strain curves during shear.Both I1 and W7 specimens are completely wetted under a high mean effective stress (p′o |
= 400 kPa), and they are located in post-collapse region. Hence, their structural bonds are mainly collapsed and their matric suction diminished during isotropic loading stage, before shearing. However, due to the same high initial effective confining stress, I1 and W7 specimens have almost the same shape of strain hardening stress–strain curves and their shear strengths are high. It is notable that the specimen I1 gives a little higher shear strength compared to W7 specimen due to relatively lower degree of saturation at the start of the shearing.However, the shear behavior of the specimens along the “main collapse” phase of deformation during isotropic loading is considerably stress path dependent, because after applying the isotropic loads, the volume changes, the degrees of saturation, and the effective confining pressure related to these specimens were quite different for different applied isotropic stress paths (, for the same values of mean net stress and matric suction, the shear strength measurements of the specimens experiencing the wetting-induced collapse are smaller than those experiencing an isotropic compression mode of collapse. Referring to , the deformation measurements of specimens subjected to wetting-induced collapse are often smaller than those subjected to isotropic compression collapse during the isotropic loading stage. Accordingly, larger shear-induced deformation and lower shear strength are expected to happen in the specimens with wetting induced collapse background. It is worthy to note that the specimens that are located in pre-collapse and post-collapse phases, have a ductile strain hardening behavior during shear and the specimens which are subjected to higher initial mean effective stress (I1 and W7 with p′o |
= 400 kPa) indicate much higher shear strength compared to that for specimens under lower initial mean effective stress (I8, W3 with p′o |
= 167 kPa and 151 kPa, respectively) irrespective of the applied initial matric suction at the start of shearing (ψ |
= 400 kPa for I8 and W3, and ψ |
= 0 for I1 and W7). Digging into , one observes that the degree of saturation at the start of shear loading for I7 and W6 specimens, equals to 0.399 and 0.328, respectively, and the initial mean effective stress for these specimens equals to 310 kPa and 288 kPa, respectively. The data presented in indicate that both degree of saturation and initial mean effective stress of these two specimens at the end of isotropic loading and the start of shear loading have meaningful distances. Therefore one can expect to observe different stress-strain and volumetric behaviors. As can be seen from a, the combination of these two factors resulted in higher shear strength and associated shear strain for specimen I7 compared to that of specimen W6. b also indicates different shapes of volumetric strain-axial strain during shear for these two specimens.The most interesting result depicted in is that the specimens with the intermediate applied matric suction that are in main collapse phase (i.e., W6 and I7), have the highest potential for shear induced collapse deformations. These sorts of specimens indicate higher initial stiffness compared to that for the specimens in pre- or post-collapse phases that can be attributed to their unbroken bonds at the start of shearing when compared to post-collapse specimens and to the higher initial effective stress when compared to pre-collapse tested specimens. However the shear behavior for these specimens is quite different showing a higher stiffness to reach to a clear peak and then the shear collapse occurs and one can observe a sudden decrease in the shear strength of the soil with further straining, showing a brittle and strain softening behavior which is an indicative of shear induced collapse. The peak deviator stresses for I7 and W6 specimens are also in a medium range compared to that for other specimens which can be attributed to the amounts of initial mean effective stresses (). Similar reasoning can be extracted by considering the data presented in In the following sections the measured shear strength data presented in is used with special attention given to two different concepts in unsaturated soil mechanics: the concept of the critical state in saturated and unsaturated states, and the concept of double hardening for unsaturated soils.Based on the concept of the critical state in saturated soils, under sustained uniform shearing at failure, a unique relationship between void ratio, e, mean effective stress, p′, and deviator stress, q, is formed in all specimens (). This means that the deviator stress applied to the specimens during shear destroys the initial soil fabric of the tested specimens, producing an ultimate soil structure which is very similar in all specimens, independent of the applied state of stress and stress paths. On the other hand, using the definition of mean effective stress (Eq. ) for unsaturated soils, it is believed that most conventional soil mechanics theories which are derived for saturated soils can be extended to the case of unsaturated conditions. Accordingly, it would be expected that the trend between the steady state deviator stress values and mean effective stress of saturated soils is consistent with that for unsaturated soils when using the effective stress approach (Eq. , the critical state line of the soil specimens under saturated conditions was drawn using the shear strength data under the condition of zero suction (solid line). Also the critical state line considering all data (saturated and unsaturated) is drawn in this figure with a dashed line. In this plot, the effective stress, p′, was obtained using the measured values of Se obtained from the experimental measurements at shear failure. As observed in this figure, all steady state points approximately fall on the CSL defined for saturated specimens with a slope of 1.154 (R2 |
= 0.974) and there is no considerable difference between the saturated CSL and unsaturated one. Therefore the uniqueness of CSL for saturated and unsaturated soils is examined and proved.The definition of effective stress proposed by ) is very similar to the Bishop's effective stress framework with ps |
= |
χ |
× |
ψ. For a comparative study of the applicability of different approaches for unsaturated loessial soils, other methodologies that are proposed for Bishop's effective stress parameter were also used to define the effective stress parameter and suction stress of unsaturated loessial soils. In this regard, suggested the following effective stress parameter: describes the suction value making the transition between unsaturated and saturated states ( proposed the value of χ to be equal to Se. represents the variation of χ with ψ. If the variations of the suction stress, ps, are plotted against the matric suction, ψ, then the “Suction Stress Characteristic Curves” (SSCC) is created. the variations of these two parameters (χ and ps) with matric suction indicate a better agreement between the experimental measurements and those predicted using χ |
= |
Se or χ |
= |
Sr when compared with other relationships. for the effective stress of unsaturated soils, the data presented in is used to calculate the variation of volume change with respect to p′ as illustrated in show the pore collapse stage of the tests during an isotropic compression collapse or wetting induced collapse and the dashed lines represent the suction equilibrium stage at the beginning of the tests. As shown, for the specimens experiencing an isotropic compression collapse, the mean effective stress increases as the mean net stress is increased from its initial value to the desired value. These changes in mean effective stress result in a decrease in the volumetric strain of the specimens. However, the behavior is different during the wetting-induced collapse tests. When wetting occurs in the loess specimens, two different deformation processes may occur under different conditions: collapse and reduction in the volume of the specimen as a result of suction decrease, and an elastic rebound happening due to the mean effective stress decrease. In collapsible specimens tested in this study, the amount of volume decrease due to pore collapse is observed to be much greater than the amount of dilation or elastic rebound due to decrease in mean effective stress. Therefore, the resultant has been the decrease in volume of the specimens while mean effective stress decreases at the same time. also show that the soil specimens may experience hardening or softening during the test, depending on the level of applied mean net stress or matric suction. For the specimens that are wetted to lower levels of suction before compression, flooding of voids with water may result in reduced stability of the soil skeleton. As a result of this softening, an inward movement of the compression curve occurs. However, for the specimens experiencing wetting-induced collapse, an initial increase in the applied net stress may result in a plastic decrease in the volume of the specimen, stabilizing the soil skeleton against interparticle slippage. This phenomenon has the effect of shifting the volumetric strain curve to the right. described a double hardening mechanism to explain the hardening/softening behavior that soils experience under unsaturated conditions. Based on this mechanism, the soil specimen may experience a hardening/softening behavior due to either plastic deformation of the soil skeleton under a change in the mean effective stress or due to changes in matric suction during drying or wetting. described the hardening effects of plastic changes in volume and changes in the degree of saturation during drying and wetting in an incremental form, as follows:where pc′ is the mean apparent pre-consolidation stress (i.e., the mean yield stress), b is the double-hardening parameter, which governs the rate of change in pc′ that is caused by changes in Se, dep is an increment of plastic change in void ratio, dSe is an increment of change of effective saturation, λ is the slope of the virgin compression curve, and κ is the slope of the elastic rebound curve. A similar expression has been proposed by for incremental changes in Sr. In order to properly capture the nonlinear behavior of pc′ with matric suction, in this study, an empirical equation for b was considered as follows:where Se is the effective saturation, Se,sat is the value of Se at zero suction, and b1 and b2 are fitting parameters of the hardening model.The values of λ and κ (equal to 0.04 and 0.01, respectively, for loess in this study) can be measured from the results of the isotropic compression collapse test at zero suction and hardening parameters, b1 and b2, can be determined by fitting Eq. to the measured values of pc′ at different suction levels for the specimens subjected to isotropic compression collapse (data points in ). The variation of pc′ predicted using Eqs. with matric suction along with the corresponding soil water retention curve (SWRC) are also presented in . As shown in this figure, for the range of suction less than 10 kPa, due to the small changes in Sr only small changes in pc′ are expected. However, for values of suction greater than 10 kPa, changes in pc′ happen at a greater rate as the changes in ψ lead to significant changes in Sr.A conventional triaxial test device was upgraded to assess the hydro-mechanical behavior of a highly collapsible loessial soil during both isotropic and shear loadings. The combination of suction control using the axis translation technique, pressure control using a closed circuit of electronic pressure regulators and pressure sensors, and water flow measurements using two digital volume change measuring devices allowed making precise and continuous measurements of moisture content and volume changes in the specimens.The soil specimens were subjected to two different mechanisms of pore structure collapse during the isotropic loading stage: isotropic compression collapse, and wetting-induced collapse. During the isotropic compression collapse stage of testing, due to the collapse of air voids in the pore space, all of the tested specimens exhibited collapse accompanied by an increase in the degree of saturation with an increase in pn. Similar behavior was observed in specimens experiencing wetting under a constant mean net stress before shearing. The rate of changes in volume and degree of saturation in both cases was, however, dependent on the level of suction and the applied mean net stress.Experiments indicate that depending on the amount of change in mean net stress, matric suction and/or shear stress, the magnitude of collapse is different during isotropic and shear loading stages. The magnitude and proportion of collapse at each stage depends on the magnitude of applied suction and mechanical loadings during the corresponding stage. For higher matric suctions, very little or no collapse could be observed during each stage of loading and the shear strength curves showed dilative and brittle behavior with a peak value during the shear loading stage while at lower levels of matric suction or higher levels of mean net stress, a ductile behavior in the shear stress curves was observed and most specimens experienced a decrease in volume (collapse) during shear. Generally, an increase in isotropic loads, suction and shear loads, resulted in an increase in the amount of collapse.As part of the study, the applicability of the suction stress concept to describe the state of stress in loessial soils was investigated. In this regard, the extended Bishop's effective stress approach was coupled with the effective stress parameter definition χ |
= |
Se and the concept of suction stress, to describe the state of stress in the loessial soils. From the results of this analysis, the application of the concept of suction stress was found to be efficient for unsaturated loessial soils, as long as the extent of both mechanical loading and wetting are considered, when defining the state of stress in this type of geo-material. In addition, a good agreement between the measured χ values and Se was observed and a unique critical state line was obtained for specimens sheared under varying stress state conditions. Furthermore, a hardening constitutive law was presented based on the effective stress concept to demonstrate changes in the yield surface with mean net stress and matric suction for collapsible soils.Heterogeneous compressive responses of additively manufactured Ti-6Al-4V lattice structures by varying geometric parameters of cellsIt is vital to develop lattice structures with excellent performance in structural lightweight and multi-functional applications. However, the inherent single mechanical response of the lattice structure limits its application to different physical scenarios. In this study, to achieve the tailored mechanical properties adjustment, we propose a method for creating lattice structures with varying morphology and relative density by adjusting the geometric parameters of the lattice unit cell. A theoretical model for the preliminary prediction of mechanical properties was established, and a uniaxial quasi-static compression experiment was performed on Ti-6Al-4V lattice samples fabricated by laser powder bed fusion. Additionally, the compressive response of these lattice structures was analyzed by numerical simulation. The results show that the adjusting geometric parameters can achieve various heterogeneous mechanical responses, including shear band failure and uniform compression buckling failure. Furthermore, the mechanical properties can be realized in a larger range of compressive modulus from 77.04 MPa to 1073.5 MPa, and compressive strength from 3.96 MPa to 89.23 MPa. Therefore, the customized requirements of structural load-bearing capacity (large modulus and high strength) and energy absorption (stable platform stage) can be met.Due to high porosity and excellent mechanical properties, lattice structures are widely used in lightweight design, surgical implants, sound absorption, noise reduction, protection, impact resistance, etc. ]. However, the fabrication of lattice structures is still challenging due to the complex internal structure and small strut size. Traditional processing methods such as space holder, powder metallurgy, and sintering can be used to fabricate lattice structures As an important index in characterizing the macroscopic performance of the lattice structure, the mechanical properties of lattices have attracted attention. For example, Hedayati et al. The topology of the unit cell is therefore critical to the mechanical properties of the lattice structure. To obtain lattice structures with excellent mechanical properties, researchers continue to explore new lattice structures, such as structures with deformed struts []. The force form of the rod element is determined by its lattice type. To adjust to the mechanical properties of the structure, the rod size can be changed. However, the manufacturing process restricts the available sizes. It is common to change the topological form of the structure to match the actual application of different mechanical response requirements, which undoubtedly increases the burden of structural design.Body-centered cubic (BCC) lattice structure has attracted the attention of many researchers for its simple configuration, isotropy, and excellent laser additive manufacturing quality []; it is one of the most extensively studied lattice structures. Researchers systematically studied the mechanical properties, failure mechanism, and energy absorption characteristics of the BCC structure by theoretical analysis, numerical simulation, and experiments In this work, we do not change the topology of the structure by adjusting the sizes of the existing lattice structure, but we change the force form of the lattice structure rod unit to achieve a diversified mechanical response and a wide range of mechanical properties. Thus, our lattice structures can meet the customized requirements of practical engineering applications. Considering the typical BCC structure as an example, the structure is extended in one direction to form a series of body-centered tetragonal structures with varying relative densities and shapes. A theoretical prediction model for this type of structure is established based on the beam theory. Subsequently, the corresponding titanium alloy lattice structures were prepared by laser powder bed fusion. Additionally, a quasi-static compressive experiment was carried out. Moreover, its failure mode was analyzed by numerical simulation technology. In addition, to evaluate the load-bearing capacity and energy absorption capacity of the lattice structure, the compressive modulus, compressive strength, and energy absorption of various lattice structures were quantitatively analyzed. Therefore, the relationship between the performance of the lattice structure and the geometric parameters of the structure was established.The BCC was selected as the original model. To adjust the force form of the rod elements of the structure, a dimensional extension was carried out in one direction to form the body-centered tetragonal structure, as shown in (a). In practical engineering applications, the structure often needs to meet specific mechanical properties. Therefore, establishing a predictive model of mechanical properties can evaluate the rationality of the designed structure beforehand. Here, the conventional BCC structure is taken as an example for the force analysis. The structure and the simplified beam element deformation mode are shown in (b). Subsequently, the structural parameters are expanded to obtain the prediction model of the mechanical properties of the body-centered tetragonal structure.The offset of the end of the rod h is given bywhere ω is the end deflection, θ is the angle between the rod and the horizontal line.The strain of lattice structure ε is given asSimilarly, the strain ε can also be expressed aswhere σz is the loading stress in z-direction and E* represents the compression stiffness of the lattice structure. Moreover, the loading stress σz can be expressed aswhere Fz is loading force applied to lattice unit cell in z-direction and L is the base length of the unit cell. Based on the force analysis ((b)), the unit cell loading force Fz and the single beam tangential force F are related as, the deflection of the rod end is given byAccording to the Timoshenko beam theory, the beam element satisfieswhere ψ represents the beam element rotation, EI represents the bending stiffness of the beam, and I is the area moment.For beam elements, the bending moment on the cross section M(x) is given bywhere x is the distance from the cross section to endpoint, the endpoint bending moment M1 = Fl/2, l is the single rod length. combine boundary conditions ψ(x = l) = 0 to solve the first-order differential equationThe slope of the beam neutral axis is given bywhere κ2 is the shape factor. For circular cross-sections, κ2 takes the value 1/1.1. G and A are the shear stiffness and cross-sectional area, respectively.The deflection value at the endpoint is given byBy ignoring the influence of shear effects and substituting , the general stiffness model of the body-centered lattice structure E* is obtainedwhere Es is Young's modulus of base materials and D is the rod diameter of the unit cell.Owing to the actual assembly process, some materials will be removed at both ends of the single rod, rendering it incapable of taking the node spacing at the two ends according to the CAD design. By analyzing the geometrical parameters of the rod section, as shown in , the distance between the force nodes can be obtained by subtracting the distance x from both ends of the rod. This distance is defined bywhere a and b are special distance parameters, as shown in The rod tilt angle is related to the aspect ratio as followsThe stiffness model obtained by substituting To study the influence of geometric parameters on the mechanical properties of the lattice structure, the rod diameter D and aspect ratio α (α = H/L) are considered as variables. The base of the unit cell structure is fixed, the side length L is 4 mm, and the selected ratios α are 0.50, 0.75, 1.00, 1.25, and 1.50, in sequence. In addition, to study the effect of relative density on structural performance, four rod diameters are selected for each unit cell structure. In sequence, the rod diameters D are 0.5 mm, 0.6 mm, 0.7 mm, and 0.8 mm. For the convenience of subsequent analysis, a unique naming method is adopted. For example, a structure with a ratio of 0.50 and a rod diameter of 0.5 mm is named A050D5, and with a ratio of 1.25, and a rod diameter of 0.7 mm is named A125D7. Because the number of unit cells affects the structure's mechanical properties, existing studies have shown that a structure with a unit cell number of 3 × 3 × 3 or more is sufficient to elaborate the mechanical properties of this type of structure . The A150 structure has the least number of unit cells that exceeds 3 in the longitudinal direction, which meets the needs of the experiments.Metallic materials have the advantage of high modulus and strength. Metallic lattice structure has splendid load-bearing and energy-absorbing capabilities. Therefore, it is a commonly used lattice structure base material. Titanium and its alloys are widely used in industry, biomedicine, and other fields because of their excellent mechanical properties and biocompatibility The powder quality significantly affects the molding quality of the sample. Existing research In evaluating the powder forming ability, Zeiss Sigma 300 (Carl Zeiss AG, Germany) was used to observe the micromorphology of the powder, as shown in (a). It is observed that the titanium alloy powder has a high degree of spheroidization, smooth particle surface, and good fluidity, which is beneficial to powder spreading and laser cladding. The particle size analysis software was used to analyze particle size statistics of the powder in the field of view. The particle size distribution histogram of the titanium alloy powder is shown in (b). The particle size of the powder is relatively concentrated and uniform, which ensures the reliability of processing. According to the designed CAD model, the laser sintering system SLM 500 (SLM Solutions Group AG, Germany) was used to process the designed lattice samples. Two samples of each form were processed. The optimized processing parameters are shown in . Subsequently, the samples were taken out from the substrate plate by wire cutting. To later observe the microscopic morphology of the samples, ultrasonic waves were used to clean the residual powder on the surface in anhydrous ethanol, and the experimental samples were finally obtained.To evaluate the quality of the processed samples, the weight and size of the samples were measured with electronic balances and vernier calipers, respectively. During the measurement, the values were measured thrice to eliminate other interferences. Combined with the density of solid base material of 4.51 g.cm−3, the actual relative density of the sample was calculated by the mass method. The scanning electron microscope TESCAN VEGA3 (TESCAN, Czech Republic) was used to observe the microscopic characteristics of the samples. The acceleration voltage was 20 kV, and the magnification was between 20 and 100.To measure the mechanical properties of lattice structures, observe the deformation process of lattice structures under large strain conditions, and analyze the energy absorption capacity and failure mechanism of lattice structures, a quasi-static compression test on lattice structures was carried out. According to ISO 13314: 2011, the initial strain rate for static compression of porous metals is between 10−3 s −1 and 10−2 s −1. Here, the loading rate was selected as 3 mm.min−1 (the initial strain rate is 2.5 × 10−3 s −1). Loading was performed at 25 °C on an MTS 809.10 (MTS Systems Corporation, USA) with a maximum load of 100 kN and stopped at the densification stage or 16 mm displacement. Two samples are tested for each category. Furthermore, to analyze the failure behavior of the sample, during the loading process, the entire compression process was recorded, and the frame corresponding to the strain was extracted to show the deformation behavior.To predict the mechanical properties of the SLM lattice structure and observe the stress distribution of the lattice sample during the deformation process, the commercial software Abaqus 2016 (Dassault Systemes Simulia Corp., USA) was used for finite element analysis. For the simulation parameters of the base material, the elastic modulus of the base material Ti-6Al-4V is 90 GPa from the dog bone coupons tensile test, and the stress-strain curve is shown in . The Poisson's ratio was 0.3, and the measured solid base material density was 4.51 g.cm−3. In addition, to accurately describe the failure mode of the titanium alloy lattice structure during compression, the Johnson-Cook model εf=[D1+D2exp(D3σ*)][1+D4ln(ε˙pl*)][1−D5T*],where A, B, C, m, n are the inherent parameters of the material, and D1, D2, D3, D4, D5 are the material failure parameters, all of which can be obtained through experimental tests. σ* is stress triaxiality, εpl is the equivalent plastic strain, ε˙pl* is the equivalent plastic strain rate, and T* is the dimensionless temperature parameter.Considering that the test process is quasi-static compression and the slight temperature change of the structure, the influence of temperature and loading strain rate can be ignored. Therefore, the property parameters of base material only need to consider the parameters A, B, n, D1, D2, D3 (refer to [. Here, it should be noted that there is a sign difference between the D3 parameter in the Abaqus software and the original formula. In Abaqus, considering that the equivalent plastic strain of most materials decreases with increasing stress triaxiality, D3 is usually a negative value To evaluate the manufacturing quality of the lattice samples, the relative density of each experimental sample ((b)) was measured using the dry weight method, and the relative density of the two samples was calculated to obtain the actual processing. The relative densities of the sample and the designed model were compared, as shown in (a). Almost all the relative densities of the samples were larger than the design, but the difference is slight, it meets the demands of the design. After measuring, the size of the processed samples was found to be close to the design size. Therefore, the increase in the object's mass became the main factor for the relative density of the actual sample. Combined with the electron micrograph of the sample (), the main reasons for the increased relative density of the samples are: 1) There were many unmelted powders on the surface of the structure, and many powders appeared agglomerated; 2) There were overhangs at the intersection of the rods, which further increased the structural mass. From the electron micrograph, it was found that the aspect ratio of the structure had a significant impact on the residual powder processed. The structure with a smaller aspect ratio had more unmelted powder particles remaining at the nodes, making the relative density deviation greater after processing the structure. In addition, the structure with a smaller rod diameter had less residual powder than the structure with a larger one and better surface quality. However, due to the lightweight nature of the structure, the deviation in relative density is greater, as shown in previous studies of titanium alloy lattices []. Furthermore, the actual processing conditions must be considered in the lattice structure design process, especially the appropriate rod diameter and the inclination angle of the strut, failing which may cause processing difficulty of the designed lattice structure.In addition, the angle between the rod nodes of the laser-sintered sample was blunt, as shown in (h), and the connection between the rods was smooth. Previous studies have shown that the smooth inclined angle can effectively improve the mechanical properties of the structure , the top view of the fabrication direction was observed, as shown in . Thus, there were fewer powder particles of the rod in the top view direction than in the front. This is because the powder particles processed in the top view direction are mainly located in the middle of the molten pool during the melting process. Furthermore, the higher temperature causes more melting. However, the structure observed from the front view is mainly at the edge of the molten pool. The lower temperature powder particles are not fully melted, resulting in more residual unmelted powder. The microscopic fish-scale layer structure and the staircase effect formed between the layers of the laser melting are shown in . Some particles were not completely melted. Some were embedded in the solid rod structure, which provides a reference for the future optimization and structural design of metal laser processing technology.The deformation mode of the lattice structure can directly reflect the compressive response of the structure, which is beneficial to the analysis of the failure mechanism of the structure. Through the sample compression process diagram, it can be deduced that there are obvious differences in the deformation process of the structure. During the experiment, it was found that the deformation mode of the same morphological structure was mildly affected by the relative density. Therefore, the recorded deformation process diagram is the structure with a rod diameter of 0.8 mm. The comparison and analysis of the lattice structure compression experiment and the simulated deformation process diagram are shown in . The finite element results perfectly match the experimental results. The failure mode of the structure also shows noticeable differences with changes in aspect ratio. The structure with a small aspect ratio shows good toughness during the compression process. The structure did not reveal fracture failure of the components. However, it showed uniform deformation and layer-by-layer compaction, which is very similar to the previous deformation process of ductile materials []. Owing to the increase in the aspect ratio of the lattice structure, the structure exhibits obvious brittleness. The failure mode is a typical shear band failure and local brittle crushing, which is highly similar to the metallic lattice structures’ failure mode in the previous research [Further analysis of the finite element simulation results, as shown in , found that the aspect ratio significantly affects the failure mode of the structure. When its value was small, such as the A050 structure, it did not reveal macroscopic failure during compression. The rods were uniformly deformed, the mechanical response relatively stable, and there was obvious tensile behavior during the structural deformation, indicating that this type of structure has good toughness. However, the lattice structure with a larger aspect ratio had more cracks before failure. These cracks began at the nodes and propagated along the intersecting lines between the rods until the adjacent rods were separated at the nodes. The failure of the structure was macroscopically manifested as the rod falling off at the node. In addition, the deformation modes of the rods in different regions of the lattice structure were also quite different. The outer rods had more obvious tensile deformation, while the inner rods showed typical buckling. In practical engineering applications, the number of lattice unit cells is large, and the deformation mode of its internal rod elements determines its final mechanical response. Therefore, from the perspective of microstructure deformation, these body-centered tetragonal structures still belong to the bending-dominated structure.The mechanical properties of the periodic lattice structure are predictable. Before obtaining the experimental results, the directional prediction results can provide a reference for subsequent structural design. Substituting the geometric parameters D, L, and α values of various lattice structures into , we can obtain the compressive modulus of the structure. The comparison with the experimental results is shown in . The theoretical prediction model can correspond to the experimental results well when the structure is smaller in diameter. As the diameter of the rod increases, the deviation between the theoretical and experimental results gradually increases. For structures with a small aspect ratio, see (a), the deviation from the experimental results is slight. But for structures with a large aspect ratio, see (b), the theoretical value is generally larger than the experimental result, which is mainly because the processed samples are affected by manufacturing defects and node performance In addition, the thick-rod structure exhibits shear behavior when node failure occurs. However, we neglected the shear behavior to simplify the calculation process. It is one of the main reasons for the deviation between the experiment and theory. Note that the changing trend of the theoretical prediction model is consistent with the experimental results. In the large aspect ratio structure, the structure's mechanical properties gradually increase as the aspect ratio increases. Nonetheless, it has better mechanical properties under the same rod diameter for a smaller aspect ratio structure. It is because the relative density of the small aspect ratio structure is much greater than the other structures under the same rod diameter, as shown in (a). The theoretical prediction results perfectly reflect this trend. Therefore, the theoretical prediction of the structure's mechanical properties is feasible.The mechanical response curve of the lattice structure from compression to densification is shown in the first column of . Evidently, the mechanical response curve has the same changing trend for the lattice structure of the same configuration, and the difference lies in the stress value. The rod diameter increases with the increasing relative density of the structure, and the mechanical properties also increase significantly; however, the strain value at the densification onset decreases. The trends of the structural curves of different shapes are different nonetheless. When the aspect ratio is relatively small, the lattice structure can maintain a long period of strain after reaching the highest strength, it has good toughness, its platform is relatively stable and long, and there will be no prior structural damage. Because the energy absorption characteristics of porous structures mainly depend on the plateau stage of the mechanical curve ], reflecting 1) this type of structure has obvious brittleness; 2) the overall shear band failure and local brittle crushing occurs during the compression process. This nonlinear failure process can also be directly observed in the structural deformation process diagram in The comparison between experiment and simulation is shown in the second column of . Evidently, the simulation curve effectively matches the experimental results. The difference between the simulation and the experimental curve lies mainly in the stress trough value. The reason is the lattice components will fail after reaching the fracture equivalent plastic strain, and the broken components will no longer bear the burden of the mesh deletion. However, the rods that fall off in the actual experiment can still play a bearing role, which makes the test curve of the lattice structure stronger after failure. Similarly, after the structural failure, the upward trend of the simulated stress-strain curve always lags behind the experimental curve, which is similar to previous numerical analysis research on lattice structures [Furthermore, to qualitatively describe the structure's mechanical properties and evaluate the structure's load-bearing capacity, the compressive modulus and the compressive strength in the compressive mechanical curve were compared. Here, we can obtain compressive modulus from the slope of the linear elastic stage. Our previous work . It is clear that when the relative density is the same, the mechanical properties of the structure with the larger aspect ratio are better, which is suitable for fields with higher structural strength requirements and has a positive effect on the design of lightweight structures. Because the solid model used in the simulation process is the same as the design structure, the relative density of the model is less than the actual processed sample, as shown in (a). Thus, many simulation results were smaller than the experimental results. However, most of the deviations between simulation and experiment results were within 10%, and the maximum deviation did not exceed 13%, indicating that the simulation results can match the experimental results well. Combined with the comparison of the deformation process (), the constructed numerical model can accurately describe the lattice structures’ compression response. Considering the convenience and low-cost of numerical analysis, it is very conducive when a large amount of experimental data needs to be examined.The lattice structure has high porosity. It can absorb energy through deformation under a large impact load so as to achieve internal device protection. The energy absorption capacity of this type of structure is expressed in W per unit volume energy absorption given bywhere εd is the maximum amount of strain compressed to the densification stage, and σ and ε represent compressive stress and strain, respectively.Due to significant differences in our lattice structure's mechanical response, the structure's mechanical response curve with a small aspect ratio has a stable plateau stage. The densification strain of the structure is calculated using the energy absorption efficiency method. The results show that the energy absorption efficiency is at maximum when it reaches densification . the energy absorption value is obtained by integrating the area of the curve, as shown in . It shows that structures with smaller aspect ratio have smaller densification strain values. Moreover, the strain value is further reduced with the increase in the relative density. However, the energy absorption value of this structure is larger than that of other structures, indicating an excellent energy absorption capacity. Although the larger aspect ratio structure has a larger densification strain, its plateau stage curve fluctuates greatly and has a smaller energy absorption value. This corresponds to the previous mechanical response curve (). It is also consistent with the previous study According to research on the lattice structure [], the mechanical properties have a power-law relationship with the relative density, and the index can reflect the mechanical response of the structure better than the pre-factor. A summary of the mechanical properties of the lattice structure obtained in the experiment is shown in . The power law can effectively fit the relationship between the mechanical properties of the structure and its relative density. Combined with the previous prediction model of mechanical properties, it is evident that under the same relative density, the mechanical properties significantly improve as the aspect ratio increases, which positively affects the lightweight and high-strength lattice structure design. Furthermore, the series of lattice structures formed by changing the aspect ratio of the structure can achieve a large range of mechanical performance adjustments.The power-law parameter values are shown in in comparison with the existing research on lattice structures. These findings suit the mechanical properties of various current complex structures with a relatively simple structure form, which can be applied in engineering scenes with different mechanical performance requirements. By analyzing the power exponent, it is found that the base material has little effect on the power exponent of the formula; however, the index difference between different structures is large. For the relative modulus index n, the stretching-dominated structure is close to 1, and the bending-dominated structure is close to 2. This corresponds with the original Gibson-Ashby study on porous materials In this study, a series of body-centered tetragonal lattice structures with different configurations and relative densities were obtained by varying the geometric parameters (aspect ratio and rod diameter) of the BCC lattice unit cell. Then, the failure modes, mechanical properties, and energy absorption capacity of these lattice structures were studied by utilizing experiments, finite element methods, and theoretical prediction models. The main conclusions are as follows:The compression responses of the lattice structures with different aspect ratios show obvious differences. Structure with a small aspect ratio, such as the A050 structure, has good toughness and excellent energy absorption capacity and has application potential in buffering energy absorption and fatigue resistance. In contrast, the large aspect ratio structure, such as the A150 structure, has outstanding advantages in the lightweight and high-strength structures owing to its high modulus and high strength. Furthermore, a wide range of mechanical performance changes can be achieved by adjusting the structural rod diameter. The compressive modulus varies from 77.04 MPa to 1073.5 MPa, and the compressive strength is between 3.96 MPa and 89.23 MPa.By changing the aspect ratio of the unit cell, the brittle Ti-6Al-4V lattice structure will deform uniformly under compression. From the deformation mode of the finite element simulation rod and the exponent of the power-law fitting formula for the mechanical properties, it is evident that the aspect ratio change of the body-centered structure does not influence the bending-dominated character of the structure. Nevertheless, reducing the aspect ratio of the structure can affect its failure strength, which makes the originally oscillatory mechanical response curve stabilize.By varying the aspect ratio of cells, new configurations of lattice structures can be obtained, which can not only adapt to different application requirements but also expand the types of existing lattice structures.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.An experimental study of the relationship between settling flocs and eroded flocs of kaolinite in aqueous mediaAspects of the relationship between flocs in suspension and those held in a cohesive sediment bed were investigated experimentally using an erosion rig with kaolinite as the sample material under different medium conditions. The critical shear–stress, τc, required to initiate the erosion were measured, and the floc sizes of the eroded products (dE) were analysed in situ using macro-photography. Factors such as age, density, pH and ionic strength were investigated. Separate experiments were performed to measure the floc size in the settling zone (dA). The results show that the floc sizes from the above two different measurements show the same variance with respect to physico-chemical (pH and ionic strength) changes in the environment. This work has been very successful in showing the relationship between the flocs in suspension and those eroded from a bed of sediment, so one property can be predicted from knowledge of another.settling rate of slurry-supernatant interface (cm h−1)average (equivalent) aggregate diameter (μm)stoke's velocity for single aggregates (cm h−1)ratio of volume concentration of the aggregates to kaoliniteeffective density of aggregates (kg m−3)Floc breakage is generally undesirable in solid–liquid separation processes employing coagulation and flocculation because it reduces efficiency of the separation. In a typical flocculation basin, effort has been paid to reduce the floc breakage caused by the motion of the paddles and scrapers. Optimal flocculation performance requires a balance between floc growth by interparticle collisions and floc breakage due to the hydrodynamic force (). Therefore unless the threshold stress are correctly identified and quantified, efforts made to reduce the velocity gradient in a flocculation/coagulation can just as likely produce negative effects as beneficial ones.Previous studies have intensively focused on the floc strength prediction, based on the results of studies of flocs break-up, prior to settling (). Not much effort has been made on flocs that have settled. This study is thus aimed at relating the behaviour of settling flocs to the eroded flocs which may have undergone some consolidation. Thus, one property can be predicted from knowledge of the other. This concept allows prediction of the bed surface structures which, as yet, have not been very well quantified and are important in the erosion process itself.The experimental part of this work involved designing an erosion rig capable of producing an increasing uniform flow to shear an initial pre-formed bed. Once this was completed, parameters influencing the erosion were investigated (i.e. age, pH, density and ionic strength). Separate tests involving observations of the settling behaviour (i.e. floc size, settling rate) were made on flocs settling in suspension to investigate the relationship between these basic properties for settling and the properties of eroded flocs. Kaolinite is used as the sample material in this study due to its well-characterised properties. Furthermore, it is representative of materials encountered in natural and industrial environments.Kaolinite, a hydrated aluminium silicate of composition Al2O3·2SiO2·2H2O, occurs in the form of thin, roughly hexagonal platelets, of length-to-thickness ratio of about 10. Kaolinite layers have amphoteric properties. The faces or surfaces carry a permanent negative charge and, depending on the pH, there is positive or negative charge on the edges (). Kaolinite platelets can associate in edge–edge (E–E), edge–face (E–F), and face–face (F–F) configurations (). The formation of the different types of association depends on the balance of electrostatic interactions (attractive or repulsive), which are controlled by the chemistry of the dispersions, and the attractive van der Waals forces between the particles (In acidic environments, aluminol groups exposed on the edges of the particles apparently bind hydrogen ions in water thus generating positive charge. Thus, edges and faces of particles will mutually attract giving rise to face–edge attraction and coagulation of kaolinite dispersions referred to as “card-house” structure. Under alkaline conditions, the edge charge is either absent (neutral charge) or negative, and the particles are deflocculated, provided the electrolyte concentration in solution is low. At high electrolyte concentrations, electrostatic repulsion (or attraction) between the particles is reduced because of electrical double layer compression or ion shielding of the surface charges. Thus, the particles adhere to one another along their basal surfaces, forming a “card-pack” structure (). Association of the F–F type gives small aggregates of higher density, whereas E–F and E–E associations lead to lower density aggregates of larger volume ( empirical correlation for the group-settling rate of uniform spherical particles isFor flocculated systems, such as kaolinite, suggest that the aggregate diameter, dA, is relatively independent of concentration over the “dilute” range, and that dA dose not change once settling has begun. The dilute settling rate of independent aggregates size resulting from drag predicted by Stokes law allows Eq. A material balance on the kaolinite givesCAK=ϕAϕk=VolumeofaggregateVolumekaoliniteinaggregatesIf dA is expressed in microns, the density of kaolinite, ρK, is 2600 kg m−3 and the viscosity of water, μw, is 0.893 cp at 25 °C, then VSA, the Stokes’ settling velocity for single aggregate, isTherefore, if Qo1/4.65 plotted as a function of ϕK, a straight line should result and the floc size, dA, can be estimated from the slope and intercept of this line.The phenomenon of the erosion of cohesive sediment has attracted the interest of many researchers (). In the present study, two important parameters have been deduced from erosion tests namely the critical shear–stress for erosion, τc, and the average eroded floc diameter, dE. The critical shear–stress, τc, which is assumed to be equal to wall shear–stress, τw, can be estimated from the flow rate through the pipe at the inception of erosion and this is acceptable for the shallow sediment beds used here. Another assumption made is that the bed acts like a solid and does not move due to the presence of eroding fluid movement. Considering that the relative movement of the eroding fluid and the bed is very close to that of the eroding fluid itself, this assumption is justified and validated elsewhere (Following the above assumptions, τw is found from a force balance under condition of no momentum change for steady state, fully development flow (see where di is the pipe diameter. The frictional pressure drop (ΔPf) iswhere the friction factor, f, is a function of the flow Reynolds number (Re) and its governing equation depends on whether the flow is laminar or turbulent (). In this study, the flow encountered is turbulent (see Section ), therefore f is estimated from the following equationwhere er is the pipe wall roughness. The measurement procedures and the estimation of the above parameters are presented in the experimental sections.The experimental rig used in this study was designed to study the erosion of kaolinite. A circular Perspex pipe of a uniform cross-section is used. A pipe with 50 mm inside diameter and 3 m length was chosen, due to practical considerations of the flow rates involved (increasing the pipe diameter two fold would result in a four fold volumetric flow rate increase). Controlling the hydrodynamics of the pipe is very important so that quantification of the stress causing the erosion/floc break-up can be made accurately. Strict measures must be taken to ensure that fully developed flow is present at the location where bed erosion occurs. This is to avoid the error of flow irregularity occurring due to entrance effects.Under normal conditions, the 3 m length is not sufficient for fully developed flow to occur (). However, by inserting a straightening vane, the turbulent boundary layer can be triggered from entrance (). Therefore, the turbulent boundary layer is established, even though the transition to fully turbulent flow is not complete. Considering that the erosion process happens in the region of the turbulent boundary layer, and the viscous sub-layer errors arising from less than fully developed flow are likely to be insignificant. The diameter of each straightening vane should be one tenth of the pipe diameter, which is 5 mm. illustrates the erosion rig used in the experimentation. A constant head tank (T1) is used to maintain a uniform and constant flow rate during the erosion process. There are a number of side exit points on T1 for overflow to T3. This arrangement allows a constant water head to be maintained at different levels. Water to the constant head tank is supplied by a Clark pump (model TMA 1000, UK) capable of a maximum flow rate of 40 l min−1 from the reservoir tank (T3). The receiving tank (T2) has three exit points in parallel connected to the water collection tank (T4). This allows the water level T2 to be fixed and maintained at 30 mm above the Perspex tube entrance.The bed is formed from a kaolinite suspension. The kaolinite suspension having the required density is initially prepared using a stirred tank (T5) with a mounted impeller. The slurry is then introduced into the Perspex tube via valve V3. A peristaltic pump (P2) is used to circulate the slurry towards the outlet point situated at a distance of 400 mm from the inlet. This is necessary to ensure uniform distribution of the kaolinite slurry in the tube.A square cross-section perspex column of 40 mm length is fixed to the tube at 2 m from the entrance. It is filled with water covering the cross-section of tube. The purpose of this is to enable photographs of the erosion product to be taken by minimizing the spurious reflections due to the circular section pipe. This illustrated in To investigate the relationship between settling flocs and the settled cohesive bed, characteristics properties need to be determined under different operating conditions. In this study, the effect of the suspension pH, ionic strength and bed age on the settling floc and the erosion product were investigated. For each experiment, three similar runs were carried out to ensure reproducibility of the results.Calibration of the flow rate is necessary to quantify the hydrodynamic stress during the experiment. This was achieved by measuring the flow rate with respect to the full range of valve opening values. If the water levels in the two tanks (T1 and T2) are constant, the flow rate is fixed for each value of valve opening. The flow rate can be measured by noting the time taken, t, for the observed water level increase (Δh) on side glass of collection tank T4. Since T4 has a uniform circular cross-section, the volumetric flow rate Eq. The result of the flow calibration curve is shown in . For any valve opening value, the flow rate can be determined quite readily.The kaolinite used was ‘Supreme’ grade china clay provided by courtesy of Imerys, UK. It is well known that some deflocculants are added to the kaolinite for stabilisation purposes, and there is a low level of natural impurity (). Homogeneous homoionic sodium kaolinite dispersions were obtained by following the surface preparation methods of . The technique involved repeated washing of the kaolinite in NaCl solution (1 M) at pH equal 3; the kaolinite–NaCl suspension is then prepared and allowed to settle over a 24 h period, supernatant is removed and fresh NaCl solution (1 M) is added. The electrophoretic mobility of the kaolinite suspension is checked periodically until consistent measurements are obtained. The mobility became constant after six washes. Further washing with distilled water caused the sodium ions to be expelled from the kaolinite by osmotic diffusion. About 8–12 washes, each lasting 24 h, are required to reduce the supernatant conductivity to 2 μmho and to produce the kaolinite in its natural unsubstituted form. Subsequently, the kaolinite slurries are stored under distilled water. The texture and shape of the particles are observed in scanning electron microscopy (SEM) (FEI, Quanta 200, Czech Republic) photographs, as shown in . It can be seen that the kaolinite particles are plate-like, having a major dimension between 0.1 and 2.0 μm and a thickness ratio between 10:1 and 30:1.These tests are required to determine the floc size of the settling flocs for kaolinite suspensions. Initially, the treated kaolinite is diluted with deionised water to bring the density of the suspension to the range between 1004 and 1010 kg m−3 corresponding to a volume fraction of 0.003–0.008 as proposed by . The slurry density is measured using DMA 35N Digital density Meter (Sheen Instruments, UK).The samples are prepared using different sodium chloride (NaCl) concentrations (0.001 and 0.1 M) and pH values to produce different kaolinite floc structures (i.e. Edge–Face or Face–Face structures). Each suspension is mixed for 1 min, and thereafter the prepared kaolinite suspensions are transferred to 500 ml measuring cylinders (5.5 cm in diameter). Subsequently, the settling rate is recorded as a function of time. Therefore, considering Eq. , if one plots the initial settling rates Qo1/4.65 as a function of the corresponding kaolinite volume fractions ϕK, a straight line should result and, from the slope and intercept, one can estimate the floc size.The first step to measure is the τc by increasing the flow rate of the water through the experimental test section by increasing the opening valve V1 until surface erosion occurs. At this point, the critical shear–stress for particle transport is reached. The value of the valve opening is recorded.It is important to note that pore and eroding fluid properties must be similar to prevent osmotic diffusion of ions or water molecules to the clay particle surfaces. The net effect of this is the weakening of interparticle bonds as reported by . Therefore, for each experiment, the pH and ionic strength of the water in tanks T1 and T2 must be the same as that of the kaolinite slurry in T5. This can be done by adding the appropriate amount of NaCl and HCl to tanks T1 and T3. The pH is monitored using a Corning 240 pH meter, while the ionic conductivity is checked by a Philips PW9525 conductivity meter.A total of seven different bed age were tested at 1, 2, 3, 4, 8, 16 and 36 h, and were made at a standard pH with an ionic strength of NaCl solution (0.001 M). This arrangement is thought to enable a representative indication of consolidation property change where significant changes occur during the initial phase. The slurry density used in all runs is kept constant at 1010 kg m−3, which corresponding to a 3 mm thick bed from visual observation.In order to make a fair comparison between the behaviour of a settling floc and an eroded floc, the effect of pH is investigated in a pH range of 4–7 (similar to settling tests) for a 2 h age bed at different NaCl concentrations (0.001 and 0.1 M) and a slurry density of 1010 kg m−3.Once τc is reached, the flow rate is gradually decreased to enable photography of the eroded flocs using the arrangement shown in . As far as the photographic unit is concerned, macro-photography is necessary to produce photographs of the eroded flocs. The macro-photography unit used in this study is the micro-mode of 8.0 Mega Pixel camera (CASIO, QV-R61). The camera is placed on a tripod so that the photographs are not affected by operator induced camera vibration. A black background is also needed to provide good quality images. A measuring tape with a scale in millimeters is attached to the surface of the circular column to provide a direct indication of eroded floc size (dE). The camera is attached to the computer and an image analysis tool (UTHSCA, Version 3.0 Texas, USA,) is used to examine the digital photographs. The image could be enlarged to a certain extent by means of the software. For each image, the number of pixels between each two points on the measuring tape is determined; the accurate diameter of the floc (dE) is determined in terms of pixels and is subsequently converted to length (μm). When the floc is spherical, dE can be directly measured. With regard to irregularly shaped flocs, the shape is described rather subjectively by comparison with standard shapes or defined by coefficient (). In this study, the floc sphericity factor pertaining to the floc shape is determined using the standard set of shapes for the determination of particle sphericity (Kynch theory of batch sedimentation analysis was used to estimate the initial settling rates by plotting the height, Z, of the interfacial plane between the slurry and the supernatant as a function of time ( shows the sediment as a function of time for different volume fraction for kaolinite suspension in water at pH 5. The results show that the produced aggregates were small and spherically uniform shaped, hence, the floc size, dA, can be estimated from the relationship between the initial settling rate and volume fraction of kaolinite suggested by Eq. . The results were found to be reproducible and comparable to date reported by Michaels and Bolger (1962) which is valid only within the dilute limit as shown in . Volume fractions of kaolinite in the range of 0.003–0.008 are found to delineate the limits of the dilute region for all flocculated kaolinite–NaCl suspensions. Average floc sizes estimated using Eq. for kaolinite suspensions experiencing different electrolyte conditions are summarized in allows one to suggest that a higher degree of E–F interaction leads to larger dA (i.e. high water content or less dense). In addition increasing the ionic strength weakens the E–F but strengthens the F–F. At low pH (i.e. pH 4), the electrostatic attraction between edges and faces will produces an E–F structure. The E–F interactions result in voluminous, three dimensional, card-house flocs having high void ratios (high water content).As the pH increases, the positive charge on the edge gradually decreases and becomes neutral or negative, subsequently, the flocs breakdown if the electrolyte concentration is not sufficient to induce the flocculation. At high pH, both face and edge surfaces are negative and any increase in electrolyte concentration will reduce the repulsive force between the face and edge and lead to weakly structured flocs that may consist of any random combination of F–F and E–E associations (). These formed flocs are found to be relatively small and dense (see where the floc size for kaolinite in NaCl (0.001 M) at pH 4 is bigger than at pH 7).A total of seven different bed age tests at 1, 2, 3, 4, 8, 16 and 36 h are made at pH equal 5, using an ionic strength of NaCl solution (0.001 M). In order to estimate the critical stress, τc, the flow rate, Qv, known from as a function of control valve setting, can be converted to the mean velocity (u) by dividing Qv by the pipe cross-sectional area. Thus, by substituting this value into equations 9, 10 and 11, τc is obtained.The values of the critical shear–stress for erosion in the range 0.05 ≤ |
τc |
≤ 0.08 Pa show good agreement with those reported by and slight difference with those reported by . These differences in the values of τc could be related to differences in the measurement methodologies and also the source and subsequent treatment of the kaolinite. The treatment procedures used in the preparation of kaolinite suspensions have a significant effect on the electro-kinetic and rheological behaviour of kaolinite suspensions (The eroded floc diameter, dE, is obtained using the procedure described in Section . The experimental results of bed variation are shown in shows the erosion results obtained in two separate runs. The trend lines for both runs are similar and suggest that the results are reproducible. The results in show that the critical shear–stress increases with time up to 4 h, after which it remains constant. This evidently coincides with the sharp drop of dE in Following the above observations, one is able to note that, if the bed is sheared immediately after formation (i.e. t |
= 0 h), then the characteristic eroded floc diameter (dE) associated with the erosion process should be of similar magnitude to the settling floc size (dA) seen in the settling experiment. In the current case, the size of settling flocs and eroded flocs (at t |
= 0 h) are approximately equal, because the effects of consolidation are absent at this stage. The results also show that, after the consolidation occurs in beds of increasing age then the eroded flocs reflect the bed property in that the eroded floc diameters, dE, are less than that of fresh settling flocs, dA. This agrees with the notion that as, time increases, the layers of relatively large settled flocs comprising the bed consolidate, and this is reflected in the appearance of smaller, more strongly linked flocs that are also more dense.The effects of pH and ionic strength on the critical stress and floc size of the eroded floc of 2 h bed age are shown in , respectively. The results show good agreement, in term of floc sizes, between the settling and eroded flocs. shows that the critical shear–stress decreases with increase in pH at a low ionic strength of 0.001 M. This is expected here, because at both low pH and ionic strength, the edge has a high positive charge and the face has a constant negative charge which leads to a greater force of attraction between the kaolinite particles in the E–F flocculation structure. Subsequently, this produces a strong flocs having large dE as shown in . Hence, the shear–stress required to erode the flocs, τc, is higher as well. In addition, as the pH increases, the E–F interaction forces are reduced and then the particles adhere to one another along their basal surfaces, forming F–F, E–E and possibly some E–F associations. These associations give small settling flocs having a small dA and produce dense and weak beds having a low dE and τc. also shows that τc decreases with an increase in ionic strength at low pH, and increases with an increase in ionic strength at high pH. When the electrolyte is added to the E–F flocculated kaolinite dispersions at low pH, the dominant E–F interaction forces will be reduced resulting in a weaker interparticle bond. The net effect is to weaken the floc strength. However, at pH 7 there is an increase in τc with ionic strength. At high pH, there are three possible interactions F–F, E–F and E–E. The F–F interaction is strongly repulsive in dilute electrolyte since the electrostatic repulsion is between the relatively large facial areas of the platelets. The E–F and E–E interactions will also be repulsive, but the overall force will be less than the F–F because of the smaller area of interaction. As the electrolyte concentration is increased, the electrostatic repulsion is reduced, but the van der Waals attractive forces remain unaffected. Under these conditions it is possible for a net attractive force to arise and this will lead to some flocculation and consolidation which is reflected in the increase in the τc and dE. Thus, in these conditions random combinations of F–F, E–F and E–E interactions give rise to the growth of the sediment bed. Note these flocs will not be as strong as the E–F flocs found at low pH since here the van der Waals and electrostatic forces are not in opposition. All these findings are in agreement with work concerning the compressive yield stress and static yield reported by A relationship between the settling behaviour and bed erosion is found when cohesive sediment beds made from kaolinite suspensions are investigated under conditions of different pH and ionic strength and the following conclusions are achieved:If the bed is sheared immediately after formation (i.e. t |
= 0 h), then the characteristic eroded floc diameter (dE) associated with the erosion process should be of similar magnitude to the settling floc size (dA) seen in the settling experiment, because the effects of consolidation are absent at this stage. On the other hand, after the consolidation occurs in beds of increasing age, then the eroded flocs reflect the bed property in that the eroded floc diameters, dE, are less than that of fresh settling flocs, dA.The settling and eroded flocs have same variance with respect to physico-chemical (pH and ionic strength) changes in the environment. It is found that the critical shear–stress, τc, decreases with increase in pH. This is expected here, because at low pH, the edge has a high positive charge and the face has a constant negative charge and this leads to a greater force of attraction between the kaolinite particles in an E–F flocculation structure. Subsequently, this produces large dA and strong flocs having high settling rates and produces less dense bed having a large dE. As the pH increases, the E–F interaction forces are reduced and then the particles adhere to one another along their basal surfaces, forming F–F, E–E and possible some E–F associations. Note these flocs will not be as strong as the E–F flocs found at low pH since here the van der Waals and electrostatic forces are not in opposition. Under this alkaline condition, settling flocs having a small, dA, are formed and this produced a dense and weak bed structure having a small dE and τc.The present study also shows that studies of floc strength in industrial processes and the erosion of cohesive sediment in natural environments share a common basis. As such, this should be considered in any future studies.Polyamide 6/acrylonitrile–butadiene–styrene terpolymer compatibilized blendMulticomponent blends based on polyamide 6 and styrenic polymers: morphology and melt rheologyThe role of each blend component on blend morphology and melt rheological properties was investigated for multicomponent compatibilized blends of polyamide 6 (PA6) and acrylonitrile–butadiene–styrene terpolymer (ABS). Blends with PA6 content of 50 wt% were prepared at similar processing conditions on a ZSK 30 twin screw extruder. PA6/styrene–acrylonitrile co-polymer (SAN) blends showed a dispersed morphology with PA6 as matrix. Addition of reactive compatibilizer, styrene–acrylonitrile–maleic anhydride co-polymer (SANMA), up to 5 wt%, changed the morphology from a dispersed to a co-continuous structure. PA6/ABS, having a part of the SAN substituted by rubber, exhibited a coarse co-continuous structure which could be explained with the yield stress of the ABS. Addition of the compatibilizer to this system refined the co-continuous structure and increased the viscosity as well as the elasticity.Polyamide 6/acrylonitrile–butadiene–styrene terpolymer compatibilized blendMulticomponent compatibilized blends of polyamide 6 (PA6) with acrylonitrile–butadiene–styrene terpolymer (ABS) are of high commercial interest as high performance alloys owing to their excellent potential for applications where super tough materials with high thermal stability, good chemical resistance and excellent dimensional stability are required. On the other hand, the ease of processing and stability of the blend over wide processing conditions make this blend suitable for engineering applications All the materials (Polyamide 6 Durethan B29, SAN Lustran M80, ABS Novodur Graft (SAN-g-PB) and SANMA) supplied by Bayer AG were in pellet form except for SAN-g-PB which was delivered in a powder form. These materials were used for melt blending from air sealed bags without any further treatment.The blends were prepared on a ZSK 30 twin screw extruder (L/D ratio of 41) with simultaneous feeding of all blend components at one feeding point (common melting). Prior to melt blending the SAN and SANMA were dry blended and fed through a single feeder. ABS was produced in situ by simultaneous addition of SAN and the SAN-g-PB during the extrusion process. The processing temperature of 260 °C, feeding rate of 10 kg/h, a unique screw and barrel configuration and screw speed of 200 rpm were used for all blends preparation. The melt strands were quenched by passing them through a water bath at room temperature and then chopped to pellets. Two non-reactive uncompatibilized binary blends, namely PA6/SAN, and PA6/ABS, as well as two reactive compatibilized ternary blends, namely PA6/SAN/SANMA, and PA6/ABS/SANMA, were made with an identical blend composition (keeping PA6 content constant at 50 wt%). The compatibilizer level was less than 5 wt% of the total blends. In addition to these series of blends, a binary reactive blend of PA6/SANMA was produced under similar processing conditions in which the blending ratio was kept similar to that of the ternary blends. This blend was used to study the individual effect of SANMA on PA6 properties.Scanning electron microscopy (SEM) was used to study the morphology of extruded blend strands. The smooth surface obtained by a steel knife on a rotational microtom (Jung RM 2055, Leica) was etched in formic acid for 4 h in order to remove the polyamide phase of the blends or in tetra hydrofuran (THF) for 24 h to etch out the SAN component. The samples were hanged into the solvents within about 2–5 mm. The etched surface after proper drying was gold sputtered and observed under a LEO 435 VP (LEO Elektronenmikroskopie, Germany) SEM. The digitized images were recorded at different magnifications.Melt rheological investigations were conducted by an ARES Rheometer (Advanced Rheometric Expansion System, Rheometric Inc.) in parallel plates oscillation mode on granulated and properly dried samples. Frequency sweeps of 0.1–100 rad/s were performed at temperature of 260 °C and strain of 5% in N2 atmosphere.The morphology of the etched cut surface of the PA6/SAN binary blend is shown in . THF was used to dissolve the SAN fraction of the blend revealing the PA6 structure. In this blend SAN forms spherical domains uniformly dispersed in the PA6 matrix. These SAN domains are between 1 and 7 μm in diameter. Although the blend contains SAN as the major volumetric component and PA6 as minor component, the PA6 is the component, which forms the matrix. This is due to lower viscosity of PA6 as compared to the SAN.There are several models to estimate which phase forms the matrix by predicting the phase inversion composition based on the viscosities (η) of the blend components. According to the empirical relationship for prediction of the phase inversion suggested by Avgeropoulos where η and φ denote the viscosity and volume fraction of the blend components, respectively.where the intrinsic viscosity was assumed to be 1.9 for spherical domains.where F is expressed according to Utracki The predicted phase inversion composition according to the above three models are shown in . Some other relationships were also proposed by Ho with introduction of some pre-factor or exponents to achieve better fits for their experimental results.The rheological investigations made by an oscillation rheometer at 260 °C shown in indicate that the viscosity of PA6 is lower than that of the SAN. The extrapolated zero shear rate viscosity is about 1000 Pa s for SAN and about 300 Pa s for PA6. Assuming the validity of Cox–Merz rule relating steady shear viscosity with the absolute value of complex viscosity Taking into account the viscosity ratio of 0.73 and using , the phase inversion point at which the SAN forms the continuous phase or the matrix, is found to be at higher concentration than the actual SAN content of the blend. Therefore, SAN should form the dispersed phase. Thus, according to all the three models, the morphology obtained is in accordance with the expectation based on the viscosity ratio for binary blend of PA6/SAN.shows the morphology of etched cut surface of PA6/ABS blend. As compared to the PA6/SAN blend, here a part of SAN is replaced by the SAN-g-PB. For this blend formic acid was used to etch out the polyamide component hence revealing the remaining ABS structure. The morphology appears coarse co-continuous. To check the co-continuity in addition etching was performed with THF to etch out the SAN fraction. By this procedure it is assumed that the embedded SAN-g-PB particles are also removed from the sample surface. An example showing the comparison of surfaces etched in THF and formic acid for a PA6/ABS blend having a slightly different composition is shown in . These morphological investigations indicate that the addition of the rubber to SAN induces a change in the morphology type from a dispersed type to a coarse co-continuous morphology. Looking at the rheology of the blend components one can notice that ABS has much higher viscosity than the SAN. This increase of viscosity is caused by the addition of the rubber particles. Moreover, ABS does not show a Newtonian plateau at low frequencies but a linear increase in viscosity with decreasing the shear rate. It also exhibits a very high elasticity (see G′ in ), which determines mainly the complex viscosity.Using the same procedure to calculate the phase inversion composition by applying for the viscosity ratio (ηPA6/ηABS) of 0.25, the ABS phase should form the dispersed phase according to all the three models (). Although the actual ABS content is far away from the phase inversion composition ABS exists as a continuous phase. It is well known that there can be a co-continuous region around the phase inversion composition whose composition range depends mainly on the interfacial tension ) and the existence of a yield stress of the ABS as evident from the sharp increase of melt viscosity at low frequencies. This rheological behavior is typical for thermoplastic elastomers and filled systems The SANMA, a terpolymer of styrene, acrylonitrile, and maleic anhydride, is miscible with the SAN or the SAN part of ABS. On the other hand, the maleic anhydride segments of this terpolymer which are located at the interface, are capable of reacting with the amine end groups of PA6 known as imidization reaction, forming co-polymers at the interface (These interactions result in the stabilization of the interface by reducing the coalescence, reduction of interfacial tension, and enhancing the interfacial viscosity and adhesion. Thus, SANMA can act as an excellent reactive compatibilizer for PA6/ABS blends. In order to estimate the effect of the reaction and the consequent interfacial interactions on the rheological behavior and resulting morphology, a binary reactive blend of PA6/SANMA was made keeping the blending ratio similar to that of the ternary compatibilized blends. shows a comparison between the melt viscosity of the PA6 with that of binary reactive blend of PA6 with SANMA. The melt viscosity () increase significantly as a result of the reactive blending. At a shear rate of 100 s−1 the viscosity of the PA6/SANMA blend is almost double of the neat PA6.This is a reactive compatibilized ternary blend obtained by addition of the SANMA terpolymer to PA6/SAN. Morphology of the cut surface etched by formic acid, hence exposing the SAN structure, is shown in . As compared to the binary non-reactive blend (PA6/SAN) this blend shows a co-continuous structure. The addition of the compatibilizer leads to a change in morphology that is a transition from a dispersed structure to a co-continuous structure occurs.Now let us examine the effect of further addition of the rubber component into the reactive PA6/SAN/SANMA system. As discussed earlier by replacing a part of SAN with rubber grafted component (SAN-g-PB) in the non-reactive system, a significant increase in melt viscosity and a yield stress were observed which resulted in change of morphology type from a dispersed to a coarse co-continuous structure. For the reactive system containing rubber, addition of the SANMA causes significant refinement of the co-continuous structure as evident from the SEM micrographs shown in . This can be explained by the reduced interfacial tension, which stabilizes the interface and the hindered coalescence. In addition, the viscosity ratio between PA6 reacted with SANMA and ABS becomes smaller but still far away from the calculated phase inversion composition (). The skeletal structure is clearly visible in the magnified micrograph.In this section we investigate how these morphological differences influence the rheological behavior of the blends. presents the melt rheological behavior of the blends containing SAN (both non-reactive and reactive blends) in combination with the pure components. From one can notice that the melt viscosity of the PA6/SAN blend follows almost a linear mixing rule. This means the viscosity of this blend is in between the viscosities of PA6 and SAN neat components. The compatibilized blend (PA6/SAN/SANMA) can be regarded as a blend of PA6 modified with SANMA (PA6/SANMA) and SAN. Its behavior is quite different as compared to the components. At low frequencies this blend shows a significant increase in viscosity. This change in behavior is related to the existence of the co-continuous structure, which can be explained by extra stresses connected with the shape relaxation. This kind of behavior is also reported by some other authors The same relationship exist for both storage modulus G′ and the loss modulus G″ as it can be seen in , respectively. The non-reactive blend shows modulus between the constituent components whereas, the reactive compatibilized blend show higher G′ and G″ values than those of the constituents components. This effect is more pronounced concerning the elastic properties clearly visible in the storage modulus values. shows the relationship between the storage modulus and the loss modulus with the frequency as a parameter for the SAN based blends. This kind of plot was introduced by Han The rheological behavior for the PA6/ABS and PA6/ABS+SANMA blends is shown in . One has to consider that these ABS based blends have much higher viscosities than the SAN based blends. As it is seen from , both the reactive and non-reactive ABS blends show viscosities between the constituents components. The reactive compatibilized blend can be considered as a combination between PA6 modified with SANMA and the ABS. Viscosities of the both ABS blends, reactive and non-reactive ones, are higher than the values expected by application of a linear mixing rule. The blends show a linear increase in viscosity with decreasing frequency, indicating the existence of a yield stress not only in the ABS but also in the blends based on ABS. Similar to the previous system, here also these changes are more pronounced in G′ as compared to the G″ values () indicates that both the compatibilized and uncompatibilized ABS blends have the same qualitative microstructure (co-continuous), as the curves are nearly the same for both the blends.This systematic study was carried out to understand the complex nature of the commercially important compatibilized PA6/ABS multicomponent blend. For this purpose, blends of PA6 with SAN and ABS, with and without compatibilizer, having PA6 content of 50 wt%, were investigated. The approach was to start with a binary blend of PA6/SAN and to add additional components one by one to reach to the final blend formulation. The effect of addition of SAN, the grafted rubber component (SAN-g-PB), the compatibilizer and the overall combined effects on the blend morphology and the melt rheology were studied. PA6/SAN blend showed a dispersed morphology with PA6 as matrix. Addition of the reactive compatibilizer led to a significant change in morphology to a co-continuous structure. The resulting changes in the melt rheological properties were also dramatic. The increase in viscosity at low frequencies indicated the existence of the co-continuous structure. PA6/ABS exhibited a coarse co-continuous structure. The formation of the co-continuous structure could not be explained based on the viscosity ratios of the components but seemed to be connected with the yield stress of the ABS due to its rubber component. Addition of the reactive compatibilizer to this system refined the co-continuous structure and increased the viscosity as well as the elasticity.Fluorinated polynorbornene dicarboximideThe effect of fluorine atoms on gas transport properties of new polynorbornene dicarboximidesThe synthesis and ring opening metathesis polymerization (ROMP) of the new N-4-trifluoromethylphenyl-norbornene-5,6-dicarboximide (2a) and N-3,5-bis(trifluoromethyl)phenyl-norbornene-5,6-dicarboximide (2b) mixtures of exo and endo monomers were performed. The gas transport properties of the corresponding polymer (Poly-2a) were determined and found to be one of the largest reported to date in glassy polynorbornene dicarboximides.The new N-4-trifluoromethylphenyl-norbornene-5,6-dicarboximide (2a) and N-3,5-bis(trifluoromethyl)phenyl-norbornene-5,6-dicarboximide (2b) mixtures of exo and endo monomers were synthesized and polymerized via ring opening metathesis polymerization (ROMP) using bis(tricyclohexylphosphine) benzylidene ruthenium(IV) dichloride (I) and tricyclohexylphosphine [1,3-bis(2,4,6-trimethylphenyl)-4,5-dihydroimidazol-2-ylidene][benzylidene] ruthenium dichloride (II) to produce the corresponding polynorbornene dicarboximides Poly-2a and Poly-2b, respectively. The transport of five gases He, N2, O2, CO2 and CH4 across membranes prepared from Poly-2a was determined at 35 °C using a constant volume permeation cell. The gas transport properties of the fluorine containing polymer Poly-2a were compared with those found for membranes from non-fluorinated poly(N-phenyl-exo-endo-norbornene-5,6-dicarboximide) (P-PhNDI). Gas permeability, diffusion and solubility coefficients of the fluorine containing polynorbornene Poly-2a were up to an order of magnitude larger than those of the non-fluorinated one. Poly-2a was found to have one of the largest gas transport coefficients reported to date in glassy polynorbornene dicarboximides.Fluorinated polynorbornene dicarboximideFluorine containing polymers have attracted much attention due to their outstanding properties. These kinds of polymer exhibit high thermostability, chemical inertness and good hydrophobicity. It is important to note that low intermolecular and intramolecular interactions in fluorine containing polymers are important factor for gas permeability properties of membranes. Thus, we have already reported gas transport properties of polynorbornenes containing adamantyl, cyclohexyl and cyclopentyl imide side chain groups N bonds in polynorbornene dicarboximides. It is expected that the introduction of fluorine atoms into polynorbornene dicarboximides will decrease interchain interactions between polar imide side chain groups and this effect will increase the gas permeability across them without detriment to the selectivity. The ROMP of norbornene derivatives with various fluorine-containing units is well established With the aim of investigating the effect of fluorine atoms on gas permeability of polynorbornene dicarboximides, the new poly(N-4-trifluoromethylphenyl-exo-endo-norbornene-5,6-dicarboximide) (Poly-2a) was synthesized and gas transport properties of membranes prepared from this polymer were studied.Monomers 2a and 2b were prepared in high yields. 4-Trifluoromethyl aniline and 3,5-bis(trifluoromethyl) aniline reacted with NDA to the corresponding amic acids (1a, 1b) which were cyclized to imides using acetic anhydride as dehydrating agent (). 1H, 13C and 19F NMR spectra and elemental analysis confirmed monomer structure and purity. The infrared spectra of monomer showed characteristic peaks at 1774 and 1706 cm−1 (asymmetric and symmetric CN stretching). ROMP of 2a and 2b using ruthenium catalysts I and II were carried out in 1,2-dichloroethane at 45 °C ( summarizes the results of the polymerizations of 2a, 2b and PhNDI, the molecular weight distribution (MWD) of the polymers Poly-2a, Poly-2b and P-PhNDI obtained using II is about Mw/Mn |
= 1.22–1.32 which is broader than polymers prepared using I (Mw/Mn |
= 1.11–1.17) due to the slower initiation of the latter catalyst Catalyst I gave polymers with predominantly trans configuration of the double bonds (75–84%), whereas catalyst II produced polymers with a mixture of cis and trans double bonds (50–56% of cis structure). shows the 1H NMR spectra of (a) monomer 2a and (b) polymer Poly-2a prepared using I. The exo and endo monomer olefinic signals at δ |
= 6.35–6.25 ppm are replaced by new signals at δ |
= 5.80–5.58 ppm, which correspond respectively to the trans and cis H at the double bonds of the product polymer.The effect that CF3 group substitutions on the pendant phenyl ring in the polynorbornene dicarboximide had on the physical properties of polynorbornenes with similar structures is compared in . The non-substituted phenyl ring polynorbornene dicarboximide, P-PhNDI, has a higher Tg and Td than the previously reported poly(exo-N-3,5-bis(trifluoromethyl)phenyl-7-oxanorbornene-5,6-dicarboximide) P-TFmPhONDI, indicate that the presence of two CF3 moieties increases density of the polynorbornene dicarboximide (P-TFmPhONDI), followed by the one with a single CF3 substitution, Poly-2a, as compared to the non-fluorine substituted polynorbornene dicarboximide, P-PhNDI. It is also reported in the fractional free volume (FFV), as calculated from Bondi's group contribution method from the following equation where V is the specific volume (1/ρ), Vo is the specific occupied volume which according to Bondi's method can be calculated from the Van der Waals volume, Vw as Vo |
= 1.3 |
Vw.FFV is a measure of the intermolecular distance between polymer chains. From FFV increases drastically with the presence of CF3 groups on the pendant phenyl moiety in the polynorbornene dicarboximides. FFV of P-TFmPhONDI is almost twice that of the non-substituted polynorbornene, P-PhNDI. The increase in FFV is related to a larger intermolecular distance between the polymer chains, which is related to an inhibition of packing by the presence of the CF3 groups.The presence of CF3 moieties in the phenyl ring of the polynorbornene dicarboximide structures becomes important for their gas permeability coefficients, see . It is seen that the polynorbornene dicarboximide with two CF3 substitutions and the larger FFV, P-TFmPhONDI, has around twice the gas permeability coefficients found for the polynorbornene dicarboximide with a single CF3 substitution, Poly-2a. While the latter has gas permeability coefficients that are with the exception of CO2 an order of magnitude higher than those of the polynorbornene dicarboximide without fluorine groups, P-PhNDI. The larger gas permeability coefficients in the CF3 substituted polynorbornenes are related to the larger FFV, which in turn facilitates the diffusion of the gas molecules through the polymer. The latter result is clearly seen by the increase in gas diffusion coefficients, D, as the number of CF3 groups increases in the polynorbornene. As a general trade off when the gas permeability coefficients increase, the gas separation capacity or ideal gas separation factor, as defined for Eq. where PA and PB are the pure gas permeability coefficients for gases A and B. In the ideal gas separation factors for the commercially important gas mixtures O2/N2 and CO2/CH4 are presented. They follow the expected trend since as the permeability coefficient increases in the polynorbornene dicarboximide, the ideal separation factor decreases. However, since the difference in gas permeability coefficients is at least one order of magnitude higher in P-TFmPhONDI, as compared to P-PhNDI the CF3 substituted polynorbornene may present an advantage for developing a technical separation where the large gas permeability coefficients will compensate for the loss in selectivity for the gas separation because the loss in selectivity is not large than 1.2.Exo(90%)-endo(10%) monomer mixtures 2a and 2b were synthesized and polymerized via ROMP using well defined ruthenium alkylidene catalysts I and II. Tg for Poly-2a was observed at 155 °C. The catalyst I produced polymers with predominantly trans configuration of the double bonds whereas catalyst II gave polymers with a mixture of cis and trans double bonds. A comparison of Poly-2a physical and gas transport properties with a non-fluorinated analogous P-PhNDI and a polynorbornene with two CF3 groups in the phenyl ring, P-TFmPhONDI, was performed. Thermal properties such as Tg and Td are lower in Poly-2a as compared to those of the analogous non-fluorinated P-PhNDI, a fact that was attributed to a larger polymer interchain distance. Density and fractional free volume are larger in the fluorine substituted polymers due to the presence of the bulky CF3 groups. The large fractional free volume found in Poly-2a as compared to the non-fluorine substituted polynorbornene, P-PhNDI, produces one of the largest permeability and diffusion coefficients found in polynorbornene dicarboximides.1H NMR, 13C NMR and 19F NMR spectra were recorded on a Varian spectrometer at 300, 75 and 300 MHz, respectively, in CDCl3. Tetramethylsilane (TMS) and trifluoroacetic acid (TFA) were used as internal standards, respectively. FT-IR spectra were obtained on a Nicolet 510 p spectrometer. Glass transition temperature, Tg, was determined in a DSC-7 Perkin Elmer Inc., at scanning rate of 10 °C/min under nitrogen atmosphere. The sample was encapsulated in a standard aluminum DSC pan. The sample was run twice in the temperature range 30–300 °C under a nitrogen atmosphere. Onset of decomposition temperature, Td, was determined using thermogravimetric analysis, TGA, which was performed at a heating rate of 10 °C/min under a nitrogen atmosphere with a DuPont 2100 instrument. Mechanical properties under tension, Young's modulus (E) and stress (σ), were measured in a Universal Mechanical Testing Machine Instron 1125–5500R using a 50 Kg cell at a crosshead speed of 10 mm/min according to the method ASTM D1708 in film samples of 0.5 mm of thickness at room temperature. Molecular weights and molecular weight distributions were determined with reference to polystyrene standards on a Varian 9012 GPC at 30 °C in chloroform using a universal column and a flow rate of 1 mL min−1. Density of the polynorbornenes was measured by the density gradient column method for films cast from solution. The gradient was established by Ca(NO3)2 solutions at 23 °C using glass standards. Films of Poly-2a, P-TFmPhONDI and P-PhNDI were cast from chloroform solutions, 5 wt.%, of each polynorbornene at room temperature. The solutions were dried overnight in a solvent atmosphere until a self-standing film developed. The films were transfer to a vacuum oven and kept at 80 °C to insure that chloroform was totally eliminated. The thickness of the films used for gas transport properties was around 75 μm.Gas transport properties were measured in a constant volume type gas permeation cell as described elsewhere Exo(90%)-endo(10%) mixture of norbornene-5,6-dicarboxylic anhydride (NDA) was prepared via Diels-Alder condensation of cyclopentadiene and maleic anhydride according to literature NDA (5 g, 30.5 mmol) was dissolved in 50 mL of dichloromethane. An amount of 4.9 g (30.4 mmol) of 4-trifluoromethylaniline in 5 mL of dichloromethane is added dropwise to the stirred solution of NDA. The reaction was maintained at reflux for 2 h and then cooled to room temperature. The precipitate was recovered by filtration and dried to give 9.7 g of amic acid 1a. The obtained amic acid 1a (9.7 g, 29.8 mmol), anhydrous sodium acetate (1.1 g, 13.6 mmol) and acetic anhydride (12.0 g, 117 mmol) were heated at 70–80 °C for 7 h and then cooled. The solid which is crystallized out on cooling was filtered, washed several times with cold water and dried in a vacuum oven at 50 °C overnight. A mixture of exo(90%) and endo(10%) monomers 2a () was obtained after two recrystallizations from ethanol: yield = 89%. m.p. = 181–183 °C.1H NMR (300 MHz, CDCl3, ppm): δ 7.74–7.26 (4H, m), 6.35 (1H, s), 6.25 (1H, s), 3.41 (2H, m), 2.87 (2H, s), 1.81–1.20 (2H, m).13C NMR (75 MHz, CDCl3, ppm): δ 176.3, 137.9, 134.6, 126.1, 52.2, 47.8, 45.8, 45.5, 42.9.19F NMR (300 MHz, CDCl3, ppm): δ |
− 62.0.Anal. Calcd. (%) for C16H12O2F3N (307): C, 62.54; H, 3.90; O, 10.42; F, 18.56; N, 4.56. Found: C, 62.84; H, 3.62; N, 4.95.NDA (5 g, 30.5 mmol) was dissolved in 50 mL of dichloromethane. An amount of 7.0 g (30.5 mmol) of 3,5-bis(trifluoromethyl) aniline in 5 mL of dichloromethane is added dropwise to the stirred solution of NDA. The reaction was maintained at reflux for 2 h and then cooled to room temperature. The precipitate was recovered by filtration and dried to give 11.5 g of amic acid 1b. The obtained amic acid 1b (11.5 g, 29.2 mmol), anhydrous sodium acetate (2.2 g, 26.8 mmol) and acetic anhydride (34.0 g, 333 mmol) were heated at 90–100 °C for 4 h and then cooled. The solid which is crystallized out on cooling was filtered, washed several times with cold water and dried in a vacuum oven at 50 °C overnight. A mixture of exo(90%) and endo(10%) monomers 2b () was obtained after two recrystallizations from hexane: yield = 92%. m.p. = 105–108 °C.N), 1337, 1286, 1181, 1129, 922, 872, 844, 751 cm−1.1H NMR (300 MHz, CDCl3, ppm): δ 7.86–7.69 (3H, m), 6.21 (2H, s), 6.31 (2H, t), 3.55–3.48 (2H, m), 2.82 (2H, s), 1.85–1.63 (2H, m).13C NMR (75 MHz, CDCl3, ppm): δ 175.8, 134.7, 132.6–120.9, 52.4, 45.6, 37.6.19F NMR (300 MHz, CDCl3, ppm): δ |
− 62.2.Anal. Calcd. (%) for C17H11O2F6N (375): C, 54.40; H, 2.93; O, 8.53; F, 30.40; N, 3.93. Found: C, 54.80; H, 2.70; N, 4.06.Polymerizations were carried out in a glass vial under a dry nitrogen atmosphere. After terminating the polymerization by addition of a small amount of ethyl vinyl ether, the solution was poured into an excess of methanol. The polymer was purified by precipitation in methanol from chloroform containing a few drops of 1N HCl. The obtained polymer was dried in a vacuum oven at 40 °C to constant weight.Monomer 2a (1.0 g, 3.25 mmol) and catalyst I (2.68 × 10−3 |
g, 0.0032 mmol) were stirred in 4.6 mL of 1,2-dichloroethane at 45 °C for 2 h (). The obtained polymer Poly-2a was soluble in chloroform and dichloromethane. The values of the number-average molecular weight, Mn, polydispersity, Mw/Mn, glass transition (Tg) and decomposition (Td) temperature of poly(N-4-trifluoromethylphenyl-exo-endo-norbornene-5,6-dicarboximide) were, respectively, Mn |
= 279,000, Mw/Mn |
= 1.11, Tg |
= 155 °C, Td |
= 402 °C.1H NMR (300 MHz, CDCl3, ppm): δ 7.73–7.26 (4H, m), 5.80 (1H, s, trans), 5.58 (1H, s, cis), 3.18 (2H, s), 2.87 (2H, s), 2.23 (1H, s), 1.70 (1H, s).13C NMR (75 MHz, CDCl3, ppm): δ 176.5, 134.8, 131.8, 130.4, 130.0, 126.4, 121.7, 50.8, 46.1.19F NMR (300 MHz, CDCl3, ppm): δ |
− 67.3.Monomer 2b (1.0 g, 2.66 mmol) and catalyst I (2.19 × 10−3 |
g, 0.0026 mmol) were stirred in 3.8 mL of 1,2-dichloroethane at 45 °C for 2 h (). The obtained polymer Poly-2b was soluble in chloroform and dichloromethane. The values of the number-average molecular weight, Mn, polydispersity, Mw/Mn, glass transition (Tg) and decomposition (Td) temperature of poly(N-3,5-bis(trifluoromethyl)phenyl-exo-endo-norbornene-5,6-dicarboximide) were, respectively, Mn |
= 341,000, Mw/Mn |
= 1.15, Tg |
= 168 °C, Td |
= 393 °C.1H NMR (300 MHz, CDCl3, ppm): δ 7.89–7.69 (3H, m), 5.85 (1H, s, trans), 5.67 (1H, s, cis), 3.46 (2H, s), 3.09 (2H, s), 2.02 (1H, s), 1.51 (1H, s).13C NMR (75 MHz, CDCl3, ppm): δ 174.0, 133.2, 132.6, 129.1, 126.4, 122.1, 120.9, 48.9, 45.3, 40.6.19F NMR (300 MHz, CDCl3, ppm): δ |
− 62.0.Environmentally assisted cracking of 18%Ni maraging steelSlow strain rate testing of notched cylindrical specimens of 18Ni2400 maraging steel has been carried out in air with 30% relative humidity and synthetic seawater environments. Peak-aged condition has been chosen, considering the relevance to engineering applications. Studies have also been carried out with different notch geometries to understand the effect of stress concentration factor. It is concluded from the study that (i) degree of stress concentration at the notch influences the notched tensile strength (ii) mild hydrogen embrittlement seems to occur in air environment, (iii) synthetic seawater environment drastically brings down the notched tensile strength and time to fracture (iv) environmentally assisted cracking occurs in air tests in quasicleavage and microvoid coalescence modes and in seawater tests in intercrystalline mode.Maraging steels, possessing the unique combination of performance characteristics – high strength, high toughness and good formability – have been widely used in aerospace, military and other critical applications. Different grades of maraging steel are commercially available covering a strength range of 1400–2400 MPa. With increasing strength level, the fracture toughness and formability decrease. Accordingly, the lower strength variants are used where high fracture toughness/ductility are important for design. The higher strength variants are used for applications where one can manage with moderate levels of fracture toughness but strength is more important. Titanium is used as the primary strengthening element in these steels and precipitation of a fine dispersion of titanium bearing intermetallic particles in martensite as a result of aging leads to a very high strength condition. Hence, the titanium level in the steel increases as one moves from low strength to high strength variants. Aging has to be optimally carried out to realize the maximum strengthening effect of the precipitates. Important developments and applications have been reviewed in 1988 Symposium It is known that environmentally assisted cracking (EAC) can lead to severe degradation of high strength steels. The higher the strength level, the more is the expected susceptibility to stress corrosion cracking (SCC) and hydrogen embrittlement (HE). The threshold stress intensity for SCC for high strength steels decreases with increasing yield strength. Increasing the yield strength of martensitic and precipitation hardening stainless steels, for example, increases the probability of cracking by SCC Maraging steels stand out for their high strength level and as such it is important to know as to what extent the phenomenon of EAC comes in the way of their usage for high load bearing structural applications. There is some published literature on EAC studies specific to maraging steels. It has been reported that the threshold stress intensity needed for SCC of maraging steels in aqueous environments decreases as yield strength increases The purpose of the present investigation is to study the susceptibility to EAC of 18Ni2400 grade maraging steel in synthetic and 30% relative humidity air environments using notched specimens and slow strain rate testing. The effect of varying notch severity on the cracking process in the two environments was also studied. Material was tested in the peak-aged condition with the corresponding strength level being the highest obtainable with the commercially available 18%Ni maraging steels. Previous researchers The 18Ni2400 grade maraging steel used in this investigation was processed through vacuum induction melting followed by vacuum arc remelting. Hot working of the resulting ingot was carried out to produce the material in the form of rods 15 mm in diameter. The chemical composition of the alloy in weight percent was 18.22 Ni, 3.94 Mo, 1.57 Ti, 0.1 Al, 0.003 C, 0.1 Si, 0.1 Mn, 0.001 S, 0.006 P and balance Fe. The material was in the solution annealed condition with a hardness level of 331 BHN (35.5 HRC).The drawing of the notched tensile specimen adopted in this study is shown in . Specimens with different values of stress concentration factor (Kt) in the range 2.82–4.80 were prepared from the rod material in the solution annealed condition. The Kt factor was derived from . After the specimens were machined, peak aging treatment was given to them. The treatment comprised of 3.5 soaking hours at 510 °C. Viswanathan et al. carried out detailed Transmission Electron Microscopy of this grade of steel and concluded that two types of precipitates exist in the peak-aged condition – rod shaped Ni3 (Ti, Mo) and spherical Fe2Mo intermetallic phases The tests were carried out in two environments: (i) air having a relative humidity of ∼30% (henceforth referred to as 30% RH air) (ii) synthetic seawater. The seawater has been prepared by the method devised by Kester et al. The susceptibility to cracking in synthetic seawater has been calculated as the fractional loss of NTS in seawater environment compared to air environment as shown below:NTS loss=[NTS(in air)-NTS(in synthetic seawater)]NTS(in air)The susceptibility to cracking in synthetic seawater has also been calculated as the fractional drop (tf) in seawater compared to air environment:tf=tf(in air)-tf(in synthetic water)]tf(in air)Tensile fractured specimens were examined in a scanning electron microscope (SEM) to get information about crack initiation sites and mode of fracture.For the tests carried out at the strain rate of 4.17 × 10−6 |
s−1, the NTS has been plotted in as a function of the Kt. There appears to be a decreasing trend of NTS with increasing Kt. INCO has published results of a similar study carried out on 18Ni1700, a lower strength variant of 18%Ni maraging steel shows the three data points experimentally obtained in the phase field of strain rate vs. NTS for samples with Kt of 3.35 tested in 30% RH air. There appears to be a decreasing tendency of NTS with decreasing strain rate. More data points would enable to reach a definitive conclusion. It is seen that the test carried at the lowest strain rate has given the lowest NTS of all the tests carried out in 30% RH air in this study.Fractographic examination of fracture surfaces revealed that crack initiation occurred at the root of the notch. The dependence of NTS on Kt can be explained by assuming that hydrogen in the environment is playing a role in the fracture process. A higher Kt associated with the root of the notch is expected to lead to a higher degree of accumulation of atomic hydrogen at the notch tip, higher degree of embrittlement and consequently lower applied stress level at which failure occurs. Hardie and Liu The apparent dependence of NTS on strain rate can also be explained based on the assumption that hydrogen is playing a role in the fracture mechanism. It has been well documented for the high strength steels that the extent of HE increases with decreasing strain rate The question then to be answered is whether HE of 18Ni2400 steel is possible in 30% RH air environment. There are several pieces of evidence to support the view point that it is possible. For the lower strength cobalt-free 18%Ni maraging steel T-250 (yield strength ∼ 1700 MPa), Zhang et al. concluded shows the NTS value as a function of strain rate for tests carried out on specimens with Kt in the range – 3.04–3.09. This range being narrow, effect of variation in Kt on NTS can be ignored as far as results in are concerned. There are test results available on two specimens for the intermediate strain rate 8.33 × 10−7 |
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