Crystal plasticity finite element simulations on extruded Mg-10Gd rod with texture gradient

The mechanical properties of an extruded Mg-10Gd sample, specifically designed for vascular stents, are crucial for predicting its behavior under service conditions. Achieving homogeneous stresses in the hoop direction, essential for characterizing vascular stents, poses challenges in experimental testing based on standard specimens featuring a reduced cross section. This study utilizes an elasto-visco-plastic self-consistent polycrystal model(ΔEVPSC) with the predominant twinning reorientation(PTR) scheme as a numerical tool, offering an alternative to mechanical testing. For verification, various mechanical experiments, such as uniaxial tension, compression, notched-bar tension, three-point bending, and C-ring compression tests, were conducted. The resulting force vs. displacement curves and textures were then compared with those based on the ΔEVPSC model. The computational model's significance is highlighted by simulation results demonstrating that the differential hardening along with a weak strength differential effect observed in the Mg-10Gd sample is a result of the interplay between micromechanical deformation mechanisms and deformation-induced texture evolution. Furthermore, the study highlights that incorporating the axisymmetric texture from the as-received material incorporating the measured texture gradient significantly improves predictive accuracy on the strength in the hoop direction. Ultimately, the findings suggest that the ΔEVPSC model can effectively predict the mechanical behavior resulting from loading scenarios that are impossible to realize experimentally, emphasizing its valuable contribution as a digital twin.

Grain statistics effect on deformation behavior in asymmetric rolling of pure copper foil by crystal plasticity finite element model

The grain statistics effect was investigated through asymmetric rolling of pure copper foil by a realistic polycrystalline aggregates model and crystal plasticity element finite model.A polycrystalline aggregate model was generated and a crystal plasticity-based finite element model was developed for each grain and the specimen as a whole.The crystal plasticity model itself is rate dependent and accounts for local dissipative hardening effects and the original orientation of each grain was generated based on the orientation distribution function（ODF）.The deformation behaviors,including inhomogeneous material flow,decrease of contact press and roll force with the increase of grain size for the constant size of specimens,were studied.It is revealed that when the specimens are composed of only a few grains across thickness,the grains with different sizes,shapes and orientations are unevenly distributed in the specimen and each grain plays a significant role in micro-scale plastic deformation and leads to inhomogeneous deformation and the scatter of experimental and simulation results.The slip system activity was examined and the predicted results are consistent with the surface layer model.The slip band is strictly influenced by the misorientation of neighbor grain with consideration of slip system activity.Furthermore,it is found that the decrease of roll force and the most active of slip system in surface grains are caused by the increase of free surface grain effect when the grain size is increased.The results of the physical experiment and simulation provide a basic understanding of micro-scaled plastic deformation behavior in asymmetric foil rolling.

Deformation mechanism of cold ring rolling in view of texture evolution predicted by a newly proposed polycrystal plasticity model

An explicit polycrystal plasticity model was proposed to investigate the deformation mechanism of cold ring rolling in view of texture evolution. The model was created by deducing a set of linear incremental controlling equations within the framework of crystal plasticity theory. It was directly solved by a linear algorithm within a two-level procedure so that its efficiency and stability were guaranteed. A subroutine VUMAT for ABAQUS/Explicit was developed to combine this model with the 3D FE model of cold ring rolling. Results indicate that the model is reliable in predictions of stress-strain response and texture evolution in the dynamic complicated forming process; the shear strain in RD of the ring is the critical deformation mode according to the sharp Goss component （{110}？100？） of deformed ring; texture and crystallographic structure of the ring blank do not affect texture type of the deformed ring;texture evolves rapidly at the later stage of rolling, which results in a dramatically increasing deformation of the ring.

Micro-bending of metallic crystalline foils by non-local dislocation density based crystal plasticity finite element model

A non-local dislocation density based crystal plasticity model, which takes account of the microstrncture inhomogeneity, was used to investigate the micro-bending of metallic crystalline foils. In this model, both statistically stored dislocations （SSDs） and geometrically necessary dislocations （GNDs） are taken as the internal state variables. The strain gradient hardening in micro-bending of single-grained metal foils was predicted by evolution of GNDs. The predicted results were compared with the micro-hardness distribution of the previous micro-bending experiments of CuZn37 a-brass foils with coarse grains and fine grains. Comparison of the simulated dislocation densities distribution of SSDs and GNDs with the experimental results shows that different micro-hardness distribution patterns of the coarse and fine grain foils can be attributed to the corresponding SSDs and GNDs distributions. The present model provides a physical insight into the deformation mechanism and dislocation densities evolution of the micro-bending process.

Scale effect mechanism on micro rod upsetting deformation analyzed by crystal plasticity model

To analyze the effect of single grain deformation behaviors on microforming process, a crystal plasticity model was developed considering grains at free surface layer as single grains. Based on the rate-dependent crystal plasticity theory, the analysis of the scale effect mechanism on upsetting deformation of micro rods was performed with respect to specimen dimension, original grain orientation and its distribution. The results show that flow stress decreases significantly with the scaling down of the specimen. The distribution of the grain orientation has an evident effect on flow stress of the micro specimen, and the effect becomes smaller with the progress of plastic deformation. For the anisotropy of single grains, inhomogeneous deformation occurs at the surface layer, which leads to the increase of surface roughness, especially for small specimens. The effect of grain anisotropy on the surface topography can be decreased by the transition grains. The simulation results are validated by upsetting deformation experiments. This indicates that the developed model is suitable for the analysis of microforming processes with characteristics, such as scale dependency, scatter of flow stress and inhomogeneous deformation.

Application of crystal plasticity modeling in equal channel angular extrusion

Some applications of crystal plasticity modeling in equal channel angular extrusion（ECAE） of face-centered cubic metals were highlighted.The results show that such simulations can elucidate the dependency of grain refinement efficiency on processing route and the directionality of substructure development,which cannot be explained by theories that consider only the macroscopic deformation behavior.They can also capture satisfactorily the orientation stability and texture evolution under various processing conditions.It is demonstrated that crystal plasticity models are useful tools in exploring the crystallographic nature of grain deformation and associated behavior that are overlooked or sometimes erroneously interpreted by existing phenomenological theories.

High-energy x-ray diffraction study on phase transition asymmetry of plastic crystal neopentylglycol

As a prototype material of colossal barocaloric effects, neopentylglycol is investigated by combining high-precision differential scanning calorimetric measurement and high-energy x-ray diffraction measurement. The diffraction data at constant temperatures indicate a first-order phase transition with thermal hysteresis as well as the phase transition asymmetry,specifically, the phase transition is completed faster at cooling than at heating. The analysis of resulting pair distribution function confirms the intermolecular disorder in the high-temperature phase. The phase transition asymmetry is quantitatively characterized by time-resolved x-ray diffraction, which is in agreement with the thermal measurement. Also, such an asymmetry is observed to be suppressed at high pressures.

Simulation of mechanical behavior of AZ31 magnesium alloy during twin-dominated large plastic deformation

Experiments and visco-plastic self-consistent (VPSC) simulations were used to quantify the amount of twinning and the relationship to stress?strain behavior in a textured Mg?3Al?1Zn plate. Two different compression directions were utilized to favor{1012} extension or{1011} compression twinning.{1012} twins nucleate at the beginning of plastic deformation and grow to consume the parent grains completely. During compression along the normal direction,{1011} twinning and{1011}?{1012} double twinning start at strain of 0.05, and the number of twins increases until rupture, above strain of 0.15.{1011} and{1011}?{1012} twinning also occur during compression along the transverse direction, start at strain of 0.06 and then multiply in grains totally reoriented by{1012} twins. Using suitable parameters, the VPSC model can accurately predict the occurrence of extension, compression and double-twinning as well as the flow stresses and deformed textures. According to VPSC simulations, twinning and slip have the same latent hardening parameters.

Investigation of the alloying effect on deformation behavior in Mg by Visco-Plastic Self-Consistent modeling

Alloying elements can drastically alter the deformation behavior of Mg.In the present work,Visco-Plastic Self-Consistent(VPSC)modeling was employed to investigate the effect of alloying elements on Mg’s tensile behavior,in particular the relative activity of different slip and twinning modes.Mg-0.47 wt.%Ca,Mg-2 wt.%Nd,and AZ31 extruded alloys were deformed by micro-tensile tests in a scanning electron microscope(SEM).Texture and grain size measured by electron backscatter diffraction(EBSD)were used as the input for VPSC.After parameter optimization,the VPSC model successfully reproduced the stress-strain curve of each alloy.Simulation results indicate that the slip/twinning activity in the three alloys are different.Mg-0.47 wt.%Ca shows strong extrusion texture,and prismatic slip was quite active during its tensile deformation.In contrast,Mg-2 wt.%Nd shows weak extrusion texture,and basal slip was dominant.This alloy also developed more twinning activity than the other two alloys.AZ31 shows strong extrusion texture similar as Mg-0.47 wt.%Ca,but prismatic slip was less active in it.The slip/twinning activity revealed by the VPSC model can explain the difference in the tensile behavior of the three alloys.

Prediction of grain scale plasticity of NiTi shape memory alloy based on crystal plasticity finite element method

Grain scale plasticity of NiTi shape memory alloy(SMA)during uniaxial compression deformation at 400℃was investigated through two-dimensional crystal plasticity finite element simulation and corresponding analysis based on the obtained orientation data.Stress and strain distributions of the deformed NiTi SMA samples confirm that there exhibits a heterogeneous plastic deformation at grain scale.Statistically stored dislocation(SSD)density and geometrically necessary dislocation(GND)density were further used in order to illuminate the microstructure evolution during uniaxial compression.SSD is responsible for sustaining plastic deformation and it increases along with the increase of plastic strain.GND plays an important role in accommodating compatible deformation between individual grains and thus it is correlated with the misorientation between neighboring grains,namely,a high GND density corresponds to large misorientation between grains and a low GND density corresponds to small misorientation between grains.

Effect of microvoids on microplasticity behavior of dual-phase titanium alloy under high cyclic loading(Ⅰ):Crystal plasticity analysis

A crystal plasticity finite element(CPFE)model was established and 2D simulations were carried out to study the relationship between microvoids and the microplasticity deformation behavior of the dual-phase titanium alloy under high cyclic loading.Results show that geometrically necessary dislocations(GND)tend to accumulate around the microvoids,leading to an increment of average GND density.The influence of curvature in the tip plastic zone(TPZ)on GND density is greater than that of the size of the microvoid.As the curvature in TPZ and the size of the microvoid increase,the cumulative shear strain(CSS)in the primaryα,secondaryα,andβphases increases.Shear deformation in the prismatic slip system is dominant in the primaryαphase.As the distance between the microvoids increases,the interactive influence of the microvoids on the cumulative shear strain decreases.

Quasi-solid-state polymer plastic crystal electrolyte for subzero lithium-ion batteries

Succinonitrile(SN)-based polymer plastic crystal electrolytes(PPCEs)have attracted considerable attention as solid-state electrolytes owing to their high ionic conductivities similar to those of liquid electrolytes,excellent contacts with the electrodes,and good mechanic properties.As a crucial property of a solid-state electrolyte,the ionic conductivity of the PPCE directly depends on the interactions between the constituent parts including the polymer,lithium salt,and SN.A few studies have focused on the effects of polymer–lithium–salt and polymer–SN interactions on the PPCE ionic conductivity.Nevertheless,the impact of the lithium–salt–SN combination on the PPCE ionic conductivity has not been analyzed.In particular,tuning of the lithium-salt–SN interaction to fabricate a subzero PPCE with a high low-temperature ionic conductivity has not been reported.In this study,we design and fabricate five PPCE membranes with different weight ratios of Li N(SO2 CF3)2(Li TFSI)and SN to investigate the effect of the Li TFSI–SN interaction on the PPCE ionic conductivity.The ionic conductivities of the five PPCEs are investigated in the temperature range of–20 to 60°C by electro-chemical impedance spectroscopy.The interaction is analyzed by Fourier-transform infrared spectroscopy,Raman spectroscopy,and differential scanning calorimetry.The Li TFSI–SN interaction significantly influences the melting point of the PPCE,dissociation of the Li TFSI salt,and thus the PPCE ionic conductivity.By tuning the Li TFSI–SN interaction,a subzero workable PPCE membrane having an excellent low-temperature ionic conductivity(6×10-4 S cm–1 at 0°C)is obtained.The electro-chemical performance of the optimal PPCE is evaluated by using a Li Co O2/PPCE/Li4 Ti5 O12 cell,which confirms the application feasibility of the proposed quasisolid-state electrolyte in subzero workable lithium-ion batteries.

CRYSTALLOGRAPHIC HOMOGENIZATION FINITE ELEMENT METHOD AND ITS APPLICATION ON SIMULATION OF EVOLUTION OF PLASTIC DEFORMATION INDUCED TEXTURE

A crystallographic homogenization method is proposed and implemented to predict the evolution of plastic deformation induced texture and plastic anisotropy （earring） in the stamping of polycrystalline sheet metals. The microscopic inhomogeneity of crystal aggregate has been taken into account with the microstructure made up of a representative aggregate of single crystal grains. Multi-scale analysis is performed by coupling the microscopic crystal plasticity with the macroscopic continuum response through the present homogenization procedure. The macroscopic stress is defined as the volume average of the corresponding microscopic crystal aggregations, which simultaneously satisfies the equation of motion in both micro- and macro-states. The proposed numerical implementation is based on a finite element discretization of the macrocontinuum, which is locally coupled at each Gaussian point with a finite element discretization of the attached micro-structure. The solution strategy for the macro-continuum and the pointwiseattached micro-structure is implemented by the simultaneous employment of dynamic explicit FE formulation. The rate-dependent crystal plasticity model is used for the constitutive description of the constituent single crystal grains. It has been confirmed that Taylor＇s constant strain homogenization assumption yields an undue concentration of the preferred crystal orientation compared with the present homogenization in the prediction of texture evolution, with the latter having relaxed the constraints on the crystal grains. Two kinds of numerical examples are presented to demonstrate the capability of the developed code： 1） The texture evolution of three representative deformation modes, and 2） Plastic anisotropy （earring） prediction in the hemispherical cup deep drawing process of aluminum alloy A5052 with initial texture. By comparison of simulation results with those obtained employing direct crystal plasticity calculation adopting Taylor assumption, conclusions are drawn that the proposed dynamic explicit crystallographic homogenization FEM is able to more accurately predict the plastic deformation induced texture evolution and plastic anisotropy in the deep drawing process.

Simulation of lattice orientation effects on void growth and coalescence by crystal plasticity

A three dimensional rate-dependent crystal plasticity model is applied to study the influence of crystal orientation and grain boundary on the void growth and coalescence. The 3D computational model is a unit cell including one sphere void or two sphere voids. The results of three different orientations for single crystal and bicrystals are compared. It is found that crystallographic orientation has noticeable influences on the void growth directionvoid shape, and void coalescence of single crystal. The void growth rate of bicrystals depends on the crystallographic orientations and grain boundary direction.

Simulation of strain induced abnormal grain growth in aluminum alloy by coupling crystal plasticity and phase field methods

A mesoscale modeling methodology is proposed to predict the strain induced abnormal grain growth in the annealing process of deformed aluminum alloys. Firstly, crystal plasticity finite element(CPFE) analysis is performed to calculate dislocation density and stored deformation energy distribution during the plastic deformation. A modified phase field(PF) model is then established by extending the continuum field method to consider both stored energy and local interface curvature as driving forces of grain boundary migration. An interpolation mapping approach is adopted to transfer the stored energy distribution from CPFE to PF efficiently. This modified PF model is implemented to a hypothetical bicrystal firstly for verification and then the coupled CPFE-PF framework is further applied to simulating the 2D synthetic polycrystalline microstructure evolution in annealing process of deformed AA3102 aluminum alloy.Results show that the nuclei with low stored energy embedded within deformed matrix tend to grow up, and abnormal large grains occur when the deformation is close to the critical plastic strain, attributing to the limited number of recrystallized nuclei and inhomogeneity of the stored energy.

ON PLASTIC ANISOTROPY OF CONSTITUTIVE MODELFOR RATE-DEPENDENT SINGLE CRYSTAL

An algorithm for single crystals was developed and implemented to simulate plastic anisotropy using a rate-dependent slip model. The proposed procedure was a slightly modified form of single crystal constitutive model of Sarma and Zacharia. Modified Euler method, together with Newton-Raphson method was used to integrate this equation which was stable and efficient. The model together with the developed algorithm was used to study three problems. First, plastic anisotropy was examined by simulating the crystal deformation in tension and plane strain compression, respectively. Secondly, the orientation effect of some material parameters in the model and applied strain rate on plastic anisotropy for single crystal also is investigated. Thirdly, the influence of loading direction on the active slip system was discussed.

Poly(carbonate)-based ionic plastic crystal fast ion-conductor for solid-state rechargeable lithium batteries

Liquid plasticizers with a relatively higher dielectric coefficient like ethylene carbonate(EC),propylene carbonate(PC),and ethyl methyl carbonate(EMC) are the most commonly used electrolyte materials in commercial rechargeable lithium batteries(LIBs) due to their outstanding dissociation ability to lithium salts.However,volatility and fluidity result in their inevitable demerits like leakage and potential safety problem of the final LIBs.Here we for the first time device a subtle method to prepare a novel thermal-stable and non-fluid poly(carbonate) solid-state electrolyte to merge EC with lithium carriers.To this aim,a series of carbonate substituted imidazole ionic plastic crystals(G-NTOC) with different polymerization degrees have been synthesized.The resulting G-NTOC shows an excellent solid-state temperature window(R.T.-115℃).More importantly,the maximum ionic conductivity and lithium transference number of the prepared G-NTOC reach 0.36 × 10^(-3) S cm^(-1) and 0.523 at 30℃,respectively.Galvanostatic cycling test results reveal that the developed G-NTOC solid-state electrolytes are favorable to restraining the growth of lithium dendrite due to the excellent compatibility between the electrode and the produced plastic crystal electrolyte.The fabricated LiIG-NTOCILiFeP04 all-solid-state cell initially delivers a maximum discharge capacity of 152.1 mAh g^(-1) at the discharge rate of 0.1 C.After chargingdischarging the cell for 60 times,Coulombic efficiency of the solid-state cell still exceeds 97%.Notably,the LiIG-NTOCILiFeP04 cell can stably light a commercial LED with a rated power of 0.06 W for more than1 h at 30℃,and the output power nearly maintains unchanged with the charging-discharging cycling test,implying a sizeable potential application in the next generation of solid-state LIBs.

An explicit integration scheme for hypo-elastic viscoplastic crystal plasticity

An explicit integration scheme for rate-dependent crystal plasticity （CP） was developed. Additive decomposition of the velocity gradient tensor into lattice and plastic parts is adopted for describing the kinematics; the Cauchy stress is calculated by using a hypo-elastic formulation, applying the Jaumann stress rate. This CP scheme has been implemented into a commercial finite element code （CPFEM）. Uniaxial compression and roiling processes were simulated. The results show good accuracy and reliability of the integration scheme. The results were compared with simulations using one hyper-elastic CPFEM implementation which involves multiplicative decomposition of the deformation gradient tensor. It is found that the hypo-elastic implementation is only slightly faster and has a similar accuracy as the hyper-elastic formulation.

A combined experimental and crystal plasticity study of grain size effects in magnesium alloys

This work presents a method to incorporate the micro Hall-Petch equation into the crystal plasticity finite element(CPFE) framework accounting for the microstructural features to understand the coupling between grain size, texture, and loading direction in magnesium alloys.The effect of grain size and texture is accounted for by modifying the slip resistances of individual basal and prismatic systems based on the micro Hall-Petch equation. The modification based on the micro Hall-Petch equation endows every slip system at each microstructural point with a slip system-level grain size and maximum compatibility factor, which are in turn used to modify the slip resistance. While the slip-system level grain size is a measure of the grain size, the maximum compatibility factor encodes the effect of the grain boundary on the slip system resistance modification and is computed based on the Luster-Morris factor. The model is calibrated using experimental stress-strain curves of Mg-4Al samples with three different grain sizes from which the Hall-Petch coefficients are extracted and compared with Hall-Petch coefficients predicted using original parameters from previous work. The predictability of the model is then evaluated for a Mg-4Al sample with different texture and three grain sizes subjected to loading in different directions. The calibrated parameters are then used for some parametric studies to investigate the variation of Hall-Petch slope for different degrees of simulated spread in basal texture,variation of Hall-Petch slope with loading direction relative to basal poles for a microstructure with strong basal texture, and variation of yield strength with change in grain morphology. The proposed approach to incorporate the micro Hall-Petch equation into the CPFE framework provides a foundation to quantitatively model more complicated scenarios of coupling between grain size, texture and loading direction in the plasticity of Mg alloys.

Geometrically-Compatible Dislocation Pattern and Modeling of Crystal Plasticity in Body-Centered Cubic(BCC)Crystal at Micron Scale Dedicated to Professor Karl Stark Pister for his 95th birthday

The microstructure of crystal defects,e.g.,dislocation patterns,are not arbitrary,and it is possible that some of them may be related to the microstructure of crystals itself,i.e.,the lattice structure.We call those dislocation patterns or substructures that are related to the corresponding crystal microstructure as the Geometrically Compatible Dislocation Patterns(GCDP).Based on this notion,we have developed a Multiscale Crystal Defect Dynamics(MCDD)to model crystal plasticity without or with minimum empiricism.In this work,we employ the multiscale dislocation pattern dynamics,i.e.,MCDD,to simulate crystal plasticity in body-centered cubic(BCC)single crystals,mainlyα-phase Tantalum(α-Ta)single crystals.The main novelties of the work are:(1)We have successfully simulated crystal plasticity at micron scale without any empirical parameter inputs;(2)We have successfully employed MCDD to perform direct numerical simulation of inelastic hysteresis of the BCC crystal;(3)We have used MCDD crystal plasticity model to demonstrate the size-effect of crystal plasticity and(4)We have captured cross-slip which may lead to size-effect.