Three-dimensional crystal plasticity and HR-EBSD analysis of the local stress-strain fields induced during twin propagation and thickening in magnesium alloys

Present work focuses on analysis of the stress and strain fields inside and around the individual {10–12} twin in magnesium alloy. The 3D crystal plasticity model represents twin as an ellipsoidal inclusion surrounded by the matrix. Five different twin thicknesses and three different lateral twin lengths are used for stress/strain analysis. The simulations are complemented with experimental observations using high-resolution electron backscattered diffraction. The simulations and experiments show a similar distribution of the shear stress and the spatial activity of individual slip systems(basal, prismatic, pyramidal). Plasticity induced inside the twin is dominantly caused by the prismatic dislocations slip and does not influence twin back stress which is identical to pure elastic twin. The twin with larger lateral dimension requires lower equilibrium stress which suggests anisotropic twin propagation and increased thickness of such twins. The lateral twin propagation is mostly influenced by prismatic and pyramidal slip in the twin vicinity. The twin thickness can reach a maximal level that is driven by the critical resolved shear stress values for dislocation slip with the significant influence of basal slip.

The Influence of Crystallographic Orientation and Grain Boundary on Nanoindentation Behavior of Inconel 718 Superalloy Based on Crystal Plasticity Theory

The crystal plasticity finite element method(CPFEM)is widely used to explore the microscopic mechanical behavior of materials and understand the deformation mechanism at the grain-level.However,few CPFEM simulation studies have been carried out to analyze the nanoindentation deformation mechanism of polycrystalline materials at the microscale level.In this study,a three-dimensional CPFEM-based nanoindentation simulation is performed on an Inconel 718 polycrystalline material to examine the influence of different crystallographic parameters on nanoindentation behavior.A representative volume element model is developed to calibrate the crystal plastic constitutive parameters by comparing the stress-strain data with the experimental results.The indentation force-displacement curves,stress distributions,and pile-up patterns are obtained by CPFEM simulation.The results show that the crystallographic orientation and grain boundary have little influence on the force-displacement curves of the nanoindentation,but significantly influence the local stress distributions and shape of the pile-up patterns.As the difference in crystallographic orientation between grains increases,changes in the pile-up patterns and stress distributions caused by this effect become more significant.In addition,the simulation results reveal that the existence of grain boundaries affects the continuity of the stress distribution.The obstruction on the continuity of stress distribution increases as the grain boundary angle increases.This research demonstrates that the proposed CPFEM model can well describe the microscopic compressive deformation behaviors of Inconel 718 under nanoindentation.

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.

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.

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.

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.

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.

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.

Inspection of free energy functions in gradient crystal plasticity

The dislocation density tensor computed as the cud of plastic distortion is regarded as a new constitutive variable in crystal plasticity. The dependence of the free energy function on the dislocation density tensor is explored starting from a quadratic ansatz. Rank one and logarithmic dependencies are then envisaged based on considerations from the statistical theory of dislocations. The rele- vance of the presented free energy potentials is evaluated from the corresponding analytical solutions of the periodic two-phase laminate problem under shear where one layer is a single crystal material undergoing single slip and the second one remains purely elastic.

Plastic deformation modelling of tempered martensite steel block structure by a nonlocal crystal plasticity model

The plastic deformations of tempered martensite steel representative volume elements with different martensite block structures have been investi- gated by using a nonlocal crystal plasticity model which considers isotropic and kinematic hardening produced by plastic strain gradients. It was found that pro- nounced strain gradients occur in the grain boundary region even under homo- geneous loading. The isotropic hardening of strain gradients strongly influences the global stress-strain diagram while the kinematic hardening of strain gradi- ents influences the local deformation behaviour. It is found that the additional strain gradient hardening is not only dependent on the block width but also on the misorientations or the deformation incompatibilities in adjacent blocks.

Temperature-dependent constitutive modeling of a magnesium alloy ZEK100 sheet using crystal plasticity models combined with in situ high-energy X-ray diffraction experiment

A multiscale crystal plasticity model accounting for temperature-dependent mechanical behaviors without introducing a larger number of unknown parameters was developed.The model was implemented in elastic-plastic self-consistent(EPSC)and crystal plasticity finite element(CPFE)frameworks for grain-scale simulations.A computationally efficient EPSC model was first employed to estimate the critical resolved shear stress and hardening parameters of the slip and twin systems available in a hexagonal close-packed magnesium alloy,ZEK100.The constitutive parameters were thereafter refined using the CPFE.The crystal plasticity frameworks incorporated with the temperature-dependent constitutive model were used to predict stress–strain curves in macroscale and lattice strains in microscale at different testing temperatures up to 200℃.In particular,the predictions by the crystal plasticity models were compared with the measured lattice strain data at the elevated temperatures by in situ high-energy X-ray diffraction,for the first time.The comparison in the multiscale improved the fidelity of the developed temperature-dependent constitutive model and validated the assumption with regard to the temperature dependency of available slip and twin systems in the magnesium alloy.Finally,this work provides a time-efficient and precise modeling scheme for magnesium alloys at elevated temperatures.

Modeling texture development during cold rolling of IF steel by crystal plasticity finite element method

With the consideration of slip deformation mechanism and various slip systems of body centered cubic （BCC） metals, Taylor-type and finite element polycrystal models were embedded into the commercial finite element code ABAQUS to realize crystal plasticity finite element modeling, based on the rate dependent crystal constitutive equations. Initial orientations measured by electron backscatter diffraction （EBSD） were directly input into the crystal plasticity finite element model to simulate the develop- ment of rolling texture of interstitial-free steel （IF steel） at various reductions. The modeled results show a good agreement with the experimental results. With increasing reduction, the predicted and experimental rolling textures tend to sharper, and the results simulated by the Taylor-type model are stronger than those simulated by finite element model.＇Conclusions are obtained that rolling textures calculated with 48 { 110} 〈 111 〉＋ { 112 } 〈 111〉＋ { 123 } 〈 111 〉 slip systems are more approximate to EBSD results.

Texture evolution and inhomogeneous deformation of polycrystalline Cu based on crystal plasticity finite element method and particle swarm optimization algorithm

Texture evolution and inhomogeneous deformation of polycrystalline Cu during uniaxial compression are investigated at the grain scale by combining crystal plasticity finite element method(CPFEM) with particle swarm optimization(PSO) algorithm. The texture-based representative volume element(TBRVE) is used in the crystal plasticity finite element model, where a given number of crystallographic orientations are obtained by means of discretizing the orientation distribution function(ODF) based on electron backscattered diffraction(EBSD) experiment data. Three-dimensional grains with different morphologies are generated on the basis of Voronoi tessellation. The PSO algorithm plays a significant role in identifying the material parameters and saving computational time. The macroscopic stress–strain curve is predicted based on CPFEM, where the simulation results are in good agreement with the experimental ones. Therefore, CPFEM is a powerful candidate for capturing the texture evolution and clarifying the inhomogeneous plastic deformation of polycrystalline Cu. The simulation results indicate that the <110> fiber texture is generated finally with the progression of plastic deformation. The inhomogeneous distribution of rotation angles lays the foundation for the inhomogeneous deformation of polycrystalline Cu in terms of grain scale.

Simulation of polycrystalline aluminum tensile test with crystal plasticity finite element method

The crystal plasticity was implemented in the finite element method(FEM) software ABAQUS through the user subroutine UMAT. By means of discretizing the space at the grain level with the Voronoi diagram method, a polycrystal model was built and used in the FEM analysis. The initial orientation of each grain was generated based on the orientation distribution function(ODF). The developed model was successfully applied in simulation of polycrystalline aluminium samples deformed by the tensile tests. The theoretical strain—stress relation was in good agreement with the experimental result. The simulation results show that the grain size has significant effect on the deformation behavior. The initial plastic deformation usually occurs at grain boundaries, and multiple slip often results in an enhanced local hardening at grain boundaries.