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.

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.

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.

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.

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.

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.

Thermo-kinetic characteristics on stabilizing hetero-phase interface of metal matrix composites by crystal plasticity finite element method

Using dislocation-based constitutive modeling in three-dimension crystal plasticity finite element(3D CPFE)simulations,co-deformation and instability of hetero-phase interface in different material systems were herein studied for polycrystalline metal matrix composites(MMCs).Local stress and strain fields in two types of 3layer MMCs such as fcc/fcc Cu-Ag and fcc/bcc Cu-Nb have been predicted under simple compressive deformations.Accordingly,more severe strain-induced interface instability can be observed in the fcc/bcc systems than in the fcc/fcc systems upon refining to metallic nanolayered composites(MNCs).By detailed analysis of stress and strain localization,it has been demonstrated that the interface instability is always accompanied by high-stress concentration,i.e.,thermodynamic characteristics,or high strain prevention i.e.,kinetic characteristics,at the hetero-phase interface.It then follows that the thermodynamic driving forceG and the kinetic energy barrier Q during dislocation and shear banding can be adopted to classify the deformation modes,following the so-called thermo-kinetic correlation.Then by inserting a high density of high-energy interfaces into the Cu-Nb composites,such thermo-kinetic integration at the hetero-phase interface allows a successful establishment of MMCs with the high△G-high Q deformation mode,which ensures high hardening and uniform strain distri-bution,thus efficiently suppressing the shear band,stabilizing the hetero-phase interface,and obtaining an exceptional combination in strength and ductility.Such hetero-phase interface chosen by a couple of thermodynamics and kinetics can be defined as breaking the thermo-kinetic correlation and has been proposed for artificially designing MNCs.

A Cyclic Constitutive Model Based on Crystal Plasticity for Body-Centered Cubic Cyclic Softening Metals

Under the framework of the small deformation crystal plasticity theory,a crystal plastic cyclic constitutive model for body-centered cubic(BCC)cyclic softening polycrystalline metals is established.The constitutive model introduces the isotropic softening rule that includes two different mechanisms:namely softening under monotonic deformation and softening under cyclic deformation on each slip system.Meanwhile,a modified Armstrong-Frederick nonlinear kinematic hardening rule is adopted.The appropriate explicit scale transition rule is selected to extend the single crystal constitutive model to the polycrystalline constitutive model.Then the model is used to predict the uniaxial and multiaxial ratcheting deformation of BCC axle steel EA4T to verify the rationality of the proposed model.The simulation results indicate that the newly established crystal plasticity model can not only describe the cyclic softening characteristics of BCC axle steel EA4T well,but also reasonably describe the evolution laws of uniaxial ratcheting and nonproportional multiaxial ratcheting deformation.Moreover,the established crystal plastic cyclic constitutive model can reasonably predict the ratcheting behavior of BCC single crystal as well.

Mechanical Anisotropy of Selective Laser Melted Ti-6Al-4V Using a Reduced-order Crystal Plasticity Finite Element Model

In this study,a reduced-order crystal plasticity finite element(CPFE)model was developed to study the effects of the microstructural morphology and crystallographic texture on the mechanical anisotropy of selective laser melted(SLMed)Ti-6Al-4V.First,both hierarchical and equiaxed microstructures in columnar prior grains were modeled to examine the influence of the microstructural morphology on mechanical anisotropy.Second,the effects of crystallographic anisotropy and textural variability on mechanical anisotropy were investigated at the granular and representative volume element(RVE)scales,respectively.The results show that hierarchical and equiaxed CPFE models with the same crystallographic texture exhibit the same mechanical anisotropy.At the granular scale,the significance of crystallographic anisotropy varies with different crystal orientations.This indicates that the present SLMed Ti-6Al-4V sample with weak mechanical anisotropy resulted from the synthetic effect of crystallographic anisotropies at the granular scale.Therefore,combinations of various crystallographic textures were applied to the reduced-order CPFE model to design SLMed Ti-6Al-4V with different mechanical anisotropies.Thus,the crystallographic texture is considered the main controlling variable for the mechanical anisotropy of SLMed Ti-6Al-4V in this study.

Analysis of the mechanism of orientations evolution during hot rolling and mechanical properties of TiBw/TA15 composites based on crystal plasticity finite element model

An in-depth understanding of the crystal orientation evolution during hot rolling of TiB whisker(TiBw)/TA15 composites and the anisotropy of the as-rolled plates can help fully utilize the material proper-ties.In this paper,the crystal plasticity finite element models of high-temperature(HT)β-phase and room-temperature(RT)α-phase were constructed from electron backscattering diffraction data.Based on this,the orientation evolution during hot rolling in the single-phase region and the effects of the matrix texture on the mechanical properties of the as-rolled plates were analyzed.The effect of TiBw on the anisotropy was studied by the composites finite element model.Results showed that theα-fiber texture of theβ-phase was formed during HT rolling.This texture was converted to the T-texture of theα-phase at RT during cooling according to the Burgers orientation relationships.The TiBw had little effect on the matrix texture composition.The TiBw and matrix texture caused the matrix to have higher strength along the rolling direction and the transverse direction,respectively.The matrix texture dominated the difference in mechanical properties because its effect exceeded that of TiBw.The effect of the matrix on the mechanical properties was caused by the Schmid factors(SFs)and the critical resolved shear stress(CRSS)of the slip system together.The slip mode was influenced by SFs determined by the angular rela-tionship between the crystal orientation and the loading direction.The CRSS of the activated slip system determined the yield strength.

Role of slip and {10-12} twin on the crystal plasticity in Mg-RE alloy during deformation process at room temperature

The deformation mechanism of slips and twins has a considerable influence on the plasticity of magnesium alloys. However, the roles of slips and twins in the room-temperature deformation of Mg-rare earth(Mg-RE) alloys with high contents of rare earth elements is rarely investigated. Here, the microstructural evolution and deformation mechanism of an aged Mg-5 Y-2 Nd-3 Sm-0.5 Zr alloy during uniaxial compression at room temperature were systematically investigated using in-situ electron-backscattered diffraction and transmission electron microscopy. The results indicated that in the early stage of deformation, the Mg-RE alloy was mainly controlled by the slip of dislocations in the basal plane and the coordinated c-axis strain of the {10-12} twin. With an increase in the strain, the grain orientation became more suitable for the initiation of pyramidal Ⅱ dislocations in the later stage of deformation;these dominated the deformation mechanism. In the twin evolution of the Mg-RE alloy, there were three types of twin-twin interaction behaviors:(i) single twin variant 'parallel' structure,(ii) single twin variant 'cross' structure, and(iii) multi twin variant 'cross' structure. In addition, three types of twin-grain boundary interaction behaviors were summarized:(i) twin 'refracting through' grain boundary,(ii) twin'parallel through' grain boundary, and(iii) twin 'fusing through' grain boundary, which are expected to act as new means and solutions for the twin strengthening of magnesium alloys.

Origins of high ductility exhibited by an extruded magnesium alloy Mg-1.8Zn-0.2Ca:Experiments and crystal plasticity modeling

Low ductility and strength are major bottlenecks against Mg alloys’wide applications.In this work,we systematically design the composition and fabrication process for a low-alloyed Mg-Zn-Ca alloy,showing that it can be extruded at low temperatures(~250℃)and high speeds(~2 mm/s).After the extrusion,this alloy exhibits a substantially weakened basal texture,relatively small grain size,very high tensile elongation(~30%),and good strength.The origin of the considerably improved ductility was studied using a combination of three-dimensional atom probe tomography(3D-APT),transmission electron microscopy(TEM),electron backscattered diffraction(EBSD)in conjunction with surface slip trace analysis,in-situ synchrotron X-ray diffraction,and elasto-plastic self-consistent(EPSC)modeling.Co-segregation of Zn and Ca atoms at a grain boundary is observed and associated with texture weakening and grain boundary mediated plasticity,both improving the ductility.While basal slip and prismatic slip are identified as the dominant deformation systems in the alloy,the ratio between their slip resistances is substantially reduced relative to pure Mg and most other Mg alloys,significantly contributing to the improved ductility of the alloy.This Mg-Zn-Ca alloy exhibiting excellent mechanical properties and low fabrication cost is a promising candidate for industrial productions.

Crystal plasticity behavior of single-crystal pure magnesium under plane-strain compression

A phenomenological crystal plasticity constitu- tive model for magnesium single crystal was presented. Four deformation mechanisms （including basal （a）, pris- matic （a）, pyramidal （c ＋ a） slip and tension twin） and their interactions were considered. Twin-induced lattice reorientation was also incorporated in the model. The proposed model was then applied to the simulation of plane-strain compression deformation for different orien- tations. Related material parameters were calibrated at first according to the classical channel-die tests. The predicted macro-and microscopic responses, along with the experi- mental results, show strong orientation-dependent proper- ties. It is also found in the simulation that basal slip in the twinned region is active even before the saturation of twin activity in a twin-favored case. Furthermore, the effect of an initial deviation angle on the mechanical responses was evaluated, which is proved to be also orientation-depen- dent. Basal slip is found to be easily activated due to a slight deviation, while a slight deviation in the twin-fa- vored case could result in a significant difference in the mechanical behavior after the reorientation. The effort on the study of magnesium single crystal in the present work contributes to further polycrystalline analysis.

Texture evolution and slip mode of a Ti-5.5Mo-7.2Al-4.5Zr-2.6Sn-2.1Cr dual-phase alloy during cold rolling based on multiscale crystal plasticity finite element model

The complex micromechanical response among grains remains a persistent challenge to understand the deformation mechanism of titanium alloys during cold rolling.Therefore,in this work,a multiscale crystal plasticity finite element method of dual-phase alloy was proposed and secondarily developed based on LS-DYNA software.Afterward,the texture evolution and slip mode of a Ti-5.5Mo-7.2Al-4.5Zr-2.6Sn-2.1Cr alloy,based on the realistic 3D microstructure,during cold rolling(20%thickness reduction)were systematically investigated.The relative activity of the■slip system in theαphase gradually increased,and then served as the main slip mode at lower Schmid factor(<0.2).In contrast,the contribution of the■slip system to the overall plastic deformation was relatively limited.For theβphase,the relative activity of the<111>{110}slip system showed an upward tendency,indicating the important role of the critical resolved shear stress relationship in the relative activity evolutions.Furthermore,the abnormally high strain of very fewβgrains was found,which was attributed to their severe rotations compelled by the neighboring pre-deformedαgrains.The calculated pole figures,rotation axes,and compelled rotation behavior exhibited good agreement to the experimental results.

Cold dwell behaviour of Ti6Al alloy:Understanding load shedding using digital image correlation and dislocation based crystal plasticity simulations

Digital image correlation(DIC)and dislocation based crystal plasticity simulation were utilised to study cold dwell behaviour in a coarse grain Ti-6Al alloy at 3 different temperatures up to 230℃.Strains extracted from large volume grains were measured during creep by DIC and were used to calibrate the crystal plasticity model.The values of critical resolved shear stresses(CRSS)of the two main slip systems(basal and prismatic)were determined as a function of temperature.Stress along paths across the boundaries of four grain pairs,three“rogue”grain pairs and one“non-rogue”grain pair,were determined at different temperatures.Large load shedding was observed in one of the“rogue”grain pairs,where a stress increment during the creep period was found in the“hard”grain.A minor load shedding mechanism was observed in two non-typical“rogue”grain pairs,in which the plastic deformation is nonuniform inside the grains and geometrically necessary dislocations accumulate in the centre of the grains.At elevated temperatures,120℃was found to be the worst case scenario as the stress difference at the grain boundaries of these four grain pairs was found to be the largest among the three temperatures analysed.The origin of this critical temperature is debated in the literature and it is investigated for the first time in the present work by analysing the simultaneous effects of the geometrically necessary dislocations(GND)and the strain rate sensitivity(SRS)of the slip systems.The analysis shows that the combined effects of the peak SRS of both prismatic and basal slip systems at 80℃and of the increase of the spread of the GND distribution around the grain boundary at higher temperatures are the origin of the observed worst case scenario.

A crystal plasticity FE study of macro-and micro-subdivision in aluminium single crystals{001}<110>multi-pass rolled to a high reduction

In this study,the substructure formation in a multi-pass rolled aluminium single crystal{001}<110>was investigated by the crystal plasticity finite element model,and the predations were validated by experimental observations at both macro-and micro-scale.A finite element model for multi-pass rolling was developed to follow the real experimental rolling scheme,by which the through-thickness macroscopic subdivision was successfully predicted up to a 90%reduction.The macro-subdivision was featured by forming matrix bands through the thickness,and the deformation behaviours,in terms of slip activity,shear strain and crystal rotation,alternated between matrix bands.The development of matrix bands,stability of crystal orientations,and correlation between slip activity,shear strain and crystal rotation have been investigated.Another modelling method,Submodel,was used to exceedingly increase the mesh resolution in smaller regions of interest,and the experimentally observed microstructure,i.e.,micro-subdivision was explicitly and spatially revealed.Similar predictions were obtained in Submodels with different element sizes,which proves the feasibility of this method in predicting microstructure formation.It was found that the substructure formation by varying slip activity and crystal rotation between domains is energy favourable.The procedure of substructure formation was explained based on the predictions,three types of substructure have been identified,and the substructure formation was discussed.

Simultaneous enhancement of strength and ductility in friction stir processed 2205 duplex stainless steel with a bimodal structure:experiments and crystal plasticity modeling

Achieving excellent strength-ductility synergy is a long-lasting research theme for structural materials.However,attempts to enhance strength usually induce a loss of ductility,i.e.,the strength-ductility trade-off.In the present study,the strength-ductility trade-off in duplex stainless steel(DSS)was overcome by developing a bimodal structure using friction stir processing(FSP).The ultimate tensile strength and elongation were improved by 140%and 109%,respectively,compared with those of the asreceived materials.Plastic deformation and concurrent dynamic recrystallization(DRX)during FSP were responsible for the formation of bimodal structure.Incompatible deformation resulted in the accumulation of dislocations at the phase boundaries,which triggered interpenetrating nucleation between the austenite and ferrite phases during DRX,leading to a bimodal structure.The in situ mechanical responses of the bimodal structure during tensile deformation were investigated by crystal plasticity finite element modeling(CPFEM).The stress field distribution obtained from CPFEM revealed that the simultaneous enhancement of strength and ductility in a bimodal structure could be attributed to the formation of a unique dispersion-strengthened system with the austenite and ferrite phases.It is indicated that the present design of alternating fine austenite and coarse ferrite layers is a promising strategy for optimizing the mechanical properties of DSSs.