Crystal Plasticity Finite Element Model Research Articles

Modeling crystal plasticity with an enhanced twinning–detwinning model to simulate cyclic behavior of AZ31B magnesium alloy at various temperatures

In this study, a multiscale model within crystal plasticity finite element (CPFE) framework was developed to predict the cyclic loading behaviors of a wrought magnesium alloy, AZ31B, at various testing temperatures. The temperature dependency was systematically modeled by employing a modified strain-hardening model, implemented in the CPFE. The developed model was further extended to cyclic loading scenarios, under which abnormal mechanical responses were observed, using an enhanced twinning–detwinning model based on the well-known predominant twinning reorientation scheme. For the first time, the concept of variable residual twin fraction was introduced in the twinning–detwinning model as a criterion for the inactivation of detwinning. The newly developed model was employed to predict the mechanical responses under monotonic in-plane tension and compression at testing temperatures ranging from room temperature to 200°C. In addition, the mechanical behaviors of the alloy under cyclic loadings at these testing temperatures were also predicted using the CPFE model. These predictions were then compared with the experimentally measured data. The micromechanical responses, such as the evolution of twin volume fraction and activation of slip/twin/detwin systems, under various loading and temperature conditions were also predicted and compared with the reported data.

Effect of deformation modes on continuous dynamic recrystallization of extruded AZ31 Mg alloy

Herein, uniaxial compression experiments, with a series of true strains at different temperatures (573–673 K) and strain rates (3 ×10−3 - 3 ×10−1 s−1), are conducted on AZ31 magnesium alloy with different initial textures. The deformation modes and dynamic recrystallization (DRX) behavior are investigated using electron back-scattered diffraction /transmission electron microscopy and crystal plasticity finite element modeling (CPFEM). A unitive constitutive equation is established for different initial textures, and the activation energies of extrusion direction (ED) and transverse direction (TD) samples are found to be 134.5 kJ/mol and 138.4 kJ/mol, respectively. The microstructural investigations and CPFEM simulations are performed to identify the characteristics of DRX processing during compression and categorize according to the deformation modes originating from the difference in initial texture of alloy. Moreover, it is revealed that basal<a> slip prevails in the TD sample at all strain rates under consideration, whereas prismatic<a> slip dominates the initial deformation of the ED specimen. Consequently, more pronounced kink bands and superior compressed peak stress are observed, corresponding to the higher density of prismatic<a> slip in the ED sample than that in the TD sample. Accordingly, these kink bands along with elevated deformation energies accelerate the development of an early continuous dynamic recrystallization with a higher volume fraction and a smaller grain size of the ED sample compared to the TD specimen. The improvement in strength and ductility of the ED sample after being deformed at a strain of 1.2 is attributed to the smaller grains and the weaker texture than those of the TD specimen. For the first time, the role of prismatic slips and kink bands in the recrystallization process is discussed in detail.

Crystal plasticity model of residual stress in additive manufacturing using the element elimination and reactivation method

Selective laser melting is receiving increasing interest as an additive manufacturing technique. Residual stresses induced by the large temperature gradients and inhomogeneous cooling process can favour the generation of cracks. In this work, a crystal plasticity finite element model is developed to simulate the formation of residual stresses and to understand the correlation between plastic deformation, grain orientation and residual stresses in the additive manufacturing process. The temperature profile and grain structure from thermal-fluid flow and grain growth simulations are implemented into the crystal plasticity model. An element elimination and reactivation method is proposed to model the melting and solidification and to reinitialize state variables, such as the plastic deformation, in the reactivated elements. The accuracy of this method is judged against previous method based on the stiffness degradation of liquid regions by comparing the plastic deformation as a function of time induced by thermal stresses. The method is used to investigate residual stresses parallel and perpendicular to the laser scan direction, and the correlation with the maximum Schmid factor of the grains along those directions. The magnitude of the residual stress can be predicted as a function of the depth, grain orientation and position with respect to the molten pool. The simulation results are directly comparable to X-ray diffraction experiments and stress–strain curves.

Development of microstructure-sensitive damage models for zirconium polycrystals

The incorporation of four different microstructure-sensitive damage mechanisms into a crystal plasticity finite element model is described in detail. The nucleation and propagation of cracks are based on (1) the local principal stress and normal to the corresponding principal plane, (2) the local principal plastic strain and normal to the corresponding principal plane, (3) the local maximum slip and normal to the predominant slip system, and (4) the energy stored in dislocations and normal to the predominant slip system. To study the performance of each model in predicting crack nucleation and propagation, the “as-measured” microstructure in the vicinity of a sharp notch in a pure zirconium specimen is imported into the crystal plasticity model. The numerical results are compared with those measured by the electron backscatter diffraction technique. This is followed by a numerical study of the effects of crystal orientation on the prediction of each model for a notched single crystal zirconium specimen. For the specimen texture studied here, results show that the principal stress and the maximum slip methods can correctly predict the location of major cracks, where only the latter replicates the correct direction of crack propagation. Predictions from the energy method or the principal plastic strain method mainly coincide with the minor cracks or those that propagate at higher applied strains.

Crystal plasticity-based finite element modeling of twin transmission across grain boundaries in magnesium

For polycrystalline materials with the deformation mechanism of twinning, the interaction between the twins and grain boundaries are substantial to their deformation behavior. In the current work, the twin transmission across the grain boundaries in a magnesium bicrystal is investigated with the aid of crystal plasticity finite element model. The influencing factors, such as the crystallographic orientation of grains, GB misorientation, critical resolved shear stress (CRSS), dislocation slip, and twin-induced stress relaxation are considered. The commonly used geometric factors of macroscopic Schmid factor (MSF), geometric compatibility factor (GCF), and the lately proposed composite Schmid factor (CSF) are assessed by comparing the simulations and available experiments. The CSF can interpret the twin transmission better than either the MSF or the GCF. Moreover, the available twin transmission ability characterized in terms of the fraction of twin transmitted GBs is well captured by the CSF.

Strain-Gradient Crystal Plasticity Finite Element Modeling of Slip Band Formation in α-Zirconium

Two methods for the determination of geometrically necessary dislocation (GND) densities are implemented in a lower-order strain-gradient crystal plasticity finite element model. The equations are implemented in user material (UMAT) subroutines. Method I has a direct and unique solution for the density of GNDs, while Method II has unlimited solutions, where an optimization technique is used to determine GND densities. The performance of each method for capturing the formation of slip bands based on the calculated GND maps is critically analyzed. First, the model parameters are identified using single crystal simulations. This is followed by importing the as-measured microstructure for a deformed α-zirconium specimen into the finite element solver to compare the numerical results obtained from the models to those measured experimentally using the high angular resolution electron backscatter diffraction technique. It is shown that both methods are capable of modeling the formation of slip bands that are parallel to those observed experimentally. Formation of such bands is observed in both GND maps and plastic shear strain maps without pre-determining the slip band domain. Further, there is a negligible difference between the calculated grain-scale stresses and elastic lattice rotations from the two methods, where the modeling results are close to the measured ones. However, the magnitudes and distributions of calculated GND densities from the two methods are very different.

Accurate Effective Stress Measures: Predicting Creep Life for 3D Stresses Using 2D and 1D Creep Rupture Simulations and Data

Operating structural components experience complex loading conditions resulting in 3D stress states. Current design practice estimates multiaxial creep rupture life by mapping a general state of stress to a uniaxial creep rupture correlation using effective stress measures. The data supporting the development of effective stress measures are nearly always only uniaxial and biaxial, as 3D creep rupture tests are not widely available. This limitation means current effective stress measures must extrapolate from 2D to 3D stress states, potentially introducing extrapolation error. In this work, we use a physics-based, crystal plasticity finite element model to simulate uniaxial, biaxial, and triaxial creep rupture. We use the virtual dataset to assess the accuracy of current and novel effective stress measures in extrapolating from 2D to 3D stresses and also explore how the predictive accuracy of the effective stress measures might change if experimental 3D rupture data was available. We confirm these conclusions, based on simulation data, against multiaxial creep rupture experimental data for several materials, drawn from the literature. The results of the virtual experiments show that calibrating effective stress measures using triaxial test data would significantly improve accuracy and that some effective stress measures are more accurate than others, particularly for highly triaxial stress states. Results obtained using experimental data confirm the numerical findings and suggest that a unified effective stress measure should include an explicit dependence on the first stress invariant, the maximum tensile principal stress, and the von Mises stress.

Simulation of crystal plasticity of P92 heat resistant steel considering martensitic lath structure

Based on the theory of crystal plasticity, coupled with dislocation and lath hardening models, this paper establishes a crystal plasticity finite element model describing the high temperature creep of P92 steel. Open source software was used to generate lath models with an average size of 350nm, 650nm and 950nm to explore the effect of lath coarsening on the high-temperature creep behavior of P92 steel. The results show that the roughening of the slats increases the rate of creep deformation, resulting in a decrease in the service life of the material. Observing the slat model, it can be seen that the roughening of the slats enlarges the numerical gradient of stress and strain, and aggravates the overall plastic strain of the model. The coarsening of the slats accelerates the movement of dislocations, causing the density of movable dislocations to increase, and at the same time the shear strain amplitude of the slip system increases, thereby reducing the hardening behavior of the material.

Modeling and numerical investigation of mechanical twinning in β-HMX crystals subjected to shock loading

This manuscript establishes a crystal plasticity finite element (CPFE) model with large volumetric deformation for β-HMX (1,3,5,7-tetranitro-1,3,5,7-tetrazocane) energetic crystals with emphasis on the deformation twinning behavior under shock loading conditions. The CPFE model captures the nonlinear response of the monoclinic crystal through the application of large volumetric change under shock condition, dislocation slip at low and high moving speeds and mechanical twinning idealized by the twin volume fraction evolution. The twinning behavior is distinguished from dislocation slip through the decomposition of the plastic velocity gradient in which dislocation slip, twinning and slip in the twinned region are separately considered. Third-order Birch Murnaghan EOS is incorporated in the CPFE framework to describe the volumetric deformation under extreme pressure induced by explosion or impact. The results of the numerical investigations show that the twinning behavior exhibits strong orientation dependency, which becomes more evident at higher loading regime. Particle shape significantly affects the twin concentration. Peak twin volume fraction in HMX polycrystalline with regularized particle shapes is lower compared with mesostructure with realistic particle morphologies.

Roughness evolution of constrained surface based on crystal plasticity finite element model and coupled Eulerian-Lagrangian method

This paper focuses on the roughness evolution and surface topography variation of constrained surface, which is restricted by the mold or tool in the forming process. A crystal plasticity finite element model, which couples the microstructure of polycrystalline, the crystal plasticity constitutive model and the real surface topography of the material, is developed. How to use the real surface of the workpiece as the surface topography of the finite element model is proposed, in which number and location of peaks and valleys on the surface, are accurately captured in the constructed real surface model. The comparison shows that simulation predictions of both the deformed surface topography and the surface roughness agree reasonably well with experimental measurements at various press down ratio of mold. The influences from workpiece and mold on the roughness evolution of constrained surface are comprehensively analyzed. It can be seen clearly that roughness evolution of constrained surface is the combination result of both the surface flattening due to the mold restriction and the surface roughening due to the material inhomogeneity of the workpiece. The lubricant existing in the contact surface of the workpiece and mold should been paid much more attention in the roughness evolution analysis. The influence of the lubrication condition on the roughness evolution of constrained surface is analyzed by combining the CEL finite element method and compression experiments. In deformation stage II of the roughness evolution, the closed cavities begin to form on the surface. Lubricant in the closed cavities plays an important role in limiting the flattening behavior of the surface topography. This paper provides a deeper insight into the comprehensive understanding of the roughness evolution of constrained surface, which contributes to the surface roughness control of plastic deformation products considering the effects of the workpiece, mold and lubrication condition.

Integrating phase field and crystal plasticity finite element models for simulations of titanium alloy Ti-5553

The ability to simultaneously predict the microstructure and bulk material properties of 3D printed (additively manufactured or AM) metals is critical to the development of process intelligence that can be used by a digital-twin for forecasting and optimising alloy composition and fabrication parameters. This study proposes a simulation framework for predicting the microstructure and corresponding meso- and macro-scale properties of AM materials. This is achieved by integrating phase-field and crystal plasticity modelling techniques, whereby the phase field model predicts the microstructure and the crystal plasticity constitutive model computes the stress–strain evolution using the microstructure as the input. The simulation of multiple microstructures demonstrates that this integrated approach can be used to test the influence of different microstructures on the mechanical properties of titanium alloy Ti-5553. This includes the influence of grain size and grain orientation on both the meso- and macro-scale behaviour.

Crystal Plasticity Finite Element Modeling of Extension Twinning in WE43 Mg Alloys: Calibration and Validation

Crystal Plasticity Finite Element Modeling of Extension Twinning in WE43 Mg Alloys: Calibration and Validation

Microstructural evolution in pure copper during accumulative skin pass rolling: experimental and crystal plasticity numerical investigations

Surface mechanical treatments are known to introduce deformation heterogeneity, thus entailing a combination of excellent strength and ductility in metallic metals. Accumulative skin pass rolling (ASPR) was employed to introduce heterogeneous structure in pure copper, which significantly improved yield strength and maintained high ductility. The experimental observations of the ASPR processed copper showed that surface grains possessed a much larger magnitude of misorientations and geometrically necessary dislocations (GNDs) than the centre grains. Crystal plasticity finite element modelling was utilised to provide an in-depth understanding of microstructure evolution during ASPR. It was found that the surface grains accommodated higher shear strain and had higher slip resistance than the centre grains. The multiple active slip systems in the surface grains induce the lattice rotations and then the formation of intragranular misorientations accompanied by a high density of GNDs, while the single active slip system in the centre grains can accommodate the applied material rotation without the lattice rotation.

Crystal Plasticity Simulation of Grain Size Effect on Deformation Behavior in Face Center Cubic Polycrystal

A improved method is developed to model the effect of grain size on deformation behavior in polycrystalline pure copper. In this method, a grain size controlled polycrystalline geometry model based on the Voronoi tessellation is employed to generate virtual grain structures that are statistically equivalent to metallographic measurements in terms of grain size distributions, and a crystal plasticity constitutive model considering size effect is proposed on the basis of Hall-Petch type relationship. Then, a set of crystal plasticity finite element models are developed to simulate the tension flow stresses of polycrystalline pure copper with different mean grain size. The results show that the size constants τ0', k1, τs', k2 and ns in the crystal plasticity constitutive model are determined as 13.754, 65.584, 152.653, −4.820 and 0.418, respectively, and the simulated data of flow stresses show good agreement with experimental ones. In comparison with the classical method, the shear strain distributions and the differences of their ranges are remarkable, and more local shear strain concentrations can be observed in the transition zones between the larger grains and the smaller ones, when the improved method is applied.

Experiment and non-local crystal plasticity finite element study of nanoindentation on Al-8Ce-10Mg alloy

Cerium and magnesium strengthened aluminum alloys, or Al-Ce-Mg, is a recently developed alloy family that exhibits good mechanical properties at elevated temperatures (~300 °C). To examine the single-crystal properties of Al-Ce-Mg alloys, nanoindentation experiments are conducted in this study. A crystal plasticity finite element model (CPFEM) with the evolution of geometrically necessary dislocations (GNDs) is applied to simulate the indentation in individual grains. A parametric study is carried out to investigate the sensitivity of each crystal plasticity model parameter to the indentation behavior. The highly sensitive parameters are calibrated by matching the indentation load-depth curves, while the rest parameters are obtained from bulk polycrystal uniaxial tension tests. Overall, satisfactory matching between experiment and simulation is obtained for each individual grain. The calculated hardness, as determined from the experiment, shows the dependence on indent depth, which is captured by the GND model. Furthermore, the effect of grain orientation and neighboring grains to nanoindentation behavior have been discussed with the comparison between the simulation and experiments.

The impact of heterogeneous microstructural features on crystal plasticity modeling of plastic anisotropy

Crystal plasticity finite element models typically assume each grain starts with a spatially uniform dislocation distribution, meaning each grain is initialized with a single lattice orientation and all grains share the same slip resistance. This study assessed that assumption by comparing crystal plasticity simulations of tensile tests against experiments on an extruded aluminum 7079 alloy. The simulations utilized computational microstructures with ‘pancaked’ grains and a significant degree of crystallographic texture, consistent with experimental measurements. In one case, the computational microstructures were assigned a single slip resistance and a single lattice orientation for each grain prior to the tension tests. In another case, the extrusion process prior to the tension tests was simulated to cause nonuniform slip resistances, nonuniform crystal orientations within each grain, and nonuniform slip resistances at each material point. Both approaches produced reasonably accurate predictions of the measured yield stress and lateral strain ratio anisotropy, but the predictions considering the initial nonuniformity exhibited less prediction error. Other factors, such as latent vs self hardening of slip systems and fine vs coarse grains, did not have as large an impact. These results suggest that dislocation heterogeneity should be experimentally characterized and fed into future crystal plasticity simulations.

Modeling lattice rotation fields from discrete crystallographic slip bands in superalloys

In this work, we investigate the relationship between an intense slip band (ISB) and the zone of large lattice rotations that forms ahead of the tip of the ISB. We develop a crystal plasticity finite element model of a discrete ISB lying within an oligocrystalline assembly and calculate the local crystalline stress and lattice rotation fields generated by the ISB. The calculations demonstrate that, first, a region of severe lattice rotations, commonly referred to as a microvolume, does not form without the ISB, and second, large amounts of accumulated slip in the ISB are required to enlarge the microvolume to sizes and rotation magnitudes observed experimentally. Ahead of the ISB tip, the quintessential plastic zone always forms, but the atypical microvolume forms when non-concentrated and spatially diffuse slip is activated by the ISB-induced stress field. This result suggests that the detrimental ISB/microvolume pair will likely appear in pairs of crystals in which transmission of the slip from the ISB is severely blocked by the grain boundary, a hypothesis that we verify with a few target cases.

Geometry-considered 3D pseudorandom grain-scale modelling for crystalline material miniature parts

Grain-scale modelling and simulation is of vital importance during the full lifecycle of crystalline material miniature parts, whose mechanical responses depend on the actual material microstructure, part geometry and their correlation. Unfortunately, current studies fail to comprehensively consider indispensable microstructure information, and lack the consideration regarding part geometry. Therefore, this paper proposes and implements a geometry-considered 3D pseudorandom grain-scale modelling method, which takes into account the necessary actual microstructure information, part geometry and their mutual relations to generate accurate and efficient microstructure-dependent crystal plasticity finite element (M−CPFE) models. Firstly, the 3D actual grain-scale microstructure was acquired efficiently by combining 2D actual microstructures. Then the geometry-considered grain-scale microstructure was created pseudorandomly based on the actual 3D grain size, orientation and misorientation distributions. On this basis, the M−CPFE model was constructed accurately. The proposed method has been proved to have higher accuracy and robustness than the Voronoi random method on macroscopic response prediction, microstructure generation and microstructure evolution prediction. Furthermore, the applicability in micro-manufacturing and service has been demonstrated by micro sheet bending and micro impeller rotation simulations. There is a great potential for the full lifecycle tracking of crystalline material miniature parts with the help of the proposed method.

Controlled single and repeated impact testing for material plastic behaviour characterisation under high strain rates

AbstractInstrumented single‐shot experiments provide crucial information of a material's response to impact events that can be used in shot‐peening modelling. However, no authors successfully used such test for constitutive model identification and validation as existing test rig generally cannot provide an accurate determination of the shot trajectory in three dimensions over a wide velocity range. In this work, a shot‐peening test rig that can propel single shot under the process conditions with a high aiming accuracy is presented. The test rig propels industrial shot by sudden pressurised gas release. A methodology to recover the propelled shot three‐dimensional trajectory within a 200‐μm accuracy using two high‐frequency cameras is developed in an open‐source in‐house code. The test rig can propel 0.5‐, 1.19‐ and 2.5‐mm‐diameter shot at velocity ranging from 0.8 to 143 m s−1 and can send several shots at the same position when using the largest shot diameter. Two potential applications of the set‐up are presented for (i) coefficient of restitution measurement with different shooting angles and velocities and (ii) crystal plasticity finite element model validation using the impact dent topology, the shot displacement curve and the crystal misorientation field under the dent.

Micromechanical study of strengthening mechanisms for Ti65(AlCrNb)35 medium-entropy alloy

Metal solutions, such as high- and medium-entropy alloys, exhibit extraordinary mechanical performance in comparison to regular alloys. In this study, we employ a crystal plasticity finite element model (CPFEM) to study the strengthening mechanisms of a new medium-entropy alloy, Ti65(AlCrNb)35. A 3D representative model is constructed by processing experimental results for Ti65(AlCrNb)35, such as average grain size, grain size distribution, and initial texture, using the open-source software Dream.3D. The constitutive law for the grains is described by the crystal plasticity and implemented in Abaqus user-defined material (UMAT). The results of uniaxial tensile tests are utilized to calibrate the required parameters in the CPFEM. Strengthening effects resulting from the grain size, strain rate, and cyclic loading for Ti65(AlCrNb)35 are investigated by performing numerical simulations based on the proposed computational framework. Numerical simulation results show that the yield strength increases with decreasing initial grain size, which agrees well with experimental observations of the Hall–Petch effect. In addition, the rate-dependent yield stress increases as the applied strain rate increases in the tensile tests. Moreover, the cyclic loading results demonstrate the isotropic hardening behaviors and the saturation of yielding strength when the maximum strain reaches 10%. Finally, we discuss the contributions of different strengthening mechanisms on the yield strength of Ti65(AlCrNb)35 under different load conditions.