Crystal Plasticity Simulations Research Articles

Effect of hydrogen on plasticity of [formula omitted]-Fe: A multi-scale assessment

A multi-scale study was carried out to quantify the effect of interstitial hydrogen concentration on plasticity in α-Fe. In this work, the influence of hydrogen on the screw dislocation glide behavior was examined across several length-scales. The insights obtained were integrated to provide an accurate continuum description for the effect of hydrogen on the dislocation based plasticity in polycrystalline α-Fe. At the outset of this work, a new FeH interatomic potential was formulated that enhanced the atomistic estimation of the variation in dislocation glide behavior in presence of hydrogen. Next, the dislocation core reconstruction observed due to the addition of hydrogen using atomistic simulations was validated with the help of large-scale DFT calculations based on the DFT-FE framework. Several atomistic simulations were carried out to comprehensively quantify the effect of hydrogen on the non-Schmid behavior exhibited during the dislocation glide in α-Fe. Finally, crystal plasticity simulations were carried out to understand the effect of hydrogen on the meso-scale deformation behavior of polycrystalline α-Fe.

Modeling Bainite Dual-Phase Steels: A High-Resolution Crystal Plasticity Simulation Study

A bainite dual-phase (FB) steel containing polygonal ferrite and granular bainite is thermo-mechanically rolled, followed by an accelerated cooling. Two different cooling rates are applied to obtain two different materials. The aim of the study is to explore the reasons for the differences in the mechanical response experimentally observed for these two materials which are modeled by means of high-resolution crystal plasticity simulations with a phenomenological constitutive description. First, the CP parameters of the individual constituents are determined. Second, different three-dimensional (3D) representative volume elements (RVEs)—one of which includes the substructure of bainite—are used to study the mechanical properties of both FB microstructures. It is shown that, in contrast to the macroscopic response, the microscopic response differs among the RVEs. Third, a comparison of both materials is performed by analyzing their stress–strain response. The onset of plasticity in granular bainite is found to be different for both materials in addition to the strain partitioning, although they both obeyed the iso-work assumption. Finally, a parameter study is carried out in order to investigate the correlation between different microstructures and damage initiation that can be seen experimentally in this steel. It is shown that the difference in ultimate elongation may depend on whether the first voids appear within polygonal ferrite or at the phase boundary.

Study on the crack nucleation mechanism of Ti-2Al-2.5Zr alloy in low cycle fatigue: Quasi in-situ experiments and crystal plasticity simulation

The fatigue crack nucleation mechanism of Ti-2Al-2.5Zr alloy was investigated using the coupling method of quasi in-situ tests with crystal plasticity (CP) simulation. The constitutive parameters in the CP model were validated by digital image correlation based on scanning electron microscope (SEM-DIC). It was found that the transgranular and intergranular cracks nucleated inside grains and at grain boundaries (GBs), respectively, due to slip intrusions/extrusions along prismatic planes with highest SFpris. values, while quasi transgranular cracks were induced by the adjacent microstructure or cracks. The angle Ω between the sample surface and the slip direction of slip planes where the transgranular cracks nucleated was within the range of 20–55°. Three factors for predicting intergranular cracks were identified, and the slip shearing mechanism of GBs was proposed. The CP results revealed that a significant plastic strain difference was generated at GBs where intergranular cracks nucleated. The band averaging method showed better prediction ability than the grain averaging method, and a unified fatigue indicator parameter (FIP) combining the accumulated plastic strain, the strain incompatibility parameter (SIP), and the abovementioned crack prediction factors, was proposed, which improved the unified prediction ability for both transgranular and intergranular cracks.

Nano-structuring of a high entropy alloy by severe plastic deformation: Experiments and crystal plasticity simulations

The evolution of microstructure, texture, and mechanical properties of an induction melted non-equiatomic Al6Co23.5Fe23.5Mn23.5Ni23.5 (at.%) high entropy alloy subjected to severe plastic deformation was investigated experimentally and by simulations. Analyses using electron backscatter diffraction and transmission Kikuchi diffraction images revealed the evolution of the microstructures. The coarse-grained initial structure was deformed down to an average grain size of 50 nm after a shear strain of 11 by employing the high-pressure compressive shearing process, at room temperature. Transmission electron microscopy analysis showed the presence of nano-twins. The high deformation led to a significant increase in the strength, up to ≈ 1.0 GPa. X-ray diffraction macro-texture analysis revealed a shear texture with the dominance of the B/B¯{112}110-type component whose intensity varied with strain. A two-step Taylor-type polycrystal plasticity simulation approach reproduced the texture by a correlation value of 91%. In the first part of the modeling, grain fragmentation was simulated, while in the second part, grain boundary shearing and deformation twinning were considered together with the operation of {111}112-type partial slip. The effect of twinning was also examined in the texture modeling and the simulations estimated that its fraction was less than 2%.

Parameter identification and pileup behavior of TiAl alloy through nanoindentation and crystal plasticity simulation

In this work, the load-displacement curves of γ and B2 phases in Ti-43.5Al-4 Nb-1Mo-0.1B (TNM) alloy were obtained from nanoindentation experiments and corresponding crystal plasticity finite element (CPFE) simulations. The good consistency of constitutive curves and the small error of hardness between experiments and simulation results confirmed that the constitutive parameters of γ and B2 phase in TiAl alloy could be well verified by nanoindentation. Based on nanoindentation tests and CPFE simulation, the pileup morphology of each grain around the indents has been systematically discussed. The pileup morphology is closely related to the slip behavior around the indents, which could be analyzed by the calculation of Schmid factors, including surface Schmid factor (SSF) and interior Schmid factor (ISF). Results show that a large SSF and a small ISF will promote the accumulation of cumulative shear strain at the surface of the materials, further facilitating the pileup profile. Besides, the pileup morphology is closely related with the movement of dislocation, which greatly influences the flow ability of the material, further altering the height of pileup profiles.

Life Prediction for Directed Energy Deposition‐Manufactured 316L Stainless Steel using a Coupled Crystal Plasticity–Machine Learning Framework

Additively manufactured stainless steels have become increasingly popular due to their desirable properties, but their mechanical behavior in structural parts is not yet fully understood. Specifically, the impact of columnar microstructures on fatigue behavior is still unclear. A typical directed energy deposition (DED)‐fabricated 316L stainless steel microstructure consists of distinct zones with equiaxed and columnar grains. To answer the question of how these zones of a DED‐fabricated 316L stainless steel microstructure affect the local mechanical behavior individually, such as the fatigue strength, stress/strain distribution, and fatigue life, crystal plasticity simulations are conducted to investigate the influence of microstructure on local mechanical behavior such as fatigue strength, stress/strain distribution, and fatigue life. The simulations find that columnar microstructures exhibit better fatigue strength than equiaxed structures when the load is parallel to the major axis of the columnar grains, but the strength decreases when the load is perpendicular. This study also uses machine learning to predict fatigue life, which shows good agreement with crystal plasticity modeling. The study suggests that the combined crystal plasticity–machine learning approach is an effective way to predict the fatigue behavior of additively manufactured components.

Mesoscale slip behavior in single crystal and bicrystal tantalum

Single-crystal and bicrystal tensile specimens of various orientations were prepared from coarse-grained, pure Ta to investigate fundamental BCC slip behavior at the mesoscale, that is, without considering discrete dislocation mechanisms. Single crystal yield behavior was well-represented by concurrent {110} and {112} slip modes with the initial CRSS for {110} 6% lower than for {112}. A new metric quantitatively representing slip multiplicity in a crystal visco-plastic context was introduced. Initial strain hardening correlates positively with this “activity index” tending to confirm the dominant role of latent hardening in single crystals. Anelastic hysteresis at least as significant as in polycrystal/polyphase alloys was observed, with loop width increasing with pre-strain rather than solely with flow stress as previously supposed. Tensile tests of “triplets” consisting of a bicrystal specimen and its two constituent single crystal specimens revealed the differential effects of grain boundaries (GB) on strength and anelastic hysteresis. Two triplets followed the rule-of-mixtures (ROM); two triplets showed synergistic strength and anelasticity. Crystal plasticity (CP) simulations with two slip modes having different hardening behaviors predicted the single crystal stress-strain curves reasonably for various orientations. Plastic deformation incompatibility was identified as the likely source of deviation from rule-of-mixture behavior. CP simulations predicted the appearance of additional slip systems near the GBs in the synergistic triplets, but did not predict the observed strength and anelastic hysteresis.

Understanding the anisotropic tensile deformation behavior of commercially pure titanium by experiments and crystal plasticity simulations

Current work reveals the anisotropic tensile deformation mechanisms of commercially pure titanium (CP-Ti) along rolling direction (RD) and transverse direction (TD) by the statistical analysis of electron back scattered diffraction (EBSD) data and crystal plasticity (CP) simulations. The analysis of texture evolution, misorientation angle distribution, in-grain misorientation axis (IGMA) and Schmid factor indicates that the anisotropic tensile deformation behavior is originating from the anisotropic slip modes. Further CP simulation results confirm this conjecture and reveal that the higher fraction of basal slip accommodates the deformation and leads to the lower strain hardening behavior along TD. The lower uniform elongation along TD is caused by the heterogeneous strain distribution in the microstructure as deduced from digital image correlation (DIC) results and kernel average misorientation (KAM) maps.

Prediction of Fatigue Crack Initiation of 7075 Aluminum Alloy by Crystal Plasticity Simulation.

The 7075 aluminum alloy is a promising material for the aerospace industry due to its combination of light weight and high strength. This study proposed a method for predicting fatigue crack initiation of the 7075 aluminum alloy by crystal plasticity finite element analysis considering microstructures. In order to accurately predict the total fatigue life, it is necessary to calculate the number of cycles for fatigue crack initiation, small crack growth, and long crack growth. The long crack growth life can be estimated by the Paris law, but fatigue crack initiation and small crack growth are sensitive to the microstructures and have been difficult to predict. In this work, the microstructure of 7075 aluminum alloy was reconstructed based on experimental observations in the literature and crystal plasticity simulations were performed to calculate the elasto-plastic deformation behavior in the reconstructed polycrystalline model under cyclic deformation. The calculated local plastic strain was introduced into the crack initiation criterion (Tanaka and Mura, 1981) to predict fatigue crack initiation life. The predicted crack initiation life and crack morphology were in good agreement with the experimental results, indicating that the proposed method is effective in predicting fatigue crack initiation in aluminum alloys. From the obtained results, future issues regarding the prediction of fatigue crack initiation were discussed.

Dislocation structures formation induced by thermal stress in additive manufacturing: Multiscale crystal plasticity modeling of dislocation transport

The motion of dislocations governs the plastic deformation of crystalline materials, which in turn determines the mechanical properties. The complex thermal history, large temperature gradients and high cooling rates during the process of additive manufacturing (AM) can induce high dislocation density and unique dislocation structures in the material. The origin of these dislocation structures and their stability during mechanical loading are debated. A novel temperature dependent continuum dislocation dynamics (CDD) model is developed, in which four state variables are used for each slip system representing the total dislocation density, edge and screw geometrically necessary dislocation densities and dislocation curvature. The CDD model is fully coupled with a crystal plasticity solver, which captures the plastic deformation induced by the dislocation motion. A hybrid continuous and discontinuous Galerkin formulation is developed to accurately reproduce the dynamics of highly discontinuous dislocation density fields that are typical of dislocation structures. A multiscale modeling approach is used, in which the thermally induced deformation in specific grains of a polycrystal is extracted from larger scale crystal plasticity simulations of the laser powder-bed fusion process, and is then used for single crystal scale dislocation dynamics simulations. Simulation results reveal the dynamics of dislocation structure formation in grains at different positions during laser scanning and cooling stages. The effect of the cyclic thermal stress during multi-layer AM fabrication is also investigated. The simulations provide a new perspective on the specific conditions that should be satisfied during AM process for the formation of stable dislocation structures.

An experimental and crystal plasticity investigation of anisotropic compression behaviour of Mg-Sn-Ca alloy

The ductility of Magnesium alloys is often limited due to the strong basal texture. Initial attempts were made to reduce the intensity of the basal textures by adding rare earth(RE) elements. However, owing to the cost and scarcity of RE elements, alloys with calcium and tin were recently introduced. Among them, Mg-2Sn-2Ca alloys are the most promising, with high strength reported in the extruded condition. In this work, we report, for the first time, the mechanical properties of the alloy in the sheet form. In plane mechanical anisotropy in compressive behaviour is studied along with the detailed characterisation of texture, microstructure and the deformation twins in the material. Unlike strongly basal textured Mg alloys, deformation twinning was also observed in samples loaded along the normal direction. Crystal plasticity simulations were performed to confirm the slip and twin activity. Furthermore, a detailed analysis of deformation twins revealed that the so called Schmid twins accommodate strain by both twin growth and slip, whereas the non-Schmid twins accommodate the strain exclusively by crystallographic slip.

Mechanisms of the preferential cleavage of Ti2AlNb-based alloy: The influence of grain size and local plasticity

An in-depth understanding on the preferential cleavage of the matrix B2 phase, with an ordered body-centered cubic (BCC) structure, is pivotal to improve the processability of Ti2AlNb-based alloys. This research employed in-situ micro tensile tests, multiscale microstructure characterizations, and crystal plasticity simulations to study the grain-size dependent cleavage of the alloy with a full B2 phase. The material was intentionally prepared with two grain sizes differing by order of magnitude, i.e., the millimeter-level coarse grain (CG) and the micron-level fine grain (FG). The experimental results showed that the cleavage of CGs always occurred on the {100} planes, even when the loading direction was much less favorable for the cleavage of these planes, whereas the cleavage of FGs took place on both {100} and {110} planes. The investigation demonstrated that the plastic deformation takes a critical role in selecting cleavage planes. Full-field crystal plasticity simulations demonstrated that, for the CGs, the plastic deformation associated with cleavage on {100} planes is less than that associated with cleavage on {110} planes, indicating a less plastic deformation-induced blunting effect with cleavage on {100} planes. For the FG material, however, the existence of plentiful grain boundaries (GBs) leads to significantly heterogeneous plastic deformation, local stress distribution deviating from the imposed global stress, and hot spots of stress and strain concentration at GB triple junctions. These local plasticity heterogeneities enable the possibility for cleavage on both the {100} and {110} planes.

Application of machine learning in the design and optimization of bimodal structural materials

Bimodal structures (BS) receive wide concern due to their enhanced combination between strength and ductility. However, it is generally time-consuming and labor-intensive to obtain adequate performance data through traditional experimental and simulation methods. In this paper, a small-sample machine learning (ML) model combined with crystal plasticity (CP) simulations is developed to predict mechanical properties for BS materials with different microstructures. The proposed ML model shows better prediction capacities with regard to yield strength and uniform elongation among traditional ML models, which are validated by both simulative and experimental data. Afterwards, the Pareto front for BS is obtained by multi-objective optimization algorithm (MOOA), showing the mechanical properties of BS with optimal microstructures are much better than those of homogenous structures with the uniform grain size. To realize personalized customization for different target performance, the Pareto front is divided into three parts, then the corresponding three-dimensional design diagrams are established to seek for the best strength and elongation. The proposed exploration framework integrates finite element simulation, ML and MOOA, which can identify the optimized design of heterogeneous structures (HS) using limited data.

In situ synchrotron X-ray multimodal experiment to study polycrystal plasticity.

The microstructure of polycrystals is known to govern the performance of structural materials. This drives the need for mechanical characterization methods capable of probing large representative volumes at the grain and sub-grain scales. In this paper, the use of in situ diffraction contrast tomography (DCT) along with far-field 3D X-ray diffraction (ff-3DXRD) at the Psiché beamline of Soleil is presented and applied to study crystal plasticity in commercially pure titanium. A tensile stress rig was modified to comply with the DCT acquisition geometry and used for in situ testing. DCT and ff-3DXRD measurements were carried out during a tensile test of a tomographic Ti specimen up to 1.1% strain. The evolution of the microstructure was analyzed in a central region of interest comprising about 2000 grains. Using the 6DTV algorithm, DCT reconstructions were successfully obtained and allowed the characterization of the evolution of lattice rotation in the entire microstructure. The results are backed up by comparisons with EBSD and DCT maps acquired at ESRF-ID11 that allowed the validation of the orientation field measurements in the bulk. Difficulties at the grain boundaries are highlighted and discussed in line with increasing plastic strain during the tensile test. Finally, a new outlook is provided on the potential of ff-3DXRD to enrich the present dataset with access to average lattice elastic strain data per grain, on the possibility of performing crystal plasticity simulations from DCT reconstructions, and ultimately on comparisons between experiments and simulations at the scale of the grain.

Interpretable Calibration of Crystal Plasticity Model Using a Bayesian Surrogate-Assisted Genetic Algorithm

The accurate calibration of material parameters in crystal plasticity models is essential for applying crystal plasticity (CP) simulations. Identifying these parameters usually requires unfeasible single-crystal experiments or expensive time costs due to the use of traditional genetic algorithm (GA) optimization. This study proposed an efficient and interpretable method for calibrating the constitutive parameters with macroscopic mechanical tests. This approach utilized the Bayesian neural network (BNN)-based surrogate-assisted GA (SGA) optimization method to identify a group of constitutive parameters that can reproduce the experimental stress–strain curve and crystallographic orientation by crystal plasticity simulation. The proposed approach was performed on the calibration of typical high-entropy alloy material parameters in two different CP models. The use of the surrogate model reduces the call count of simulation in the parameter searching process and speeds up the calibration significantly. With the help of infill sampling, the accuracy of this optimization method is consistent with the CP simulation and not limited by the accuracy of the surrogate model. Another merit of this method is that the pattern that the BNN surrogate found in the model parameters can be interpreted with its integrated gradients, which helps us to understand the relationship between constitutive parameters and the output mechanical response. The interpretation of BNN can guide further experiment design to decouple particular parameters and add constraints provided by the attached experiment or prior knowledge.

Developing a new method to represent the low and high angle grain boundaries by using multi-scale modeling of crystal plasticity

The main goal of the research is an investigation on a multi-scale crystal plasticity of a finite element model for polycrystalline material by using a hierarchical computational framework and macro/micro structure analysis. Therefore, several systematic numerical studies on the evolution of the microstructure and texture of pure Aluminum during torsion have been performed to identify crystal misorientation. The framework is integrated into ABAQUS finite element package using Düsseldorf Advanced Materials Simulation Kit (DAMASK) software. Then a Python algorithm was developed to examine the high and low grain boundaries, and the results were compared to experimental data of electron back scattering diffraction (EBSD). The findings showed that the torsion texture of pure Aluminum is completely attributed to dislocation sliding, and it was predictable by crystal plasticity. It was also shown that the Brass component with (φ1,ϕ,φ2)=(35°,45°,0°) appeared in the deformed sample. As a result, it is demonstrated that the multi-scale crystal plasticity simulation can predict the effect of inhomogeneous strain on the deformed texture.

Influence of Local Microstructural Variations on the Bendability of Aluminum Extrusions: Experiments and Crystal Plasticity Analyses

Abstract The bendability of extruded profiles of an age hardenable aluminum alloy is investigated using mechanical tests on flat tensile specimens and bending specimens. Two profile geometries are considered, where the profiles exhibit different grain structures. The microstructure of the profiles in terms of the crystallographic texture and constituent particles is otherwise comparable. While the tensile properties are not that different for the two profiles, their bendability is strongly dependent on the grain structure and is about twice as high for one profile than for the other. A newly proposed coupled damage and single crystal plasticity model is used in finite element analyses of the mechanical tests to investigate the influence of the grain structure on the bending behavior, and the numerical results are compared to the experimental tests. The crystallographic texture and the grain morphology of the profiles, found by the electron back-scatter diffraction technique, are explicitly represented in the finite element models. The crystal plasticity simulations capture the difference in the bendability of the two profiles, and in agreement with the experiments predict a considerably higher bendability for one of the profiles. It is found that the grain structure affects the shear band formation in these profiles, but also the local texture where the shear bands are located is important for crack initiation and propagation as grains with certain crystallographic orientations may have a higher fracture resistance.

A machine learning model to predict yield surfaces from crystal plasticity simulations

We introduce a microstructurally informed machine learning model for predicting the anisotropic yield surfaces of polycrystalline materials. A full-field, spatially resolved crystal plasticity model is employed to generate a data set describing the yield response of an aluminum alloy, enabling the training of a neural network yield function and the calibration of 3D yield criteria of plastically anisotropic polycrystals. This novel formulation explores the flexibility of neural networks to describe complex-shaped yield loci and avoids common problems associated with conventional 3D yield functions, such as the non-trivial parameter identification and non-uniqueness of the anisotropy coefficients. Here, Bayesian optimization is applied to obtain an optimal neural network architecture and allows for an automated model design. The neural network yield function is able to learn intrinsic properties such as the convexity of the yield hull and tension–compression symmetry from a relatively small number of data points. The fully data-driven yield criterion can accurately reproduce multiaxial flow response and planar anisotropy despite of its material blind initial state. Stress gradients can also be computed from the neural network through automatic differentiation as derived quantities with good fidelity. This allows the calculation of r-values and provides a pathway for implementing the neural network yield model into finite element codes.

The Effect of the Energy Release Rate on the Local Damage Evolution in TRIP Steel Composite Reinforced with Zirconia Particles

In this study, the effect of the energy release rate on the transformation-induced plasticity (TRIP) steel composite reinforced with 5 vol% ceramic particles is determined using the crystal plasticity simulation of the coupled brittle-ductile damage model and validated by experimental results. A miniature dog bone tensile sample is subjected to an interrupted in situ quasi-static tensile test up to a true strain of 20.3%. Using the commercial digital image correlation program VEDDAC and the image processing method in MATLAB, the test data are utilized to monitor the progress of local microstrain and damage. The impact of the energy release rate of ceramic particles is investigated by simulation using a coupled crystal plasticity-dislocation density model with ductile-brittle criteria for the corresponding phases. It can be shown that the local deformations predicted by the numerical simulation and the experimental data are qualitatively comparable. The damage pixel of the experiment, smaller Ecr (1.0 × 108), and larger Ecr (1.2 × 108) cases of energy release rates are 4.9%, 4.3%, and 5.1%, respectively. Furthermore, on a global strain of 20.3%, the relative error between simulation and experimental validation of smaller Ecr (1.0 × 108) and larger Ecr (1.2 × 108) cases is 12.2% and 4%, respectively.

Experimental and numerical study on strain path and crystal orientation dependences of phase transformation behaviors of QP1180 steel

Phase transformation behaviors of a quenching & partitioning (QP) steel, QP1180, under different strain paths are investigated by both experiment and crystal plasticity simulation. Experiments of various strain paths including uniaxial tension (UT), uniaxial compression (UC), plane strain tension (PST) and equi-biaxial tension (EBT) are conducted, and the mechanical stability of retained austenite (RA) shows obvious strain path and orientation dependences. A crystal plasticity-phase transformation model with multiple-variant kinetics is proposed and used to predict the transformation behaviors. The single crystal analysis with 11 typical orientations is performed under various loading paths. Different variant types and volume fraction evolutions are observed in 11 orientations, which results in the overall path and orientation dependences of phase transformation in polycrystal. Eight major texture components of the RA grains show a similar strain path dependence and determine the transformation behaviors of the QP1180 steel. A numerical simulation comparison between single-variant and multiple-variant kinetics shows that both theories can capture strain path dependence and texture evolution in phase transformation of the current QP1180, but the multiple-variant kinetics can better reproduce the texture of newly formed martensite. The effects of non-proportional loadings on transformation and the related mechanism are also studied with the proposed model.