Crystal Plasticity Finite Element Model Research Articles

Modeling complex polycrystalline alloys using a Generative Adversarial Network enabled computational platform

Creating statistically equivalent virtual microstructures (SEVM) for polycrystalline materials with complex microstructures that encompass multi-modal morphological and crystallographic distributions is a challenging enterprise. Cold spray-formed (CSF) AA7050 alloy containing coarse-grained prior particles and ultra-fine grains (UFG) and additively manufactured (AM) Ti64 alloys with alpha laths in beta substrates. The paper introduces an approach strategically integrating a Generative Adversarial Network (GAN) for multi-modal microstructures with a synthetic microstructure builder DREAM.3D for packing grains conforming to statistics in electron backscatter diffraction (EBSD) maps for generating SEVMs of CSF and AM alloy microstructures. A robust multiscale model is subsequently developed for self-consistent coupling of crystal plasticity finite element model (CPFEM) for coarse-grained crystals with an upscaled constitutive model for UFGs. Sub-volume elements are simulated for efficient computations and their responses are averaged for overall stress-strain response. The methods developed are important for image-based micromechanical modeling that is necessary for microstructure-property relations.

Hierarchical Deformation and Anisotropic Behavior of (α+β) Ti Alloys: A Microstructure-Informed Multiscale Constitutive Model Study

In this study, the hierarchical deformation and anisotropic behavior of (α+β) Ti alloys are investigated using a novel microstructure-informed multiscale constitutive model. State-of-the-art crystal plasticity finite element (CPFE) models, due to their emphasis on a single length scale, are inadequate for capturing the complex hierarchical behavior of additively manufactured (AM) (α+β) titanium alloys, which are characterized by columnar grains and lamellar subgrain features at distinct length scales. To overcome this limitation, a decoupled multiscale framework was developed, integrating representative volume elements (RVEs) for both the columnar grain structure at the higher length scale and the subgrain microstructure at the lower length scale, with equal emphasis on each. The material behaviors at these scales were modeled using an anisotropic classical plasticity model and a mechanism-based CPFE model, respectively. The framework was experimentally validated for Directed Energy Deposition (DED) manufactured Ti-6Al-4V and used to investigate microscopic stress/strain fields, deformation localizations at grain and subgrain levels, and stress partitioning among neighboring grains. Insights from these studies led to the proposal of a new theory of anisotropy in AM (α+β) titanium alloys.

Calibration and surrogate model-based sensitivity analysis of crystal plasticity finite element models

Crystal plasticity models are powerful tools for predicting the deformation behaviour of polycrystalline materials accounting for underlying grain morphology and texture. These models typically have a large number of parameters, an understanding of which is required to effectively calibrate and apply the model. This study presents a structured framework for the global sensitivity analysis of the effect of crystal plasticity parameters on model outputs. Due to the computational cost of evaluating crystal plasticity models multiple times within a finite element framework, a Gaussian process regression surrogate was constructed and used to conduct the sensitivity analysis. Influential parameters from the sensitivity analysis were carried forward for calibration using both a local Nelder-Mead and global differential evolution optimisation algorithm. The results show that the surrogate based global sensitivity analysis is able to efficiently identify influential crystal plasticity parameters and parameter combinations. Comparison of the Nelder-Mead and differential evolution algorithms demonstrated that only the differential evolution algorithm was able to reliably find the global optimum due to the presence of local minima in the calibration objective function. However, the performance of the differential evolution algorithm was dependent on the optimisation hyperparameters selected.

Understanding of additively manufactured material cyclic behavior at the grain scale by neutron diffraction and crystal plasticity modeling

Additive manufacturing (AM) offers distinct advantages in terms of complexity, reduced material waste, and shorter production times. However, the microstructures of AM alloys differ significantly from conventionally manufactured ones, and their impact on grain behavior remains uncertain. This study employs neutron diffraction, coupled with Crystal Plasticity Finite Element (CPFE) modeling, to investigate microstructural effects on cyclic behavior in 316L LPBF alloys. Neutron diffraction provides high-resolution strain and stress data at the polycrystalline level during loading, offering valuable insights into grain behavior. The CPFE model is initially validated at the grain scale using neutron diffraction, demonstrating its ability to predict local mechanical behavior in additively manufactured materials. This methodology holds promise for broader applications in various AM alloys, particularly when macroscopic identification of mechanical behavior is insufficient. Furthermore, the comparison between neutron diffraction and CPFE predictions allows to identify the influence of dendrites and dislocation substructures on the mechanical behavior at the grain scale. Notably, the micromechanical anisotropy resulting from dislocation organization along dendritic structures with specific orientations is highlighted. This study shows that despite the observed anisotropy, experimental measurement of intragranular strain distribution are correctly captured with a quantification of the deviation observed on some specific orientations due to the above cited microstructure sub-structures.

Crystal plasticity-driven evaluation of notch fatigue behavior in IN718

The aim of this study was to establish a method for evaluating notch fatigue behavior through crystal plasticity finite element (CPFE) simulations based on the actual microstructure of the nickel-based alloy Inconel 718 (IN718). Initially, the equivalent plastic strain, εeps, which reflects the comprehensive slip at the grain scale, was employed to analyze the fatigue crack initiation mechanism of IN718, revealing that twinning and triple junctions of grain boundaries were high-risk locations for fatigue crack initiation. Next, fatigue simulations were performed on notched specimens using the CPFE model, with a material-level CPFE model particularly employed at the notch root. The increment of εeps, Δεeps, in a stable cycle was used as the fatigue damage control parameter and correlated with the fatigue life, Nf, revealing that the Δεeps-Nf relationship at material-level satisfied the form of the Mason-Coffin model. Finally, fatigue life prediction of IN718 notched specimens was carried out based on the Δεeps-Nf relationship, with the predicted results falling within the 2-fold scatter band, demonstrating good prediction accuracy.

Integrating crystal plasticity and experimentation for investigating the size effect on the deformation characteristics of AISI304 microtubes manufactured by free bending technology

During the deformation process of micro-bending, the size effect resulting from the variation in the grain size of the microtubes is the primary factor affecting the bending behavior. The current study on free bending mainly focuses on using macroscopic finite element simulation and experimental analysis to investigate the factors affecting the bending radius and forming quality. However, due to the size effect, the practices and insights gained from macroscopic forming may not directly apply to microforming. Thus, this study aims to reveal and explain the reason for the increase in the bending radius of microtubes with decreasing grain size by combining experimental investigations with crystal plasticity finite element modeling (CPFEM). It was determined that the grain size is a crucial consideration in the micro-bending process of microtubes. Additionally, the CPFEM approach can provide guidance for the process parameters of free bending forming of microtubes.

Comparative analysis of irradiation-stimulated hardening in the austenite and ferrite phases of F321 stainless steel

F321 stainless steel is renowned for its outstanding mechanical properties and corrosion resistance, making it a crucial structural material in light water reactors and high-temperature gas reactors. With irradiation (IR), F321 stainless steel undergoes microstructural alterations, such as the formation of IR-stimulated defects (e.g., stacking fault tetrahedrons (SFTs), dislocation loops (DLs), and clusters), resulting in IR hardening. This study compares the IR-stimulated hardening in the austenitic and ferritic phases of F321 stainless steel through both experimental methods and numerical simulations. In the austenitic phase, the size and number density of IR defects (DLs and SFTs) were determined, which were proportional to the IR dose. In the ferritic phase, IR-induced DL parameters were quantified, and the effects of IR on spinodal decomposition were analyzed. The interaction processes and mechanisms between dislocations and IR defects in the austenitic phase were evaluated using molecular dynamics (MD) simulations, leading to the development of a model for IR defect-induced hardening strength. Additionally, an MD data-driven crystal-plasticity-finite-element-model (CPFEM) was established. The nano-indentation hardness of the austenitic and ferritic phases was measured and calculated through both experimental methods and CPFEM simulations. The results show that the nano-indentation hardness of the ferritic phase is reduced compared to the austenitic phase, due to a lower density of IR defects. Understanding these effects provides deeper insights into how IR influences the mechanical and microstructural properties of F321 steel, which is essential for predicting the material's long-term performance and reliability.

Anisotropic formability and deformation mechanism of near-α titanium alloy sheet under continuous nonlinear strain paths at high temperature

In the present study, the anisotropic formability and underlying deformation mechanism of near-α TA32 titanium alloy sheet under continuous nonlinear strain paths (CNSPs) at high temperature were investigated in depth. To achieve this goal, a new experimental method combining hot gas bulging with step-combined dies was proposed, and the hot CNSPs of metal sheets can be flexibly and conveniently realized by changing the number and shape of step-combined dies. Based on this method, the anisotropic deformation behavior and forming limits of TA32 sheet under fifteen CNSPs were tested at 800 ℃ with a strain rate of 0.001 s−1. Then, two advanced constitutive models with different scales were embedded into the classical Marciniak-Kuczyński (M-K) theory to predict the forming limits of TA32 sheet under different strain paths: the macro-scale viscoplastic model coupled with Hill48 yield criterion and non-associated flow rule (NAFR) as well as the meso-scale three-dimensional crystal plasticity finite element (CPFE) model coupled with cellular automata (CA). The results demonstrate that the CPFE-CA-MK coupled model exhibits higher accuracy in predicting the forming limits of TA32 sheet under linear and continuous nonlinear strain paths. Especially for the tension-tension strain paths, the CPFE-CA-MK coupled model improves accuracy by at least 3.1 % compared to macro-scale models. Due to the material anisotropy, the initial inclination angle of the groove in the CPFE-CA-MK model is closely related to the strain path and significantly affects the prediction accuracy. Based on the CPFE simulation, the effects of anisotropy and strain path change on the dislocation slip mode of different texture components was analyzed in depth, which provides a theoretical guidance for the optimization of hot forming process of TA32 titanium alloy complex components.

Asymmetrical plastic deformation during spherical micro-indentation of magnesium

The complex deformation of magnesium (Mg) and its alloys has been the focus of many studies in lightweight technologies. In this paper, spherical micro-indentation tests followed by post-test electron microscopy were carried out on large grain pure Mg to isolate the effects of crystal orientation on the activation of deformation along different slip or twinning systems. Both pre- and post-indentation crystal orientations were measured using electron backscatter diffraction (EBSD). The pre-indentation orientations were mapped into a crystal plasticity finite element (CPFE) model to further analyze the results. It is shown that the resulting deformation twinning and the degree of indentation-induced misorientation were strongly correlated with the crystal orientation in the region of the indentation. Depending on the crystal orientation, multiple waves of basal slip were observed to form asymmetrically around the indents. These slip bands lead to more than 12° lattice rotations that are captured by CPFE modeling. For the first time, it is shown that indentation can lead to significant out-of-plane displacement field that can induce twin nucleation at the interface of far-field (>100 μm) neighbouring grains. CPFE simulations indicate that maintaining far-field strain compatibility leads to the nucleation of twins rather than a slip transfer or slip-induced twinning mechanism.

Digital twin-based identification of crystal plastic material parameters for weld joints of orthotropic steel decks

The identification of crystal plasticity (CP) material parameters is indispensable for using CP models to simulate and understand the microcrack initiation and propagation of orthotropic steel decks (OSD). This study proposes a digital twin (DT)-based framework for identifying CP material parameters of weld joints of OSD by fusing multiscale CP finite element model (CPFEM) with macroscale stress–strain material tests. The material tests of the specimen (physical entity) cut from the weld joints of OSD and sliced to the centimeter scale are carried out using the standard dynamic test system. The CPFEM simulation is used to develop a multiscale virtual entity to map the physical entity. The particle swarm optimization algorithm is used to fuse the CPFEM simulation with the material test data to identify CP material parameters and produce a DT. The results demonstrate that the CP material parameters identified by the proposed framework are more accurate than those identified by a single representative volume element method. The results also show that the DT-based identification of CP material parameters has high applicability.

A deep learning-based crystal plasticity finite element model

This study presents an innovative deep learning-based surrogate model for the Crystal Plasticity Finite Element (CPFE) method, fundamentally transforming the generation of mechanical properties such as stress-strain curves in the study of crystal plasticity. Stress-strain curves are pivotal in understanding material deformation, elucidating the intricate relationship between a material's structure and its properties. Traditional CPFE methods, though thorough in their analysis, face significant computational challenges, largely due to the complexity of the crystal plasticity framework. The proposed model circumvents this bottleneck by utilizing an autoencoder architecture to learn intermediate data representations, which are then used to predict the plastic component of deformation. This predicted plastic component serves as a foundation for computing stress-strain curves, effectively bypassing the most time-intensive aspect of traditional CPFE methods, the plasticity self-consistency procedure (achieving a 29.3x speed increase without compromising accuracy).

Texture and bendability evolution mechanism of 6063 aluminum alloy tube formed by free-bending technology employing cross-scale numerical modeling

With the improvement of application requirements, the combination of precise shape and high performance of tube components has become a burning issue. This work investigates the free-bending process of 6063 aluminum alloy tubes using cross-scale numerical modeling. The cross-scale framework integrates macroscopic finite element model (FEM) and crystal plasticity finite element model (CPFEM) through strain history. CPFEM exhibits excellent agreement with the macroscopic FEM and experimental results for both the Mises stress and texture evolution. Predictions indicate that as bending deformation increases, the volume fractions of the initial Cube texture decrease, while the Goss texture component increases. The overall texture strength continuously decreases. Meanwhile, slip mode plays a critical role in texture evolution, causing similar trends in the inner and outer bend regions. Additionally, the findings from the cross-scale simulation accurately predict the detailed texture evolution of the 6063 aluminum alloy tube under various feeding speeds. The development of Goss texture in various forming regions and the formation of substructures within Goss-oriented grains are primary factors contributing to reduced tube formability, which could illustrate the primary mechanisms for variation in tube bendability effectively. The proposed cross-scale method lays the foundation for research on complex spatial tube components as well. Moreover, cross-scale simulation facilitates the prediction of macroscopic deformation and microstructural evolution in critical regions of tube components, allowing for the optimization of bending processes based on cross-scale simulation results.

Investigating grain-resolved evolution of lattice strains during plasticity and creep using 3DXRD and crystal plasticity modelling

Microstructure-informed crystal plasticity finite element models have shown great promise in predicting plastic and creep deformation in polycrystalline materials. These models can provide substantial insight into the design, fabrication and lifetime assessment of critical metallic components during operation, for instance, in thermal power plants. However, to correctly incorporate damage prediction into models, the microstructural strain simulated at the grain level must be accurately predicted with suitable validation. For this reason, a 3D X-ray Diffraction (3DXRD) experiment was carried out on 316H stainless steel, a material commonly used in thermal power plants, to obtain the per-grain strain response during plastic and creep deformation at 550°C. Several hundred grains within a probed X-ray volume were tracked and measured whilst loading in-situ, obtaining per-grain centre-of-mass positions, crystallographic orientations, and average lattice strain over individual grains. These data were used to calibrate a crystal plasticity model to study the plastic and creep deformation using macroscopic stress-strain and stress-relaxation data. Subsequently, the model was used to predict the average elastic strain in different grains during the cyclic creep experiment, which was validated by 3DXRD datasets. The model results reveal that {100} or {311} grain families are strongly sensitive to microstructure, thereby a polycrystal model that describes specific orientation and neighbourhood characteristics is essential to predict the local response of these grain families. Whereas, self-consistent models are suitable for {110} and {111} grain families. This study shows that only with a suitable calibration of subsurface grain behaviour, crystal plasticity models reveal grain characteristic-dependent micromechanical behaviour.

Effect of wire diameter compression ratio on drawing deformation of micro copper wire

A crystal plasticity finite element model was developed for the drawing deformation of pure copper micro wire, based on rate-dependent crystal plasticity theory. The impact of wire diameter compression ratio on the micro-mechanical deformation behavior during the wire drawing process was investigated. Results indicate that the internal deformation and slip of the drawn wire are unevenly distributed, forming distinct slip and non-slip zones. Additionally, horizontal strain concentration bands develop within the drawn wire. As the wire diameter compression ratio increases, the strength of the slip systems and the extent of slip zones inside the deformation zone also increase. However, the fluctuating stress state, induced by contact pressure and frictional stress, results in a rough and uneven wire surface and diminishes the stability of the drawing process.

Effect of pre-straining direction on the microstructure, mechanical properties and microstructural response of AA2099-T83 Al-Li alloy

Understanding the microstructural evolution and anisotropic behavior of Al-Li alloys after pre-deformation in different directions is crucial for optimizing their forming performance. This study investigates the microstructural evolution in AA2099 Al-Li alloy rolled sheets after pre-deformation in the extrusion direction (ED) and transverse direction (TD), and the resulting changes in mechanical properties during subsequent tensile deformation. A crystal plasticity finite element model (CPFEM) was established to quantitatively analyze the link between pre-deformation direction and the microstructural response during the hardening stages of tensile deformation. The results showed that the differences in mechanical properties due to pre-deformation direction are mainly attributed to the variations in volume fraction and diameter of the T1 precipitates. The contributions of T1 phase to yield strength are estimated to be 239 MPa (ED) and 223 MPa (TD), respectively. An increase in T1 (Al2CuLi) phase volume fraction and a decrease in phase diameter lead to higher average von Mises stress and average maximum principal strain values during the hardening stages.

The development of grain resolved stress fields around notch tips in soft-textured zirconium polycrystals: A three-dimensional synchrotron X-ray diffraction study

Texture, microstructure, and local grain neighbourhood contribute to the development of localized stresses in polycrystals. For hexagonal close-packed materials, crystal's elastic and plastic anisotropy can also be a major contributing factor, yet there is a paucity of experimental studies focusing on the extent of contribution of such parameters on the magnitude of localized stresses at microscales. This study focuses on addressing this knowledge gap by deforming double-edge-notched soft-textured α-zirconium specimens in-situ, while measuring grain scale tensorial stresses using high energy synchrotron X-ray diffraction. The specimens were subjected to cyclic loads to study the evolution of stresses in the vicinity of both shallow and deep notches. The soft-texture of the specimens is such that there are no c-axes of grains aligned along the macroscopic loading direction thereby inhibiting deformation twinning. The “as-measured” microstructures and notch geometries were imported into a crystal plasticity finite element model for further analysis. Results show that despite the absence of c-axes of grains aligned along loading direction, the developed stresses were substantially influenced by crystallographic orientations. Stress drop was observed near the onset of plasticity with further loading and the orientation and position effects were highlighted. A plastic deformation mechanism was revealed where, upon specimen loading, the mechanical constraints enforced during grain-grain interactions led to hardening. Accordingly, a parameter was devised to quantify the grain level hardening arising from this mechanism. It was shown that grain-scale stress concentration factors vary significantly before the onset of plasticity, but they settle in the plastic zone and with the progression of cycles.

Physically based modelling of orientation deviation effect on mechanical behavior for dual‐phase single‐crystal superalloy

AbstractThis work systematically investigates the orientation deviation effect on the elastoplastic deformation of a dual‐phase, nickel‐based single‐crystal superalloy through a combined experimental study and crystal plasticity finite element modelling method (CPFEM). Physically based, dual‐phase microstructural model was developed based on scanning electron microscopy (SEM), which was implemented by finite element (FE) modelling using a representative volume element (RVE) with periodic boundary conditions. An extended equivalent yield criterion coupled with CPFEM was adopted to describe the non‐uniform yield behavior induced by octahedral and cubic slip systems. The predicted results have shown that both the bulk behavior and localized stress–strain nature are orientation deviation dependent and that the first Euler angle plays a more important role in elastoplastic behavior than the second Euler angle. This study has thus advanced the basic understanding of the relationship between orientation deviation and the bulk deformation behavior of the dual‐phase nickel‐based single crystal.

The micromechanics of fracture of zirconium hydrides

Zirconium alloys are susceptible to hydrogen embrittlement and hydride precipitation. The precipitation of hydrides is accompanied by a transformation strain, but the contribution of this strain to the fracture of hydrides is not well-understood. In this study, deformation mechanisms and the micromechanics of fracture of hydrides are investigated by conducting in-situ and interrupted ex-situ tensile experiments on hydrided zirconium specimens. Electron backscatter diffraction (EBSD) is used to measure the macro-EBSD maps that contain the grains located in the gauge section of the specimens’ surfaces. Further, high spatial resolution EBSD is used to determine orientation variations induced by the precipitation of hydrides and by the external mechanical load. The measured grain orientations are mapped into a crystal plasticity finite element (CPFE) model to examine the performance of eight different crack initiation criteria. It is shown that a multiscale approach is essential for studying the fracture of hydrides as the details of hydride morphology, orientation, local grain neighborhood, and hydride-hydride interactions are important in such analysis. It is shown that neglecting the effects of hydride-induced transformation strain leads to inaccuracies in predicting both the location and direction of microcracks within hydrides. Among the examined methods, the combination of resolved shear stress and resolved shear strain on slip systems, i.e., the highest shear energy density, consistently predicts the correct locations of hydride microcracks as well as their propagation direction. Further, it is shown that the significant deformation that takes place within hydrides is the main driving force for the fracture of hydrides.

Numerical modeling of shear band effect on Goss grain recrystallization in electrical steels: Crystal plasticity finite element and phase field modeling

This study investigates the effect of shear band evolution on the nucleation of Goss {110}<001> texture during the primary recrystallization of 3.24 wt% Si grain-oriented electrical steel. Nucleation at the early stage of primary recrystallization of the steel is explored both experimentally and numerically. The experimental approach involves cold rolling the steel specimens to obtain a thickness reduction ratio of 76 % and then applying heat treatment to them at 600 °C for less than 1 min. The numerical simulation employes crystal plasticity (CP) finite element model (FEM) to simulate the plastic deformation induced by the dislocation slips on predefined slip systems and non-crystallographic shear bands during cold rolling. Based on the CPFEM results, the generalized strain energy release maximization (GSERM) model is used to predict the preferential orientation probability of recrystallized nuclei for the steel by considering shear band formation. Subsequently, the microstructure evolution during the early stage of primary recrystallization of the steel is simulated using the phase field model (PFM). The developed CP model successfully predicted shear band activation and evolution in the γ-fibers centered on the {111}<112> texture component. The model also demonstrated that shear bands would be the preferred nucleation sites at the early stage of primary recrystallization because of their high stored energy. Moreover, by coupling with the GSERM model, the PFM could reproduce the nucleation of Goss grains at the beginning of primary recrystallization in shear bands.

Atomic-scale three-dimensional irradiation-induced defect kinetics models for bcc Fe-based alloys

The interaction between irradiation defects and dislocations could lead to macroscopic hardening and embrittlement. In this study, molecular dynamics (MD) and machine learning were conducted to study three-dimensional void- and Cu-cluster-induced kinetics models under interaction with dislocations in body-centered cubic Fe-based alloys. MD Results show that dislocation climb and shear are two types of interaction mechanism based on the defect size. Combined MD results and machine learning, it was found that the dislocation length increased linearly with an increase in the size of the defects after the interaction. In addition, the number of atoms in the Cu-rich cluster and the reduced number of vacancies in the voids had a square relationship with the defect size where 0.85D2 is for Cu-rich cluster and 0.50D2 is for void. Furthermore, atomic-scale three-dimensional irradiation-induced defect kinetics models were developed and incorporated into the crystal plasticity finite element model (CPFEM). We also analyzed the contributions of various defects to the increase in the yield stress during CPFEM simulation. Compared with DBH model, the prediction of MD data-driven CPFEM matches better with the experimental data. Cluster contributed the most to hardening with low obstacle strength due to the higher number density compared with dislocation loops and voids. The loops also contributed to hardening; however, their contribution was smaller than that of the clusters. Although the number density and size of voids were minimized, they may have contributed because of the high obstacle strengths. This work can indeed deepen the understanding of irradiation effect in Fe-based alloys.