Coupling Crystal Plasticity Research Articles

Coupled crystal plasticity and damage model for micro crack propagation in polycrystalline microstructures

Coupled crystal plasticity and damage model for micro crack propagation in polycrystalline microstructures

Three-dimensional modeling of grain structure growth within ceramic tool material

Ceramic cutting tool materials possess specific advantages, including high hardness, excellent wear resistance, and high chemical stability, making them unparalleled in the machining of difficult-to-process materials compared to traditional cutting tools. The mechanical performance of these materials is primarily determined by their microstructure. Therefore, it is necessary to simulate and optimize the microstructure of ceramic cutting tool materials to provide theoretical guidance for further enhancing their fracture toughness. In this paper, a simulation model based on sintering densification theory was proposed, coupling crystal plasticity with a three-dimensional cellular automaton, to investigate the impact of nanoparticle content, sintering temperature, sintering pressure, and holding time on grain growth in composite ceramic materials using spark plasma sintering (SPS). Furthermore, an evolution model for grain growth of TiB2-TiC-SiC nanocomposite ceramic materials in cutting tools is established, and the optimal sintering process parameters are obtained. Finally, SPS experiments were conducted. Under the conditions of a sintering temperature of 1600 °C, holding time of 7 min, and sintering pressure of 40 MPa, optimal mechanical performance composite ceramic cutting tool materials were prepared. The experimental results, including a hardness of 25.6 GPa, fracture toughness of 7.1 MPa·m1/2, and flexural strength of 628.2 MPa, were consistent with the simulation outcomes. This indicates that the designed simulation model for nanocomposite ceramic grain growth reliably reflects the physical process of grain growth in the material and provides valuable guidance for further understanding the mechanisms underlying grain growth.

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.

Simulation of dislocation slip and twin propagation in Mg through coupling crystal plasticity and phase field models

A numerical strategy to simulate plastic deformation in Mg alloys including dislocation slip and twin propagation is presented. Dislocation slip is included through a crystal plasticity model which is solved using the finite element method while twin propagation is taken into account by means of a phase field model which is solved using a fast Fourier transform algorithm. The coupled crystal plasticity and phase field equations were solved using different discretizations of the simulation domain using the same time step for both of them. The numerical strategy was used to simulate the deformation in compression of a Mg micro-pillar along the [101̄0] direction. The stress–strain curve predicted by the model as well as the dominant deformation mechanisms were in agreement with the experimental data in the literature and demonstrate the viability of the strategy to take explicitly into account twin propagation during the simulation of plastic deformation of Mg alloys. Finally, an example of slip/twin interaction in polycrystals was simulated to show the capabilities of the model.

Coupled crystal plasticity and micromechanics damage model based on viscoplastic self-consistent theory and X-ray computed tomography

In recent years, coupled crystal plastic and micromechanics damage models have been applied to effectively deal with the complex interactions between the polycrystalline environments and void behaviors. The classical viscoplastic self-consistent (VPSC) model, as a widely used analytical model with excellent computational efficiency, has been extended to the dilatational-VPSC (DVPSC) model. However, as proposed by the model developers (Lebensohn et al., 2004), there are two main challenges hindering the further extension of the DVPSC model, including (1) the lack of the void nucleation and coalescence and (2) the effective experimental verification. Aiming at the above challenges, a modified-DVPSC model considering the void nucleation and coalescence was proposed and experimentally verified in this work. Accordingly, some improvements were made on the original DVPSC model including the linearization method, the self-consistent equations, and also the volume update equations. Then, with the support of the X-ray computed tomography (CT) technique, the void evolution and fracture mode were analyzed and revealed during the uniaxial tension deformation of 2055 aluminum alloy, through which the essential parameters of the modified model were calibrated. Compared to the previous VPSC and DVPSC models, this modified model accurately describes the stress-strain state, the porosity evolution, and fracture behaviors. Finally, the modified model was applied to investigate the effects of the different loading directions, exhibiting a substantial influence of texture on the void evolution. This research is thereby an innovative attempt for the improvement of the DVPSC model, which can provide inspirations for the future extensions of this theoretical system.

Initial grain orientation controls static recrystallization outcomes in cold-worked iron: Insight from coupled crystal plasticity/vertex dynamics modeling

Recrystallization of metallic materials is an important metallurgical treatment to bring cold-worked alloys to a usable state. Static recrystallization (SRX) occurs after deformation, once the material has built up sufficient plastic strain energy to trigger grain boundary motion. However, we have very limited knowledge about the combined effects on recrystallization kinetics of temperature, amount of cold working, triple junction mobility, and level of recovery in the deformed microstructure. In particular, little is still known about the microstructural factors that control the onset of SRX. Here we develop a comprehensive physical model based on coupling crystal plasticity and grain boundary kinetics utilizing curvature and differential plastic strain energy as driving forces for SRX in polycrystalline iron. The model links finite-element polycrystal plasticity simulations with a two-dimensional vertex dynamics approach, and is used to probe the large parameter space influencing static recrystallization. Our main finding is that the initial texture (defined by the polycrystal’s grain orientation and size distribution) is the dominant feature triggering and controlling SRX kinetics. We find a direct correlation between the degree of dislocation density buildup and the relative grain orientation across a grain boundary at the beginning of the deformation phase. Indeed, analysis of our results points to the maximum Schmid factor of a grain as the best predictor for activation of its grain boundaries during the recrystallization phase. We also find that the amount of post-deformation recovery only has a limited effect on the evolution of the recrystallized microstructure. Finally, using a definition based on the rate of transformation of the material, we find a recrystallization temperature of 600 ∘C, consistent with experimental observations in high-purity iron specimens.

Simulation of strain induced abnormal grain growth in aluminum alloy by coupling crystal plasticity and phase field methods

A mesoscale modeling methodology is proposed to predict the strain induced abnormal grain growth in the annealing process of deformed aluminum alloys. Firstly, crystal plasticity finite element (CPFE) analysis is performed to calculate dislocation density and stored deformation energy distribution during the plastic deformation. A modified phase field (PF) model is then established by extending the continuum field method to consider both stored energy and local interface curvature as driving forces of grain boundary migration. An interpolation mapping approach is adopted to transfer the stored energy distribution from CPFE to PF efficiently. This modified PF model is implemented to a hypothetical bicrystal firstly for verification and then the coupled CPFE-PF framework is further applied to simulating the 2D synthetic polycrystalline microstructure evolution in annealing process of deformed AA3102 aluminum alloy. Results show that the nuclei with low stored energy embedded within deformed matrix tend to grow up, and abnormal large grains occur when the deformation is close to the critical plastic strain, attributing to the limited number of recrystallized nuclei and inhomogeneity of the stored energy.

Damage Evolution Simulations via a Coupled Crystal Plasticity and Cohesive Zone Model for Additively Manufactured Austenitic SS 316L DED Components

This study presents a microstructural model applicable to additively manufactured (AM) austenitic SS 316L components fabricated via a direct energy deposition (DED) process. The model is primarily intended to give an understanding of the effect of microscale and mesoscale features, such as grains and melt pool sizes, on the mechanical properties of manufactured components. Based on experimental observations, initial assumptions for the numerical model regarding grain size and melt pool dimensions were considered. Experimental observations based on miniature-sized 316L stainless steel DED-fabricated samples were carried out to shed light on the deformation mechanism of FCC materials at the grain scale. Furthermore, the dependency of latent strain hardening parameters based on the Bassani–Wu hardening model for a single crystal scale is investigated, where the Voronoi tessellation method and probability theory are utilized for the definition of the grain distribution. A hierarchical polycrystalline modeling methodology based on a representative volume element (RVE) with the realistic impact of grain boundaries was adopted for fracture assessment of the AM parts. To qualify the validity of process–structure–property relationships, cohesive zone damage surfaces were used between melt pool boundaries as the predefined initial cracks and the performance of the model is validated based on the experimental observations.

Coupling crystal plasticity and cellular automaton models to study meta-dynamic recrystallization during hot rolling at high strain rates

Predicting microstructure and (micro-)texture evolution during thermo-mechanical processing requires the combined simulation of plastic deformation and recrystallization. Here, a simulation approach based on the coupling of a full-field dislocation density based crystal plasticity model and a cellular automaton model is presented. A regridding/remeshing procedure is used to transfer data between the deformed mesh of the large-strain crystal plasticity model and the regular grid of the cellular automaton. Moreover, a physics based nucleation criterion has been developed based on dislocation density difference and changes in orientation due to deformation. The developed framework is used to study meta-dynamic recrystallization during double-hit compression tests and multi-stand rolling in high-resolution representative volume elements. These simulations reveal a good agreement with experimental results in terms of texture evolution, mechanical behaviour and growth kinetics, while enabling insights regarding the effect of nucleation on kinetics and crystallographic texture evolution.

Coupling Crystal Plasticity and Cellular Automaton Models to Study Meta-Dynamic Recrystallization During Hot Rolling at High Strain Rates

Coupling Crystal Plasticity and Cellular Automaton Models to Study Meta-Dynamic Recrystallization During Hot Rolling at High Strain Rates

Coupling crystal plasticity and stochastic cluster dynamics models of irradiation damage in tungsten

Irradiation damage is known to alter a material’s microstructure due to the accumulation of high densities of defect clusters. Such irradiated microstructures change the mechanical response of the material due to dislocation-defect interactions, which leads to a host of issues such as hardening, swelling, irradiation creep, embrittlement, etc. Traditionally, the effect of irradiation on the mechanical response of materials is evaluated via tensile tests of pre-irradiated specimens at different doses and temperatures. From a modeling perspective, methods exist that simulate irradiation and deformation as separate processes, with the former based on kinetic transport theory and the latter on crystal plasticity (CP). Generally, these are connected by a state variable, usually in the form of a characteristic length scale, that represents the defect concentration and strength and its effect on dislocation-mediated slip. However, cases where deformation takes place during irradiation are also important despite being less common. In this paper, we develop a coupled CP and stochastic cluster dynamics (SCD) approach capable of treating all instances of irradiation/deformation in irradiated materials. We apply the methodology to tungsten crystals due to its importance as a high-temperature candidate structural material and to its extensive defect and mechanical data base. SCD evolves the defect microstructure stochastically, providing a statistically-averaged defect cluster spacing parameter that informs CP calculations of the material’s mechanical deformation. The coupling is bi-directional in the sense that the SCD method updates the obstacle density and furnishes a resistance stress to the CP model, while CP feeds updated dislocation densities that act as defect sinks in the SCD calculation cycles. The coupling can be done sequentially, as in standard tensile tests of pre-irradiated materials, or concurrently, as in in situ straining tests during irradiation. We carry out simulations of realistic irradiation/deformation scenarios and highlight the differences between the present method and past works considering similar situations.

Thermodynamically consistent formulation coupling crystal plasticity theory and Johnson-Cook damage model to simulate micromachining of copper

In this work, a microstructural-related model was developed to simulate micromachining of FCC polycrystalline copper. Indeed, a crystal plasticity framework was adopted to describe the anisotropy of the mechanical behavior. Some material microstructure characteristics (such as grain size, grain misorientation and crystallographic orientation) are explicitly considered through the constitutive model. For describing the material removal during chip formation, a modified thermodynamically consistent formulation of the Johnson-Cook damage model was used. The model was implemented in the ABAQUS/Explicit finite element solver with a user-defined subroutine, and the experimental validation was performed using data on the cutting forces available in the literature. Finally, the model was used to investigate the effect of the microstructure on the micro-machining cutting forces and chip formation process. According to the results, the proposed model allows capturing the cutting forces trends due to the crystallographic anisotropy.

Coupled crystal plasticity finite element-phase field model with kinetics-controlled twinning mechanism for hexagonal metals

Hexagonal metals plastically deform through evolution of dislocations and twins. Deformation twinning is unidirectional and results in twin domain associated with crystal reorientation. Growth of a twin domain is accomplished through nucleation and motion of twinning dislocations/ disconnections (TDs) at atomic scale, and described by migration of twin boundaries (TBs) at micro/macro-scales. Corresponding to kinetics-controlled migration mechanisms of twin boundaries, a coupled crystal plasticity finite element-phase field (CPFE-PF) model was developed through implementing microscale twinning model with anisotropic mobilities of twin boundaries. Crystal plasticity finite element model (CPFEM) is used to solve elastic fields and plastic deformation (carried by both dislocation slip and twinning). Phase field (PF) method is adopted to spatially distinguish twin domains from matrix and track the migration of TBs. Migration of TBs is controlled by both anisotropic mobility coefficients that are correlated to experimental measured twinning strain rate, and the twin driving force contributed by strain energy that is calculated from CPFEM, and change of interface energy including chemical energy and gradient energy that is calculated using finite volume method. It is worth mentioning that experimental measured interface energies of TBs and a critical gradient criterion are adopted in PF model to confine the width of TBs. Our CPFE-PF model exhibits the capability of predicting twin growth with experimental observed twin morphologies, and can be further developed to study twinning related microstructural evolution and mechanical behavior for hexagonal metals.

Coupling crystal plasticity and continuum damage mechanics for creep assessment in Cr-based power-plant steel

To improve the design and safety of power plant components, long-term high-temperature creep behaviour of a power-plant material, such as Cr-based alloy, should be assessed. Prior studies indicate that power-plant components undergo material degradation and premature failure by nucleation, growth and coalescence of microvoids as a result of creep damage. In classical crystal-plasticity-based models, a flow rule and a hardening law do not account for global stiffness degradation of materials due to evolving microvoids, having a significant influence on material behaviour, especially under large deformations. In this study, a crystal-plasticity scheme coupled with an appropriate continuum damage model is developed to capture the anisotropic creep-damage effect on the overall deformation behaviour of Cr-based power-plant steel. Numerical simulations show that the developed approach can characterize creep deformation of the material exposed to a range of stress levels and temperatures under consideration of stiffness degradation under large deformation.

Chemo-thermo-mechanically Coupled Crystal Plasticity Simulation of Stress Evolution in Thermally Strained β-Sn Films

Whisker formation in tin films is a mode of stress relaxation, but the exact conditions causing them are yet to be established. In this work, a three-dimensional full-field chemo-thermo-mechanically coupled crystal plasticity simulation of thermally strained tin films was performed to evaluate the stress evolution and connect it to the redistribution of vacancies. Spatial heterogeneity in the hydrostatic stress along the grain boundary network (that served as the primary conduit for mass transport) was observed, which became more homogeneous towards the film surface. Normal and shear tractions on the columnar grain boundaries were evaluated as they might be crucial to breaking of the oxide layer (formed on the film surface) especially when inclined grain boundaries are present. With such an advanced multi-physics framework, several crystallographic and geometrical factors influencing whisker formation can be analyzed thereby leading to a better understanding of the factors modulating the nucleation and growth of such whiskers.

Experimental and Numerical Studies on Recrystallization Behavior of Single-Crystal Ni-Base Superalloy.

The recrystallization (RX) behavior of superalloy during standard solution heat treatment (SSHT) varies significantly with deformation temperature. Single-crystal (SX) samples of Ni-base superalloy were compressed to 5% plastic deformation at room temperature (RT) and 980 °C, and the deformed samples were then subjected to SSHT process which consists of 1290 °C/1 h, 1300 °C/2 h, and 1315 °C/4 h, air cooling. RT-deformed samples showed almost no RX grains until the annealing temperature was elevated to 1315 °C, while 980 °C-deformed samples showed a large number of RX grains in the initial stage of SSHT. It is inferred that the strengthening effect of γ’ phases and the stacking faults in them increase the driving force of RX for 980 °C-deformed samples. The RX grains nucleate and grow in dendritic arms preferentially when the microstructural inhomogeneity is not completely eliminated by SSHT. A model coupling crystal plasticity finite element method (CPFEM) and cellular automaton (CA) method was proposed to simulate the RX evolution during SSHT. One ({111} <110>) and three ({111} <110>, {100} <110>, {111} <112>) slip modes were assumed to be activated at RT and 980 °C in CPFEM calculations, respectively. The simulation takes the inhomogeneous as-cast dendritic microstructure into consideration. The simulated RX morphology and density conform well to experimental results.

FFT-based modelling of transformation plasticity in polycrystalline materials during diffusive phase transformation

During heat treatment processes of steel products, transformation plasticity is known to play an important role as it affects the final product quality such as shape and residual stresses. To investigate this well-known phenomenon, a model coupling crystal plasticity with diffusive phase transformation is developed by using a fast Fourier transform (FFT) numerical scheme. Diffusional transformation including a plastically accommodated volume change is considered (i.e. the Greenwood–Johnson mechanism). The model is then used to determine the pre-hardening effect on transformation plasticity. It is revealed that pre-hardening results in an anisotropic transformation strain; pre-tension decreases transformation strain and pre-compression increases transformation expansion along the pre-hardened direction. The model is also used to assess the existing analytical model developed by Leblond and Taleb. In this attempt, some features that contribute to the transformation plasticity are discussed. Among those, it is found that plastic deformation in daughter phase is non-negligibly small especially in the end of phase transformation. These analytical solutions predict linear relation between applied stress and transformation plastic strain. This reasoning attributes the linear relation to the solution of equivalent plastic strain increase with transformation by only the transformation expansion effect neglecting the applied stress effect

A Coupled Crystal Plasticity and Anisotropic Yield Function Model to Identify the Anisotropic Plastic Properties and Friction Behavior of an AA 3003 Alloy

A multi-scale simulation of the tip test, developed to determine the tribological characteristics of the back-extrusion process, was conducted on an AA 3003 alloy. A microstructure-level simulation, coupled with crystal plasticity finite element (CPFE) analysis, was utilized to characterize the macro-mechanical properties of the AA 3003. Owing to the limited size of the material provided, we performed CPFE analyses rather than multiple mechanical tests to determine the plastic anisotropy characteristics of the AA 3003 alloy. A three-dimensional finite element (FE) model of the tip test was developed using two different yield functions, namely the generalized von Mises yield function and Hill’s (1948) yield function, with material parameters identified from the CPFE analyses. The results revealed the following: 1. The directionality observed during the tip test is governed by the plastic anisotropy, rather than the frictional conditions. 2. The plastic anisotropy results in different Coulomb friction values. Therefore, the anisotropy should be carefully addressed in the tip test.

Constitutive modeling of strain induced grain boundary migration via coupling crystal plasticity and phase-field methods

We have developed a thermodynamically–consistent finite-deformation-based constitutive theory to describe strain induced grain boundary migration due to the heterogeneity of stored deformation energy in a plastically deformed polycrystalline cubic metal. Considering a representative volume element, a mesoscale continuum theory is developed based on the coupling between dislocation density-based crystal plasticity and phase field methods. Using the Taylor model-based homogenization method, a multiscale coupled finite-element and phase-field staggered time integration procedure is developed and implemented into the Abaqus/Standard finite element package via a user-defined material subroutine. The developed constitutive model is then used to perform numerical simulations of strain induced grain boundary migration in polycrystalline tantalum. The simulation results are shown to qualitatively and quantitatively agree with experimental results.

Investigation of primary static recrystallization in a NiTiFe shape memory alloy subjected to cold canning compression using the coupling crystal plasticity finite element method with cellular automaton

The behavior of primary static recrystallization (SRX) in a NiTiFe shape memory alloy (SMA) subjected to cold canning compression was investigated using the coupling crystal plasticity finite element method (CPFEM) with the cellular automaton (CA) method, where the distribution of the dislocation density and the deformed grain topology quantified by CPFEM were used as the input for the subsequent SRX simulation performed using the CA method. The simulation results were confirmed by the experimental ones in terms of microstructures, average grain size and recrystallization fraction, which indicates that the proposed coupling method is well able to describe the SRX behavior of the NiTiFe SMA. The results show that the dislocation density exhibits an inhomogeneous distribution in the deformed sample and the recrystallization nuclei mainly concentrate on zones where the dislocation density is relatively higher. An increase in the compressive deformation degree leads to an increase in nucleation rate and a decrease in grain boundary spaces in the compression direction, which reduces the growth spaces for the SRX nuclei and impedes their further growth. In addition, both the mechanisms of local grain refinement in the incomplete SRX and the influence of compressive deformation degree on the grain size of SRX were vividly illustrated by the corresponding physical models.