We develop a polycrystal plasticity constitutive law based on the elasto-plastic self-consistent (EPSC) theory for the prediction of cyclic tension-compression deformation. The crystallography based ...model integrates a dislocation based hardening model and accounts for inter-granular stresses and slip system level backstresses, which make it capable of capturing non-linear unloading and the Bauschinger effect (BE). Furthermore, the model features dissolution of dislocation population upon the load reversal, which enables it to predict the change in hardening rate during reverse loading from that during forward loading. To demonstrate these capabilities of the model, we investigate elasto–plastic behavior of AA6022-T4 sheets under in-plane cyclic tension–compression. From a set of carefully performed cyclic tests to several strain levels, we observe that the material exhibits (1) a typical decreasing hardening rate during forward loading, (2) a linear followed by non-linear unloading upon the load reversal, (3) a transient softening followed by rapid work hardening (the BE), and (4) a decrease in subsequent hardening rate during reverse loading (the permanent softening phenomenon). To predict these effects, we calibrate the model to establish a set of material parameters using a portion of the measured data. The remaining measured data is used for verification of the model. We show that using the single set of material parameters, the developed model is capable of predicting all the particularities pertaining to the cyclic deformation of the material with great accuracy. From the favorable comparison of the predictions and experimental data, we infer first that the non-linearity of unloading increases with the amount of pre-strain, next that the backstresses have a dominant effect in capturing non-linear unloading while both the backstresses and inter-granular stresses govern the BE, and finally that the inclusion of reversible dislocation motion is the key for capturing hardening rates during reverse loading.
•A new elasto-plastic polycrystal model for the prediction of cyclic deformation is developed.•The model considers forward and reverse dislocation glide in evolving slip resistance.•The model accounts for the inter-granular stresses and intra-granular backstresses.•Anisotropy, hardening, non-linear unloading, Bauschinger effect are simultaneously predicted.
This work advances a recently developed high-performance, full-field elasto-viscoplastic fast Fourier transform (MPI-ACC-EVPCUFFT) formulation to model large plastic deformation and low-cycle fatigue ...behavior of Inconel 718 (IN718). Specifically, the recently developed model of Eghtesad et al., 2020 1 incorporating a strain rate, temperature, and strain-path sensitive hardening law based on the evolution of dislocation density and a slip system-level back-stress law influencing the resolved shear stress is advanced in several aspects. First, strengthening effects due to grain size and shape, solid solution, shearing of small precipitates, and Orowan looping around larger precipitates are incorporated into the initial slip resistance, which evolves with the hardening law including the latent hardening. Second, the resolved shear stress on the slip plane in the direction of slip is altered by accounting for the two orthogonal shear stress components and the three normal stress components, in addition to the slip system-level kinematic effects. The model is used to interpret the complex mechanical behavior and microstructural data for samples of alloy IN718 in additively manufactured (AM) forms before and after hot isostatic pressing (HIP) and in a wrought form. Voxel-based microstructural cells consistent with the characterization data are synthetically constructed to initialize the model setups for predicting simple compression, tension, load reversal, and low cycle fatigue behavior of the alloy. Variation in the microstructural features such as the distribution of grain size and shape, crystallographic texture, content of annealing twins, and precipitates among the samples facilitated reliable calibration and validation of the model parameters. Predicted anisotropy, tension/compression asymmetry, non-linear unloading upon the load reversal, the Bauschinger effect, reverse hardening, texture evolution as well as cyclic hardening/softening along with the mean stress relaxation during low-cycle fatigue are in good agreement with the corresponding experimental data for the alloy. Furthermore, the simulations based on the high-resolution microstructural cells facilitated the discussion of the mechanical fields induced by microstructure, and especially annealing twins.
Slip system hardening behavior of a given slip system is influenced more by shearing on another slip system known, as latent hardening, than by shearing on itself, known as self-hardening. This paper ...extends a recently developed dislocation-based hardening law within the elasto-plastic self-consistent polycrystal plasticity model to incorporate the latent hardening effects for predicting anisotropic response of polycrystalline face-centered cubic metals. In doing so, a new approach to overcome singularities associated with the self-consistent Eshelby solution procedure is proposed. The new approach is validated using a regularized Schmid law, where the singularity in Eshelby tensor calculation is intrinsically suppressed. Moreover, the solution procedure for single crystal stress increment is advanced to be based on a methodology involving the singular value decomposition to solve for shear increments. It is found that modeling crystallographic texture evolution and latent hardening successfully captures the anisotropic behavior of polycrystalline AA6022-T4 alloy. The model is subsequently successfully applied to predict large strain cyclic deformation of the same material. The implementation and insights from these predictions are presented and discussed in this paper.
•A new method to implement a hardening law with latent effects in EPSC is developed.•The implementation overcomes singularities associated with the Eshelby solution procedure.•Origin of anisotropic behavior of AA6022-T4 sheets is studied using the new model.•Latent hardening along with crystallographic texture control anisotropy in AA6022-T4.•The model predicts hardening, non-linear unloading, and Bauschinger effect in cyclic loading.
•An implicit formulation of the elasto-plastic self-consistent crystal plasticity model is developed.•A system of non-linear equations is suitably defined at the crystal level and at the ...homogenization level.•A stress update algorithm is derived to couple the formulation and implicit finite elements.•Several benchmarks and applications are presented to illustrate the developed multi-level approach.
Elasto-plastic self-consistent (EPSC) polycrystal plasticity theory has been used extensively in understanding and predicting anisotropic thermo-mechanical response and underlying microstructure evolution of polycrystalline metals. This paper describes the first implicit formulation of the EPSC model and its implementation in implicit finite elements. To this end, a suitably defined system of non-linear equations at the single crystal level and that at the polycrystal level homogenizing the single crystal solutions in terms of the rotation-neutralized increments in Cauchy stress and strain are formulated and numerically solved. The implicit EPSC model is first validated using the original explicit EPSC model. Subsequently, the implicit EPSC model is coupled with implicit finite elements (FE) through the use of the user material subroutine in Abaqus. To facilitate the efficient coupling, a stress update algorithm is developed and the consistent tangent stiffness operator is analytically derived. Here, every FE integration point embeds the implicit EPSC constitutive law taking into account microstructure evolution and the directionality of deformation mechanisms acting at the single crystal level. The multi-level FE-EPSC model is benchmarked using the single crystal data for copper and then applied to simulate drawing of a cup from an AA6022-T4 sheet. The implementation and insights from these predictions are presented and discussed in this paper.
This paper presents experimental verification of a multi-level simulation framework aimed at sheet metal forming analysis. Specifically, deep drawing of a cylindrical cup simulations from alloy ...AA6022-T4 sheets are carried out using a physically based elasto-plastic self-consistent (EPSC) polycrystalline homogenization model embedded in implicit finite elements and verified experimentally. The EPSC model takes into account the evolution of microstructure and directionality of deformation mechanisms acting at the single-crystal level in predicting material behavior. It is calibrated and validated as a standalone model using flow stress and R-ratio data as well as iso-shear contours measured along several directions of the sheet through uniaxial and plane strain tension experiments. Furthermore, the particularities pertaining to cyclic response including non-linear unloading and the Bauschinger effect are also calibrated through large strain tension–compression data. Consistent with experimental measurements, the process simulations in finite elements predict directionally dependent thinning of the cup, especially around the punch radius and variation in the cup height around the rim of the cup, referred to as earing. By comparing experiments and predictions, role of the R-ratio is revealed as critical for the accurate prediction of the cup height. Further sensitivity analysis shows that initial texture has a strong influence on the R-ratio, while introducing a minor effect on hardening. The analysis into the choice of finite element types in terms of their accuracy and efficiency shows that the 3D 8 nodal elements (C3D8R) and continuum shell 3D 8 nodal elements (SC8R) are superior over the planar shell 3D 4 nodal elements (S4R) with the former being the most accurate and the latter being computationally efficient. It is demonstrated that the simulation framework presented in this paper can be used to predict phenomena pertaining to material behavior and resulting geometrical changes important for optimization of the sheet metal forming processes.
•Grain-to-polycrystal-to-component level models are linked to simulate cup drawing.•Hardening, unloading, Bauschinger effect, and geometrical changes are predicted.•Crystallographic texture is found to govern R-ratio.•Role of R-ratio in predicting cup height is explained.•Continuum 3D elements are recommended for crystal plasticity sheet metal forming.
We present a multiscale model for anisotropic, elasto-plastic, rate- and temperature-sensitive deformation of polycrystalline aggregates to large plastic strains. The model accounts for a ...dislocation-based hardening law for multiple slip modes and links a single-crystal to a polycrystalline response using a crystal plasticity finite element based homogenization. It is capable of predicting local stress and strain fields based on evolving microstructure including the explicit evolution of dislocation density and crystallographic grain reorientation. We apply the model to simulate monotonic mechanical response of a hexagonal close-packed metal, zirconium (Zr), and a body-centered cubic metal, niobium (Nb), and study the texture evolution and deformation mechanisms in a two-phase Zr/Nb layered composite under severe plastic deformation. The model predicts well the texture in both co-deforming phases to very large plastic strains. In addition, it offers insights into the active slip systems underlying texture evolution, indicating that the observed textures develop by a combination of prismatic, pyramidal, and anomalous basal slip in Zr and primarily {110}〈111〉 slip and secondly {112}〈111〉 slip in Nb.
•A thermally activated rate law for dislocation density evolution is integrated in a CPFE model.•The model predicts texture development in a composite of Zr and Nb during ARB to high strains.•Deformation mechanisms in the phases of the composite during co-deformation are predicted.
In this work, we develop a physically-based crystal plasticity model for the prediction of cyclic tension–compression deformation of multi-phase materials, specifically dual-phase (DP) steels. The ...model is elasto–plastic in nature and integrates a hardening law based on statistically stored dislocation density, localized hardening due to geometrically necessary dislocations (GNDs), slip-system-level kinematic backstresses, and annihilation of dislocations. The model further features a two level homogenization scheme where the first level is the overall response of a two-phase polycrystalline aggregate and the second level is the homogenized response of the martensite polycrystalline regions. The model is applied to simulate a cyclic tension–compression–tension deformation behavior of DP590 steel sheets. From experiments, we observe that the material exhibits a typical decreasing hardening rate during forward loading, followed by a linear and then a non-linear unloading upon the load reversal, the Bauschinger effect, and changes in hardening rate during strain reversals. To predict these effects, we identify the model parameters using a portion of the measured data and validate and verify them using the remaining data. The developed model is capable of predicting all the particular features of the cyclic deformation of DP590 steel, with great accuracy. From the predictions, we infer and discuss the effects of GNDs, the backstresses, dislocation annihilation, and the two-level homogenization scheme on capturing the cyclic deformation behavior of the material.
•Cyclic tension–compression to large plastic strains of dual-phase steel sheets is characterized.•A new model for the prediction of cyclic deformation of two-phase metals is developed.•The model is physically-based accounting for statistically stored and geometrically necessary dislocations.•The model further features slip-system-level backstresses, annihilation of dislocations, and two-level homogenization.•The model predicts hardening rates, non-linear unloading, and Bauschinger effect of DP 590 steel.
In this work, we employ the recently developed framework for the explicit modeling of discrete twin lamellae within a three-dimensional (3D) crystal plasticity finite element (CPFE) model to examine ...the effects of dislocation densities in the twin domain on twin thickening. Simulations are carried out for 1¯012101¯1 extension twins in a magnesium AZ31 alloy. The model for the twin lamellae accounts for the crystallographic twin-matrix orientation relationship and characteristic twin shear transformation strain. The calculations for the mechanical fields as a result of twinning consider that one of three types of twin-dislocation density interactions have occurred. One case assumes that the expanding twin retains in its domain the same dislocation density as the parent. The second one considers that twin expansion has lowered the dislocation density as the twin thickens, and the last one, the Basinski effect, assumes that when twin sweeps the region, the dislocation density incorporated in the twin domain is amplified. In the modeling approach, the twin is thickened according to a criterion that maintains the stress state in the vicinity of the grain at a pre-defined characteristic twin resistance. The calculations show that most of the averaged properties, such as the rate of dislocation storage in the entire twin grain, the twin growth rate, the stress field in the twinned grain and neighboring grains, and the slip activity in the parent matrix are not significantly altered by dislocation storage in the twin. The results indicate that, however, the slip activity in the twinned domain is affected. In particular, in the increased dislocation density case, the rate of dislocation density in the twin domain increases at low strains when the twin is first growing from 2% to 5% volume fraction. This initial boost in the dislocation density storage rate causes the newly expanded dislocation twin to contain more stored dislocations than the other cases for all strain levels. Another interesting difference concerns the preference for one or two twins for the same total twin volume fraction; for the increased dislocation twin or twin that retains the dislocation density as it grows, formation of two twins is favored. For a twin that removes dislocation density, only one twin is preferred. The results imply that in the case with reduced dislocation density leads to lower stored dislocations and dislocation storage rates, and lower pyramidal slip activity.
•Effects of dislocation storage in twin domain on twin thickening are studied using CPFE.•Slip activity in twin domain is enhanced by dislocations contained in the twin.•Rate of twin lamella thickening decreases with the rate of stored dislocations in the twin.•Formation of one vs. multiple twin lamellae is influenced by dislocations stored in the twin.
A large number of massive crystal-plasticity-finite-element (CPFE) simulations are performed and post-processed to reveal the effects of element type and mesh resolution on accuracy of predicted ...mechanical fields over explicit grain structures. A CPFE model coupled with Abaqus/Standard is used to simulate simple-tension and simple-shear deformations to facilitate such quantitative mesh sensitivity studies. A grid-based polycrystalline grain structure is created synthetically by a phase-field simulation and converted to interface-conformal hexahedral and tetrahedral meshes of variable resolution. Procedures for such interface-conformal mesh generation over complex shapes are developed. FE meshes consisting of either hexahedral or tetrahedral, fully integrated as linear or quadratic elements are used for the CPFE simulations. It is shown that quadratic tetrahedral and linear hexahedral elements are more accurate for CPFE modeling than linear tetrahedral and quadratic hexahedral elements. Furthermore, tetrahedral elements are more desirable due to fast mesh generation and flexibility to describe geometries of grain structures.
In this work, we describe a finite element (FE) implementation of an elasto-plastic self-consistent (EPSC) polycrystal plasticity model termed FE-EPSC, which is intended for simulations of metal ...forming. To this end, we present an analytical Jacobian, which is necessary for the implicit coupling and ensuring a fast convergence. Every FE integration point is a material point that can be represented either by a single crystal or a polycrystalline material. The constituent crystal can deform by a combination of anisotropic elasticity, crystallographic slip, and deformation twinning. The model is validated and applied to a suite of tests, including monotonic compression, cyclic forward loading, unloading and reverse loading and non-monotonic four-point bending, and materials, such as different alloy compositions, crystal structures, and initial microstructures. The same FE-EPSC framework is applied for all these cases with the main differences pertaining to intrinsic properties, such as the available slip and twinning deformation modes, and the material parameters for activating and hardening of these modes. Full characterization for these parameters for high-purity α-Ti is presented here for the first time. Through these examples we show that, in addition to being predictive with great accuracy, the key advantage of this model lies in its versatility. It accounts for the development of backstress aided dislocation glide, thermally activated storage of dislocations, elastic anisotropy, crystallographic slip and deformation twinning via multiple modes, and de-twinning as well as multi-level homogenizations.
•An elasto-plastic self-consistent crystal plasticity model is embedded in an implicit finite element framework.•A fully analytical Jacobian matrix enabling an efficient coupling and fast convergence is presented.•A single crystal or a polycrystalline material point can be considered at a finite element integration point.•Several validation and application case studies are presented illustrating the versatility of the new model.•The model predicts the evolution of elasto-plastic anisotropy, hardening, unloading, Bauschinger effect, and geometry.
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