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Two sets of single crystal constitutive equations used for the crystal plasticity finite element analysis are comparatively investigated by simulating simple deformation of oriented single crystals. The first of these consists of conventional constitutive equations, which have been adopted for the prediction of deformation texture and their parameters are generally obtained by back-fitting polycrystalline stress-strain response. The other set uses interactions between moving dislocations on the primary slip system and the corresponding forest dislocations. The idealized Orowan hardening mechanism is adopted for the calculation of the critical force, and constitutive parameters are determined by the geometry of dislocations, thus less fitting procedure is involved. The stress-strain curves of copper single crystal are used to demonstrate how the two models work for the orientation dependent stress-strain responses.

In this study, the FEM material model based on the crystal plasticity is introduced for the numerical simulation of deep drawing process of A5052 aluminum alloy sheet. For calculating the deformation and stress in a crystal of aluminum alloy sheet, Taylor's model is employed. To find the texture evolution, the crystallographic orientation is updated by computing the crystal lattice rotation. In order to verify the crystal plasticity-based FEM material model, the strain distribution and the draw-in amount are compared with experimental measurements. The crystal FEM strains agree well with measured strains. The comparison of draw-in amount shows less 1.96% discrepancy. Texture evolution depends on the initial texture.

An effort has been made to create an integrated Crystal Plasticity FE (CPFE) system. This enables micro-forming process simulation to be carried out easily and the important features in forming micro-parts can be captured. Firstly, based on Voronoi tessellation and the probability theory, a VGRAIN system is created for the generation of grains and grain boundaries for micro-materials. Numerical procedures have been established to link the physical parameters of a material to the control variable in a gamma distribution equation. An interface has been created, so that the generated virtual microstructure of the material can be inputted in the commercial FE code, ABAQUS, for mesh generation. Secondly, FE analyses have been carried out to demonstrate the effectiveness of the integrated system for the investigation of uncontrollable curvature and localized necking in extrusion of micro-pins and hydro-forming of micro-tubes.

In ultra-precision machining (UPM), the depth of cut is within an extremely small fraction of the average grain size of the substrate materials to be cut. Polycrystalline materials commonly treated as homogeneous in conventional machining have to be considered as heterogeneous. The cutting force, one of the dominant factors influencing the integrity of the machined surface in UPM, is observed to strongly depend on the grain orientations. To accurately capture the intrinsic features and gain insight into the mechanisms of UPM of single crystals, the crystal plasticity constitutive model has been incorporated into the commercial FE software Marc by coding the user material subroutine Hypela2 available within it. The enhanced capability of the FE software will be adopted to simulate factors influencing the micro-cutting processes, such as grain orientation variation, the tool edge radius and the rake angle. The simulation results will provide useful information for the optimization of critical processing parameters and enhancement of quality of machined products.

Mechanical micromachining is a powerful and effective way for manufacturing small sized machine parts. Even though the micromachining process is similar to the traditional machining, the material behavior during the process is much different. In particular, many researchers report that the basic mechanics of the work material is affected by microstructures and their crystallographic orientations. For example, crystallographic orientations of the work material have significant influence on force response, chip formation and surface finish. In order to thoroughly understand the effect of crystallographic orientations on the micromachining process, finite-element model (FEM) simulating orthogonal cutting process of single crystallographic material was presented. For modeling the work material, rate sensitive single crystal plasticity of face-centered cubic (FCC) crystal was implemented. For the chip formation during the simulation, element deletion technique was used. The simulation model is developed using ABAQUS/explicit with user material subroutine via user material subroutine (VUMAT). Simulations showed that variation of the specific cutting energy at different crystallographic orientations of work material shows significant anisotropy. The developed FEM model can be a useful prediction tool of micromachining of crystalline materials.

To further investigate interaction and competition among various deformation modes in magnesium, a crystal plasticity model incorporating slip, twin, and secondary slip and twin systems is established. This study extends recent molecular dynamics findings to the crystal plasticity framework, introducing a new slip hardening model that incorporates twin boundaries. The proposed unified twin hardening model suitable for both tensile and compressive twins, considers twin stages of nucleation, propagation and growth, thereby simulating twin saturation and coexistence of multiple twin variants. Initially applied to single crystal magnesium, the numerical results agree with experimental findings by Kelley and Hosford, demonstrating twin saturation. We observe that plastic contributions from secondary slip and twin are smaller than those from slip and twins in the parent phase. Furthermore, the plastic contribution from pyramidal I slip is preferred to pyramidal II slip. Next, to study the serious influence of voids on the stress–strain response of ductile solids during manufacturing, the proposed model is then applied to single crystal magnesium containing a void along $c$-axis tension and compression. Both simulations confirm the validity of our crystal plasticity model and its potential to analyze future experimental and molecular dynamic findings.

A rate- and lengthscale-dependent crystal plasticity model is employed with a representative volume element for a two-phase austenitic steel under hot-forming conditions to investigate the role of austenite and MnS particle crystallographic orientation on local stress and slip conditions at austenite–MnS interfaces.

It was found that austenite–MnS particle interfacial stress magnifications are determined largely by the crystallographic orientation of the MnS and not significantly by the austenite orientations. However, the crystallographic orientation of an austenite grain neighboring a MnS particle has a dramatic effect on slip localization and slip magnitude in the absence of any significant change in interfacial stress magnitude. The results suggest that it is the crystallographic orientation of the MnS rather than that of the austenite which determines the onset and rapidity of void nucleation. The results also show that there are very particular combinations of austenite–MnS particle orientations which lead to the highest interfacial stresses, and that the peak stress magnification arises not from the properties of the second phase particles but from their orientation. Micromechanical models based on isotropic plasticity will not capture correctly the interfacial stresses.

An integrated crystal viscoplastic modeling process has been developed to account for the effect of microstructure in the mechanical response of polycrystalline materials. Grain distributions, including size, shape and orientation, are generated automatically based on probability theories using VGRAIN software. For each set of control parameters (average, maximum and minimum grain size) used in the micro-film simulations, six grain orientation patterns were generated randomly for a micro-film based on a gamma distribution; a large number of analyses have been carried out to account for statistical variations in the spatial pattern of grain orientations. The simulations are used to investigate the effects of grain size and orientation on necking and flow stress in stainless steel under uniaxial tension, and to quantify the extent that variability in the spatial distribution of orientations affects the predictions. Based on the numerical studies, a map was generated indicating under what circumstances macro-mechanics theory can be used and when Crystal Plasticity (CP) theory must be used to ensure the accuracy of the analysis; if the theories are not used appropriately, huge errors can be expected.

In the present work a multiscale modeling framework is used to predict yield surfaces for a pearlitic steel. On the mesoscale a model taking into account the features of the pearlite colonies, i.e., the crystallographic orientations of the ferrite and the cementite lamella orientation, is used. The microscale model includes both the ferrite matrix and the cementite lamellae and the interactions between these phases. The model is used to predict yield surfaces for both isotropic and deformed mesomodels.

Crystal plasticity parameters for numerical simulations are difficult to experimentally measure on the microscopic scale. One possible approach to avoid the difficulty is to determine the parameters that can be used to reproduce the stress–strain curve by employing a polycrystalline aggregate model. In this study, the effect of crystal plasticity parameters on stress–strain curves on a macroscopic scale and on stress distribution on a microscopic scale was investigated by using polycrystalline aggregate simulation. The parameters investigated were initial slip strength (τ₀), initial hardening modulus (h₀) and saturation slip strength (τ_s). The effect of these parameters on macroscopic stress–strain curves was found to be the followings: τ₀ controls the yield stress or proof stress, and both h₀ and τ_s control the strain-hardening behavior. The effect of these parameters on microscopic stress distribution was also investigated because similar stress–strain curve can be obtained by using different sets of crystal plasticity parameters. Consequently, even if these parameters are slightly different, a similar microscopic stress distribution can be obtained by properly reproducing the macroscopic stress–strain curve.

A three-dimensional (3D) boundary element method for small strains crystal plasticity is described. The method, developed for polycrystalline aggregates, makes use of a set of boundary integral equations for modeling the individual grains, which are represented as anisotropic elasto-plastic domains. Crystal plasticity is modeled using an initial strains boundary integral approach. The integration of strongly singular volume integrals in the anisotropic elasto-plastic grain-boundary equations are discussed. Voronoi-tessellation micro-morphologies are discretized using nonstructured boundary and volume meshes. A grain-boundary incremental/iterative algorithm, with rate-dependent flow and hardening rules, is developed and discussed. The method has been assessed through several numerical simulations, which confirm robustness and accuracy.

The refinement of grains in a polycrystalline material leads to an increase in strength but as a counterpart to a decrease in elongation to fracture. Different routes are proposed in the literature to try to overpass this strength-ductility dilemma, based on the combination of grains with highly contrasted sizes. In the simplest concept, coarse grains are used to provide relaxation locations for the highly stressed fine grains. In this work, a model bimodal polycrystalline system with a single coarse grain embedded in a matrix of fine grains is considered. Numerical full-field micro-mechanical analyses are performed to characterize the impact of this coarse grain on the stress-strain constitutive behavior of the polycrystal: the effect on plasticity is assessed by means of crystal plasticity finite element modeling [B. Flipon, C. Keller, L. Garcia de la Cruz, E. Hug and F. Barbe, Tensile properties of spark plasma sintered AISI 316L stainless steel with unimodal and bimodal grain size distributions, Mater. Sci. Eng. A729 (2018) 248–256] while the effect on intergranular fracture behavior is studied by using boundary element modeling [I. Benedetti and V. Gulizzi, A grain-scale model for high-cycle fatigue degradation in polycrystalline materials, Int. J. Fract.116 (2018) 90–105]. The analysis of the computational results, compared to the experimentally characterized tensile properties of a bimodal 316L stainless steel, suggests that the elasto-plastic interactions taking place prior to micro-cracking may play an important role in the mechanics of fracture of this steel.

This paper reports the modeling and simulation of cyclic behavior of single crystal nickel-based superalloy by using the crystal plasticity finite element method. Material constitutive model based on the crystal plasticity theory is developed and is implemented in a parallel way as user subroutine modules embedded in the commercial Abaqus${}^{\text{®}}$ software. For simplicity in calibration and without loss of generality, the crystal plasticity constitutive relationship used in this work takes the form that only contains a few parameters. The parameters are optimized by using the Powell algorithm. We employ the calibrated constitutive model with the finite element solver on a cuboid and a blade to simulate cyclic and anisotropic properties of single crystal superalloy. Results show that the predicted stress–strain curves are in good agreement with the experimental measurements, and anisotropic results are presented in both elastic and plastic regions.

The large strain torsion of polycrystalline materials with the hexagonal close packed (HCP) crystallographic structure is numerically studied by using a special purpose finite element. All simulations are based on the recently developed large strain elastic visco-plastic self-consistent (EVPSC) model for polycrystalline materials. For the first time, the effect of twinning on the large strain torsion is assessed in the present study. It is found that the response of the large strain torsion of HCP polycrystals is very sensitive to the initial texture and texture evolution. Numerical results indicate that excluding texture evolution dramatically reduces the development of the second-order axial strain under free-end torsion, or the axial force under fixed-end torsion. It is also numerically demonstrated that twinning has a significant influence on the large strain torsion of HCP polycrystals. For the magnesium alloy AZ31 extruded bar, the predicted results are in good qualitative agreement with experimental observations.

Large strain behavior of FCC polycrystals during reversed torsion are investigated through the special purpose finite element based on the classical Taylor model and the elastic-viscoplastic self-consistent (EVPSC) model with various Self-Consistent Schemes (SCSs). It is found that the response of both the fixed-end and free-end torsion is very sensitive to the constitutive models. The models are assessed through comparing their predictions to the corresponding experiments in terms of the stress and strain curves, the Swift effect and texture evolution. It is demonstrated that none of the models examined can precisely predict all the experimental results. However, more careful observation reveals that, among the models considered, the tangent model gives the worst overall performance. It is also demonstrated that the intensity of residual texture during reverse twisting is dependent on the amounts of pre-shear strain during forward twisting and the model used.

Magnesium alloys exhibit significant inelastic behavior during unloading, especially when twinning and detwinning are involved. It is commonly accepted that noteworthy inelastic behavior will be observed during unloading if twinning occurs during previous loading. However, this phenomenon is not always observed for Mg sheets with strong rolled texture. Therefore, the inelasticity of AZ31B rolled sheets with different rolled textures during cyclic loading-unloading are investigated by elastic viscoplastic self-consistent polycrystal plasticity model. The incorporation of the twinning and detwinning model enables the treatment of detwinning, which plays an important role for inelastic behavior during unloading. The effects of texture, deformation history, and especially twinning and detwinning on the inelastic behaviors are carefully investigated and found to be remarkable. The simulated results are in agreement with the available experimental observations, which reveals that the inelastic behavior for strongly rolled sheets is very different than the extruded bars.

With the hypothesis of a small deformation, the novel cyclic visco-plasticity constitutive model (CV-CM) is constructed to study the cyclic deformation responses of polycrystalline metals. In this model, a modified Armstrong–Frederick nonlinear kinematic hardening (NKH) law is adopted to simulate the ratchetting deformation more precisely. The cyclic hardening characteristic of FCC polycrystalline copper is investigated with the use of flow stress evolution of slip system. For the issue of the transition from single crystal to polycrystalline crystals, the explicit $\beta$ rule is introduced to compute the polycrystalline response. Finally, through comparison with the experimental data, the proposed model is verified. It is demonstrated that the uniaxial ratchetting response of FCC metal can be precisely captured. The ratchetting response of copper single crystal and its relation with the crystallographic directions can be exactly traced by the present model as well.

A crystal plasticity based finite element model (i.e., FE model) is used in this paper to simulate the cyclic deformation of polycrystalline aluminum alloy plates. The Armstrong–Frederick nonlinear kinematic hardening rule is employed in the single crystal constitutive model to capture the Bauschinger effect and ratcheting of aluminum single crystal presented under the cyclic loading conditions. A simple model of latent hardening is used to consider the interaction of dislocations between different slipping systems. The proposed single crystal constitutive model is implemented numerically into a FE code, i.e., ABAQUS. Then, the proposed model is verified by comparing the simulated results of cyclic deformation with the corresponding experimental ones of a face-centered cubic polycrystalline metal, i.e., rolled 5083 aluminum alloy. In the meantime, it is shown that the model is capable of predicting local heterogeneous deformation in single crystal scale, which plays an important role in the macroscopic deformation of polycrystalline aggregates. Under the cyclic loading conditions, the effect of applied strain amplitude on the responded stress amplitude and the dependence of ratcheting strain on the applied stress level are reproduced reasonably.

This paper discusses a coupled mechanics–phase-field model that can predict microstructure evolution in metallic polycrystals and in particular evolution of lattice orientation due to either deformation or grain boundary migration. The modeling framework relies on the link between lattice curvature and geometrically necessary dislocations and connects a micropolar or Cosserat theory with an orientation phase-field model. Some focus is placed on the underlying theory and in particular the theory of dislocations within a continuum single crystal plasticity setting. The model is finally applied to the triple junction problem for which there is an analytic solution if the grain boundary energies are known. The attention is drawn on the evolution of skew–symmetric stresses inside the grain boundary during migration.

Recent developments in generalized continuum modeling methods ranging from coarse-grained atomistics to micromorphic theory offer potential to make more intimate physical contact with dislocation field problems framed at length scales on the order of microns. We explore a range of discrete dynamical and continuum mechanics approaches to crystal plasticity that are relevant to modeling behavior of populations of dislocations. Predictive atomistic and coarse-grained atomistic models are limited in terms of length and time scales that can be accessed; examples of the latter are discussed in terms of interactions of multiple dislocations in heterogeneous systems. Generalized continuum models alleviate restrictions to a significant extent in modeling larger scales of dislocation configurations and reactions, and are useful to consider effects of dislocation configuration on strength at characteristic length scales of sub-micron and above; these models require a combination of bottomup models and top-down experimental information to inform parameters and model form. The concurrent atomistic-continuum (CAC) method is extended to model complex multicomponent alloy systems using an average atom approach. Examples of CAC are presented, along with potential to assist in informing parameters of a recently developed micropolar crystal plasticity model based on a set of sub-micron dislocation field problems. Prospects for further developments are discussed.