On the strain hardening and texture evolution in high manganese steels: Experiments and numerical investigation

We present a systematic investigation on the strain hardening and texture evolution in high manganese steels where twinning induced plasticity (TWIP) plays a significant role for the materials' plastic deformation. Motivated by the stress–strain behavior of typical TWIP steels with compositions of Fe, Mn, and C, we develop a mechanistic model to explain the strain-hardening in crystals where deformation twinning dominates the plastic deformation. The classical single crystal plasticity model accounting for both dislocation slip and deformation twinning are then employed to simulate the plastic deformation in polycrystalline TWIP steels. While only deformation twinning is activated for plasticity, the simulations with samples composed of voronoi grains cannot fully capture the texture evolution of the TWIP steel. By including both twinning deformation and dislocation slip, the model is able to capture both the stress–strain behaviors and the texture evolution in Fe–Mn–C TWIP steel in different boundary-value problems. Further analysis on the strain contributions by both mechanisms suggests that deformation twinning plays the dominant role at the initial stage of plasticity in TWIP steels, and dislocation slip becomes increasingly important at large strains.     

On the coupling of plastic slip and deformation-induced twinning in magnesium: A variationally consistent approach based on energy minimization

The present paper is concerned with the analysis of the deformation systems in single crystal magnesium at the micro-scale and with the resulting texture evolution in a polycrystal representing the macroscopic mechanical response. For that purpose, a variationally consistent approach based on energy minimization is proposed. It is suitable for the modeling of crystal plasticity at finite strains including the phase transition associated with deformation-induced twinning. The method relies strongly on the variational structure of crystal plasticity theory, i.e., an incremental minimization principle can be derived which allows to determine the unknown slip rates by computing the stationarity conditions of a (pseudo) potential. Phase transition associated with twinning is modeled in a similar fashion. More precisely, a solid-solid phase transition corresponding to twinning is assumed, if this is energetically favorable. Mathematically speaking, the aforementioned transition can be interpreted as a certain rank-one convexification. Since such a scheme is computationally very expensive and thus, it cannot be applied to the analysis of a polycrystal, a computationally more efficient approximation is elaborated. Within this approximation, the deformation induced by twinning is decomposed into the reorientation of the crystal lattice and simple shear. The latter is assumed to be governed by means of a standard Schmid-type plasticity law (pseudo-dislocation), while the reorientation of the crystal lattice is considered, when the respective plastic shear strain reaches a certain threshold value. The underlying idea is in line with experimental observations, where dislocation slip within the twinned domain is most frequently seen, if the twin laminate reaches a critical volume. The resulting model predicts a stress-strain response in good agreement with that of a rank-one convexification method, while showing the same numerical efficiency as a classical Taylor-type approximation. Consequently, it combines the advantages of both limiting cases. The model is calibrated for single crystal magnesium by means of the channel die test and finally applied to the analysis of texture evolution in a polycrystal. Comparisons of the predicted numerical results to their experimental counterparts show that the novel model is able to capture the characteristic mechanical response of magnesium very well.     

A dislocation density based crystal plasticity finite element model: Application to a two-phase polycrystalline HCP/BCC composites

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.     

镁合金晶体塑性本构模型与非均匀孪生变形分析

微结构演化对镁合金材料力学性能有着显著的影响，为了揭示镁合金宏观塑性各向异性特性与非均匀孪生变形的关系，开展了不同路径下的单轴加载试验以及采用含滑移、孪生机制的晶体塑性本构模型对试验条件下的镁合金变形行为进行数值模拟研究。文中本构模型描述了滑移与孪生变形机制以及晶格转动的机制，同时研究采用三维微结构代表性有限元模型，其包含晶粒尺寸、晶向和晶界倾角等微结构参数。研究结果表明，轧制镁合金具有强烈的宏观塑性各向异性行为，并对这种镁合金塑性各向异性行为的模拟结果以及多晶织构的模拟演化结果与试验测量进行对比，结果都基本吻合。对孪生非均匀变形模拟分析表明，镁合金宏观塑性各向异性行为与滑移、孪生变形机制的不同启动组合紧密相关，同时多晶体内应力的非均匀分布受到孪生变形的严重影响。而不同晶粒尺寸的晶粒所发生的孪生变形有比较大的差异，造成孪晶变体在晶粒内的分布极不均匀。本研究可为通过微结构的合理配置来设计和控制材料的力学性能提供理论依据.     

A dislocation-based constitutive law for pure Zr including temperature effects

In this work, a single crystal constitutive law for multiple slip and twinning modes in single phase hcp materials is developed. For each slip mode, a dislocation population is evolved explicitly as a function of temperature and strain rate through thermally-activated recovery and debris formation and the associated hardening includes stage IV. A stress-based hardening law for twin activation accounts for temperature effects through its interaction with slip dislocations. For model validation against macroscopic measurement, this single crystal law is implemented into a visco-plastic-self-consistent (VPSC) polycrystal model which accounts for texture evolution and contains a subgrain micromechanical model for twin reorientation and morphology. Slip and twinning dislocations interact with the twin boundaries through a directional Hall–Petch mechanism. The model is adjusted to predict the plastic anisotropy of clock-rolled pure Zr for three different deformation paths and at four temperatures ranging from 76 K to 450 K (at a quasi-static rate of 10⁻³ 1/s). The model captures the transition from slip-dominated to twinning-dominated deformation as temperature decreases, and identifies microstructural mechanisms, such as twin nucleation and twin–slip interactions, where future characterization is needed.     

Interaction between phase transformations and dislocations at the nanoscale. Part 1. General phase field approach

Thermodynamically consistent, three-dimensional (3D) phase field approach (PFA) for coupled multivariant martensitic transformations (PTs), including cyclic PTs, variant–variant transformations (i.e., twinning), and dislocation evolution is developed at large strains. One of our key points is in the justification of the multiplicative decomposition of the deformation gradient into elastic, transformational, and plastic parts. The plastic part includes four mechanisms: dislocation motion in martensite along slip systems of martensite and slip systems of austenite inherited during PT and dislocation motion in austenite along slip systems of austenite and slip systems of martensite inherited during reverse PT. The plastic part of the velocity gradient for all these mechanisms is defined in the crystal lattice of the austenite utilizing just slip systems of austenite and inherited slip systems of martensite, and just two corresponding types of order parameters. The explicit expressions for the Helmholtz free energy and the transformation and plastic deformation gradients are presented to satisfy the formulated conditions related to homogeneous thermodynamic equilibrium states of crystal lattice and their instabilities. In particular, they result in a constant (i.e., stress- and temperature-independent) transformation deformation gradient and Burgers vectors. Thermodynamic treatment resulted in the determination of the driving forces for change of the order parameters for PTs and dislocations. It also determined the boundary conditions for the order parameters that include a variation of the surface energy during PT and exit of dislocations. Ginzburg–Landau equations for dislocations include variation of properties during PTs, which in turn produces additional contributions from dislocations to the Ginzburg–Landau equations for PTs. A complete system of coupled PFA and mechanics equations is presented. A similar theory can be developed for PFA to dislocations and other PTs, like reconstructive PTs and diffusive PTs described by the Cahn–Hilliard equation, as well as twinning and grain boundaries evolution.     

Continuum modeling of the response of a Mg alloy AZ31 rolled sheet during uniaxial deformation

Lightweight magnesium alloys, such as AZ31, constitute alternative materials of interest for many industrial sectors such as the transport industry. For instance, reducing vehicle weight and thus fuel consumption can actively benefit the global efforts of the current environmental industry policies. To this end, several research groups are focusing their experimental efforts on the development of advanced Mg alloys. However, comparatively little computational work has been oriented towards the simulation of the micromechanisms underlying the deformation of these metals. Among them, the model developed by Staroselsky and Anand [Staroselsky, A., Anand, L., 2003. A constitutive model for HCP materials deforming by slip and twinning: application to magnesium alloy AZ31B. International Journal of Plasticity 19 (10), 1843–1864] successfully captured some of the intrinsic features of deformation in Magnesium alloys. Nevertheless, some deformation micromechanisms, such as cross-hardening between slip and twin systems, have been either simplified or disregarded. In this work, we propose the development of a crystal plasticity continuum model aimed at fully describing the intrinsic deformation mechanisms between slip and twin systems. In order to calibrate and validate the proposed model, an experimental campaign consisting of a set of quasi-static compression tests at room temperature along the rolling and normal directions of a polycrystalline AZ31 rolled sheet, as well as an analysis of the crystallographic texture at different stages of deformation, has been carried out. The model is then exploited by investigating stress and strain fields, texture evolution, and slip and twin activities during deformation. The flexibility of the overall model is ultimately demonstrated by casting light on an experimental controversy on the role of the pyramidal slip 〈c + a〉 versus compression twinning in the late stage of polycrystalline deformation, and a failure criterion related to basal slip activity is proposed.     

Micromechanical quantification of elastic,twinning, and slip strain partitioning exhibited by polycrystalline,monoclinic nickel–titanium during large uniaxial deformations measured via in-situ neutron diffraction

We draw upon existing knowledge of twinning and slip mechanics to develop a diffraction analysis model that allows for empirical quantification of individual deformation mechanisms to the macroscopic behaviors of low symmetry and phase transforming crystalline solids. These methods are applied in studying elasticity, accommodation twinning, deformation twinning, and slip through neutron diffraction data of tensile and compressive deformations of monoclinic NiTi to ~18% true strain. A deeper understanding of tension–compression asymmetry in NiTi is gained by connecting crystallographic calculations of polycrystalline twinning strains with in situ diffraction measurements. Our analyses culminate in empirical, micromechanical quantification of individual elastic, accommodation twinning, deformation twinning, and slip contributions to the total macroscopic stress–strain response of a monoclinic material subjected to large deformations. From these results, we find that 20–40% of the total plastic response at high strains is due to deformation twinning and 60–80% due to slip.     

Self-consistent modeling of large plastic deformation, texture and morphology evolution in semi-crystalline polymers

A self-consistent model for semi-crystalline polymers is proposed to study their constitutive behavior, texture and morphology evolution during large plastic deformation. The material is considered as an aggregate of composite inclusions, each representing a stack of crystalline lamellae with their adjacent amorphous layers. The deformation within the inclusions is volume-averaged over the phases. The interlamellar shear is modeled as an additional slip system with a slip direction depending on the inclusion's stress. Hardening of the amorphous phase due to molecular orientation and, eventually, coarse slip, is introduced via Arruda-Boyce hardening law for the corresponding plastic resistance. The morphology evolution is accounted for through the change of shape of the inclusions under the applied deformation gradient. The overall behavior is obtained via a viscoplastic tangent self-consistent scheme. The model is applied to high density polyethylene (HDPE). The stress-strain response, texture and morphology changes are simulated under different modes of straining and compared to experimental data as well as to the predictions of other models.     

A finite strain elastic-viscoplastic self-consistent model for polycrystalline materials

A large strain elastic-viscoplastic self-consistent (EVPSC) model for polycrystalline materials is developed. At single crystal level, both the rate sensitive slip and twinning are included as the plastic deformation mechanisms, while elastic anisotropy is accounted for in the elastic moduli. The transition from single crystal plasticity to polycrystal plasticity is based on a completely self-consistent approach. It is shown that the differences in the predicted stress-strain curves and texture evolutions based on the EVPSC and the viscoplastic self-consistent (VPSC) model proposed by Lebensohn and Tomé (1993) are negligible at large strains for monotonic loadings. For the deformations involving unloading and strain path changes, the EVPSC predicts a smooth elasto-plastic transition, while the VPSC model gives a discontinuous response due to lack of elastic deformation. It is also demonstrated that the EVPSC model can capture some important experimental features which cannot be simulated by using the VPSC model.     

An efficient constitutive model for room-temperature,low-rate plasticity of annealed Mg AZ31B sheet

Metals and alloys with hexagonal close packed (HCP) crystal structures can undergo twinning in addition to dislocation slip when loaded mechanically. The complexity of the plastic response and the limited extent of twinning are impediments to their room-temperature formability and thus their widespread adoption. In order to exploit the unusual deformation characteristics of twinning sheet materials in designing novel forming operations, a practical plane stress material model for finite element implementation was sought. Such a model, TWINLAW, has been constructed based on three phenomenological deformation modes for Mg AZ31B: S (slip), T (twinning), and U (untwinning). The modes correspond to three testing regimes: initial in-plane tension (from the annealed state), initial in-plane compression, and in-plane tension following compression, respectively. A von Mises yield surface with initial non-zero back stress was employed to account for plastic yielding asymmetry, with evolution according to a novel isotropic and nonlinear kinematic hardening model. Texture and its evolution were represented throughout deformation using a weighted discrete probability density function of c-axis orientations. The orientation of c-axes evolves with twinning or untwinning using explicit rules incorporated in the model.     

Orientation evolution in Hadfield steel single crystals under combined slip and twinning

The tensile deformation response and texture evolution of aluminum alloyed Hadfield steel single crystals oriented in the 〈1 6 9〉 direction is investigated. In this material, the strain hardening response is governed by the high-density dislocation walls (HDDWs) that interact with glide dislocations. A microstructure-based visco-plastic self-consistent model was modified to account for mechanical twinning in addition to the prevailing contribution of the HDDWs. Simulations revealed the contribution of twinning to the overall work hardening at the later stages of deformation. Moreover, both the deformation response and the rotation of the loading axis associated with plastic flow are successfully predicted even at the high-strain levels attained (0.53). Predicting the texture evolution serves as a separate check for validating the model, motivating its utilization in single and polycrystals of other alloys that exhibit combined HDDWs and twinning.     

Anisotropic response of high-purity α-titanium: Experimental characterization and constitutive modeling

This paper presents a comprehensive experimental and theoretical investigation of the deformation behavior of high-purity, polycrystalline α-titanium under quasi-static conditions at room temperature. The initial material in this study was a cross-rolled plate with a strong basal texture. To quantify the plastic anisotropy and the tension–compression asymmetry of this material, monotonic tensile and compressive tests were conducted, on samples cut along different directions of the plate. A new anisotropic elastic/plastic model was developed to describe the quasi-static macroscopic response of the aggregate. Key in its formulation is the use of an anisotropic yield criterion that captures strength-differential effects and an anisotropic hardening rule that accounts for texture evolution associated to twinning. A very good agreement between FE simulations using the model developed and uniaxial data was obtained.     

镁合金塑性机制研究综述

纯镁具有丰富的微观塑性机制，尤其是孪晶，导致其塑性变形错综复杂，力学性能也与常见的面心及体心立方金属有显著差异。由于现今学界对位错滑移与孪晶变形等塑性机制缺乏充分认识，镁合金性能调控效果尚不理想，与铝合金相比，镁合金的力学性能还有很大的提升空间。基于此背景，本文首先回顾了镁合金的发展历史与应用现状。然后介绍了镁中位错滑移与孪晶变形等塑性机制的研究进展，重点阐述位错、孪晶、晶界、析出相、溶质原子等重要的微结构，并简要介绍了计算机模拟方法。最后展望了强韧性能方面值得重视的若干研究方向。