Anisotropy of martensitic transformations in modeling of shape memory alloy polycrystals

Based on the knowledge of the anisotropy associated with the martensitic transformations obtained from tension/compression experiments with oriented CuAlNi single crystals, a simple constant stress averaging approach is employed to model the SMA polycrystal deformation behaviors. Only elastic and inelastic strains due to the martensitic transformation, variant reorientations in the martensite phase and martensite to martensite transformations in thermomechanical loads are considered. The model starts from theoretical calculation of the stress-temperature transformation conditions and their orientation dependence from basic crystallographic and material attributes of the martensitic transformations. Results of the simulations of the NiTi, NiAl, and Cu-based SMA polycrystals in stress–strain tests are shown. It follows that SMA polycrystals, even with randomly oriented grains, typically exhibit tension/compression asymmetry of the shape of the pseudoelastic σ−ε curves in transformation strain, transformation stress, hysteresis widths, character of the pseudoelastic flow and in the slope of temperature dependence of the transformation stresses. It is concluded that some macroscopic features of the SMA polycrystal behaviors originate directly from the crystallography of the undergoing MT's. The model shows clearly the crystallographic origin of these phenomena by providing a link from the crystallographic and material attributes of martensitic transformations towards the macroscopic σ−ε−T behaviors of SMA polycrystals.     

Simulations of localized thermo-mechanical behavior in a NiTi shape memory alloy

Previous experiments have shown that stress-induced martensitic transformation in certain polycrystalline NiTi shape memory alloys can lead to strain localization and propagation phenomena when loaded in uniaxial tension. The number of nucleation events and kinetics of transformation fronts were found to be sensitive to the nature of the ambient media and imposed loading rate due to the release/absorption of latent heat and the material's inherent temperature sensitivity of the transformation stress. A special plasticity-based constitutive model used within a 3-D finite element framework has previously been shown to capture the isothermal, purely mechanical front features seen in experiments of thin uniaxial NiTi strips. This paper extends the approach to include the thermo-mechanical coupling of the material with its environment. The simulations successfully capture the nucleation and evolution of fronts and the corresponding temperature fields seen during the experiments.     

纳米单晶NiTi合金单程形状记忆效应的分子动力学模拟

采用基于第二近邻修正型嵌入原子势的分子动力学方法研究了纳米单晶NiTi合金的单程形状记忆效应,详细阐明了温度诱发马氏体相变和应力诱发马氏体重定向过程中纳米单晶的变形行为和微结构演化,进一步分析了加/卸载速率对NiTi合金单程形状记忆效应的影响。结果表明,NiTi纳米单晶在应力加载过程中发生马氏体重定向,卸载后存在残余应变;当加热到奥氏体转变结束温度以上时,马氏体逆相变为奥氏体相,残余应变逐渐减小,但未完全回复;随着应力加载速率的增加,重定向临界应力和模量逐渐增加;再次降温过程中不同加载速率下的原子结构演化各不相同。     

纳米单晶NiTi合金单程形状记忆效应的分子动力学模拟

采用基于第二近邻修正型嵌入原子势的分子动力学方法研究了纳米单晶NiTi合金的单程形状记忆效应,详细阐明了温度诱发马氏体相变和应力诱发马氏体重定向过程中纳米单晶的变形行为和微结构演化,进一步分析了加/卸载速率对NiTi合金单程形状记忆效应的影响。结果表明,NiTi纳米单晶在应力加载过程中发生马氏体重定向,卸载后存在残余应变;当加热到奥氏体转变结束温度以上时,马氏体逆相变为奥氏体相,残余应变逐渐减小,但未完全回复;随着应力加载速率的增加,重定向临界应力和模量逐渐增加;再次降温过程中不同加载速率下的原子结构演化各不相同。     

A combined experimental-numerical approach for elasto-plastic fracture of individual grain boundaries

The parameters for a crystal plasticity finite element constitutive law were calibrated for the aluminum–lithium alloy 2198 using micro-column compression testing on single crystalline volumes. The calibrated material model was applied to simulations of micro-cantilever deflection tests designed for micro-fracture experiments on single grain boundaries. It was shown that the load–displacement response and the local deformation of the grains, which was measured by digital image correlation, were predicted by the simulations. The fracture properties of individual grain boundaries were then determined in terms of a traction–separation-law associated with a cohesive zone. This combination of experiments and crystal plasticity finite element simulations allows the investigation of the fracture behavior of individual grain boundaries in plastically deforming metals.     

纳米多晶NiTi形状记忆合金超弹性的晶粒取向依赖性相场研究

本文基于Ginzburg-Landau理论,建立了一个反映纳米多晶NiTi形状记忆合金取向依赖性的二维多晶相场模型,研究了晶粒取向对其超弹性性能的影响。结果表明,纳米多晶NiTi形状记忆合金的超弹性行为依赖于晶粒取向分布,即：多晶模型中在所研究的参数变化范围内,晶粒取向分布范围越广、晶粒间取向差越大（无明显织构）,超弹性性能越差;而晶粒取向分布范围越窄、晶粒间取向差越小（织构越强）,超弹性性能越好。该晶粒取向依赖性可解释为：由于晶粒取向的不同,马氏体相变过程中相邻晶粒间的变形不匹配程度不同,因此,多晶模型中在所研究的参数变化范围内,晶粒间取向差异越大,晶界处的变形失配越严重,由此而产生的局部内应力将阻碍其附近马氏体相变的扩展,进而导致纳米多晶NiTi形状记忆合金超弹性性能下降。     

Stress-induced transformation behavior of a polycrystalline NiTi shape memory alloy: micro and macromechanical investigations via in situ optical microscopy

An experimental investigation of the micro and macromechanical transformation behavior of polycrystalline NiTi shape memory alloys was undertaken. Special attention was paid to macroscopic banding, variant microstructure, effects of cyclic loading, strain rate and temperature effects. Use of an interference filter on the microscope enabled observation of grain boundaries and martensitic plate formation and growth without recourse to etching or other chemical surface preparation. Key results of the experiments on the NiTi include observation of localized plastic deformation after only a few cycles, excellent temperature and stress relaxation correlation, a refined definition of “full transformation” for polycrystalline materials, and strain rate dependent effects. Several of these findings have critical implications for understanding and modeling of shape memory alloy behavior.     

Grain size effects in multiphase steels assisted by transformation-induced plasticity

The influence of the austenitic grain size on the overall stress–strain behavior in a multiphase carbon steel is analyzed through three-dimensional finite element simulations. A recently developed multiscale martensitic transformation model is combined with a plasticity model to simulate the transformation-induced plasticity effects of a grain of retained austenite embedded in a ferrite-based matrix. Grain size effects are included via a surface energy term in the Helmholtz energy. Tensile simulations for representative orientations of the grain of retained austenite show that the initial stability of the austenite increases as the grain size decreases. Consequently, the effective strength is initially higher for smaller grains. The influence of the grain size on the evolution of the transformation process strongly depends on the grain orientation. For “hard” orientations, the transformation rate is higher for larger grains. In addition, the phase transformation is partially suppressed as the grain size decreases. In contrast, for “soft” orientations, the transformation rate is lower for larger grains. The phase transformation is more homogeneous for smaller grains and, consequently, the effective transformation strain is larger. Nevertheless, in multiphase carbon steels with a relatively low percentage of retained austenite, the influence of the austenitic grain size on the overall constitutive response is smaller than the influence of the austenitic grain orientation.     

应力引起的镍钛单晶形状记忆合金相变的实验研究

在单晶形状记忆合金试样中,由于没有晶粒之间的约束,它的马氏体相界面移动比多晶容易,用实验方法研究其相变的特点,对建立新的理论模型有意义,因而对它的实验分析显得重要。本文利用高分辨率的CCD系统监测到NiTi单晶形状记忆合金在拉伸时的相变伪弹性的过程;利用X射线衍射法得到了NiTi单晶试样在拉伸方向的晶向;运用高分辨率的云纹干涉技术,获得了应力引起的NiTi单晶形状记忆合金相变时的变形场;利用高分辨率、高灵敏度的红外相机记录了NiTi单晶在拉伸状态下的温度变化规律;对低温下NiTi单晶的拉伸性能做了初步的研究,得到一些有意义的现象。     

The role of texture in tension–compression asymmetry in polycrystalline NiTi

The purpose of the present study is to thoroughly understand the stress–strain behavior of polycrystalline NiTi deformed under tension versus compression. To do this, a micro-mechanical model is used which incorporates single crystal constitutive relationships and experimentally measured polycrystalline texture into the self-consistent formulation. For the first time it is quantitatively demonstrated that texture measurements coupled with a micro-mechanical model can accurately predict tension/compression asymmetry in NiTi shape memory alloys. The predicted critical transformation stress levels and transformation stress–strain slopes under both tensile and compressive loading are consistent with experimental results. For textured polycrystalline NiTi deformed under tension it is demonstrated that the martensite evolution is very abrupt, consistent with the Luders type deformation experimentally observed. The abrupt transformation under tension is attributed to the fact that the majority of the grains are oriented along the [111] crystallographic direction, which is soft under tensile loading. Since single crystals of the [111] orientation are hard under compression it is also demonstrated that under compression the martensite in textured polycrystalline NiTi evolves relatively slower.     

超弹性形状记忆合金管单向拉伸试验的数值模拟

NiTi形状记忆合金具有很强的超弹性行为,这种超弹性行为是由于材料在应力作用下发生可逆的马氏体相变所引起。最近Sun和Lee^[4]在NiTi形状记忆合金管单向拉伸试验中观测到,应力诱导马氏体相变具有螺旋带状的形貌特征,本文对此作了数值模拟研究。采用包含应变软化效应的三线性本构关系,建立了NiTi形状记忆合金管的三维有限元模型。通过迭代计算,成功地再现了试验中所观察到的螺旋状相变带从形成到长大的全过程。数值计算结果表明,产生这一独特现象的力学机制,在于NiTi形状记忆合金管在拉伸状态下出现的局部变形失稳极其传播。     

应力作用下NiTi形状记忆合金微结构演化的相场模拟及其本征应变率敏感性

基于Ginzburg-Landau动力学控制方程建立了NiTi形状记忆合金非等温相场模型,实现了对NiTi合金内应力诱导马氏体相变的数值模拟。同时将晶界能密度引入系统局部自由能密度,从而考虑多晶系统中晶界的重要作用。数值计算了单晶和多晶NiTi形状记忆合金在单轴机械载荷作用下微结构的动态演化过程和宏观力学行为,并重点研究了晶粒尺寸为60 nm的NiTi纳米多晶在低应变率下（0.0005～15 s?1）力学行为的本征应变率敏感性。研究结果表明,单晶NiTi合金系统高温拉伸-卸载过程中马氏体相变均匀发生,未形成奥氏体-马氏体界面。而纳米多晶系统在加载阶段出现了马氏体带的形成-扩展现象,在卸载阶段出现了马氏体带的收缩-消失现象。相同外载作用过程中,NiTi单晶系统的宏观应力-应变曲线具有更大的滞回环面积,拥有更优的超弹性变形能力。计算结果显示,在中低应变率下纳米晶NiTi形状记忆合金应力-应变关系表现出较明显的应变率相关性,应变率升高导致材料相变应力提升。这一应变率相关性主要源于相场模型中外加载荷速率与马氏体空间演化速度的相互竞争关系。     

Evaluation of finite element based analysis of 3D multicrystalline aggregates plasticity: Application to crystal plasticity model identification and the study of stress and strain fields near grain boundaries

Plastic heterogeneities of hexagonal close-packed (HCP) materials are numerically investigated at the grain level. Intensive use of parallel Finite Elements computations enables us to study micro-plasticity of realistic 3D multicrystalline aggregates, including, macroscopic mechanical responses but also average responses in each grain and particularly local stress and strain fields. This paper focuses on three applications of this simulation method. The first part of this paper is devoted to a fine analysis of micro-plasticity of HCP materials. Intergranular but also intragranular stress and strain heterogeneities are described and micro-plasticity patterns are displayed throughout the 3D microstructures. A special attention is paid to the sensitivity of simulations with respect to the mesh discretization, the element interpolation and the geometrical representation of grain boundaries, in terms of macroscopic and local responses. Later, a simplified homogenization method is evaluated, regarding results of the first part. Afterwards, this method is applied with a zirconium alloy to identify a set of coefficients for a single crystal plasticity model. Finally, in order to provide critical information for intergranular damage phenomena (reported in literature for zirconium alloys), the third part provides a statistical analysis of over-stresses at grain boundaries.     

Analysis of grain size effects on transformation-induced plasticity based on a discrete dislocation-transformation model

There is much interest recently in the possibility of combining two strengthening effects, namely the reduction of grain size (Hall-Petch effect) and the transformation-induced plasticity effect (strengthening due to a martensitic transformation). The present work is concerned with the analysis of the combination of these two effects using a discrete dislocation-transformation model. The transformation-induced plasticity mechanism is studied for aggregates of grains of ferrite and austenite of different sizes. The discrete model allows to simulate the behavior at sub-grain length scales, capturing the complex interaction between pile-ups at grain boundaries and the evolution of the microstructure due to transformation. The simulations indicate that, as the average grain size decreases, the relative strengthening due to the formation of martensite is significantly reduced and that the overall strengthening is mostly due to a Hall-Petch effect. This finding suggests that strengthening by the transformation-induced plasticity mechanism is ineffective in the presence of fine-grained microstructures.     

SUPER-ELASTIC CONSTITUTIVE MODEL CONSIDERING PLASTICITY AND ITS FINITE ELEMENT IMPLEMENTATION

Based on the experimental results of super-elastic NiTi alloy, a three-dimensional super-elastic constitutive model including both of stress-induced martensite transformation and plasticity is constructed in a framework of general inelasticity. In the proposed model, transformation hardening, reverse transformation of stress-induced martensite, elastic mismatch between the austenite and martensite phases, and temperature-dependence of transformation stress and elastic modulus of each phase are considered. The plastic yielding of martensite occurred under high stress is addressed by a bilinear isotropic hardening rule. Drucker-Prager-typed transformation surfaces are employed to describe the asymmetric behavior of NiTi alloy in tension and compression. The prediction capability of the proposed model is verified by comparing the simulated results with the correspondent experimental ones. Based on backward Euler＇s integration, a new expression of consistent tangent modulus is derived. The proposed model is then implemented into a finite element package ABAQUS by user-subroutine UMAT. Finally, the validity of such implementation was verified by some numerical samples.     

Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation

A strain gradient dependent crystal plasticity approach is used to model the constitutive behaviour of polycrystal FCC metals under large plastic deformation. Material points are considered as aggregates of grains, subdivided into several fictitious grain fractions: a single crystal volume element stands for the grain interior whereas grain boundaries are represented by bi-crystal volume elements, each having the crystallographic lattice orientations of its adjacent crystals. A relaxed Taylor-like interaction law is used for the transition from the local to the global scale. It is relaxed with respect to the bi-crystals, providing compatibility and stress equilibrium at their internal interface. During loading, the bi-crystal boundaries deform dissimilar to the associated grain interior. Arising from this heterogeneity, a geometrically necessary dislocation (GND) density can be computed, which is required to restore compatibility of the crystallographic lattice. This effect provides a physically based method to account for the additional hardening as introduced by the GNDs, the magnitude of which is related to the grain size. Hence, a scale-dependent response is obtained, for which the numerical simulations predict a mechanical behaviour corresponding to the Hall-Petch effect. Compared to a full-scale finite element model reported in the literature, the present polycrystalline crystal plasticity model is of equal quality yet much more efficient from a computational point of view for simulating uniaxial tension experiments with various grain sizes.     

Three-dimensional local stress analysis on grain boundaries in polycrystalline material

In order to understand the initiation behavior of microstructurally small cracks in a stress corrosion cracking condition, it is important to know the tensile normal stress acting on the grain boundary (normal GB stress). The local stress in a polycrystalline body is enhanced by the inhomogeneity which stems from the shape and orientation of each grain. The stress in a three-dimensional polycrystalline body consisting of 100 grains with random orientation, under a remote uniform tensile stress condition, is evaluated by the finite element method. It was revealed that the local stress on the polycrystalline body is inhomogeneous under uniform applied stress and becomes large at those grain boundaries that are perpendicular to the load axis, though there is large fluctuation. It was also shown that the normal GB stress tends to be large near the triple points due to the deformation constraint caused by adjacent grains. Finally, the maximum stress on the surface of a large component caused by the inhomogeneity was evaluated by using Gumbel statistics.     

A computational model for the indentation and phase transformation of a martensitic thin film

We propose a computational model for a stress-induced martensitic phase transformation of a single-crystal thin film by indentation and its reverse transformation to austenite by heating. Our model utilizes a surface energy that allows sharp interfaces with finite energy and a penalty that forces the film to lie above the indenter and undergo a stress-induced austenite-to-martensite phase transformation. We introduce a method to nucleate the martensite-to-austenite phase transformation since in our model the film would otherwise remain in the martensitic phase in a local minimum of the energy.     

NiTi形状记忆合金裂纹尖端热力耦合行为研究

本文对NiTi形状记忆合金I型裂纹尖端热力耦合行为进行了数值仿真分析和实验验证。建立了包含相变和热力耦合的本构模型,通过有限元计算得到了裂纹尖端附近的纵向应变、马氏体体积分数和温度场分布,依据马氏体相变情况对裂纹尖端有效应力强度因子进行了修正,揭示了加载速率对形状记忆合金裂纹尖端有效应力强度影子的影响规律。参数研究表明,随着加载频率的增加,裂纹尖端附近温度逐渐升高,马氏体相变区域逐渐缩小,有效应力强度因子呈下降趋势,形状记忆合金表现出增韧效应,有助于减缓裂纹扩展。本研究结果对于揭示热力耦合作用下超弹性形状记忆合金疲劳裂纹扩展规律具有重要参考意义。