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。     

梯度纳米晶NiTi形状记忆合金的超弹性和形状记忆效应相场模拟

通过建立考虑两个马氏体变体的二维相场模型,对梯度纳米晶镍钛(NiTi)合金系统的超弹性、单程和应力辅助双程形状记忆过程进行了模拟和预测.模拟结果显示: 在梯度纳米晶NiTi合金的超弹性过程中,较粗晶粒的区域保留了传统粗晶的马氏体相变和逆相变特征,即局部马氏体带的形核-扩展和缩减-消失, 而随着晶粒尺寸的减小,细晶粒区域表现为均匀相变的特点, 即无局部马氏体带产生; 此外,在超弹性和形状记忆过程中,马氏体相变和重取向都首先在较粗晶粒区域开始并逐步向细晶粒区域传播,而逆相变则相反.马氏体相变和重取向的逐步扩展使梯度纳米晶NiTi合金的应力-应变和应变-温度曲线呈现出“硬化状”,其可归因于纳米多晶NiTi合金中马氏体相变对晶粒尺寸的依赖性,即随着晶粒尺寸的减小, 相变或重取向壁垒逐渐增大,马氏体相变或重取向的形核、扩展越来越困难. 可见,梯度纳米晶结构具有比传统均匀晶粒尺寸NiTi合金更宽的相变应力区间、重取向应力区间和相变温度区间,可显著提高该合金非弹性变形的可控性.      

Size effects in martensitic microstructures: Finite-strain phase field model versus sharp-interface approach

A finite-strain phase field model for martensitic phase transformation and twinning in shape memory alloys is developed and confronted with the corresponding sharp-interface approach extended to interfacial energy effects. The model is set in the energy framework so that the kinetic equations and conditions of mechanical equilibrium are fully defined by specifying the free energy and dissipation potentials. The free energy density involves the bulk and interfacial energy contributions, the latter describing the energy of diffuse interfaces in a manner typical for phase-field approaches. To ensure volume preservation during martensite reorientation at finite deformation within a diffuse interface, it is proposed to apply linear mixing of the logarithmic transformation strains. The physically different nature of phase interfaces and twin boundaries in the martensitic phase is reflected by introducing two order-parameters in a hierarchical manner, one as the reference volume fraction of austenite, and thus of the whole martensite, and the second as the volume fraction of one variant of martensite in the martensitic phase only. The microstructure evolution problem is given a variational formulation in terms of incremental fields of displacement and order parameters, with unilateral constraints on volume fractions explicitly enforced by applying the augmented Lagrangian method. As an application, size-dependent microstructures with diffuse interfaces are calculated for the cubic-to-orthorhombic transformation in a CuAlNi shape memory alloy and compared with the sharp-interface microstructures with interfacial energy effects.     

A thermodynamical constitutive model for shape memory materials. Part I. The monolithic shape memory alloy

Pseudoelasticity and the shape memory effect (SME) due to martensitic transformation and reorientation of polycrystalline shape memory alloy (SMA) materials are modeled using a free energy function and a dissipation potential. Three different cases are considered, based on the number of internal state variables in the free energy: (1) austenite plus a variable number of martensite variants; (2) austenite plus two types of martensite; and (3) austenite and one type of martensite. Each model accounts for three-dimensional simultaneous transformation and reorientation. The single-martensite model was chosen for detailed study because of its simplicity and its ease of experimental verification. Closed form equations are derived for the damping capacity and the actuator efficiency of converting heat into work. The first law of thermodynamics is used to demonstrate that significantly more work is required to complete the adiabatic transformation than the isothermal transformation. Also, as the hardening due to the austenite/martensite misfit stresses approaches zero, the transformation approaches the isothermal, infinite specific heat conditions of a first-order transformation. In a second paper, the single-martensite model is used in a mesomechanical derivation of the constitutive equations of an active composite with an SMA phase.     

A 3-D phenomenological constitutive model for shape memory alloys under multiaxial loadings

This paper presents a new phenomenological constitutive model for shape memory alloys, developed within the framework of irreversible thermodynamics and based on a scalar and a tensorial internal variable. In particular, the model uses a measure of the amount of stress-induced martensite as scalar internal variable and the preferred direction of variants as independent tensorial internal variable. Using this approach, it is possible to account for variant reorientation and for the effects of multiaxial non-proportional loadings in a more accurate form than previously done. In particular, we propose a model that has the property of completely decoupling the pure reorientation mechanism from the pure transformation mechanism. Numerical tests show the ability to reproduce main features of shape memory alloys in proportional loadings and also to improve prediction capabilities under non-proportional loadings, as proven by the comparison with several experimental results available in the literature.     

A NEW MODEL OF SHAPE MEMORY ALLOYS

A new constitutive model of shape memory alloys ( SMAs) based on Tanaka ' s martensite fraction exponential expression is produced. This new model can present recoverable shape memory strain during different phase transformation, and reflect the action of martensite reorientation . Also it can overcome the defect of Tanaka ' s Model when the SMAs ' microstructure is fully martensite . The model is very simple and suitable for using , and the correct behavior of the model is proved by test.     

A CONSTITUTIVE MODEL FOR TRANSFORMATION, REORIENTATION AND PLASTIC DEFORMATION OF SHAPE MEMORY ALLOYS

A constitutive model is developed for the transformation, reorientation and plastic deformation of shape memory alloys (SMAs). It is based on the concept that an SMA is a mixture composed of austenite and martensite, the volume fraction of each phase is transformable with the change of applied thermal-mechanical loading, and the constitutive behavior of the SMA is the combination of the individual behavior of its two phases. The deformation of the martensite is separated into elastic, thermal, reorientation and plastic parts, and that of the austenite is separated into elastic, thermal and plastic parts. Making use of the Tanaka’s transformation rule modified by taking into account the effect of plastic deformation, the constitutive model of the SMA is obtained. The ferroelasticity, pseudoelasticity and shape memory effect of SMA Au-47.5 at.%Cd, and the pseudoelasticity and shape memory effect as well as plastic deformation and its effect of an NiTi SMA, are analyzed and compared with experimental results.     

On the modeling of equilibrium twin interfaces in a single-crystalline magnetic shape memory alloy sample. II: numerical algorithm

This is part II of this series of papers. The aim of the current paper was to solve the governing PDE system derived in part I numerically, such that the procedure of variant reorientation in a magnetic shape memory alloy (MSMA) sample can be simulated. The sample to be considered in this paper has a 3D cuboid shape and is subject to typical magnetic and mechanical loading conditions. To investigate the demagnetization effect on the sample’s response, the surrounding space of the sample is taken into account. By considering the different properties of the independent variables, an iterative numerical algorithm is proposed to solve the governing system. The related mathematical formulas and some techniques facilitating the numerical calculations are introduced. Based on the results of numerical simulations, the distributions of some important physical quantities (e.g., magnetization, demagnetization field, and mechanical stress) in the sample can be determined. Furthermore, the properties of configurational force on the twin interfaces are investigated. By virtue of the twin interface movement criteria derived in part I, the whole procedure of magnetic field- or stress-induced variant reorientations in the MSMA sample can be properly simulated.     

A 3D finite strain phenomenological constitutive model for shape memory alloys considering martensite reorientation

Most devices based on shape memory alloys experience both finite deformations and non-proportional loading conditions in engineering applications. This motivates the development of constitutive models considering finite strain as well as martensite variant reorientation. To this end, in the present article, based on the principles of continuum thermodynamics with internal variables, a three-dimensional finite strain phenomenological constitutive model is proposed taking its basis from the recent model in the small strain regime proposed by Panico and Brinson (J Mech Phys Solids 55:2491–2511, 2007). In the finite strain constitutive model derivation, a multiplicative decomposition of the deformation gradient into elastic and inelastic parts, together with an additive decomposition of the inelastic strain rate tensor into transformation and reorientation parts is adopted. Moreover, it is shown that, when linearized, the proposed model reduces exactly to the original small strain model.     

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。     

A three-dimensional phenomenological model for martensite reorientation in shape memory alloys

In this work, we propose a macroscopic phenomenological model that is based on the classical framework of thermodynamics of irreversible processes and accounts for the effect of multiaxial stress states and non-proportional loading histories. The model is able to account for the evolution of both twinned and detwinned martensite. Moreover, reorientation of the product phase according to loading direction is specifically accounted for. Towards this purpose the inelastic strain is split into two contributions deriving, respectively, from creation of detwinned martensite and reorientation of previously existing martensite variants. Computational tests demonstrate the ability of the model to simulate the main aspects of the shape memory response in a one-dimensional setting and some of the features that have been experimentally found in the case of multiaxial non-proportional loading histories. Experimental non-proportional loading paths have also been simulated and a good qualitative agreement between numerical and experimental response is observed.     

A three-dimensional model of the thermomechanical behavior of shape memory alloys

A new macro-scale model of shape memory alloys is developed within the framework of generalized standard materials with internal constraints [Moumni, Z., 1995. Sur la modélisation du changement de phase à l’état solide. Ph.D. Thesis, École Nationale Supérieure des Ponts et Chaussées]. It is shown that the introduction of two state variables: the martensite volume fraction and the martensite orientation strain tensor, is sufficient to account for several effects exhibited by SMAs subject to thermomechanical loading, namely: self-accommodation, orientation and reorientation or martensite, as well as superelasticity and one-way shape memory. These phenomena are simulated using the same set of constitutive equations and evolution laws. A simple procedure for identifying the parameters of the model is described in detail and a validation against experimental data is conducted. The model is then used to analyze a 3D SMA structure representing a superelastic stent. Cyclic loading and other pertaining phenomena like training and two-way shape memory are considered in the second part of this paper.     

Micromechanical study of formation and evolution of martensite for Cu–Al–Ni single crystal by moiré interferometry

The basic properties of pseudoelasticity of Cu–Al–Ni single crystal are studied to analyze the morphology associated with the formation and evolution of martensite and the shape memory recovery process at different temperatures. Use is made of a multifunctional macro–micro moiré interferometry measurement system. The β₁ to β₁^′ phase changes are identified with the stress-induced transformation of a Cu–13.7%Al–4.18%Ni (wt%) alloy. The invariant plane between the martensite and the parent phase is shown directly by fringe patterns. It is found that martensite appears in the shape of bands or thin plates on the surface of the specimen. The formation of martensite is a very rapid process and martensite ‘jumps' out until the specimen is completely transformed into a single variant. The results reveal the mechanism and process of stress-type and temperature-induced martensitic transformation.     

CONSTITUTIVE MODELING OF ROLLED SHAPE MEMORY ALLOY SHEETS TAKING INTO ACCOUNT PRE-TEXTURE AND ANISOTROPIC HARDENING

The drawing or rolling process endows polycrystal shape memory alloy with a crys- tallographic texture, which can result in macroscopic anisotropy. The main purpose of this work is to develop a constitutive model to predict the thermomechanical behavior of shape memory alloy sheets, which accounts for the crystallographic texture. The total macroscopic strain is decom- posed into elastic strain and macro-transformation strain under isothermal condition. Considering the transformation strain in local grains and the orientation distribution function of crystallo- graphic texture, the macro-transformation strain and the effective elastic modulus of textured polycrystal shape memory alloy are developed by using tensor expressions. The kinetic equation is established to calculate the volume fraction of the martensite transformation under given stress. Furthermore, the Hill＇s quadratic model is developed for anisotropic transformation hardening of textured SMA sheets. All the calculation results are in good agreement with experimental data, which show that the present model can accurately describe the macro-anisotropic behaviors of textured shape memory alloy sheets.     

Shape recovery behaviour of NiTi strips in bending: experiments and modelling

We present a theoretical and experimental investigation of the bending recovery performances for a commercial NiTi shape memory alloy strip. We evaluate the mechanical properties and the shape setting parameters and estimate the evolution of the curvature during heating in an Ethylene Glycol-based water solution. To model the strip bending response, we use a one-dimensional phenomenological constitutive equation for the shape memory material, based on the introduction of (twinned and detwinned) martensite and austenite volume fractions as internal variables. Under the assumption of uniform bending, we calculate a quasi-closed-form solution for the stress and martensite fraction distributions in a shape memory beam during bending and subsequent shape recovery. Using our characterisation data as input parameters of the model, we find that the theoretical curvature evolution is in good agreement with experimental data.     

On the modeling of equilibrium twin interfaces in a single-crystalline magnetic shape-memory alloy sample—III: Magneto-mechanical behaviors

This is the concluding part III of a series of papers. The aim of the current paper is to simulate and analyze the procedure of variant reorientation in a magnetic shape-memory alloy (MSMA) sample and to predict the response of the sample subject to various loading conditions. The sample to be considered in this paper has a 3D cuboid shape and is subject to typical magneto-mechanical loading conditions. Variant reorientation in the sample is realized through twin interface movements. To investigate the key features of twin interface movements, the properties of configurational forces on the twin interfaces are analyzed. For both the stress-assisted MFIS tests and the field-assisted quasi-elasticity tests, the magneto-mechanical behavior of the MSMA sample during the whole loading procedure is simulated by using the finite element method. The influence of the initial variant distribution in the sample on its global response is discussed. The obtained numerical results are compared with the experimental results. It can be seen that the model predictions can fit the experimental results both at a qualitative as well as at a quantitative level.     

On the modeling of equilibrium twin interfaces in a single-crystalline magnetic shape memory alloy sample. I: theoretical formulation

In this paper, a variational approach is proposed to study the response of a single-crystalline magnetic shape memory alloy (MSMA) sample subject to external forces and magnetic fields. Especially, some criteria are derived to model the (quasi-static) movements of twin interfaces in the sample. By considering the compatibility condition, twin interfaces between two martensite variants are found to be flat planes with given normal vectors. To adopt the variational method, a total energy functional for the whole magneto-mechanical system is proposed. By calculating the variations of the total energy functional with respect to the independent variables, the equilibrium equations and the evolution laws for the internal variables can be derived. By further considering the variation of the total energy functional with respect to the variant distribution, some criteria for twin interface movements can be derived. The governing system of the current model is then formulated by composing the equilibrium equations, the evolution laws for the internal variables and the twin interface movement criteria. To show the validity of the governing system, some analytical results are constructed under certain simplified conditions, which can be used to simulate the magneto-mechanical response of the MSMA sample.     

铁磁形状记忆合金的力学行为研究进展

铁磁形状记忆合金是一种新型的多功能材料,它除了具有传统的温控和应力控制记忆合金的一般特点外, 还可以在磁场的作用下输出应变,极大地拓展了传统的形状记忆合金应用前景.材料力学行为的研究是材料得以广泛应用的前提.本文对铁磁形状记忆合金力学行为的研究文献进行了综述,着重介绍了铁磁形状记忆合金力学行为的研究现状, 系统阐述了晶体的成分、磁场强度、外应力以及温度等因素对力学行为的影响,并概述了铁磁形状记忆合金本构模型的研究进展.      

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。