An effective interaction potential model for the shape memory alloy AuCd

The unusual properties of shape memory alloys (SMAs) result from a lattice level martensitic transformation (MT) corresponding to an instability of the SMAs crystal structure. Currently, there exists a shortage of material models that can capture the details of lattice level MTs occurring in SMAs and that can be used for efficient computational investigations of the interaction between MTs and larger-scale features found in typical materials. These larger-scale features could include precipitates, dislocation networks, voids, and even cracks. In this article, one such model is developed for the SMA AuCd. The model is based on effective interaction potentials (EIPs). These are atomic interaction potentials that are explicit functions of temperature. In particular, the Morse pair potential is used and its adjustable coefficients are taken to be temperature dependent. An extensive exploration of the Morse pair potential is performed to identify an appropriate functional form for the temperature dependence of the potential parameters. A fitting procedure is developed for the EIPs that matches, at suitable temperatures, the stress-free equilibrium lattice parameters, instantaneous bulk moduli, cohesive energies, thermal expansion coefficients, and heat capacities of FCC Au, HCP Cd, and the B2 cubic austenite phase of the Au-47.5at%Cd alloy. The resulting model is explored using branch-following and bifurcation techniques. A hysteretic temperature-induced MT between the B2 cubic and B19 orthorhombic crystal structures is predicted. This is the behavior that is observed in the real material. In addition to reproducing the important properties mentioned above, the model predicts, to reasonable accuracy, the transformation strain tensor and captures the latent heat and thermal hysteresis to within an order of magnitude.     

Reversible stress-induced martensitic phase transformations in a bi-atomic crystal

In an earlier work, Elliott et al. [2006a, Stability of crystalline solids—II: application to temperature-induced martensitic phase transformations in bi-atomic crystals. Journal of the Mechanics and Physics of Solids 54(1), 193-232], the authors used temperature-dependent atomic potentials and path-following bifurcation techniques to solve the nonlinear equilibrium equations and find the temperature-induced martensitic phase transformations in stress-free, perfect, equi-atomic binary B2 crystals. Using the same theoretical framework, the current work adds the influence of stress to study the model's stress-induced martensitic phase transformations.The imposition of a uniaxial Biot stress on the austenite (B2) crystal, lowers the symmetry of the problem, compared to the stress-free case, and leads to a large number of stable equilibrium paths. To determine which ones are possible reversible martensitic transformations, we use the (kinematic) concept of the maximal Ericksen-Pitteri neighborhood (max EPN) to select those equilibrium paths with lattice deformations that are closest, with respect to lattice-invariant shear, to the austenite phase and thus capable of a reversible transformation. It turns out that for our chosen parameters only one stable structure (distorted αIrV) is found within the max EPN of the austenite in an appropriate stress window. The energy density of the corresponding configurations shows features of a stress-induced phase transformation between the higher symmetry austenite and lower symmetry martensite paths and suggests the existence of hysteretic stress-strain loops under isothermal load-unload conditions. Although the perfect crystal model developed in this work over-predicts many key material properties, such as the transformation stress and the Clausious-Clapeyron slope, when compared to real experimental values (based on actual polycrystalline specimens with defects), it is—to the authors' knowledge—the first atomistic model that has been demonstrated to capture all essential trends and behavior observed in shape memory alloys.     

Modelling and numerical simulation of martensitic transformation in shape memory alloys

We consider the evolution of martensitic fine structures in shape memory alloys which undergo an isothermal phase-transformation. This process is modelled on a microscopical, continuum-mechanical level by partial differential equations. Here a homogeneous degree-1 dissipation potential is involved which can reflect specific energies needed for rate-independent phase transformations. An interface energy is incorporated by a nonlocal term, and hard-device loading is considered. After setting up the model and specifying its energy balance properties, three-dimensional numerical experiments for the cubic-to-tetragonal transformation in an InTl single crystal are presented which demonstrate geometrical/material interactions under tensile and shear loading.Received: 27 June 2002, Accepted: 18 March 2003, Published online: 27 June 2003PACS: 81.30Kf     

CuAlNi单晶形状记忆合金压缩特性的实验研究

具有相变伪弹性特性的CuAlNi单晶是目前应用最广泛的形状记忆合金之一。这种材料被广泛应用在工程、生物和医学科学等领域。由于单晶是各向异性，没有多晶中晶粒之间的相互作用，因而在特定晶向上的力学性能稳定。但是这种材料的一些基本性质，如压缩状态下马氏体的发生、生长和传播等还没有人详细研究。本文主要研究CuAlNi单晶在特定晶向上的变形过程，它的应力—应变特性，并利用特殊的显微成像系统首次获得了沿[110]方向压缩时二维马氏体的发生、生长和传播过程。     

热弹性马氏体相变连续介质热力学研究

介绍形状记忆合金热弹性马氏体相变连续介质热力学研究方法和最新进展, 着重分析了在推广的非线性弹性力学的框架下, 应用变分方法研究热弹性马氏体相变的理论和方法、存在的问题及发展趋势. 首先介绍如何计算马氏体相变24种变体的变形梯度, 然后拓展非线性弹性力学, 引入描述相变的多阱非凸弹性势能, 进而讨论了界面能和非局部能对相变微结构和相变过程的影响的相关研究理论方法和进展.      

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。     

Modelling of laminated microstructures in stress-induced martensitic transformations

This paper is concerned with micromechanical modelling of stress-induced martensitic transformations in crystalline solids, with the focus on distinct elastic anisotropy of the phases and the associated redistribution of internal stresses. Micro-macro transition in stresses and strains is analysed for a laminated microstructure of austenite and martensite phases. Propagation of a phase transformation front is governed by a time-independent thermodynamic criterion. Plasticity-like macroscopic constitutive rate equations are derived in which the transformed volume fraction is incrementally related to the overall strain or stress. As an application, numerical simulations are performed for cubic β₁ (austenite) to orthorhombic γ₁′ (martensite) phase transformation in a single crystal of Cu-Al-Ni shape memory alloy. The pseudoelasticity effect in tension and compression is investigated along with the corresponding evolution of internal stresses and microstructure.     

Constitutive equations for two‐step thermoelastic phase transformations

A number of hypotheses on the mechanical behavior of shape memory alloys such as titanium nickelide in twostep (martensitic and rhombohedral) phase transformations are formulated on the basis of experimental data. A system of relations linking stresses, strains, temperature, and phase composition in such transitions is proposed.     

A thermo-mechanically coupled field model for shape memory alloys

The impressive properties of shape memory alloys are produced by means of solid-to-solid phase transformations where thermal effects play an important role. In this paper, we present a model for polycrystalline shape memory alloys which takes full thermo-mechanical coupling into account. Starting from the equations of the first and the second law of thermodynamics, we derive evolution equations for the volume fractions of the different martensitic variants and a related equation for heat conduction. A thermodynamic analysis allows to formulate a complete expression for the dissipation caused by phase transformation and heat flux. This allows to model the experimentally well-documented transformation fronts in tension tests by a finite element scheme without further assumptions. Additionally, the number of required model parameters is very small in comparison with phenomenological approaches. Numerical examples are presented which show a good agreement with experimental observations.     

Rate dependence of temperature fields and energy dissipations in non-static pseudoelasticity

The temperature fields and the energy dissipations of shape memory alloys during the stress-induced martensitic transformations are studied theoretically and experimentally. The effect of the loading rate is analyzed. It was found that the temperature field inside a shape memory alloy sample varies strongly in space and time. The increase rate of the temperature is given by the difference between the rate of the latent heat release and the rate of the heat convection and conduction. The notion and the rate dependence of the energy dissipation are discussed in connection with the stress–strain hysteresis, the entropy production, and the Clausius–Duhem inequality.     

On the Three Phase Mixtures in Martensitic Transformations of Shape Memory Alloys: Thermodynamical Modeling and Characteristic Temperatures

We study here the thermally-induced martensitic transformation process of shape memory alloys. Taking the internal energy of phase mixtures as the potential function and introducing coherency energies between martensite and austenite and between different variants of the martensitic phase, we are able to use thermodynamical arguments to obtain hysteresis diagrams which could be measured experimentally. The characteristic temperatures for martensitic transformation, (martensite start and finish) and (austenite start and finish) can be identified explicitly and are closely related to the coherency parameters of the coherency energies. Received September 12, 1997     

Effect of structural transformation and deformation nonlinearity on the stability of a shape memory alloy rod

Within the framework of a model of nonlinear deformations of shape memory alloys (SMA) under phase and structural transformations and for different statements of the problem, an analytical solution of the problem of stability of an SMA rod undergoing a direct martensitic phase transformation under the action of a compressive load is obtained. It is shown that taking account of the nonlinearity of the deformation process and structural transformation in the transition into the adjacent form of equilibrium significantly changes the solution for sufficiently flexible rods. At the same time, taking into account the strains developed in a phase transition is topical for thick-walled SMA elements.     

Nonlinear dynamics and chaos in coupled shape memory oscillators

Shape memory and pseudoelastic effects are thermomechanical phenomena associated with martensitic phase transformations, presented by shape memory alloys. This contribution concerns with the dynamical response of coupled shape memory oscillators. Equations of motion are formulated by assuming a polynomial constitutive model to describe the restitution force of the oscillators and, since they are associated with a five-dimensional system, the analysis is performed by splitting the state space in subspaces. Free and forced vibrations are analyzed showing different kinds of responses. Periodic, quasi-periodic, chaos and hyperchaos are all possible in this system. Numerical investigations show interesting and complex behaviors. Dynamical jumps in free vibration and amplitude variation when temperature characteristics are changed are some examples. This article also shown some characteristics related to chaos–hyperchaos transition.     

Landau-Ginzburg model for a deformation-driven experiment on shape memory alloys

A Landau-Ginzburg model describing first order martensitic phase transitions in shape memory alloys is considered. The model developed by Falk is transformed in order to simulate deformation-driven experiments done by I. Müller and his co-workers. In these experiments, they do not only observe load-deformation hysteresis loops but also small loops inside these hysteresis loops. Numerical simulations for a CuZnAl single crystal show good agreement with the experiment. We find, for example, nucleation processes, moving phase boundaries, rate-independent hysteresis loops and interior loops. Received January 25, 1996     

A three-dimensional constitutive model for shape memory alloys

Shape memory alloys (SMAs) are materials that, among other characteristics, have the ability to present high deformation levels when subjected to mechanical loading, returning to their original form after a temperature change. Literature presents numerous constitutive models that describe the phenomenological features of the thermomechanical behavior of SMAs. The present paper introduces a novel three-dimensional constitutive model that describes the martensitic phase transformations within the scope of standard generalized materials. The model is capable of describing the main features of the thermomechanical behavior of SMAs by considering four macroscopic phases associated with austenitic phase and three variants of martensite. A numerical procedure is proposed to deal with the nonlinearities of the model. Numerical simulations are carried out dealing with uniaxial and multiaxial single-point tests showing the capability of the introduced model to describe the general behavior of SMAs. Specifically, uniaxial tests show pseudoelasticity, shape memory effect, phase transformation due to temperature change and internal subloops due to incomplete phase transformations. Concerning multiaxial tests, the pure shear stress and hydrostatic tests are discussed showing qualitatively coherent results. Moreover, other tensile–shear tests are conducted modeling the general three-dimensional behavior of SMAs. It is shown that the multiaxial results are qualitative coherent with the related data presented in the literature.