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。     

Mesoscale kinetics produces martensitic microstructure

We present molecular dynamics (MD) simulations of a martensitic phase transformation studying post-transformation microstructure and moving austenite-martensite interfaces. Unlike in energy-minimisation theories, the transformation dynamics dominate the martensite morphology. We use a binary Lennard-Jones potential to describe a square-to-hexagonal transformation by shear-and-shuffle. The high-T stable square lattice and low-T hexagonal lattice represent austenite and martensite, giving four martensitic variants. Compatible twin variants have no lattice misfit and zero interfacial energies which makes our model directly comparable with the crystallographic theory of martensite. Although our dynamical interpretation is different to previous work, our MD simulations exhibit very similar martensitic morphologies to real materials. We observe the nucleation of wedge-shaped, twinned martensite plates, plate growth at narrow, travelling transformation zones, subsonic transformation waves, elastic precursors inducing secondary nucleations and the formation of martensitic domains. Martensite is produced within narrow transformation zones where atoms change their lattice sites in a co-operative manner so as to form crystallographic layers. These motions produce inertia forces on the mesoscopic length-scale which induce the formation of twin variants in the subsequent layers to transform.     

Numerical investigation of the interaction between the martensitic transformation front and the plastic strain in austenite

Phase-field simulations of the martensitic transformation (MT) in an austenitic matrix which has already undergone the plastic deformation are carried out. For this purpose the elasto-plastic phase-field approach of incoherent MT developed in a previous work [Kundin et al., 2011. A phase-field model for incoherent martensitic transformations including plastic accommodation processes in the austenite. J. Mech. Phys. Solids 59, 2082–2012] is used. The evolution equation for the dislocation density field is extended by taking into account the thermal and athermal annihilation of the dislocations in the austenitic matrix and the athermal annihilation at the transformation front. It is shown that the plastic deformation in the austenite caused by the MT interacts with the dislocation field and the MT front that leads to an inhomogeneous increasing of the total dislocation density. During the phase transformation one part of the dislocations in the austenite is inherited by the martensitic phase and this inheritance depends on the kinetics and the crystallography of MT. Another part of dislocations annihilates at the transformation front and decreases the dislocation density in the growing martensite. Based on the simulation results the specific type of phenomenological dependency between the inherited dislocations, the martensite phase fraction and the plastic deformation is proposed.     

A thermodynamical constitutive model for shape memory materials. Part II. The SMA composite material

The phenomenological SMA equations developed in Part I are used in this second paper to derive the free energy and dissipation of a SMA composite material. The derivation consists of solving a boundary value problem formulated over a mesoscale representative volume element, followed by an averaging procedure to obtain the macroscopic composite constitutive equations. Explicit equations are derived for the transformation tensors that relate the composite transformation strain rate to the phase transformation rate in the fiber and matrix. Some key findings for the two-way SME in a SMA fiber/elastomer matrix composite are that processing-induced residual stresses alter the composite austenite start and martensite start temperatures, as well as the amount of composite strain recovered during a complete cycle of temperature and fiber martensite volume fraction. Relative to the two-way SME response of stiff-matrix composites, it was found that compliant-matrix composites: (1) complete the phase transformation over a narrower temperature range; (2) exhibit greater transformation strain during the reverse transformation; and (3) undergo an incomplete strain cycle during a complete cycle of temperature and fiber martensite volume fraction. Due to the interaction of the fiber and matrix during transformation, macroscopic proportional stressing of the composite results in non-proportional fiber stressing, which in turn causes a small amount of martensitic reorientation to occur simultaneously with the transformation.     

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.     

Micromechanical modelling of the effect of plastic deformation on the mechanical behaviour in pseudoelastic shape memory alloys

Except for the recoverable strain induced by phase transformation, NiTi alloys are very ductile even in the martensite phase. The purpose of the present paper is to study the influence of permanent deformation, which results from plastic deformation of martensite, on the mechanical behaviour of pseudoelastic NiTi alloys. Based on phenomenological theory of martensitic transformation and crystal plasticity, a new three dimensional micromechanical model is proposed by coupling both the slip and twinning deformation mechanisms. The present model is implemented as User MATerial subroutine (UMAT) into ABAQUS/Standard to study the influences of plastic deformation on the stress and strain fields, and on the evolution of martensite transformation. Results show that with the increasing of plastic deformation the residual strain increases and the phase transformation stress–strain curves from the martensite to austenite become steeper and less obvious. Both characteristics, stabilisation of martensite and impedance of the reverse transformation, due to plastic deformation are captured.     

A multiscale thermomechanical model for cubic to tetragonal martensitic phase transformations

We develop a multiscale thermomechanical model to analyze martensitic phase transformations from a cubic crystalline lattice to a tetragonal crystalline lattice. The model is intended for simulating the thermomechanical response of single-crystal grains of austenite. Based on the geometrically nonlinear theory of martensitic transformations, we incorporate microstructural effects from several subgrain length scales. The effective stiffness tensor at the grain level is obtained through an averaging scheme, and preserves crystallographic information from the lattice scale as well as the influence of volumetric changes due to the transformation. The model further incorporates a transformation criterion that includes a surface energy term, which takes into account the creation of interfaces between martensite and austenite. These effects, which are often neglected in martensitic transformation models, thus appear explicitly in the expression of the transformation driving force that controls the onset and evolution of the transformation. In the derivation of the transformation driving force, we clarify the relations between different combinations of thermodynamic potentials and state variables. The predictions of the model are illustrated by analyzing the response of a phase-changing material subjected to various types of deformations. Although the model is developed for cubic to tetragonal transformations, it can be adapted to simulate martensitic transformations for other crystalline structures.     

形状记忆合金椭圆孔口问题的有限单元法

基于Lagoudas形状记忆合金(SMA)三维本构模型,假设材料为各向同性,推导了SMA平面应力状态的增量型本构方程,继而编写了ABAQUS用户自定义材料(UMAT)子程序,研究了在双向拉伸情况下,外载荷、温度、椭圆孔口长短轴之比对超弹性SMA椭圆孔口板中应力诱发马氏体相变区的影响。数值结果表明:应力诱发马氏体相变首先发生在椭圆孔口长轴端点部位,在外加载荷作用下逐渐扩展到板内,并由内向外形成马氏体相区、相变混合区和奥氏体相区;SMA板内应力诱发马氏体完全相变区面积与施加外载荷成正相关,与温度成负相关;随着椭圆孔口长短轴之比增大,SMA板内应力诱发马氏体完全相变区面积呈现出先减小后增大的趋势;拉应力差值相同时,相较于拉应力沿椭圆孔口长轴方向较大的情况,当拉应力沿椭圆孔口短轴方向较大时,SMA板内完全相变区面积较大,椭圆孔口周边应力集中现象更明显。     

The step-wise martensite to austenite reversible transformation

The step-wise martensite to austenite reversible transformation (SMART) in shape memory alloys (SMA) is a martensitic thermoelastic transformation where a step-wise kinetics is induced by a partial cycling procedure within the hysteresis cycle (incomplete cycle on heating (ICH) procedure). The ICH procedure has been proved effective in inducing a reversible microstructural modification of the martensitic phase. Results till now obtained both on the SMART behaviour and on the effects of the ICH procedure are reviewed here: the hypotheses advanced till now are discussed to explain experimental evidences.

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Sommario Con l'acronimo di SMART (step-wise martensite to austenite reversible transformation) si indica una trasformazione martensitica termoelastica in cui la cinetica di trasformazione risulta modificata dall'esecuzione di un'appropriata procedura di ciclaggio termico parziale (procedura ICH — Incomplete Cycle on Heating) nell'intervallo di temperatura in cui ha luogo la trasformazione martensitica inversa. Vengono qui presentati i risultati sperimentali relativi sia alla SMART sia agli effetti indotti dalla procedure ICH e responsabili delle modifiche della cinetica di trasformazione. Vengono inoltre discusse le ipotesi sino ad ora avanzate per spiegare i risultati sperimentali.

     

The elastic field caused by a general ellipsoidal inclusion and the application to martensite formation 2

The elastic field throughout an ellipsoidal inclusion in an indefinitely-extended anisotropic material is investigated when an eigenstrain (a stress-free transformation strain) is periodically distributed throughout the inclusion. This is an extention of the results obtained by J.D. Eshelby (1961) for uniform eigenstrains and by R.J. Asaro and D.M. Barnett (1975) for polynomial eigenstrains. The solution is applied to the evaluation of elastic strain energies of a disc-shaped martensite with alternating twins and of a spherical precipitate with a banded structure. The significant amount of the elastic strain energies explains the necessity of the supercooling of austenite steel for the martensitic transformation to occur.     

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.     

Martensite Strain Memory in the Shape Memory Alloy Nickel-Titanium Under Mechanical Cycling

This paper describes an experimental study of stress-induced martensitic phase transformation in the SMA Nickel-Titanium. The rich local thermo-mechanical interactions that underlie transformation are examined using three-dimensional Digital Image Correlation (strain fields) and infrared imaging (thermal fields). We quantify the complex local interactions between released/absorbed latent heat and the extent of transformation, and explore the characteristics of the phase fronts and the evolution of martensitic volume fraction. We also quantify a strong strain memory in the martensite that forms in the wake of the phase transformation front. The accommodated strain in the martensite will remain constant during loading, even as the existing phase front propagates. There also exists a remarkable strain memory in the martensite that persists from cycle to cycle, indicating that the local elastic stress fields in the martensite are driven by a dislocation structure and martensitic nuclei that largely stabilize during the first loading cycle.     

On consistent micromechanical estimation of macroscopic elastic energy,coherence energy and phase transformation strains for SMA materials

An apparatus of micromechanics is used to isolate the key ingredients entering macroscopic Gibbs free energy function of a shape memory alloy (SMA) material. A new self-equilibrated eigenstrains influence moduli (SEIM) method is developed for consistent estimation of effective (macroscopic) thermostatic properties of solid materials, which in microscale can be regarded as amalgams of n-phase linear thermoelastic component materials with eigenstrains. The SEIM satisfy the self-consistency conditions, following from elastic reciprocity (Betti) theorem. The method allowed expressing macroscopic coherency energy and elastic complementary energy terms present in the general form of macroscopic Gibbs free energy of SMA materials in the form of semilinear and semiquadratic functions of the phase composition. Consistent SEIM estimates of elastic complementary energy, coherency energy and phase transformation strains corresponding to classical Reuss and Voigt conjectures are explicitly specified. The Voigt explicit relations served as inspiration for working out an original engineering practice-oriented semiexperimental SEIM estimates. They are especially conveniently applicable for an isotropic aggregate (composite) composed of a mixture of n isotropic phases. Using experimental data for NiTi alloy and adopting conjecture that it can be treated as an isotropic aggregate of two isotropic phases, it is shown that the NiTi coherency energy and macroscopic phase strain are practically not influenced by the difference in values of austenite and martensite elastic constants. It is shown that existence of nonzero fluctuating part of phase microeigenstrains field is responsible for building up of so-called stored energy of coherency, which is accumulated in pure martensitic phase after full completion of phase transition. Experimental data for NiTi alloy show that the stored coherency energy cannot be neglected as it considerably influences the characteristic phase transition temperatures of SMA material.     

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.     

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.     

Self-accommodation in martensite

The shape-memory effect is a phenomenon wherein an apparently plastically deformed specimen recovers all strain when heated above a critical temperature. This is observed in some crystalline solids that undergo martensitic phase transformation. The martensitic transformation is a temperature-induced, diffusionless solid-to-solid phase transformation involving a change in crystalline symmetry. Shape-memory materials are able to transform from the high-temperature austenite to the low-temperature martensite phase without any apparent change in shape. This is known as self-accommodation. Necessary and sufficient conditions that the lattice parameters of a material must satisfy for the material to form a self-accommodating microstructure are derived. The main result states that if the austenite is cubic, the material is self-accommodating if and only if the transformation is volume preserving. On the other hand, if the symmetry of the austenite is not cubic, it is not possible to construct any microstructure that is self-accommodating unless the transformation strain or the Bain strain satisfies additional, rather strict, conditions. These results show good agreement with the available experimental data. The analysis here is significantly different from previous studies because it makes no a priori assumption on the microstructure.     

Experimental characterization and micromechanical modeling of superelastic response of a porous NiTi shape-memory alloy

Porous shape-memory alloys are usually brittle due to the presence of various nickel-titanium intermetallic compounds that are produced in the course of most commonly used synthesizing techniques. We consider here a porous NiTi shape-memory alloy (SMA), synthesized by spark-plasma sintering, that is ductile and displays full shape-memory effects over the entire appropriate range of strains. The porosity however is only 12% but the basic synthesizing technique has potential for producing shape-memory alloys with greater porosity that still are expected to display superelasticity and shape-memory effects. The current material has been characterized experimentally using quasi-static and dynamic tests at various initial temperatures, mostly within the superelastic strain range, but also into the plastic deformation regime of the stress-induced martensite phase. To obtain a relatively constant strain rate in the high strain-rate tests, a novel pulse-shaping technique is introduced. The results of the quasi-static experiments are compared with the predictions by a model that can be used to calculate the stress-strain response of porous NiTi shape-memory alloys during the austenite-to-martensite and reverse phase transformations in uniaxial quasi-static loading and unloading at constant temperatures. In the austenite-to-martensite transformation, the porous shape-memory alloy is modeled as a three-phase composite with the parent phase (austenite) as the matrix and the product phase (martensite) and the voids as the embedded inclusions, reversing the roles of austenite and martensite during the reverse transformation from fully martensite to fully austenite phase. The criterion of the stress-induced martensitic transformation and its reversal is based on equilibrium thermodynamics, balancing the thermodynamic driving force for the phase transformation, associated with the reduction of Gibbs’ free energy, with the resistive force corresponding to the required energy to create new interface surfaces and to overcome the energy barriers posed by various microstructural obstacles. The change in Gibbs’ free energy that produces the driving thermodynamic force for phase transformation is assumed to be due to the reduction of mechanical potential energy corresponding to the applied stress, and the reduction of the chemical energy corresponding to the imposed temperature. The energy required to overcome the resistance imposed by various nano- and subnano-scale defects and like barriers, is modeled empirically, involving three constitutive constants that are then fixed based on the experimental data. Reasonably good correlation is obtained between the experimental and model predictions.     

Transformation-induced plasticity in ferrous alloys

We study the mechanical behavior of a class of multiphase carbon steels where metastable austenite at room temperature is found in grains dispersed in a ferrite-based matrix. During mechanical loading, the austenite undergoes a displacive phase change and transforms into martensite. This transformation is accommodated by plastic deformations in the surrounding matrix. Experimental results show that the presence of austenite typically enhances the ductility and strength of the steel. We use a recently developed model (Turteltaub and Suiker, 2005) to analyze in detail the contribution of the martensitic transformation to the overall stress-strain response of a specimen containing a single island of austenite embedded in a ferrite-based matrix. Results show that the performance of the material depends strongly on the lattice orientation of the austenite with respect to the loading direction. More importantly, we identify cases in which the presence of austenite can in fact be detrimental in terms of strength, which is relevant information in order to improve the behavior of this class of steels.