马氏体相变微结构演化过程的模拟与分析

实验中观察到形状记忆合金在应力诱发马氏体相变过程中,出现多界面的微结构,马氏体相会逐渐长大变粗,同时会出现由马氏体形核造成的应力突然降低.用多阱的弹性能函数来刻画此相变与微结构演化过程,发现相变时会出现多界面的微结构且伴随着马氏体相的形核至奥氏体相的消失过程,出现了界面数先增后减的变化,同时应力会出现跳跃而不连续.相对应的动力学模型的有限差分的计算结果同样显示形核时出现了多界面的微结构并伴随着应力的大幅振荡,随着载荷的增加界面位置随之移动,使得马氏体相区域逐渐长大.理论分析与数值模拟的结果较好地刻画了实验中观察到的马氏体相变过程中的形核,产生多界面,再到马氏体逐渐长大这一微结构的演化过程.     

Localization in NiTi tubes under bending

Nearly equiatomic NiTi can exhibit pseudoelastic behavior due to reversible solid-to-solid stress induced phase transformation at room level temperatures. In tension, the transformation leads to localized deformation of several percent that tends to spread at nearly constant stress. The deformation is recovered upon unloading while again localized deformation is exhibited. Under compression, while still pseudoelastic, the transformation strains are smaller, the stress is higher, the response is monotonic, and the deformation is essentially homogeneous. This study examines how this texture-driven, complex material asymmetry affects a simple structure: the bending of a tube. To this end, NiTi tubes are bent in a custom four-point bending facility under rotation control and isothermal conditions. The phase transformations lead to a closed moment-rotation hysteresis comprised of loading and unloading moment plateaus. During loading, localized nucleation of martensite results in a high curvature for the transformed sections of the tube and low curvature for the untransformed. Martensite, which corresponds to the higher curvature regime, spreads gradually while the moment remains nearly constant. The nucleation of martensite is in the form of bands inclined to the axis of the tube that organize themselves into diamond shaped deformation patterns on the tensioned side of the structure. The patterns are similar to those observed in bending of steel tubes with Lüders bands, however, for NiTi they develop only on the tensioned side due to the material asymmetry. A lower moment plateau is traced upon unloading with similar localized bending and the erasure of the diamond deformation patterns. This complex behavior was found to repeat for a number of temperatures in the pseudoelastic regime of NiTi with the moment-rotation hysteresis moving to higher or lower moment levels depending on the temperature.     

Structural changes without stable intermediate state in inelastic material. Part II. Applications to displacive and diffusional–displacive phase transformations,strain-induced chemical reactions and ductile fracture

A number of simple examples demonstrate the applicability of the general theory developed in Part I of this paper to various structural changes in solids, namely to displacive and generalized second-order phase transformations, twinning and reorientation of crystal lattice, ductile fracture, and strain-induced chemical reactions. The theory is extended to diffusional-displacive phase transitions. The following problems for elastic and elastoplastic materials are solved analytically: displacive and diffusional–displacive phase transitions in a spherical particle inside the space under external pressure, martensitic phase transition and twinning in ellipsoidal inclusion under applied shear stress, spherical void nucleation, crack propagation in a similar framework to the Dugdale model for a plane stress state. In most cases explicit expressions for the thermodynamic and kinetic conditions for structural changes and the geometric parameters of the nucleus are obtained and analyzed. The following typical cases in the determination of the geometric parameters of nucleus are found: solely from the principle of the minimum of transformation time and the kinetic equation without any constraints or with thermodynamic constraint; from the principle of the minimum of transformation mass and the thermodynamic criterion of structural changes (thermodynamically admissible nucleus); as an interatomic distance. For diffusional–displacive phase transformations, additional variants are related to the necessity to consider the diffusion equation (for the diffusion-controlled transformation) and constraints related to the maximum and minimum possible volume fraction of solute atoms. The nucleation kinetics for various nucleus geometries is compared.     

A micromechanics-inspired constitutive model for shape-memory alloys that accounts for initiation and saturation of phase transformation

A constitutive model to describe macroscopic elastic and transformation behaviors of polycrystalline shape-memory alloys is formulated using an internal variable thermodynamic framework. In a departure from prior phenomenological models, the proposed model treats initiation, growth kinetics, and saturation of transformation distinctly, consistent with physics revealed by recent multi-scale experiments and theoretical studies. Specifically, the proposed approach captures the macroscopic manifestations of three micromechanial facts, even though microstructures are not explicitly modeled: (1) Individual grains with favorable orientations and stresses for transformation are the first to nucleate martensite, and the local nucleation strain is relatively large. (2) Then, transformation interfaces propagate according to growth kinetics to traverse networks of grains, while previously formed martensite may reorient. (3) Ultimately, transformation saturates prior to 100% completion as some unfavorably-oriented grains do not transform; thus the total transformation strain of a polycrystal is modest relative to the initial, local nucleation strain. The proposed formulation also accounts for tension–compression asymmetry, processing anisotropy, and the distinction between stress-induced and temperature-induced transformations. Consequently, the model describes thermoelastic responses of shape-memory alloys subject to complex, multi-axial thermo-mechanical loadings. These abilities are demonstrated through detailed comparisons of simulations with experiments.     

Impact of texture on stress growth in thermotropic liquid crystalline polymers subjected to step-shear

The Landau-de Gennes tensor order parameter equations of nemato-dynamics are formulated, solved and used to find the impact of textural transformation on stress growth in thermotropic liquid crystalline polymers subjected to shear start-up flow. The simulated textural transformations include nucleation and annihilation of twist inversion walls. Coarsening processes include wall-wall annihilation, wall pinching and wall-bounding surface reactions. In the absence of defect-related effects, the stress growth is characterized by an early stress plateau, intermediate power law growth, and a late stage stress plateau. As the Deborah number (De) increases, flow-induced textural transformations affect the late stage and then the intermediate stress growth stage. Defects are found to be stress sinks, and so removal of defects increases stress. At lower Deborah numbers, few defects arise and coarsening rates are low, so the main texture effect in this regime is in the late stage plateau region, causing localized step increases. At Deborah numbers close to one, nucleation and coarsening rates increase, and textural effects appear closer and closer to the intermediate stress growth regime. As De increases further, coarsening by pinching processes overcomes nucleation, and all defects disappear in the intermediate stress growth regime, causing the stress growth to exhibit a smooth staircase shape. Strain and amplitude scaling is not observed. Simulated textural transformations show that smooth staircase stress growth is the result of defect annihilation processes. The non-monotonic stress growth is consistent with experimental observations. Simulated textures provide specific knowledge important to the eventual understanding of the rheologies of textured liquid crystal polymers.     

On the transformation toughening of a crack along an interface between a shape memory alloy and an isotropic medium

In this study, a bilinear cohesive zone model is employed to describe the transformation toughening behavior of a slowly propagating crack along an interface between a shape memory alloy and a linear elastic or elasto-plastic isotropic material. Small scale transformation zones and plane strain conditions are assumed. The crack growth is numerically simulated within a finite element scheme and its transformation toughening is obtained by means of resistance curves. It is found that the choice of the cohesive strength t₀ and the stress intensity factor phase angle φ greatly influence the toughening behavior of the bimaterial. The presented methodology is generalized for the case of an interface crack between a fiber reinforced shape memory alloy composite and a linear elastic, isotropic material. The effect of the cohesive strength t₀, as well as the fiber volume fraction are examined.     

A stochastic approach to the internal damage in a structure solid: Part 1: Theoretical model

The material system is considered as heterogenous medium of actual microstructural elements. These elements exhibit random geometric and physical characteristics and are further disturbed by a latitude of randomly oriented, second phase particles. A stochastic model is presented for the occurring damage process due to the nucleation and growth of microvoids under external loading. From a micromechanical point of view, the nucleation of a void at a partile-matrix interface is considered to be associated with the cut-off of the interfacial binding potential. The growth of an elemental void is seen, then, to follow a random walk of the discrete Markov type. The latter is associated with the build-up of strain in front of the tip of the advancing void and the redistribution of local stress. As the void reaches the boundary between neighbouring elements, a dicrete inter-elemental fracture process is examined in relation to the intensities of transformation within the elemental boundary.     

Rheological characteristics of trimethylolethane hydrate slurry treated with drag-reducing surfactants

Rheological characteristics of trimethylolethane (TME) clathrate–hydrate slurry treated with drag-reducing surfactants were investigated. Friction coefficients and apparent viscosities were measured when the concentration of TME and its hydrate fraction treated with and without drag-reducing surfactants were changed in several steps. From the results, it is found that the surfactant addition causes effective drag reduction in a pipe flow when the hydrate fraction becomes high, while effective drag reduction disappears in the cases of low hydrate fraction. The results of viscosity measurements indicate that the TME molecules disturb the formation of shear-induced structures (SIS) causing drag reduction phenomena. To investigate this interaction between TME and surfactant micelles, the effect of TME concentration on viscosity and relaxation time of solutions was discussed. From this, it was found out that there exists a critical concentration of TME on the formation of SIS and that it becomes larger as shear rate increases. Thus, we conclude that this interaction between TME and micellar structures causes less drag reduction for the cases of low hydrate fraction, while the drag reduction appears in cases of high hydrate fraction because TME concentration in liquid phase becomes small.     

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.     

Influences of Marangoni effect on solidification of curved interfaces with constant curvature

The asymptotic method and phase field simulation are applied to study the influences of variation of the surface tension with temperature on the movements of solid-liquid interfaces in the solidification process of spherical and cylindrical nuclei, respectively. Results indicate that Marangoni effect will increase the critical nucleation radius, slow up the movement of interface. The tip speed of dendrite decreases linearly with Marangoni number for melt without convection. The results of phase field simulation are qualitatively in accord with that of asymptotic method.     

Preparation,characterization and combustion properties of Zr/ZrH_2 particles coated with α-FeOOH crystal grains

Zr/ZrH2 particles with irregular morphologies and broad size distribution were uniformly coated with acicular-FeOOH crystal grains via a facile route without using polymers or surfactants. The as-synthesized material was characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), energy dispersive X-ray (EDX), UV-vis diffusion reflection (UV-vis) and Raman spectrometry. Based on these characterizations, the synthesis mechanism was explained in terms of combined heterogeneous nucleation and...     

CuAlNi单晶应力诱发马氏体相变与微结构演化的实验观察与分析

基于CuAlNi形状记忆合金单晶的一维准静态拉伸实验,着重研究相变过程中条带状马氏体的微观结构.通过金相显微镜对整个试样表面进行拍照,并利用图像处理技术和均匀化的方法,提取到了不同载荷下马氏体的含量(相分量)和条带的数量(界面数)在试样各处的分布与变化情况,找到了加载和卸载过程中相变微结构的演化规律,从而实现了对条带状马氏体相变微结构的量化处理.     

Micromechanical modeling of stress-induced phase transformations. Part 2. Computational algorithms and examples

Based on the theory developed in Part 1 of this paper [Levitas, V.I., Ozsoy, I.B., 2008. Micromechanical modeling of stress-induced phase transformations. Part 1. Thermodynamics and kinetics of coupled interface propagation and reorientation. Int. J. Plasticity. doi:10.1016/j.ijplas.2008.02.004], various non-trivial examples of microstructure evolution under complex multiaxial loading are presented. For the case without interface rotation, the effect of the athermal thresholds for austenite (A)–martensite (M) and martensitic variant M_I–variant M_II interfaces and loading paths on stress–strain curves and phase transformations was studied. For coupled interface propagation and rotation, two types of numerical simulations were carried out. The tetragonal–orthorhombic transformation has been studied under general three-dimensional interface orientation and zero athermal threshold. The cubic–tetragonal transformation was treated with allowing for an athermal threshold and interface reorientation within a plane. The effect of the athermal threshold, the number of martensitic variants and an interface orientation in the embryo was studied in detail. It was found that an instability in the interface normal leads to a jump-like interface reorientation that has the following features of the energetics of a first-order transformation: there are multiple energy minima versus interface orientation that are separated by an energy barrier; positions of minima do not change during loading but their depth varies; when the barrier disappears (i.e. one of the minima transforms to the local saddle or maximum points), the system rapidly evolves toward another stable orientation. Depending on the loading and material parameters, we observed a large continuous change in interface orientation, a jump in interface reorientation, a jump in volume fractions and stresses, an expected stress relaxation during the phase transition and unexpected stress growth during the transition because of large change in elastic moduli.     

A physically motivated anisotropic tensorial representation of damage with separate functions for void nucleation,growth, and coalescence

A phenomenological anisotropic damage progression formulation for porous ductile metals with second phases is described through mechanisms of void nucleation, growth and coalescence. The model is motivated from fracture mechanisms and microscale physical observations. To describe the creation of new pores, the decohesion at the particle–matrix interface and the fragmentation of second phase particles, the void-crack nucleation equation is related to several microstructural parameters (fracture toughness, length scale parameter, particle size, volume and fraction of second phase), the plastic strain level, and the stress state. Nucleation is represented by a general symmetric second rank tensor, and its components are proportional to the absolute value of the plastic strain rate components. Based on the Rice and Tracey model, void growth is a scalar function of the trace of damage tensor and the positive triaxiality. Like nucleation, coalescence is a second rank tensor governed by the plastic strain rate tensor and the stress state. The coalescence threshold is related to the void length scale for void impingement and void sheet mechanisms. The coupling of damage with the Bammann–Chiesa–Johnson (BCJ) plasticity model is written in the thermodynamic framework and derives from the concept of effective stress assuming the hypothesis of energy equivalence. A full-implicit algorithm is used for the stress integration and the determination of the consistent tangent operator. Finally, macroscale correlations to cast A356 AL alloy and wrought 6061-T6 AL alloy experimental data are completed with predictive void-crack evolution to illustrate the applicability of the anisotropic damage model.     

Rate-dependent domain spacing in a stretched NiTi strip

Superelastic fine-grained Nickel–Titanium (NiTi) polycrystalline shape memory alloys under tensile loading deform collectively via the nucleation and growth of macroscopic martensite domains. Recent experiments on a stretched NiTi strip showed that the number of nucleated domains (or the domain spacing) increased (decreased) with increasing applied stretching rate. It is also shown that the rate dependence of the domain formation is due to the coupling between the transfer of the locally released heat and the temperature dependence of the transformation stress. In this paper, a simple one-dimensional model is developed to quantify this effect of thermo-mechanical coupling on the observed domain spacing. Analytical relationship between the domain number, thermo-mechanical properties of the material, heat transfer boundary conditions and the externally applied strain rate is established. It is found that for the case of strong heat convection the domain spacing is inversely proportional to the applied stretching rate, while for the case of weak convection, the domain spacing is dictated by a power-law scaling with exponent ?0.5. The latter theoretical prediction agrees well quantitatively with the experimental data in stagnant air.     

Molecular dynamics simulation study of microstructure evolution during cyclic martensitic transformations

Shape memory alloys (SMA) exhibit a number of features which are not easily explained by equilibrium thermodynamics, including hysteresis in the phase transformation and “reverse” shape memory in the high symmetry phase. Processing can change these features: repeated cycling can “train” the reverse shape memory effect, while changing the amount of hysteresis and other functional properties. These effects are likely to be due to formations of localised defects and these can be studied by atomistic methods. Here we present a molecular dynamics simulation study of such behaviour employing a two-dimensional, binary Lennard-Jones model. Our atomistic model exhibits a symmetry breaking, displacive phase transition from a high temperature, entropically stabilised, austenite-like phase to a low temperature martensite-like phase. The simulations show transformations in this model material proceed by non-diffusive nucleation and growth processes and produce distinct microstructures. We observe the generation of persistent lattice defects during forward-and-reverse transformations which serve as nucleation centres in subsequent transformation processes. These defects interfere the temporal and spatial progression of transformations and thereby affect subsequent product morphologies. During cyclic transformations we observe accumulations of lattice defects so as to establish new microstructural elements which represent a memory of the previous morphologies. These new elements are self-organised and they provide a basis of the reversible shape memory effect in the model material.     

Formulation of a macroscale corrosion damage internal state variable model

A new consistent formulation coupling kinematics, thermodynamics, and kinetics with damage using an extended multiplicative decomposition of the deformation gradient that accounts for corrosion effects is proposed. The corrosion model, based upon internal state variable (ISV) theory, captures the effects of general corrosion, pit nucleation, pit growth, pit coalescence, and intergranular corrosion. The different geometrically-affected rate equations are given for each mechanism after the ISV formalism and have a thermodynamic force pair that acts as an internal stress. Pit nucleation is defined as the number density that changes as a function of time driven by the local galvanic electrochemical potential between base matrix material and second phase material. Pit growth is defined as pit surface area growth. Pit coalescence is the interaction of the pits as they grow together and is often characterized by transgranular corrosion and is mathematically constructed from Coulomb’s Law and the Maxwell stress. General corrosion is signified by thickness loss of the material and is characterized by a modified Faraday’s Law. The intergranular corrosion rate is related to the grain boundary effects so that it is characterized by the misorientation between grains. The total damage (void volume or area fraction) is the addition of the general, pitting, and intergranular corrosion. The ability of the model to predict aspects of the corrosion mechanisms and aging history effects of an engineering material are then illustrated by comparison with experimental data of an extruded AZ31 magnesium alloy.     

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。