Polycrystalline Shape Memory Alloys Research Articles

Wave propagation in shape memory alloy rods under impulsive loads

A dynamic analysis is given of the wave propagation in a polycrystalline shape memory alloy semi-infinite rod subject to an impulsive load described by a rectangular loading function. This is a continuation of the previous study for which the impact load is described by a step loading function, and for which the rod undergoes martensitic phase transformation only. In the presence of unloading, the rod also undergoes reverse transformation from martensite to austenite. A maximum internal dissipation criterion is proposed to select a unique dynamic solution, in which an elastic unloading wave front precedes the reverse transformation wave front. This elastic unloading wave will meet with the forward transformation wave at a later time, leading to a sequence of wave encounters and progressively more complicated profiles of the state variables. The asymptotic behaviour of the solution and the energy dissipation are discussed.

Stress-induced phase transformation and detwinning in NiTi polycrystalline shape memory alloy tubes

Deformation behavior associated with initial austenite (A), rhombohedral (R) and martensite (M) phase structures was studied in polycrystalline NiTi shape memory alloy tubes by tensile testing at different temperatures. The nominal stress–strain curves of the tubes from room temperature (23 °C) to 70 °C were recorded. The deformation of NiTi tubes with initial structure of R-phase proceeded via R → M martensitic transformation, while the deformation of NiTi tubes with initial structure of M-phase proceeded via martensitic detwinning. It was found that the R → M martensitic type transformation was realized, at the macroscopic level, by nucleation and growth of an inclined cylindrical band, while the detwinning process of the tube was macroscopically homogeneous. Further, two-stage yielding, which is associated with austenite to rhombohedral (A → R) and R → M phase transformations, was observed in the stress–strain curves of NiTi tubes in a certain testing temperature range. With a further increase in temperature, the shape of the nucleated band remained cylindrical until 60 °C (> A f) when the shape of the initial band suddenly became helical which was well observed in the superelastic microtubing.

A homogenized free energy model for hysteresis in thin-film shape memory alloys

Thin-film shape memory alloys (SMAs) have become excellent candidates for microactuator fabrication in microelectromechanical systems due to their capability to achieve very high work densities, produce large deformations, and generate high stresses. In general, the material behavior of SMAs is nonlinear and hysteretic. To achieve the full potential of SMA actuators, it is necessary to develop models that characterize the nonlinearities and hysteresis inherent to the constituent materials. We develop a model that quantifies the nonlinearities and hysteresis inherent to SMAs. The fully thermomechanical model is based on free energy principles combined with stochastic homogenization techniques. It predicts rate-dependent, polycrystalline SMA behavior, and it accommodates heat transfer issues pertinent to thin-film SMAs. The main advantages of this model are that it admits a simple, low-order formulation suitable for implementation and subsequent control design, and that most of the model parameters are identifiable directly from standard measurements. We illustrate aspects of the model through comparison with thin-film SMA superelastic and shape memory effect hysteresis data.

Role of phase transition in the unusual microwear behavior of superelastic NiTi shape memory alloy

The excellent microwear performance of nano-grained superelastic nickel titanium (NiTi) polycrystalline shape memory alloy (SMA) is reported in this paper. The microwear test was conducted at temperatures ranging from 22 to 120 °C by a Hysitron triboindenter. The results showed that the NiTi SMA has superior microwear resistance compared to traditional tribo-materials such as stainless steel AISI 304 and that the material exhibits unusual hardness dependence of wear within certain temperature regimes. With the increase in temperature from 22 to 120 °C, wear resistance was found to decrease anomalously with an increase in hardness. Further investigation and analysis confirmed that the stress-induced phase transition during contact and wear play an essential role in the material's high wear resistance. It is demonstrated through contact mechanics analysis that the increase of hardness with temperature was mainly due to the increase in the phase transition stress. The observed applied threshold load that corresponds to the onset of the plastic deformation in the contact area was strongly influenced by the phase transition process at the tip region. For the investigated superelastic NiTi, the temperature-dependent interplay between reversible phase transition and irreversible plastic yielding plays a key role in the temperature dependence of the wear performance and is responsible for the observed apparent unusual hardness–wear relationships.

Constitutive equations for martensitic reorientation and detwinning in shape-memory alloys

A crystal-inelasticity-based constitutive model for martensitic reorientation and detwinning in shape-memory alloys (SMAs) has been developed from basic thermodynamics principles. The model has been implemented in a finite-element program by writing a user-material subroutine. We perform two sets of finite-element simulations to model the behavior of polycrystalline SMAs: (1) The full finite-element model where each finite element represents a collection of martensitic microstructures which originated from within an austenite single crystal, chosen from a set of crystal orientations that approximates the initial austentic crystallographic texture. The macroscopic stress–strain responses are calculated as volume averages over the entire aggregate: (2) The Taylor model (J. Inst. Metals 62 (1938) 32) where an integration point in a finite element represents a material point which consist of sets of martensitic microstructures which originated from within respective austenite single-crystals. Here the macroscopic stress–strain responses are calculated through a homogenization scheme. Experiments in tension and compression were conducted on textured polycrystalline Ti–Ni rod initially in the martensitic phase by Xie et al (Acta Mater. 46 (1998) 1989). The material parameters for the constitutive model were calibrated by fitting the tensile stress–strain response from a full finite-element calculation of a polycrystalline aggregate to the simple tension experiment. With the material parameters calibrated the predicted stress–strain curve for simple compression is in very good accord with the corresponding experiment. By comparing the simulated stress–strain response in simple tension and simple compression it is shown that the constitutive model is able to predict the observed tension–compression asymmetry exhibited by polycrystalline Ti–Ni to good accuracy. Furthermore, our calculations also show that the macroscopic stress–strain response depends strongly on the initial martensitic microstructure and crystallographic texture of the material. We also show that the Taylor model predicts the macroscopic stress–strain curves in simple tension and simple compression reasonably well. Therefore, it may be used as a relatively inexpensive computational tool for the design of components made from shape-memory materials.

1508 非比例負荷下における多結晶形状記憶合金の変形挙動解析(OS-15B,OS-15 多様なスケールにおける相変態および形態形成解析)

1508 非比例負荷下における多結晶形状記憶合金の変形挙動解析(OS-15B,OS-15 多様なスケールにおける相変態および形態形成解析)

A phenomenological model for hysteresis in polycrystalline shape memory alloys

AbstractWe propose a phenomenological model describing stress and temperature induced transformations in polycrystalline shape memory alloys. Polycrystallinity is mimicked on the level of a finite element discretization: Each element is treated as a single grain of a randomly chosen orientation. This heterogeneity destroys the undesirable effect of instantaneous transformation under spatially homogeneous loading or heating. We present various computational experiments on the hysteretic effects.

Two internal-friction peaks related to thermoelastic martensitic transformations inCuAlNiMnTishape-memory alloy

A partial phase transition method was used in internal friction measurements to study the motion of phase interface in martensitic transition of CuAlNiMnTi polycrystalline shape memory alloy. It is found that the IF peak arisen from the reversible martensitic transition is in fact composed of two independent IF peaks that relate to different motion modes of the interface. The low-temperature peak corresponds to the minimum of relative dynamic modulus and is attributed to an elastic modulus softening effect caused by the viscous motion of the phase interface. The high-temperature peak corresponds to the inflection point of the relative dynamic modulus and the volume change produced by the normal motion of the phase interface is responsible for the peak.

A fast algorithm for the simulation of polycrystalline misfits. II. Martensitic transformations in three space dimensions

We present a fast numerical method for the simulation of martensitic transformations in three–dimensional polycrystals. To produce the relevant overall elastic energy arising from given boundary conditions, this method proceeds by reducing the corresponding non–convex minimization problem to minimization of a certain quadratic form—over the set of arrays of transformation strains which are compatible with a given distribution of crystallite orientations. The evaluation of this quadratic form for a given array of transformation strains requires solution of certain linear elasticity problems. An acceleration strategy we use, which for a polycrystal containing N grains reduces the complexity of the algorithm from O(N^2) to O(N) operations, results from a formulation of the minimization problem which takes advantage of certain decorrelations present in the minimizing arrays of transformation strains. We illustrate our presentation with a number of examples involving cubic–to–monoclinic and cubic–to–orthorhombic polycrystalline phase transitions, such as those arising in the TiNi and CuAl shape–memory alloys. In particular, our study quantifies the effects of texture on the overall properties of such polycrystalline shape–memory alloys.

Mechanistic simulation of thermomechanical behaviour of thermoelastic martensitic transformations in polycrystalline shape memory alloys

This paper proposes a mechanistic model to simulate the thermal and mechanical behaviour of shape memory alloys. The model is based on the thermodynamic concept of chemical, elastic and frictional energies for thermoelastic martensitic transformations and plasticity concept of grain interior and grain boundary phases. In a thermoelastic martensitic transformation system, a thermally induced transformation and a mechanically induced (stress-induced) transformation require different operating mechanisms from a mechanistic viewpoint. For a thermally induced transformation, the driving force arises from within the matrix and internal stresses are created as a result of frictional movement. For a mechanically induced transformation, the driving force is provided externally and the frictional move- ment occurs when the stress exceeds a critical value. This paper proposes a unified mechanistic model taking into account this difference. The model is able to describe, in a schematic and qualitative manner, the behaviour of a thermoelastic martensitic transformation system in both thermally induced and me- chanically induced processes, including full and partial thermal transformation cycles, stress-induced martensitic transformation, pseudoelastic deformation and ferroelastic deformation via martensite vari- ant reorientation. Such a model allows the discussion of several aspects concerning the thermal and mechanical behaviour of thermoelastic martensitic transformations, such as the non-linear pseudoelas- ticity, deformation-induced two-way memory effect, strain dependence of mechanical hysteresis and minor loop behaviour of deformation.

Stress analysis of martensitic transformation in Cu–Al–Be polycrystalline and single-crystalline shape memory alloy

The aim of this study is to analyze the martensitic transformation in a shape memory alloy during a superelastic loading, focusing on internal strains, stresses and phases fractions. The behavior of the austenite phase is studied by X-ray diffraction stress analysis during in situ tensile test at room temperature. Both single-crystal and polycrystal samples have been investigated. The results are discussed with the aim to correlate the microstructural variations with the local stress state evolution in the austenitic phase while variants of martensite form and develop during a superelastic loading.

A micromechanical model for polycrystalline shape-memory alloys

We develop an energy-based model for polycrystalline shape-memory alloys which allows to predict all relevant features such as pseudoelasticity and the shape-memory effect. The theory is based on orientation-distribution of martensite-variants and the minimization of total elastic strain energy and dissipation due to phase-transformation. Applications in a two-dimensional context are given.

Martensitic and magnetic domain structures in polycrystalline shape memory alloys Ni _{2+x} Mn _{1-x} Ga

Martensitic and magnetic domain structures in polycrystalline shape memory alloys Ni _{2+x} Mn _{1-x} Ga

Phase transformation yield surface determination for some shape memory alloys

Like in the “plasticity” theory, the prediction of phase transformation yield surfaces constitutes an essential issue in the modelling of polycrystalline shape memory alloys thermomechanical behaviour. Usually for “micro–macro” integration, the nature of the interface between austenite and twinned or untwinned martensite under stress free state and the choice of correspondence variants (CV) or habit plane variant (HPV) are predominant toward the explicit shape of the phase transformation surface. If the predictions for Cu–Al–Be, Cu–Al–Zn (interface between austenite and one single variant of martensite for cubic to monoclinic phase transformation) and Cu–Al–Ni (interface between austenite and twinned martensite for cubic to orthorhombic phase transformation) are fairly good; the prediction is not efficient in the important case of Ti–Ni (interface between austenite and twinned martensite with stress free state for cubic to monoclinic phase transformation). The usual hypothesis consisting in neglecting the effect of stress on the interface geometrical configuration must be revised.

多結晶形状記憶合金の変態条件と変形挙動の解析(OS6d 相変態解析の新展開)

多結晶形状記憶合金の変態条件と変形挙動の解析(OS6d 相変態解析の新展開)

介在物法を用いた多結晶形状記憶合金の変形・変態挙動解析(S13-4 形状記憶合金・多孔質材・特性同定,S13 数理弾性力学応用の最前線)

介在物法を用いた多結晶形状記憶合金の変形・変態挙動解析(S13-4 形状記憶合金・多孔質材・特性同定,S13 数理弾性力学応用の最前線)

To simulate the behavior of shape memory alloys under thermomechanical cycling

In this paper, a thermodynamic constitutive model previously proposed by the authors was further developed in order to be applicable for the simulation of thermomechanical behavior of shape memory alloys under different loading conditions. The volume fractions of austenite and martensite variants were used as internal variables to describe the microstructural evolution. The model was used to investigate the behavior of a round tube Cu–Al–Zn–Mn polycrystalline shape memory alloy under various mechanical loads, including non-proportional loading, torsion cycling in opposite directions and the shape memory effect. The non-proportional loading simulation results were compared with experimental results reported in the literature.

Modeling of polycrystalline shape memory alloys at finite strains based upon the logarithmic stress rate

A thermomechanical model describing pseudoelasticity at finite strains is developed. It is Eulerian type and based upon the additive decomposition of the stretching D into an elastic and an elastic-inelastic phase transformation part and the multiplicative decomposition of the deformation gradient F into an elastic and an inelastic phase transformation part [1]. A thermodynamic framework with internal variables is utilized in order to explain the occurrence and evolution of the martensitic phase transformation [2]. The free energy for polycrystalline shape memory alloys is obtained from the specific free energies of the austenitic and martensitic phases and the interaction energy between them. The state of the material is determined by the temperature, the total strain and the total mass fraction of martensite. Suitable evolution laws for the latter and the transformation strain are proposed.

Constitutive Response of Polycrystalline Shape Memory Alloys

Constitutive Response of Polycrystalline Shape Memory Alloys

713 熱・力学的負荷のもとでの多結晶形状記憶合金におけるバリアント選択機構の解析

713 熱・力学的負荷のもとでの多結晶形状記憶合金におけるバリアント選択機構の解析