Micromechanical prediction of the two-way shape memory effect in shape memory alloy composites

The two-way shape memory effect in monolithic shape memory alloys has been widely investigated both theoretically and experimentally. In the present study, this effect is analyzed for shape memory alloy composites by employing a micromechanical model. To this end, the responses of polymeric matrix and metal matrix unidirectional composites with embedded shape memory alloy fibers are determined. For the polymeric matrix composite, the effect of axial, transverse and shear loadings as well as the fiber volume fraction on the resulting two-way shape memory behavior are studied. The local distributions of stresses among the shape memory alloy fiber and epoxy matrix in the low- and high-temperature shapes of the composite are also investigated. Two training procedures that generate the two-way shape memory effect in the metal matrix composite are offered. The present analysis shows that the two-way shape memory effect in the chosen type of metal matrix composite is not as useful as in the polymeric matrix one. Finally, for a polymeric matrix composite that is subjected to a transverse normal loading, the effect of imperfect bonding between the shape memory alloy fibers and the neighboring matrix is investigated.     

Local displacements and load transfer in shape memory alloy composites

Although there has been a significant amount of research dedicated to characterizing and modeling the response of shape memory alloys (SMAs) alone, little experimental work has been done to understand the behavior of SMAs embedded in a host material. The interaction between SMA wires and a host polymer matrix was investigated by correlating local displacements and stress fields induced by the embedded wires with SMA/polymer adhesion. Most SMA composite applications require transfer of strain from the wire to the matrix. In these applications, maximum interfacial adhesion between the SMA wire and the polymer matrix is most desirable. The adhesion was varied by considering four different surface treatments: untreated, acid etched, hand sanded and sandblasted. The average interfacial bond strength of the SMA wires embedded in an epoxy matrix was measured by standard pull out tests. Sandblasting significantly increased the bond strength, whereas hand sanding and acid cleaning actually reduced interface strength. In situ displacements of embedded, surface-treated SMA wires were measured using heterodyne interferometry, whereas the resulting stresses induced in the polymer matrix were investigated using photoelasticity. Increased wire adhesion resulted in lower axial wire displacement and higher interfacial stresses due to the restraining effect of the matrix on the actuated wire. A simplified theoretical analysis was carried out to estimate the shear stress induced in the matrix due to wire actuation. The maximum shear stress predicted for the case of a perfect interfacial bond was about 7 percent larger than the value measured experimentally for the sand-blasted wire.     

Qualitative and quantitative evaluation of the interface in activated shape memory alloy composites

The interfacial quality of shape memory alloy (SMA) composites was experimentally evaluated by differential scanning calorimetry, and quantitatively calculated using a combination of Šittner's model and a composite cylinder model. Results have shown that the damage level of the interface in a heating process can be quantitatively evaluated by measuring the transformation enthalpy of the subsequent heating cycle and comparing it with the S-shaped enthalpy kinetic curve. A combination of Šittner's model and a composite cylinder model is capable of calculating both the thermal behavior and the triaxial stress state of SMA composites.     

Phase transitions and thermodynamics for the shape memory alloy AuZn

A model for shape memory alloys described by a intermediate pattern between a first and a second order phase transition is studied. Moreover, by the thermodynamic compatibility of the model, we provide suitable restrictions on the potentials of the Ginzburg-Landau system. Finally, we present numerical simulations of this shape memory model, which are in good agreement with experimental data.     

Modeling crystallization of a binary alloy

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 39–45, July–August, 1989.     

Shakedown analysis of shape memory alloy structures

Phase transformational shakedown of a structure refers to a status that plastic strains cease developing after a finite number of loading cycles, and subsequently the structure undergoes only elastic deformation and alternating phase transformations with limited magnitudes. Due to the intrinsic complexity in the constitutive relations of shape memory alloys (SMA), there is as yet a lack of effective methods for modeling the mechanical responses of SMA structures, especially when they develop both phase transformation and plastic deformation. This paper is devoted to present an algorithm for analyzing shakedown of SMA structures subjected to cyclic or varying loads within specified domains. Based on the phase transformation and plastic yield criteria of von Mises-type and their associated flow rules, a simplified three-dimensional phenomenological constitutive model is first formulated accounting for different regimes of elastic–plastic deformation and phase transformation. Different responses possible for SMA bodies exposed to varying loads are discussed. The classical Melan shakedown theorem is extended to determine a lower bound of loads for transformational shakedown of SMA bodies without necessity of a step-by-step analysis along the loading history. Finally, a simple example is given to illustrate the application of the present theory as well as some basic features of shakedown of SMA structures. It is interesting to find that phase transformation may either increase or decrease the load-bearing capacity of a structure, depending upon its constitutive relations, geometries and the loading mode.     

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。     

Modeling and simulation of magnetic-shape-memory polymer composites

Composites of small magnetic-shape-memory (MSM) particles embedded in a polymer matrix have been proposed as an energy damping mechanism and as actuators. Compared to a single crystal bulk material, the production is simpler and more flexible, as both type of the polymer and geometry of the microstructure can be tuned. Compared to polycrystals, in composites the soft polymer matrix permits the active grains to deform to some extent independently; in particular the rigidity of grain boundaries arising from incompatible orientations is reduced. We study the magnetic-field-induced deformation of composites, on the basis of a continuous model incorporating elasticity and micromagnetism, in a reduced two-dimensional, plane-strain setting. The aim is to give conceptual guidance for the design of composite materials independent of the concrete macroscopic device. Thus, on the background of homogenization theory, we determine the macroscopic behavior by studying an affine-periodic cell problem. An energy descent algorithm is developed, whose main ingredients are a boundary element method for the computation of the elastic and magnetic field energies; and a combinatorial component reflecting the phase transition in the individual particles, which are assumed to be of single-domain type. Our numerical results demonstrate the behavior of the macroscopic material properties for different possible microstructures, and give suggestions for the optimization of the composite.     

Modeling cylindrical waves in nonlinear elastic composites

A procedure of deriving nonlinear wave equations that describe the propagation and interaction of hyperelastic cylindrical waves in composite materials modeled by a mixture with two elastic constituents is outlined. Nonlinearity is introduced by metric coefficients, Cauchy-Green strain tensor, and Murnaghan potential. It is the quadratic nonlinearity of all governing relations. For a configuration (state) dependent on the radial coordinate and independent of the angular and axial coordinates, quadratically nonlinear wave equations for stresses are derived and a relationship between the components of the stress tensor and partial strain gradient is established. Four combinations of physical and geometrical nonlinearities in systems of wave equations are examined. Nonlinear wave equations are explicitly written for three of the combinations __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 63–72, June 2007.     

Coupling effects in bending problems for beams of a shape memory alloy

Coupling effects of boundary-value problems that arise for shape-memory alloys whose phase compositions depend on the acting stresses and whose elastic moduli change with variation in the fraction of martensite are studied. Algorithms and results of solution of a number of beam bending problems are given. It is established that in coupled problems, the changes in the stress-strain state upon cooling proceed more smoothly than in uncoupled problems. This is due to the propagation of the front of the beginning of the transformation over the cross section. Overload of the outer layers of the beam and unloading of the inner layers of the beam are found to be related to the propagation of the front of completion of the transformation. Moscow State Aviation Institute, Moscow 125871. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 164–173, January–February, 1998.     

Phase transitions in the shape memory alloy CuAlNi

Shape memory alloys exhibit a complex load-deformation temperature behaviour. In CuAlNi different maximal recoverable deformations may be observed in tensile experiments. We have found five phases and their corresponding phase transitions, two of them are reversible and the others exhibit hysteresis. We use a thermodynamic theory to calculate the energy landscape that describes the behaviour of the CuAlNi specimen.Received: 8 March 2004, Accepted: 9 March 2004, Published online: 12 May 2004 Correspondence to: A. Musolff     

Almost compatible X-microstructures in CuAlNi shape memory alloy

A systematic study of a specific martensitic microstructure, called the X-microstructure, is carried out with the focus on the CuAlNi shape memory alloy undergoing the cubic-to-orthorhombic transformation. The set of all crystallographically distinct candidate X-microstructures is determined, and it is shown that, according to the crystallographic theory of martensite, none of them is compatible. Almost compatible X-microstructures, which involve elastic strains, are thus examined. These microstructures are searched in the neighborhood of all candidate X-microstructures by minimizing the total elastic strain energy with respect to the microstructure parameters. Several low-energy X-microstructures are found, and it is shown that the total elastic strain energy correlates reasonably well with one of the indicators which characterize incompatibility of the corresponding candidate X-microstructure.     

SMA纤维复合材料梁振动半主动控制

分析了一类形状记忆合金(SMA)纤维混杂层合粱用于振动控制的动力学模型和作用机理．采用多胞模型、形状记忆合金一维本构关系分析方法,同时考虑横向剪切的影响,建立了层合梁的数学模型．半主动控制是通过改变受控结构的参数来减小结构振动的响应．根据开关控制原理确定可变刚度系统的控制律,进行SMA纤维混杂层合粱的半主动控制的数值仿真．结果表明,将半主动控制应用于梁的振动控制是一种有效的方法．     

Modeling the dynamic behavior of shape memory alloys

The paper studies the single degree of freedom vibration of a rigid mass suspended by a thin-walled shape memory alloy tube under torsional loading. The behavior is analyzed for the cases of quasiplasticity (low temperatures) and pseudoelasticity (high temperatures) on the basis of an improved version of the Müller–Achenbach model. To illustrate the strong hysteresis-induced damping capacity and the non-linear vibration characteristics, both, free and forced vibrations are considered in the first part of the paper. This is done on the basis of an isothermal version of the model, while the second part of the paper focuses on the effect of non-constant temperature caused by the rate-dependent release and absorption of latent heats.     

A macroscopic multi-mechanism based constitutive model for the thermo-mechanical cyclic degeneration of shape memory effect of NiTi shape memory alloy

A macroscopic based multi-mechanism constitutive model is constructed in the framework of irreversible thermodynamics to describe the degeneration of shape memory effect occurring in the thermo-mechanical cyclic deformation of NiTi shape memory alloys(SMAs). Three phases,austenite A, twinned martensite Mtand detwinned martensite M~d, as well as the phase transitions occurring between each pair of phases( A → M~t, M~t→ A, A → M~d,M~d→ A, and M~t→ M~d) are considered in the proposed model. Meanwhile, two kinds of inelastic deformation mechanisms, martensite transformation-induced plasticity and reorientation-induced plasticity, are used to explain the degeneration of shape memory effects of NiTi SMAs. The evolution equations of internal variables are proposed by attributing the degeneration of shape memory effect to the interaction between the three phases(A, M~t, and M~d) and plastic deformation. Finally, the capability of the proposed model is verified by comparing the predictions with the experimental results of NiTi SMAs. It is shown that the degeneration of shape memory effect and its dependence on the loading level can be reasonably described by the proposed model.     

A phenomenological model for the simulation of functional fatigue in shape memory alloy wires

In this contribution, a modelling framework for functional fatigue in shape memory alloy wires is introduced. The approach is in particular designed to reproduce the effective response determined by experiments as published in, e.g., Eggeler et al. (Mat Sci Eng A 378:24–33, 2004). In this context, the decrease of transformation stresses, the increase of irreversible strains, and the occurrence of “characteristic points” with respect to the stress-strain relation is explicitly covered in the model formulation. The modelling approach for the phase transformations itself offers a large potential for further micromechanically well-motivated model extensions.