Asymptotic Self-Similarity of Minimizers and Local Bounds in a Model of Shape-Memory Alloys

We prove that microstructures in shape-memory alloys have a self-similar refinement pattern close to austenite-martensite interfaces, working within the scalar Kohn-Müller model. The latter is based on nonlinear elasticity and includes a singular perturbation representing the energy of the interfaces between martensitic variants. Our results include the case of low-hysteresis materials in which one variant has a small volume fraction. Precisely, we prove asymptotic self-similarity in the sense of strong convergence of blow-ups around points at the austenite-martensite interface. Key ingredients in the proof are pointwise estimates and local energy bounds. This generalizes previous results by one of us to various boundary conditions, arbitrary rectangular domains, and arbitrary volume fractions of the martensitic variants, including the regime in which the energy scales as $\varepsilon ^{2/3}$ ε 2 / 3 as well as the one where the energy scales as $\varepsilon ^{1/2}$ ε 1 / 2 .

Shape Change and Crystal Orientation of B19 Martensite in Equiatomic TiPd Alloy by Isobaric Test

We investigated the texture and the shape change in the equiatomic TiPd alloy, and discussed the relationship between the shape change and the atomic movements associated with martensitic transformation. Thermomechanical analyzer tests indicate that the direction of the shape change was different between the 0° and 90° samples, cutting out parallel and perpendicular to the hearth side of button ingot, respectively. In the 0° sample, shrinking and expansion were observed during the reverse and forward martensitic transformations, respectively, whereas the opposite tendency was confirmed in the 90° sample compared to the 0° sample. During the isobaric test, the martensitic variants were oriented to a (010) plane with compressive loading, and the B2 parent phase crystals also became coarse. There is a close relationship between the shape change due to the crystal orientation by the isobaric test and the shear-shuffling direction due to martensitic transformation.

An exact formulation for exponential-logarithmic transformation stretches in a multiphase phase field approach to martensitic transformations

A general theoretical and computational procedure for dealing with an exponential-logarithmic kinematic model for transformation stretch tensor in a multiphase phase field approach to stress- and temperature-induced martensitic transformations with N martensitic variants is developed for transformations between all possible crystal lattices. This kinematic model, where the natural logarithm of transformation stretch tensor is a linear combination of natural logarithm of the Bain tensors, yields isochoric variant–variant transformations for the entire transformation path. Such a condition is plausible and cannot be satisfied by the widely used kinematic model where the transformation stretch tensor is linear in Bain tensors. Earlier general multiphase phase field studies can handle commutative Bain tensors only. In the present treatment, the exact expressions for the first and second derivatives of the transformation stretch tensor with respect to the order parameters are obtained. Using these relations, the transformation work for austenite ↔ martensite and variant ↔ variant transformations is analyzed and the thermodynamic instability criteria for all homogeneous phases are expressed explicitly. The finite element procedure with an emphasis on the derivation of the tangent matrix for the phase field equations, which involves second derivatives of the transformation deformation gradients with respect to the order parameters, is developed. Change in anisotropic elastic properties during austenite–martensitic variants and variant–variant transformations is taken into account. The numerical results exhibiting twinned microstructures for cubic to orthorhombic and cubic to monoclinic-I transformations are presented.

Energy scaling laws for geometrically linear elasticity models for microstructures in shape memory alloys

We consider a singularly-perturbed two-well problem in the context of planar geometrically linear elasticity to model a rectangular martensitic nucleus in an austenitic matrix. We derive the scaling regimes for the minimal energy in terms of the problem parameters, which represent the shape of the nucleus, the quotient of the elastic moduli of the two phases, the surface energy constant, and the volume fraction of the two martensitic variants. We identify several different scaling regimes, which are distinguished either by the exponents in the parameters, or by logarithmic corrections, for which we have matching upper and lower bounds.

In situsynchrotron X-ray diffraction analysis of deformation behaviour in Ti–Ni-based thin films

Deformation mechanisms of as-deposited and post-annealed Ti50.2Ni49.6, Ti50.3Ni46.2Cu3.5and Ti48.5Ni40.8Cu7.5thin films were investigated using thein situsynchrotron X-ray diffraction technique. Results showed that initial crystalline phases determined the deformation mechanisms of all the films during tensile loading. For the films dominated by monoclinic martensites (B19′), tensile stress induced the detwinning of 〈011〉 type-II twins and resulted in the preferred orientations of (002)B19′parallel to the loading direction (∥ LD) and (020)B19′perpendicular to the LD (⊥ LD). For the films dominated by austenite (B2), the austenite directly transformed into martensitic variants (B19′) with preferred orientations of (002)B19′ ∥ LD and (020)B19′ ⊥ LD. For the Ti50.3Ni46.2Cu3.5and Ti48.1Ni40.8Cu7.5films, martensitic transformation temperatures decreased apparently after post-annealing because of the large thermal stress generated in the films due to the large differences in thermal expansion coefficients between the film and substrate.

Influence of the Texture and Strain on the Behaviour of Ni53.6Mn27.1Ga19.3 and Ni54.2Mn29.4Ga16.4 Shape Memory Alloys

Polycrystalline samples of Ni53.6Mn27.1Ga19.3 and Ni54.2Mn29.4Ga16.4 shape memory alloys were investigated using dilatometry. The longitudinal axes of the samples were perpendicular to the columnar grains. Both alloys showed positive shape memory effects. The martensitic phase transformation occurred without hysteresis in both alloys with transformation temperatures of 174°C for the Ni53.6Mn27.1Ga19.3 alloy and 253°C for the Ni54.2Mn29.4Ga16.4 alloy. The dilatation characteristics for both alloys were determined in three perpendicular directions. The strain associated with the internal stress at the interface between the two martensitic structures and the two grains affected the dilatation characteristics in the y and z directions (perpendicular to the longitudinal axis of the sample). The microstructure was determined for all the directions investigated. To investigate the mechanical history, a round cross-section of the Ni54.2Mn29.4Ga16.4 sample was machined using a milling machine along the longitudinal axis so that both sides of the sample were symmetrical. This sample treatment changed the dilatation characteristics of the martensite and austenite. The study and analysis of the dilatation characteristics of the thermal cycle showed the relaxation of internal stresses and the reorientation of the martensitic variants.