In a recent communication, James and Zhang proposed four criteria for hysteresis width minimization for alloys exhibiting a first order solid–solid phase transformation. In the present work, four different phase transformations are investigated through four different alloys: cubic→trigonal R-phase for NiTi, cubic→monoclinic II for Cu–Zn–Al, cubic→monoclinic I for NiTi and cubic→tetragonal for Ni–Mn–Ga. The first aim of this paper is to validate the efficiency of these four criteria of reversibility. The second aim of the paper is to show how the crystallographic theory of martensite, built to predict microstructure under stress free state or dead loads, can be used for continuous loadings. Except for Ni–Mn–Ga, the criteria predictions are in good agreement with the experimental observations and with the choice of the Helmholtz free energy function expression.

Like in the plasticity theory, the prediction of phase transformation yield surfaces constitutes a key point in the modeling of polycrystalline shape memory alloys thermomechanical behavior. Generally in some micro-macro integration, the nature of the interface between austenite and twinned or untwinned martensite under stress free state and the choice of correspondance variants (CV) or habit plane variant (HPV) are determining for the explicit expression of the yield criterion. If the prediction of some copper-based alloys (interface between austenite and one single variant of martensite) and the Cu-Al-Ni for cubic to orthorhombic phase transformation (interface between austenite and twinned martensite) is fairly good, the prediction is not efficient for the important case of Ti-Ni (interface between austenite and twinned martensite with stress free state). The usual hypothesis consisting in neglecting the effect of stress on the interface geometrical configuration must be revisited.

On the one hand, Chu (Thesis, Minnesota, 1993), Abeyaratne et al. (Philos. Mag. A 73 (2) (1996) 457-497) performed biaxial tensile tests on a single crystal Cu-Al-Ni plate, in order to analyze the reorientation process of martensite variants. On the other hand, use is made of a constitutive model with n + I internal variables (the volume fractions of austenite and of the n martensite variants) specific to the thermornechanical behavior of SMA single crystals in order to simulate the martensite variant reorientation. The comparison between experimental results and model prediction is fairly good. (C) 2003 Academie dos sciences/Editions scientifiques et medicales Elsevier SAS. All rights reserved.

Biaxial proportional loading such as tension (compression)–internal pressure and bi-compression tests are performed on a Cu-Zn-Al and Cu-Al-Be shape memory polycrystals. These tests lead to the experimental determination of the initial surface of phase transformation (austenite→martensite) in the principal stress space (σ1,σ2). A first “micro–macro” modeling is performed as follows. Lattice measurements of the cubic austenite and the monoclinic martensite cells are used to determine the “nature” of the phase transformation, i.e. an exact interface between the parent phase and an untwinned martensite variant. The yield surface is obtained by a simple (Sachs constant stress) averaging procedure assuming random texture. A second modeling, performed in the context of the thermodynamics of irreversible processes, consists of a phenomenological approach at the scale of the polycrystal. These two models fit the experimental phase transformation surface well.

On the one hand, biaxial dead load (σ1,σ2) on a Cu Al Ni single crystal martensite plate have been performed by Chu, James and Abeyaratne. The reorientation process from one variant of martensite to an another variant is analyzed. The volume fraction of one martensite variant as a function of (σ1 - σ2) exhibits an unusual hysteresis.

On one hand, the lattice measurements of the austenite and the martensite cells for one CuZnAl and one CuAlBe alloys permit to determine the nature of the phase transformation i.e. an "exact" interface between the parent phase and an untwinned martensite variant.Hence, for single crystals, the yield surface looks like a polygon with several sectors. Each sector is defined by its peculiar activated variant.On the other hand, a "micro-macro" integration allows to predict the yield curve for biaxial proportional mechanical tests on polycrystals. This homogenisation process is in agreement with the prediction of a phenomenological approach at the macroscopic scale and fits well the yield experimental points.