Modeling the effects of stress state and crystal orientation on the stress-induced transformation of NiTi single crystal
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INTRODUCTION
CONSTITUTIVE models that describe the mechanical behavior of NiTi and other shape memory alloys (SMAs) allow efficient exploitation of the unique characteristics of this class of materials. Several types of models for predicting the constitutive behavior of SMAs have previously been proposed, some of the more recent and comprehensive models are described in References 1 through 3. However, few prior constitutive models consider the relationship between the macroscopic shape memory effect (SME) and the crystallographic origins of the SME. Thus, aspects of the SME that depend on crystal orientation, such as the mechanical response of single crystal SMAs and the effect of texture on the asymmetry and anisotropy of SMA response, cannot be incorporated into most prior constitutive models in a fundamental way. The present article describes a simple constitutive model, based on crystallographic aspects of the martensitic transformation, that predicts the mechanical response of a single-crystal SMA subjected to an arbitrary multiaxial stress state. NiTi is used as the example SMA for the present model, but the fundamental principles upon which the model is based are applicable to any SMA. Crystallographic aspects of the martensitic transformation in NiTi are described by the WLR theory, a phenomenological theory originally proposed by Lieberman et al.. ~4] T h e WLR theory combines the Bain distortion, a lattice invariant shear (LIS), and a rigid body rotation to obtain a total distortion matrix associated with transformation of austenite to a pair of martensite variants. This total distortion matrix describes distortion of a volume element in a crystal that undergoes a martensitic transformation, subject to the constraint that an invariant plane (habit plane) exists between the parent and product phases. Application of the WLR theory requires knowledge of the lattice parameters of the parent and martensitic phases, the lattice correspondences between the two phases, and the characteristics of the LIS. The WLR T.E. BUCHHEIT, Graduate Student, and J.A. WERT, Professor, are with the Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22903-2442. Manuscript submitted November 17, 1993. METALLURGICAL AND MATERIALS TRANSACTIONS A
theory yields the total distortion matrix associated with the martensitic transformation from which the habit plane normal, and direction and magnitude of shear can be extracted. The information required to apply the WLR theory to the B2 to B 19 martensite transformation in NiTi is given by Knowles and Smith. tsl Matsumoto et al. t6] identify (0.72053,1,1}(011) type II twinning as the prevalent LIS. In NiTi, there are 12 lattice correspondences between the austenitic (B2) and martensitic (B19) phases, which represent the 12 martensite crystal orientations that can form from the parent lattice. In the present article, we adopt the lattice correspondence identification method of Miyazaki et al., t71 in which the correspondence are numbered 1 thr
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