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A multivariant micromechanical model for SMAs. I: Crystallographic issues for single crystal model. II: Polycrystal model. (English) Zbl 0986.74053

From the summary: We develop a general three-dimensional multivariant model for shape memory alloy constitutive behavior. The model is based on the habit planes and transformation directions for variants of martensite, and uses a thermodynamic and micromechanics approach to derive the governing equations for thermomechanical response. The model accounts for the self-accomodating group structure exhibited during martensitic plate formation, and utilizes this concept in the calculation of interaction energy between variants. In this paper, we expand the multivariant model to consider the influence of inclusion shape on model predictions. A direction selection scheme proposed for penny-shaped inclusions is based on the fact that several habit plane variants tend to cluster about one of the \(\{011\}\) or \(\{00 1\}\) poles. We also explore in detail the crystallographic basis of material response and the influence of specific crystallographic changes on the macroscopic single crystal constitutive response. Then an averaging scheme is combined with the multivariant mechanical approach to simulate the behaviour of a polycrystalline shape memory alloy (SMA) specimen.

MSC:

74M05 Control, switches and devices (“smart materials”) in solid mechanics
74M25 Micromechanics of solids
74N05 Crystals in solids
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