Efficient Analysis of Shape Memory Alloy Single Crystalline and Textured Polycrystalline Responses Via Anisotropic Yield Surfaces

Phenomenological constitutive models for shape memory alloys (SMAs) based on the legacy of classical plasticity provide several analysis advantages when compared to micromechanical approaches, especially in terms of computational efficiency. For this reason, they are attractive options for the analysis of large computational domains. However, such approaches have largely been limited by symmetry assumptions inherent in the stress invariants used to form transformation criteria and associated evolution equations. Thus, they have not been effective for the analysis of problems dominated by single crystal responses (e.g., inclusion, inter-granular fracture, or granular interaction problems). In a new development, a computationally efficient modeling framework conventionally applied at the macroscopic scale is extended to accurately account for single crystal response at the micro scale by incorporation of an anisotropic transformation function and associated evolution equations. The model predicts single crystal behaviors accurately and is applied to the analysis of complex boundary value problems. Example analyses considering texture effects in a polycrystalline RVE and the effects of precipitates in a single crystal are demonstrated.