Constitutive model for the numerical analysis of phase transformation in polycrystalline shape memory alloys
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This work presents new developments in the thermomechanical constitutive modeling of shape memory alloys (SMAs). The proposed phenomenological constitutive model is motivated by the earlier work of Boyd and Lagoudas (1996) and considers three characteristics of SMA response that have not been addressed in a unified manner to date. First, it captures the smooth transition in the thermal and mechanical responses often observed as the martensitic transformation is initiated and completed. Secondly, it considers the effect of applied stress magnitude on the generation of favored martensitic variants without explicitly considering the process of martensitic reorientation, resulting in a computationally efficient and accurate analysis tool. Finally, it generalizes the concept of the critical thermodynamic forces for transformation, which become dependent on transformation direction and applied stress magnitude. These improvements, introduced within a thermodynamically consistent mathematical framework, increase model fidelity over a wide range of SMA material systems. The full numerical implementation of the model in an efficient scheme is described. Experimental results associated with various thermomechanical paths are compared to the analysis predictions, including stress-induced and thermally induced transformations under uniaxial and non-proportional mechanical loads. Stress-free calorimetric results are also simulated. Analysis of a boundary value problem considering large rotations and local non-proportional loadings is described. 2011 Elsevier Ltd. All rights reserved.