Gradient-enhanced thermomechanical 3D model for simulation of transformation patterns in pseudoelastic shape memory alloys
Abstract
Stress-induced martensitic transformation in polycrystalline NiTi under tension often proceeds through formation and propagation of macroscopic phase transformation fronts, i.e., diffuse interfaces that separate the transformed and untransformed domains. A gradient-enhanced 3D finite-strain model of pseudoelasticity is developed in this work with the aim to describe the related phenomena.
The underlying softening response is regularized by enhancing the Helmholtz free energy of a non-gradient model with a gradient term expressed in terms of the martensite volume fraction. To facilitate finite-element implementation, a micromorphic-type regularization is then introduced following the approach developed recently in the 1D small-strain context.
The complete evolution problem is formulated within the incremental energy minimization framework, and the resulting non-smooth minimization problem is solved by employing the augmented Lagrangian technique. In order to account for the thermomechanical coupling effects, a general thermomechanical framework, which is consistent with the second law of thermodynamics and considers all related couplings, is also developed.
Finite-element simulations of representative 3D problems show that the model is capable of representing the loading-rate effects in a NiTi dogbone specimen and complex transformation patterns in a NiTi tube under tension. A parametric study is also carried out to investigate the effect of various parameters on the characteristics of the macroscopic transformation front.