The phase field microelasticity theory is used to formulate a three-dimensional phase field model of a multivariant martensitic transformation under external load. The model is based on the exact solution of the elasticity problem in the homogeneous modulus approximation. The transformation-induced coherency strain and applied stress are explicitly taken into account. Computer simulations are performed for a generic cubic → tetragonal martensitic transformation in a multilayer system consisting of alternating active and inert layers. The development of the martensitic transformation through nucleation, growth and coarsening of orientation variants is simulated at different levels of the applied stress. The simulated martensitic structure has a complex polytwinned morphology. The simulation predicted such effects as the formation of texture and the stress-induced transformation that are in a general agreement with the experimental observations. The simulation produced realistic stress-strain hysteresis loops, which, in principle, can be used for the formulation of the constitutive equations of the macroscopic mechanics for the active system.

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Journal Acta Materialia
Artemev, A, Wang, Y. (Y.), & Khachaturyan, A.G. (A. G.). (2000). Three-dimensional phase field model and simulation of martensitic transformation in multilayer systems under applied stresses. Acta Materialia, 48(10), 2503–2518. doi:10.1016/S1359-6454(00)00071-9