For a better understanding of martensitic transformation, a novel phase field model is built up to simulate the evolution of the microstructures in shape memory alloys. The model is set in the energetic framework so that the kinetic equations and mechanical equilibrium equations are defined to construct the constitutive model for symmetry-breaking phase transformation. The proposed free energy density function involves the bulk elastic energy and interfacial energy. The latter describes the energy of diffusive interfaces with a specific phase field ansatz. In order to capture the effects of different interfacial energies of austenite-martensite interfaces on twin boundaries, the order parameters are introduced in a hierarchical manner. Considering the solution to crystallographi...[ Read more ]

For a better understanding of martensitic transformation, a novel phase field model is built up to simulate the evolution of the microstructures in shape memory alloys. The model is set in the energetic framework so that the kinetic equations and mechanical equilibrium equations are defined to construct the constitutive model for symmetry-breaking phase transformation. The proposed free energy density function involves the bulk elastic energy and interfacial energy. The latter describes the energy of diffusive interfaces with a specific phase field ansatz. In order to capture the effects of different interfacial energies of austenite-martensite interfaces on twin boundaries, the order parameters are introduced in a hierarchical manner. Considering the solution to crystallographic equations of martensite, we propose a kinematic model for transformation strain tensors. Besides, the bulk energy is given in a way to avoid the unphysical shift of equilibrium state of order parameters. To make the phase field model capable of simulating martensitic transformation under different temperature conditions, the proposed free energy function explicitly incorporates temperature and latent heat.

We numerically solved the kinetic equations based on the proposed constitutive model, which is implemented by the finite element solver COMSOL. Different simulations are performed under various boundary conditions. The numerical results are consistent with the experimental observations and the solution to crystallographic equations of martensite. Through a series of simulations, the effects of crystal orientation, boundary condition, temperature and loading rate on the evolution of microstructures and thermomechanical properties of shape memory alloys are discussed.