Thermodynamically consistent phase field approach to phase transformations with interface stresses

Thermodynamically consistent phase field theory for multivariant martensitic transformations is developed with the main focus on introducing correct interface stresses (tension). The nontrivial point is that the interface tension (physical phenomenon) is introduced with the help of some geometric nonlinearities, even when strains are infinitesimal. Total stress at the diffuse interface consists of elastic and dissipative parts which are determined by the solution of the coupled system of phase field and viscoelasticity equations and the introduced interface stresses. An explicit expression for the free energy is derived that results in the desired expression for the interface stresses consistent with the sharp interface for the propagating nonequilibrium interface. Analytical expressions for nonequilibrium interface energy, width, entropy excess, as well as distribution of the interface tension are derived and parametrically studied. Interface stress tensor distribution is also obtained and analyzed for a critical martensitic nucleus. The possibility of extending the developed approach to other phenomena and more general models is discussed.