Numerical investigation of the evolution of new phase domains in an elastic solid

Designing and using functional (smart) materials and structural elements requires understanding and quantifying the effects caused by phase transformations. This paper investigates the problem of evolution of new phase domains in an elastic solid arising as a result of stress-induced phase transformations during deformation. The phase transition is accompanied by the transformation strain and a change in elastic moduli. The motion of the domain boundary - the interface - is described by a kinetic equation relating the normal component of the interface velocity with a configurational (thermodynamic) force equal to the jump of the normal component of the Eshelby energy-momentum tensor. A finite element procedure has been developed and verified by considering the problem of thermodynamic equilibrium and the kinetics of a new phase plane layer that has an analytical solution. The distributions of the configurational force along the interface are constructed. It is shown that these distributions can be used as a tool for predicting the characteristic features of the new phase domain evolution. The numerical experiments revealed various scenarios of the new phase domain evolution under external deformation, which allow or exclude the existence of equilibrium two-phase configuration. Using the example of an elliptical hole, it is demonstrated that a stress concentrator can cause the development of a new phase even at small external strains, at which a phase transition does not occur in a homogeneous body. It is shown that the new phase domain itself can induce stress concentration, which contributes to a further phase transformation.