A finite element-based level-set method of an interface motion driven by a diffusion field: Application to a phase transformation problem

The level-set method is becoming one of the most effective tools for predicting the shape and position of moving interfaces. However, this method has not yet been fully developed in the area of mechanics of materials, where interfaces, are generally treated as discrete entities. In this work, numerical simulations of an interface motion associated with a diffusion-driven phase transformation are performed using the level-set method. The constitutive relation of the mobile interface, linking its thermodynamical driving force with its velocity, is derived from the dissipation function. The governing partial differential equation for the coupled diffusion field-level-set function was motivated by the original work of Adalsteinsson and Sethian [D. Adalsteinsson, J.A. Sethian, J. Comput. Phys. 185 (2003) 271-288], and is here developed further to enforce the requirement that Fick's second law be satisfied locally in a direction normal to the interface. The coupled diffusion-level-set model is implemented into the finite element (FE) method and is then used to solve a phase transformation problem in a Ni-base superalloy.