Finite element modeling of martensitic phase transformation
MetadataShow full item record
Two finite element approaches are suggested for the modeling of multi-variant martensitic phase transitions in elastic materials at different length scales. The first one is designed for the modeling of phase transformation at a large length scale including meso-scale. It is based on the thermomechanical phenomenological model for phase transformation that represents strain softening during phase transition. In contrast to the known publications on phase transformation, which apply the standard elasto-plastic models with strain softening, our model is related to multi-variant martensitic phase transformation. Rate dependent constitutive equations used in the model facilitate avoidance of the mesh sensitivity at the numerical implementation of the approach. Due to strain softening a microstructure containing pure martensitic and austenitic domains with the small transition zones can be obtained as the solution of the corresponding boundary value problem. A finite element algorithm for the first approach is developed and implemented into the software ABAQUS. Several two dimensional problems for martensitic phase transformation in single crystal and poly crystal elastic materials are solved and analyzed. The second approach is developed for the description of phase transition at nano-scale and based on the Ginzburg-Landau theory with a new thermodynamic potential that captures the main features of macroscopic stress-strain curves. Distributions of different martensitic variants are the solution of the coupled system of the evolution equations (time dependent Ginzburg- andau equation) for the order parameters, which represent different phases, and the elasto-dynamics equations. Due to similarity between the evolution equations and heat transfer equations, numerical simulations of evolving microstructure during phase transition can be obtained from the solution of the coupled heat transfer and elasticity equations with the replacement of temperature by different order parameters. In known approaches based on the Ginzburg-Landau theory, constant stresses are used, or stresses are calculated by solving elasto-static equations which are a particular case of elasto-dynamic equations. However, in our model, the general elasto-dynamic equations are used for the calculation of stresses. A numerical algorithm for the solution of the coupled system of equations is suggested and implemented into the finite element program 'FEAP'. Several numerical examples of the modeling of evolving microstructure during multi-variant martensitic phase transition such as phase transition in 2-D single and poly-crystal, and 3-D single crystal specimens are solved and analyzed. The results are compared with the solutions using the elasto-static equations and show the importance of inertial forces.