A fully coupled diffusional-mechanical formulation for growth kinetics of precipitates in laser powder bed fusion process using a phase field approach

摘要

This paper formulates a general thermodynamically consistent theory of the coupled solute transport and largestrain to describe the transformation kinetics of precipitation in a supersaturated matrix during laser additivemanufacturing (AM) by selective laser melting of powder bed using phase field method. The structure of theconstitutive equations is derived utilizing multiplicative kinematic decomposition of the total deformationgradient into elastic and eigen transformation parts. Expressions for the first Piola–Kirchhoff stress and theCauchy stress are derived. The stress-dependent diffusion potential accounts for nonlinear, finite deformation.A high nonlinear Ginsburg–Landau kinetic equations coupled to Cahn-Hilliard type of diffusion-drift equationfor solute atom concentration are derived. The Voigt/Taylor homogenization theory is used to model thedependence of total stress on the phase-field, which assumes equal elastic strains in the different phases at thediffuse interface region. To describe the effects of temperature and fluid velocity distributions and thermalhistory on the precipitate growth mechanisms a linking of microscale model with the macroscopic AMprocessing conditions is discussed. Then the proposed model is applied to cylindrical precipitate growth toexplore the stress evolution with taking account of finite deformation and plastic deformation.