Phase-field simulation of dendritic growth under externally applied deformation

Defects, i.e. hot tears, macrosegragation, and pores, formed in metal castings are a result of stresses and strains in the solid-liquid mushy zone. Numerical simulation of solidification of deforming dendrite crystal promises to improve insight into the mechanical behavior of mushy zones under an applied load. The primary goal of this thesis is to develop numerical methodologies for performing solidification simulation of deforming dendrites. Such simulation encounters difficulties associated with the interface dynamics due to phase change or interaction among the dendrites, and large visco-plastic deformation applied to them. Phase-field simulation of dendritic solidification is promising for the treatment of the complex interface dynamics. Free energy based formulation allows the model to incorporate bridging and wetting phenomena occurring at grain boundaries through an extra energy term which arises from a mismatch of the crystallographic orientation. The particle method would be attractive to handle large inelastic deformation without suffering mesh entanglement. In order to investigate the effect of solid deformations on the evolving microstructure, the material point method with elasto-visco-plasticity constitutive model is developed to couple to a phase-field model of solidification. The changes in the crystallographic orientation of a growing dendrite crystal due to solid deformation are carefully accounted for through the coupling methodology. The developed numerical framework is applicable to the simulation for single and multiple crystals, and is capable of handling complex morphological change. The wide variety of validations and practical problems solved in this thesis demonstrates the capability of investigating deformation behavior of growing crystals.