Prediction of thermal stresses during vertical solidification of a pure metal with density change

A numerical methodology for the calculation of the thermal stresses in a solidifying body with volume contraction due to solid-liquid density change is developed and applied to the vertical solidification of pure aluminum. In this algorithm, the phase-change heat-transfer analysis is performed by a finite-volume method (FVM) and the thermal-stresses analysis in a solidifying body by a finite-element method (FEM). Difficulties associated with the time-dependent solid and liquid domains, the shapes of which are also a part of the solutions, are overcome by employing the boundary-fitted coordinate system. A hypoelastic-viscoplastic constitutive model and a rate form of the principle of virtual work are involved to model the stresses and the deformation. The effect of various cooling rates on the motion of the solid-liquid interface, on the temperatures and on the thermal stresses is presented and discussed.