Thermomechanical effects in solidification and related problems.

The present dissertation is submitted as a collection of four manuscripts based on research that has been conducted by the author as a graduate student at The University of Michigan. During a casting process, the thermal and mechanical problems are coupled through the boundary conditions. The major difficulties are: (1) the heat conduction problem with phase change, (2) determination of the instantaneous stress field, and (3) stability analysis. In the second chapter, a linear perturbation method is used to solve the two-dimensional heat conduction problem of planar solidification. Results are obtained for the consequent sinusoidal perturbation in the solid/melt boundary as a function of time and for the temperature distribution throughout the solid shell. The inverse problem, in which the melt/solid boundary is prescribed and the mold temperature is to be determined, is also briefly discussed. In the third chapter, a numerical solution is obtained for the heat conduction and thermal stress problems. The distribution of the residual stresses in axisymmetric castings due to solidification is calculated. Particular attention is paid to the asymptotic behavior of the temperature and stress fields at the last instant of solidification. In the fourth chapter, a linear perturbation method is used to examine the stability of a unidirectional solidification problem in which there is a pressure-dependent thermal contact resistance at the plane mold. The heat transfer and thermal stress problems are coupled through the boundary conditions and yield two coupling ordinary differential equations which then reduced to a single equation being solved numerically. The results show that an initially infinitesimal perturbation will grow substantially during the solidification process if the thermal contact resistance is very pressure-sensitive.PhDApplied MechanicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/103850/1/9034466.pdfDescription of 9034466.pdf : Restricted to UM users only