Predictions of distortion and residual stress for rectangular bars, quenched on one surface, are compared with experimental measurements. The heat flow is unidirectional, and the dominant stress component acts along the length of the bars. Thermocouples measure the transient temperature distribution, and displacement transducers monitor the distortion of the bars into circular arcs. The thermal history inferred from an inverse heat transfer calculation drives the mechanical stress and deformation analysis. The numerical analyses demonstrate the sensitivity of the quench distortion to the thermal boundary conditions, the thermophysical properties and the constitutive model. Agreement between the predicted and measured distortion is only qualitative. The predicted residual stress field compares very well with the residual stress inferred from layer removal techniques.

A method is developed in this paper to calculate the unknown boundary cooling condition and contact heat transfer coefficient for solidification of alloys. In this method, an objective functional is constructed based on a least squares approach and the difference between measured and estimated temperatures. This functional is minimized to obtain the boundary cooling condition and the contact heat transfer coefficient. The estimated temperatures are calculated by solving the corresponding direct problem. Beck's future time method and a regularization method are used to stabilize the numerical algorithm. A moving finite element method is used to solve the direct problem, where the velocities of the solid/mush and mush/liquid interfaces are primary variables and both interfaces are tracked continuously. In the procedure of solving the direct alloy solidification problem, complete solute mixing with no mass diffusion is assumed and the relationship between the solid fraction and the temperature in the mushy region is known in advance. In the example problems, solidification of binary alloys is studied and Scheil's equation is used to calculate the solid fraction in the mushy region.