| Popis: |
A nonlinear viscoelastic model with temperature-dependent Young's modulus and viscosity is proposed for the mechanical behavior of metals at high temperatures or low strain-rates. The model is then used in the formulation of the one-dimensional solidification problem for a rectangular mold subject to uniform but nonsteady surface temperature and pressure. Although the resulting equations are highly nonlinear, solutions are obtained for the special case of slow cooling using a linearizing perturbation procedure. In particular, analytical expressions are obtained for the stresses in the solidifying skin and for the time required for an air-gap to form between the skin and the mold. For the case of a constant rate of surface-temperature drop, the stresses are found to be uniform through the skin and to remain compressive up to the time of air-gap formation. Furthermore, no air-gap is possible if the pressure exceeds a critical value. For a case of increasing rate of surfacetemperature drop, the stresses in the outer surface of the ingot are found to become tensile prior to air-gap formation. |
