Criteria for determining element size and time step for thermal shock simulation

Rapid energy deposition into spallation source targets can lead to their temperature rise at enormous rates, giving rise to dynamic thermoelastic stresses. Understanding and predicting the resulting stress waves are crucial for robust design and safe operation of such devices. To simulate the thermal shock phenomenon accurately, many factors should be carefully considered, such as geometry, surface condition, energy deposition profile, equation of state, possible cavitation, viscous damping, rate-dependent constitutive equation, element size, and time step. In this paper a closed form expression for the induced stress in slender bars with distributed energy deposition has been directly derived; it is then used to test the accuracy of computed results with FEA codes. It was found that significant errors can occur unless care is taken to restrict element size and time step depending on the boundary conditions, steepness of temperature profiles and rise rate. Criteria have been proposed for determining the above two parameters. Numerical simulation with the well-established ANSYS5.5 code system showed that excellent results could be achieved if the proposed criteria are met.