Formulation of laser-induced thermal stresses: Stress boundary at the surface

Laser heating of solids results in a high-temperature gradient inside the substrate material. This, in turn, results in high stress levels in the region irradiated by a laser beam. In the present study, laser heating of solid substrate is formulated and a closed-form solution for the stress field inside the substrate material is obtained. Time exponentially decaying laser pulse intensity is employed in the analysis. In order to account for the recoil pressure effect on the resulting stress field, the stress boundary at the solid surface is employed in the analysis. The Laplace transformation method is used when deriving the closed-form solutions. It is found that a stress wave propagates into the solid bulk with a wave speed c₁. The amplitude of the stress wave reduces as the distance from the substrate increases towards the solid bulk. The occurrence of peak stress inside the substrate material differs for the stress-free boundary and the stress boundary at the free surface cases.