Elastic Waves Induced by Surface Heating in a Half-Space

Rapid surface heating will induce waves in an elastic material. Closed form solutions for the resulting longitudinal and transverse thermal stresses are derived using Laplace Transforms. The model is one-dimensional, consisting of a half-space subjected to a step change in the surface heating. The transverse stress at the wave peak is found to exceed the surface stress for short times, while for long times the surface stress far exceeds either of the stresses at the wave peak. Both the longitudinal and transverse stresses at the peak of the wave reach steady state values after a few dimensionless times. Introduction Rapid surface heating, such as that created by a laser, can induce numerous phenomena in solids. Some of these include melting, vaporization, thermal waves [1], and plastic deformation. In many applications, such as mirrors, such phenomena must be avoided in order to ensure a long life. In this paper, I derive a closed-form solution for onedimensional elastic waves induced by a step change in surface heating. This creates a temperature field in which the surface temperature increases as the square root of the pulse time. It is assumed that the heat is deposited at the surface, there is no cooling, the heat transport is diffusional, and that the elastic and thermal equations are uncoupled.