ONE-DIMENSIONAL DYNAMIC THERMAL STRESSES GENERATED IN AN ELASTIC HALF-SPACE BY LASER PULSES

Abstract

An improved solution to the one-dimensional dynamic thermal stress problem for an elastic half-space analyzed previously by Daniłowskaya [3] is given. In this problem the temperature and stress fields are produced by a particular heat supply generated by absorption of a laser pulse incident on the half-space. The betterment comprises: (i) eliminating some substantial and formal errors occurring in Danilowskaya [3], (ii) providing a qualitative and quantitative analysis of the solution that is missing in Daniłowskaya [3],.and (iii) generalizing the solution to include an arbitrary step-like profile of the laser pulse. In particular, it is shown that for a rectangular pulse of duration t_* > 0 and for a given cross section x₀ > 0 of the half-space both the temperature and stress are continuous functions for every time t ≥ 0; while their time derivatives suffer jumps on the t-axis, the temperature rate jumps at the consecutive times t = 0 + 0 and t = t_*, and the stress rate exhibits discontinuities at t = t_* and t = t_* +x₀/c₁, where c₁ denotes the longitudinal wave velocity in an unbounded isotropic and homogeneous elastic medium.