Dynamic thermoelastic effects for half-planes and half-spaces with nearly-planar surfaces

Abstract

The effects of non-planarity on the dynamic surface temperature changes induced for plane-strain and 3D problems on the nearly-planar surfaces of, respectively, coupled thermoelastic half-planes and half-spaces by surface heat fluxes are treated. The nearly-planar nature of the surfaces allows the problem solutions to be written, following a standard perturbation scheme, as series expansions in a dimensionless surface contour amplitude parameter. The first, or zero-order, terms represent the ideal (planar) surface solutions, while the second, or first-order, terms represent corrections for non-planarity.

Because the characteristic thermoelastic time is of O(10⁻⁷)μs, large-time asymptotic forms of the exact integral transform solutions can be used. These can be inverted exactly and used in Green's function operations to yield analytic, or integrals of analytic, expressions. Two types of thermal loading for the half-plane and yet a third type of thermal loading for the half-space are considered. Comparison of the zero- and first-order surface temperature changes for each case indicate that non-planarity gives rise for large times to changes in surface regions beyond those predicted by an ideal surface analysis. Moreover, the magnitudes of these changes can be more significant than the ideal surface results.