Thermoelastic Response Induced by Volumetric Absorption of Uniform Laser Radiation in a Half-Space

Abstract

In this paper, the thermoelastic response in a generalized thermoelastic half-space induced by absorption of a penetrating pulsed laser radiation inside the medium is studied using the generalized theory with Dual-Phase-Lag (DPL). The surface of the target is considered stresses free and exposed to temperature-dependent heat losses. Laplace integral transform is used analytically for obtaining the general solution, while its inverse is carried out numerically. The copper element is used as an application to compare the predictions induced by volumetric absorption of the Dual-Phase-lag theory with those for Lord–Shulman (LS) and classical coupled (CTE) theories, moreover the response induced by volumetric absorption for (LS) and (CTE) models in this work were compared with those induced by surface absorption in a previous work.

Heating a 2D Thermoelastic Half-Space Induced by Volumetric Absorption of a Laser Radiation

“…as a parameter in the absence of cooling, calculated for   needs more time and consumes more energy to reach its maximum; this behavior is similar to the behavior that appears in [31] for the classical coupled theory. .…”

“…The figure shows that compared to the chosen temporal pulse shape, Q(t), for τ 1 > τ 2 , the maximum surface temperature becomes smaller and shifts evidently towards greater time than that for τ 1 < τ 2 . This means that the surface temperature for τ 1 > τ 2 needs more time and consumes more energy to reach its maximum; this behavior is similar to the behavior that appears in [31] for the classical coupled theory.…”

“…  , the maximum surface temperature becomes smaller and shifts evidently towards greater time than that for 12   . This means that the surface temperature for 12   needs more time and consumes more energy to reach its maximum; this behavior is similar to the behavior that appears in [31] for the classical coupled theory. Figure 3 represents the time-dependent laser pulse shape and the surface temperature, with τ 1 as a parameter in the absence of cooling, calculated for r = 5 × 10 − 4 .…”

“…Substituting Equations ( 51)-(53) into Equation (31) and setting (z = 0), this gives the surface temperature θ(α, 0, s) as follows:…”

“…Abouelregal and Zenkour [29] employed the generalized two-temperature thermoelastic theory to discuss thermoelastic responses in a half-space, whose pounding plane was exposed to a laser pulse. Tayel and Hassan [30] and Tayel [31] studied the thermoelastic interaction induced by both surface and volumetric absorption techniques, respectively, in a one-dimensional semi-infinite medium, considering the absence and existence of cooling, by employing various thermoelasticity theories.…”