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.
Issue Section:
Brief Notes
1.
Joseph
, D. D.
, and Preziosi
, L.
, 1989
, “Heat Waves
,” Rev. Mod. Phys.
, 61
(1
), p. 41
41
.2.
Sternberg
, E.
, and Chakravorty
, J.
, 1959
, “On Inertia Effects in a Transient Thermoelastic Problem
,” ASME J. Appl. Mech.
, 26
, p. 503
503
.3.
Gladysz
, J.
, 1985
, “Propagation of a Plane Wave in a Thermoelastic Half-Space Under Smooth Heating of Its Boundary
,” J. Therm. Stresses
, 8
, p. 227
227
.4.
White
, R.
, 1963
, “Generation of Elastic Waves by Transient Surface Heating
,” J. Appl. Phys.
, 34
(12
), p. 3559
3559
.5.
Boley, B., and Weiner, J., 1960, Theory of Thermal Stresses, John Wiley and Sons, New York, p. 54.
6.
Bushnell
, J.
, and McCloskey
, D.
, 1968
, “Thermoelastic Stress Production in Solids
,” J. Appl. Phys.
, 39
(12
), p. 5541
5541
.7.
Mozina
, J.
, and Dovc
, M.
, 1994
, “One-Dimensional Model of Optically Induced Thermoelastic Waves
,” Mod. Phys. Lett. A
, 8
(28
), p. 1791
1791
.8.
Galka
, A.
, and Wojnar
, R.
, 1995
, “One-Dimensional Dynamic Thermal Stresses Generated in an Elastic Half-Space by Laser Pulses
,” J. Therm. Stresses
, 18
, p. 113
113
.9.
Boley
, B.
, and Tolins
, I.
, 1962
, “Transient Coupled Thermoelastic Boundary Value Problems in the Half-Space
,” ASME J. Appl. Mech.
, 29
, p. 637
637
.10.
Kao
, T.
, 1976
, “On Thermally Induced Non-Fourier Stress Waves in a Semi-Infinite Medium
,” AIAA J.
, 14
(6
), p. 818
818
.11.
Wang
, X.
, and Xu
, X.
, 2001
, “Thermoelastic Wave Induced by Pulsed Laser Heating
,” Appl. Phys. A: Mater. Sci. Process.
, 73
, p. 107
107
.12.
Ko¨rner
, C.
, and Bergmann
, H. W.
, 1998
, “The Physical Defect of the Hyperbolic Heat Conduction Equation
,” Appl. Phys. A: Mater. Sci. Process.
, 67
, p. 397
397
.13.
Carslaw, H., and Jaeger, J., 1959, Conduction of Heat in Solids, Oxford Clarendon Press, London, p. 75.
14.
Kaufman, R., 1966, Table of Laplace Transforms, W. B. Saunders, Philadelphia, PA.
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