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Thermoelastic Problem for a Griffith Crack in a Plate whose Shear Modulus is an Exponential Function of the Temperature
Author(s) -
Hata T.
Publication year - 1981
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19810610204
Subject(s) - thermoelastic damping , stress intensity factor , exponential function , shear modulus , materials science , shear stress , thermal expansion , mechanics , mathematical analysis , thermal , mathematics , fracture mechanics , thermodynamics , physics , composite material
In this paper, we examine an analysis of thermal stresses taking into account the temperature‐dependent properties, in which the variation of the shear modulus with temperature assumed to be an exponential function. Using the perturbation method, general equations for the displacements are found. The equations can be solved by using four displacement functions. Following this method, a solution is derived for calculating the stress intensity factor for a Griffith crack in a temperature‐sensitive plate under a linear temperature distribution, where we assume that the temperature field is not disturbed by the crack. (Under these conditions, if a plate is temperature‐insensitive, the stress intensity factor for the crack is zero.) In this case, whether the stress intensity factor is zero or not depends only on the temperature variation of the coefficient of thermal expansion. A numerical example is given for a plate made of steel. Results show the effect of temperature‐dependent properties clearly.