Abstract
Stress intensity factors are determined for a crack in an infinite orthotropic layer. The crack is situated parallel to the plane surfaces of the layer. Stresses are solved for two kinds of the boundary conditions with respect to temperature field. In the first problem, the upper surface of the layer is heated to maintain a constant temperature T 0, while the lower surface is cooled to maintain a constant temperature −T 0. In the other problem, uniform heat flows perpendicular to the crack. The surfaces of the crack are assumed to be insulated. The boundary conditions are reduced to dual integral equations using the Fourier transform technique. To satisfy the boundary conditions outside the crack, the difference in temperature at the crack surfaces and differences in displacements are expanded in a series of functions that vanish outside the crack. The unknown coefficients in each series are evaluated using the Schmidt method. Stress intensity factors are then calculated numerically for a steel layer that behaves as an isotropic material and for a tyrannohex layer that behaves as an orthotropic material.
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References
Atkinson, C. and Clements, D.L. (1977). On some crack problems in anisotropic thermoelasticity. International Journal of Solids and Structures 13, 855–864.
Baoxing, C. (1995). Orthtropic thermoelasticity problem of an antisymmetric heat flow disturbed by three coplanar cracks. International Journal of Fracture 70, 267–273.
Baoxing, C. and Xiangzhou, Z. (1988). Thermoelasticity problem of an orthotropic plate with two collinear cracks. International Journal of Fracture 38, 161–192.
Baoxing, C. and Xiangzhou, Z. (1993). On plane thermoelasticity problem of an orthotropic strip with two collinear cracks. Journal of Northwestern Polytechnical University 11, 121–126.
Baoxing, C. and Xiangzhou, Z. (1994). Orthotropic thermoelasticity problem of symmetrical heat flow disturbed by three coplanar cracks. International Journal of Fracture 67, 301–314.
Itou, S. and Haliding, H. (1997). Dynamic stress intensity factors around two parallel cracks in an infinite orthotropic plane subjected to incident harmonic stress waves. International Journal of Solids and Structures 34, 1145–1165.
Nowinski, J.L. (1978). Theory of Thermoelasticity with Applications. Sijthoff and Noordhoff, The Netherlands.
Tsai, Y. M. (1984). Orthotropic thermoelastic problem of uniform heat flow disturbed by a central crack. Journal of Composite Materials 18, 122–131.
Tsai, Y.M. (1986). Thermal stress in an orthotropic plate containing a pair of coplanar central cracks. Journal of Thermal Stresses 9, 225–235.
Yau, W.F. (1967). Axisymmetric slipless indentation of an infinite elastic cylinder. SIAM Journal on Applied Mathematics 15, 219–227.
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Itou, S. Thermal stress intensity factors of an infinite orthotropic layer with a crack. International Journal of Fracture 103, 279–291 (2000). https://doi.org/10.1023/A:1007630808737
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DOI: https://doi.org/10.1023/A:1007630808737