A stress intensity factor solution for a cracked slab subjected to an arbitrary thermal shock on one surface has been derived. As a first step, the transient temperature distribution was calculated for an arbitrary surface loading through the use of Duhamul’s integral relationship and the unit response for a slab that is insulated on the other face. The arbitrary nature of the transient surface loading was accommodated by a versatile polynomial containing both integral- and half-order terms. Once the resulting transient stress states were determined via elasticity theory, the resulting stress intensification for an arbitrary crack was approximated using a weight-function approach. The procedure was checked with known stress intensity solutions for an edge-cracked plate subjected to a linear down shock followed by a constant temperature soak. Excellent agreement was observed for this test case for a variety of crack lengths.
Mode-I Stress-Intensity Factors for a Cracked Slab Under an Arbitrary Thermal Shock
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Segall, A. E., and Meeker, J. (June 1, 2006). "Mode-I Stress-Intensity Factors for a Cracked Slab Under an Arbitrary Thermal Shock." ASME. J. Pressure Vessel Technol. May 2007; 129(2): 306–312. https://doi.org/10.1115/1.2716435
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