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My idealized case involves a sheet of infinite extent in length and width direction, to which a linear thermal gradient in the depth dimension is applied, i.e. deltaT/deltaz=constant. We could express this as T=T1 at z=0 and T=T2 at z=d. The material has a known thermal expansion coefficient alpha and elastic Young's modulus M, so we can calculate the stress induced by the temperature difference - assuming zero stress at the mid-plane, the tensile/compressive stress at the surfaces will be +/- (T2-T1)/2*alpha*M . Now I'd like to know if the material will undergo plastic deformation or brittle fracture as a result of the temperature gradient. I assume that this is much more likely with a steep temperature gradient (such as would be induced by thermal shock) than with a mild gradient - that is if the same temperature difference is imposed across a sheet of thickness 1 mm and a sheet of thickness 1 m, the former would be more likely to fail. But I'm struggling to come up with the formulas that would allow me to calculate shear stress levels that I could compare to the moduli of such failures - where does the thickness come in? It must be simple (I think) - please help!