Orthotropic semi-infinite medium with a crack under thermal shock

A cracked orthotropic semi-infinite plate under thermal shock is investigated. The thermal stresses are generated due to sudden cooling of the boundary by ramp function temperature change. The superposition technique is used to solve the problem. The crack problem is formulated by applying the thermal stresses obtained from the uncracked plate with opposite sign to be the only external loads on the crack surfaces as the crack surface tractions. The Fourier transform technique is used to solve the problem leading to a singular equation of the Cauchy type. The singular integral equation is solved numerically using the expansion method. The influence of the material orthotropy on the stress intensity factors is shown by comparing the results obtained for different orthotropic materials and isotropic materials in the case of plane stress. The numerical results of the stress intensity factors are demonstrated as a function of time, crack length, location of the crack and the duration of the cooling rate.