Cracks in the Framework of Fractional Thermoelasticity

A real solid, as a rule, contains a large number of different type defects: point defectsPoint defect, dislocations, disclinations, slits, inclusions, voids and cracks. Physical processes occurring in solids depend significantly on the presence of such defects. During sudden cooling of a solid, there can arise very high thermal stresses near crack tips. For brittle materials, thermal shock is an important fracture mechanism. The fractional thermoelasticity problems are solved for a plane with a line crackLine crack and for a plane with an external line crack as well as for a solid with a penny-shaped crackPenny-shaped crack and for a solid with an external circular crack under heat flux loading. The solutions are obtained using the integral transforms technique. The displacement potentialDisplacement potential, Airy’s biharmonic function, and Love’s biharmonic function are used. To find the additional stresses which allow satisfying the boundary conditionsBoundary condition at the crack surfaces, the dual integral equations are solved. The temperature field and the thermal stress field are obtained, and the stress intensity factors are calculated for different values of the order of fractional derivative.