Thermal stress near tip of crack terminating at interface in dissimilar materials
Inoue Tadanobu; Hojo Masaki; Ochiai Shojiro
Abstract:The plane problem of a crack terminating at an interface in dissimilar materials subjected to thermal loading is considered. The thermal stresses near the crack tip are theoretically derived using the Airy stress function through the Mellin transform, and those are represented by a linear combination of the singular solutions of type rp-1 and rp-1log r, the no singularity solutions and the particular solutions which are independent of distance r from the crack tip. Then, the solutions are determined from roots (a real root, a complex root and a double root) of an eigen equation and unknown functions which depend on the wedge angles of the materials, their mechanical properties and the root. When the root is a double root, the singular solution of type rp-1log r, together with the singular one of type rp-1, appears in the thermal stresses. The appeared order and variation of the root are shown on the k12 (stiffness ratio) - y1 (wedge angle of material 1) plane. Key Words:composite material, elasticity, thermal stress, crack problem, stress intensity, theoretical analysis