The problems of two bonded half planes containing multiple cracks in arbitrary positions and directions is considered.
In order to solve the proposed problem, an elementary solution is presented. Physically, the elementary solution is a particular solution for the bonded half planes containing one crack, and the crack borders are applied by two pairs of concentrated forces and some distributed tractions. Using the proposed elementary solution and taking some density distributions of the elementary solution along each crack as undetermined functions, a system of Fredholm integral equations can be easily established. The SIF values at the crack tips can be easily calculated and several numerical examples are given.
NOMENCLATURE
S + upper half plane S -lower half plane L boundary of two bonded half planes L, crack contour in upper plane (in plane elasticity) 0 &), Y &) principal part of cP,(z), Y,(z), 2 E (S + u L u S -) -L, m,<(z), Y,,(z) complement part of Q,(z), Y,(z). z 6 S-u L Q,(z) = Q, ,p(z) +@,,(z), Y ,(z) = Y ,Jz) +Y Jz) complex potentials (elementary solution) in the upper half plane, ZE (S-" ,5-L, @(z), Y*(z) complex potentials (elementary solution) in the lower half plane, ZE S-u L (in antiplane elasticity) R ,p(z) principal part of Q,(z), z E (S + u L u Sm)-L, Q,,(z) complement part of n,(z), z E S+ u L Q,(z) = R ,p(z) + R &) complex potential (elementary solution) in the upper half plane, z E (S+ v L) -L, Q,(z) complex potential (elementary solution) in the lower half plane, z E S-v L p = exp (28) q = 2ih expm pz + 4 symmetric point of z with respect to the boundary L