The antiplane elasticity problem for a functionally; graded coating bo
nded to a homogeneous half space is considered, The coating is assumed
to contain periodic cracks perpendicular to the surface. The problem
is formulated in terms of an integral equation with strongly singular
kernels. Three dimensionless parameters representing the crack depth,
the material nonhomogeneity and the crack periodicity are identified.
In addition to the mode III stress intensity factor calculated by vary
ing these three parameters, the results presented include a qualitativ
e discussion of the question of fracture instability, the effect of pe
riodic cracking on the relaxation of stresses on the coating surface,
and the comparison of the total strain energy released as a result of
surface cracking with that assumed in a simple stress relaxation model
.