On an elliptic crack embedded in an anisotropic material

A generalized Strohʹs formalism for three-dimensional anisotropic elasticity is applied to study the elliptic crack problem. The traction on the crack plane is expressed in a simple one-dimensional integral. The integrand contains one of the Barnett±Lothe tensors which can be calculated directly from the elastic constants. It is shown that with respect to a local coordinate system, the traction on the crack plane and relative crack face displacement in the vicinity of the crack edge have the same form as their two-dimensional counterparts. A systematic method to derive the stress intensity factors for polynomial loadings is discussed. Explicit results are given for constant, linear and quadratic loadings.