The normal displacement of a crack surface with arbitrary shape - Zhou, Yong (Engineering fracture mechanics, 1990)
This research has basically solved the problem of determining the normal displacement field of crack surface with arbitrary shape in an infinite elastic body under uniform pressure or more general loads, exactly or approximately. All the solutions for crack problems are originated from a general solution of a two dimensional integro-differential equation which has been found by taking advantage of the constitutive function and the specific expansions. The results show that for the crack whose boundary contour π(θ) has the forms π( θ) = Θ 1(1, cos 2 θ,…, cos 2 kθ) π(θ) = Θ 2(1,¦cosθ¦,…,¦coskθ¦) π(θ) = Θ 3(1,¦sinθ¦,…,|sinkθ¦) and the forms combined by the three cases, exact or approximate solutions of polymonial forms attached √1-( r/ ρ) 2 or other closed forms for the normal displacement of the crack surface can be obtained easily. As on part of the research work, this paper has established a general theory and has given the complete exact solution of an elliptic crack subject to polymonial loads of even and odd powers.