On semi-infinite crack problems in elastic-plastic bodies; uniqueness and examples

摘要

First, the conditions for uniqueness of the stress boundary value problem for infinite cracks in elastic-plastic bodies are discussed on the basis of the Laurent series representation of the plastic boundary in an elastic perfectly plastic body in anti-plane strain (mode Ⅲ). Next, for two cases, exact closed-form solutions of the shape of the elastic-plastic boundary are found in terms of elementary functions. A crack under shear stress acting on its surfaces, and a crack under constant remote shear stress σ_(13)~∞ = - p, are considered. In the first case, also the complete stress distribution is obtained, for the second the physical coordinates as functions of stresses are found. The new elastic-plastic solutions are compared with ones predicted by linear elastic fracture mechanics.