Application of the crack compliance method to long axial cracks in pipes with allowance for geometrical nonlinearity and shape imperfections (dents)

Abstract

Application of the crack compliance method to the analysis of thin-walled rings with a radial crack has two features: a crack is considered as a concentrated angular compliance and the deformation of all other sections of the rings is calculated as for a curvilinear beam. The latter can be most conveniently found by the method of initial parameters where the values of generalized forces and displacements at the end of some zone are determined as a linear combination of their values at the beginning of the zone. The goal of the study is to derive and apply the method of initial parameters equations taking into account the influence of circumferential stresses on the ring curvature. As far as the authors know, this is the first time that the stress intensity factor has been derived for an elastic thin-walled pipe with a radial crack in a geometrically nonlinear formulation. Here, an increase in pressure leads to a somewhat slowed increase in the stress intensity factor. In addition, a number of problems for dents are considered. The effect of the dent shape on the stress–strain state is analyzed. An expression for the stress intensity factor for a complex defect, a crack emanating from the dent apex, is presented.