Strain Concentration in Apices of Radial Cracks in a Thin Coated Pipe Wall

Abstract

The well-known discontinuous solution method, used in the study of infinite and semi-infinite domains, is generalised during the construction of solutions in Fourier series. This makes it possible to reduce the problem of the mechanics of a deformable solid for a limited region containing cuts or inclusions to the solution of an integral equation (or system) with respect to discontinuities of the functions being defined. Methods The method was implemented through the application to the solution of the theoretical elasticity problem for a pipe section (plane deformation) weakened by an internal radial crack. The pipe was loaded with hydrostatic pressure and a thin coating is applied on its inner surface, improving its physical and mechanical properties. The applied method, combined with the conventional integral transformation, can be effectively used in the construction of discontinuous solutions of three-dimensional problems of the theory of elasticity. Results Specially formulated boundary conditions were used as a coating model. In order to verify the adequacy of the adopted model, a series of numerical experiments was carried out. In some cases, calculations were carried out for the cross-section of a coated pipe in finite-element ANSYS and COMSOL software packages. In others, benefiting from the extensive capabilities of the FlexPDE software package, an uncoated pipe model was constructed, although using special boundary conditions. Comparison of the results obtained made it possible to ascertain the adequacy of the models constructed across a certain range of geometric and physical parameters. Conclusion The problem is reduced to the solution of a singular integral equation with a Cauchy kernel with respect to the derivative of the jump in the tangential component of the displacement vector on the crack edges. Its solution is determined by the collocation method with a pre-selected feature. The ultimate goal of the study is to determine the values of the strain intensity coefficient at the apices of the crack.