A generalized solution to the combo-crack problem-II. Remote load

In Part I, we studied the combo-crack problem, which contains an interior penny-shaped crack (PSC) and a coplanar and concentric externally circular crack (ECC), under pressure load applied to the surface of the interior PSC. In fact, a more common type of loading experienced by cracked media might be remote tension normal to the crack plane. For a combo crack under remote tension, a reliable solution remains deficient. In this paper, we extend our discussion to the case of remote tension in the theoretical framework developed in Part I. We for the first time formulate the concerned mixed boundary value problem into a single inhomogeneous Fredholm integral equation, which is then solved numerically with a Gauss-Lobatto quadrature-based algorithm. The normal stress in the ligament (bonded) region on the plane of the crack, the stress intensity factors at the tips of PSC and ECC, and the critical force load for trigging crack propagation are determined, showing an excellent agreement with the finite element results. Our work provides a highprecision numerical solution to the combo-crack problem for the most basic loading case. The obtained results should be of general value to the resolution of a bunch of fracture and adhesion problems in combo-crack configuration in engineering and deserve to be absorbed into the updated handbook for basic crack problems.

Automated summary

This study extends the discussion of the combo-crack problem to the case of remote tension and formulates the related boundary value problem into a single inhomogeneous Fredholm integral equation. Numerical solutions are obtained using a Gauss-Lobatto quadrature-based algorithm, and the results show excellent agreement with finite element results.