Interaction of a parallel circular cracks subjected to arbitrary loading in transversely isotropic elastic space

Abstract

The complete solution to the penny shaped crack problem, obtained previously by the author, in combination with the reciprocal theorem, is being used for derivation of the governing integral equations for the title problem. The derived set of equations is non singular and can be solved numerically with desired degree of accuracy. An approximate analytical solution is suggested for the general case. The case of two qua1 coaxial cracks under axisymmetric loading is considered in detail. The problem reduced in this case to just one integral equation which is non singular and can be solved by any regular method. The numerical results in this case are in agreement with those of Ufliand.

The practical utility of the derived results goes well beyond just the crack interaction. The governing equations can be used to describe, for ezample, interaction of cracks with inclusions. Yet another application to use governing equations to describe interactions inside a half space. This can be achieved by designating one of the cracks stress free, placing it in the plane z = 0, and then extending its radius to infinity. In a similar vein, we may consider cracks inside an elastic plate. We need here to designate two stress free cracks and then to extend their radius to infinity. In the case of isotropy, the method is applicable to intersecting cracks, so we can solve problems in finite elastic bodies by presenting them as cut outs from a full space by several infinite cracks, for example, an elastic parallelepiped can be produced by 6 intersecting cracks

Keywords:

• linear elasticity
• crack interactions
• reciprocal theorem
• integral equations
• stress intensity factors