Semi-analytical modelling of cracks with interacting faces in isotropic materials under harmonic load

In structural materials the existing cracks often have a nonzero initial opening or a complex shape. Under the consequent dynamic loading the opposite crack faces move with respect to each other and interact. The contact interaction results in the appearance of the contact forces in the contact region and changes significantly the stress and strain distribution near the crack tips. The shape of the contact region will change in time and must be determined as a part of solution. The complexity of the problem is further compounded by the fact that the contact behaviour is very sensitive to the materials of two contacting surfaces and the type of the external loading. Such dependences make the contact problem for crack faces highly non-linear. As the consequence, in the majority of studies the interaction of crack faces was neglected and, therefore, the real stress-strain distribution was ignored due to the difficulties of finding the appropriate solution.

The present work is devoted to the investigation of the contact interaction of the faces of a crack located in the homogeneous, isotropic, linear elastic 3-D medium under harmonic loading. The Signorini contact constraints are imposed and the friction is governed by the Coulomb law.

The problem is solved by the method of the boundary integral equations with the use of the iterative procedure. The solution is refined during the iteration process until the distribution of physical values satisfy the contact constraints. The contact forces and displacement discontinuity on the crack surface are investigated for different wave parameters (frequency, direction, etc) and different values of the friction coefficient. The effect of the parameters on the stress intensity factors is studied. The results are compared with those obtained without allowance for the contact interaction. The significant difference between compared results confirms the crucial importance of taking the crack faces contact interaction into account.