Effect of the crack closure in three-dimensional problems for interface microcracks under dynamic loading

The present paper investigates the elastodynamic response of inter-component microcracks in composite materials with the focus on the effect of crack closure leading to contact interaction of the opposite crack faces. The opposite faces of the existing crack interact with each other under dynamic loading, affecting significantly the stress and strain fields. The nature of the contact interaction between two crack surfaces is very complex. The shape of the contact region is unknown beforehand; it changes in time under deformation of the body 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 material properties of two contacting surfaces and the type of the external loading. Such dependences make the contact crack problem highly non-linear. In this study, application of boundary integral equations to the problem of interface microcracks between two dissimilar elastic half-spaces under harmonic loading is discussed in detail. The system of linear algebraic equations is derived for several configurations of cracks and loading schemes in order to solve the problem numerically. The distributions of the displacements and tractions at the interface and the crack surface are obtained and analysed. The stress intensity factors (opening and shear modes) are computed for different values of the wave frequency and different properties of the half-spaces. It is shown that the limiting cases of the obtained solution are in a very good agreement with the analytical static solution for an interface crack and with the numerical dynamic solution for a crack in the homogeneous body.