Fracture of Highly Elastic and Composite Materials in Compression Along Near-Surface Crack

A problem of the fracture of a semi-infinite body with a penny-shaped crack located near the surface of the body under compressive loading along the crack was considered. It is assumed that the fracture process under such loading scheme is initiated by a local buckling of a part of the material adjacent to the crack. The case of a short distance between the surface of the body and the crack plane was analyzed. To study this problem, the approach in the framework of 3D linearized theory of stability of deformable bodies was applied. The technique based on Bubnov–Galerkin method to investigate resolving Fredholm integral equations of the second kind was also used. The critical (limiting) loading parameters corresponding to the local buckling of the material in the cracks vicinity under compression were calculated for some types of highly elastic materials and composites. The dependence of these critical parameters on the distance between the surface of the body and the crack plane was studied. The results obtained give the possibility to evaluate the applicability limits of the approximate approach, so called “beam approximation”, in the analysis of this problem.