On One Approach in Fracture Mechanics of Composites with Parallel Cracks Under the Action of Initial (Residual) Stresses

The paper presents a novel approach that allowing one the unified consideration of the problems of composite materials fracture by taking into account the initial (residual) stresses acting along cracks and the fracture of composites in compression along cracks. This methodology is based on the relations of linearized mechanics of deformable solid bodies. Its use was exemplified by investigating spatial axisymmetric problems for certain laminar and fibrous composites containing periodic arrays of parallel coaxial mode I, II, and III cracks. These composites are modeled within the homogenization approach with transversely isotropic materials. Corresponding boundary-value problems were reduced to paired (dual) integral equations and then to resolving Fredholm integral equations of the second kind, which permit an efficient numerical investigation. The influence of initial (residual) stresses on stress intensity factors in the vicinity of cracks was analyzed. With reliance on the approach proposed, from the numerical results obtained in the study of non-homogeneous boundary-value problems on pre-stressed bodies containing cracks, the critical loading parameters corresponding to the beginning (start) of the process of materials fracture under compression of the bodies along parallel cracks were determined. The dependences of these critical loading parameters on geometric parameters of the problems, as well as material mechanical characteristics were investigated.