Mathematical simulation of transverse cut in the fiber of a composite reinforced with unidirectional fibers with linear cohesion cracks

Abstract

In the reviewed paper, the case of a transverse displacement plane with two pairs of biperiodic (corresponding to the X and Y axes) cohesive cracks of unequal size, weakened by biperiodic circular holes, is considered. The circular holes are filled with reinforcing fibers and the surface is covered with a thin homogeneous non-metallic material of the same thickness. In this case, boundary issues between filler and coating, coating and matrix, and boundary issues along cohesion cracks are determined. For both cases, the solution to the problem is sought in the form of an analytical function with complex variables. According to the boundary conditions of the case, a system of unequal algebraic equations is found along the holes, and singular integral equations are constructed along the cohesion cracks. Currently, the singular integral equations are brought to the system of finite linear algebraic equations with the help of mathematical transformations. Both systems are solved together using the Gaussian method and the crack growth is determined using the stress intensity factor formulas at the crack tips. During the solution of the problem, the stress intensity coefficients at the end are found by the variation of the length of the cracks based on the radius of the circular holes.