Matrix Reinforcement Coefficients Models for Fracture Investigation of Orthotropic Materials

In this paper, the new theory has been3 proposed to investigate the fracture behavior of cracked composite materials. Conforming to this theory, crack is created and distributes in the isotropic matrix. Therefore, contrary to the previous theories related to fracture mechanics of these types of material, which assumes that crack growth occurs in anisotropic homogenous material, the new theory assumes that crack growth occurs in the isotropic matrix, which is affected by fibers in the composite structure of the material. In this approach, fibers are considered as isotropic matrix reinforcements and the reinforcement effects are defined as coefficients in stress state of the isotropic matrix. The coefficients are called reinforcement factors and derived via three different approaches to study the arbitrary crack in 2D materials. Quantifying the reinforcing effects of fibers are conducted when tension across and along fibers and shear loadings exerted on the body. The three methods demonstrate that the reinforcement factors depend on elastic properties, crack growth location and the crack and fiber orientations. However, the method, derived from the micro-mechanic approach, displays their dependence on the fiber volum ratio. Comparing the results of these cofficients with the existing fracture theories illustrates the efficiency and ability of the reinforcement factors in investigation and explanation of the fracture behavior of orthotropic materials.In this paper, the new theory has been3 proposed to investigate the fracture behavior of cracked composite materials. Conforming to this theory, crack is created and distributes in the isotropic matrix. Therefore, contrary to the previous theories related to fracture mechanics of these types of material, which assumes that crack growth occurs in anisotropic homogenous material, the new theory assumes that crack growth occurs in the isotropic matrix, which is affected by fibers in the composite structure of the material. In this approach, fibers are considered as isotropic matrix reinforcements and the reinforcement effects are defined as coefficients in stress state of the isotropic matrix. The coefficients are called reinforcement factors and derived via three different approaches to study the arbitrary crack in 2D materials. Quantifying the reinforcing effects of fibers are conducted when tension across and along fibers and shear loadings exerted on the body. The three methods demonstrate that the reinforcement factors depend on elastic properties, crack growth location and the crack and fiber orientations. However, the method, derived from the micro-mechanic approach, displays their dependence on the fiber volum ratio. Comparing the results of these cofficients with the existing fracture theories illustrates the efficiency and ability of the reinforcement factors in investigation and explanation of the fracture behavior of orthotropic materials.