The application of advanced composite materials, such as graphite/epoxy, has been on the rise for the last four decades. The mechanical advantages, such as their higher specific stiffness and strength as compared to monolithic materials, make them attractive for aerospace and automotive applications. Despite these advantages, composites with brittle fibers have lower ductility and fracture toughness than monolithic materials. One way to increase the fracture toughness of composites is to have a weak fiber-matrix interface that would blunt crack tips by crack deflection into the interface and hence enhance fracture toughness. However, this also reduces the transverse properties of the composite. Therefore, an optimum fiber-matrix interface would be the one that is just weak enough to cause crack deflection into interface. This study investigates the effect of fiber-to-matrix moduli ratio, fiber-volume fraction, fiber orthotropy, and thermal stresses on the possibility of crack deflection. A finite element model is used to analyze a 2-D axisymmetric representative volume element- a three-phase composite cylinder made of fiber, matrix, and composite. A penny shaped crack is assumed in the fiber. To determine whether the crack would deflect into the interface or propagate into the matrix, maximum stresses at the fiber-matrix interface and in the matrix are compared to the interface and matrix strengths. As opposed to most studies in the literature, this study found that fiber-volume fractions do have an impact on crack deflection and this impact increases with large fiber-to-matrix moduli ratios. The presence of orthotropic fiber in the composite increases the possibility of crack deflection with increasing fibervolume fraction in the early and middle stages of the fiber crack growth. The thermal stresses decrease the likelihood of crack deflection when the thermal expansion coefficient of the matrix is larger than that of the fiber.