The interaction of fracture mechanics and material failure through a size effect is modeled in ABAQUS with IM7-8552 fiber reinforced laminated composite plates. The model uses a cohesive zone to model fracture in the finite element program ABAQUS to predict peak loads in double-edge notched compression specimens using IM7-8552 cross ply laminated composite plates. The formulation of the model uses previous work that provides a numerical solution for the fracture toughness curve of the material and a procedure to superpose cohesive elements to obtain a bilinear cohesive softening behavior that has been shown to better approximate the fracture properties for composite materials loaded in tension. The model is calibrated using a curve fitting of the bilinear approximation to the fracture toughness curve and applying the resulting parameters to the finite element model. The results from the model are then compared to recorded data obtained through experimental work performed at NASA Langley Research Center to demonstrate the viability of the presented procedure. The model with bilinear softening underpredicts the experimental strength with an average difference of 4.7%. The model is also able to capture the size effect that is observed well. However, when compared to a model that implements a linear softening cohesive law, the bilinear softening model shows minimal improvement over the linear softening model.