Fracture mechanics and optimization — a useful tool for fibre-reinforced composite design

This paper will demonstrate the application of fracture mechanics and optimization techniques for the optimum design of fibre-reinforced composite laminates (FRC). First, a boundary-value problem of a cracked composite laminate is solved within the framework of linear elastic fracture mechanics (LEFM). The solution relates the stress intensity factor at a crack tip and the crack-induced interfacial stresses to the laminate configuration. These results are then used in two types of the optimum design of fibre-reinforced composite laminates. In the first type of optimum design, namely a crack-insensitive design of the laminate, the crack driving force and interfacial principal tensile stress are both minimized by using single- and multicriterion optimization techniques. The second type of optimum design involves in situ strength design of multidirectional angle-ply laminates. In this case, a set of in situ strength parameters are proposed based on theoretical analysis and experimental observations. This optimization problem is a min {max} one and non-differentiable. A proper treatment of the non-differentiability is introduced and the min {max} optimization problem is converted into a differentiable single-criterion one using the bound-formulation technique. All the optimization problems are solved by non-linear mathematical programming. The results show that optimization can greatly enhance the load carrying capacity of the laminates.