A procedure for superposing linear cohesive laws to represent multiple damage mechanisms in the fracture of composites

The relationships between a resistance curve (R-curve), the corresponding fracture process zone length, the shape of the traction-displacement softening law, and the propagation of fracture are examined in the context of the through-the-thickness fracture of composite laminates. A procedure for superposing linear cohesive laws to approximate an experimentally-determined R-curve is proposed. Simple equations are developed for determining the separation of the critical energy release rates and the strengths that define the independent contributions of each linear softening law in the superposition. The proposed procedure is demonstrated for the longitudinal fracture of a fiber-reinforced polymer-matrix composite. It is shown that the R-curve measured with a Compact Tension Specimen test cannot be predicted using a linear softening law, but can be reproduced by superposing two linear softening laws.