Modeling brittle constrained fracture with cohesive zone models

A load-independent parameter quantifying constraint is first defined on the basis of linear elastic fracture mechanics. The apparent fracture toughness and constraint is then computed for center cracked, single edge notch tensile, four point bending and double cantilever beam polymethyl methacrylate specimens of various dimensions. The apparent fracture toughness is shown to decrease with increasing constraint. Using cohesive zone models (CZMs) with rate-independent traction-separation laws of various shapes, it is shown that the constraint has no effect on the loads necessary to advance a crack, unless the cohesive zone length is excessively large. For realistic values of cohesive strength and critical opening displacement, the only relevant parameter is the fracture energy. The analysis is refined by employing a rate-dependent CZM that aims at modeling the craze in front of the crack tip. The rate and pressure dependence of craze initiation is accounted for by combining a rate-independent multiaxial with a rate-dependent uniaxial criterion. Craze growth in width is modeled using a linear spring and a nonlinear viscous element in series. Fibril breakdown is assumed to occur by disentanglement of polymer chains. Shear yielding in the bulk is modeled by the Arruda-Boyce model. The model results are found to be unaffected by the stress at which a craze is initiated. No significant plastic deformation is predicted for any of the explored specimens. Differences in the crack tip fibril stress histories among specimens of various constraints are found to be caused by different loading rates, even for cases where significant plastic deformation occurs. It is thus concluded that the crack tip fibril stress history is independent of constraint, unless the crack is grown over a significant distance