MICROMECHANICS OF CRACK-GROWTH INTO A CRAZE IN A POLYMER GLASS

The problem of craze failure near the tip of a crack embedded inside a craze is investigated in this work. Our micromechanics model is based on the presence of cross-tie fibrils in the craze microstructure. These cross-tie fibrils give the craze some small lateral load-bearing capacity so that they can transfer stress between the main fibrils. This load-transfer mechanism allows the normal stress on the fibrils directly ahead of the crack tip in the center of the craze to reach the breaking stress of the chains. An exact solution is obtained for the deformation field near the crack tip, and this solution is used to relate craze failure to the external loading and microstructural quantities such as the draw stress, the fibril spacing, and the chain breaking force. The relationship between energy flow to the crack tip due to external loading and the work of local fracture by fibril breakdown is also obtained. Our analysis shows that the normal stress-sigma(n) acting on the fibrils at the crack tip increases linearly as the square root of the craze thickness assuming that the normal stress distribution is uniform and is equal to the drawing stress acting on the craze-bulk interface. However, our result shows that sigma(n) is very sensitive to the stress distribution at the craze-bulk interface so that the assumption of a constant draw stress acting on the craze-bulk interface ahead of the crack tip may underestimate sigma(n). We also derived an approximate expression which relates the shear and tensile modulus of the crazed material to the underlying microstructural variables such as fibril spacing and fibril diameter.