TABLE OF CONTENTS Using the Hutchinson [3 5] theory of fracture for embedded process zones (EPZs), such as crazes at crack tips, the fracture energy is approximated using the J-integral approach as shown earlier in Figure 6.1. The EPZ model addresses small-scale yielding at the crack tip and describes the work of separation as a function of deformation rate, yield stress, and the stress integral as a function of displacement ?, in the zone. The vector percolation model describes the maximum stresses attainable in the deformation zone. However, the crack opening displacement ? is determined by the drawability or ductility of the entangled matrix, as described by Kramer et al. [44, 45]. This process is exceedingly complex, and for polymers, it involves the non-Newtonian flow and plastic deformation of the strain-hardened, craze-like material in the zone. The craze fibrillar structure evolves from a combination of Saffmann-Taylor meniscus finger instability, combined with cavitation processes, depending on the rate and the molecular weight, as discussed in [1]. Most materials exhibit the craze-like fibrillar structure under dilatational plane-strain conditions. The microstructure of crazes formed from entangled amorphous polymers was well described by Kramer and Berger [45] and Kambour [46]. Thus, the deformation zone initiates when the stress field at the crack tip exceeds the yield stress, ? y, and propagates with increasing traction stresses ?, up to the maximum stress ?*. Bjerke and Lambros...
