Abstract
We construct a model for a craze preceding a crack, with fibrils which are work-hardened, except for a small active (α) region (of thickness Δ) near the ends of each fibril. In this active region, ductile deformations take place. The ultimate fibril (nearest to the crack tip) is exposed to a high stress σ1 as pointed out by Brown. In one regime, discussed by Brown, the fibril breaks where σ1 reaches a threshold for chemical scission. In another regime, we propose here that the thickness Δ increases with σ1 up to a point where Δ becomes larger than the size of a (distorted) coil inside the fibril: then there remain no chains connecting the bulk glassy polymer to the work-hardened region: the β region yields by plastic flow. This leads to a fracture energy GIC scaling roughly like M2, provided that the molecular weight M be smaller than a certain limit M* above which chain scission dominates. The same ideas can be applied to the healing experiments of Kausch and others. In the chain scission regime, we do expect GIC ∼ t1/2 (where t is the healing time) provided that, in both the original blocks, chain ends were attracted to the surface of the block.