fails by chain pullout rather than by chain scission this transition can be shifted to higher values of areal density Σ† or suppressed altogether[4]. The degree of polymerization of the block where this starts to occur is of the order of the average degree of polymerization between entanglements Ne. Therefore a reasonably good picture of the fracture mechanisms is given by a plot of Σ/Σ∗ as a function of N/Ne as shown on figure 2[1]. The limiting value for Σ, which we will define as Σsat is a decreasing function of N for steric reasons so that maximum values of Gc are typically obtained for values of N/Ne between 4 and 8. Σ/Σ∗ N/Ne 1 1 simple chain pullout simple chain scission 4-5 crazing failure mostly by chain pullout crazing failure by by chain scission Σsat/Σ∗ Σ†/Σ∗ Figure 2: Fracture mechanisms map for interfaces between glassy polymers reinforced with connecting chains. Failure mechanisms are represented as a function of normalized degree of polymerization N/Ne and normalized areal density of connectors Σ/Σ∗ . CRAZE GROWTH AND STABILITY In the regime where fracture of the interface is preceded by a craze, the fracture toughness can be related to the interfacial stress with the help of a model recently proposed by Brown for crack growth in a craze[5]. The key features of the model are the description of the craze zone as an elastic anisotropic strip with a local stress concentration at the crack tip. The larger the stress that the interface can sustain and the larger will be the amount of elastic energy needed in the strip for the crack to propagate. Since this amount of elastic energy is directly proportional to the width of the craze, we now have a direct connection between the maximum width of the craze hf and the interfacial stress. Remembering that the macroscopic Gc is given for such a strip model by[6]: Gc ~ σcraze hf A direct connection can be made between Gc and the interfacial stress. The final result of the model which can be experimentally tested is[5,7,8]: ( ) [ ] { } 2 1 int / ln 1 1.2 − − = σ σ σ δ craze craze c m G (3) which reduces to: craze c σ σ δ 2 int 1.44 m = G (4)
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