Craze fibril formation and breakdown

As crazes grow in areal extent they also increase in width. The areal growth involves craze tip advance which has been shown to occur by the Taylor meniscus instability. Craze widening, at least for air crazes, occurs by drawing more fibrillar material from the craze‐bulk polymer interfaces at essentially constant extension ratio. Simple arguments will be given to predict the scale of the fibrillation in terms of the stress S at the craze tip and interfaces and an effective polymer surface energy (Γ) where: which assumes that all entangled chain crossing the surface are broken [γ represents the van‐der‐Waals (intermolecular) surface energy, d is the entanglement mesh size, vE is the entanglement density, and Ub is the energy required to break a single backbone bond]. These arguments also give the rate of fibrillation as a function of S, a nominal plastic resistance σy and Γ and can explain the fact that the stress for crazing increases relative to that for shear deformation as the entanglement density of the polymer is increased. The geometrically necessary entanglement loss (either by scission as assumed above or by disentanglement‐ at temperatures just below Tg) that accompanies fibril formation has important consequences for fibril stability. The probability p that a given entangled chain is lost can be computed from simple geometrical considerations knowing the fibril diameter D, its extension ratio λ and the mesh size d; p increases rapidly as Dλ½ becomes comparable to or less than d. These concepts can be tested in blends of high molecular weight polymer with chains of the same polymer that are too short to entangle.