A molecular theory of the fracture toughness of low molecular weight polymers

Abstract

Recent experiments by Robertson show that the fracture toughness G _IC of glassy polystyrene PS does not decrease to the ideal brittle value 2γ (where γ is the surface energy for PS) at molecular weights M _w below M _c the entanglement molecular weight. Instead G _IC is more than an order of magnitude above 2γ at M _c and decreases slowly below M _c. It is postulated that a small craze exists at the crack tip in such low molecular weight glassy polymers. However, since entanglements do not occur single molecules must span this craze; if they do not the craze becomes unstable and the crack advances. Under these conditions a critical craze surface displacement exists and G _C can be computed to be G _IC=S _c(λ−1) 〈R ²〉^1/2, where λ and S _c are the craze fibril extension ratio and craze surface drawing stress observed in high molecular weight crazes (both quantities should be only weak functions of M _w) and 〈R ²〉^1/2 is the root mean square end-to-end distance of the PS molecule in the glass from neutron scattering measurements. The fracture toughness is predicted to decrease as M ^1/2_w ; this prediction and the absolute magnitude of G _IC are in excellent agreement with experiment.