A simple viscoelastic model for fatigue crack propagation in polymers as a function of molecular weight

A simple theory is presented to explain the strong influence of molecular weight (M) on rates of fatigue crack propagation (FCP) in amorphous polymers. It is proposed that the equation describing FCP rates may be expressed as the product of two functions, one involving the stress intensity factor (ΔK), and the other characterizing the relaxation process occurring in the plastic zone. To provide a physical network in the plastic zone that can sustain fatigue loading, it is proposed that one needs a sufficient fraction of molecular fibrils per unit area ($\text{W1}$) whose lengths are greater than M_c, the critical value of M required for entanglement. This effect can be summarized as a generalized rate process (confined at the plastic zone) expressed by A exp (Bσ) where σ is a stress and A and B are constants (B including the volume of activation). It is deduced that M influences the activation volume through the values of $\text{W1}$ and W, the weight fraction of molecules whose M>M_c. Using the equation developed it was possible to correlate FCP data of PVC and PMMA as a function of M with a high degree of confidence. Also, the value of activation volumes obtained compared favourably with those in the literature for static tests. The complementary value of $\text{W1}$ for these polymers was also seen to approximate closely to the void fraction in a craze. Extension to other cases such as semi-crystalline materials also seems possible.