On the Influence of Vibrational Heating on the Fracture Propagation in Polymeric Materials

Abstract

According to the basic concept of S. N. Zhurkov [1, 2], the fracture of solids is a process which takes place in time under any stress and is controlled by certain kinetics due to thermal fluctuations and is strongly affected by temperature and stress. Let us denote the average sample lifetime at temperature T and tensile stress σ by t ₀ = t ₀ (σ, T). For the evaluation of the time of failure t ^*₀ for the case of an alternating stress σ (t), Bailey’s rule of damage summation will be used [3], i.e.

$$\int\limits_0^{t_0^*} {\frac{{dt}}{{{t_0}(\sigma (t),T)}}} = 1$$

((0.1))

following from the assumption that each moment the average rate of the damage process is the same as if the acting stress were constant in time (quasi-stationarity).