A stochastic equation for predicting tensile fractures in ductile polymer solids

The statistical fracture behavior of isotactic polypropylene solids under different tensile speeds at room temperature was investigated. Tensile tests were performed more than one hundred times at different tensile speeds, and the statistical data, such as the time to break, the ultimate stress, and the tensile toughness were examined as a function of crosshead speed. All probability distribution curves of fracture time, ultimate stress, and tensile toughness followed Gaussian statistics approximately. With increasing tensile speed, the fracture time tended to decrease and the mean ultimate strength increased, whereas the toughness was independent of the tensile speed. We found an analogy in the mathematical mechanism between the ductile fracture of polymer solids and particle Brownian diffusion.