Stochastic Study on Discontinuous Slow Crack Growth Kinetics from an Arbitrarily Located Defect of Polyethylene Based on the Crack Layer Theory

The major failure aspect of high-density polyethylene pipes under the service condition is the discontinuous slow crack growth (DSCG) from the initial defects inside the pipe wall. In this study, the DSCG kinetics for an internal eccentric crack is theoretically simulated by developing a crack-layer growth model for an eccentric crack. The present model precisely mimics the experimental DSCG kinetics for the eccentric crack, and it also estimates the final failure time accurately. Furthermore, to investigate the reliability of the DSCG-dominated failure concerning the uncertainties related to the initial crack, a stochastic study on the lifetime distribution due to the probabilistic distribution of the initial crack size is performed. Additionally, lifetime distribution fitting using the Birnbaum–Saunders (B-S) distribution function and the maximum likelihood estimation method is conducted for various initial crack locations, sizes, and applied stresses. The B-S function accurately describes the simulated lifetime distribution, and the equations for estimating the scale and shape parameters of the B-S function with regard to the initial crack distributions at various crack locations and remote stress levels are presented.