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.

高密度聚乙烯管道在使用条件下的主要失效方面是管道壁内的初始缺陷导致的不连续缓慢裂纹扩展（DSCG）。在本研究中，理论上通过建立偏心裂纹的裂纹层扩展模型来模拟内部偏心裂纹的DSCG动力学。本模型精确地模拟了偏心裂纹的实验DSCG动力学，并且还准确地估计了最终的失效时间。此外，为了研究与初始裂纹相关的不确定性的DSCG主导失效的可靠性，对由于初始裂纹尺寸的概率分布而导致的寿命分布进行了随机研究。此外，使用Birnbaum-Saunders（BS）分布函数和最大似然估计方法对整个初始裂纹位置，大小和所施加的应力进行寿命分布拟合。BS函数准确地描述了模拟的寿命分布，并给出了用于估算BS函数的尺度和形状参数的方程，这些方程涉及各个裂纹位置和远程应力水平下的初始裂纹分布。