Data-driven evaluation of the Paris’ law parameters in polyethylene pipe grades — Increasing the precision of fracture mechanical lifetime estimation

The Paris’ Law parameters $A$ and $m$ are a necessity for predicting lifetimes of structural components under static or fatigue loading that fail due to crack initiation and propagation. Conventional methods require measurements of crack growth kinetics that involve direct or indirect monitoring of physical crack extension during long-term experiments. Usually, measurement series also involve multiple specimens in order to obtain a crack growth controlled failure diagram of an investigated material under relevant load conditions. In this contribution a combination of simple numerical, statistical and analytical approaches is presented to obtain $A$ and $m$ without the need to measure actual crack growth. This is accomplished by reformulating the Paris’ Law to express $A$ as a function of $m$. The parameter $m$ is varied within a reasonable range to generate an analytical function for $A$ that solves the equation of the Paris’ Law based lifetime for a single specimen. A subsequent superposition of all available specimens reveals an intersection of all $A$ functions at the technically relevant pair of $A$ and $m$ values that are capable of describing the lifetime of all specimens with a minimum error. The obtained best-fitting $A$ and $m$ are in good agreement with literature and are able to predict the lifetime of previously published sample data based upon cyclic Cracked Round Bar test results with an average error of 3.30 ± 2.67%.