Probabilistic fracture mechanics

Abstract

This paper develops the methodology for probabilistic fracture mechanics analysis (PFM) of structural components with crack-like imperfections. Details are given for the development and application of both a simple nomographic method and a basic numerical tool for PFM applications. The tool is a computer program that uses Monte-Carlo simulation to predict the probability distribution of a structural performance parameter from known distributions of input parameters used to model the problem. The structural performance parameter might be the strength margin (strength minus stress), the life ratio (actual fatigue life divided by design fatigue life), or any other relevant model of the failure modes. Two illustrative applications based on linear elastic fracture mechanics are included to demonstrate the utility of PFM to problems of interest to the electric power generation industry. The first example selects the mean yield strength of an alloy in order to minimize the probability of failure for a hypothetical component with two failure modes, yielding and brittle fracture. The example shows that no single value of mean yield stress or of yield-related safety factor, such as specified as part of conventional engineering practice, suffices to minimize failure for all combinations of working stress and flaw size distribution. PFM analysis is required to compute the optimum value of mean yield stress for a given working stress and material quality (flaw size distribution). A second example is presented for which the residual life of a turbine rotor is assumed to be related to three parameters. The parameters are applied stress, material crack growth rate, and initial flaw size. Known variations of the input parameters are translated into variations in residual life. The residual life distribution is required to formulate improved fatigue design criteria. The effects on the turbine life distribution of mutual interdependence of the input random variables and of finite crack initiation life are examined. The second example points out the need for and current unavailability of required input data. It is recommended that data collection efforts be increased to quantify the variational characteristics of the required input parameters, as well as mean, typical, or worst-case values.