16 - Locally initiated failure and risk reduction

Abstract

This chapter elucidates the methodology used for determining the locally initiated failure and risk reduction. It discusses the methods developed for specifying the maximum acceptable level of the flaw number density and the maximum size of the stressed volume, which guarantee that the probability of failure initiated by flaws remains below a maximum acceptable level. Powerful equations and efficient algorithms are proposed for determining the probability of failure of loaded components with complex shape, containing multiple types of flaws. The equations are based on the concept of conditional individual probability of initiating failure. This is the probability that a single defect or flaw will initiate failure given that it resides somewhere in the stressed component. The conditional individual probability characterizing a single flaw is estimated by using a Monte Carlo simulation and a failure criterion. This chapter examines a common special case in determining the conditional individual probability, related to globular flaws whose locations follow a homogeneous Poisson process in the volume of the component. By calculating the probability of failure at different loading levels, the lower tail of the strength distribution of any loaded component with internal flaws can be constructed. This chapter describes the method that can be generalized for any system containing a random number of entities or events where failure is initiated locally, from a single entity or event. This chapter presents the equation that can also be generalized for determining the fatigue life distribution of a loaded component whose surface contains manufacturing defects or defects caused by a mechanical damage, with a specified number density, geometry and size distribution.