Reliability analysis of mechanical components containing random flaws

Abstract

The goal of structural reliability is to assure that a structure adequately performs its intended function when operating under specified environmental conditions. The major source of unreliability is the variability that characterizes engineering structures subjected to inherent randomness in material properties, loading and geometrical parameters. A sensible approach to structural reliability must be able to evaluate and control the effects of this variability, quantifying the uncertainties in the design variables and measuring their impact on the strength of the final product. The objective of this research is to assess the role that uncertainties in material microstructure, in particular concerning the presence of defects such as pores, inclusions and through-thickness cracks, have in the failure of engineering structures. For this purpose, a computational procedure, based on the coupled use of Finite Element Analysis and Monte Carlo simulation, is proposed to evaluate the failure probability of complex mechanical components containing random flaws. The proposed methodology is particularly suited for the structural design of ceramic components, whose strength properties are significantly affected by the presence of microstructural defects. Material flaws are modelled by a population of volume-embedded micro-cracks characterized by different geometrical features and size distributions. For each population the number of flaws is assumed to follow a homogenous Poisson process and flaws are sampled with a uniform spatial distribution and a random orientation. The interaction of a crack with the stress field produced in the component by the applied load is determined through a mixed-mode fracture criterion. Several solutions have been compared in this respect. The study conducted clearly shows how the application of a traditional deterministic approach may lead to incorrect conclusions. Due to the stochastic nature of the flaw distribution, failure of a component may not be initiated at the point of highest nominal stress. The whole component volume contributes to the total probability of failure and therefore the entire stress field must be considered. Moreover, the sensitivity analysis carried out indicates that the parameters controlling the failure process are strictly dependent on loading conditions. In particular, a significant difference in behaviour between uniform and non-uniform stress states was identified. A new failure criterion for brittle materials is also proposed. The criterion is based on the maximum admissible individual probability of failure and is applicable to biaxial stress conditions.