Constraint effects on probabilistic analysis of cracks in ductile solids

Abstract

This paper presents a method for evaluating constraint effects on probabilistic elastic-plastic analysis of cracks in ductile solids. It is based on fracture parameters J and Q, correlation between Q and J-resistance curve of the material, and J-tearing theory for predicting fracture initiation and instability in cracked structures. Based on experimental data from small-scale fracture specimens, correlation equations were developed for fracture toughness at crack initiation and the slope of the J-resistance curve as a function of constraint condition. The random parameters may involve crack geometry, tensile and fracture toughness properties of the material, and applied loads. Standard reliability methods were applied to predict probabilistic fracture response and reliability of cracked structures. The results suggest that crack-tip constraints have little effect on the probability of crack initiation. However, the probability of fracture instability can be significantly reduced when constraint effects are taken into account. Hence, for a structure where some amount of stable crack-growth can be tolerated, crack-tip constraints should be considered for probabilistic fracture-mechanics analysis.