Numerical analyses of possible correlation between fracture and the effective stiffness in a brittle solid material

The subject of the present work is micro cracking in brittle materials. The main objective is to examine the hypothesis: does a quantitative correlation exist between progression toward failure and the loss of effective stiffness? This hypothesis is investigated by the development of a computer program to calculate Stress Intensity Factors (SIFs) and effective compliance based on the method of analysis developed by Kachanov (1987, 1993) that assumes non-uniform interaction traction distributions on crack faces can be approximated by stress fields emitted by neighboring cracks loaded with uniform average tractions. Based on a number of case studies involving multiple 2D micro cracks under remote loading conditions, strong fluctuations in SIF were observed resulting from mutual positions among neighboring cracks. In contrast the effective compliance remained essentially unchanged. Therefore monitoring of local quantities (stress concentration, in particular) via volume average properties such as effective stiffness may not be fully reliable, in the sense that stable quantitative correlations between the two properties may not exist.