Proposal of An Approximate Analytical Expression of Maximum Energy Release Rate of A Mixed Mode Crack in Relation to Reliability Evaluation of Ceramic Components

Abstract

Use of some mixed mode fracture criterion becomes necessary when reliability evaluation of ceramic components is made based on flaw distributions, since most components are subjected to multi-axial stresses in service conditions. The maximum energy release rate criterion is one of the wellknown criteria for mixed mode fracture. In the case of a mixed mode crack, the energy release rate, G, takes a maximum value, G_max, when the crack extends in a certain direction. The maximum energy release rate criterion (G_max criterion) assumes that unstable crack extension occurs when G_max reaches a certain critical value. Unfortunately, a reliable analytical expression of G_max in terms of the stress intensity factors has not yet been obtained. This is an obstacle to analytical treatments based on G_max criterion. Thus, it was attempted in this paper to derive an analytical expression of G_max for a two-dimensional crack. The approximate analytical expression G_max=(K_I²+3K_II²+K_I√K_I²+6K_II²)/2E' was obtained, where K_I(>0) and K_II are the mode I and mode II stress intensity factors, and E'=E for plane stress and E'=E/(1-ν²) for plane strain with E and ν being usual elastic constants. From comparison of this expression with the exact value of G_max evaluated numerically, it was shown that the proposed expression is quite accurate. It was also shown that the expression of G_max given by Hellen and used by Lamon for reliability evaluation of ceramic components is not adequate.