THE EQUIVALENT ELASTIC CRACK .2. X-Y EQUIVALENCES AND ASYMPTOTIC ANALYSIS

The use of crack growth resistance curves (R-DELTAa) to predict the be haviour of cracked specimens is a well-established practice for cerami cs and materials. In Part 1 of this work, the authors showed that the use of R-DELTAa curves may imply a certain elastic equivalence between an actual specimen governed by a cohesive crack model and a virtual e quivalent linear elastic specimen. Part 1 included the analysis of cer tain classes of equivalences (P-Y equivalences) where the loads acting on the actual and on the equivalent specimen were forced to be equal. This paper analyzes more general equivalences in which two arbitrary variables X and Y are forced to be identical in the actual and in the equivalent specimens. In particular, the J-CTOD equivalence and the si ze-effect-based equivalence put forward by Bazant are analyzed. The fi rst part of the paper deals with the bases and general applicability o f these equivalences. The second part presents the results of asymptot ic analyses intended to assess the applicability of the equivalences t o specimens of relatively large size.