On the equivalence between semiempirical fracture analyses and R-curves

The relationships between several semiempirical fracture analyses (Brockrath and Glassco, 1974; Newman, 1973; Kuhn, 1968; Orange, 1971; Feddersen, 1971) and the R-curve concept of fracture mechanics are examined. Some characteristics of the R-curve concept when applied to finite-width specimens are reviewed, and conditions for equivalence between a semiempirical analysis (SEFA) and an R-curve are derived. The relationship between R-curves and SEFAs is studied for a hypothetical material. It is shown that for each SEFA there is an equivalent R-curve, the magnitude and shape of which are determined by the SEFA formulation and parameters, and which predicts precisely the same relationship between fracture stress and original crack length. A given SEFA correlates residual strength data closely if its equivalent R-curve closely matches the actual R-curve of the material studied. The SEFA given by Newman is found to yield best results for the hypothetical case considered. Equivalent R-curves for real materials are developed using data from the literature.