Analytical study of J estimation formulas. Three-point bend specimen and compact specimen.

Rice has reported a simplified method for estimating the J-integral for a deeply cracked bend bar. For a compact specimen, Merkle and Corten have shown a simplified method for estimating the J-integral which is taken into account the axial force. Ohji has also suggested a simplified method for estimating the J-integral for a deeply cracked bend bar. In this study, the relation between the Rice formula and the Ohji formula for a three-point bend specimen is analytically studied. J-estimation formula where is equivalent to Merkle-Corten formula for a compact specimen is also proposed. Results show that the Ohji formula for a three-point bend specimen is equal to the Rice formula. Based on the results, we can conclude that simplified methods for estimating the J-integral from the load and the displacement should be used when the strain hardening exponent is known.