Analytical Study of J Estimation Formulas for Three-Point Bend Specimen : Series A : Solid-Mechanics, Strength of Materials

Rice has shown a simplified method for estimating the J-integral of a deeply cracked bend bar, that is J==2U/Bb where U is the area under the load versus the load point displacement curve, B is the specimen thickness and b is the remaining ligament. It has not been made clear, however, how deep is a deep enough crack for finite size specimens. In this study, an applicable range of the Rice formula for the three-point bend specimen used in the elastic-plastic fracture toughness JIC test is studied analytically. The Rice formula is compared directly with the definition of J as a change in potential energy. Results show that an assumption of a deep crack is required only for a linear elastic material and is not required necessarily for a rigid perfectly-plastic material. In order to obtain the quantitative data, the conditional equation is calculated numerically by varying the crack length for three materials; linear elastic, rigid perfectly-plastic and elastic perfectly-plastic. Results show that the Rice formula is valid when a/Wg0.4 for a linear elastic material. Based on the results, a recommended precrack length of the three-point bend specimen in the JIC test is newly proposed.