A Direct Energy Balance Approach for Determining Energy Release Rates in Three and Four Point Bend End Notched Flexure Tests

A direct energy balance approach has been developed and used to determine energy release rates in three and four point bend end notched flexure tests. This study was performed in the context of the larger goal of understanding the wide variation in mode II toughnesses that have been obtained by the two tests when used on the same material. The primary motivation for developing the direct energy balance approach was to fully account for the effects of friction, large deformations, and other geometric nonlinearities that occur during these tests. The direct energy balance approach simulates crack advance as it occurs in physical testing. Most significantly, this approach accounts for frictional dissipation that occurs during crack advance, which is an effect that has been neglected in previous analyses of these tests. The direct energy balance approach is used to show that, for most cases of practical interest, the virtual crack closure technique is quite accurate, and predictions by this latter approach are only in error when moderately large geometric nonlinearities occur prior to crack advance. Based on these results, a “cut-off value,” expressed in terms of the maximum slope in the specimen as predicted by classical beam theory, is suggested for the upper limit of applicability of the virtual crack closure technique.