Wide range compliance of chevron-notched three-point bend round bars based on slice synthesis method

Abstract

The chevron-notched three-point bend (3PB) round bars ( Fig. 1) are useful for fracture toughness testing of brittle materials and this kind of specimen was recently recommended by the International Society for Rock Mechanics (ISRM) for testing Kto of rocks [1]. However, calibration work for its compliance is very limited, e.g. [2,3], and practical choosing of specimen parameters other than those specified by ISRM is impossible if costly calibration of experimental and numerical work is to be avoided.Recently, the author published some analytical results for the wide range compliance of edge-cracked 3PB round bars based on slice synthesis method [4]. The comparison with existing data showed good accuracy of the slice synthesis method [5] and the results were found useful by other scientists [6][7][8]. Encouraged by this situation, wide range compliance data for chevron-notched 3PB round bars are presented in this report.The detailed formulation was published in [9], and will not be repeated here. The basic idea of slice synthesis method is that the dimensionless compliance C (i.e. (8/P)DE, see Fig. 1, E is elastic modulus) is a synthesis of compliances of slices with a rectangular cross-section and straight-through crack Cij and C~ as follows 1 2 ~ '~tt I 2 tcLx At2 -2.., ~+ --2, 'where t, and t 2 are thicknesses for the slices shown in Fig. 1, respectively. The only difference in the present analysis as compared with (11) in [9] is the formula used for the calculation of Clj and C w The present formula is given belowwhere the first and second terms are deflection compliance caused by bend and shear deformation, respectively, for a 3PB strip without a crack, the third term Int Journ of Fracture @8