Crack initiation, propagation and branching in a disk of brittle material under axisymmetric tension

Abstract

The most stable crack nucleation and crack branching patterns in an infinite plate under axisymmetric tension were analysed by using Griffith theory. The analytical results were compared with the experimental results of flexural tests on glass, ceramic, and acryl disks. The strain energy released by nucleation of a star-shaped crack, U, was approximately given by U = (2πσ 2a 2/E)(1 − 1/n) , and the strain energy release rate, G n , by G n = (47πσ 2a/E)(1/n)(1 − 1/n) , were σ is nominal tensile stress, a is crack length, n is crack number, and E is elastic modulus. The energy consideration on the basis of Griffith theory indicated that the most stable crack nucleation shape in a homogeneous brittle material is a line-shaped crack ( n = 2). In addition, the most stable crack length after the ith branching has occurred, a i , is given as: a i = {(2 2i + 1)/(2 i + 1 − 1)}{Eγ/πσ i 2])} , where σ i is the nominal stress at the ith crack branching and γ is the surface energy per unit area. The experimental results of flexural tests on the disk specimens of brittle materials corresponded well to the analytical results.