Crack Initiation Pattern in a Disk of Brittle Material under Axisymmetric Tension

The most stable crack initiation pattern in an infinite plate under axisymmetric tension was analyzed by using Griffith theory. The result was compared with the experimental results of flexural tests using glass and ceramic disks. The strain energy release rate Gn for nucleation or propagation of a star-shaped crack is approximately expressed as Gn=(4πσ2a/E)(1/n)(1-1/n), where a is the crack length, n is the number of cracks, σ is the applied stress, and E is the elastic modulus. The energy consideration on the basis of Griffith theory indicated that the most stable crack uncleation pattern in homogeneous and uniform brittle materials under uniform tension is a line shaped crack (n=2). In addition, even if a star-shaped crack happens to pre-exist in a brittle material, it may propagate only as a line-shaped macro-crack. This theoretical deduction was confirmed by the flexural tests on glass and ceramic disks.