Difference between fracture of thin brittle sheets and two-dimensional fracture

Abstract

Recently there has been some suggestions that fragmentation of thin brittle sheets is qualitatively different from pure two-dimensional fragmentation. The obvious reason for such a discrepancy is the possibility of the sheet to deform out of plane. There is a generic crack-branching mechanism that creates power-law fragment size distribution in the small fragment range for two-dimensional (2D) and three-dimensional bulk fragmentation with the power exponent (2D-1)/D. For thin sheets, the power exponent seems to be close to 1.2 which differs from the D=2 exponent 1.5. In order to make a distinct separation between sheet and 2D fragmentation, high-resolution fragment size distributions are required for fragmentation models with minimal differencies other than dimensionality. Here a very efficient numerical model which can be switched from 2D fragmentation to out-of-plane sheet fragmentation with minimal changes is used to produce high-resolution fragment size distribution for the two cases. The model results cast some doubt on the existence of separate universality classes for sheet and 2D fragmentation.