Analysis of the brittle fragmentation of an expanding ring

The current research extends our previous work on brittle fragmentation of a one-dimensional bar [F. Zhou, J.-F. Molinari, K.T. Ramesh, A cohesive-model based fragmentation analysis: effects of strain rate and initial defects distribution, International Journal of Solids and Structures 42 (2005) 5181–5207] to a circular ring that is dynamically expanded (e.g. by explosive loading). The expanding ring test is a convenient and effective technique to study the dynamic fracture and fragmentation properties of materials under high strain rate tensile loading. In this paper we describe the basic elastodynamic equations that govern the expansion of the ring, and develop a numerical integration scheme based on characteristic line differential relationships to solve these equations. A dynamic crack initiation criterion and a cohesive crack growth model are used to describe the failure and fracture process. With this methodology we investigate the fragmentation processes of rings under two typical loading conditions: forced constant velocity expansion and free expansion. The effects of ring size and the fracture properties of the material are investigated. The Rayleigh distribution function is used to describe the statistical characteristics of the fragment populations. Finally we discuss the energy conversions during the fragmentation process.