| Fracture and fragmentation of brittle solids is one of the most fundamental problems in applied mechanics. Because of the difficulty in monitoring the fragmentation sequence inside a solid under impact loading, our knowledge on dynamic fragmentation process is quite limited; thereby fragmentation is still mainly modeled by empirical approach. The main objective of this thesis is to provide a comprehensive approach to investigate fragmentation by using analytical, experimental and numerical analyses. First of all, an analytical solution of an elastic sphere subject to a pair of suddenly-applied patch loads along a diameter is obtained. For the special case that the patch loads converges to a pair of point load, our solution is comparable to those obtained by Jingu and Nezu (1985); when transmission of waves through the two rigid platens is allowed, the long term solutions converge to the static solutions given by Hiramatsu and Oka (1966) and Chau et al. (2000) for the cases of uniform and Hertz contact loads respectively. Contour plots provide the time evolution of dynamic stress patterns and can be used to interpret the position of fracture initiation and patterns of fragmentation. In our experiments, brittle spheres made of plaster of two different strengths and three different sizes were compressed dynamically between two rigid platens at various impact energy levels. Both impact velocity and contact force at the impactor can be measured accurately as a function of time. Finally, a newly developed computer program, DIFAR, is used to simulate the dynamic failure and fragmentation of a sphere subject to double impacts. The computer program is based on an elastic finite element analysis of solids incorporated with a loading-rate-sensitive Mohr-Coulomb criterion with a tensile cut-off for damage checking. Both elastic modulus and strength of all elements follow a Weibull distribution spatially, thus the randomness of the initiation of fragmentation can be modeled. The numerical simulations agree well with the general pattern of observations in experiments. The results of this thesis should provide some insight on dynamic fragmentation for spheres or non-spherical particles and a bench study for further research in the area. |
