Fragmentation of brittle spheres under static and dynamic compressions: Experiments and analyses

For static compressions of spheres, a new stress analysis for isotropic elastic spheres compressed between two flat rigid platens is proposed by incorporating the Hertz contact stress. The predictions of the failure load for various sizes and strengths of spheres agree very well with our static experiments on a brittle plaster material. For dynamic compressions of spheres, a simple crushing analysis illustrates that the size of the contact zone can be estimated quite accurately in terms of the size of the sphere, the dynamic hardness, and the impact energy. Although the maximum contact force at failure is larger in the static case than that in the dynamic case, the energy required for fragmentation of the solid spheres is larger under dynamic test than under static test. Comparisons of the static and dynamic tests show that the impact energy required for fragmentation of a sphere can be approximated as 1.5 times of that for the static test. As expected, the impact energy for fragmentation increases monotonically with the size and strength of the spheres. The contact time at failure, however, does not exhibit a clear trend with the changes in size and strength of the spheres.