Dynamic and static compressions of rock-like spheres between two flat platens

For static compressions of spheres, a new stress analysis for isotropic elastic spheres compressed between two rigid piatens 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 experiments. For dynamic compressions of spheres, asimple 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 alone. We found that although the maximum contact force is larger in the dynamic case than in the static case, the energy required to fracture the sphere is larger under dynamic situation. By comparing the static and dynamic tests, we found that the dynamic impact energy required to fracture a sphere can be approximated as 1, 5 times of those for the static test. As expected, the dynamic impact energy increases monotonically with the size and strength of the spheres. However, the contact time at failure does not exhibit a clear trend with the changes in size and strength of the spheres.