A fragmentation problem for an elastic plate

Abstract

We examine fragmentation in a linearly elastic plate subjected to the action of a moving load. The load is assumed to “run” at a “supersonic” constant velocity along one of the plate's sides. A loading of this type is encountered, for example, in explosive forming and explosive welding, during an oblique collision of two plates, etc. Fragmentation is understood as destruction of solid or liquid bodies occurring as a result of compression-wave reflection from free surfaces or from the interface between two bodies, one of which possesses a lower acoustic stiffness. Many interesting cases of fragmentation are described in Rinehart and Pearson's book [1], which also contains extensive literature references on the subject. Most of these papers give an acoustic interpretation of the fragmentation phenomenon with conditions of one-dimensional deformation. Lenskii [2] has tried to apply the theory of elasticity to the description of the fragmentation phenomenon in a plate experiencing a concentrated force. Ogurtsov [3] has obtained an exact solution to a stress problem for an elastic plate under a concentrated load; however, due to its complexity, his solution has yet to be applied to the fragmentation problem. In the present formulation of the problem, a simple exact expression for the stress waves in a plate, from which the fragmentation parameters can be determined, is obtained with relative ease. The solution can be used to obtain certain fragmentation data for a plate under a concentrated load, and also for an explosion in an elastic half-space. For example, it is possible to determine the approximate form of fragmentation cracks and formations near the epicenter.