Abstract
In the aim of predicting the fragmentation of expanding structures, a Mott type approach is applied to the potential failure points driven from an instability analysis. Substantially, fragmentation is preceded by the localization of plastic deformation in multiple necks forming potential sites for failure. This pattern is predicted by a combination of periodic instable eigenmodes of the structure, the necks being the maxima with varying spacing and amplitudes of the instable perurbation. Obscuration conditions, linked to the propagation of unloading waves, are next written for this set of potential failure points and yield a distribution of fragments. The approach is developed for an expanding ring experiment justifying the scatter in fragment sizes. It shows incidentally that the unloading waves must propagate at a celerity much lower than the elastic wave speed.
Highlights
Necking instability initial radius r0The fragmentation of structures under dynamic expansion is governed by the competition between the activation of failure points when deformation increases and the inhibition of failure in areas obscured by the unloading waves emerging from these points
For ductile materials, fragmentation is initiated by the localization of plastic deformation and these sites are clearly related with the necking pattern emerging in this first phase
The onset of localization is ruled by the existence of instable eigenmodes of the structure and it is treated in a linear stability analysis framework
Summary
The fragmentation of structures under dynamic expansion is governed by the competition between the activation of failure points when deformation increases and the inhibition of failure in areas obscured by the unloading waves emerging from these points. The aim of the present work is to apply the approach of Mott to a discrete set of potential failure points identified as the maxima of an instable perturbation (forming necks in thickness of the structure): a combination of instable modes is retained in order to get maxima of various amplitudes and spacing as shown in [3]. This justifies the scatter in failure times which is at the origin of the obscuration process. The one dimensional case of an expanding ring, assimilated to a stretching rod, is developed and, as an illustration, the predictions are compared to the sizes of fragments recovered after an explosive expansion experiment
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