Statistics of dynamic fragmentation for a necking instability

The fragmentation of a stretching rod in ductile material is investigated with the approach of Mott applied to a set of necking points. Namely, instead of randomly distributed point defects, the potential sites of fracture are the maxima of the necking instability derived from a linear perturbation analysis. The process is supposed to be dominated by the fastest growing eigenmode giving distances between potential failure sites of the order of the critical wavelength. The scatter in failure times, which is at the origin of the obscuration process controlling fragmentation, is successively linked to a probabilistic threshold for failure and the combination of several modes giving maxima of varying amplitudes. The first assumption leads to continuous fragment size distributions of the same shape as the ones obtained for a random seeding of point defects, with potential sizes limited to multiples of the critical wavelength. On the contrary, the multimodal character of the instable perturbation introduces correlations between neighboring failure points which affect the distributions significantly.