Dynamic fragmentation of shells: scale effects

The effect of the diameter of the shells of structural steel (0.6% C) on the parameters of the cumulative number distribution of fragments by mass and the cumulative mass distribution on fragment length is studied. We tested geometrically similar closed cylinders of different diameters with different wall thicknesses, but maintaining a constant ratio of wall thickness to diameter of the shells equal to 0.175. Detonation velocity and pressure were 8300 m/s and 27 GPa, respectively.It was found that statistical fragment distributions by mass of the shells of different diameters are well described by the linear exponential relations, and with decreasing shell diameter, indices in these relations equal to reciprocal value of the characteristic mass increases. The diameter of the shell may affect the indices of cumulative mass distributions of fragments along their length described by a power function. With the increase in shell diameter, exponents in these equations are reduced, and the distributions are shifted to a shorter length fragments. These changes in the character and location of distributions are explained by change in the fragmentation mechanism. In the diagram, plotted using of the cumulated mass distributions on the fragment length for shells with different diameters, three parts corresponding to the three regimes of fragmentation is marked out.The initial stage of fragmentation of shells of small diameter (section I of the mass-fragment length distribution) is connected with the formation of small but numerous fragments limited by initial shear cracks on the inner surface of the shell. In the middle section II, which is linear in double logarithmic coordinates, the main spectrum fragments are formed, and this process develops steadily on the section II a, and with acceleration on the section II b, probably due to the transition from the shear to radial rupture fracture, accompanied by an increase in thickness of the fragments. On the last section III, corresponding to the fragment distribution of shell with the largest diameter, the length of the fragments is growing, but the cumulative mass remains almost constant, that is likely due to the formation of a relatively small number of longitudinal fragments of lesser thickness.