Fragmentation of Shells

We present a theoretical and experimental study of the fragmentation of closed thin shells made of a disordered brittle material. Experiments were performed on brown and white hen egg shells under two different loading conditions: impact with a hard wall and explosion by a combustible mixture. Both give rise to power law fragment size distributions. A three-dimensional discrete element model of shells is worked out. Based on simulations of the model, we give evidence that power law fragment mass distributions arise due to an underlying phase transition which proved to be abrupt for explosion and continuous for impact. We demonstrate that the fragmentation of closed shells defines a new universality class of fragmentation phenomena.

Figure 1

Time evolution of the explosion of an egg shell. (a) Ignition, (b) instant of explosion, (c) final state.

Figure 2

Comparison of fragment mass distributions obtained in explosion experiments with two hole sizes and in the impact experiment to the simulation results. Inset: scanned pieces of an impact experiment.

Figure 3

Final fragmented states for (a) impact and (b) pressure pulse loading. Particle positions are projected back to the initial state on the surface. Black lines indicate cracks.

Figure 4

$\langle M_{\mathrm{m}\mathrm{a}\mathrm{x}}/M_{\mathrm{t}\mathrm{o}\mathrm{t}}\rangle$ versus $P_0$ and $E_0$. The values of $P_c$ and $E_c$ are also indicated.

Figure 5

Normalized mass of the largest fragment (a) and average fragment mass (b) as a function of the distance from the critical point. Rescaled plots of the fragment mass distributions (c) for explosion and (d) for impact.