Study on the fragmentation of shells

Falk K Wittel,Ferenc Kun,Hans J Herrmann,Bernd Kröplin

doi:10.1007/s10704-005-3995-7

Falk K Wittel, Ferenc Kun + Show 2 more

Open Access

https://doi.org/10.1007/s10704-005-3995-7

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Abstract

Fragmentation can be observed in nature and in everyday life on a wide range of length scales and for all kinds of technical applications. Most studies on dynamic failure focus on the behaviour of bulk systems in one, two and three dimensions under impact and explosive loading, showing universal power law behaviour of fragment size distribution. However, hardly any studies have been devoted to fragmentation of shells. We present a detailed experimental and theoretical study on the fragmentation of closed thin shells of various materials, due to an excess load inside the system and impact with a hard wall. Characteristic fragmentation mechanisms are identified by means of a high speed camera and fragment shapes and mass distributions are evaluated. Theoretical rationalisation is given by means of stochastic break-up models and large-scale discrete element simulations with spherical shell systems under different extreme loading situations. By this we explain fragment shapes and distributions and prove a power law for the fragment mass distribution. Satisfactory agreement between experimental findings and numerical predictions of the exponents of the power laws for the fragment shapes is obtained

Highlights

Closed shells made of solid materials are used in every day life, in industrial applications in form of containers, pressure vessels or combustion chambers and in nature e.g., as nature's oldest container for protecting life - the egg-shell
We present a detailed theoretical and experimental study on the fragmentation of closed thin shells made of disordered brittle material, due to an excess load inside the system
5 SUMMARY We presented a theoretical and experimental study of the fragmentation of closed brittle shells arising due to an excess load inside the shell

Summary

INTRODUCTION

Closed shells made of solid materials are used in every day life, in industrial applications in form of containers, pressure vessels or combustion chambers and in nature e.g., as nature's oldest container for protecting life - the egg-shell. Fragmentation, i.e. the breaking of particulate materials into smaller pieces is abundant in nature occurring on a broad range of length scales from meteor impacts through geological phenomena and industrial applications down to the break-up of large molecules and heavy nuclei [1,2,3,4]. The most striking observation concerning fragmentation is that the distribution of fragment sizes shows power law behaviour independent on the way of imparting energy, relevant microscopic interactions and length scales involved, with an exponent depending solely on the dimensionality of the system [2,3,4,5,6,7,8,9,10,11]. The peculiarity of the fragmentation of closed shells originates from the fact that their local structure is inherently two-dimensional, the dynamics of the systems, deformation and stress states are three dimensional which allows for a rich variety of failure modes

EXPERIMENTS ON SHELL FRAGMENTATION

PREDICTIONS OF FRAGMENT MASSES