# Fragmentation of shells: An analogy with the crack formation in tree bark

## TL;DR

This paper introduces a new theory and model for shell fragmentation based on an analogy with tree bark cracking, addressing limitations of previous theories and accurately predicting fragmentation patterns.

## Contribution

It proposes a novel physical mechanism for shell fragmentation, using an analogy with tree bark cracking, and provides a closed-form model for predicting the number of fragments.

## Key findings

- The model accurately predicts the number of fragments based on expansion velocity.
- The theory explains the constant saturation fragment length despite increased velocity.
- Experimental results align well with the theoretical predictions.

## Abstract

How does a shell explode into a series of fragments upon impact? The well accepted explanation is Mott's theory, which considers the fragmentation of shells as a random process controlled by defects. However, Mott's theory is inadequate due to its assumption of energy conversion, and it is incapable of explaining the lack of change in saturation fragment length with the increase in expansion velocity. In this paper, we present a theory to explain the physical mechanism for fragmentation of shells and propose a highly efficient model for predicting the number of necks after fragmentation. We recognize that the fragmentation problem in shells is analogous to the cracking behavior of tree bark, and closed form solutions is obtained to describe the relationship between the expansion velocity and the number of necks with consideration of the strain rate dependent strength of the shell material. The theoretical results show excellent correlation with the experimental results.