  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.
