Exploring effects of property variation on fragmentation of metal rings using a simple model

A simple finite element implementation of the Mott model for fragmentation of a thin walled ring has been implemented and used to explore the effect of local variations in fracture strain around the ring. The model has successfully reproduced the fragment size distributions previously reported, which follow a characteristic “Mott distribution” form, providing sufficient (1000) simulations are run. It has been shown that this form is retained even when there are large differences in the random distribution of fracture strains or a different choice of function used to describe the fracture strain scatter. In these cases, the strain rate has a much stronger effect than fracture strain distribution the on the average fragment size and fragment distribution. However, for cases where there are a small number of local defects that strongly reduce the fracture strain at certain locations around the ring, the predicted fragment size distribution develops a bimodal character. This is also the case for large but gradual variations in fracture strain with position around the ring. The results have implications for cases where a small number of large pre-existing defects exist, or processing has led to macrozones in the microstructure. The utility of a simple fast running model to study these cases is discussed.