A model for the work hardening of WC-Co "hard metals"

Conventional theory shows that if the mean free path of newly formed dislocations is independent of plastic strain, then the plastic strain is proportional to the square of the stress. If the mean free path decreases during deformation, being proportional to the distance between neighbouring stored dislocations, then the plastic strain is linear in the stress. Experiments on WC-Co hard metals show a region in which the plastic strain increases as the fourth power of the stress, followed by a catastrophic increase. This suggests that the mean free path of dislocations increases with strain and stress. A model is developed in which dislocations travel almost freely in the Co binder and form inverted pile-ups in the terminating WC grains, as in the analysis by Bilby, Cottrell and Swinden of the spread of plastic yield from a notch. The model reproduces the rapid increase of plastic strain with increasing stress reasonably satisfactorily and predicts a very high rate of work hardening as is observed.