Introduction

In Chapter 3 we formulated conditions describing when yielding may or may not occur. In this chapter we begin to explore what may happen if the stress point arrives at the yield surface. We intuitively expect that yielding will be accompanied by some form of increased deformation, over and above the elastic deformation that has gone on while the stress point has been inside the yield surface. We expect plastic behaviour to be softer than elastic behaviour, with the result that strains will accumulate more quickly. The term plastic flow is used to describe the deformation following yield.

One of the main differences between plastic response and elastic response is that plastic flow will be irreversible. While the material is elastic we can increase the stress with a consequent increase in strain, and then completely recover those strains by simply returning the stress state to its initial value. If yield occurs this will not be possible. Plastic deformation will not be recoverable from simple unloading. If we do reduce the stress to its initial value we will recover whatever elastic strain that has occurred in getting to the yield state, but the plastic strain will be locked within the body.

In order to describe plastic flow we might attempt to derive a constitutive relationship linking plastic strain to the current stress state. But this will immediately lead to difficulties owing precisely to the irreversibility mentioned above.