TABLE OF CONTENTS The terms flow criterion, yield criterion, and failure criterion have different meanings. Failure criterion has its historical origin in applications where the onset of plastic deformation indicated failure. However, in deformation-processing operations this is obviously not the case, and plastic flow is desired. Yield criterion applies only to materials that are in the annealed condition. It is known that, when a material is previously deformed by, for instance, rolling, its yield stress increases due to work-hardening. (See Chapter 6.) The term flow stress is usually reserved for the onset of plastic flow in a previously deformed material. Failure criterion is applied to brittle materials, in which the limit of elastic deformation coincides with failure. To be completely general, a flow criterion has to be valid for any stress state. In a uniaxial stress state, plastic flow starts when the stress strain curve deviates from its initial linear range. Uniaxial stress strain curves are very easily obtained experimentally, and the deformation response of a material is usually known for this situation. The main function of flow criteria is to predict the onset of plastic deformation in a complex state of stress when one knows the flow stress (under uniaxial tension) of the material. Note that the value of the flow stress is strongly dependent on the state of stress, and if this effect is not considered, it can lead to potentially dangerous errors in design. We next present some of...
