Yield Criteria for Ductile Materials and Fracture Mechanics of Brittle Materials

Brittle materials are materials that display Hookean behavior (linear relationship between stress and strain) and which fail at a discrete strain. Plastic materials display a variety of yielding behaviors associated with changes in the internal structure of the material at a fixed level of strain and at a fixed rate of strain. The time dependence to yielding behavior is due to the structural changes that must occur in order for the material to yield. Then an understanding of yielding in plastic materials requires a detailed understanding of the microstructure of a material and the mechanisms available to the microstructure to deform and absorb energy. A ductile material displays a simple plastic yielding behavior characterized by a gradual and non-discrete reduction in the slope of the stress strain curve. Ductile yielding can not be recovered by release of the stress, that is, it is a permanent deformation. Ductile behavior is observed for simple metal microstructures such as aluminum and is used for cold drawing of metals. Several simple continuum models (ignoring microstructure) have been proposed to predict (not understand) yielding behavior in simple ductile materials.