When stressed beyond a critical stress, ductile materials such as metals and alloys display a nonlinear plastic response. This is sketched in Fig. 26.1 for a uniaxial tensile test of a smooth specimen, where some relevant terms are defined. In general, plastic yielding is gradual when resolved at typical strain levels (e.g., ∼ 10−4). A critical stress, called the yield stress, is defined, which is the stress in uniaxial tension, or compression, required to cause a small, yet finite, permanent strain that is not recovered after unloading. It is common to take this onset yield strain as ey = 0.002 = 0.2%. Some common general features of plastic flow, with reference to stress vs. strain curves, are:

• The σ vs. e response is nonlinear and characterized by a decreasing intensity of strain hardening, measured by the slope dσ/de, as the strain increases. Generally, dσ/de ≥ 0.

• Unloading is nearly elastic.

• Plastic deformation of nonporous metals is essentially incompressible, i.e., volume preserving. A discussion of the physical basis for plastic deformation in subsequent chapters will explain why this is so.

As noted, a schematic stress-strain curve during uniaxial loading and unloading of an elastoplastic material is shown in Fig. 26.1. The initial yield stress is Y (later terms such as σy will be used to denote yield stress). Note that the yield stress is now ideally represented as a stress level at which an abrupt transition from linear, purely elastic, to nonlinear, elastic-plastic deformation occurs.