Yielding

Any increase in stress beyond the yield point will cause the material to be deformed permanently. Also in this so-called yielding region, the deformation will be relatively large for small, almost negligible increases in the stress. This process, characterized by a near-zero slope to the stress-strain curve, is often referred to as perfect plasticity.

In the tensile test, the strain in the specimen is gradually increased and no unloading occurs. If the yield point was passed during loading and the specimen was then unloaded, however, the behavior would be very different from that in the elastic region. At the end of the unloading, there would exist a permanent strain (sometimes referred to as a ``set'') in the material. In other words, the specimen would appear to be stretched in comparison to its original configuration, even though no loads would be acting on it. This notion is illustrated in Figure 6, below.

Figure 6: Stress-strain curve for a process of loading past the elastic region, followed by unloading. Subsequent reloading proceeds up a new linear curve, until the original loading curve is reached.

Subsequent loading would proceed up this new loading curve, with the slope again being the Young's Modulus of the material. In this region the material will again behave linear elastically. You should also note that the process introduces a new yield point as shown in Figure 6a.

Figure 6a: Linear elasticity is again exhibited in the unloading curve.

Exercise: Use the java applet for the tensile test to load the bar past the elastic region, but before the ultimate tensile strength is reached. Unload after some yielding has occured, so that you obtain a permanent set in the bar. How can you introduce even more permanent set?

Quick Quiz: True or false? During plastic deformation, the volume of the specimen, as well as its cross-sectional area, decrease.

True
False