In this chapter we consider the transition from elastic to plastic behavior (the yield point). This transition implies that the material undergoes irreversible shape changes in response to external forces. A simple example is a piece of metal permanently bent into a new shape. Several physical mechanisms can cause plastic deformation. Plasticity in metals is usually associated with the motion of dislocations, while in brittle materials it is caused predominantly by slip at microcracks. After introducing the most important criteria for yielding, the concept of plastic flow and the definition of hardness, we will consider various examples of indentation, sliding and rolling involving plastically deformed objects. These processes are severely affected by the friction at the contact interfaces, which is also discussed in the chapter. We will also mention the importance of plasticity in geotechnics, where it determines the safety of a structure founded on a soil. In this context, a peculiar role is played by the angle of internal friction of the materials.

Plasticity

A typical stress–strain curve for a material in simple tension is shown in Fig. 12.1. The initial part of the curve is a straight line with a slope equal to the Young's modulus E of the material. The linear relationship between σ and ε ends at a certain point, corresponding to the yield strength Y. At this point plastic deformation occurs. The value of Y depends on the manufacturing process and on the purity of the material. For metals, it is typically in the range of 10–100 MPa. If the material is stressed further in the plastic range and the load is released, the recovery is elastic, with the same value of E as in the first loading. This key assumption was carefully verified by Tabor in a series of measurements on soft metals using spherical and conical indenters [327, 321]. A subsequent loading of the material results in an increased value of the yield strength, as seen in Fig. 12.1. This effect is known as work hardening or strain hardening.