3 - Continuum Plasticity

Summary

The handling of stress and strain during elastic deformation is covered in the preceding chapter. However, the situation becomes more complex after the onset of plastic deformation. Whereas elastic straining essentially occurs just via changes in interatomic spacing, the mechanisms involved in plastic (permanent) deformation are far from simple. These mechanisms are described in some detail in the next chapter. The current chapter is based, as is the previous one, on treating the material as a homogeneous continuum, albeit one that may be anisotropic (i.e. exhibit different responses in different directions). Much of the coverage concerns conditions for the onset of plasticity (often described as “yielding”) and subsequent rises in applied stress that are required for further plastic straining (“work hardening”). Two yielding criteria are in common use and these are described. The work-hardening behavior is often quantified using empirical constitutive laws and two of the most prominent of these are also outlined. This chapter also covers the representation of temporal effects – both the changes in stress–strain characteristics that occur when high strain rates are imposed and the progressive straining that can take place over long periods under constant stress, which is often termed “creep.”