Introduction

With elastic deformation, the strains are proportional to the stress, so every level of stress causes some elastic deformation. However, a definite level of stress must be applied before any plastic deformation occurs. As the stress is further increased, the amount of deformation increases, but not linearly. After plastic deformation starts, the total strain is the sum of the elastic strain (which still obeys Hooke's law) and the plastic strain. Because the elastic part of the strain is usually much less than the plastic part, it will be neglected in this chapter and the symbol e will signify the true plastic strain.

The terms strain hardening and work hardening are used interchangeably to describe the increase of the stress level necessary to continue plastic deformation. The term flow stress is used to describe the stress necessary to continue deformation at any stage of plastic strain. Mathematical descriptions of true stress—strain curves are needed in engineering analyses that involve plastic deformation, such as predicting energy absorption in automobile crashes, designing of dies for stamping parts, and analyzing the stresses around cracks. Various approximations are possible. Which approximation is best depends on the material, the nature of the problem, and the need for accuracy. This chapter will consider several approximations and their applications.