3.2 Plastic Deformation in Tension

Figure 3.3 shows a number of stress strain curves for the same material: AISI 1040 steel. This might look surprising at first, but it merely reflects the complexity of the microstructural mechanical behavior interactions. Both engineering and true stress strain curves are shown. (The definitions of these are given in Chapter 2.) Engineering (or nominal) stress is defined as P/ A ₀, while true stress is P/ A, where A ₀ and A are the initial and current cross-sectional areas, respectively. Engineering (or nominal) strain is defined as ? L/ L ₀, while true strain is ln L/ L ₀, where L and L ₀ are the current and initial lengths, respectively. The yield stress varies from 250 to 1,100 MPa, depending on the heat treatment. Conversely, the total strain varies from 0.38 to 0.1. The properties of steel are highly dependent upon heat treatment, and quenching produces a hard, martensitic structure, which is gradually softened by tempering treatments at higher temperatures (200, 400, and 600 C). The annealed structure is ductile, but has a low yield stress. The ultimate tensile stresses (the maximum engineering stresses) are marked by arrows. After these points, plastic deformation becomes localized (called necking), and the engineering stresses drop because of the localized reduction in cross-sectional area. However, the true stress continues to rise because the cross-sectional area decreases and the material work-hardens in the neck region. The true-stress true-strain curves...