The engineering stress-strain data is calculated by using the initial cross-sectional area of the test sample, consequently it neglects the actual area reduction that takes place during elongation. To calculate a more correct value of the stress, the true cross-sectional area for each data point needs to be considered. This means that the true stress is slightly higher than the engineering stress, as the diagram shows.
Engineering stress is defined as the applied force divided by the initial cross-sectional area, F/A0. While true stress is defined as applied force divided by the current cross-sectional area, F/A. Engineering strain is defined as the increase in length divided by the initial length, ΔL/L0. While true strain is defined as dε=dL/L, by integration from L0 to L0+ΔL.
When necking occurs during deformation, the material undergoes significant localized deformation resulting in a heavily reduced cross-sectional area. This can lead to a drop in load-carrying capacity, causing the engineering stress to decrease. However, the true stress, which takes into account the actual area reduction, will continue to increase with increasing strain. Nevertheless, after necking, the true stress-strain curve becomes difficult to measure accurately due to inhomogeneous deformation. This is why different material models are used to describe the true stress-strain behavior after necking, such as the models represented by the dotted line in the diagram below.