True stress-strain diagrams
“Why is there a negative slope on a stress-strain diagram and how can we fix it?”
The stress-strain diagram is probably one of the most used concepts in all of engineering. However, there seems to be one counterintuitive aspect to it. Specifically, after the ultimate strength is reached, the stress-strain slope seems to become negative. This can’t be, since the stress can only increase with strain, not the other way around. So what exactly is behind this incongruity? Well, it all comes down to one simple fact. When constructing an engineering stress-strain curve, the cross-sectional area of the object is assumed to be static. However, due to the law’s of Poisson’s ratio, an elongation in length must be countered by a decrease in the associated cross-sectional area. And since this cross-sectional area will have s smaller capacity to carry force, the force distribution will go down. Therefore, if we do not include an updated area with the force, the stress will decrease with strain. Structural Engineers and Materials Scientists have recognized this flaw and have created true stress-strain diagram in response, which uses an ever-changing cross-sectional area. True stress-strain diagrams never have negative slopes, and are commonly used for research purposes.