# Stress-strain Curve Interpretation

A significant barrier to my understanding of typical engineering stress vs. engineering strain curves is that for certain values of stress, there are multiple values of strain (i.e., the stress-strain curve is not invertible in the mathematical sense). This is an issue for me because in my mind, I make sense of stress-strain curves in terms of the tension test I'd conduct to make the plot. I imagine that in a tension test, tension is added to a specimen incrementally and at each increment, the specimen's strain is noted.

This simple experiment must provide a curve that is 1:1 in that every tension value corresponds to one strain value (and vice versa). Therefore, this experiment cannot lead to the tensions that correspond to the specimen's necking region which for one tension value have two strain values.

How must I modify my view of the tension test used in obtaining experimental stress-strain curves to improve my understanding of what the curves are working to communicate? I am sure most of you reading this know the typical stress-strain figure I have in mind, but I have provided a basic example from Wikipedia below just in case:

The stress-strain curve isn't created using a incremental load.

Instead what most standards for tensile testing nowadays require a constant displacement rate. I.e. you have a setup similar to the following (it may vary of course)

Figure: Tensile test setup (source engineeringarchives)

The crosshead (horizontal bar that the load cell is attacheds) moves at a constant rate. As the displacement changes, the load required changes. The end result is recorded values of displacement and force.

## True stress-strain curve.

Since you are mathematically inclined the True stress-strain curve in some cases is mathematically invertible (compared to the engineering stress-strain curve).

Below is a comparison of the two (engineering vs true) for different materials.

Stress strain for steel Stress strain for a ductile material without a specific yield point.