The Stress-Strain Curve

The stress-strain curve characterizes the behavior of the material tested. It is most often plotted using engineering stress and strain measures, because the reference length and cross-sectional area are easily measured. Stress-strain curves generated from tensile test results help engineers gain insight into the constitutive relationship between stress and strain for a particular material. The constitutive relationship can be thought of as providing an answer to the following question: Given a strain history for a specimen, what is the state of stress? As we shall see, even for the simplest of materials, this relationship can be very complicated.

A very useful page to aid you in your study of stress-strain curves can be found at key-to-steel.com. It elaborates on the information contained in the tutorial.

In addition to providing quantitative information that is useful for the constitutive relationship, the stress-strain curve can also be used to qualitatively describe and classify the material. Typical regions that can be observed in a stress-strain curve are:

1. Elastic region
2. Yielding
3. Strain Hardening
4. Necking and Failure

A stress-strain curve with each region identified is shown below in Figure 5. The curve has been sketched using the assumption that the strain in the specimen is monotonically increasing - no unloading occurs. It should also be emphasized that a lot of variation from what's shown is possible with real materials, and each of the above regions will not always be so clearly delineated. It should be emphasized that the extent of each region in stress-strain space is material dependent, and that not all materials exhibit all of the above regions. We describe each of the regions in more detail in the following sections.

Figure 5: Various regions and points on the stress-strain curve. Click on the figure to launch it in a separate window, which might be useful as you read through this section.

Quick Quiz: What would be the correct outcome after a specimen has been loaded and unloaded to its .2 percent offset yield strength?

The material will be .2 percent weaker in strength.
The material will be .2 percent longer than before the test.
The material will decrease in cross-sectional area by .2 percent.
None of the above