Types of stress-strain diagrams

The elastic-plastic behaviour of materials is frequently described by stress-strain curves measured in tensile tests. Tensile tests are used to determine material parameters that are then listed in tables, for example in ISO standards. These parameters are used in selecting materials and in component design. Even if the shape of the component is complex and the stress state multiaxial, criteria can be used that allow to employ the parameters determined in tensile tests. We will see in section 3.3 how this is done in the case of plasticity. 

In a tensile test, the specimen is lengthened at constant speed, and the extension AL and the required force are measured. To make results comparable, standardised specimens are used (see figure 3.4 for an example). Most common specimens have a spherical cross section, with a diameter that is constant along the gauge length. To avoid failure at the clampings, the specimen is made thicker there, and the transition between the different diameters is 

To transform the measured quantities (force F and extension AL) to material parameters, the nominal stress a and the nominal strain e are calculated  

So is the original cross-sectional area, and Lq is the initial gauge length. The stress measure a in equation (3.9) is not the true stress in the material, for it is always calculated based on the original cross-sectional area So, whereas the cross section of the specimen changes during the test. This is the reason for the term nominal stress. The actual stress in the material in a tensile test is called the true stress CTf 

The shape of the stress-strain curves obtained in tensile tests differs between the different material classes. The characteristic shapes are summarised in figure 3.5. 

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Figure 7.2 Various types of stress-strain diagrams.

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