Bases of Stress and Strain Curves
Stress–strain curves are generated by conducting tensile tests. During such tests, a material is mechanically loaded from its free state, which results in a deformation (strain) according to Hooke’s law. The applied force (stress) is plotted over the resulting deformation (strain) as shown in Figure 1. The curve represents the relationship between the strain and the stress. Stress–strain curves are used to evaluate the mechanical properties of materials, including yield strength, tensile strength, modulus of elasticity, fracture strain, and fracture strength.
Figure 1. Stress–strain curve.
True Stress–Strain Curve
True stress–strain curves are obtained by considering the actual area of the specimen when computing the applied force. The standard model of Hooke’s law states that the stress is equal to the applied force per undeformed area, where the area of the specimen is assumed to be constant. However, in a tensile test, the area decreases when the specimen is stretched. For this reason, true stress and strain must be used to more accurately describe the physical properties of a specimen (Figure 2).
True stress is the actual force divided by the actual area of the specimen, which is equal to the applied force divided by the area at the midpoint of the specimen. True strain is the actual increase in length divided by the initial length of the specimen. True stress–strain curves are usually obtained using true strain, as it is relatively easier to measure accurately.
Figure 2. True stress–strain curve.
In a true stress–strain curve, the elastic portion is much less curved than in the standard stress–strain curve. This is because the area at the start of the test is much larger than the true area at high strains. True stress–strain curves display the actual force applied to the specimen. One of the main benefits of a true stress–strain curve is that it can be used to accurately calculate the actual strain at yield.
Engineering Stress–Strain Curve
Engineering stress–strain curves are generated using engineering stress and strain. Unlike true stress–strain curves, the area of the specimen is assumed to remain constant. Therefore, engineering stress is obtained by dividing the applied force by the area at the start of the specimen. On the other hand, engineering strain is calculated as the increase in length divided by the initial length. The resulting curve can then be plotted using engineering stress and strain (Figure 3).
Figure 3. Engineering stress–strain curve.
An engineering stress–strain curve is usually generated during a tensile test because it is easier to measure. However, the yield point in an engineering stress–strain curve does not represent the true strength of the specimen, as it does not account for the decrease in area at high strain. For this reason, an engineering stress–strain curve can be valuable for general comparison between different materials but not for accurate strength calculations.
Conclusion
Stress–strain curves are obtained by conducting tensile tests on a material. The resulting curve describes the mechanical properties of the material. In order to obtain accurate strength calculations, true stress–strain curves should be used, as engineering stress–strain curves do not accurately account for the decrease in area at high strain.
