What are the advantages and disadvantages of using true stress and true strain?

1 Engineering stress and strain

Engineering stress and strain are the simplest and most widely used definitions of stress and strain. They are based on the initial dimensions of the material before any deformation occurs. Engineering stress is the ratio of the applied load to the original cross-sectional area of the material, while engineering strain is the ratio of the change in length to the original length of the material. Engineering stress and strain are easy to measure and calculate, and they can be used to compare the strength and stiffness of different materials. However, they do not account for the changes in the geometry and volume of the material as it deforms, which can lead to inaccurate results at large strains or in non-linear materials.

2 True stress and strain

True stress and strain are more accurate definitions of stress and strain that take into account the changes in the dimensions of the material during deformation. True stress is the ratio of the applied load to the instantaneous cross-sectional area of the material, while true strain is the natural logarithm of the ratio of the instantaneous length to the original length of the material. True stress and strain can capture the actual behavior of the material at any level of deformation, and they can be used to determine the ductility and fracture toughness of the material. However, they are more difficult to measure and calculate, and they require more complex equations and assumptions to relate them to the engineering stress and strain.

3 Stress-strain curve

The stress-strain curve is a graphical representation of the relationship between stress and strain for a given material and loading condition. It can provide valuable information about the material properties, such as the modulus of elasticity, the yield strength, the ultimate strength, and the strain hardening. However, the shape and position of the curve can vary depending on whether engineering or true stress and strain are used. Engineering stress and strain tend to produce a linear curve up to the yield point, followed by a curved region until the ultimate point, and then a drop until fracture. True stress and strain tend to produce a continuously rising curve that does not drop until fracture. The true stress-strain curve is always above the engineering stress-strain curve, because true stress accounts for the decrease in area and true strain accounts for the increase in length as the material deforms.

5 Disadvantages of true stress and strain

Using true stress and strain has some disadvantages compared to engineering stress and strain, particularly for materials and situations that involve small or uniform deformations. Measuring and calculating true stress and strain is more complex, as it requires knowing the instantaneous dimensions of the material. Additionally, more complex equations and assumptions are needed to relate true stress and strain to engineering stress and strain, which can lead to errors or uncertainty in the analysis. Furthermore, true stress and strain may not be compatible with certain standards or conventions, such as ASTM or ISO, resulting in confusion or inconsistency in the results.

6 Here’s what else to consider

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