True stress and engineering stress are two different ways of measuring stress in materials, and they are related to the material's deformation under load. The key difference lies in how they account for changes in the material's cross-sectional area during deformation.
- Engineering Stress: Engineering stress (or nominal stress) is the more commonly used stress measure in engineering applications. It is calculated by dividing the applied force (load) by the original cross-sectional area of the material before deformation. The formula for engineering stress is:
Engineering Stress (σ) = Load / Original Cross-sectional Area
The engineering stress assumes that the cross-sectional area remains constant during deformation, even though in reality, the area may change due to elongation or compression. This is a simplification and becomes less accurate as the material undergoes significant deformation. As a result, engineering stress tends to overestimate the material's strength and stiffness as the area decreases.
- True Stress: True stress is a more precise measure of stress that considers the actual instantaneous cross-sectional area of the material at any given point during deformation. It takes into account the changes in the material's cross-sectional area as it undergoes stretching or compression. The formula for true stress is:
True Stress (σ_true) = Load / Instantaneous Cross-sectional Area
Since true stress considers the changing cross-sectional area, it provides a more accurate representation of the material's strength and deformation behavior. As a material undergoes elongation, the true stress will increase more rapidly than the engineering stress because the cross-sectional area decreases as the material elongates.
In general, for small deformations, the difference between engineering stress and true stress is relatively small, and engineering stress can be a reasonable approximation. However, as deformations become more significant, and the material experiences significant changes in its cross-sectional area, the difference between the two stress measures becomes more pronounced.
In summary, engineering stress is a simplified and more conservative measure of stress that assumes a constant cross-sectional area during deformation. True stress, on the other hand, considers the actual changing cross-sectional area and provides a more accurate representation of the material's behavior under load, especially during large deformations.