18.5 : True Stress and True Strain

Engineering stress is calculated as the load divided by the original, undeformed cross-sectional area. It approximates a material under load. This approximation is especially relevant post-yield in ductile materials. Though engineering stress-strain diagrams are often used for their convenience and accessibility, they can sometimes fall short in accuracy, particularly when dealing with large strain values.

In contrast, true stress offers a more precise portrayal. It is computed by dividing the applied load by the instantaneous cross-sectional area of the specimen during deformation. As the load increases, the cross-sectional area decreases, which is accurately reflected in the true stress value. During the necking phase, the true stress keeps increasing as it is proportional to the load while being inversely proportional to the area, and this continues until the specimen eventually ruptures.

The concept of true strain further enhances this accurate depiction. It considers successive recorded length values. Each increment of the distance between the gauge marks is divided by its corresponding length to obtain the elementary strain. The true strain is the accumulation of these elementary strain values, precisely reflecting the material's behavior. Unlike engineering stress-strain diagrams, true stress versus true strain diagrams maintain consistency during the necking phase and across various tests, such as tensile and compressive tests.