18.5:
True Stress and True Strain
Engineering stress is the ratio of the load and the undeformed original cross-sectional area. Engineering stress approximates strain which represents the material under load, which is relevant for ductile materials post-yield.
Engineering stress-strain diagrams are often used for convenience, but a true stress-strain diagram provides a more accurate depiction, especially with large strains.
True stress is calculated by dividing the load by the cross-sectional area of the specimen at the particular instant of deformation. As load increases, the cross-sectional area decreases, reflecting true stress.
During the necking phase, the true stress, which is proportional to the load but inversely proportional to the area, keeps increasing until the specimen ruptures.
The true strain uses successive recorded values of length. Each increment of the distance between the gauge marks, divided by the corresponding length, gives the elementary strain.
True strain is the sum of all elementary strain values, reflecting the material's behavior more accurately.
Unlike engineering stress-strain plots, true stress versus true strain diagrams remain consistent during necking and across tensile and compressive tests.
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.