18.5 : 真応力と真ひずみ

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.