TrueStressStrain

True stress and true strain describe material deformation using the instantaneous dimensions of the specimen, rather than the original gauge dimensions. They provide a more accurate description of material behavior at large deformations, common in metals during plastic flow and forming processes. The true stress is defined as the applied force divided by the current cross-sectional area, sigma_t = F / A_i. The true strain is defined as the natural logarithm of the length ratio, epsilon_t = ln(L_i / L_0) = ∫(dL / L).

In comparison, engineering (or nominal) stress and strain use the original cross-sectional area and length: sigma = F / A_0 and epsilon = (L_i − L_0) / L_0. The two measures are related by sigma_t = sigma_eng * (1 + epsilon_eng) and epsilon_t = ln(1 + epsilon_eng). True stress and true strain are particularly valuable for large-deformation regimes where necking occurs, because they continue to increase beyond the onset of necking, whereas engineering stress typically drops.

Applications include material property characterization, metal forming simulations, and constitutive modeling in finite element analysis. True-stress–true-strain curves are used to calibrate plasticity models, assess work hardening, and compare materials under significant deformation.

Measurement considerations involve determining the instantaneous cross-sectional area, which may require imaging techniques or non-contact methods in nonuniform deformation. While exact area measurement can be challenging, true-stress concepts remain foundational for understanding and modeling large-strain material behavior.