Stress-Strain Calculator

Engineering stress uses the original cross-sectional area: sigma_eng = F / A0. True stress uses the instantaneous area as the material necks: sigma_true = F / A_inst. At small strains both are nearly equal. At large strains (near fracture) true stress is much higher than engineering stress because the neck area is much smaller than A0.

Engineering (nominal) strain: epsilon_eng = (L - L0) / L0 = delta_L / L0. True (logarithmic) strain: epsilon_true = ln(L / L0) = ln(1 + epsilon_eng). True strain is additive for sequential deformations; engineering strain is not. For strains above about 5%, the difference becomes significant.

Yield strength is the stress at which a material begins to deform plastically. Below yield strength, deformation is elastic (recoverable). Above it, permanent plastic deformation occurs. The 0.2% offset yield strength is commonly used: the stress corresponding to 0.2% plastic strain, found by drawing a line parallel to the elastic region offset by 0.002 strain.

Ultimate tensile strength is the maximum stress on the engineering stress-strain curve. It corresponds to the onset of necking. After UTS, the local cross-section contracts rapidly (necking) and the engineering stress falls, even though the true stress continues to rise until fracture.

True strain = ln(1 + engineering strain). True stress = engineering stress * (1 + engineering strain). These conversions are valid until necking begins. After necking, a more complex analysis based on the instantaneous cross-section area is required to find the true stress-strain relationship.