Young's Modulus

Young’s modulus (E) characterizes stiffness in the elastic regime: how much stress is required to produce a small recoverable strain. For isotropic homogeneous solids under uniaxial tension or compression, σ = Eε holds until proportional limit or yield supersedes linearity.

E is determined from the slope of the stress–strain curve in the initial linear region. High-precision measurement requires high-resolution extensometers or non-contact strain measurement and subtraction of machine and grip compliance, which otherwise underestimate E.

For polycrystalline metals, E is relatively insensitive to microstructure compared to yield strength, but texture in rolled sheet can produce apparent directional moduli if off-axis specimens are tested. Composites and polymers exhibit viscoelasticity; “modulus” then depends on time, temperature, and strain rate.

Designers use E with second moments of area to estimate deflections, resonant frequencies, and buckling loads. It should not be confused with tangent modulus or secant modulus used beyond yield in nonlinear analysis.