Hollomonrelatie

The Hollomonrelatie, or Hollomon equation, is an empirical constitutive model used to describe the plastic deformation of metals by relating true stress to true plastic strain through a power law.

The equation is written as sigma = K * epsilon^n, where sigma is the true stress, epsilon is the true plastic strain, K is the strength coefficient, and n is the strain-hardening exponent. The coefficient K reflects the material’s strength at unit strain, while n indicates how rapidly the material hardens with increasing plastic strain. For many metals, n falls between 0 and 1; a larger n signifies stronger work hardening, whereas a smaller n corresponds to weaker hardening.

Parameters K and n are typically determined from experimental data, usually from the plastic portion of a tensile test. A common method is to plot log(sigma) versus log(epsilon) and extract the slope as n and the intercept as log(K). The model is most accurate within the range where plastic deformation dominates and elastic effects are limited; it is temperature- and rate-sensitive and may lose accuracy outside the tested conditions.

Applications of the Hollomon relation include quick estimates of forming forces, parameter fitting for numerical simulations of metal forming, and interpretation of work-hardening behavior. It is a simple, widely used empirical model, but it does not account for complex microstructural changes, anisotropy, or non-idealities at very high strains, extreme temperatures, or high strain rates.