Hollomon Strain Hardening Calculator
Calculate true stress from true strain using the Hollomon power law.
Enter strength coefficient K and strain hardening exponent n to model work hardening and estimate UTS.
The Hollomon equation (also called the power-law hardening model) describes how a metal’s true stress increases with true strain during plastic deformation:
sigma_true = K * epsilon_true^n
where K is the strength coefficient (MPa) and n is the strain hardening exponent.
Interpreting n. n = 0 means perfectly plastic (no hardening). n = 1 means linear hardening (rare). For most structural metals, n falls between 0.1 and 0.5. Low-carbon steels: n ~ 0.2. Cold-worked aluminum: n ~ 0.1. Annealed copper: n ~ 0.5. Higher n means more capacity to redistribute strain before necking.
Relationship to tensile test. The UTS and uniform elongation can be estimated from the Hollomon constants using the Considere criterion. Necking begins when the true strain equals n:
epsilon_neck = n sigma_UTS = K * (n / e)^n (where e is Euler’s number, 2.718…)
True stress vs engineering stress. Engineering stress is force divided by original area. True stress is force divided by current (smaller) area. The two diverge after yielding. The conversion is: sigma_true = sigma_eng * (1 + epsilon_eng), valid before necking.
Determining K and n from test data. Take a log-log plot of true stress vs true strain: the slope gives n and the intercept at epsilon = 1 gives K. Two points from the plastic region are sufficient if you trust the Hollomon model to hold. Real metals sometimes show two-stage hardening not captured by a single Hollomon fit.