There are two common mathematical descriptions of the work hardening phenomenon. Hollomon's equation is a power law relationship between the stress and the amount of plastic strain:
where σ is the stress, K is the strength index or strength coefficient, ε is the plastic strain and n is the strain hardening exponent. Ludwik's equation is similar but includes the yield stress:
If a material has been subjected to prior deformation (at low temperature) then the yield stress will be increased by a factor depending on the amount of prior plastic strain ε:
The constant K is structure dependent and is influenced by processing while n is a material property normally lying in the range 0.2–0.5. The strain hardening index can be described by:
This equation can be evaluated from the slope of a log(σ) – log(ε) plot. Rearranging allows a determination of the rate of strain hardening at a given stress and strain: