Strain hardening exponent
# Strain hardening exponent

The strain hardening exponent (also called the strain hardening index), usually denoted $n$, a constant often used in calculations relating to stress–strain behavior in work hardening. It occurs in the formula known as Hollomon's equation (after John Herbert Hollomon Jr.) who originally posited it as

$\sigma =K\epsilon ^{n}$

where $\sigma$ represents the applied true stress on the material, $\epsilon$ is the true strain, and $K$ is the strength coefficient.

The value of the strain hardening exponent lies between 0 and 1, with a value of 0 implying a perfectly plastic solid and a value of 1 representing a perfectly elastic solid. Most metals have an $n$-value between 0.10 and 0.50.

## Tabulation

Tabulation of $n$- and $K$-values for several alloys :

| Material | n | K (MPa) |
| - | - | - |
| Aluminum 1100–O (annealed) | 0.20 | 180 |
| 2024 aluminum alloy (heat treated—T3) | 0.16 | 690 |
| 5052-O | 0.13 | 210 |
| Aluminum 6061–O (annealed) | 0.20 | 205 |
| Aluminum 6061–T6 | 0.05 | 410 |
| Aluminum 7075–O (annealed) | 0.17 | 400 |
| Brass, Naval (annealed) | 0.49 | 895 |
| Brass 70–30 (annealed) | 0.49 | 900 |
| Brass 85–15 (cold-rolled) | 0.34 | 580 |
| Cobalt-base alloy (heat-treated) | 0.50 | 2,070 |
| Copper (annealed) | 0.54 | 325 |
| AZ-31B magnesium alloy (annealed) | 0.16 | 450 |
| Low-carbon steel (annealed) | 0.26 | 530 |
| 4340 steel alloy (tempered @ 315 °C) | 0.15 | 640 |
| 304 stainless steel (annealed) | 0.450 | 1275 |
