Strain hardening exponent explained
The strain hardening exponent (also called the strain hardening index), usually denoted
, is a measured parameter that quantifies the ability of a material to become stronger due to strain hardening.
Strain hardening (work hardening) is the process by which a material's load-bearing capacity increases during plastic (permanent)
strain, or
deformation. This characteristic is what sets ductile materials apart from brittle materials.
[1] The uniaxial tension test is the primary experimental method used to directly measure a material's
stress–strain behavior, providing valuable insights into its strain-hardening behavior.
The strain hardening exponent is sometimes regarded as a constant and occurs in forging and forming calculations as well as the formula known as Hollomon's equation (after John Herbert Hollomon Jr.) who originally posited it as:
[2] where
represents the applied
true stress on the material,
is the
true strain, and
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
-value between 0.10 and 0.50. In one study, strain hardening exponent values extracted from tensile data from 58 steel pipes from natural gas pipelines were found to range from 0.08 to 0.25, with the lower end of the range dominated by
high-strength low alloy steels and the upper end of the range mostly normalized steels.
Tabulation
Tabulation of
- and
-values for several alloys [3] ! 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 |
| Low-carbon steel (cold worked) | 0.08 | 700 |
| 4340 steel alloy (tempered @ 315 °C) | 0.15 | 640 |
| 304 stainless steel (annealed) | 0.450 | 1275 | |
External links
Notes and References
- Scales . M. . Kornuta . J.A. . Switzner . N. . Veloo . P. . 2023-12-01 . Automated Calculation of Strain Hardening Parameters from Tensile Stress vs. Strain Data for Low Carbon Steel Exhibiting Yield Point Elongation . Experimental Techniques . en . 47 . 6 . 1311–1322 . 10.1007/s40799-023-00626-4 . 1747-1567.
- J. H. Hollomon, Tensile deformation, Trans. AIME, vol. 162, (1945), pp. 268-290.
- Book: ASM handbook. ASM International. Handbook Committee.. 2005. 978-0-87170-377-4. 10th. Materials Park, Ohio. 482. 41.2 Roll Formed Aluminum Alloy Components. 21034891.
