Strain hardening exponent

The strain hardening exponent (also called the strain hardening index), usually denoted ${\displaystyle n}$, 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.^[1]

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:

${\displaystyle \sigma =K\epsilon ^{n}}$^[2]

where ${\displaystyle \sigma }$ represents the applied true stress on the material, ${\displaystyle \epsilon }$ is the true strain, and ${\displaystyle K}$ 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 ${\displaystyle n}$-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,^[1] 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 ${\displaystyle n}$- and ${\displaystyle K}$-values for several alloys ^[3]^[4]^[5]

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

References

1. 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. 47 (6): 1311–1322. doi:10.1007/s40799-023-00626-4. ISSN 1747-1567.
2. J. H. Hollomon, Tensile deformation, Trans. AIME, vol. 162, (1945), pp. 268-290.
3. Callister, Jr., William D (2005), Fundamentals of Materials Science and Engineering (2nd ed.), United States of America: John Furkan & Sons, p. 199, ISBN 978-0-471-47014-4
4. Kalpakjian, S (2014), Manufacturing engineering and technology (2nd ed.), Singapore: Pearson Education South Asia Pte, p. 62
5. "41.2 Roll Formed Aluminum Alloy Components". ASM handbook (10th ed.). Materials Park, Ohio: ASM International. Handbook Committee. 2005. p. 482. ISBN 978-0-87170-377-4. OCLC 21034891.

External links

• More complete picture about the strain hardening exponent in the stress–strain curve on www.key-to-steel.com