Strain hardening exponent

The strain hardening exponent (also called strain hardening index), noted as n, is a material's constant which is used in calculations for stress–strain behavior in work hardening. It occurs in the formula known as Hollomons equation after John Herbert Hollomon Jr. who originally proposed it[1]:

σ = K ε ⁿ,
where σ represents the applied stress on the material,
ε is the strain,
and K is the strength coefficient.

The value of the strain hardening exponent lies between 0 and 1. A value of 0 means that a material is a perfectly plastic solid, while a value of 1 represents a 100% elastic solid. Most metals have a n value between 0.10 and 0.50.

Tabulation

Tabulation of n and K Values for Several Alloys [2] [3]

Material	n	K (MPa)
Aluminum 1100–O (annealed)	0.20	180
2024 aluminum alloy (heat treated—T3)	0.16	690
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	315
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

References

1. J. H. Hollomon, Tensile deformation, Trans. AIME, vol. 162, (1945), pp. 268-290.
2. Callister, Jr., William D (2005), Fundamentals of Materials Science and Engineering (2nd ed.), United States of America: John Wiley & Sons, p. 199, ISBN 978-0-471-47014-4
3. Kalpakjian, S (2014), Manufacturing engineering and technology (2nd ed.), Singapore: Pearson Education South Asia Pte, p. 62

External links

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