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The strain hardening exponent (also called the strain hardening index), usually denoted $n$ , 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:

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

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. 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 $n$ - and $K$ -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

^ ^a ^b ^c 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.
^ J. H. Hollomon, Tensile deformation, Trans. AIME, vol. 162, (1945), pp. 268-290.
^ 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
^ Kalpakjian, S (2014), Manufacturing engineering and technology (2nd ed.), Singapore: Pearson Education South Asia Pte, p. 62
^ "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

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[:0-1] 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.

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@@ Line 1: / Line 1: @@
+{{Short description|Measurement in material science}}
-The '''strain hardening exponent''' (also called '''strain hardening index'''), noted as ''n'', is a materials constant which is used in calculations for [[Stress–strain curve|stress–strain behavior]] in [[work hardening]].
+{{Context|date=June 2021}}
+The '''strain hardening exponent''' (also called the '''strain hardening index'''), usually denoted <math>n</math>, is a measured parameter that quantifies the ability of a material to become stronger due to strain hardening. [[Work hardening|Strain hardening]] (work hardening) is the process by which a material's load-bearing capacity increases during plastic (permanent) [[Strain (mechanics)|strain]], or [[Deformation (engineering)|deformation]]. This characteristic is what sets ductile materials apart from brittle materials.<ref name=":0">{{Cite journal |last=Scales |first=M. |last2=Kornuta |first2=J.A. |last3=Switzner |first3=N. |last4=Veloo |first4=P. |date=2023-12-01 |title=Automated Calculation of Strain Hardening Parameters from Tensile Stress vs. Strain Data for Low Carbon Steel Exhibiting Yield Point Elongation |url=https://doi.org/10.1007/s40799-023-00626-4 |journal=Experimental Techniques |language=en |volume=47 |issue=6 |pages=1311–1322 |doi=10.1007/s40799-023-00626-4 |issn=1747-1567}}</ref> The uniaxial tension test is the primary experimental method used to directly measure a material's [[Stress–strain curve|stress–strain behavior]], providing valuable insights into its strain-hardening behavior.<ref name=":0" />
+The strain hardening exponent is sometimes regarded as a constant and occurs in [[forging]] and [[Forming (metalworking)|forming]] calculations as well as the formula known as Hollomon's equation (after [[John Herbert Hollomon Jr.]]) who originally posited it as:
-In the formula σ = K ε <sup>n</sup>,<br />
-σ represents the applied [[Stress (physics)|stress]] on the material,<br />
-ε is the [[Strain (materials science)|strain]],<br />
-K is the strength coefficient.
+<math>\sigma=K\epsilon^n</math><ref>J. H. Hollomon, Tensile deformation, Trans. AIME, vol. 162, (1945), pp. 268-290.</ref>
-The value of the strain hardening exponent lies between 0 and 1. A value of 0 means that a material is a perfectly [[Plasticity (physics)|plastic]] solid, while a value of 1 represents a 100% [[Elasticity (physics)|elastic]] solid. Most metals have an n value between 0.10 and 0.50.
+where <math>\sigma</math> represents the applied [[Stress (physics)|true stress]] on the material, <math>\epsilon</math> is the [[Strain (materials science)|true strain]], and <math>K</math> is the strength coefficient.
+The value of the strain hardening exponent lies between 0 and 1, with a value of 0 implying a perfectly [[Plasticity (physics)|plastic]] solid and a value of 1 representing a perfectly [[Elasticity (physics)|elastic]] solid. Most metals have an <math>n</math>-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,<ref name=":0" /> with the lower end of the range dominated by [[High-strength low-alloy steel|high-strength low alloy]] steels and the upper end of the range mostly [[Annealing (metallurgy)#Normalization|normalized]] steels.
 ==Tabulation==
 {| class="wikitable"
-|+ Tabulation of n and K Values for Several Alloys <ref>{{Citation
+|+ Tabulation of <math>n</math>- and <math>K</math>-values for several alloys <ref>{{Citation
   | first = William D | last = Callister, Jr.
   | title = Fundamentals of Materials Science and Engineering
   | place = United States of America
-  | publisher = [[John Wiley & Sons]]
+  | publisher = [[John Furkan & Sons]]
   | edition = 2nd
   | year = 2005
   | page = 199
   | isbn = 978-0-471-47014-4
-}}</ref>
+}}</ref><ref>{{Citation
+  | first = S | last = Kalpakjian
+  | title = Manufacturing engineering and technology
+  | place = Singapore
+  | publisher = [[Pearson Education South Asia Pte]]
+  | edition = 2nd
+  | year = 2014
+  | page = 62
+}}</ref><ref>{{Cite book|url=https://www.worldcat.org/oclc/21034891|title=ASM handbook|publisher=ASM International. Handbook Committee.|year=2005|isbn=978-0-87170-377-4|edition=10th|location=Materials Park, Ohio|pages=482|chapter=41.2 Roll Formed Aluminum Alloy Components|oclc=21034891}}</ref>
 ! Material !! n !! K (MPa)
 |-
-| Low-carbon steel (annealed) || 0.21 || 600
+| Aluminum 1100–O (annealed) || 0.20 || 180
 |-
-| 4340 steel alloy (tempered @ 315 °C) || 0.12 || 2650
+| 2024 aluminum alloy (heat treated—T3) || 0.16 || 690
 |-
+|5052-O
-| 304 stainless steel (annealed) || 0.43 || 1400
+|0.13
+|210
 |-
-| Copper (annealed) || 0.44 || 530
+| Aluminum 6061–O (annealed) || 0.20 || 205
 |-
-| Naval brass (annealed) || 0.21 || 585
+| Aluminum 6061–T6 || 0.05 || 410
 |-
-| 2024 aluminum alloy (heat treated—T3) || 0.17 || 780
+| 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&nbsp;°C) || 0.15 || 640
+|-
+| 304 stainless steel (annealed) || 0.450 || 1275
 |}
@@ Line 42: / Line 75: @@
 ==External links==
-* [http://steel.keytometals.com/Articles/Art42.htm More complete picture about the strain hardening exponent in the stress–strain curve on ''www.key-to-steel.com'']
+* [https://web.archive.org/web/20081230025544/http://steel.keytometals.com/Articles/Art42.htm More complete picture about the strain hardening exponent in the stress–strain curve on ''www.key-to-steel.com'']
-{{engineering-stub}}
 [[Category:Mechanical engineering]]
 [[Category:Solid mechanics]]
+{{engineering-stub}}