Page 49 - Metalorming Magazine January/February 2023

Metal Matters By Daniel J. Schaeffler, Ph.D.
Metal Properties:
Strain-Hardening Exponent (n-Value)
700 600 500 400 300 200 100
DP 340Y/590T Tensile Curve
n = 0.173 when determined
n = 0.205 when determined
from 10% to UE (uniform elongation)
from 4% to 6%
Engineering Stress (MPa)
With some metal alloys, the range over which n-value is calculated changes the calculated n-value.
0
0 5 10 15 20 25 30
Engineering Strain (%)
Plastic deformation strengthens all metal alloys. Rolling in sheet production, straightening dur- ing coil processing and stamp- ing sheet metal into engi- neered part shapes all are forms of plastic deformation.
The interchangeable terms strain hardening and work hardening describe the strengthening that results from plastic deformation; the mag- nitude of this strengthening varies based on the alloy type and the deformation severity. Despite the terms used, this is a strengthening mechanism, not a hardening one.
Strain hardening begins
once deformation exceeds the material’s yield strength and continues until the tensile-test dogbone sample or the engi-
neered stamping either frac-
tures or, instead, reaches the targeted strain level or part shape.
The general shape of a stress-strain curve produced during tensile testing illustrates the influence of strain hard- ening, with the material strengthening
Dr. Danny Schaeffler, with 30 years of materi- als and applications experience, is president of Engineering Quality Solutions (EQS) and chief content officer of 4M Partners. EQS provides product-applications assistance to materials and manufacturing com-
panies; 4M teaches fundamentals and practical details of material properties, forming technolo- gies, processes and troubleshooting needed to form high-quality components. Schaeffler is the metallurgy and forming technical editor of the AHSS Application Guidelines available from Worl- dAutoSteel at AHSSinsights.org.
Danny Schaeffler
248/66-STEEL • www.EQSgroup.com
E-mail ds@eqsgroup.com or Danny@learning4m.com
on the vertical axis and increasing strain on the horizontal axis. Strengthening appears to stop at the tensile strength, but this perceived peak only is an artifact of the effects of the rapidly decreasing cross-sec- tional area of the tensile dogbone sample overpowering the increase in strain hardening.
In 1945, U.S. Army researcher John Holloman discovered a power-law rela- tionship between stress and strain for steels (and some other metal alloys) in the region of uniform plastic defor- mation, which extends from the yield strength to the tensile strength:
σ = Kɛn (eq. 1)
σ, true stress; K, strength coefficient; ɛ, true strain; n, strain-hardening exponent.
Remember that true stress and true strain are based on the ever-changing dimensions as the sample or stamping
deforms, as opposed to engineering stress and engineering strain where changes relate to the initial tensile-bar dimensions.
Determining the strain-hardening exponent (n) requires converting this equation to logarithmic form:
log(σ) = log(K) + n*log (ɛ) (eq. 2)
For metal alloys where the Holloman relationship accurately represents the flow curve, n-value is the slope of eq. 2, and K is the true stress at a true strain ɛ=1.
n-Value Effect on Stamped Parts
Looking at eq. 1, an n-value of 0 corresponds to no work hardening and constant stress for all strains, as any number raised to the power of 0 equals 1. Stress equals the load divided by cross-sectional area, so any deforma- tion leading to a locally reduced thick- ness results in immediate failure once
46 MetalForming/January/February 2023
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