# Strength Coefficient and Strain-Hardening Exponent

Here's the problem:
A metal is deformed in a tension test into its plastic region. The starting specimen had a gage length = 2.0 in and an area .50 sq. in. At one point in the tensile test, the gage length = 2.5 in and the corresponding engineering stress = 24000 psi; at another point in the test prior to necking, the gage length = 3.2 in and the corresponding engineering stress = 28000 psi. Determine the strength coefficient and strain-hardening exponent.

To summarize,
L0 = 2.0 in
A0 = .50 sq. in.
L1 = 2.5 in engineering stress = 24000 psi
L2 = 3.2 in engineering stress = 28000 psi
Here's my solution:

*At the first point given, we can find engineering strain by e = (L1-L0)/L0 = (2.5 - 2.0)/2.0 = .25
-We can then use the engineering stress and the engineering strain to find the true stress by the relationship:
true stress = engineering stress (1+engineering strain) = 24000(1+.25) = 30000 psi
-The true strain is given by ln (L1/L0) = ln (2.5/2.0) = .22

* For the second point, engineering strain = (L2-L0)/L0 = (3.2-2.0)/2.0
= .6
- Hence, true stress = engineering stress (1+engineering strain) =
28000(1+.6) = 44800 psi
- True strain is ln (L2/L0) = ln (3.2/2.0) = ln 1.6 = .47

*So we now have two points on our true stress-strain curve: (.22, 30000) and (.47, 44800).
The book plots these points using a log scale and then finds the slope to determine the strain hardening exponent. So n = (log 44800 - log 30000)/(log .47 - log .22) = .52
Does this seem right...I know n for most metals is between 0 and .5, so is .52 a reasonable result???

*The strength coefficient, K, equals the value of true stress at a true strain value equal to 1.
Using the point slope equation with the x-coordinate (true strain) equal to 1, I get:
y - y1 = m(x-x1)
log y - log 30000 = .52 (log x - log .22)
log y - log 30000 = .52 (1 - log .22)
log y - log 30000 = .8619402
y = 218304 psi
K = 218304 psi

Does this seem correct? It seems a little large!

Thanks for reading! Any help much appreciated!

I apologize for

Calculations for n look fine.. I'd say the question is the problem ;)

In fact I'm surprised the answers are even close to reasonable, I'd be worried any time you'd have to do a straight line fit between just two points.

Most the time I have to calculate a slope from data I use 3 to 5 points to smooth out results due to inevitable noise/errors

Hi dear
I think that you mistake in calculation k,beacuse stead(log X)you should write (log 1)that means(0),but you write log X=1. !!!!!
https://www.physicsforums.com/showpost.php?p=1460020&postcount=2 [Broken]

yeah I think this is the error here.. with log 1 you get something like 123 psi

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