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Calculating Yield Strength using a Load vs. Displacement Curve 
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#1
Apr710, 12:54 PM

P: 4

Hi,
This question came up on my midterm and I had no idea how to answer it without redrawing the entire curve as a stress vs. strain curve (which obviously took too long to do). Anyway, I'm just requesting a general procedure, not a numerical answer. If you had a Load (yaxis) vs. Displacement (xaxis) curve, how do you calculate the yield strength? I know for a stress vs. strain curve, you have to have a 0.2% (0.002) offset, but my Professor told me that the offset is not of the same value in a Load vs. Displacement curve (which makes sense). However ... what <i>is</i> the actual offset supposed to be? Is there a formula to calculate it? Any help would be very much appreciated! :) Thank you, Gina 


#2
Apr710, 05:33 PM

Admin
P: 21,810

The 0.2% (0.002) is a value of strain, which is arbitrary, but it covers somewhat the uncertainty of when a given material actually departs from the purely linear (elastic) relationship between stress and strain.
Let l = length, then strain ε = (l  l_{o})/l_{o}, where l_{o} = original length (usually the gauge length). Also, the displacement, d, is given by (l  l_{o}), so strain ε = d/l_{o}. Similar the stress, σ, is just the load/force F divided by area A, i.e. σ = F/A, where A is constant until the specimen reaches UTS, which corresponds to the limit of uniform elongation, and necking begins. Now back to length/displacement  with ε = (l  l_{o})/l_{o}, one rewrites the equation as ε = l/l_{o}  1, and reorganizing the terms, l = l_{o} (1+ε), so the length equivalent to the strain offset of 0.002 is just l = l_{o}*1.002, or d (0.002) = 0.002 l_{o}. 


#3
Sep1310, 11:03 PM

P: 450

A = 0.36m^{2} F = 9800N @ 0.2% offset Then [sigma] = 9800/0.36 = 2.7*10^{4} Pa ?? I just have a problem regarding the constant area. Wouldn't the crosssectional area be decreasing while the object is strained (stretched)? 


#4
Sep1410, 12:25 PM

Sci Advisor
P: 2,283

Calculating Yield Strength using a Load vs. Displacement Curve
CS 


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