Quick note about the calculation of yield strength and doing precision error analysis

We only collected two runs of data in the lab, but I have learned from the professors that we (the GSIs) are you going to give all of you one additional set of data from another lab section so you can have a bit more data for the precision analysis. You will still use the data you collected in your own lab section to create the final stress-strain curve, and the extra data set will simply be used to quantify uncertainty due to precision (I should be sending out an email about this soon).

Another very important item that you will all encounter is the calculation of the yield strength of the brass, which is required by the task letter. Now, what some of you may find is when you find your inflection point (where the brass yielded) in the stress-strain curve and get a yield stress, it may be a bit under the yield stress you see quoted as standard. This is because using the inflection point in the curve is the classical definition of yield stress. Generally, this is not what manufacturers or material properties texts will quote. Rather, they will give you a yield strength with some offset (oftentimes this is either 0.2% or 0.5%). What this means is that in order for you to calculate a yield strength that can be properly compared to the standard, you will need to account for this offset.

How do you do that? Glad you asked. What you need to do is plot a straight line with the same slope as the elastic modulus that starts on the abscissa from whatever the offset strain is, and intersects with your stress-strain curve. The intersection of those two lines will give you a value that is much more comparable to the quoted standard, and when you are giving your value and the standard please make sure you mention that it is the yield stress with a given offset.

I mentioned this during labs this week, but it bears mentioning again. Any time you calculate some value that can be compared to a standard (i.e. density, elastic modulus, etc.) ALWAYS mention what you calculated with your uncertainty and compare it to the standard. The purpose of this is two-fold...it is a sanity check to you that you are using a reasonable value in further calculations and it also convinces the client you actually know what you are doing (essentially you are supposed to convince me of this fact when I'm grading the labs).