How to plot stress - strain and work out the Young's modulus

[Roshane]

Homework Statement

I have the following table

Load 25 50 75 100 125 150 160 170
Extension 0.38 0.75 1.15 1.53 2.8 8.6 15 28
and I need to:

1. Plot the stress – strain or (load-extension) graph and determine

(a) Approximate value of the elastic limit

(b) Young’s Modulus for the material

Homework Equations

c) Compare this value with the reference books and state what material it may be.

(d) The 0.5 per cent proof stress

The Attempt at a Solution

· When the graph is plotted and I attempt to work it out with software, it shows that the data has a systematic error (It doesn’t intercept y at the origin).

This is again shown when a graph of the natural log of strain vs stress is plotted. It should result in a straight line going through the origin, but it doesn’t.

 

[Dr. Courtney]

Many fitting programs have an option to set the vertical intercept to zero.

Also, knowing the units would be helpful in advising the solution.

 

[DEvens]

What would an elastic system become if you stretched it too far? How does that relate to part (a) of this question?

You are expecting a nice F = - k x kind of Hooke's law behaviour. But, if a system is behaving elastically, then you stretch it too far, how will the stress-strain curve behave? And does your data look like you would expect it to look if this is the case?

 

[Chestermiller]

The first four points fall on almost a perfect straight line through the origin.

Chet

 

[Dr. Courtney]

That's a good point. For the first four points, the material shows elastic behavior and only deviates significantly from a line through the origin for loads above 100.

This suggest an approach to finding an elastic limit would be to graph the points. Then try fitting subsets of the points to a line. When there is a significant deviation from a line or the line does not go through the origin, you must be fitting to points where the load is above the elastic limit.