Calculating Young's Modulus from this Stress/Strain Graph

[Ben_Walker1978]

Homework Statement

Young's Modulus

Relevant Equations

e = Stress/Strain

I am trying to calculate Young's Modulus on the graph below.

I have run the test through some software, now want to calculate Young's Modulus to ensure my analysis can be relied upon to be scientifically sound.

This is what i have calculated from learning online. Is this correct? I have 2 more graphs to do after this.

As you can see i have drawn a line in black to calculate, although not sure if it is correct, or in the correct place.

0.18% Mild Steel

My calculations:

Young's Modulus
$$Slope = e /Θ=Stress /Strain =2.00e + 02 / 0.250e − 02 = 200 /0.00250 = 80,000MPa $$Is this correct to calculate Young's Modulus from this graph?

If not where have i gone wrong?

Thomas.

 

[Chestermiller]

It looks about right, although the graph at small strains should approach a straight line.

 

[Ben_Walker1978]

Thank you for your reply. What do you mean small strains? I don't undertsand

 

[Dr_Nate]

Your calculation is not correct. You need two pairs of values. This is because your data has a 'toe' region that is from initial slippage of the material in the apparatus. See https://www.ipc.org/TM/2.4.18.3.pdf

You also made an error reading from the graph and plugging the value in your equation.

 

[Ben_Walker1978]

Hello @Dr_Nate Thanks for the reply. Not heard of this before. I have looked at 'toe' region. What error have i made from the graph? This is where i though i may have gone wrong

 

[Dr_Nate]

Glad I could help. But, I was intentionally vague. You've only got two values that you took from the graph. I'm sure you'll figure out which one it is. You are off by a factor of 10.

 

[Ben_Walker1978]

So one of the Stress or strain values is incorrect? Is it the strain as i did -02

 

[haruspex]

So one of the Stress or strain values is incorrect? Is it the strain as i did -02

Sort of, but it might be more natural to consider the error as the position of the decimal point in the 0.25.
Wrt to the toe, you need to start your straight line slope where the curve straightens, round about stress = 1.0e+2, and make it as long as possible, so going to a stress of around 3.0e+2.

 

[Ben_Walker1978]

Ok i understand. But then from the straight line what is the best way to calculate the stress and strain? Like i have attached? I have 3 samples of steel to do this on. Just want to get the correct way before i calculate on all 3. I the image i have drawn the black line from the straight part (Toe). Then the red line to calculate the stress/strain. Is this correct? And what now? Thanks.

 

[Dr_Nate]

Just a point of vocabulary: the toe region is the region at the beginning from 0 to approximately 1.5E-5.

To find the slope of the line you need two pairs of points. One pair is often (0, 0) so you may have overlooked this. Look at the image here.

 

[Ben_Walker1978]

So basically i have done only one point, but need to do two. The question i have now is where do i place the 2 points ? How do i determine where they go? Then i will have a go at the problem and post on here. Thank you for your help

 

[haruspex]

Ok i understand. But then from the straight line what is the best way to calculate the stress and strain? Like i have attached? I have 3 samples of steel to do this on. Just want to get the correct way before i calculate on all 3. I the image i have drawn the black line from the straight part (Toe). Then the red line to calculate the stress/strain. Is this correct? And what now? Thanks.

View attachment 260399

Forget the red line, you want the slope of the black line. That is, the height of the black line, from its bottom to its top, divided by its width, from leftmost to rightmost.

 

[Ben_Walker1978]

I have attempted that. Attache is my graph with the lines, and the calculation. Is this correct now? Thank you for your constant help, much appreciated whilst trying to learn this.

Slope = e /Θ=Stress /Strain =2.00e + 02 / 1.250e − 02 = 200 /0.00125 = 160,000MPa

Is this now correct?

 

[haruspex]

I have attempted that. Attache is my graph with the lines, and the calculation. Is this correct now? Thank you for your constant help, much appreciated whilst trying to learn this.

View attachment 260466

Slope = e /Θ=Stress /Strain =2.00e + 02 / 1.250e − 02 = 200 /0.00125 = 160,000MPa

Is this now correct?

You have a factor of 10 error again.
Since I don't know what units your stress and strain measurements are in, I can't tell if MPa is right.

 

[Dr_Nate]

I have attempted that. Attache is my graph with the lines, and the calculation. Is this correct now? Thank you for your constant help, much appreciated whilst trying to learn this.

View attachment 260466

Slope = e /Θ=Stress /Strain =2.00e + 02 / 1.250e − 02 = 200 /0.00125 = 160,000MPa

Is this now correct?

If you fix the factor of 10 that @haruspex mentioned then you are doing the calculation correctly. However, I am unsure if this software is giving you the correct values. You should be getting an answer close to 200 GPa for steels. Your black crosshair doesn't match with the stress axis, but neither of those values will give you a value close to 200 GPa.

 

[Ben_Walker1978]

All i have is that graph to go from. I select the 5 carbon steel then it creates that graph. So i guess its MPa. Where am i going wrong with the factor of 10? Can someone show me please. What do you mean my black line doesn't match with the stress axis?

 

[haruspex]

So i guess its MPa. Where am i going wrong with the factor of 10?

Here's the factor of ten error:

.../1.250e − 02 = ... /0.00125

Unfortunately, as @Dr_Nate points out, correcting that makes the modulus about a tenth of what it should be.

 

[Ben_Walker1978]

So it needs to be 1.250e-01 which = 0.0125

Also i have been given this software to use to learn for a unit. So now this is confusing me even more that it could be wrong.

Can you see anywhere else i could be going wrong to be out by so much? Or the software is just wrong?

 

[haruspex]

So it needs to be 1.250e-01 which = 0.0125

No, 1.250e-02 which = 0.0125

 

[Dr_Nate]

So it needs to be 1.250e-01 which = 0.0125

Also i have been given this software to use to learn for a unit. So now this is confusing me even more that it could be wrong.

Can you see anywhere else i could be going wrong to be out by so much? Or the software is just wrong?

It really seems to be that the numbers they give you are wrong. This is not unheard of with these types of programs. Can you share an image of a different graph? Maybe, another one will have correct values.

 

[Ben_Walker1978]

This is what i have:

You are provided with samples of steel, each with a different % of carbon. You have access to virtual tensile testing equipment (destructive) at http://classroom.materials.ac.uk/tensile.php

You are required to carry out tests on a 0.18% mild steel, 0.41% medium carbon steel and a 0.8% high carbon steel using the virtual tensile testing equipment and you should present the results and graphs in a formal laboratory report. You will produce a laboratory report which is structured to follow a formal scientific method for the tensile test and present your results and calculate the Youngs modulus, thus ensuring your analysis can be relied upon to be scientifically sound.

Below is the 3 graphs produced in the software. I need to calculate Youngs Modulus for all 3.

Thank you for keep trying to help me solve.

 

[Dr_Nate]

I've checked out the software. It is definitely buggy. If you move the cursor (black crosshairs) horizontally, you can see the strain jump to numbers it shouldn't. If you move the cursor vertically, you can see it jump to numbers you shouldn't.

Luckily, in the region that you need to measure the cursor works fine. That must be how you got your numbers. Therefore, you are good to go. You have the right answer.

 

[Ben_Walker1978]

Thank you for looking. So the software is just about good enough.

From the help off you guys i have completed all 3 graphs. Would it be possible for someone to look and check my answers? Hopefully have finally got this learned after a week of learning it. Below are my attempts drawn on the graphs and calculations.

In my strain i have placed +00 as in my graphs in the software below 5.00E-02 it says +00 at the end.

Also is this in MPa or Pa?

0.8%

Stress/Strain = 4.00E+02/2.50E+00 = 400/2.70 = 160MPa

0.18%

Stess/Strain = 2.00E+02/1.50E+00 = 200/1.5 = 1.33 MPa

0.41%

Stress/Strain = 3.80E+02/2.50E+00 = 380/2.50 = 152MPa

 

[Dr_Nate]

Have a closer look at the final image you shared. All the slopes are extremely similar. Don't you think that your Young modulus numbers should be very close? One of your values is far off because the software is giving you an erroneous number.

 

[Dr_Nate]

I can see why the units are confusing. The software isn't displaying things in a standard way. It say's "Pa millions", so that means MPa.

 

[Ben_Walker1978]

Thank you.

They are quite close.133MPa, 152MPa, 160MPa.

Shall i make the Toe smaller on some to get closer?

How can i make them closer?

 

[Dr_Nate]

Thank you.

They are quite close.133MPa, 152MPa, 160MPa.

Shall i make the Toe smaller on some to get closer?

How can i make them closer?

You want to go further into the region where the data curves and was caused by experimental error? The definition of Young's modulus requires a linear regime.

 

[Ben_Walker1978]

Like This??

 

[Dr_Nate]

No. You've been doing it right. Why are you trying to change things? Your black line to fits well with the coloured lines. You are done. There is nothing more to discuss here.

 

[Ben_Walker1978]

Ok. Thank you very much for your help. Very much appreciated.