# How do I work out ultimate tensile stress?

1. Jun 5, 2012

### sunnydee

Hey guys!

I'm really stuck and would be grateful for any help. I'm a postgraduate researcher, though not a physicist so this may be a relatively simple problem for some of you (I hope!).

I use a program called Bluehill which is coupled with an Instron machine. The instron is a mechanical testing device that stretches a material gradually and feeds the load and extension applied data to Bluehill which then draws a lovely graph for me (force vs. tensile strain). I know when to stop the machine when I see failure of the material (sudden fall in the graph). Anyway the software also gives me values for the maximum load and elastic modulus (EM) but based on pre-set values for length and area (basically for all dimensions) of the material. So, I have to re-draw the graph from the raw data (raw data containing time, extension and load applied) to recalculate the EM and I use the correct dimensions subsequently work out the correct EM. Similarly, I have to work out the correct ultimate tensile stress (UTS) but not sure how to do this. From the replotted graph, I have the maximum load but which equation do I use do work out the UTS?

Last edited: Jun 5, 2012
2. Jun 5, 2012

### Studiot

Welcome to Physics Forums sunnydee.

Forgive me for asking but if you don't understand what you are doing why are you using that machine and program?

What do you think the ultimate tensile stress signifies?

Do you know the difference between 'engineering stress' and 'true stress'?

We need the answers to be able to help you, particularly to the last question since that may be the source of your difficulty.

3. Jun 5, 2012

### sunnydee

Hi Studiot! Thanks for your reply! We use the program and machine in the lab to determine the mechanical properties of biological materials. Then we use the mechanical data to look for patterns and research the cellular basis of the material's strength. UTS should be in Pa and that is force over area which in my case should be the max load over unit area. However, I've been given an equation to use which doesn't make complete sense to me and I checked with someone else who gave me a different equation to use. The two equations give me different values. So I thought here was the best place to go for help. And it would be true stess, not engineering stress. Thanks!

4. Jun 5, 2012

### Studiot

The test machines do not measure stress directly.

They measure distance (extension) and load (force).

As you stretch something it gets thinner so its Xsectional area decreases.

Engineering stress just measures the extension and the load and computes a stress value assuming the xsection remains as per original.

So engineering stress = Force/original xsection area

If you want Pascals use force in Newtons and Area in metres squared.

http://www.unitjuggler.com/convert-pressure-from-Nm-2-to-Pa.html

If you are measuring true stress you also have to measure the Xsection area as well at each point on the graph and divide the force by this value to calculate the true stress.

It's that simple.

You may well find that when you draw a graph of true stress the curve does not drop at the ultimate.

What are you plotting the graph against extension or strain?

Last edited: Jun 5, 2012
5. Jun 5, 2012

### sunnydee

Thanks again Studiot. It's not possible for me to calculate the area at the maximum load so I guess we have to accept it as engineering stress although true stress actually occurs. I re-plot the graph as force (N) vs extension (mm) directly from the raw data. I think I understand which equation to use i.e. Fmax x 4 / pi x d ^ 2 but I'm not sure whether I should then multiply this value by the set diameter / the actual diameter squared. I've been told to do the latter but not sure why as I use the actual diameter value in the first equation anyway.

6. Jun 5, 2012

### Studiot

Not sure I follow.

You say you can't calculate the true diameter then you say you must multiply by a factor including the actual diameter, then you say you use the actual diameter.

So why can't you calculate the actual stress?

Incidentally you realise that the strain is not the extension?

Strain = extension/original length

and the elastic modulus is stress/strain.

7. Jun 5, 2012

### Studiot

One more point.

The ultimate stress is defined as the highest load recorded in the test divided by the original area.

It is not normally a very useful parameter, since it is procedure dependent.

8. Jun 5, 2012

### sunnydee

Sorry, actual diameter as in the actual diameter of the specimen that I measured before starting the mechanical testing on the Instron. We take images of the specimen then use image j to work out the original diameter later on. Then this value is taken as the actual value whereas the program has a preset value for the diameter which is not the actual value. Please can you elaborate a little on why UTS is not a good parameter? Thanks!

9. Jun 5, 2012

### Studiot

OK you are not the first biological science postgrad to ask questions here about testing biological materials.

I will be off for a couple of hours but will post something later.

Meanwhile I suggest a forum search would be fruitful.