Stress strain

[bidga1]

I apologise if this is obvious. I was having a discussion at work and someone said that back calculating stress from Young’s Modulus isn’t good practice. The problem is that the analyst has calculated the compressive stress from the deflection using sigma = (E x extension) / length. Does anyone know if this is good or bad practice?

 

[hydtools]

How would you otherwise do it without knowing force and area?

Ted

 

[rb1957]

How would you know the extension (contraction) ? I'm trying to visualise structures in compression that are not directly loaded ???

I guess the issue, without knowing the cross-section, is (could be) that this would be the average stress, not the peak stress.



another day in paradise, or is paradise one day closer ?

 

[EdStainless]

We used to take very accurate E data for tensile tests, but we did them a bit differently.
We would put a sample into the machine and then load it to about 50% of the yield, then unload to about 10%, and then very slowly reapply load. This would take the slack and flex out of the system.
Taking a E from a standard tensile or compression test is not usually very reliable. After all how often do you encounter a material where the E is not a well known value?

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P.E. Metallurgy

 

[rb1957]

I assumed it was the handbook/spec E ?

another day in paradise, or is paradise one day closer ?

 

[EdStainless]

When you very severely cold work a metal (steel wire, 400ksi UTS) you can alter the E, for springs this can be a disaster as it changes the spring rate. In very high strength wire we were required to measure and report the E, it was measurably different from the handbook value , and there was a tolerance on it.

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P.E. Metallurgy

 

[phamENG]

E is usually an approximate value - depending on the data set from testing you could be using a tangent modulus, chord modulus, initial tangent modulus, or a secant modulus (I may have forgotten one). In other words, the stress-strain relationship of any real world material is non-linear, even when behaving elastically. For us structural folks, it's good enough 99.99999% of the time. If you need a highly accurate stress value for some critical machine part - I would not rely on E=stress/strain.

 

[STrctPono]

So long as the material remains linear elastic, I don't know how else you would do it. For a non-linear problem, then yes, this would be a bad idea to use Young's Modulus.

 

[EdStainless]

One place that I worked we had a rig to measure the speed of sound in samples, and since that is directly related to E we could calculate the exact values. For a large range of carbon and low alloy steels in many different HT conditions we always had values in the range of 27.5-30.0 mpsi. Specific grade/HT combinations would repeat withing +/-0.2 mpsi.

In the old days with manual tensile test machines we had a 'triangle' made of plex and the slope of it was 29 mpsi. This is how the technician would draw the line to get Yield strength.

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P.E. Metallurgy

 

[rb1957]

"we had a rig to measure the speed of sound in samples" … must've been a very neat experiment … to measure something like 6000 m/sec with any sort of accuracy.

mind you there are youtubes showing how to calculate the speed of light using marshmallows and a microwave !!

 

[bidga1]

Hi STrctPono

Yes that's what I thought. As long as you are in the elastic range it would be fine. I'm not sure what you would do in the plastic region

 

[phamENG]

The problem is that there is no perfectly "linear" elastic range. For most general engineering applications, it's close enough to linear that we can use published values (especially in steel) and most structural engineering applications refer to linear elastic behavior because, again, it's "close enough." But it's important to remember that the linearity is an approximation and, depending on your material, the approximation could be off by quite a bit at various load levels.

So in some cases, yes, it's just fine to use the E=stress/strain relationship to approximate the stress in a member based on strain. But it's also important to remember that it will never tell you definitively what the exact stress is.

 

[bidga1]

Thanks phamENG. That's a great help

 

[EdStainless]

and remember that the Yield Strength that we use in engineering is a constructed value any way, it is out of convenience not true material behavior. And since it is an approximation the methods for determining it are also approximations. We just have to accept that.

If you have never done flex and alignment measurements on a tensile machine it is very interesting. And it causes you to question all of your yield strength measurements.

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P.E. Metallurgy

 

[bidga1]

But a conservative approximation?

 

[EdStainless]

A reasonable approximation.
When was the last time that you actually loaded a finished product to yield, on purpose?
Sure you get some distortion, but in many systems that slight distortion is acceptable.

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P.E. Metallurgy

 

[bidga1]

Thanks