Young's modulus height dependent

[cobram]

Hello!

First I want to apologize for my broken english.

The problem I don't understand is this.
We have rod porous materials and we want to measure modulus. We made compression tests and if I have diferent height of tablet or rod for example, the diameter is about 12mm and height is 2,3,6,9,15,...mm we got always diferent modulus. The material is not plastic, it goes back to original size after 2-3 days.

How can we obtain modulus of elasticity for our material???

Aleš

 

[Metalguy]

Eliminate the porosity.

"You see, wire telegraph is like a very long cat. You pull his tail in New York and his head is meowing in Los Angeles. Do you understand this? Radio operates the same way: You send signals here, they receive them there. The only difference is there is no cat." A. Einstein

 

[Metalguy]

Unless the porosity is necessary and you cannot eliminate it, it would have to be very uniform in order to get a repeatable modulus measurement.

"You see, wire telegraph is like a very long cat. You pull his tail in New York and his head is meowing in Los Angeles. Do you understand this? Radio operates the same way: You send signals here, they receive them there. The only difference is there is no cat." A. Einstein

 

[EdStainless]

This material slowly recovers to original size?
It does not have an elastic modulus, they call it something else in cases like this.

= = = = = = = = = = = = = = = = = = = =
Plymouth Tube

 

[Japo]

So your material is strongly non linear... So? Do you have any reason to expect linearity from such a material?

 

[btrueblood]

One quick thought - are you deflecting the samples by the same percentage of height?

 

[blacksmith37]

Sounds like a rheology problem: Properties being a function of time.

 

[cobram]

I made compression test with Instron and I got linear curves. But when I take tablets with higher height I get smaller modulus. And when I take rod with diameter cca 14mm and height 45 mm I get modulus ~ 7Mpa. And for d 14mm and h 30 mm modulus ~ 8Mpa, d14mm h 15mm E=16Mpa ecetera.

We were first thinking that our material (porous monolith) is plastic. But after few days it goes back to original size. We want to predict from small amounts of our material the properties of the cylinder with dimensions d ~ 12mm and h~20cm.

Is there any book, equation, theory... that explains similar problems? Thank you all for comments. I will examine the propose of time depending properties.

 

[btrueblood]

Is the material buckling under compression?

 

[SWComposites]

How are you measuring strain?

How are you calculating the modulus values?

 

[btrueblood]

Actually sitting for a few minutes and thinking about how you are likely running your test, and with SW's post to jar the dust loose...

You are likely measuring end effects when using shorter samples. I.e., the friction restraint of the loading platens is constraining movement of the material at the ends of the pills, giving a locally higher stiffness. Unless you measure strain at or near the center of the part, and with a part long enough that the end effects can be neglected, you will measure higher load for a given deflection for shorter parts.

A possible way around this would be to model the material with an FEA analysis, looking at how end restraint conditions affect the longitudinal stiffness. That, plus a lot of testing to verify results across a lot of batches of material might give you enough correlating data to predict the compression stiffness of larger lengths given a test of a short sample.

 

[Ron]

My guess is that you have a high Poisson's ratio material, so the longer the specimen, the more error you'll have.

 

[Compositepro]

You are seeing twice the modulus when your specimen is half the length. You are calculating strain and modulus incorrectly. Strain is a dimensionless number. It is change in length per unit length not just change in length.

 

[cobram]

First, thank you for answers. It's really helpful.

I'm not calculating the strain by myself, because the software of machine do it. And yes it is dl/l. I think that the problem is not in calculations, because the software do it for me.

Bthrueblood,Can you give me some more information about FEA analysis? I will consider all answers and tell make some new calculations. I will report you when I will discover something new.

Thank you for all answers and for helping me.

 

[cloa]

What is the base material? What is the porosity? It could be acting like a foam and getting elastic buckling of the cells- hence people's question of how uniform the porosity is so more cells could be buckling in a shorter length.

 

[btrueblood]

cobram,

FEA = Finite Element Analysis, i.e. numerical stress analysis. Can you post a sketch of your experimental setup, and what/how data is collected? There's a lot of guessing by all of us to fix your problem, so some more complete explanation would help. I am assuming the load and deflection are being recorded, with you putting the sample height into the machine for it to do the dL/L calculation, thus my concern for end effects. And Ron is right, those end effects (frictional restraint) are magnified a lot by having high Poisson ratio materials, as they want to expand more in section for a given amount of compressive strain.

If my assumption of your test is incorrect, could you describe how the deflection is measured? Is there an extensometer measuring deflection of the sample over a short gauge length of the sample, or an electronic strain gage bonded to the sample, or an optical measurement?

Local buckling of cells is a possibility I thought of too, but it should be a non-issue as long as the sample height is much greater than the typical pore size (another assumption), though cellular materials to show higher Poissons ratios than non-celled (back to end effects).

Remember the saying "a picture is worth 1000 words"...

 

[cobram]

Hello!

My apologize for answering so late...(holiday and then flu)...anyway

I have read a lot of literature about poroelasticity and I discover that the porous materials have diferent laws and eqations that govern their mechanical behavior.

We have a monolith porous material with open pores and we pump water into our material. I discovered Biot articles about flow, porosity and mechanical behavior of poromaterials. I'm a chemist and I know almost nothing about engineering...

We want to measure in our laboratory our material sintetized in diferent ways so we can obtain the best material for our product.

Which measurement we must do to make than good FEA analysis.
From articles I assumed that we must measure dV and dP for jacketed and unjacketed sample and also measure pore pressure. From this measurement they say we obtain K (bulk modulus), B,alpha (biot coeficients) that are needed for FEA analysis.

So what I have to measure, how I have to measure and which coeficients/measurements are needed for computer analysis?
We first thing that this is usual elastic mechanics so we measure with compression and flex tests elastic moduli. Mistake.

Our material is like this:

and we think that because we can pump water through it is like this:

 

[bradleyelwood]

cobram

First, I hope you are over the flu and feeling better.

Second, I think that btrueblood has the right explanation, the end effects constrain the material. Your material probably has a poison's ratio approaching 0.5 and as the height to diameter ratio gets smaller, the results appear stiffer (larger Young's modulus). You are probably measuring the deflection of the testing machine, is that correct?

Think of it this way: suppose you made a test coupon 50 mm diameter only 1 mm in height, most of the volume of the coupon would be constrained and be prevented from deflecting laterally and you would get an even higher modulus.

Also, to prove or disprove the end effect explanation do this: measure a coupon's diameter at the bottom, middle, and top before and during test. (stop the test and measure with a dial caliper) If our explanation is correct, the coupon will be barell shaped, bigger at the middle, smaller at the ends.

If you are trying to compare this material to other materials, find out how they test the other materials and test in the same manner.

 

[cloa]

Does it need to have structural measurable properties while in air or with water pumped through it or both? It going to behave quite different with water as the water is nearly incompressible.

 

[Ron]

Use a standardized test method. At least it will be repeatable.

Keep in mind that standardized tests don't give you the ONLY answer, nor do they give you, necessarily, the "right" answer, but they give you an answer by which you may compare your results to others.