Young Modulus Calculation

[Khinfai]

Say I had one cantilever beam which is made from three type of materials.

The cantilever is made of three layers of material, assume that they are bonded to each other perfectly and had no chance of tipping off.

How do I calculate the Young Modulus for this cantilever beam ?

 

[CoryPad]

Try an Internet search for laminated beam theory.

 

[rb1957]

you need to transform the section to one of the material modulus. this should be covered in most strength of materials texts, or google "rule of mixtures"

 

[Khinfai]

CoryPad; Laminated Beam theory is too complex for me.

rb1957: rule of mixtures normally are for composite materials but not in this case.

To be clearer, the three layers of bonded material had their own Young's modulus, Poisson ratio etc. Once they are bonded as one, I assume their Young 's modulus etc, will change. And I wanna know how can I calculate it out ?

Or I need to practically run a tensile strength test to see its elongation etc to calculate the Young's modulus ? If that so, it will be a very costly experiment.

 

[Cockroach]

Deflect your theoretical beam in FEA and obtain deflection vs force curve. You can then apply Hooke's Law sine you remain in the elastic zone and assume the layers act as a uniform cross section. Solve for Youngster Modulus based on your FEA results.

Regards,
Cockroach

 

[hemisboats]

Always calculate using the weakest material of the composite. (Assuming your theoretical starting point of perfect) But I always over-engineer by 5%.

 

[FeX32]

'Composite materials' is a specialty topic in mechanics of materials. There are numerous text's on exactly what you are attempting. You should be able to use the dimensions of the beam and the 'E' of all the materials to compute an 'equivalent' modulus. Here are some basics: (not exactly what you want however)

http://www.mech.utah.edu/~rusmeeha/labNotes/composites.html

There was a text we used in uni. but I forget it's name.




Fe

 

[dhengr]

Khinfai:
You probably shouldn’t be doing this problem if it is too complex for you, particularly if it could hurt someone other than just you. As Rb1957 suggested, dig out your Strength of Materials, and Theory of Elasticity text books; you have to deal with a transformed section, as a function of the three different E’s. But, you still have three distinct E’s, working together, not some average or calc’d. E. Once the three materials are bonded together (are they really?), they will deflect together when loaded, and now the trick becomes, not over stressing any one of the materials. You must check the shear flow at each one of the bond surfaces (faying surfaces) to be sure that you don’t over stress the allowable bond strength btwn. the two materials, and the glue (whatever?) at that surface. You assume that the strain will be the same in the two materials at that surface, but their E’s don’t change and will lead to different stresses in each material at that surface. Alternatively, if the member is continuously loaded or stressed, then you must also watch out for creep in bonding materials (glues), which will allow the strains to vary at that surface. In the first case you are assuming the strain varies linearly through the depth of the beam, in the latter instance one of the materials has yielded or creep has taken place, at a bond surface, and now the problem does become more complex.

 

[desertfox]

Hi Khinfai

Scrool down this link till you come to examples of composite beams
the example shows three different materials and how to obtain equivalent modulus

http://www.roymech.co.uk/Useful_Tables/Beams/Beam_theory.html

 

[hemisboats]

dhenger is correct, IMHO

Listen, a chain is only as strong as the weakest link. This holds true in composite materials unless you are talking interwoven, mesh and carbon fiber, etc. Lamination's, as questioned above cannot be achieved (perfect layered adhesion) when working with "different molecular materials" 100% cohesion is theoretically not possible. From works of life.

Get the right person for the job, before some, including yourself.

 

[dvd]

Hooke's Law for springs in parallel comes to mind....

I agree with the comments on making assumptions about perfect bonding.

 

[izax1]

The Youngs modulus of each material will not change, but you will need to find a "model" for the effetive Stiffness. The stiffness is a combination of material stiffness (Youngs modulus) and geometrical stiffness. (Thickness, Area moment of Inertia). So the number you are after is dependet on if the cantilever is subject to bending, axial load or torsion (or any combination of these).

I agree with dhengr. This should be treated with care and by someone with the right experiene and skill for this problem.

 

[rb1957]

from the OP's response to my post, i wonder if we've made an assumption regarding "different types of materials", and "three layers of materials".

maybe the OP does have a composite beam, ie face sheets and core. if so, then "rule of mixures" wouldn't apply, and you'd have to combine the different materials into the [A], , [D] matrices. some pre-processors will do this (i know PATRAN does).

 

[Cockroach]

Exactly, Izac1. Deflection is a combination of inertia, geometry and Young's Modulus for stresses within the elastic zone. The big question is the relative contribution of each composite layer to the deflection of the composite beam and whether the assumptions made regarding shear between layers is valid.

For this reason I have suggested building a beam representative of the different materials and performing simple tests. You could do a cantilever setup and compute Young's Modulus from deflection and load testing, I.e. Hooke Law. Then I would do simple supported beam with a central load and see if you could predict the deflection based on your experimentally determined Young's Modulus.

Simple enough to perform and a quick "yes" or "no" outcome.

Regards,
Cockroach