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# In plane shear help??

## In plane shear help??

(OP)
Hi,

I did some uni axial and flexural testing and I am using the Tsai wu failure criterion for anisotropic materials to prove failure. So I have my E11 from unixial testing and E22 from the flexural test. I am assuming plane stress, so terms in the 3rd laminate co-ordinate axes are eliminated. I need to find the value for "σ12". Can I work it out with this formula
σ12= v12 (poissons ratio in the direction)/E13. If so how do i determine the poissons ratio? or is there another way??

Also I worked out the shear modulus G12 using the rule of mixtures: 1/Gc=vf/Gf+Vm/Gm. Is this correct??

My composite is a unidirectional carbon fibre tape of 10 layers in 0 degrees and also a sample in 90 degrees with epoxy resin.

Thx

### RE: In plane shear help??

12 and 13 usually denote shear directions. σ is almost always a direct stress and capital E is always a Young's modulus. σ12 would normally be written τ12 and E13 should probably be G13.

You have written stress12 = poisson's12/modulus13. This makes no sense to me. Stress of any type is not related to any sort of stiffness by a Poisson's ratio. ν12 relates the stiffnesses (E) and strains (ε) in the 11 direction to those in the 22 direction and ν21 relates the properties in the 22 direction to those in the 11 direction.

For your unidirectional material the 12 shear direction is often used as a reasonable approximation for the 13 direction and the 22 direction is used as a reasonable approximation for the 33 direction. In both cases the fibres and resin are being deformed by applied stresses in a very similar way and they actually fail in very similar ways, making the equivalence between the directions apply for failure stresses as well as stiffnesses.

### RE: In plane shear help??

(OP)
Hi RPstress, thx for your reply. I had actually meant v12/E12 and I got this from a book when plane stress applies.

You said for a uni directional, 12 shear direction is approx used for 13 direction but how do I work the shear stress in the 12 direction in the first place??

Would I need to mechanical test a composite with 45 degree fiber direction?? I am towards the end of the project and this is not possible for me.
If there are no fibers in 45 degree angle, is it a fair assumption to consider any shear stress in 12 direction as negligible??

### RE: In plane shear help??

I'm afraid that almost nothing you say makes any sense to me. There is no E12 that I know of; direct moduli are called E1, E2 and E3 (or maybe E11, E22 and E33). For an isotropic material G = E/(2*(1+nu)) but nu is not usually otherwise divided into E (or E into nu). I can't guess what your reference meant by E12. Perhaps if you tell us what the reference is it might make it clearer, and perhaps post a scan of the page with the relevant equation.

It is in the nature of an orthotropic material like an all-0° UD laminate that shear is not related to direct stresses and stiffnesses. Unlike an isotropic material G12 is not any function of E/nu. You must measure shear properties separately, usually by pulling a layup made of + and - 45° plies. The modulus measured from such a test is not too bad for low strains, though the strength is less useful.

In your original post you asked if 1/Gc = vf/Gf + vm/Gm. Assuming v here is the volume fraction this is correct. Gm is generally accessible because the matrix is usually isotropic. Gf may be harder to pin down. If the fiber is glass then the fiber is isotropic and Gf may be accessible, but if it's carbon or Kevlar then it's not, as the fiber itself is orthotropic.

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