Calculation of shear modulus
Calculation of shear modulus
(OP)
Hi,
How do I calculate the shear modulus G12, G13 and G23 of a lamina/ply if I know the :
Thickness
Resin Wt
Fiber WT
Laminate Wt
Density
Vf
Ex, 1-direction
Ey, 2-direction
How do I calculate the shear modulus G12, G13 and G23 of a lamina/ply if I know the :
Thickness
Resin Wt
Fiber WT
Laminate Wt
Density
Vf
Ex, 1-direction
Ey, 2-direction





RE: Calculation of shear modulus
For conventional material combinations, such as woven glass or carbon fibres and a polymer matrix, the in-plane direct moduli (the E's) are largely a function of fibre longitudinal stiffness (not true of E2 of unidirectional material), and the in-plane shear is largely a combination of matrix shear (also matrix extension for a roughly isotropic matrix such as most polymers) and fibre shear (for glass fibre, which is roughly isotropic, this is also more or less a function of longitudinal stiffness; not true for carbon fibres, which are themselves orthotropic).
So, if you know the sort of fibres and matrix present it is possible to make a reasonable guess for the Gxy, or just use Gxy for a similar material.
Finding the through-thickness shear moduli is similar. Even if you have the through-thickness E values there is no simple relationship with the G's. However, once you know the in-plane Gxy (or G12—strictly, x, y and xy apply to laminates and 1, 2 and 12 apply to laminae) you can make a reasonable estimate of the out-of-plane Gs.
RE: Calculation of shear modulus
What is your specific material?
RE: Calculation of shear modulus
My material is GFRP, i.e glassfiber reinforced polymer.
I just have a material datasheet with information on
Laminate - Vacuum infused
Thickness 1.45 mm
Resin Wt 0.83 kg/sq.m
Fiber Wt 1.90 kg/sq.m
Density 1.90 g/cc
Vf 51.95 by Vol
0 degree Modulus, Ex
90 degree modulus, Ey
And the ultimate stresses in 0 and 90 degree
I need to now shear modulus G12, G13, G23 and poissons ratio aswell.
Any ideas or do I need more Information about the material to obtain these?
RE: Calculation of shear modulus
what cure temp?
as we said above, you need more info.
or, just use these approximate values
G12 = G12 = 0.6 msi
G13 = 0.4 msi
v12 = 0.3 if it is a uni tape material, v12 = 0.06 if it is a fabric
SW
RE: Calculation of shear modulus
It's likely to be continuous fibre with those weights in kgsm and that Vf of 52%, and quite possibly woven. It's also likely to be E-glass (not S- or R-glass or something fancy). Verification of this sort of thing would be sensible.
http://www.cmh17.org/ ($$$)
http://assist.daps.dla.mil/quicksearch/ (needs some fiddling about to find it: Enter MIL-HDBK-17 in the 'Document ID' box for a starter)
http://snap.lbl.gov/pub/bscw.cgi/98090
http://w
MIL-HDBK-17 only has shear modulus for one E-glass material that I can spot; SW's numbers are of course fine. There is one wet knockdown if that's of interest (comes to 0.65 times at RT).
RE: Calculation of shear modulus
Do you have any idea why I cant use the Huber formula for orthotropic lamina in a single plane :
G12= sqrt(E1*E2)/2(1+sqrt(ny12*ny21))
RE: Calculation of shear modulus
RE: Calculation of shear modulus
RE: Calculation of shear modulus
I'm not too sure about the 'Huber formula.' I last saw something similar used for bodged equations for skin wrinkling of carbon on honeycomb (on the discontinued Ariane V H10 interstage). The skin there was sort of not-quite quasi-isotropic.
The formula is demonstrably wrong for the limiting case of woven lamina material: E1 = E2 and nu12 = nu21, so you'd get E/(2(1+nu)). For E1 = E2 = 25 GPa and nu = 0.06, G12predicted = 25/(2*1.06) ~= 12 GPa, fc. ~4 GPa. As the laminate becomes more isotropic it will behave more in accordance with E/(2(1+nu)), but the basic orthotropic material will never do so.
For UD glass E1 ~= 45 GPa, E2 ~= 10 GPa, nu12 ~= 0.3, nu21 ~= 0.02 and G12predicted would be ~10 GPa; a fair bit out from the actual 4 GPa. (G12 is roughly the same for woven and UD).
[G12predicted = sqrt(45*10)/2/(1+sqrt(0.3*0.02))]
So no, this won't work. It might be acceptable for a small difference from isotropic, such as a rolled metallic plate or even the formula for skin wrinkling that I used for an almost QI laminate. I confess I've not heard of Huber other than just looking him up via Google.
If you require some sort of reason for a number rather than quoting the (free!) MIL-HDBK-17 data, you could try a micro-mechanics approach. The glass fibre G is about 72000/(2(1+0.3)) = 28000 MPa (like aluminium) and the polyester E will be about 3000 MPa, giving a G of maybe 3000/(2*(1+0.35)) = 1100 MPa; I think fibers in series with a matrix for G12glasspolyester would then be, er, 1100*[(28000*(1+0.52) + 1100*0.48) / (28000*0.48 + 1100*(1+0.52))] = 3200 MPa??? (460 ksi.)
(See http:/
Well, maybe. You're better off with MIL-HDBK-17.
RE: Calculation of shear modulus
I just have one question. When I'm using the equation for G12 on the last link u posted, it says G12,f which means shear modulus in the 12 direction of the fiber? But the glass-fiber is isotropic I suppose? Why is there an index of the fiber shear modulus when its isotropic?
Best regards
RE: Calculation of shear modulus
G23=E22/2(1+nu23)
By the way, Why does e-glass have a minor poissons ratio and a minor poissons ratio when it is isotropic?
RE: Calculation of shear modulus
Until today I hadn't thought about G23 = G33/(2(1+nu23)). You're deforming fibres and matrix in series so it should work: G33 ~= G22unidirectional ~= 10e3 MPa for glass, and nu23 ~= nu12unidirectional = 0.3, so G23 ~= 10e3/2.6 = 3850 MPa, not a mile out. Thanks. Note: the out-of-plane G13 should be a bit less than the in-plane G12 as through the thickness the shear stress drops to zero at the free surface and varies through the thickness in the classic way assumed for a rectangular section, so G13 ~= 5/6 * G12 for metallics (SW's value of 2/3 is quite typical for composite laminate, where the plate is not uniform through its thickness).
(You wanted G23 = E22/(2(1+nu23)), which assumes E33 = E22; pretty true for unidirectional material, not anywhere near true for woven.)
It may get complicated, as G23 is only approximately = G13 (shouldn't be too bad for glass) and G13 is quite different from G31 (think G12 vs G21), whereas G32 should be similar to G23. (All for UD; it's different for woven.)
I think that this addresses your last question "...why does e-glass have a minor poissons ratio and a minor poissons ratio when it is isotropic?".
I think that usually for the glass itself it's usual to assume isotropy. The differences come for the fibre-matrix composite, where stretching UD composite along the fibres will reduce the thickness with a nu of about 0.3, as will stretching the material across the fibres; however, stretching the material through its thickness will not reduce the in-plane fibre-direction length very much (stiff fibres), whereas the across-fibres in-plane dimension will reduce by about 0.3 again. I don't really understand your question, so this may not be much help.