pantelis182
Mechanical
What issues are associated with anisotropy? And how such issues can be addressed and the consequential effect on mechanical properties?
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Carbon fibre composite materials 1
- Thread starter pantelis182
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The world is anisotropic.
You have posted here so I assume it has something to do with a fibre reinforced material of some sort. To paraphrase Professor Gordon the properties of stiff fibres in a less stiff matrix are pretty much what one might expect. See his three books for an excellent introduction to materials and structures in general, their anisotropy and how one takes account of it in design.
When many more major engineering structures were made out of wood, anisotropy was a more major part of engineering design. For about five thousand years shipwrights have been taking it into intimate account usually quite successfully.
What aspect of "anisotropy" is of concern to you? Do you want to distinguish between anisotropy and orthotropy?
You have posted here so I assume it has something to do with a fibre reinforced material of some sort. To paraphrase Professor Gordon the properties of stiff fibres in a less stiff matrix are pretty much what one might expect. See his three books for an excellent introduction to materials and structures in general, their anisotropy and how one takes account of it in design.
When many more major engineering structures were made out of wood, anisotropy was a more major part of engineering design. For about five thousand years shipwrights have been taking it into intimate account usually quite successfully.
What aspect of "anisotropy" is of concern to you? Do you want to distinguish between anisotropy and orthotropy?
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pantelis182
Mechanical
Well I'm interested in what are the effects of anisotropy on the mechanical behavior of carbon fibre reinforced polymers!!!
The mechanical properties of an anisotropic material are a function of orientation. An anisotropic material has properties that vary with direction within the material. This directional dependence is observed for other material properties such as ultimate strength, Poisson’s ratio and thermal expansion coefcient. Material property data, including fibre concentration, matrix properties and properties of the composite in the principal material directions,are incorporated into micro-mechanical models to estimate the fibre properties.
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The basic woven or unidirectional ply of carbon/polymer composite is orthotropic, as are most laminates made using such plies.
There are some subtleties to do with 'coupling' between the forces deforming a laminate and the deflections the laminate undergoes in response. For instance if the number of +angle plies is not equal to the number of -angle plies then 'shear-extension' coupling is present, so the laminate will shear a bit when stretched. This also happens when a laminate shrinks on cooling down from elevated temperature cure or infusion with a hot thermoplastic.
Balancing 90° UD plies on each side of the lamninate centerline is also important. If a 90° ply is opposite a 0° ply the laminate will undergo extension-bend coupling. In fact because a (0/90) laminate is (90/0) when looked at from 90° it will undergo extension-bend in the opposite sense at 90° to the sense at 0°. This means a (0/90) laminate will become saddle-shaped when it shrinks in both directions on cool-down. This is also true of a single ply of harness satin weave, a ply of which is about 80% like a pair of (0/90) plies of UD.
With unidirectional plies you also get 'bend-twist' coupling. This is even if the number of +angle equals the number of -angle ones.
[tt]
<---
1 ///////// + angle 2 \\\\\\\\\ - angle | Moment M
|
3 \\\\\\\\\ - angle /
4 ///////// + angle /
---
[/tt]
Ply 1 is in compression and will shear out of the page a bit, ply 2 into it a bit less. Ply 3 is in tension and will shear the opposite direction to ply 2 the same amount, ply 4 the opposite direction to ply 1 the same amount. This gives a couple, so all practical UD laminates twist a little bit when bent, even when balanced. Note that the way a harness satin ply is like two plies of UD at right angles means that HS woven material laminates will do this a bit too.
As a laminate cools it shrinks in thickness by about 30 microstrain per kelvin (through-thickness thermal strain is dominated by the resin which is typically about 80 microstrain/K). If the laminate is curved the carbon fibres at the inside and outside are moved closer together, but they don't change in length themselves (they would need to shrink in length the same 30 microstrain/K to stay the same shape). This means that laminates tend to increase in curvature as they cool. This is 'spring-in', and is one of the defining characteristics of making things out of carbon. (It happens with glass too, but a bit less.) Traditionally this is allowed for by experience and making tools which can be changed after the first-off part is assessed, i.e. trial and error.
Occasionally it is desired to have bend-twist coupling, for instance with the forward swept wings of the X-29. In this case the whole wing structure needed the coupling, which meant that the top skin needed to shear one way when the bottom skin sheared the other as the wing bent. This needed skin laminates with entension-shear coupling.
Generally coupling is a bad thing. With sensitive structures like an optical bench or telescope, to remove all coupling needs tweaking of the thicknesses of plies of different angles. When this is done a laminate that is very nearly orthotropic or quasi-isotropic can be made.
There are some subtleties to do with 'coupling' between the forces deforming a laminate and the deflections the laminate undergoes in response. For instance if the number of +angle plies is not equal to the number of -angle plies then 'shear-extension' coupling is present, so the laminate will shear a bit when stretched. This also happens when a laminate shrinks on cooling down from elevated temperature cure or infusion with a hot thermoplastic.
Balancing 90° UD plies on each side of the lamninate centerline is also important. If a 90° ply is opposite a 0° ply the laminate will undergo extension-bend coupling. In fact because a (0/90) laminate is (90/0) when looked at from 90° it will undergo extension-bend in the opposite sense at 90° to the sense at 0°. This means a (0/90) laminate will become saddle-shaped when it shrinks in both directions on cool-down. This is also true of a single ply of harness satin weave, a ply of which is about 80% like a pair of (0/90) plies of UD.
With unidirectional plies you also get 'bend-twist' coupling. This is even if the number of +angle equals the number of -angle ones.
[tt]
<---
1 ///////// + angle 2 \\\\\\\\\ - angle | Moment M
|
3 \\\\\\\\\ - angle /
4 ///////// + angle /
---
[/tt]
Ply 1 is in compression and will shear out of the page a bit, ply 2 into it a bit less. Ply 3 is in tension and will shear the opposite direction to ply 2 the same amount, ply 4 the opposite direction to ply 1 the same amount. This gives a couple, so all practical UD laminates twist a little bit when bent, even when balanced. Note that the way a harness satin ply is like two plies of UD at right angles means that HS woven material laminates will do this a bit too.
As a laminate cools it shrinks in thickness by about 30 microstrain per kelvin (through-thickness thermal strain is dominated by the resin which is typically about 80 microstrain/K). If the laminate is curved the carbon fibres at the inside and outside are moved closer together, but they don't change in length themselves (they would need to shrink in length the same 30 microstrain/K to stay the same shape). This means that laminates tend to increase in curvature as they cool. This is 'spring-in', and is one of the defining characteristics of making things out of carbon. (It happens with glass too, but a bit less.) Traditionally this is allowed for by experience and making tools which can be changed after the first-off part is assessed, i.e. trial and error.
Occasionally it is desired to have bend-twist coupling, for instance with the forward swept wings of the X-29. In this case the whole wing structure needed the coupling, which meant that the top skin needed to shear one way when the bottom skin sheared the other as the wing bent. This needed skin laminates with entension-shear coupling.
Generally coupling is a bad thing. With sensitive structures like an optical bench or telescope, to remove all coupling needs tweaking of the thicknesses of plies of different angles. When this is done a laminate that is very nearly orthotropic or quasi-isotropic can be made.
My fixed pitch text "drawing" got mangled a bit.
Leading spaces got knurdled. Changing them to dots:
[tt]
.................... <---
1 ///////// + angle ..... 2 \\\\\\\\\ - angle ...... ........................... | Moment M
........................... |
3 \\\\\\\\\ - angle ...... /
4 ///////// + angle ..... /
..................... ---
[/tt]
The Preview button says that's not too bad.
It might be worth mentioning that the ABD matrix describes the laminate's elastic behavior due to in-plane forces and bending (the ABD doesn't address through-thickness stresses and strains and it is used for 2D shell elements in finite element work). Coupling is described by bits off the main diagonal being non-zero. Only Poisson's ratio coupling is permissable for isotropic behavior (A12, A21, D12 and D21).
Leading spaces got knurdled. Changing them to dots:
[tt]
.................... <---
1 ///////// + angle ..... 2 \\\\\\\\\ - angle ...... ........................... | Moment M
........................... |
3 \\\\\\\\\ - angle ...... /
4 ///////// + angle ..... /
..................... ---
[/tt]
The Preview button says that's not too bad.
It might be worth mentioning that the ABD matrix describes the laminate's elastic behavior due to in-plane forces and bending (the ABD doesn't address through-thickness stresses and strains and it is used for 2D shell elements in finite element work). Coupling is described by bits off the main diagonal being non-zero. Only Poisson's ratio coupling is permissable for isotropic behavior (A12, A21, D12 and D21).
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