For fiber glass epoxy , the orientation of fibers at +45 degree or -45 degree in a ply increase the torsional stiffness and buckling resistance. I need to understand the reasons.
You are right, the orientations of +45° and -45° permit to resist to shear stress (torsion).
It is a classical result of continuum mechanics : if a volume of materials is submitted to shear stress, after diagonalisation, the eigenvalues of the stress tensor are oriented in +45° and -45°. Therefore, if you put fibers in these directions, you can increase the shear stiffness.
Thank you Sir very much, What about Buckling Resistance?
In fact my application is wind turbine blade made from fiber glass-epoxy plies.
Resisting the local buckling is important for me , I want to understand why such orientation helps to increase buckling resistance.
Thank you in advance !
The plies +45° and -45° do not enhance really the buckling resistance of a composite structure loaded in the 0° direction, but increase the global resistance of the structure. You have to consider that if you use only 0° plies, the resistance of the laminates will be very good in this direction, but very poor in all other directions. Therefore, a very small instability or a small defect into one plies, or a small change of direction of the loading, could destroy the structure.
That is the reason that everybody uses laminates with a minimum of plies in every direction (0°;90°, +45°, -45°) for classical applications.
The calculation of the sequence of plies is a classical exercise in mechanics of materials and you could find it into several books of mechanical engineering devoted to composites materials. For instance here : http://books.google.fr/books/about/Composite_Materials.html?id=51ATTG_tbkgC&redir_esc=y
A much simpler answer is that fibers ( glass, cotton, silk, rayon, and many
others ) are strong in tension in one axis only. A woven mat of fibers is
strong in tension in two directions only that are 90 degrees apart.
For example sails on a sailing ship.
If you laminate two layers of any woven fabric with a bonding agent,
it becomes strong in tension in 4 directions if the layers of fabric are
laminated at a 45 degree rotation.
You could than laminate 4 layers of fabric at 22.5 degrees of rotation and the
fibers are strong in tension in 8 directions, but it now weighs more.
Can you imagine the weight of a sail on a sailing ship if it was laminated,
with something like rubber, and was 4 layers thick. It would be strong,
but the masts and the rigging would be massive just to raise the sail.
When you are looking at torsion, you are looking at the sharing of tension
in fibers in the laminated mats that are not ideally oriented where the
forces are axial to fibers. The shearing forces in the epoxy are the means
of transfer of the forces to the axial oriented fibers in the woven fabric.
One layer : 90 degrees
two layers: 45 degrees
three layers 30 degrees
4 layers: 22.5 degrees
The strength goes up, but so does the weight
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