You are here
How to use rule-of-mixtures in order to obtain mechanical properties of bidirectional composites?
Sun, 2016-10-09 07:11 - farhadzed
Dear all,
We are easily able to obtain mechanical properties (such as elastic modulus, Poisson's ratio and ...) of a unidirectional lamina composite by means of rule-of-mixture.
For instance, in case of "longitudinal loading", strength of the fiber-reinforced composite for long continuous fibers will be like:
Ec=Ef*Vf+Em*Vm.
I have two main questions:
First, are these relations (longitudinal and transverse loading) hold for bidirectional composite? if not, how can we obtain relative elastic modulus?
Second, how can we calculate Young's modulus from the rule-of-mixtures when angle of applied stress and fiber direction varies (for both cases of unidirectional and bidirectional lamina composites)?
Thanks for your guides in advance.
Forums:
Although I am not clear what
Although I am not clear what you mean by bi-directional composites, the rules of mixtures you cited are only correct if the Poisson's ratio is zero. My tutorial on micromechanics at https://cdmhub.org/resources/1039/download/Micromechanics.pdf will give you some idea how to compute the material properties for bidirectional composites. There are four types of rigorous rules of mixtures you can use for your problem. If you want to use more sophisticated methods, you can always use the SwiftComp code at https://cdmhub.org/resources/scstandard.
Dear Wenbin Yu,Thanks for
Dear Wenbin Yu,
Thanks for your reply.
What I mean by stating bidirectional lamina, we put fibers in two directions orthogonal to each other (for example 0 and 90 degree with respect to applied principle stress.
Dear Farhadzed
Dear Farhadzed,
The only avaiable experiments are applied to a one- directinal composite but the formula can be extended approximately to a 3D one. Your case can be processed with two main formulae: the first one you have cited and (1/Ey)=(Vm/Em)+(Vf/Ef) when taking Ec=Ec. I am convinced that Mr Wenbin has forgotted the following formula Nu=Nuxy=Num*Vm+Nuf *Vf which is cited by Tsai in micromechanics. It is evident that when you have a tensile case the compression case is consequence in the remain direction. The only remark is that they have taken Nu16=0 when using 1, 2 and 6 directions corresponding to x, y and xy. There are other formulae using the angles for each ply laminate calculating the stresses and deformations at each ply then you have Nuxy= - epsilonx/epsilony and else. For a 90 degree it is easier to interchange Ex by Ey. You can also use (1/Gxy)=(Vm/Gm)+(Vf/Gf) using x and y axes and Nux*Ey=Nuy*Ex.
In the volumic case I have used: Nuyx*Ey=Nuxy*Ex, Nuyz*Ey=Nuzy*Ex and Nuzx*Ez=Nuxz*Ex.
There are three rules of
There are three rules of mixtures: voigt, reuss, and hybrid. voight assumes constant strain, reuss assumes constant stress and hybrid for UD composites assumes uniform normal strain along fiber direction and all the other stress components are uniform. The most applicable formulas for UD composites are hybrid rules of mixtures.