I am not sure if I should post it here or not. I apologize if this question is irrelevant here .
In some of the papers, it is showed that if two natural fibers are used in the same matrix (hybridization), a new E1 (elastic modulus) value is found which is larger than each of the individual fiber composite. To make it clear, following is an example.
In the literature it is showed that, E1 of jute/epoxy is 6.32 GPa and E1 of banana/epoxy is 10.72 GPa, Now, the E1 value of jute/banan/epoxy is 13.69 GPa. I was wondering if it is possible or not. Because analytically and numerically it is not possible. I would appreciate a feedback on this.
Regarding what is theoretically possible or not, please refer to my paper entitled introduction to micromechanics, you can find it on cdmHUB. Voigt rule of mixtures will provide the upper bound. Your cited literature example might be because they increased the volume fraction of one or both fibers.
Thank you Professor for your reply. So basically, the simple Rule of Mixture (RoM) doesn't consider Poisson's effect and that's why it is erroneous.
But finite element results are very similar to RoM. Does that mean also in finite element analysis, Poisson's effect is neglected?
Another inquiry, could I please get a reference where RoM equations for orthotropic and/or transversely isotropic materials are derived beyond Voigt estimation?
We usually also call Voigt and Reuss estimates as RoM. Beyond these two estimates, which are rigorous upper and lower bounds, you have Hashin-Shtriman bounds which are improved bounds. Then you can also have Hybrid rules of mixtures. Depending on the microstructure, you can have different rules of mixtures. For unidirectionally fiber reinforced composites, you need to assume that longitudinal strains are constant and all the other stresses are constants.
Anonymous @ on — Edited @ on
Hello,
I am not sure if I should post it here or not. I apologize if this question is irrelevant here .
In some of the papers, it is showed that if two natural fibers are used in the same matrix (hybridization), a new E1 (elastic modulus) value is found which is larger than each of the individual fiber composite. To make it clear, following is an example.
In the literature it is showed that, E1 of jute/epoxy is 6.32 GPa and E1 of banana/epoxy is 10.72 GPa, Now, the E1 value of jute/banan/epoxy is 13.69 GPa. I was wondering if it is possible or not. Because analytically and numerically it is not possible. I would appreciate a feedback on this.
Thanks in advance
Wenbin Yu @ on
Regarding what is theoretically possible or not, please refer to my paper entitled introduction to micromechanics, you can find it on cdmHUB. Voigt rule of mixtures will provide the upper bound. Your cited literature example might be because they increased the volume fraction of one or both fibers.
Anonymous @ on
Thank you Professor for your reply. So basically, the simple Rule of Mixture (RoM) doesn't consider Poisson's effect and that's why it is erroneous.
But finite element results are very similar to RoM. Does that mean also in finite element analysis, Poisson's effect is neglected?
Another inquiry, could I please get a reference where RoM equations for orthotropic and/or transversely isotropic materials are derived beyond Voigt estimation?
Thank you in advance!
Wenbin Yu @ on
We usually also call Voigt and Reuss estimates as RoM. Beyond these two estimates, which are rigorous upper and lower bounds, you have Hashin-Shtriman bounds which are improved bounds. Then you can also have Hybrid rules of mixtures. Depending on the microstructure, you can have different rules of mixtures. For unidirectionally fiber reinforced composites, you need to assume that longitudinal strains are constant and all the other stresses are constants.