As-received and nanoreinforced groups were manufactured and tested in identical conditions. The introduction of nanoreinforcement caused a decrease in fiber volume fraction, which may have contributed to some loss of composite tensile strength. Is it valid to normalize the tensile strength data by fiber volume fraction? Would this lead to a more accurate comparison?
You should first of all verify the change in fiber volume fraction. As you add another material phase, the values will change from the one with two phases. But it does not imply a change in the absolute volume or mass of fibers. The total volume of the specimen is increased by the addition of nano-sized reinforcements, and you compute the volume fraction over this new volume. As a consequence, it will be in general different from the value computed for the material without reinforcement.
Thus, if the change in volume fraction is just due to the addition of the reinforcement, there is no need to compare them. You just have to keep track of them:
2-phase specimen with X% fiber VF =becomes=> 3-phase specimen with Y% fiber VF
2-phase specimen with M% fiber VF =becomes=> 3-phase specimen with N% fiber VF
...
in order to make meaningful comparisons for the stress levels. You compare the measured stress for 2-phase specimens with X% VF ONLY with 3-phase ones with Y% VF, 2-phase specimens with M% VF ONLY with 3-phase ones with N% VF, and so on.
Furthermore, normalization stems from dimensional analysis and Buckingham theorem, by which you reduce the number of dimensional variables involved in a phenomenon thanks to the introduction of non-dimensional groups. Non-dimensional groups are combinations by simple operations (multiplication, division and elevation to power ) of dimensional quantities, in which the dimensions (length, mass, time, which are different from the units of measurements) cancel with each other to give a pure number. If you normalize stress by volume fraction, you divide a pressure (thus, mass/(length*time)) by a pure number. In this way, you loose information as the dimension remains still the one of a pressure, although the number is a pressure/volume fraction.
Thus, I would avoid the normalization by volume fraction. Density is a better candidate for normalization, as previously suggested. Otherwise, the best way to visualize the effect of volume fraction is plotting the stress against the volume fraction.
Luca
Yes.
Discontinuous fiber volume fraction, but non random orientation.
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