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3 Modeling Composite Structures
fibers, the thickness at any spot is a random variable, and also depends on how much
pressure is applied to the layer.
It is not immediately clear exactly how changing FAWT changes the conductivity. We can make a few reasonable assumptions. First of all, we note that if the
FAWT reaches zero, there are no fibers, and we must have simply resin. As far
as eddy currents are concerned, the resin looks just like freespace. Therefore , we
conclude that as FAWT decreases, conductivity decreases toward zero (freespace).
If we take into account capacitive effects , we must look at the dielectric properties
of the resin. Capacitive effects should not come into the picture for eddy-current
inspection, as long as we keep the frequencies relatively low. As FAWT increases,
the prepreg begins to look more and more like a slab of solid carbon. An increasing
number of fibers contact, making the transverse conductivity increase. It seems
reasonable to assume that as FAWT increases, both the transverse and longitudinal
conductivity approach a limit determined by the conductivity of the graphite fibers.
We can probably improve somewhat on these simple-minded observations by using
models for graphite fiber interactions found in the literature.
We note that the transverse conductivity is likely to be more affected by a
change in FAWT than the longitudinal conductivity, assuming a nominal value of
60% fiber. A simple argument is based on our previous comments. Assuming that
the transverse conductivity, denoted σ T , approaches the longitudinal conductivity,
σ L , as the fiber density approaches 100%, and given a typical anisotropy ratio of
200:1 (based on 60% fiber density) , one can get an idea of how σ T and σ L must
change when the fiber density is increased toward 100%. We note that σ T must
change by at least a factor of 200, while σ L is known to change by only a factor
of about two. Such a refined estimate of conductivity change will be useful when
we assess the accuracy of the proposed method of measurement. For now, it will be
reasonable to assume that the conductivity scales by the same percentage change as
the FAWT (the transverse and longitudinal conductivities). Actually, it is suggested
that the change in transverse conductivity is a higher order than direct-proportion
relationship; the simple model used in the reference predicts a squared relationship.
If indeed the transverse conductivity depends on the FAWT squared, or a higher
power of FAWT, then we are in a good position to measure the FAWT change. We
know from our own experience and models that our laboratory measurements are
sensitive to conductivity changes in the material. All that remains to be discovered
is the relationship between conductivity and FAWT.
Resin content appears to affect the conductivity in a perhaps complicated way.
It appears that resin content can dramatically affect the transverse conductivity,
but may have little effect on the longitudinal conductivity. One way to explain the
physical reason for the conductivity change with resin content is to think of the resin
as an insulator partially shielding the adjacent fibers (“wires”) from contacting each
other, thereby reducing σ T . Using this explanation also leads us to the conclusion
that σ L is not significantly changed by resin content, assuming that the resin content
does not significantly change the overall volume of the material, since the “wires”
conduct equally well when they are surrounded by insulation.
3 Modeling Composite Structures
fibers, the thickness at any spot is a random variable, and also depends on how much
pressure is applied to the layer.
It is not immediately clear exactly how changing FAWT changes the conductivity. We can make a few reasonable assumptions. First of all, we note that if the
FAWT reaches zero, there are no fibers, and we must have simply resin. As far
as eddy currents are concerned, the resin looks just like freespace. Therefore , we
conclude that as FAWT decreases, conductivity decreases toward zero (freespace).
If we take into account capacitive effects , we must look at the dielectric properties
of the resin. Capacitive effects should not come into the picture for eddy-current
inspection, as long as we keep the frequencies relatively low. As FAWT increases,
the prepreg begins to look more and more like a slab of solid carbon. An increasing
number of fibers contact, making the transverse conductivity increase. It seems
reasonable to assume that as FAWT increases, both the transverse and longitudinal
conductivity approach a limit determined by the conductivity of the graphite fibers.
We can probably improve somewhat on these simple-minded observations by using
models for graphite fiber interactions found in the literature.
We note that the transverse conductivity is likely to be more affected by a
change in FAWT than the longitudinal conductivity, assuming a nominal value of
60% fiber. A simple argument is based on our previous comments. Assuming that
the transverse conductivity, denoted σ T , approaches the longitudinal conductivity,
σ L , as the fiber density approaches 100%, and given a typical anisotropy ratio of
200:1 (based on 60% fiber density) , one can get an idea of how σ T and σ L must
change when the fiber density is increased toward 100%. We note that σ T must
change by at least a factor of 200, while σ L is known to change by only a factor
of about two. Such a refined estimate of conductivity change will be useful when
we assess the accuracy of the proposed method of measurement. For now, it will be
reasonable to assume that the conductivity scales by the same percentage change as
the FAWT (the transverse and longitudinal conductivities). Actually, it is suggested
that the change in transverse conductivity is a higher order than direct-proportion
relationship; the simple model used in the reference predicts a squared relationship.
If indeed the transverse conductivity depends on the FAWT squared, or a higher
power of FAWT, then we are in a good position to measure the FAWT change. We
know from our own experience and models that our laboratory measurements are
sensitive to conductivity changes in the material. All that remains to be discovered
is the relationship between conductivity and FAWT.
Resin content appears to affect the conductivity in a perhaps complicated way.
It appears that resin content can dramatically affect the transverse conductivity,
but may have little effect on the longitudinal conductivity. One way to explain the
physical reason for the conductivity change with resin content is to think of the resin
as an insulator partially shielding the adjacent fibers (“wires”) from contacting each
other, thereby reducing σ T . Using this explanation also leads us to the conclusion
that σ L is not significantly changed by resin content, assuming that the resin content
does not significantly change the overall volume of the material, since the “wires”
conduct equally well when they are surrounded by insulation.