Question:
I have searched for reference and handbook information (yes, google too)
describing the load behavior of randomly tangled wool-like fiber matte. The
interest is to design a wool-like material for elastic constant and
stiffness depending on the materials properties, volume fraction and
geometry (fiber thickness, cross section, length) of the fibers involved.
Materials will be inorganic fibers and not polymers or natural fibers.
Fibers will likely be curled or twisted and not straight. That should not
constrain the governing equations. I have no idea what governing equations
there may be. I expect there are empirical relations to use? There must be
some engineering work from ancient subjects like pillow making, steel wool,
filters or packaging. Fiber books don't cover this topic. No materials
books or chapters in them address such topics.
If there is a clue out there among you to resolve this, and you have read
this far, then let me add further refinements. Say I want to make a fibrous
matte much like Fiberfrax or the like. How might the mechanical
compressibility change if a heat treatment allows fiber interconnects to
form (sintering). Adhesives or sintering can ultimately make the matte into
a rigid structure. I wish to control stiffness or the spring constant but
maximize the compressed volume ratio. How would the properties change if I
substituted sapphire fibers for silica glass for example?
Answer:
You have a fundamental problem, in that fibre mats themselves have no
intrinsic strength. They are all resilient and easily deformed. It is only
by mechanically bonding the fibres together that any web strength is
achieved. This may involve mechanical looping, as in needle mat, where
chopped strands are held in a veil support, or chemical bonding as typified
by emulsion or powder-bound chopped strand mat, or typical insulation fibre
blankets. Another approach is to make a paper-like material of dispersed
fibres.
Saffil is like Nextel which is one of my materials. I should revisit Saffil
since the material might be engineered to a greater degree than their
commercial products. Thanks for activating that neuron that opened that
interconnect.
I wish to take advantage of the resiliency and predictably increase the
strength until the resiliency is reduced to my threshold. I had not heard
of powder-bound support, but it sounds like electrostatic binding. I wish
not to count on veil support. Instead, since I plan to avoid chopped
fibers, approach a similar state while including the coiling of fibers . I
seek 'loft' which is a term used in down (as in goose) which is another
material I wish to be biomimetic with.
I certainly don't know the answer to your question, but I have some
comments.
The Journal of the Textile Institute or Textile Research Journal might
have some relevant papers. See http://www.texi.org/pub.htm or
http://www.textileresearchjournal.com/ respectively.
I did some research on the fibres projecting from the surface of
textiles, many years ago. The stress-strain curve is roughly
exponential as one engages more and more projecting fibres, but I
stopped as soon as the body of the textile began to compress, which is
the point at which you wish to begin.
Keep friction in mind. A lot of what happens depends on friction at
the points of contact between fibres. In some circumstances, tacking
the fibres at the points of contact, by sintering or with another
material, makes very little difference to the compressive properties,
if friction was high to begin with.
The stiffness of the assembly is a very rapidly increasing function of
the packing density, because the average strut length decreases.
You might get some useful clues from "Particle Packing Characeristics"
by Randall M. German, ISBN 0-918404-83-5.
There was a paper in the Journal of the American Ceramic Society in
the last few years (sorry, I have lost the reference) that gave a
powder compression analogue of the general gas equation. There might
be some clues in that.
