Fiber composite materials
One may wonder why the materials used in soft armor, helmets, and hard armor plate backers — along with many other materials for defense and aerospace applications that exhibit a very high strength-to-weight ratio — all happen to be fiber composites. Why fibers? Why aren’t they bulk materials? Why is graphitic fiber so much stronger than graphite, and why is fiberglass so much stronger than bulk glass? The below account of the origins of fiberglass is not only interesting in its own right — it answers that question in a very elegant way.
“[Alan Arnold] Griffith had first to determine, at least approximately, the theoretical strength of the glass he was using. The Young’s modulus was easily found by a simple mechanical experiment and two or three Ångström units is a fair guess for the interatomic spacing and cannot be far out. It remained to measure the surface energy. It was here that one of the advantages of glass as an experimental material lay. Glass, like toffee, has no sharp melting point but changes gradually, as it is heated, from a brittle solid to a viscous liquid and during this process there is no important change of molecular structure. For this reason one might expect there to be no large change in surface energy between liquid and solid glass so that surface tension and therefore surface energy, measured quite easily on molten glass, ought to be approximately applicable to the same glass when hardened. When the end of a glass rod is heated in a flame the glass softens and tends to round off into a blob because surface tension remains active long after permanent mechanical resistance to deformation has disappeared. The force, which is easily measured, needed slowly to extend the rod under these conditions is therefore that which will just overcome the surface tension. From experiments of this type, done with very simple apparatus, Griffith could deduce that the strength of the glass he was using (at room temperature) ought to be nearly 2,000,000 p.s.i. or about 14,000 MN/m2. [MPa]
“Griffith then took ordinary cold rods of the same glass about a millimetre thick and broke them in tension, finding that they had a tensile strength of about 25,000 p.s.i. or 170 MN/m2 which is round about the average for laboratory glassware, window panes, beer bottles and most of the other common forms of glass but was something between a fiftieth and a hundredth of what he reckoned it ought to be. Griffith now heated his rods in the middle and drew them down to thinner and thinner fibres which after cooling he also broke in tension. As the fibres got thinner so they got stronger, slowly at first and then, when they got really thin, very rapidly. Fibres about one ten thousandth of an inch (2.5 μm) thick showed strengths up to about 900,000 p.s.i. or 6,000 MN/m2 when they were newly drawn, falling to about 500,000 p.s.i. or 3,500 MN/m2 after a few hours. The curve of size against strength was rising so rapidly that it was difficult to ascertain a maximum or upper limit to the strength. The increase of strength with thinness was not entirely smooth but showed a certain amount of scatter or variability. However, there was absolutely no doubt about the general trend.
“Griffith could not prepare or test fibres thinner than about a ten thousandth of an inch (2.5 µm) and, if he had, it would have been difficult at that time to measure the thickness with any sort of accuracy. However, by the simple mathematical device of ploting reciprocals it was possible to extend or extrapolate the size-strength curve fairly reliably so as to ascertain the strength of a fibre of negligible thickness. This turned out to be 1,600,000 p.s.i. or 11,000 MN/m2. It will be remembered that Griffith had calculated a value a little under 2,000,000 p.s.i. or 14,000 MN/m2 for the glass he was using. He therefore concluded that he had approached the theoretical strength quite closely enough to satisfy most people, and that if thinner fibres could actually be made, their strength would be very near to the theoretical value. The achievement by experiment of an approximation to the theoretical strength was of course a triumph, especially when one considers the conditions under which the work was done. During the last few years, John Morley, of Rolls Royce, has prepared silica glass fibres (with a composition different from Griffith’s glass) with strengths rather over 2,000,000 p.s.i. (14,000 MN/m2)
“Griffith wrote a classic Royal Society paper about his experiments which was published in 1920. In this paper he pointed out that the problem was not to explain why his thin fibres were strong, since a single chain of atoms must, inescapably, have either the theoretical strength or none at all, but rather to explain why the thicker fibres were weak.”
This passage was taken from the excellent “The New Science of Strong Materials,” by James Edward Gordon, a founding father of materials science. A large portion of Gordon’s book is devoted to that troublesome question above: Why are those thicker fibers so much weaker? And the answer boils down to the fact that microstructural defects, atomic inclusions, inhomogeneities, and other flaws, are always common in bulk materials. The same sorts of imperfection are often hardly present at all in very thin fibers or in nanomaterials such as graphene.
….And this is why Dyneema fibers are stronger than glossy plates of bulk polyethylene plastic. A lot stronger. Currently, Dyneema fibers exhibit a tensile strength around 4,000 MPa, on average, though values over 7,000 MPa have been reported in certain experiments. Bulk thermoplastic polyethylene — which is the same chemical substance — has a tensile strength of around 45 MPa. The theoretical strength of polyethylene fiber has been estimated at roughly 30,000-40,000 MPa — based largely on the strength of the C-C bond that forms the backbone of all polyethylene plastics.
Simply put, by reducing the proportion of flaws in the material, and by orienting its molecular and crystalline structure, polyethylene’s strength begin to approach its theoretical value.
Similarly, the strongest grades of carbon fiber currently available can attain tensile strengths of roughly 6,600-7,000 MPa. The theoretical strength of carbon fiber is roughly 70,000 MPa.
Today’s best UHMWPE and carbon fibers are just 10% as strong as theory predicts they might be. There’s plenty of room for improvement; flawless, very fine fibers can get very strong indeed.
Sadly, no one knows how to prepare a bulk ceramic or glassy material without flaws and without surface defects such as scratches. If such a thing were possible, that ceramic or glass would be both incredibly strong and incredibly tough. It would seem like an entirely new class of material. But, sadly, this seems impossible. Consider — when water freezes, ice never forms perfectly uniformly and regularly. This is why, in a cube of ice you would drop in your drink, you will always find small macroscopic defects: Bubbles and lines and planes of fracture. Ceramics, metals, etc. are much the same. Some materials, like ductile metals, can compensate for defects to some extent; other materials, like ceramics and glass, cannot.
In any case, it’s worth noting that the strength or stiffness of a composite material is not equal to the strength or stiffness of its fiber component. Let’s take stiffness, this time: Although the tensile modulus of an average high-quality UHMWPE fiber strand should be somewhere around 115 GPa, the tensile modulus of a sheet of Dyneema is always far lower. The modulus of the composite can be approximated, very roughly, via a simple rule-of-mixtures calculation:
E = EfVf + EmVm
Where Ef, Em, Vf, and Vm are the moduli and volume fractions of the fiber and the matrix, respectively.
There are better models, but they are considerably more complex. The above is presented merely for illustrative purposes.
– Fibers are strong and stiff because they’ve been rendered largely free of defects.
– Bulk materials can’t compete in this regard. The strongest bulk materials are those metals that exhibit some ductility and can thereby compensate for defects.
– The strength and stiffness of a fiber composite does not perfectly correspond to the strength and stiffness of the fibers that it is derived from. The properties of the matrix and the direction of loading must also be taken into account.