Strength and stiffness 

  Research has shown that not only glass, but also other substances have this property. Metal fibers score poorly in these tests. This can be explained because ionic bond and covalent bond are stronger than the metallic bond. It turns out that microstructures are so strong, because there are hardly any errors (“dislocations”) in them. At a macro level, there are things that have much more influence on the ultimate tensile strength than the strength of a “perfect” microfiber. The main one is “fracture energy”. This is the amount of energy absorbed by a test bar during fracture; most solids have a low fracture energy. The strong point of metals is not their absolute strength, but their resistance to breakage. Metals are not strong but tough. Carbon fibers are much stronger than metals, but have a lower breaking energy. Scratches on the surface can cause a sudden breakage. This can be explained from FIG. 2; the lines on the figure are lines of force. The load per square mm is the same everywhere, except at the tip of the crack: there 3 lines of force run close to each other and the load is three times as high. If the total load is greater than one third of the tensile strength of the bar, the tip of the crack will exceed the maximum tensile strength and increase. Now even more lines of force will be cut and the stress for the tip of the crack will be even greater: the crack breaks through the material at lightning speed!

There are different types of microstructures in solids. Glass is amorphous, i.e. the molecules do not have regular positions with respect to each other. Most substances, including metals, are crystalline, i.e. the atoms are arranged in fixed patterns. This can be done according to three structures: 1. CSC (cubic surfaces centered, like copper, α-iron); 2. CCS (cubic centered in space like γ-iron, molybdenum); 3. HCS (hexagonal closest stack, like beryllium, magnesium).

There are different types of microstructures in solids. Glass is amorphous, i.e. the molecules do not have regular positions with respect to each other. Most substances, including metals, are crystalline, i.e. the atoms are arranged in fixed patterns. This can be done according to three structures: 1. CSC (cubic surfaces centered, like copper, α-iron); 2. CCS (cubic centered in space like γ-iron, molybdenum); 3. HCS (hexagonal closest stack, like beryllium, magnesium).

The CSC and HCS structure are maximally dense stacks: the filling level is 74%; the CCS structure has a filling level of 68%. So there are always holes in every molecular structure, the so-called interstitial spaces; these may contain other atoms. The CCS structure has larger spaces  than the CSC structure, but the shape is less favorable. A carbon atom fits poorly in the γ iron crystal, but fits well in the α ‑ iron crystal. In a stack of atoms, there may be an empty space (a vacancy) or a foreign atom (a substitution). When the temperature rises, the number of vacancies increases due to the movements of atoms. Substitutional and interstitial atoms can move through vacancies (diffusion). Self-displacing dislocations develop in metals under load; these deform the grid so much that they hinder their own movement. More and more energy must be supplied for further deformation; that is why the fracture energy of metals is so high. 

   Many metals and fibers are rigid enough to build frames. Part of them are not used, due to poor resistance to varying loads; they are not strong enough, too heavy, or too expensive. If the frame builder has chosen a material, there are two methods to increase the stiffness: a larger wall thickness or a larger diameter. both result in a higher weight, but because the stiffness increases with the cube of the diameter, the builder opts for less wall thickness and a larger diameter. This makes a frame lighter and stiffer. Alloyed super steels are as stiff as low carbon steels. A thin walled tube means it is at expense of stiffness. If we look at TABLE 1, it shows that real stiffness improvement is only possible with carbon fiber. Strength-wise we can build a titanium frame that weighs half that of a steel one, but such a frame is too flexible. Again, the builder usually opts for larger tube diameters as a solution, which in turn reduces the weight advantage. Only with aluminium some progress has been made in the area of stiffness. There are aluminium-lithium alloys that are 10% stiffer (80 instead of 72 Gpa). Furthermore, aluminium can be used as a matrix in composites. Gary Klein was the first to reinforce his aluminium frames. He used boron fibers for this; this is pure boron around a tungsten core. Nowadays, particles of SiC or Al2O3 are used as reinforcement. Specialized built light frames with these “Metal Matrix” M2 tubes from the manufacturer Duralcan. Such a tube is made by heating a powder mix under high pressure to the melting point of the lowest melting component in a tubular mold. The relative stiffness is ± 15% better (see TABLE 1), but it is no longer used.

   Composites of fibers and resin differ strongly in stiffness from metals: in the longitudinal direction of the fiber the fabric is the stiffest, transversely much less. With a 45 ° fabric the same number of threads are used in length and width and the stiffness is uniform. If one wants to optimize strength or stiffness in a certain direction, one can choose Uni-Directoral (U.D.) fabric with almost all threads in the length, or carbon as warp and aramid as weft. But metal has a more homogeneous composition and the production techniques are more reliable, so that the safety factor of the frame can be chosen to be lower. A wide margin must be maintained for composites.

  It was not until the early 1970s that the price of carbon dropped to $ 100 per kilogram. We see the first tests of carbon frames around that time. The problem was that manufacturers tried clamping techniques to connect the tubes into a frame with aluminium lugs. This way of framebuilding proved unsuccessful. Certainly in the first generation of the American Graftek frames, some tubes came loose. These frames provide much less improvement in stiffness over corresponding aluminium tube-lug structures than would be expected on basis of the stiffness of the composite tube; the properties of the chosen connection method are of great influence.