Specific Strength (σ / ρ)

The stiffness twin, and a much sharper discriminator. $\sigma/\rho$ is how much load a material carries per kilogram of itself, conventionally in kN·m/kg — the same as MPa per Mg/m³. Where specific stiffness ties all the structural metals at about 25 MN·m/kg, specific strength separates them cleanly, and it separates fibre composites from all of them by a margin large enough to have changed what aeroplanes are made of.

There is a physical picture hiding in the units, and it is the best way to feel the number. Divide $\sigma/\rho$ by $g$ and you have a length: the breaking length, the length of a strip of the material hung from one end that would part under its own weight. Mild steel manages about 5 km. A good aluminium alloy manages about 18. A unidirectional carbon/epoxy ply at 1500 MPa and 1.56 g/cm³ gives 961 kN·m/kg, which is 98 km. That is the whole argument in one image.

And now the caution, which is larger here than it was for stiffness, because a composite does not have a strength — it has several, and they are nothing like each other.

Longitudinal tension is the headline figure and the one always quoted. Longitudinal compression is typically 50 to 70 percent of it, because real fibres are slightly wavy and under compression they microbuckle sideways into the resin rather than failing in their own right; the resin's shear stiffness is what resists that, so compression strength is a resin-dominated property masquerading as a fibre one. Transverse tension is a small fraction of either, often a fortieth of the longitudinal figure, because across the fibres it is the resin and the fibre-matrix interface carrying everything. In-plane shear is smaller again. Quoting the longitudinal tensile figure as "the specific strength of carbon fibre" is not so much wrong as radically incomplete, and a design built on it is a design that has not yet met its own compression allowables.

Two further things the ratio cannot see, and both of them size real parts. Composites are notch-sensitive in a way that ductile metals are not. A metal yields at a stress concentration and redistributes the load; a laminate has no yield mechanism to do that with, so an open-hole tension allowable can be half the plain-coupon strength — and since a hole is what a fastener goes through, that reduced number is what a bolted joint actually gets. Joints are usually where composite weight savings go to die. And damage tolerance: a barely visible impact, the kind a dropped tool leaves, can create an internal delamination that halves compression-after-impact strength while showing almost nothing on the surface. Most aerospace composite structure is sized by compression after impact rather than by any pristine allowable.

Fatigue runs the other way, and it is worth ending on the good news. A well-designed carbon laminate loaded along its fibres is famously insensitive to fatigue — the S-N curve is nearly flat, in sharp contrast to aluminium, which is why composite structures can be designed to a static allowable where metallic ones cannot. The resin-dominated directions are not so fortunate, and the mechanism there is matrix cracking followed by delamination, which returns the problem to fracture mechanics rather than strength.