Composites and Fiber-Reinforced Plastics
Rule of mixtures, laminates, sandwich panels, manufacturing and design rules for glass and carbon fiber parts.
What a composite is
A composite combines two materials so that the whole has properties neither has alone. In a fiber-reinforced plastic strong, stiff fibers (glass, carbon, aramid, natural fiber) carry the load, and a polymer matrix (epoxy, polyester, vinyl ester, nylon, PEEK) holds them in place, transfers the load between them and protects them. The fibers are strong because they are thin: a glass or carbon fiber of 5 to 10 µm has few flaws, and a tensile strength of 2 000 to 5 000 MPa. Composites are anisotropic: very stiff and strong along the fibers, weak across them. That is a weakness to design around and a strength to exploit (put the fibers where the load goes).
| Fiber | Modulus (GPa) | Strength (MPa) | Density (kg/m³) | Notes |
|---|---|---|---|---|
| E-glass | 73 | 2 000 to 3 500 | 2 550 | cheap, tough, the workhorse; moisture sensitive; electrically insulating |
| S-glass | 87 | 4 500 | 2 480 | higher strength and stiffness |
| Carbon (standard modulus) | 230 | 3 500 | 1 800 | stiff, light, fatigue resistant; expensive; brittle; conducts |
| Carbon (high modulus) | 350 to 550 | 2 500 to 3 500 | 1 900 | stiffness-critical structures: satellites, precision |
| Aramid (Kevlar) | 70 to 130 | 3 000 | 1 440 | tough and impact resistant; poor in compression; moisture absorbing |
| Flax, hemp (natural) | 30 to 70 | 500 to 900 | 1 400 | renewable; low cost; moisture sensitive |
The rule of mixtures
The stiffness of a unidirectional ply follows from the volume fractions. Loaded along the fibers they strain together (the Voigt or parallel model); loaded across them the fiber and matrix are in series (the Reuss model):
E1 = Vf Ef + (1 − Vf) Em 1 ÷ E2 = Vf ÷ Ef + (1 − Vf) ÷ Em ρ = Vf ρf + (1 − Vf) ρm
Worked example: carbon and glass against steel
Worked example: 55 percent fiber in epoxy (Em = 3.5 GPa, 1 200 kg/m³)
- Carbon/epoxy (Ef = 230 GPa, 1 800 kg/m³): E1 = 0.55 × 230 + 0.45 × 3.5 = 128 GPa; E2 = 1 ÷ (0.55 ÷ 230 + 0.45 ÷ 3.5) = 7.6 GPa (17 times less across); density 1 530 kg/m³; strength along the fibers about 0.8 × 0.55 × 3 500 = 1 540 MPa.
- Glass/epoxy (Ef = 73 GPa): E1 = 42 GPa, E2 = 7.3 GPa; density 1 943 kg/m³.
- Specific stiffness E1 ÷ ρ: carbon 84, glass 21, steel 26.8, aluminum 25.6 MN·m/kg: unidirectional carbon is 3.1 times as stiff as steel per unit mass along the fibers (but only when the fibers are aligned with the load).
- Replacing a 3 mm steel guard (23.6 kg/m²) with a glass-fiber mat laminate of E ≈ 15 GPa for equal bending stiffness needs t = 3 × (210 ÷ 15)1/3 = 7.3 mm at 1.9 g/cm³: 13.9 kg/m², 59 percent of the steel mass; it does not rust or conduct, but it is less tough against a flying chip.
- The ply stiffness across the fibers is so low that a 0° laminate would be weak in the other direction, which is why laminates mix orientations.
Laminates and the stacking sequence
A laminate is a stack of plies, each with its own fiber angle. A quasi-isotropic laminate [0/±45/90]s has about the same stiffness in all in-plane directions (about 35 to 40 percent of the 0° ply stiffness: 45 GPa for carbon, 15 GPa for glass here); a unidirectional one is as stiff as it can be along one direction; a ±45° layer carries shear and torsion; a 90° layer carries transverse load and controls splitting. Rules: use at least 10 percent of the plies in each of the four main directions, make the stack symmetrical about the mid-plane (otherwise it warps when cured or loaded) and balanced (equal +θ and −θ plies), do not group more than four plies of one angle together, and put the ±45° plies near the outside. A carbon prepreg ply is about 0.125 mm thick, so a 4 mm laminate has about 32 plies.
Sandwich panels
Bending stiffness grows with the square of the distance of material from the center. A sandwich places thin strong skins far apart on a light core (foam, honeycomb, balsa) that carries the shear and keeps them apart. The bending rigidity per unit width is D ≈ Es ts d² ÷ 2 for two skins of thickness ts a distance d apart.
Worked example: a 1 mm carbon skin sandwich against a solid plate
- Skins: 1 mm quasi-isotropic carbon (E = 45 GPa) either side of a 10 mm foam core (60 kg/m³): d = 11 mm. Dsandwich = 45 000 × 1 × 121 ÷ 2 = 2.72 × 10⁶ N·mm.
- A solid 2 mm plate of the same carbon (the same skin material): D = E t³ ÷ 12 = 0.030 × 10⁶ N·mm. The sandwich is 91 times as stiff for a mass of 3.7 kg/m² against 3.1 kg/m²: 19 percent heavier. This is why floors, wings, wind-turbine blades and boat hulls are sandwich structures.
- Failure modes: skin wrinkling, core shear, indentation under a concentrated load (use a denser core or an insert), and skin–core debonding.
Manufacturing processes
| Process | Fiber fraction | Cost | Use |
|---|---|---|---|
| Hand lay-up | 30 to 40 % | low | boats, tanks, one-offs; the cheapest tooling |
| Spray-up / chopped strand | 20 to 30 % | low | large simple shapes |
| Vacuum infusion (VARI) | 45 to 55 % | medium | large parts: boat hulls, wind blades |
| Prepreg and vacuum bag (oven) | 50 to 58 % | medium to high | sports goods, motorsport, UAV |
| Prepreg and autoclave | 55 to 62 % | high | aerospace primary structure |
| Pultrusion | 50 to 65 % | low per meter | constant-section profiles: ladders, rods |
| Filament winding | 55 to 65 % | medium | pipes, pressure vessels, shafts |
| Resin transfer molding (RTM) | 45 to 55 % | medium | volume production of complex parts |
| Compression molding (SMC, GMT) | 25 to 50 % | tooling heavy | automotive panels |
The part quality depends on the fiber fraction (more fiber, more stiffness and strength), the void content (voids reduce interlaminar strength: keep under 2 percent, 1 percent or less for aerospace), the cure cycle (the resin needs its temperature and time: epoxy usually 80 to 180 °C) and the fiber alignment. Typical glass transition temperatures of epoxy are 100 to 180 °C; the usable service temperature is 20 to 30 °C below Tg for a hot, wet condition (so room-temperature-cured systems are usually limited to 50 to 60 °C).
Design rules and failure modes
- Align the fibers with the load and use ±45° plies for shear; a laminate is not a metal and the rules of isotropic design do not apply to it.
- Radii: inside corner radii at least 3 times the thickness; fibers break or bridge in tight corners.
- Avoid stress concentrations: drill holes with care (backing to prevent delamination), use bonded or bolted doublers, and design bolted joints with edge distance 3 to 4 diameters and a bearing check; composites have a low bearing strength and no yield to redistribute the load.
- Adhesive bonding usually beats bolting for thin laminates (large overlaps, scarfed joints); surface preparation decides the result.
- Delamination (layer separation) is the main failure under impact and out-of-plane loads: barely visible impact damage can cut compression strength by half; inspect by ultrasonic or tap test.
- Thermal expansion: carbon has almost zero (−0.5 × 10⁻⁶/K) along the fibers; bonded to aluminum (23.6) a 500 mm long, 60 K temperature change creates 0.72 mm of mismatch. Isolate carbon from aluminum and steel with a glass ply or sealant (galvanic corrosion: Corrosion and Protection).
- Environment: glass in water slowly loses strength; UV breaks down unprotected resin (use gelcoat or paint); fire (use fire-retardant resins) and lightning (carbon conducts, needs a metal mesh) are design cases.
- Safety and waste: resin and hardener cause skin sensitization (gloves, ventilation, respirators for dust and sanding fumes), cured scrap cannot be re-melted (thermoset) and needs a recycling route.
Related
- Previous: Injection Molding and Plastics Processing. Next: Material Selection, Testing and Failure.
- Structures and Strength of Materials for bending and shear of a sandwich and the isotropic formulas.
- Materials and Processes: the whole guide.
FAQ
Is carbon fiber always better than aluminum?
It is lighter for the same stiffness, but costs 10 to 50 times as much per kilogram, is weak in impact and across the fibers, and needs special design and joining. Choose it where the weight really pays.
Why are the plies at different angles?
A single orientation is strong only along the fibers. Layers at 0°, ±45° and 90° give stiffness and strength in all directions.
Can I repair a composite?
Yes, with scarfed or stepped patches of the same fibers and resin cured under heat and pressure, or bonded external patches. Structural repairs follow the manufacturer’s manual.
What does prepreg mean?
Fibers already impregnated with a measured amount of resin, supplied as tape or fabric and stored cold; it is laid up and cured with heat and pressure for the best fiber fraction and quality.
References
- Daniel, I. M., Ishai, O., Engineering Mechanics of Composite Materials, Oxford University Press; Jones, R. M., Mechanics of Composite Materials, CRC Press; Hull, D., Clyne, T. W., An Introduction to Composite Materials, Cambridge University Press.
- Mallick, P. K., Fiber-Reinforced Composites, CRC Press; MIL-HDBK-17 / CMH-17, Composite Materials Handbook; ASTM D3039 (tensile), D7264 (flexure).
- Campbell, F. C., Structural Composite Materials, ASM International.
Last reviewed: October 2026. Fiber and ply properties are typical handbook values; use the supplier’s datasheet and tests for design.