Composite materials

Why it matters

Composites let an engineer put stiffness and strength exactly where the load is, at a fraction of the weight of metal: carbon-fibre aircraft wings and racing chassis, glass-fibre boat hulls, wind-turbine blades and pressure vessels, aluminium–SiC brake discs, and carbide cutting tools (a ceramic in a metal binder). Production engineers must also know how composites are made and why they are difficult to machine.

Key ideas

Definition. A composite combines two or more physically distinct phases — a continuous matrix and a dispersed reinforcement — with an interface between them, to get a combination of properties that neither has alone.

Roles of the constituents.

• Reinforcement (fibres, particles): carries most of the load; supplies strength and stiffness.
• Matrix: binds and positions the fibres, transfers load to them by shear at the interface, protects them from abrasion and environment, and carries transverse and shear loads. It usually controls toughness, temperature limit and environmental resistance.
• Interface: must bond well enough to transfer load, but a slightly weaker interface can deflect cracks and add toughness (crack bridging, fibre pull-out).

Classification by matrix.

• Polymer-matrix composites (PMC): thermoset (epoxy, polyester, vinyl ester) or thermoplastic (PEEK, PP, nylon) matrices. Most common; limited to about 100–250 °C.
• Metal-matrix composites (MMC): Al, Mg or Ti reinforced with SiC or Al₂O₃ particles or fibres; higher temperature capability, stiffness and wear resistance than the base alloy. Cemented carbide (WC in Co) is a particle-reinforced MMC.
• Ceramic-matrix composites (CMC): SiC/SiC, C/C, alumina reinforced with SiC whiskers; the fibres raise toughness and allow use above 1000 °C (turbine shrouds, brake discs, tool inserts).

Classification by reinforcement.

• Particle-reinforced: large-particle (concrete, cermets) or dispersion-strengthened (fine oxide particles hinder dislocations, as in ODS alloys).
• Fibre-reinforced: continuous aligned, discontinuous aligned, or random short fibres. Continuous aligned fibres give the highest properties along the fibre axis but are highly anisotropic.
• Structural: laminates (plies stacked at different angles, e.g. 0/±45/90, to give in-plane properties in several directions) and sandwich panels (stiff thin skins on a light core of foam or honeycomb; very high bending stiffness per weight).

Common fibres. E-glass (cheap, E ≈ 72 GPa), S-glass (stronger), carbon (E ≈ 230–600 GPa, very low density 1.8 g/cm³, high strength), aramid/Kevlar (very tough, impact-resistant, poor in compression), boron, SiC.

Load sharing in aligned continuous fibres. Under longitudinal load the fibres and matrix stretch equally (isostrain), so the stiffer fibres carry most of the load. Under transverse load they carry the same stress (isostress) and the composite is dominated by the soft matrix. Discontinuous fibres must be longer than a critical length for the matrix to load them to their full strength.

Manufacturing. Hand lay-up and spray-up (boats, tanks; open mould, low cost), compression moulding of sheet-moulding compound (automotive panels), resin transfer moulding (RTM), filament winding (pipes, pressure vessels, rocket casings), pultrusion (constant-section rods and beams), prepreg lay-up with autoclave cure (aerospace), and injection moulding of short-fibre thermoplastics. MMCs are made by stir casting, squeeze casting and powder metallurgy.

Machining composites. Fibres are abrasive (glass and carbon wear tools quickly; use carbide or PCD tools), and drilling causes delamination at entry and exit, fibre pull-out and matrix burning. Remedies: sharp PCD drills, low feed at exit, backing plates, abrasive water-jet or laser cutting.

Advantages and limitations. High specific strength and stiffness, tailored anisotropy, corrosion and fatigue resistance, part consolidation. Limitations: high material and processing cost, anisotropy, low through-thickness strength (delamination), damage that may be invisible, difficult repair and recycling, moisture uptake and temperature limits of polymer matrices.

Formulas

Ec,l = Ef·Vf + Em·Vm Longitudinal modulus of an aligned continuous-fibre composite (isostrain, upper bound); E in Pa, V = volume fractions with Vf + Vm = 1 (voids neglected).

1/Ec,t = Vf/Ef + Vm/Em Transverse modulus (isostress, lower bound).

Ff / Fm = Ef·Vf / (Em·Vm) Ratio of load carried by fibres to load carried by matrix under longitudinal loading.

σc,l = σf*·Vf + σm′·(1 − Vf) Longitudinal tensile strength: σf* = fibre fracture strength; σm′ = matrix stress at the fibre-failure strain (Pa). Valid when the fibres fail first.

lc = σf*·d / (2·τc) Critical fibre length (m): d = fibre diameter (m), τc = fibre–matrix interfacial shear strength (Pa). Fibres longer than about 15·lc behave as continuous.

ρc = ρf·Vf + ρm·Vm Composite density (kg/m³) by volume fractions.

Worked examples

Example 1 (standard): stiffness and density of a glass/epoxy. Given: aligned continuous E-glass in epoxy, Vf = 0.40; Ef = 72.5 GPa, Em = 3.4 GPa; ρf = 2500 kg/m³, ρm = 1200 kg/m³.

1. Ec,l = 0.40 × 72.5 + 0.60 × 3.4 = 29.0 + 2.04 = 31.0 GPa.
2. 1/Ec,t = 0.40/72.5 + 0.60/3.4 = 0.00552 + 0.1765 = 0.1820, so Ec,t = 5.49 GPa — less than a fifth of the longitudinal value.
3. ρc = 0.40 × 2500 + 0.60 × 1200 = 1480 kg/m³.

Example 2 (GATE level): load sharing, strength and critical length. Using the same composite:

1. Ff/Fm = (72.5 × 0.40)/(3.4 × 0.60) = 29.0/2.04 = 14.2.
2. Fraction of load on fibres = 14.2/(1 + 14.2) = 0.934 (93.4 %).
3. If σf* = 3450 MPa and σm′ = 30 MPa, σc,l = 3450 × 0.40 + 30 × 0.60 = 1398 MPa.
4. Critical length for a carbon fibre with σf* = 3500 MPa, d = 7 µm, τc = 40 MPa: lc = 3500 × 7 × 10⁻⁶ / (2 × 40) = 3.06 × 10⁻⁴ m = 0.31 mm; chopped fibres should be several millimetres long.

Common mistakes

• Using the isostrain rule of mixtures for transverse loading; it greatly overestimates transverse stiffness.
• Mixing weight fractions and volume fractions in the rule of mixtures.
• Forgetting that fibres shorter than lc are not loaded to their full strength.
• Assuming composites are isotropic like metals.
• Treating the matrix as unimportant; it sets temperature limit, toughness and transverse strength.
• Drilling CFRP with ordinary HSS drills at high feed, causing delamination and rapid tool wear.

For GATE PI

Expect one-mark questions on classification (PMC, MMC, CMC; particle, fibre, laminate, sandwich), roles of matrix and fibre, and manufacturing processes (pultrusion, filament winding, lay-up). Numericals apply the isostrain and isostress rules of mixtures, the fibre/matrix load split, composite density and strength, and critical fibre length.

Quick check

1. For Vf = 0.5, Ef = 400 GPa and Em = 4 GPa, find the longitudinal modulus.
2. Which process makes constant-cross-section composite rods continuously?
3. Is cemented carbide a PMC, MMC or CMC?
4. Why are sandwich panels so stiff in bending for their weight?
5. If the interfacial shear strength doubles, what happens to lc?

Answers: 1. 202 GPa; 2. Pultrusion; 3. MMC (WC particles in a cobalt matrix); 4. The stiff skins are placed far from the neutral axis by a light core, raising the second moment of area; 5. It halves.