Ceramics and their properties

Why it matters

Cutting-tool inserts, grinding wheels, furnace linings, spark-plug insulators, bearing balls, thermal-barrier coatings and electronic substrates are all ceramics. They are chosen for hardness, stiffness, temperature capability, chemical inertness and electrical insulation, but they fail suddenly from tiny flaws, so designing and processing them needs fracture mechanics and statistics rather than yield strength.

Key ideas

What a ceramic is. An inorganic, non-metallic solid made of metallic and non-metallic elements held by ionic and covalent bonds: oxides (Al₂O₃, ZrO₂, SiO₂, MgO), carbides (SiC, WC, B₄C), nitrides (Si₃N₄, cubic BN, TiN) and silicates. Most are crystalline; glasses are amorphous ceramics; glass-ceramics are glasses crystallised by controlled heat treatment.

• Traditional ceramics: from natural clay, silica and feldspar — bricks, tiles, whiteware, porcelain, refractories, cement.
• Advanced (engineering) ceramics: high-purity synthetic powders — alumina, zirconia, silicon carbide, silicon nitride, sialons, cubic boron nitride.

Structure–property links. Strong, directional ionic/covalent bonds give high melting points, high hardness and high elastic moduli (Al₂O₃ about 380 GPa, SiC about 410 GPa), low density compared with metals of similar stiffness, chemical stability and (usually) electrical insulation. The same bonds make dislocation motion almost impossible at room temperature: ionic crystals have few slip systems because slip would bring like charges together, and covalent bonds are rigid. Ceramics therefore have essentially no plasticity and are brittle.

Brittle fracture and flaws. Fracture starts at the largest or worst-oriented flaw — a pore, inclusion, grain-boundary crack or machining scratch. Stress concentrates at its tip, and failure happens when the stress intensity reaches the fracture toughness KIC (only about 3–5 MPa·√m for alumina against 50–150 MPa·√m for steels). Consequences:

• Tensile strength is much lower than compressive strength (often by a factor of about 10), so ceramics are designed to carry compression.
• Strength is usually measured in bending (modulus of rupture) because tensile specimens are hard to grip.
• Strength scatters widely and depends on specimen size (bigger parts are more likely to contain a large flaw). It is described by Weibull statistics; the Weibull modulus m is about 5–15 for ceramics against about 100 for metals.

Porosity. Sintered ceramics retain some porosity. Pores reduce strength, stiffness, thermal conductivity and density, and act as crack starters; dense (hot-pressed or HIPed) parts are stronger. Porosity is useful in insulating refractories and filters.

Toughening. Transformation toughening in partially stabilised zirconia (PSZ): metastable tetragonal particles transform to the larger monoclinic form in the stress field of a crack, squeezing the crack shut. Also fibre or whisker reinforcement, fine grains and compressive surface layers (toughened glass).

Thermal properties and thermal shock. Low thermal expansion and conductivity (except SiC, AlN) and high melting points suit refractories, but sudden temperature changes cause thermal stresses that can crack a brittle ceramic. Resistance to thermal shock is high for high strength, low expansion, low modulus and high conductivity — fused silica and Si₃N₄ are good; ordinary alumina is moderate.

Processing. Ceramics cannot be cast or forged like metals. Powders are formed by pressing (uniaxial, isostatic), slip casting, extrusion, injection moulding or tape casting, then dried and fired/sintered below the melting point so that particles bond by diffusion and the part shrinks (often 10–20 % linear). Hot pressing and hot isostatic pressing give near-full density. Glass is formed hot (blowing, pressing, drawing, float process) and can be tempered. Final finishing is by diamond grinding, which is costly.

Applications for production engineers.

• Cutting tools: alumina (white) and alumina–TiC (black) inserts, Si₃N₄ and sialon for cast iron and nickel alloys, cubic boron nitride for hardened steel, polycrystalline diamond for non-ferrous materials. Ceramics need rigid machines and negative rake to avoid chipping.
• Abrasives: Al₂O₃ and SiC grinding wheels.
• Refractories: fireclay, silica, magnesite, alumina bricks for furnace linings.
• Wear and corrosion parts: seals, bearing balls (Si₃N₄), pump liners, nozzles.

Formulas

K = Y·σ·√(π·a) and fracture when K = KIC K = stress-intensity factor (MPa·√m); Y = geometry factor (about 1–1.12 for surface cracks); σ = applied tensile stress (MPa); a = surface-crack depth or half the length of an internal crack (m); KIC = plane-strain fracture toughness (material property).

σf = KIC / (Y·√(π·a)) and a_c = (1/π)·(KIC / (Y·σ))² Fracture stress for a given flaw, and critical flaw size for a given stress.

Pf = 1 − exp[ −(σ/σ0)^m ] Weibull probability of failure for a given specimen size: σ0 = characteristic strength (63.2 % fail), m = Weibull modulus (both from test data).

ΔTc = σf·(1 − ν) / (E·α) Approximate critical temperature jump for thermal-shock cracking on sudden cooling: σf = fracture strength (Pa), ν = Poisson's ratio, E = Young's modulus (Pa), α = thermal expansion coefficient (K⁻¹).

σ = σ0·exp(−n·P) Empirical strength–porosity relation: P = volume fraction porosity; n ≈ 4–7, from data.

Worked examples

Example 1 (standard): fracture toughness from a test. Given: a ceramic plate fails at σ = 50 MPa; it has a surface crack of depth a = 5 mm; Y = 1.2.

1. KIC = Y·σ·√(π·a) = 1.2 × 50 × √(π × 0.005).
2. √(0.015708) = 0.1253.
3. KIC = 60 × 0.1253 = 7.5 MPa·√m.

Example 2 (GATE level): flaw size, strength and thermal shock of alumina. Given: KIC = 4 MPa·√m, Y = 1.12, E = 380 GPa, ν = 0.22, α = 8 × 10⁻⁶ K⁻¹.

1. Strength with a 50 µm surface flaw: σf = 4 / (1.12 × √(π × 50 × 10⁻⁶)) = 4 / (1.12 × 0.01253) = 285 MPa.
2. Largest tolerable flaw at 300 MPa (Y = 1): a_c = (1/π)(4/300)² = 5.66 × 10⁻⁵ m = 57 µm — inspection must find flaws this small.
3. Thermal shock with σf = 300 MPa: ΔTc = 300 × 10⁶ × 0.78 / (380 × 10⁹ × 8 × 10⁻⁶) = 77 °C. Quenching the part from more than about 77 °C above the bath temperature risks cracking.
4. Weibull check: if σ0 = 400 MPa and m = 10, at 300 MPa, Pf = 1 − exp[−(0.75)¹⁰] = 5.5 % — far too high for a structural part, so the design stress must be lower.

Common mistakes

• Treating KIC as something that changes with the applied stress or crack size; it is a material property, and K is what changes.
• Using the full crack length 2a of an internal crack instead of the half-length a.
• Designing ceramics on tensile strength values measured in compression.
• Assuming all ceramics are poor conductors of heat; SiC and AlN conduct heat well.
• Forgetting that bigger ceramic parts are weaker on average because they contain more flaws.
• Using uncoated ceramic tools in interrupted cuts with a positive rake, where they chip.

For GATE PI

Expect one-mark questions on why ceramics are brittle, the difference in their tensile and compressive strength, classification and examples, cutting-tool ceramics (Al₂O₃, Si₃N₄, CBN, diamond) and which work material each suits, transformation toughening of zirconia and the sintering route. Numericals use K = Yσ√(πa) to find fracture stress, toughness or critical flaw size, and occasionally thermal-shock or Weibull calculations.

Quick check

1. Why do ceramics have almost no ductility at room temperature?
2. A crack is made four times longer. By what factor does fracture stress change?
3. Which ceramic tool material is used for machining hardened steel?
4. What is the mechanism of transformation toughening?
5. Why is ceramic strength tested in bending?

Answers: 1. Strong ionic/covalent bonds and few slip systems stop dislocation motion; 2. It halves; 3. Cubic boron nitride; 4. Tetragonal zirconia near the crack tip transforms to larger monoclinic zirconia, putting the crack under compression; 5. Tensile specimens are hard to grip and align without breaking them.