Material Properties and Selection
Key Takeaways
- The three primary crystal structures are BCC (2 atoms/cell), FCC (4 atoms/cell, most ductile), and HCP (6 atoms/cell, fewer slip systems → less ductile).
- From the tensile stress–strain curve read elastic modulus E (slope), yield strength (0.2% offset), ultimate tensile strength (peak), and ductility (% elongation).
- Toughness is the total area under the stress–strain curve (energy absorbed before fracture); resilience is the area under the elastic region only.
- Hardness (Brinell, Rockwell, Vickers) measures indentation resistance and correlates with strength: for steel, σu (MPa) ≈ 3.45 × HB.
- Materials fall into metals, ceramics (hard, brittle), polymers (thermoplastic vs. thermoset), and composites; electrical behavior splits into conductors, semiconductors, and insulators.
- Material selection balances mechanical, thermal, electrical, environmental, manufacturing, weight, and cost requirements.
FE Exam Weight: Materials Science contributes 6–9 questions (~7% of the 110-question FE Other Disciplines exam). Items emphasize property definitions, reading the stress–strain curve, crystal structures, and phase-diagram interpretation. Property tables and equations are in the searchable NCEES FE Reference Handbook; learn to locate and apply them.
Atomic Bonding and Crystal Structures
Atoms in a crystalline solid arrange in a repeating lattice. Three structures dominate the metals you will see:
| Structure | Atoms/unit cell | Coordination # | Packing factor | Ductility | Examples |
|---|---|---|---|---|---|
| BCC (body-centered cubic) | 2 | 8 | 0.68 | Moderate | α-Fe, Cr, W, Mo |
| FCC (face-centered cubic) | 4 | 12 | 0.74 | High | γ-Fe, Al, Cu, Ni, Au |
| HCP (hexagonal close-packed) | 6 | 12 | 0.74 | Low | Mg, Zn, Ti, Co |
FCC and HCP both reach the maximum atomic packing factor of 0.74, but FCC is far more ductile because it has 12 active slip systems versus HCP's 3 — slip systems are the planes along which dislocations move to allow plastic deformation. Iron is polymorphic: it is BCC (ferrite) at room temperature and transforms to FCC (austenite) above 912 °C, the behavior that makes steel heat treatment possible.
Bonding type sets the property family: metallic bonds (electron sea) give conductivity and ductility; covalent/ionic bonds give ceramics their hardness and brittleness; weak van der Waals forces between polymer chains give low stiffness.
Crystalline defects control real strength. Point defects (vacancies, interstitials, substitutional atoms) underlie diffusion and solid-solution strengthening; line defects (dislocations) move under stress to produce plastic flow, and impeding their motion — by alloying, grain refinement, cold work, or precipitation — is how engineers strengthen metals. The Hall–Petch relationship captures grain-size strengthening: yield strength rises as grain size shrinks, σy = σ₀ + k·d^(−1/2), so fine-grained metals are stronger than coarse-grained ones of the same composition.
The Stress–Strain Diagram
A tensile test pulls a specimen and records engineering stress σ = P/A₀ versus engineering strain ε = ΔL/L₀. The curve reveals most mechanical properties at a glance:
| Feature on the curve | Property |
|---|---|
| Slope of the initial straight line | Elastic modulus E (stiffness), via Hooke's law σ = Eε |
| End of linearity | Proportional/elastic limit |
| 0.2% offset intercept | Yield strength σy (onset of permanent deformation) |
| Peak of the curve | Ultimate tensile strength (UTS) σu |
| Final point (fracture) | Ductility = % elongation = (L_f − L₀)/L₀ × 100 |
| Total area under the curve | Toughness (energy absorbed to fracture) |
| Area under elastic region | Modulus of resilience |
Worked example: A steel rod of 12 mm diameter (A₀ = π/4 × 12² = 113 mm²) yields at 34 kN. Yield strength σy = 34,000 N ÷ 113 mm² ≈ 301 MPa. If E = 200 GPa, the elastic strain at yield is ε = σ/E = 301/200,000 = 0.0015 (0.15%).
Distinguish ductile (large plastic region, necks before fracture; mild steel, aluminum) from brittle (little plastic deformation, < ~5% elongation; cast iron, ceramics, glass). A material can be strong yet brittle, so high UTS alone does not mean high toughness.
Hardness, Thermal, and Electrical Properties
Hardness measures resistance to indentation and correlates with strength:
| Test | Indenter | Use |
|---|---|---|
| Brinell (HB) | 10 mm steel/carbide ball | Castings, softer metals |
| Rockwell (HRC/HRB) | Diamond cone or ball | Fast shop test, most metals |
| Vickers (HV) | Diamond pyramid | Hard materials, thin sections |
For steel, σu (MPa) ≈ 3.45 × HB — a handy estimate of strength from a hardness number.
Thermal: conductivity k (W/m·K), specific heat c (J/kg·K), and coefficient of thermal expansion α (1/°C). Thermal strain is ε = αΔT — a frequent exam calculation. Cu (k ≈ 401) > Al (237) > steel (50) > stainless (16) > concrete (≈1).
Electrical: resistivity ρ sorts materials into conductors (10⁻⁸–10⁻⁶ Ω·m: Cu, Al, Ag), semiconductors (Si, Ge, GaAs), and insulators (10⁸–10²⁰ Ω·m: ceramics, polymers, glass).
The Four Material Classes
- Metals/alloys — strong, stiff, ductile, conductive (ferrous: steel, cast iron; non-ferrous: Al, Cu, Ti).
- Ceramics — very hard, high melting point, chemically stable, but brittle with poor tensile/thermal-shock resistance (alumina, SiC, concrete, glass).
- Polymers — low density, corrosion-resistant. Thermoplastics (PE, PP, PVC, nylon) soften and remold when heated; thermosets (epoxy, polyester) are permanently crosslinked; elastomers (rubber) stretch elastically.
- Composites — combine a matrix and reinforcement for superior specific properties (carbon-fiber/fiberglass FRP, reinforced concrete, metal-matrix composites).
Material Selection
Selection trades off mechanical needs (strength, stiffness, fatigue, impact), environment (temperature, corrosion, UV), manufacturing (machinability, weldability, formability), weight (strength-to-weight for aerospace/automotive), cost (raw + lifecycle), and codes/regulations. Engineers often use performance indices (e.g., specific strength σ/ρ for light, strong parts) to rank candidates objectively.
A quick sanity check on any selection: confirm the material stays within its service temperature, that its coefficient of thermal expansion is compatible with mating parts (mismatched α causes thermal stress), and that the chosen factor of safety covers fatigue and impact, not just static strength.
Which crystal structure has 4 atoms per unit cell and the highest ductility due to its 12 slip systems?
On a stress–strain diagram, which property is represented by the TOTAL area under the curve up to fracture?
A steel rod with cross-sectional area 100 mm² yields at an axial load of 28 kN. What is its yield strength?
A thermoset polymer such as cured epoxy is best described as: