Material Properties and Selection

FE Fundamentals of Engineering Exam

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2 Mathematics (8–12 Questions)

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9 Strength of Materials (9–14 Questions)

Stress and Strain Fundamentals Beam Analysis: Shear and Moment Diagrams Bending Stress and Torsion Stress Transformation and Material Failure

10 Materials Science (6–9 Questions)

Material Properties and Selection Phase Diagrams and Alloy Systems

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Fluid Properties and Statics Fluid Dynamics and Bernoulli's Equation Pumps, Turbines, and Flow Measurement

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Electrical Fundamentals and DC Circuits AC Circuits and Three-Phase Power

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Industrial Safety and Hazard Management

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Material Properties and Selection

Key Takeaways Explain This Topic AI

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.

Last updated: June 2026

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.

Hardness, Toughness, and Failure Modes

Material selection weighs several mechanical properties the FE expects you to distinguish. Hardness (Brinell, Rockwell) resists indentation and correlates with strength and wear resistance. Toughness is the total energy absorbed before fracture — the area under the full stress-strain curve — and is measured by an impact (Charpy) test. Ductility (percent elongation) is the ability to deform plastically before breaking.

Property Measures Test
Hardness Indentation resistance Brinell / Rockwell
Toughness Energy to fracture Charpy impact
Ductility Plastic strain capacity Tensile %EL
Fatigue strength Endurance under cycling S-N (fatigue) test

Fatigue failure occurs below the yield stress under repeated cycling; ferrous metals show an endurance limit (a stress below which life is effectively infinite), while aluminum does not. Creep — slow deformation under sustained load at high temperature — governs turbine and boiler parts. Matching the dominant failure mode to the service condition drives correct material choice.