Materials Selection — Engineering Reference
See also (Tier 3 family index): Steel Grades Family Index
1. At a glance
Materials selection is the systematic process of picking a material+process pair for a part. It is not the question “what is the best material” — there is no such answer divorced from context. It is the question “what material best satisfies this function, under these constraints, against this objective, with these free variables?” Reframed that way, selection becomes a well-posed engineering optimisation problem rather than a folk-knowledge ritual.
The dominant formal methodology is Ashby’s method, developed at Cambridge in the late 1980s and codified in Materials Selection in Mechanical Design (Ashby, now in its 5th edition). It pairs (a) functional design analysis to derive material indices with (b) property-property “Ashby charts” on which whole families of materials are visualised as bubbles, letting an engineer screen a database of thousands of materials down to a top-three shortlist in minutes.
Why a real process matters. Most engineers in most organisations default to “the material we always use” — historical inertia, qualification cost, available supplier base. A real selection process routinely reveals 3–5× better alternatives on the engineering objective (mass, cost, embodied CO₂, deflection). The penalty for skipping it is paid downstream: a wrong material picks up its cost as warranty claims, scrap, weight rework, or product cancellation.
Where it sits in the design stack. Materials selection is part of conceptual / embodiment design, between requirements definition and detailed analysis. It is iterative with both: requirements firm up as a selection space narrows; detailed FEA / fatigue / CFD informs whether a selected candidate truly meets the loads. In modern practice it is also entangled with process selection — a material is only as good as the process by which it can be made into the part.
The output of a selection exercise is a short ranked list (typically 3–5) of viable material+process pairs, each with a documented rationale: the indices that ranked it, the constraints it survived, the local shop and supply-chain factors that admit it, and the risks that could disqualify it.
2. Why it matters — the cost of getting it wrong
Industrial case studies of selection failure are abundant and instructive:
- Comet jet airliner (1954) — square cabin windows in 7075-T6 aluminum, fatigue cracking from stress concentration at the corners, catastrophic in-flight depressurisation. The wrong corner geometry + a fatigue-sensitive aluminum + insufficient fracture-toughness allowable. Drove the entire modern damage-tolerance framework (MMPDS, FAR Part 25.571).
- Liberty ships (1943) — A-grade carbon-steel hull plate, brittle fracture below the ductile-to-brittle transition in North Atlantic service. The plate met its tensile spec but had no Charpy requirement. Drove the development of Charpy-qualified pressure-vessel and ship-plate steels (ASTM A20, ABS Grade D/E).
- DC-10 cargo door (1974) — wrong fastener-and-latch material choice combined with inadequate failure-mode-effects analysis. 346 dead.
- Boeing 787 lithium-ion battery (2013) — cell-chemistry choice without thermal-runaway containment. Three-month grounding of the global 787 fleet.
- Volkswagen TDI dual-mass flywheel (~2005–2015) — the spring material’s fatigue endurance was misestimated; multi-billion-euro warranty programme.
Every one of these is a materials-selection failure traceable to skipping a step in the formal process: a constraint missed, an objective unstated, a process incompatibility ignored, or a property statistic taken as a single deterministic number when in service it is a probability distribution.
3. First principles — the four-step framework
Ashby’s selection is a four-step protocol applied at the level of each function-bearing component:
3.1 Function
What does the part do? Function is a one-line statement of mechanical / thermal / electrical role. Typical function classes:
- Carry a tensile load (tie)
- Carry a bending load (beam)
- Carry a compressive load (column, may buckle)
- Carry a pressure load (vessel, pipe)
- Carry torque (shaft, spring)
- Conduct heat (heat sink, fin)
- Insulate against heat (oven wall, cryogenic dewar)
- Conduct electricity (busbar, conductor)
- Insulate against electricity (cable jacket, motor slot liner)
- Store elastic energy (spring)
- Damp vibration (mount, isolator)
- Contain a fluid against permeation (fuel tank, pneumatic line)
- Resist wear (gear face, bushing)
- Withstand an environment (chemical-tank wall, exhaust manifold)
Each function class generates its own design equation in step 3 of index derivation.
3.2 Constraints
What are the must-have non-negotiables? Constraints are hard pass/fail filters. Each is independent of every other and of the objective. Common constraints:
- Operating-temperature ceiling (T_max ≥ 200 °C)
- Operating-temperature floor (cryogenic service, no DBTT above 4 K)
- Corrosion class (marine atmospheric, hot chloride, sour-gas H₂S)
- Food contact (FDA 21 CFR 177 or EU 10/2011)
- Biocompatibility (ISO 10993, USP Class VI)
- Magnetic permeability (μ_r < 1.05 for MRI suites)
- Electrical conductivity / insulation
- Optical transmissivity (radomes need ε_r ≈ 4, low loss tangent)
- Recyclability / EoL regulatory (EU ELV Directive 2000/53/EC for automotive, RoHS, REACH)
- Flammability / smoke / toxicity (FAR 25.853 for aircraft cabin)
- Regulatory pedigree (ASME BPVC stamping, NADCAP, MMPDS A/B-basis)
- Geometric feasibility (max section thickness through-hardenable, max castable size)
3.3 Objective
What is to be minimised or maximised? Exactly one (or one weighted aggregate). Common objectives:
- Mass
- Cost (raw material × billet mass + processing)
- Embodied energy / embodied CO₂
- Deflection under a fixed load
- Volume / envelope
- Time to market (favours commodity / qualified materials)
A common error is to write multiple objectives — “minimise mass and cost” — without acknowledging a Pareto front. See § 9 edge cases.
3.4 Free variables
What can the designer change? The geometric or process parameters not fixed by the function or constraints. Typically:
- Cross-section area, thickness, or wall thickness
- Tube outside diameter (with wall thickness)
- Number of plies in a laminate
- Heat-treatment condition of a metal
- Process route (cast vs forged vs machined-from-billet)
The index-derivation trick (§ 4.1) eliminates the free variable from the objective by substituting in the function equation under the constraint — leaving a pure material-property group.
4. Material indices — the heart of the method
4.1 Derivation procedure
For each function/constraint/objective combination:
- Write the objective as a function of geometry and material: e.g. mass m = ρ · A · L.
- Write the function equation containing the constraint: e.g. for a tie carrying load F without yielding, F = σ_y · A.
- Solve the function equation for the free variable (A here).
- Substitute back into the objective; collect material properties on one side, geometric / loading constants on the other.
- The material-property group is the index M. Materials with higher M are better for that function/constraint/objective combination (or lower 1/M, depending on how you write it).
Worked derivation — light, strong tie:
F = σ_y · A → A = F / σ_y m = ρ · A · L = (F · L) · (ρ / σ_y) ↓ Minimise m → Maximise M = σ_y / ρ
Worked derivation — light, stiff beam in bending (square cross-section, length L fixed, stiffness S = F/δ specified):
Beam stiffness: S = C₁ · E · I / L³, with I = b⁴/12 for square section → b² = (12 · S · L³ / (C₁ · E))^(1/2) Mass: m = ρ · b² · L = ρ · L · (12 · S · L³ / (C₁ · E))^(1/2) Collecting: m ∝ (1/L) · (ρ / √E) → Maximise M = √E / ρ
4.2 Index table — the engineer’s working reference
| # | Function & loading | Constraint | Objective | Index (maximise) |
|---|---|---|---|---|
| 1 | Tie (tensile rod, cable) | Yield | Min mass | σ_y / ρ |
| 2 | Tie (cable) | Stiffness (target deflection) | Min mass | E / ρ |
| 3 | Beam, fixed cross-section shape, length specified | Stiffness | Min mass | E^(1/2) / ρ |
| 4 | Beam, fixed cross-section shape, length specified | Yield | Min mass | σ_y^(2/3) / ρ |
| 5 | Plate (panel), thickness free | Stiffness | Min mass | E^(1/3) / ρ |
| 6 | Plate (panel), thickness free | Yield | Min mass | σ_y^(1/2) / ρ |
| 7 | Column, length and load fixed, cross-section free | Buckling | Min mass | E^(1/2) / ρ |
| 8 | Pressure vessel, thin-walled | Yield, leak-before-break | Min mass | K_IC² / σ_y |
| 9 | Pressure vessel, thin-walled | Yield (no LBB requirement) | Min mass | σ_y / ρ |
| 10 | Spring, max elastic-energy per unit mass | Yield | Max stored energy | σ_y² / (E · ρ) |
| 11 | Spring, max elastic-energy per unit volume | Yield | Max stored energy | σ_y² / E |
| 12 | Heat sink / fin | Steady-state conduction | Min mass | λ / ρ |
| 13 | Thermal-shock-resistant component | Sudden temperature change | Max ΔT survivable | σ_y · λ / (E · α) |
| 14 | Precision instrument | Dimensional stability under ΔT | Min deflection | λ / α |
| 15 | Electrical busbar | Resistive loss budget | Min mass | 1 / (ρ · ρ_e) |
| 16 | Damped strut / mount | Vibration isolation | Max damping with stiffness floor | η · E^(1/2) |
| 17 | Wear-resistant face (lubricated) | Archard wear life | Max hardness for given σ_y | H / E |
| 18 | Stiff, cheap structure | Stiffness on a budget | Min cost | E / (ρ · C_m) |
| 19 | Strong, cheap structure | Yield on a budget | Min cost | σ_y / (ρ · C_m) |
| 20 | Low-carbon structure | Stiffness on a CO₂ budget | Min embodied CO₂ | E^(1/2) / (ρ · CO₂_m) |
C_m = cost per kg of finished material; CO₂_m = embodied kg CO₂ per kg of material (cradle-to-gate, per ISO 14040 / 14044). η = loss coefficient (damping ratio). ρ_e = electrical resistivity.
4.3 Why the fractional exponents
The exponents 1/2, 2/3, 1/3 arise from the degree of freedom the geometry gives the designer:
- Tie: only cross-section area A is free; A is linear in the index, so the index is linear in (property/ρ).
- Beam, square section: both b and h scale together, so b² governs stiffness while b² also governs mass — bringing the 1/2 power.
- Plate (panel of fixed width but free thickness): only one dimension t scales, so the index gets 1/3.
The implication: the more geometric freedom you give the designer, the more leverage a light material has. A panel with free thickness rewards low ρ much more than a tie of fixed length.
5p. Theory — Ashby charts (property-property bubble maps)
An Ashby chart plots one material property against another, on log-log axes, with each material drawn as a labelled bubble whose size reflects the property scatter (alloy family, heat-treatment condition, fibre fraction). A few canonical charts:
| Chart | Axes | Used for |
|---|---|---|
| Modulus-density | E vs ρ | Stiffness-limited mass minimisation; the most-used chart in the canon |
| Strength-density | σ_y vs ρ | Strength-limited mass minimisation |
| Thermal conductivity-CTE | λ vs α | Thermal management, precision instruments |
| Fracture toughness-strength | K_IC vs σ_y | Damage tolerance, leak-before-break vessels |
| Cost-density | C_m · ρ vs ρ | Cheap structure, civil and consumer applications |
| Damping-modulus | η vs E | Vibration isolation, acoustic enclosures |
| Embodied energy / CO₂ vs density | CO₂_m vs ρ | Low-carbon design |
| Service temperature-strength | T_max vs σ_y | High-temperature components |
| Wear rate-hardness | k_A vs H | Tribology, lubricated and dry contacts |
5p.1 Reading the chart with a guideline
On an E-vs-ρ log-log chart, a constant value of M = E^(1/2)/ρ traces a straight line of slope 2 (because log E = 2 log ρ + 2 log M). Materials above that line have higher M; materials below have lower. Drawing the guideline through the current candidate and sliding it parallel toward the upper-left screens the chart visually:
- Slope 1 line (tie, M = E/ρ)
- Slope 2 line (beam, M = E^(1/2)/ρ)
- Slope 3 line (plate, M = E^(1/3)/ρ)
The slope 3 line is the most permissive; many polymers and foams rank well on plate-stiffness/mass. The slope 1 line is the strictest; only ceramics and CFRP UD beat steel for tie-stiffness/mass.
5p.2 Family clusters
Bubbles on the E-vs-ρ chart cluster into families that recur on every chart:
- Engineering ceramics (Al₂O₃, SiC, Si₃N₄): high E, moderate-to-high ρ, very low K_IC — pinned to upper-right.
- Metals and alloys: steels (E ≈ 200 GPa, ρ ≈ 7.85), aluminum (E ≈ 70 GPa, ρ ≈ 2.7), titanium (E ≈ 110 GPa, ρ ≈ 4.5) — central band.
- Polymers: E ≈ 1–4 GPa, ρ ≈ 0.9–1.4 — lower-left.
- Elastomers: E ≈ 0.001–0.1 GPa — bottom.
- Composites: CFRP UD spans E ≈ 50–250 GPa, ρ ≈ 1.5; GFRP UD E ≈ 30–60 GPa, ρ ≈ 1.9 — beat metals on most stiffness/mass indices.
- Woods: anisotropic; along-grain E ≈ 10–20 GPa at ρ ≈ 0.5; surprisingly competitive on plate-stiffness/mass.
- Foams: E ≈ 0.001–1 GPa, ρ ≈ 0.05–0.5; lower-left of polymers.
6p. Application — the two-stage filter
6p.1 Stage 1: Screening (hard constraints)
Apply each constraint as a binary filter. Any material that fails any constraint is eliminated, regardless of how well it scores on the index. Typical screens:
- Service temperature: T_max ≥ 200 °C eliminates most polymers (PEEK survives, PA6/POM/PE do not).
- Corrosion class: hot chloride eliminates 304 stainless (CPT ~15 °C); requires 316 (CPT ~25 °C), duplex 2205 (CPT ~35 °C), or super-duplex 2507 (CPT ~70 °C).
- Magnetic permeability < 1.05: eliminates all carbon and low-alloy steel; admits austenitic stainless (carefully heat-treated to avoid δ-ferrite), aluminum, copper, titanium.
- Food contact (FDA / EU 10/2011): admits 304L/316L, PEEK, PTFE, EPDM, silicone; excludes leaded brasses, free-machining 12L14, most filled polymers.
- Recyclability mandate (e.g. 95 % EU ELV): excludes thermoset composites, multi-layer coextrusions.
The screening pass typically eliminates 80–95 % of the database.
6p.2 Stage 2: Ranking (material indices)
Compute each surviving material’s index value(s). Sort. Take the top 3–5. For multi-index problems, plot one index against another and identify the Pareto front (§ 9.1).
6p.3 Stage 3: Documentation — the one-page rationale
For each shortlisted finalist, write a one-page selection brief:
- Material grade + condition + process (e.g. “6061-T6 6063 extrusion, hard anodised”)
- Why it survived screening (each constraint, each margin)
- Index value(s) and margin over next runner-up
- Known risks (galvanic corrosion with carbon steel mating part, fatigue knockdown for welded joints, supply-chain risk)
- Path to qualification (test plan, statistical-allowables strategy, cost-of-change)
6p.4 Stage 4: Local conditions — the shop reality check
Many candidates that win on indices die at the local-shop step. Questions to answer before commit:
- Can we source it in the required form (sheet, plate, tube, billet, prepreg) at production volume?
- Is the heat-treatment / process step available locally, or do parts ship out and back (cost + lead-time + tracking)?
- Can our existing inspection equipment qualify it (ultrasonic, eddy-current, dye-penetrant, CT)?
- Do we have a welding / bonding procedure qualified for it (ASME Section IX WPS, AWS D1.x)?
- Do our existing finishes (paint, plating, anodise) work on it?
- Are the assembly fasteners and tooling compatible?
A material that scores 1.4× on the index but adds three new suppliers, one new heat-treat process, and a NADCAP audit is rarely the right pick over a 1.0× material the shop already runs.
7p. Process selection — co-equal with material
A material is not a part. Material and process together define the deliverable. A grade designation like “6061” refers to a chemistry — but 6061-T6 sheet, 6061-T6 forging, 6061-T6 sand-cast, and 6061-T6 plate are different materials in practice (different grain structure, allowable, surface finish, available section).
7p.1 Process families
| Family | Examples | Strength | Limitation |
|---|---|---|---|
| Casting | Sand, investment, die-cast, lost-foam, vacuum-cast | Complex 3D shapes, internal cores | Porosity, anisotropy, large lot-economic minimum for tooling |
| Forming (bulk) | Forging (open- and closed-die), rolling, extrusion, drawing | High strength via worked microstructure | Limited to wrought-friendly alloys; tooling cost |
| Forming (sheet) | Stamping, deep-drawing, hydroforming, spinning, brake-bending | Thin-walled, high-volume, low piece-cost | Springback; tooling-amortisation lot size |
| Machining | Turning, milling, drilling, grinding, EDM | Tightest tolerances, lowest setup cost per part | Lossy (chip ratio 0.3–0.9); subtractive volume cost |
| Joining | Fusion welding, brazing, adhesive bonding, mechanical fastening | Assembly of subcomponents | HAZ properties differ from parent; weldability gates material choice |
| Powder methods | Press-and-sinter, MIM, HIP | Near-net shape, complex geometry, no waste | Porosity ~99 % theoretical density without HIP; alloy restrictions |
| Additive | LPBF (laser powder bed), DED, FDM, SLA, binder jet | One-off complex internal geometry, no tooling | Surface finish, anisotropy, slow per-part, qualification overhead |
7p.2 Process attributes — the screening dimensions
For each process, ask:
- Shape class: solid 3D, hollow 3D, 3D with cores, 2D revolved, flat-sheet 1D
- Section thickness range (e.g. sand-casting 5–500 mm; investment-casting 1–75 mm)
- Mass range (mm-gram MIM parts to multi-tonne sand castings)
- Tolerance achievable (sand-cast ±0.5 mm; investment-cast ±0.15 mm; machined ±0.025 mm; ground ±0.005 mm)
- Surface finish (Ra: sand-cast 12.5–25 μm; investment-cast 1.6–3.2 μm; turned 0.8–1.6 μm; ground 0.1–0.4 μm)
- Economic batch size (sand-cast 10–1000; die-cast 10⁴–10⁶; investment-cast 10²–10⁴; LPBF 1–1000)
- Material compatibility — the next-most-important screen
7p.3 Process-material compatibility (selected)
| Material | Forge | Sand-cast | Die-cast | Investment-cast | Extrude | LPBF | TIG-weld |
|---|---|---|---|---|---|---|---|
| AISI 1018 / A36 | ✓ | △ (poor castability) | ✗ | △ | ✓ | △ (cracking risk) | ✓ |
| AISI 4140 | ✓ (excellent) | ✓ | ✗ | ✓ | △ | ✓ (with HT) | △ (preheat + PWHT) |
| AISI 304 | ✓ | ✓ (as CF8) | ✗ | ✓ | △ | ✓ | ✓ |
| 6061 Al | ✓ | △ (use 356/319 instead) | △ | △ | ✓ | △ | ✓ |
| 7075 Al | ✓ | ✗ (hot-tearing) | ✗ | ✗ | ✓ | ✗ (cracks) | ✗ (use FSW) |
| Ti-6Al-4V | ✓ | △ (reactive vacuum-cast only) | ✗ | ✓ (vacuum) | △ | ✓ | ✓ (inert shroud) |
| CFRP (epoxy prepreg) | ✗ | ✗ | ✗ | ✗ | (pultrusion) | (AFP/ATL) | ✗ |
| Al₂O₃ ceramic | ✗ | ✗ | ✗ | (slip-cast) | ✗ | (binder-jet + sinter) | ✗ |
✓ standard, △ workable with constraints, ✗ not feasible.
A common pitfall: 7075-T6 wins the strength/mass index for an aerospace bracket, then fails casting + welding + 3D-printing. The shape constraint forces machining from billet or forging — both of which work, but at a cost-and-lead-time delta that often re-shuffles the ranking back to 6061-T6 or 2024-T3.
8p. Worked examples
8p.1 Example A — Bicycle frame tube (light, stiff beam)
Function. Tube in bending under rider + road-impact loads.
Constraints.
- σ_y > ~250 MPa to avoid yielding under realistic peak load (sprint, jump-landing).
- Corrosion-acceptable in outdoor (rain, road salt) conditions.
- Joinable by available methods (TIG-weld, lugged-and-bonded, co-cured).
- Repairable in the field (small-batch sport-equipment reality).
Objective. Minimise frame mass.
Index. Light, stiff beam → M = E^(1/2) / ρ (units (GPa^(1/2) / (Mg/m³))).
Candidate computations:
| Material | E (GPa) | ρ (Mg/m³) | σ_y (MPa) | M = √E/ρ | Notes |
|---|---|---|---|---|---|
| AISI 4130 steel | 205 | 7.85 | 460 | 1.82 | Weldable, repairable, cheap |
| 6061-T6 aluminum | 69 | 2.70 | 276 | 3.08 | Weldable; needs heat-treat after weld |
| 7005-T6 aluminum | 72 | 2.78 | 350 | 3.06 | Air-quenches on weld; no post-weld HT |
| Ti-3Al-2.5V | 100 | 4.48 | 620 | 2.23 | Excellent fatigue, costly, hard to weld |
| CFRP UD (T700, V_f 0.55) | 125 (‖) | 1.55 | 1900 (‖) | 7.21 | Wins on index by 2× |
| GFRP (E-glass, V_f 0.55) | 40 (‖) | 1.95 | 700 (‖) | 3.24 | Wins vs steel, ties vs aluminum |
Ranking by raw index: CFRP (7.21) > GFRP (3.24) ≈ 6061/7005 Al (3.08/3.06) > Ti (2.23) > steel (1.82).
Conclusion. CFRP dominates on the index by ~2× the next runner-up. In practice, CFRP wins for high-end road and time-trial frames (top 20 % of market by price). For mid-market, 6061-T6 / 7005-T6 aluminum wins because: (a) raw index difference between Al and CFRP shrinks once the matrix-dominated failure modes are included; (b) Al frames are TIG-weldable and locally repairable; (c) Al tubing is sold in standard butted sizes from dozens of suppliers; (d) end-of-life recyclability is straightforward. Steel (4130) survives in adventure-touring and rough-stock segments where field-weldability and dent-tolerance dominate over the 60 % mass penalty.
This is the canonical Ashby teaching example: the index gives the ranking, but the cost-per-unit-improvement and the manufacturing-and-repair context determine the commercial winner.
8p.2 Example B — Heat sink for a 30 W LED array (thermal conductor at min cost)
Function. Conduct heat from a thermal interface to ambient air, holding junction T ≤ 85 °C with 25 °C ambient.
Constraints.
- T_max ≥ 100 °C (LED housing temperature).
- Corrosion-acceptable in moist indoor/outdoor environments.
- Electrically insulating outer surface acceptable (anodised or painted).
Objective. Minimise cost × volume of the heat-sink material (at fixed thermal resistance R_th).
Index derivation. For 1D conduction at fixed R_th = L / (λ · A) with L fixed by geometry, A = L / (λ · R_th). Cost per part = ρ · A · L · C_m. Substituting: cost ∝ (ρ · C_m / λ). Minimise (ρ · C_m / λ) → Maximise M = λ / (ρ · C_m).
Candidate computations:
| Material | λ (W/m·K) | ρ (Mg/m³) | C_m (USD/kg) | ρ · C_m (USD/m³ ×10⁻³) | M = λ/(ρ·C_m) |
|---|---|---|---|---|---|
| Cu (C11000) | 401 | 8.94 | 9.00 | 80.5 | 4.98 |
| Al 6063-T5 (extruded) | 209 | 2.70 | 2.50 | 6.75 | 30.9 |
| Al 1100 (sheet) | 222 | 2.71 | 2.20 | 5.96 | 37.2 |
| Al-SiC (AlSiC-9, 63 % SiC) | 180 | 3.00 | 35 | 105 | 1.71 |
| Graphite (pyrolytic in-plane) | 1500 | 2.20 | 80 | 176 | 8.52 |
| Carbon-foam (Koppers L1a) | 150 | 0.55 | 25 | 13.75 | 10.9 |
Conclusion. Aluminum 6063-T5 extrusion dominates. It is the reason ~90 % of all consumer-electronic and LED heat sinks worldwide are aluminum extrusions: λ within 50 % of copper, density 3× lower, raw material 4× cheaper, and the extrusion process delivers fin geometries directly with no post-machining. Copper wins only when volume (not cost) is constrained — CPU heat-spreaders, high-power-density compact converters — where the higher absolute λ pays the volume premium.
8p.3 Example C — Pressure vessel, leak-before-break (damage-tolerant containment)
Function. Cylindrical pressure vessel for compressed gas, internal pressure P, radius R, wall thickness t.
Constraint. Leak-before-break (LBB): any through-thickness crack must reach the outer surface (causing a leak detectable by pressure-drop monitoring) before it reaches the critical length for unstable propagation. This is the standard safe-life logic for nuclear, refinery, and aerospace pressure systems.
Objective. Minimise mass at fixed P, R, design factor.
Index. The critical crack length for an internal surface flaw under hoop stress σ_h is:
a_crit = (1/π) · (K_IC / σ_h)²
For LBB, require a_crit ≥ t (the through-wall distance), so:
t ≤ (K_IC / σ_h)² / π
Combined with the thin-wall hoop equation σ_h = P · R / t and minimum mass m ∝ ρ · t at fixed R, after substitution:
Minimise mass at fixed P, R, LBB → Maximise M = K_IC² / σ_y
Note: higher σ_y is not better here. A higher-strength steel lets you go thinner — but the thinner section reaches its critical-crack-length sooner. The optimum is a moderate-strength, high-K_IC condition.
Candidate computations — AISI 4340 quenched and tempered to various conditions (per MMPDS-19 and ASM Handbook Vol 1):
| Temper temperature | σ_y (MPa) | K_IC (MPa·√m) | M = K_IC²/σ_y (MPa·m) |
|---|---|---|---|
| 200 °C | 1700 | 50 | 1.47 |
| 315 °C | 1500 | 60 | 2.40 |
| 425 °C | 1280 | 80 | 5.00 |
| 540 °C | 1070 | 110 | 11.3 |
| 650 °C | 860 | 130 | 19.7 |
Conclusion. The lowest-strength condition (650 °C temper) has the highest M — 13× higher than the highest-strength 200 °C temper. The teaching point: for damage-tolerant pressure vessels, choosing the highest yield strength is actively wrong. This is why ASME BPVC Section VIII and the ASTM A372 / A508 forgings for nuclear pressure vessels specify moderate strength (~415–620 MPa σ_y), not the maximum the alloy can deliver.
In practice: A516 Grade 70 (carbon steel, σ_y = 260 MPa, K_IC > 110 MPa·√m) and A508 Class 3 (Ni-Mo-Cr, σ_y = 345 MPa, K_IC ~ 200 MPa·√m) are the dominant LBB pressure-vessel materials, despite their unremarkable strengths.
9p. Edge cases & where the method breaks
9p.1 Multi-objective problems (Pareto fronts)
When two objectives compete — mass and cost, mass and embodied CO₂ — there is no single best material. The method outputs a Pareto front: the set of materials for which no other material is simultaneously better on both axes. The designer then chooses a point on the front using a trade-off factor α (USD/kg saved, kg CO₂/kg saved):
Penalty function: Z = (1/M_mass) + α · (1/M_cost)
For a passenger car, α ≈ 5 USD/kg saved. For commercial aircraft, α ≈ 500–1000 USD/kg saved. For deep-space launch payload, α ≈ 10,000–50,000 USD/kg saved. The same component, with the same loads, picks steel for the car, aluminum for the aircraft, CFRP for the spacecraft — all from the same Pareto front, with the choice driven by α alone.
9p.2 Coupled constraints (yield + fracture + fatigue + creep)
Each failure mode generates its own index, and each constraint cuts a different region of material space. A high-temperature pressure component must satisfy yield (σ_y at T_op), creep (Larson-Miller for 100,000 hr), fracture (K_IC at T_op), and fatigue (HCF + LCF) — often by different materials’ weakness. The selection problem becomes a multi-constraint optimisation: the intersection of the surviving regions on multiple Ashby charts.
9p.3 Function uncertainty
If the customer hasn’t decided the load yet, indices are derivable only against an assumed worst-case. Methodology: select a “robust” family that performs well across the plausible load envelope rather than optimising for a single load assumption. Aluminum 6061-T6 is a classic robust pick — fewer alloys win on any single index, but few alloys lose on multiple indices, so it earns the default position when the spec is fluid.
9p.4 Manufacturing reality vs index
The index says titanium; the shop has one TIG welder and no inert-atmosphere chamber. Either the part design changes (mechanically-fastened titanium subassembly, eliminating welds), the supplier-base changes (subcontract welded titanium subassemblies to a NADCAP shop), or the material changes (drop to 17-4 PH, which the shop can weld and machine). All three answers are legitimate; ignoring this constraint and writing “Ti-6Al-4V” on a drawing without an answer is not.
9p.5 Supply-chain and regulatory risk
- Rare-earth and strategic-metal restrictions: samarium-cobalt magnets (Sm content) face ITAR review in defence applications; cobalt sourcing (DRC) faces ethical-supply rules; neodymium prices have spiked 5–10× historically on China export quotas.
- PFAS regulation (EU REACH 2024 restriction proposal): PTFE, FKM, FEP, PFA face uncertain future availability for new designs; alternatives (PEEK, polyimide) shift the indices significantly.
- Conflict minerals (Dodd-Frank 1502) force disclosure of tin, tungsten, tantalum, gold sourcing.
A material that wins on engineering indices but introduces a single-source or sanctioned-country supplier is a sourcing-risk loss waiting to happen.
9p.6 Embodied CO₂ shifts the rankings
Switching the objective from cost to embodied CO₂ reshuffles the Pareto front. Typical cradle-to-gate embodied-CO₂ figures (GREET 2022, Ashby Materials and the Environment 3rd ed):
| Material | CO₂_m (kg CO₂ / kg material) |
|---|---|
| Recycled steel (EAF, scrap) | 0.5 |
| Primary steel (BF-BOF) | 2.0 |
| Recycled aluminum | 0.6 |
| Primary aluminum (Hall-Héroult) | 12–18 |
| Titanium (Kroll) | 35–50 |
| Magnesium (Pidgeon) | 35–45 |
| CFRP (PAN-precursor) | 22–24 |
| GFRP | 2.5–8 |
| Concrete | 0.1–0.2 |
Switching objective from mass to mass × CO₂_m moves aluminum two to three ranks down in most bicycle / consumer-product analyses, and moves CFRP from “ranked first” to “ranked third or fourth” against recycled-steel + thoughtful design.
9p.7 Anisotropic materials — which property?
For a UD CFRP lamina with E_‖ = 130 GPa and E_⊥ = 8 GPa, the index √E/ρ ranges from 7.4 to 1.8 depending on direction. Selection against composites requires (a) specifying the load direction(s), (b) using the directional property in the index, (c) verifying after laminate-design optimisation that the directional assumption holds. A 0/90 quasi-isotropic CFRP laminate (E_eff ≈ 55 GPa) ranks differently from UD CFRP, and the difference is comparable to that between two different metal alloys.
9p.8 Property scatter and statistical allowables
Material indices use a single property value, but real materials show 5–25 % scatter on σ_y and 30–100 % scatter on K_IC and fatigue limits. Aerospace and pressure-vessel codes use statistical allowables:
- A-basis (MMPDS / MIL-HDBK-5): 99 % of the population exceeds the value with 95 % confidence.
- B-basis: 90 % of the population exceeds the value with 95 % confidence.
Using a B-basis allowable in the index can shift the ranking 10–30 % relative to using a typical-value handbook number, especially among materials with very different scatter (cast vs wrought, polymer vs metal).
10p. Tools & software
10p.1 Commercial database tools
- Ansys Granta Selector (formerly CES Selector / CES EduPack) — the industry-standard Ashby tool, ~3500–4500 materials, with the indices and chart-drawing engine pre-built. The “Granta Material Universe” taxonomy is the de-facto categorisation reference. Educational version (CES EduPack) widely used in materials and mechanical-engineering curricula.
- Granta MI — enterprise materials-information management; integrates with PLM (Teamcenter, Windchill) and CAD; the platform of choice for aerospace OEMs.
- Total Materia — comparative-grade database, ~450,000 designations, cross-reference between AISI / DIN / JIS / GB / EN; especially strong for international steel and aluminum equivalents.
10p.2 Free / public-domain databases
- MatWeb — the most-used free property database. ~150,000 materials. Use for quick property lookups and grade equivalents; not for safety-critical design (no statistical allowables).
- NIST WebSciDB / Materials Data Repository — high-quality vetted thermal, electrical, mechanical reference data.
- MakeItFrom.com — clean, citation-friendly summaries of common alloys and polymers.
- AZoM.com — material articles with property tables; freelance authorship quality varies; cite the underlying datasheet where critical.
10p.3 Statistical-allowable handbooks
- MMPDS (Metallic Materials Properties Development and Standardisation) — replaced MIL-HDBK-5 in 2003. The aerospace-industry source for A-basis / B-basis allowables on metals. Current version MMPDS-19 (2024); updated annually.
- CMH-17 (Composite Materials Handbook, formerly MIL-HDBK-17) — same for composites. Vol 2 (polymer matrix structural), Vol 3 (matrix-dominated properties), Vol 5 (ceramic matrix).
- AGATE (Advanced General Aviation Transport Experiments) — composite design allowables for GA aircraft; FAA-accepted shared-database basis.
- ASME BPVC Section II Part D — allowable stresses for pressure-vessel materials at service temperature; embeds creep extrapolation (Larson-Miller P).
10p.4 Embodied-energy / carbon databases
- GREET (Argonne National Laboratory) — Greenhouse gases, Regulated Emissions, and Energy use in Technologies. Free, US DOE-maintained, the standard for cradle-to-gate energy and emissions data.
- ecoinvent — comprehensive LCI (life-cycle inventory) database for ISO 14040 / 14044 LCA work; commercial.
- ICE (Inventory of Carbon and Energy, University of Bath) — open-access UK construction-materials database; widely used in built-environment LCA.
- Granta CES Eco Audit — built-into-CES embodied-energy / CO₂ overlay on Ashby charts.
10p.5 Process and additive-manufacturing data
- Senvol Database — additive-manufacturing process + powder + property data. The reference for AM process-material compatibility.
- AM-RDF (NIST AM Reference Data) — emerging public dataset for qualified AM properties.
- ASTM F42 / ISO TC 261 standards — terminology, process classifications, test methods specific to additive manufacturing.
10p.6 Selection methodology references
- ASTM E1655-17 — Standard practices for infrared multivariate quantitative analysis (representative of the broader E11.10 family on statistical property analysis).
- ASTM E2964-14 — Standard guide for materials selection process for sustainability.
- ISO 14040:2006 / 14044:2006 — LCA principles and framework, requirements and guidelines.
- IEC 62474:2023 — material declaration for products of and for the electrotechnical industry.
11. Cross-references
[[Engineering/materials-steel]]— sibling material reference; the dominant structural metal[[Engineering/materials-aluminum]]— sibling material reference; the dominant light metal[[Engineering/materials-polymers]]— sibling material reference; thermoplastics, thermosets, elastomers[[Engineering/materials-composites]]— sibling material reference; FRP, MMC, CMC[[Engineering/materials-ceramics]]— sibling material reference; structural and functional ceramics[[Engineering/mechanics-of-materials]]— stress, strain, beam bending — the function equations from which indices derive[[Engineering/beam-theory]]— beam stiffness equation S = CEI/L³ underpinning the M = √E/ρ index[[Engineering/fasteners-bolts]]— material selection for bolts, ASTM A325/A490/F3125 and metric Grade 8.8/10.9/12.9[[Engineering/fatigue-analysis]](planned) — fatigue endurance limit and K_IC inputs to LBB and damage-tolerance indices[[Engineering/casting-forging-forming]](planned) — process-attribute screening, lot-economic charts[[Engineering/environmental-engineering]](planned) — ISO 14040/14044 LCA mechanics behind embodied CO₂ objectives[[Robotics/manipulator-design]]— material trade-offs for robot links (aluminum vs CFRP for stiffness/inertia)[[Robotics/end-effectors]]— gripper-jaw material selection (tool steel vs nylon vs aluminum)[[Languages/Tier3/construction-bim]]— STEP material assignment and naming conventions[[Languages/Tier3/industrial-automation]]— welding-procedure constraints on material+process pairs
12. Citations
- Ashby, M. F. Materials Selection in Mechanical Design, 5th ed. (Butterworth-Heinemann, 2017). The canonical reference; defines the four-step method, derives all indices, and is the source of the chart conventions used industry-wide.
- Ashby, M. F. Materials and the Environment: Eco-Informed Material Choice, 3rd ed. (Butterworth-Heinemann, 2021). Embodied energy and CO₂ data; LCA-aware extension of the method.
- Ashby, M. F., Shercliff, H., & Cebon, D. Materials: Engineering, Science, Processing and Design, 4th ed. (Butterworth-Heinemann, 2018). Undergraduate-level introduction with full Ashby-method coverage.
- Charles, J. A., Crane, F. A. A., & Furness, J. A. G. Selection and Use of Engineering Materials, 3rd ed. (Butterworth-Heinemann, 1997). Pre-Ashby UK standard reference; complementary process-oriented view.
- Dieter, G. E. (ed.) ASM Handbook Vol 20: Materials Selection and Design (ASM International, 1997). Industry-practice perspective; case studies.
- Farag, M. M. Materials and Process Selection for Engineering Design, 4th ed. (CRC Press, 2020). Process-coupled selection method; complements Ashby on the manufacturing side.
- Metallic Materials Properties Development and Standardization (MMPDS-19) (Battelle, 2024). A-basis and B-basis allowables for aerospace metals.
- Composite Materials Handbook (CMH-17), Volumes 1–6 (SAE International, current revision). Statistical allowables and design methodology for composites.
- ASTM E1655-17 — Standard Practices for Infrared Multivariate Quantitative Analysis (representative of ASTM E11 statistics-on-properties practice).
- ASTM E2964-14 — Standard Guide for Materials Selection Process for Sustainability.
- ISO 14040:2006 / 14044:2006 — Environmental management — Life cycle assessment — Principles and framework / Requirements and guidelines.
- IEC 62474:2023 — Material declaration for products of and for the electrotechnical industry.
- Ansys Granta. Granta Selector User Guide and Material Universe Taxonomy (current release).
- GREET Model 2022 (Argonne National Laboratory). Embodied-energy and emissions database for cradle-to-gate materials accounting.
- Hammond, G. P. & Jones, C. I. Inventory of Carbon and Energy (ICE) v3.0 (University of Bath, 2019). Open-access embodied-energy/CO₂ inventory.
- Senvol LLC. Senvol Database for Additive Manufacturing Machines and Materials (current release).
- ASME Boiler and Pressure Vessel Code, Section II Part D — Properties (Metric / U.S. Customary), current edition. Allowable stresses with Larson-Miller creep extrapolation.
- FAA AC 23-20 — Acceptance Guidance on Material Procurement and Process Specifications for Polymer Matrix Composite Systems.
- Ashby, M. F. & Cebon, D. “Materials selection in mechanical design,” Journal de Physique IV 3 (1993): C7-1–C7-9. The seminal paper of the method.
- Cebon, D. & Ashby, M. F. “Engineering materials informatics,” MRS Bulletin 31, no. 12 (2006): 1004–1012. Modern data-driven extension of the method.