# Material selection **Material selection** is the engineering step that turns a design intention into a named [[Material|material]], and it is the step where most of a product's mass, cost and carbon are actually decided. It is rarely a search for the strongest or the stiffest substance. A design carries an objective to minimise — usually mass or cost — together with constraints it must not violate, and the material that wins is the one that optimises the objective while meeting every constraint, which is almost never the best performer on any single property. The method that made this systematic replaces the shopping list with a small algebraic quantity, the performance index, which combines the properties that enter the objective; materials are then ranked on that index alone.[^ashby-ch5] In the microsim below the reader works on an Ashby chart of [[Young's_modulus|Young's modulus]] *E* against [[Density|density]] ρ, both on logarithmic axes, with the material families drawn as bubbles: metals, technical [[Ceramic|ceramics]], [[Polymer|polymers]], [[Composite_material|composites]], [[Foam|foams]] and woods. The single control is the shape of the loaded part, which fixes the index and hence the slope of a guideline drawn across the chart: slope 1 for a tie loaded in tension, where the index is `E/ρ`; slope 2 for a beam in bending, where it is `E^(1/2)/ρ`; slope 3 for a plate, where it is `E^(1/3)/ρ`. The reader slides the guideline up the chart, and the last bubble it touches is the answer. On the [[Materials_science|Materials science]] flagship this article serves the *Industry* section of Part VIII, where the discipline's knowledge of structure and properties is finally spent on a decision; the [[Specific_modulus|specific modulus]] and [[Specific_strength|specific strength]] variants reuse the same chart with different axes, and the [[Titanium_alloys|titanium]] and [[Magnesium_alloy|magnesium alloy]] pages highlight their own bubble on it. ## Ashby plots An Ashby plot, or material property chart, puts one property on each logarithmic axis and draws every material family as a closed bubble enclosing the range its members occupy.[^ashby-ch4] The convention matters more than it looks. Logarithmic axes are needed because engineering materials span five or six decades in stiffness and three in density; on linear axes every polymer would collapse onto the origin. Bubbles rather than points are needed because a "material" such as an [[Aluminium_alloy|aluminium alloy]] is a family whose modulus varies by a few per cent and whose strength varies tenfold with temper. The chart's power is that most of it is empty. Properties are not independent — stiffness and density both rise with atomic packing and bond strength — so the populated region is a band running from low-*E*, low-ρ foams to high-*E*, high-ρ ceramics and refractory metals. Any straight line of slope *n* on such a chart is a contour of the quantity `E^(1/n)/ρ`, so a family of parallel guidelines sweeps the chart in the order that a performance index ranks its materials. That geometric fact is the whole method: choosing a slope is choosing what the design is for. Charts exist for every pair of properties a designer might trade: modulus against strength, [[Fracture_toughness|toughness]] against strength, [[Thermal_conductivity_and_resistivity|thermal conductivity]] against thermal expansion, strength against maximum service temperature, and every property against cost. The *E*–ρ chart the microsim draws is the first of them because so many structural objectives reduce to stiffness at least mass. ## Cost issues Minimum mass is the aerospace objective; minimum cost is everyone else's. Substituting cost for mass changes only one factor in the index. If the material costs `C_m` per kilogram, the cost of a light stiff beam is proportional to `C_m·ρ/E^(1/2)`, so the index to maximise becomes `E^(1/2)/(C_m·ρ)`, and the chart to use is modulus against cost per unit volume, `C_m·ρ`. Materials that win on mass frequently lose badly on cost: carbon fibre reinforced polymer beats every metal on `E^(1/2)/ρ`, but at an order of magnitude more per kilogram it is displaced by [[Steel|steel]] or [[Aluminium|aluminium]] wherever the mass saved is not worth paying for. Three cautions belong with any cost index. Material price is only part of part cost — [[Manufacturing|manufacturing]] route, tooling, joining, scrap rate and inspection often dominate, and a cheap material that must be machined from solid can be the expensive choice. Prices move: commodity metals and polymers swing by tens of per cent over a few years, so a ranking that depends on a narrow cost margin is not robust. And a material's cost to the buyer is not its cost to the world, which is why parallel charts of embodied energy and CO₂ per kilogram are now drawn on the same axes and used with the same indices.[^ashby-ch15] ## General method for using an Ashby chart The systematic procedure has four steps, and the chart appears only in the third.[^ashby-ch5] *Translation* restates the design problem as a function, a set of constraints, an objective and the free variables: "a beam of given length must carry a given load without deflecting more than δ; minimise mass; the cross-section is free". *Screening* eliminates every material that cannot meet a constraint, by drawing a horizontal or vertical box on the chart — a minimum [[Fracture_toughness|fracture toughness]], a maximum service temperature, a requirement of biocompatibility or resistance to a particular [[Corrosion|corrosion]] environment. *Ranking* orders the survivors on the performance index. *Documentation* then investigates the top few candidates as case histories: what they are really used for, what goes wrong with them, who supplies them. Deriving the index is the only algebra. Write the objective — here mass `m = ρ·A·L` — then use the constraint to eliminate the free variable, and whatever is left containing only material properties is the index. The elimination is where the shape enters: a constraint on axial stiffness fixes area directly, while a constraint on bending stiffness fixes the second moment of area, and area enters that as a power of two or three depending on whether the section can grow in one dimension or two. On the chart, ranking is mechanical. Draw a line of the index's slope, slide it up and to the left, and stop when only a few bubbles remain above it. Everything above the line is better than everything below, regardless of where the materials sit along the line. Screening boxes and the guideline are applied together, which is why a chart beats a spreadsheet: the constraint and the objective are visible in the same picture. Translation is harder than it sounds, and the design literature treats it as a discipline of its own: stakeholder needs must become measurable requirements, each with a unit, before any material can be screened against them.[^jensen-req] Where several objectives survive translation and no single index covers them, the shortlist is closed out with a weighted decision matrix. In the Pugh form each candidate is scored −1, 0 or +1 against a baseline on every requirement, the requirement weights run 1 to 5, and the winner has the largest `S_j = Σ_i w_i·s_ij`; the matrix's real value is that it records why the losers lost.[^barnes-pugh] ## Example of using an Ashby chart The worked example below takes six representative materials, one from each of the families the microsim draws, and follows them through the three shapes. The property values are family-representative rather than specifications for any particular grade, and the modulus and density of the metals are the order of the values tabulated in the open physics texts behind this portal.[^openstax-up1-12][^openstax-up1-14] | material | *E* (GPa) | ρ (Mg/m³) | `E/ρ` | `E^(1/2)/ρ` | `E^(1/3)/ρ` | |---|---|---|---|---|---| | steel | 210 | 7.8 | 26.9 | 1.86 | 0.76 | | titanium alloy | 115 | 4.5 | 25.6 | 2.38 | 1.08 | | aluminium alloy | 70 | 2.7 | 25.9 | 3.10 | 1.53 | | magnesium alloy | 45 | 1.8 | 25.0 | 3.73 | 1.98 | | CFRP, along the fibres | 130 | 1.6 | 81.3 | 7.13 | 3.17 | | wood, along the grain | 10 | 0.7 | 14.3 | 4.52 | 3.08 | ### Performance index during tension A tie of fixed length *L* must carry a load without stretching more than a set amount, so its axial stiffness `S = E·A/L` is prescribed and its area *A* is free. Eliminating *A* from the mass `m = ρ·A·L` gives `m = S·L²·(ρ/E)`, so the lightest tie is made of the material with the largest `E/ρ`, the [[Specific_modulus|specific modulus]]. Its contours have slope 1 on the chart. The result in the table is one of the most useful facts in engineering. Steel, [[Titanium|titanium]], aluminium and [[Magnesium|magnesium]] score 26.9, 25.6, 25.9 and 25.0 — the same number to within 8 % (derived from the table). For a simple tie there is nothing to choose between the structural metals on weight; the decision falls to cost, joinability, [[Corrosion|corrosion]] or stiffness at temperature. Only the [[Carbon_fiber_reinforced_polymer|carbon fibre composite]], at 81.3, breaks the tie, and only because its fibres are stiff *and* light at once. ### Performance index during bending A beam of fixed length carrying a transverse load has a bending stiffness proportional to `E·I/L³`, with `I` the second moment of area. For a square section of side *b*, `I = b⁴/12` and `A = b²`, so a prescribed stiffness fixes `b⁴ ∝ 1/E`, hence `A ∝ E^(−1/2)` and `m = ρ·A·L ∝ ρ/E^(1/2)`. The index to maximise is `E^(1/2)/ρ`, and its contours have slope 2. Doubling the exponent's denominator changes everything, because the section is now free to grow in two directions and a light material can buy back its low modulus with depth. The metals separate: magnesium 3.73, aluminium 3.10, titanium 2.38, steel 1.86 (derived). Steel, level with magnesium as a tie, is now half as good, which is why bicycle frames, aircraft floor beams and laptop cases are made of light alloys and composites rather than steel. CFRP leads at 7.13, and wood — a cellular composite evolved for exactly this loading — comes second at 4.52, ahead of every metal. ### Selecting the best material overall A single index never decides a real design, because screening has to be applied first and the constraints are rarely only elastic. Titanium ranks poorly on both stiffness indices, yet it is chosen constantly, because its advantage lies in a different chart: high [[Specific_strength|specific strength]] that it keeps to around 400 °C, and an oxide film that makes it almost inert in seawater and in the body. Wood ranks second on the beam index but is anisotropic, variable, and limited in size and in service temperature. CFRP wins both indices but is expensive, hard to join, poor across the fibres, and difficult to inspect for internal damage. The honest output of the method is therefore a shortlist, not a winner, and the shortlist changes with the constraint set. Add a minimum fracture toughness and the technical ceramics vanish. Add a requirement to be recyclable in an existing stream and CFRP goes with them. Add a maximum price per part and the composite usually loses to aluminium. Add a manufacturing route and the palette narrows again: an additive process offers only the alloys and polymers qualified for it, so selection and process choice have to be made together.[^barnes-am-materials] What the chart guarantees is that nothing plausible was overlooked and that each rejection has a stated reason — the [[Yield_(engineering)|yield]], [[Fatigue_(material)|fatigue]] or [[Creep_(deformation)|creep]] limit it failed, or the index on which it lost. Selection also does not end when the material is named, because the same sizing arithmetic must be redone against every constraint. In the landing-strut design worked through the aerospace text behind this portal, a 4340 [[Steel|steel]] strut sized to absorb the landing stroke turns out to be overstressed against its 160 ksi allowable, and the fix is a different section, not a different material.[^johnson-strut] A material that passes on one index can still fail on another. ### Numerically understanding the chart The chart's arithmetic is worth doing once by hand, because it explains why the three slopes exist at all. A guideline of slope *n* passing through a point (ρ₀, E₀) has the equation `E = E₀·(ρ/ρ₀)^n`, so along it `E^(1/n)/ρ` is constant; a material lying above the line has a larger index and a material below a smaller one, whatever its individual *E* and ρ. Sliding the line up multiplies the index by a constant factor and does not change the ranking, which is why the *last* bubble touched is the answer. The exponents follow from how the free variable enters. For the tie, area enters the stiffness linearly and the mass linearly, so the powers cancel and the index is `E/ρ`. For the beam, stiffness goes as the fourth power of the side but mass as the second, giving the square root. For a plate of fixed length and width whose thickness *t* is free, stiffness goes as `t³` and mass as `t`, so `m ∝ ρ/E^(1/3)` and the index is `E^(1/3)/ρ`, slope 3. On that index the table reorders again: CFRP 3.17 and wood 3.08 are level, magnesium 1.98 leads the metals, and steel trails at 0.76, a factor of four behind magnesium and behind foams and woods that are barely materials at all by the standards of a stress analysis (derived). A plate is the shape that most rewards low density, which is why aircraft skins, car body panels and packaging are the places light alloys, [[Metal_foam|metal foams]] and sandwich panels earn their price. *See also:* [[Specific_strength]] · [[Specific_modulus]] · [[Titanium_alloys]] · [[Magnesium_alloy]] · [[Material]] · [[Composite_material]] · [[Finite_element_method]] · [[Strength_of_materials]] ## References [^ashby-ch4]: Ashby, M. F. (1992). *Materials Selection in Mechanical Design*. Oxford: Pergamon Press. The material property charts, including the modulus–density chart. Not a Portal Book; chapter and page to pin. [^ashby-ch5]: Ashby, M. F. (1992). *Materials Selection in Mechanical Design*. Oxford: Pergamon Press. The selection procedure — translation, screening, ranking, documentation — and the derivation of performance indices for the tie, beam and plate. Not a Portal Book; chapter and page to pin. [^ashby-ch15]: Ashby, M. F. (1992). *Materials Selection in Mechanical Design*. Oxford: Pergamon Press. Cost-based indices and charts of modulus against cost per unit volume. Not a Portal Book; chapter and page to pin. Later editions add the embodied-energy and CO₂ charts referred to here; edition and page to pin. [^openstax-up1-12]: Ling, S. J.; Sanny, J.; Moebs, W. (2016). *University Physics Volume 1*. OpenStax (Portal Book 077). Chapter 12, Static Equilibrium and Elasticity, Table 12.1 (approximate Young's moduli), chapter pp. 565–610 (table page to pin). https://openstax.org/books/university-physics-volume-1/pages/12-introduction [^openstax-up1-14]: Ling, S. J.; Sanny, J.; Moebs, W. (2016). *University Physics Volume 1*. OpenStax (Portal Book 077). Chapter 14, Fluid Mechanics, §14.1 Fluids, Density, and Pressure, Table 14.1 (densities), chapter pp. 665–720 (table page to pin). https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure [^jensen-req]: Jensen, David (2024). *Introduction to Mechanical Design and Manufacturing*. Portal Book 109. Chapter 5, Defining and Managing Design Requirements, pp. 75–96 (page to pin) — the translation step, in which stakeholder needs become measurable requirements before any material is named. [^barnes-pugh]: Barnes, John; Simpson, Timothy (2025). *Additive Manufacturing Essentials*. Portal Book 110. Chapter 4, Design for Additive Manufacturing, the Pugh concept selection matrix, p. 88 (Tables 4.7–4.8): each candidate is scored −1, 0 or +1 against a baseline on each weighted requirement and `S_j = Σ_i w_i·s_ij` decides. [^barnes-am-materials]: Barnes, John; Simpson, Timothy (2025). *Additive Manufacturing Essentials*. Portal Book 110. Chapter 3, AM Materials, pp. 49–74 (page to pin) — the restricted palette an additive process imposes on selection. [^johnson-strut]: Johnson, Eric R. (2022). *Aerospace Structures*. Portal Book 009. Chapter 14, Landing strut, pp. 417–430; the worked design uses 4340 steel with a 230 ksi yield, a 160 ksi allowable stress and a density of 0.284 lb/in³, and shows that a design feasible in stroke can still fail in strength (pp. 419–421). ## External links - [University Physics Volume 1](https://openstax.org/books/university-physics-volume-1/pages/12-introduction), OpenStax — Chapter 12 for moduli and Chapter 14 for densities, the two tables behind the chart's axes. - [Introduction to Mechanical Design and Manufacturing](https://open.umn.edu/opentextbooks/textbooks/introduction-to-mechanical-design-and-manufacturing), David Jensen, via the Open Textbook Library — requirements and the design process that precedes selection. - Further links, including the commercial selection databases, are listed on the Wikipedia pair. <!-- MATTERSIM:BEGIN g24 — Matter & Energy Cluster microsim (framework build, specs/sims/Material_selection.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework), pending deploy:** *Material selection* will play here once `https://wikitube-3d-microsims.netlify.app/matter/Material_selection.html` is live. <!-- pending: <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Material_selection.html" data-title="Material selection"></div> --> <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Material_selection) : [Wikitube](https://en.wikitube.io/wiki/Material_selection) · pinned revision [1316811566](https://en.wikipedia.org/w/index.php?oldid=1316811566) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Materials_science]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Materials_science row M44 · sim pending (matter/Material_selection).*