The charts in this article summarise material properties. Each chart appears with a brief commentary about its use. Background and data sources can be found in the book “Materials Selection in Mechanical Design” 3rd edition, by M.F. Ashby (Elsevier-Butterworth Heinemann, Oxford, 2005).
The material charts map the areas of property space occupied by each material class. They can be used in three ways:
1-To retrieve approximate values for material properties.
2-To select materials that have prescribed property profiles.
3-To design hybrid materials.
The collection of process charts, similarly, can be used as a data source or as a selection tool. The sequential application of several charts allows several design goals to be met simultaneously. The best way to tackle selection problems is to work directly on the appropriate charts. Since there are too many charts, it is not possible to give charts which plot all the possible combinations. Those presented here are the most commonly useful. Any other can be created easily using the CES software.
The data on the charts and in the tables are approximate: they typify each class of material (stainless steels, or polyethylenes, for instance) or processes (sand casting, or injection molding, for example), but within each class, there is considerable variation. They are adequate for the broad comparisons required for conceptual design, and, often, for the rough calculations of embodiment design. They are not appropriate for detailed design calculations. For these, it is essential to seek accurate data from the data sheets provided by material suppliers. The charts help in narrowing the choice of candidate materials to a sensible shortlist, but not in providing numbers for final accurate analysis. The charts are an aid to creative thinking, not a source of numerical data for precise analysis.
Material Classes and Class Members
The materials of mechanical and structural engineering fall into the broad classes listed in the tables. Within each class, the Materials Selection Charts show data for a representative set of materials, chosen both to span the full range of behavior for that class, and to include the most widely used members of it. In this way, the envelope for a class (heavy lines) encloses data not only for the materials listed here but virtually all other members of the class as well. These same materials appear on all the charts.
You will not find specific material grades on the charts. The aluminum alloy 7075 in the T6 condition (for instance) is contained in the property envelopes for Al-alloys; the Nylon 66 in those for nylons. The charts are designed for the broad, early stages of materials selection, not for retrieving the precise values of properties needed in the later, detailed design, stage.
Material Properties
The charts that follow display the properties listed here. The charts let you pick off the subset of materials with a property within a specified range: materials with modulus E between 100 and 200 GPa for instance; or materials with a thermal conductivity above 100 W/mK.
Frequently, performance is maximized by selecting the subset of materials with the greatest value of a grouping of material properties. A light, stiff beam is best made of a material with a high value of E^(1/2)/ρ; safe pressure vessels are best made of a material with a high value of Kıc^(1/2)/σf , and so on. The Charts are designed to display these groups or “material indices”, and to allow you to pick off the subset of materials which maximize them.
Multiple criteria can be used. You can pick off the subset of materials with both high E^(1/2)/ρ and high E (good for light, stiff beams) from Chart 1; that with high σf^(2)/E^3 and high E (good materials for pivots) from Chart 4. Throughout, the goal is to identify from the Charts a subset of materials, not a single material. Finding the best material for a given application involves many considerations, many of them (like availability, appearance and feel) not easily quantifiable. The Charts do not give you the final choice that requires the use of your judgement and experience. Their power is that they guide you quickly and efficiently to a subset of materials worth considering; and they make sure that you do not overlook a promising candidate.
Chart 1: Young’s Modulus (E) and Density (ρ)
This chart guides selection of materials for light, stiff components. The moduli of engineering materials span a range of 10^7, the densities span a range of 3000. The contours show the longitudinal wave speed in m/s; natural vibration frequencies are proportional to this quantity. The guide lines show the loci of points for which:
• E/ρ = C (minimum weight design of stiff ties; minimum deflection in centrifugal loading, etc.) (axial loading)
• E^(1/2)/ρ = C (minimum weight design of stiff beams, shafts and columns.) (flexural and torsional loading)
• E^(1/3)/ρ = C (minimum weight design of stiff plates.)
The value of the constant C increases as the lines are displaced upwards and to the left; materials offering the greatest stiffness-to-weight ratio lie towards the upper left hand corner. Other moduli are obtained approximately from E using:
• v = 1/3; G = 3/8E; K ≈E (metals, ceramics, glasses and glassy polymers)
• or ν ≈ 0.5; G ≈ E/3; K ≈ 10E (elastomers, rubbery polymers)
where ν is poisson’s ratio, G the shear modulus and K the bulk modulus.
Chart 2: Strength (σ_f), Against Density (ρ)
This is the chart for designing light, strong structures. The “strength” for metals is the 0.2% offset yield strength. For polymers, it is the stress at which the stress-strain curve becomes markedly nonlinear typically, a strain of about 1%. For ceramics and glasses, it is the compressive crushing strength; remember that this is roughly 15 times larger than the tensile (fracture) strength. For composites it is the tensile strength. For elastomers it is the tear strength. The chart guides selection of materials for light, strong, components. The guide lines show the loci of points for which:
(a) σf/ρ = C (minimum weight design of strong ties; maximum rotational velocity of disks) (axial loading)
(b) σf^(2/3)/ρ = C (minimum weight design of strong beams and shafts) (flexural and torsional loading)
(c) σf^(1/2)/ρ = C (minimum weight design of strong plates)
The value of the constant C increases as the lines are displaced upwards and to the left. Materials offering the greatest strength-to-weight ratio lie towards the upper left corner.
Chart 3: Young’s Modulus (E) Against Strength (σ_f)
The chart for elastic design. The “strength” for metals is the 0.2% offset yield strength. For polymers, it is the 1% yield strength. For ceramics and glasses, it is the compressive crushing strength; remember that this is roughly 15 times larger than the tensile (fracture) strength. For composites it is the tensile strength. For elastomers it is the tear strength. The chart has numerous applications among them: the selection of materials for springs, elastic hinges, pivots and elastic bearings, and for yield before buckling design. The contours show the failure strain (σf / E) . The guide lines show three of these; they are the loci of points for which:
(a) σf /E = C (elastic hinges)
(b) σf^(2)/E = C (springs, elastic energy storage per unit volume)
(c) σf^(3/2)/E = C (selection for elastic constants such as knife edges; elastic diaphragms, compression seals)
The value of the constant C increases as the lines are displaced downward and to the right.
Chart 4: Specific Modulus (E/ρ) Against Specific Strength (σ_f/ρ)
The chart for specific stiffness and strength. The contours show the yield strain, σf/E . The qualifications on strength given for Charts 2 and 4 apply here also. The chart finds application in minimum weight design of ties and springs, and in the design of rotating components to maximize rotational speed or energy storage, etc. The guide lines show the loci of points for which:
(a) σf^(2)/Eρ = C (ties, springs of minimum weight; maximum rotational velocity of disks)
(b) σf^(2/3)/Eρ^(1/2) = C
(c) σf/E = C (elastic hinge design)
The value of the constant C increases as the lines are displaced downwards and to the right
Chart 5: Fracture Toughness (K_Ic) Against Young’s Modulus (E)
The chart displays both the fracture toughness, Kıc , and (as contours) the toughness, Gıc≈Kıc^(2)/E. It allows criteria for stress and displacement-limited failure criteria ( Kıc and Kıc / E ) to be compared. The guidelines show the loci of points for which:
(a) Kıc^(2)/E=C (lines of constant toughness, Gc; energy-limited failure.)
(b) Kıc/E = C (guideline for displacementlimited brittle failure.)
The values of the constant C increases as the lines are displaced upwards and to the left. Tough materials lie towards the upper left corner, brittle materials towards the bottom right.
Chart 6: Fracture Toughness (K_Ic) Against Strength (σ_f)
The chart for safe design against fracture. The contours show the process-zone diameter, given approximately by Kıc^(2)/πσf^(2). The qualifications on “strength” given for Charts 2 and 3 apply here also. The chart guides selection of materials to meet yield-before break design criteria, in assessing plastic or process-zone sizes, and in designing samples for valid fracture toughness testing. The guide lines show the loci of points for which:
(a) Kıc/σf = C (yield-before-break)
(b) Kıc^(2)/σf = C (leak-before-break)
The value of the constant C increases as the lines are displaced upward and to the left.
Chart 7: Loss Coefficient (η) Against Young’s Modulus (E)
The chart gives guidance in selecting material for low damping (springs, vibrating reeds, etc) and for high damping (vibration-mitigating systems). The guide line shows the loci of points for which:
(a) ηE=C (rule-of-thumb for estimating damping in polymers)
The value of the constant C increases as the line is displaced upward and to the right.
Chart 8: Thermal Conductivity (λ) Against Electrical Conductivity (ρ_e)
This is the chart for exploring thermal and electrical conductivies (the electrical conductivity κ is the reciprocal of the resistivity ρe ). For metals the two are proportional (the Wiedemann-Franz law):
λ ≈κ=1/ρe
Because electronic contributions dominate both. But for other classes of solid thermal and electrical conduction arise from different sources and the correlation is lost.
Chart 9: Thermal Conductivity (λ) Against Thermal Diffusivity (a)
The chart guides in selecting materials for thermal insulation, for use as heat sinks and such like, both when heat flow is steady, (λ) and when it is transient (thermal diffusivity a = λ/ρCp where ρ is the density and Cp the specific heat). Contours show values of the volumetric specific heat, ρCp = λ/a (J/m^(3)K). The guidelines show the loci of points for which:
(a) λ/a=C (constant volumetric specific heat)
(b) λ/a^(1/2)=C (efficient insulation; thermal energy storage)
The value of constant C increases towards the upper left.
Chart 10: Thermal Expansion Coefficient (α) Against Thermal Conductivity (λ)
The chart for assessing thermal distortion. The contours show value of the ratio λ/α (W/m). Materials with a large value of this design index show small thermal distortion. They define the guide line:
(a) λ/α=C (minimization of thermal distortion)
The value of the constant C increases towards the bottom right.
Chart 11: Linear Thermal Expansion (α) Against Young’s Modulus (E)
The chart guides in selecting materials when thermal stress is important. The contours show the thermal stress generated, per Celsius temperature change, in a constrained sample. They define the guide line:
αE = CMPa/K (constant thermal stress per Kelvin)
The value of the constant C increases towards the upper right.
Chart 12: Strength (σf) Against Maximum Service Temperature Tmax
Temperature affects material performance in many ways. As the temperature is raised the material may creep, limiting its ability to carry loads. It may degrade or decompose, changing its chemical structure in ways that make it unusable. And it may oxidise or interact in other ways with the environment in which it is used, leaving it unable to perform its function. The approximate temperature at which, for any one of these reasons, it is unsafe to use a material is called its maximum service temperature Tmax . Here it is plotted against strength σf .
The chart gives a birds-eye view of the regimes of stress and temperature in which each material class, and material, is usable. Note that even the best polymers have little strength above 200C; most metals become very soft by 800C; and only ceramics offer strength above 1500C.
Chart 13: Coefficient of Friction
When two surfaces are placed in contact under a normal load Fn and one is made to slide over the other, a force Fs opposes the motion. This force is proportional to Fn but does not depend on the area of the surface and this is the single most significant result of studies of friction, since it implies that surfaces do not contact completely, but only touch over small patches, the area of which is independent of the apparent, nominal area of contact An . The coefficient friction μ is defined by:
μ=Fs/Fn
Approximate values for μ for dry that is, unlubricated sliding of materials on a steel couterface are shown here. Typically, μ ≈ 0.5. Certain materials show much higher values, either because they seize when rubbed together (a soft metal rubbed on itself with no lubrication, for instance) or because one surface has a sufficiently low modulus that it conforms to the other (rubber on rough concrete). At the other extreme are a sliding combinations with exceptionally low coefficients of friction, such as PTFE, or bronze bearings loaded graphite, sliding on polished steel. Here the coefficient of friction falls as low as 0.04, though this is still high compared with friction for lubricated surfaces, as noted at the bottom of the diagram.
Chart 14: Wear Rate Constant (ka) Against Hardness (H)
When surfaces slide, they wear. Material is lost from both surfaces, even when one is much harder than the other. The wear-rate (W) is conventionally defined as:
W=Volume of Material Removed/Distance Slid
and thus has units of m2. A more useful quantity, for our purposes, is the specific wear-rate:
Ω=W/An
which is dimensionless. It increases with bearing pressure P (the normal force Fn divided by the nominal area An ), such that the ratio:
ka=W/Fn=Ω/P
is roughly constant. The quantity ka (with units of (MPa)-1) is a measure of the propensity of a sliding couple for wear: high ka means rapid wear at a given bearing pressure. Here it is plotted against hardness (H).
Chart 15 A and B: Approximate Material Prices (Cm and ρCm)
Properties like modulus, strength or conductivity do not change with time. Cost is bothersome because it does. Supply, scarcity, speculation and inflation contribute to the considerable fluctuations in the cost per kilogram of a commodity like copper or silver.
Data for cost per kg are tabulated for some materials in daily papers and trade journals; those for others are harder to come by. Approximate values for the cost of materials per kg, and their cost per m3, are plotted in these two charts.
Most commodity materials (glass, steel, aluminum, and the common polymers) cost between 0.5 and 2 $/kg. Because they have low densities, the cost/m3 of commodity polymers is less than that of metals.
Chart 16: Young’s Modulus (E) Against Relative Cost (CRρ)
In design for minimum cost, material selection is guided by indices that involve modulus, strength and cost per unit volume. To make some correction for the influence of inflation and the units of currency in which cost is measured, we define a relative cost per unit volume Cv,R:
Cv,R=(Cost/kg x Density of Material) / (Cost/kg x Density of Mild Steel Rod)
At the time of writing, steel reinforcing rod costs about US$ 0.3/kg. The chart shows the modulus E plotted against relative cost per unit volume Cv,R ρ where ρ is the density. Cheap stiff materials lie towards the top left. Guide lines for selection materials that are stiff and cheap are plotted on the figure. The guide lines show the loci of points for which:
(a) E / Cv,R ρ = C (minimum cost design of stiff ties, etc)
(b) E^(1/2) / Cv,R ρ = (minimum cost design of stiff beams and columns)
(c) E^(1/3) / Cv,R ρ = (minimum cost design of stiff plates)
The value of the constant C increases as the lines are displayed upwards and to the left. Materials offering the greatest stiffness per unit cost lie towards the upper left corner.
Chart 17: Strength (σf) Against Relative Cost (CRρ)
Cheap strong materials are selected using this chart. It shows strength, defined as before, plotted against relative cost per unit volume, defined on chart 16. The qualifications on the definition of strength, given earlier, apply here also.
It must be emphasised that the data plotted here and on the chart 16 are less reliable than those of other charts, and subject to unpredictable change. Despite this dire warning, the two charts are genuinely useful. They allow selection of materials, using the criterion of “function per unit cost”.
The guide lines show the loci of points for which:
(a) σf / Cv,R ρ = C (minimum cost design of strong ties, rotating disks, etc)
(b) σf^(2/3) / Cv,R ρ = C (minimum cost design of strong beams and shafts)
(c) σf^(1/2) / Cv,R ρ = C (minimum cost design of strong plates)
The value of the constants C increase as the lines are displaced upwards and to the left. Materials offering the greatest strength per unit cost lie towards the upper left corner.
Charts 18 A and B: Approximate Energy Content Per Unit Mass and Per Unit Volume
The energy associated with the production of one kilogram of a material is Hp , that per unit volume is Hp ρ where ρ is the density of the material. These two bar charts show these quantities for ceramics, metals, polymers and composites. On a “per kg” basis (upper chart) glass, the material of the first container, carries the lowest penalty. Steel is higher. Polymer production carries a much higher burden than does steel. Aluminum and the other light alloys carry the highest penalty of all. But if these same materials are compared on a “per m3” basis (lower chart) the conclusions change: glass is still the lowest, but now commodity polymers such as PE and PP carry a lower burden than steel; the composite GFRP is only a little higher.
Chart 19: Young’s Modulus (E) Against Energy Content (Hp ρ)
The chart guides selection of materials for stiff, energy-economic components. The energy content per m3, Hp ρ is the energy content per kg (Hp) multiplied by the density ρ. The guide-lines show the loci of points for which:
(a) E / Hp ρ = C (minimum energy design of stiff ties; minimum deflection in centrifugal loading etc)
(b) E^(1/2) / Hp ρ = C (minimum energy design of stiff beams, shafts and columns)
(c) E^(1/3) / Hp ρ = C (minimum energy design of stiff plates)
The value of the constant C increases as the lines are displaced upwards and to the left. Materials offering the greatest stiffness per energy content lie towards the upper left corner.
Other moduli are obtained approximately from E using:
• ν = 1/3; G = 3/8E; K ≈E (metals, ceramics, glasses and glassy polymers)
• or ν ≈ 0.5; G ≈ E / 3; K ≈ 10E (elastomers, rubbery polymers)
where ν is Poisson’s ratio, G the shear modulus and K the bulk modulus.
Chart 20: Strength (σf) Against Energy Content (Hp ρ)
The chart guides selection of materials for strong, energy economic components. The “strength” for metals is the 0.2% offset yield strength. For polymers, it is the stress at which the stress strain curve becomes markedly nonlinear typically, a strain of about 1%. For ceramics and glasses, it is the compressive crushing strength; remember that this is roughly 15 times larger than the tensile (fracture) strength. For composites it is the tensile strength. For elastomers it is the tear strength. The energy content per m3 (Hp ρ) is the energy content per kg (Hp) multiplied by the density (ρ). The guide lines show the loci of points for which:
(a) σf / Hp ρ = C (minimum energy design of strong ties; maximum rotational velocity of disks)
(b) σf^(2/3) / Hp ρ = C (minimum energy design of strong beams and shafts)
(c) σf^(1/2) / Hp ρ = C (minimum energy design of strong plates)
The value of the constant C increases as the lines are displaced upwards and to the left. Materials offering the greatest strength per unit energy content lie towards the upper left corner.
Appendix: Material Indices
Introduction and Synopsis: The performance (P) of a component is characterized by a performance equation. The performance equation contains groups of material properties. These groups are the material indices. Sometimes the “group” is a single property; thus if the performance of a beam is measured by its stiffness, the performance equation contains only one property, the elastic modulus (E). It is the material index for this problem. More commonly the performance equation contains a group of two or more properties. Familiar examples are the specific stiffness (E / ρ), and the specific strength (σ y / ρ), (where σ y is the yield strength or elastic limit, and ρ is the density), but there are many others. They are a key to the optimal selection of materials.
Uses of Material Indices: Material selection components have functions: to carry loads safely, to transmit heat, to store energy, to insulate, and so forth. Each function has an associated material index. Materials with high values of the appropriate index maximize that aspect of the performance of the component. For reasons, the material index is generally independent of the details of the design. Thus the indices for beams in the tables that follow are independent of the detailed shape of the beam; that for minimizing thermal distortion of precision instruments is independent of the configuration of the instrument, and so forth. This gives them great generality.
Material Deployment or Substitution: A new material will have potential application in functions for which its indices have unusually high values. Fruitful applications for a new material can be identified by evaluating its indices and comparing them with those of existing, established materials. Similar reasoning points the way to identifying viable substitutes for an incumbent material in an established application.
How to Read The Tables: The indices listed in the Tables 1 to 7 are, for the most part, based on the objective of minimizing mass. To minimize cost, use the index for minimum mass, replacing the density ρ by the cost per unit volume, Cmρ , where Cm is the cost per kg. To minimize energy content or CO2 burden, replace ρ by Hp ρ or by CO2ρ where H p is the production energy per kg and CO2 is the CO2 burden per kg.
Sources: www.cam.ac.uk – www.grantadesign.com
