This tool draws the property ranges of materials as ellipses on a chart with logarithmic scales on both axes. Pick any two of density, Young's modulus, strength, fracture toughness, thermal conductivity and thermal expansion as the axes. When you choose a material index, a straight line of constant index is drawn, the materials on its better side are highlighted, and they are listed in order of the index. Tap an ellipse to see the value ranges of that material. The default is the Young's modulus–density chart with the line √E/ρ = 3 GPa^½/(g/cm³), the index for a light beam of given bending stiffness. The values are typical ranges from published data and are not design values.
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Chart and results
Slope of the line (log–log) and index value
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Materials on the better side (typical values)
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Materials ranked by the index
Value ranges of the selected material
The values are based on the ranges in M. F. Ashby's teaching resource “Material property data for engineering materials” (5th edition, 2021), with misprints and gaps in its tables replaced by values checked in manufacturers' data sheets and other sources. Even for materials with the same name, the values vary widely with composition, heat treatment, processing and direction. For component design, use values from standards, manufacturers' guaranteed values or measurements. Values that could not be checked (thermal conductivity and expansion of foams) are left blank and not plotted.
See it as a graph
Other inputs stay at their current values while the chosen input varies from 1/4 to 4 times its current value. The red dot is the current value.
How to read an Ashby chart
A material selection chart plots two properties, such as Young's modulus and density, on the vertical and horizontal axes and shows the range of values of each material as an ellipse. Young's modulus spans about six orders of magnitude, from about 0.001 GPa for foams and rubbers to about 700 GPa for tungsten carbide, so both axes use logarithmic scales. The size of an ellipse shows how much the values of a material with the same name vary with composition, heat treatment and processing. Materials of the same family cluster together: on the modulus–density chart, metals and ceramics occupy the upper right, polymers the middle, and elastomers and foams the lower left. This tool draws the ellipses aligned with the axes, while textbook charts sometimes tilt them along the direction in which the two properties change together.
Deriving a material index: a light beam of given bending stiffness
Consider a beam of fixed length L and square cross-section that must have a bending stiffness S, where the side b of the section is free and the mass is to be minimized. The bending stiffness is S = C₁EI/L³ (C₁ depends on how the beam is supported) and the second moment of area is I = b⁴/12. The stiffness condition gives b² = (12SL³/(C₁E))^½, and substituting into the mass m = ρb²L gives m = (12S/C₁)^½ · L^(5/2) · ρ/√E. Since S and L are fixed, the lightest beam is made from the material with the smallest ρ/√E, that is, the largest √E/ρ. For example, for steel (E = 210 GPa, ρ = 7.8 g/cm³) and an aluminum alloy (70 GPa, 2.7 g/cm³), (2.7/√70)/(7.8/√210) ≈ 0.60, so the aluminum beam, although thicker, has about 60 % of the mass of the steel beam.
Other indices: ties, panels and strength
The same approach gives indices for other uses. For a tie of length L limited by its stiffness S, S = EA/L gives the area A = SL/E and the mass m = ρAL = SL²·ρ/E, so the index is E/ρ. For a panel in bending with a fixed width w and a free thickness t, the stiffness is proportional to Et³, so t ∝ E^(−1/3) and m = ρwtL ∝ ρ/∛E, giving ∛E/ρ. If the condition is not to yield, a tie gives σf/ρ from A = F/σf; a beam, whose bending stress is 6M/b³, gives b ∝ σf^(−1/3) and the index ∛(σf²)/ρ; and a panel, whose bending stress is 6M/(wt²), gives t ∝ σf^(−1/2) and the index √σf/ρ. The smaller the exponent in the index, the more low-density materials are favored, which is why wood and foams rank high for beams and panels.
Slope of the index line and the better side
Setting √E/ρ = C gives E = C²ρ², or log E = 2 log ρ + 2 log C, a straight line of slope 2 on the modulus–density chart. In the same way, E/ρ has slope 1 and ∛E/ρ slope 3, and on the strength–density chart σf/ρ has slope 1, ∛(σf²)/ρ slope 1.5 and √σf/ρ slope 2. Materials on the same line perform equally well in that use. Moving the line parallel toward the upper left increases the index, so materials further to the upper left can make a part of the same stiffness or strength with less mass. With the default line √E/ρ = 3 GPa^½/(g/cm³), aluminum alloys (about 3.2), magnesium alloys, CFRP and wood along the grain lie on the better side by their typical values, while steels (about 1.8–1.9) lie on the worse side. If the two axes are swapped, the better side is to the lower right of the line.
Indices for yield before fracture and thermal distortion
On the fracture toughness–strength chart, lines of constant K_IC/σf are straight lines of slope 1. A part with a crack of length a yields before it fractures in a brittle way if a < (1/π)(K_IC/σf)², taking the geometry factor as 1, so materials with a larger K_IC/σf yield first even with larger cracks. With K_IC/σf = 0.1 √m, the allowable crack length is about 3.2 mm. On the thermal conductivity–expansion chart, κ/α is the index for choosing materials that distort little when heat flows into them and creates temperature differences; larger is better, and it is used in choosing materials for precision instruments. In both cases, the right index depends on how the strength or thermal conditions actually arise.
Which strength is plotted
The strength σf on this chart is the “yield strength (elastic limit)” in the data source. For metals and polymers it corresponds to the yield strength (for metals usually the 0.2 % offset yield strength). For ceramics and glasses, this value in the source is about the same as the tensile strength, not the compressive strength. Because the compressive strength of ceramics is much higher than the tensile strength, some textbook charts plot the compressive strength for ceramics, so always check which strength a chart shows. For elastomers the value is equal to or below the tensile strength (about the same for natural rubber, neoprene and silicone rubber, less than half for butyl rubber), and for composites, foams and natural materials it is the elastic limit given in the source. Fracture toughness is also hard to compare in the same sense for materials that deform greatly, such as rubbers and foams, as for metals and ceramics.
The selection procedure and how to use the chart
Materials selection starts by translating the design into function, constraints, objective and free variables, then screens out materials that fail the required conditions (service temperature, minimum fracture toughness, electrical insulation and so on), and finally ranks the remaining candidates by the material index. This chart is useful for that ranking and for seeing the broad differences between families. Even with the same index, conditions not shown on the chart, such as cost, ease of shaping and joining, corrosion and buckling, change which material is chosen. When there are two conflicting objectives, such as mass and cost, choose among the Pareto-optimal candidates by setting an exchange rate between the objectives.
About the values on this chart
The values are the ranges in M. F. Ashby's “Material property data for engineering materials” (5th edition, 2021), published as a teaching resource for Ansys Granta EduPack. The source gives two significant figures, and its ranges are broad, covering many alloys and grades. Where its tables had misprints or gaps, or differed greatly from other sources, values checked in other sources were used: the upper limit of the density of alumina (3.98 g/cm³) from the NIST Structural Ceramics Database, the upper limit of the strength of stainless steel from the specified values for 17-4PH steel, the thermal conductivity and expansion of soda-lime glass from an encyclopedia table that cites its sources, part of the thermal conductivity and expansion ranges of silica glass from Corning product data, and the thermal expansion of neoprene from NETZSCH polymer data. The ranges of the fracture toughness of aluminum alloys and of the thermal conductivity of titanium alloys, nickel alloys, stone and neoprene were widened to include values from ASM and other sources. The thermal conductivity and expansion of foams, which could not be checked in other sources, are left blank and not plotted on those charts. CFRP and GFRP are laminates with fibers distributed evenly in the plane; in a unidirectional material the strength is much higher along the fibers and much lower across them. For design, use values from standards, manufacturers' guaranteed values or tests of the actual material.
The deflection of a beam is inversely proportional to the flexural rigidity EI, and the second moment of area of a square section of side b is I = b⁴/12. To meet the specified stiffness, Eb⁴ must be constant, so b² ∝ 1/√E. The mass of the beam is m = ρb²L ∝ ρ/√E, so minimizing mass means choosing the material with the largest √E/ρ. E/ρ is the index for a tie limited by stiffness, used when the cross-sectional area enters directly. ∛E/ρ is for the bending stiffness of a plate (panel) of fixed width whose thickness alone is varied, coming from the stiffness being proportional to the cube of the thickness. In bending, stiffness increases rapidly as the section grows, so low-density materials are favored, which is why wood and CFRP are strong performers as beams.
Setting √E/ρ = C (constant) gives E = C²ρ², and taking logarithms of both sides gives log E = 2 log ρ + 2 log C, a straight line of slope 2. Materials on a line parallel to it perform equally, and the farther the line is shifted toward the upper left, the larger √E/ρ, that is, the lighter a beam of the same stiffness can be made. Slope 1 is the line of constant E/ρ (tie), and slope 3 is the line of constant ∛E/ρ (panel). Slope 1/2 is the mistake of swapping the axes and reading the slope of log ρ = (1/2) log E + constant. On a log–log chart, differences in the exponents of performance indices appear as differences in slope, so a single chart lets you read off the ranking of materials for each loading mode.
The mass of a beam with specified stiffness is proportional to ρ/√E. For the aluminum alloy it is 2.7/√70 = 2.7/8.37 ≈ 0.323, and for steel 7.8/√210 = 7.8/14.5 ≈ 0.538, so the ratio is 0.323/0.538 ≈ 0.60, about 0.60 times. The aluminum alloy beam needs a thicker section because its Young's modulus is one third, but thanks to its low density it is about 40% lighter overall. About 0.35 times looks only at the density ratio (2.7/7.8), ignoring that the section must be thicker to match stiffness. About 1.04 times is the value when mass is proportional to ρ/E, as for a tie in tension; for a tie, aluminum alloy and steel weigh almost the same.
FAQ
Why are both axes logarithmic?
Property values differ by many orders of magnitude between materials, so on linear scales most materials would be squeezed near the origin. On log–log axes, lines of constant power-law indices such as √E/ρ become straight, and their slope shows the form of the index.
How do I choose between materials whose ellipses overlap?
Overlap means the two properties cannot separate them. Compare them on charts of other properties, or by cost, ease of processing and the service environment. Since the width of an ellipse reflects differences between grades and processes, check the values of the actual grade once you have narrowed down the candidates.
If two materials have the same index value, do they give the same part?
They give the same mass only for the use and conditions from which the index was derived (for example, a square-section beam of given bending stiffness with minimum mass). If the shape of the section can change, or if buckling, local yielding or cost matter, check with other indices or conditions.
In which direction are the values for CFRP and wood?
Wood along the grain and across the grain are plotted as separate materials. CFRP and GFRP are quasi-isotropic laminates with fibers distributed evenly in the plane. In unidirectional CFRP the properties depend strongly on direction. For example, with a standard carbon fiber (Toray T700S) in epoxy at 60 % fiber volume, the Young's modulus along the fibers is about 134 GPa and the tensile strength about 2.9 GPa, far above the strength range on this chart, while the tensile strength across the fibers is only about 81 MPa.