A chart that plots two properties, such as Young's modulus and density, on log–log axes and shows the range of each material family. Lines of constant performance index are straight, and the chart is used to compare candidates.
Japanese name: 材料選択図(アシュビーの図)
Ashby chart (materials selection chart) appears in 1 practice question across 1 topic, including Materials selection and design.
A materials selection chart plots two properties on the vertical and horizontal axes, such as Young's modulus versus density, strength versus density or fracture toughness versus strength, and shows the ranges of values for many materials. Because the values span many orders of magnitude, both axes are logarithmic. Members of the same material family cluster together; on the modulus–density chart, ceramics and metals occupy the upper right, polymers and woods the middle, and foams the lower left. Individual materials are shown as ellipses or bubbles covering the range of variation with composition and processing, and material families as larger envelopes around them.
Writing the condition for a constant performance index in logarithms gives a straight line. For example, E/ρ = C gives log E = log ρ + log C, a line of slope 1; √E/ρ = C gives a line of slope 2; and ∛E/ρ = C a line of slope 3. Materials on a line parallel to it perform equally in that application, and performance increases as the line is shifted toward the upper left. Drawing such a line on the chart and moving it step by step narrows the field to the materials remaining above the line as promising candidates. Because the slope changes with the loading mode, the winning materials on the same chart change with the application.
In Ashby's method, the design requirements are first organized into function, constraints, objective and free variables, and candidates are screened by constraints such as service temperature and corrosion resistance. Next, the surviving candidates are ranked by the performance index derived from the objective, and finally the top candidates are researched for ease of fabrication into the actual shape, joining, price fluctuations, service history and so on before deciding. The selection chart is a tool for doing this screening and ranking visually. A major advantage of using it is that candidates can be surveyed across material families without fixing on a particular material from the start.
Answer: B. 2
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.
Because Young's modulus spans many orders of magnitude, from about 0.001 GPa for foams to about 1000 GPa for diamond. Also, power-law performance indices appear as straight lines, which makes comparison simple.
No. The chart is a tool for narrowing down candidates, and its values are typical ranges for material families. The final decision is made by researching data for specific alloys and grades, processing methods, cost and service history.
Yes. On strength–density charts, guidelines for σf/ρ or ∛(σf²)/ρ are drawn, and on fracture toughness–strength charts, lines of K_IC/σy, to look for light, strong materials or materials resistant to fracture.
Young's modulus Material index (performance index) Life cycle assessment Pareto optimality Specific stiffness Tramp elements Yield before fracture