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Materials selection and design

Learn Ashby materials selection charts, performance indices for light, stiff beams and light, strong ties, comparisons of cost and environmental impact, selecting materials to avoid fracture, and recyclability with multiple-choice questions, and practice calculations comparing mass and cost.

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Materials selection and design: key points

In Ashby's method, the design requirements are organized into function, constraints, objective and free variables, and eliminating the free variables yields a performance index, a combination of material properties alone. The materials that maximize E/ρ for a stiffness-limited tie, √E/ρ for a beam whose cross section can vary, ∛E/ρ for a plate whose thickness can vary, and σf/ρ for a strength-limited tie are favored. On a log–log selection chart of Young's modulus versus density, lines of constant performance index are straight, so candidates can be compared at a glance.

In real selection, besides performance, you also consider cost including the price per kg, the energy and CO₂ emissions from production to disposal, and whether a part avoids sudden fracture even with a crack (K_IC/σy). When objectives compete, the choice is made from the Pareto-optimal candidates using an exchange constant. Designing with fewer material types and easy disassembly, and controlling the elements that get mixed into scrap, are essential to improving recyclability.

All Materials selection and design questions (12)
  1. In Ashby's method of materials selection, the design requirements are organized into function, constraints, objective and free variables. In selecting the material for a bicycle frame, which of these is the objective?
  2. A tie (tension member) of fixed length L must carry a tensile load F without yielding, and its cross-sectional area may be chosen freely. To make it as light as possible, which performance index should be maximized, with σf the yield strength and ρ the density of the material?
  3. A beam of square cross section with fixed length and bending stiffness is to be made as light as possible by freely varying the size of the cross section. Which performance index should be maximized, with E the Young's modulus and ρ the density?
  4. On a log–log materials selection chart (Ashby chart) with Young's modulus E on the vertical axis and density ρ on the horizontal axis, what is the slope of the guideline along which the performance index for a light, stiff beam, √E/ρ, is constant?
  5. Beams of square cross section designed for the same length and bending stiffness are made of steel (E = 210 GPa, ρ = 7.8 g/cm³) and an aluminum alloy (E = 70 GPa, ρ = 2.7 g/cm³). If the size of the cross section can be varied freely, about how many times the mass of the steel beam is the mass of the aluminum alloy beam?
  6. A tie of fixed length and tensile stiffness is made of steel (E = 210 GPa, ρ = 7.8 g/cm³, price per kg taken as 1) and of quasi-isotropic CFRP laminate (E = 70 GPa, ρ = 1.6 g/cm³, price per kg 20 times that of steel). If the cross-sectional area can be varied freely, about how many times the material cost of the steel tie is that of the CFRP tie?
  7. For a component used at a stress equal to its yield stress σy, the largest crack size that still lets it yield before brittle fracture can be estimated as a = (1/π)(K_IC/σy)² (geometry factor Y = 1). For a steel with σy = 800 MPa and K_IC = 120 MPa·√m, which value is closest to this critical crack length?
  8. For a typical gasoline passenger car, when the energy consumed over the life cycle from material production to disposal is compared stage by stage, which stage is usually the largest, and what materials selection policy follows from it?
  9. Take the production energy of aluminum alloy as 200 MJ per kg for primary metal made from ore and 15 MJ per kg for secondary (recycled) metal made by remelting scrap. Which value is closest to the production energy per kg of a material containing 60% secondary metal by mass?
  10. When steel scrap is remelted in an electric arc furnace for recycling, which elements tend to accumulate in the steel with repeated recycling and cause problems by degrading quality (tramp elements)?
  11. Which is an appropriate materials selection and design policy for improving the recyclability of a product?
  12. You want to minimize two objectives at once, the mass and the cost of a part, but lighter materials are more expensive and no material is best on both. Which is an appropriate way to choose a material in this case?

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