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Engineering
Grade college
Material Selection (Ashby Charts) Reference Cheat Sheet
A printable reference covering Ashby charts, material indices, stiffness, strength, density, toughness, cost, and performance constraints for college engineering.
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Material selection using Ashby charts helps engineers compare material families using properties such as density, modulus, strength, toughness, thermal conductivity, and cost. This cheat sheet gives college engineering students a quick reference for reading charts and applying material indices. It is useful when a design must be light, strong, stiff, inexpensive, safe, or thermally efficient. The goal is to turn design requirements into objective screening and ranking rules.
Key Facts
- A material index ranks materials for a specific objective and constraint, such as maximizing E/rho for a light tension member with stiffness control.
- For a light stiff tie in tension, the common stiffness index is M = E/rho, where E is Young's modulus and rho is density.
- For a light strong tie in tension, the common strength index is M = sigma_y/rho, where sigma_y is yield strength.
- For a light stiff beam in bending, a common stiffness index is M = E^0.5/rho when length and stiffness requirement are fixed.
- For a light strong beam in bending, a common strength index is M = sigma_y^(2/3)/rho when length and strength requirement are fixed.
- On a log-log Ashby chart, a selection line has a slope set by the material index, and better materials lie on the preferred side of the line.
- Screening removes materials that fail hard constraints, while ranking orders the remaining materials by the chosen material index.
- A complete material choice must also consider processing method, shape, environment, availability, safety factors, joining, durability, and cost.
Vocabulary
- Ashby chart
- A log-log material property chart that compares material classes and helps engineers screen and rank candidate materials.
- Material index
- A formula that combines material properties to measure how well a material meets a specific design objective and constraint.
- Constraint
- A required limit that a design must satisfy, such as maximum deflection, minimum strength, maximum temperature, or maximum cost.
- Objective function
- The quantity a designer wants to minimize or maximize, such as mass, cost, energy use, or thermal resistance.
- Screening
- The process of eliminating materials that do not meet required limits before comparing performance.
- Ranking
- The process of ordering candidate materials by performance after they satisfy all required constraints.
Common Mistakes to Avoid
- Using one universal material index for every design is wrong because the correct index depends on the loading mode, geometry, objective, and constraint.
- Choosing the material with the highest strength alone is wrong because density, stiffness, toughness, processing, cost, and environment may control the design.
- Reading a log-log Ashby chart as if the axes were linear is wrong because equal spacing represents equal ratios, not equal arithmetic differences.
- Forgetting to screen before ranking is wrong because a material with a high index may still fail a required limit such as service temperature or corrosion resistance.
- Ignoring manufacturing and shape effects is wrong because a material that looks ideal on a property chart may be impractical, expensive, or unavailable in the needed form.
Practice Questions
- 1 A tension member is stiffness-limited and must be as light as possible. Compare Material A with E = 70 GPa and rho = 2700 kg/m^3 to Material B with E = 200 GPa and rho = 7800 kg/m^3 using M = E/rho. Which ranks higher?
- 2 A tension member is strength-limited and must be as light as possible. Compare Material A with sigma_y = 300 MPa and rho = 1600 kg/m^3 to Material B with sigma_y = 900 MPa and rho = 4500 kg/m^3 using M = sigma_y/rho. Which ranks higher?
- 3 For a bending-limited lightweight beam, calculate the index M = E^0.5/rho for a material with E = 100 GPa and rho = 5000 kg/m^3. Use the square root of E in GPa for comparison.
- 4 Two materials have similar stiffness-to-density ratios, but one is much cheaper and the other has better corrosion resistance. Explain how the final selection should depend on the design environment and objective.