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.
Understanding Material Selection (Ashby Charts) Reference
A useful selection starts by separating four parts of the problem. The function states what the part must do, such as carry a load or conduct heat. The constraints are limits that cannot be broken, such as a maximum deflection, a minimum operating temperature, or resistance to seawater.
The objective is what should be made as small or as large as possible, often mass, price, or heat loss. The free variables are choices the designer can change, including material, cross section, and manufacturing route.
This separation matters because a material property alone rarely decides the answer. A steel rod can be excellent in one design yet unsuitable in another because the geometry and loading have changed.
Material indices come from basic physical models. Start with an equation for the required performance, then replace the part dimensions using the constraint. This leaves mass or cost in terms of material properties.
For example, mass equals density times volume. A tension member controlled by elastic stretch needs enough area to limit extension. When that area is substituted into its mass, the comparison depends on stiffness relative to density.
A beam behaves differently because bending stiffness depends strongly on section shape and depth. This is why beam indices contain different powers of stiffness or strength.
The exponent is not a rule to memorize without context. It records how the load path and geometry affect the design.
Charts need careful reading because most property values cover wide ranges. A log scale gives equal visual distance to equal multiplication factors, not equal numerical differences. Moving one major step may mean a property becomes ten times larger.
Material families often form broad clouds because composition, heat treatment, fiber direction, porosity, and test conditions change the result. A selection line represents equal performance for a chosen index. Sliding that line without changing its slope finds the best attainable candidates.
The preferred direction depends on whether the goal is to maximize or minimize the index. A point near the line is not automatically a winner because published values may be typical, minimum, or maximum values from different sources.
Real components fail in ways that simple charts may not show. Yield strength is important for a ductile metal, but brittle ceramics and some polymers may fracture before yielding. Repeated loading introduces fatigue.
High temperatures can cause creep, where deformation grows slowly under a steady load. A corrosive fluid, ultraviolet light, or moisture can alter properties over time. Manufacturing can dominate the decision when a material cannot be cast, machined, welded, bonded, or recycled in the required form.
Students should practice using a clear sequence. Write the function, identify the failure mode, set hard limits, derive or choose an index, screen candidates, then check real data sheets. Finally, include safety factors, tolerances, supply limits, joining details, inspection needs, and the cost of the finished part rather than only the raw material price.