Materials Selection and Design
Property charts and indices
Ashby-style selection works in three steps: identify the function (tie, beam, panel, spring), the objective (minimum mass, minimum cost, maximum stiffness), and the constraint (strength, stiffness, or both). Eliminate the free geometric variable to derive a performance index. The material with the highest index wins, and the slope of the guide line on a log property chart is the index exponent.
Common indices to memorize
Tie rod, stiffness-limited: E/rho. Tie rod, strength-limited: sigma_y/rho. Beam of fixed length and stiffness: E^(1/2)/rho. Beam of fixed length and strength: sigma_y^(2/3)/rho. Panel of fixed width and stiffness (bending): E^(1/3)/rho. Add cost by dividing by rho*C_m for cost-per-mass objectives. Shape factors extend indices to efficient sections such as I-beams and tubes.
Design considerations
Apply suitable safety factors, fracture-safe design (leak-before-break, damage tolerance, inspection intervals), corrosion allowance, fatigue allowances, and code compliance (ASTM, ASME, ISO). Consider manufacturing route, joining, recyclability, and total life-cycle cost rather than raw material price alone.
Traps
Deriving an index and forgetting that a lower density appears in the denominator; using cost per kilogram when cost per unit volume is what a fixed-volume component needs; ignoring that a material that wins on stiffness may lose on strength; and designing past the elastic limit with a stiffness-based index.
Worked example
A tie rod of fixed length under a fixed load: mass m = rhoFL/sigma_y, so minimizing mass means maximizing sigma_y/rho. High-strength aluminum and titanium beat steel here, whereas a stiffness-limited tie rod favors beryllium and ceramics because E/rho dominates.