Materials Science
What to master
Stress and strain in tension, compression and shear; the engineering stress-strain curve (proportional limit, elastic modulus, yield strength by the 0.2% offset method, ultimate tensile strength, fracture strain, toughness as area under the curve); Poisson's ratio and the relation G = E/[2(1 + nu)]; thermal expansion strain; hardness scales and their approximate correlation with strength; fatigue (S-N curves, endurance limit, stress concentration factors); creep and elevated-temperature behavior; ductile versus brittle fracture; phase diagrams and the iron-carbon system; heat treatment (annealing, quenching, tempering); corrosion mechanisms and protection; and properties of polymers, ceramics and composites.
Traps
- Engineering stress uses the original area; true stress uses the instantaneous area. They diverge after yield.
- Ductility is measured by percent elongation or reduction of area -- not by the ultimate strength.
- Fatigue failures occur below the yield strength; a part can be safe statically and fail cyclically.
- Unit discipline: MPa = N/mm^2 = 10^6 Pa; mixing ksi and MPa is a classic distractor.
- Thermal stress appears only when expansion is restrained.
Worked example
A steel bar with E = 200 GPa carries 150 MPa of stress within the elastic range. Strain = stress/E = 150 x 10^6 / 200 x 10^9 = 7.5 x 10^-4 (dimensionless). Over a 2 m length the elongation is 1.5 mm.
Rule of thumb: check the computed stress against yield first -- if it exceeds yield, linear elastic formulas no longer apply and the answer choice based on Hooke's law is a trap.