Materials Properties and Behavior
The tensile curve is the backbone
A candidate must be fluent in the whole stress–strain curve: elastic modulus E, proportional limit, 0.2% offset yield strength, ultimate tensile strength, percent elongation and reduction of area, plus the engineering-versus-true distinction. Know that E is structure-insensitive (alloying or heat treatment barely moves it) while yield and UTS are structure-sensitive. Ductility and toughness are not synonyms: toughness is energy absorbed (area under the true curve, or K_IC for a cracked body), so a very high-strength, low-ductility steel can be less tough than a medium-strength tough grade.
Related concepts to name
Poisson's ratio, modulus of resilience, strain-hardening exponent n, the Considere construction (necking starts where true stress equals the tangent slope), Schmid's law for resolved shear stress, creep and the Larson–Miller parameter, fatigue S–N behavior (a true endurance limit exists in steels but generally not in aluminum), and thermal-expansion mismatch stresses.
Traps that show up in questions
Equating hardness with strength, or converting Rockwell C to Brinell across material families (valid only within steels). Mixing 0.1% and 0.2% offset yields. Thinking engineering stress keeps rising after UTS (the drop is an area effect, not softening). Forgetting that ceramics and polymers obey very different modulus–strength relationships, or that rubber's Poisson's ratio is ~0.5 (incompressible) while cork's is near zero.
Worked example
For a Hollomon material, sigma = K*epsilon^n, the Considere condition gives necking at true strain epsilon = n. With n = 0.20, necking occurs at about 20% true strain and true UTS = K(0.20)^0.20 = 0.72K. Rule of thumb: n is both the necking strain and a rough ductility index.