Mechanical Metallurgy
Mechanical Metallurgy tests how metals deform, strengthen, and fail under stress: elasticity, plasticity, dislocation theory, fracture, fatigue, and creep. Questions often require choosing the correct stress/strain measure and failure criterion.
Core rules
- Engineering stress s=P/A0 and engineering strain e=ΔL/L0; true stress σ=P/A and true strain ε=ln(L/L0). Before necking, σ=s(1+e) and ε=ln(1+e).
- Yielding: Tresca uses maximum shear stress; von Mises uses distortional energy. For uniaxial tension, both predict the same yield stress, but multiaxial predictions differ.
- Dislocation motion produces slip; strengthening by grain refinement, solid solution, precipitation, and cold work.
- Fracture mechanics: K=Yσ√(πa); fracture occurs when K reaches KIC.
- Fatigue: initiation, crack growth, final fracture; Paris law da/dN=C(ΔK)^m.
- Creep: primary, steady-state, tertiary; Norton law ε̇=Aσ^n exp(−Q/RT).
Worked example
A wire is cold-drawn to a 50% reduction in area, so Af/A0=0.5. True strain ε=ln(A0/Af)=ln(1/0.5)=0.693. Constant volume gives Lf/L0=A0/Af=2, so engineering strain e=(Lf−L0)/L0=1.0. The true strain 0.693 and engineering strain 1.0 describe the same deformation; using the wrong measure changes the flow-stress interpretation.
Traps
- Using engineering stress beyond necking.
- Confusing plane stress and plane strain K.
- Ignoring mean stress in fatigue.
- Treating creep strain as constant.
- Applying Hall-Petch to nanocrystalline metals beyond its limit.