Materials, Manufacturing and Industrial Engineering
This domain bundles three question streams: structure and properties of materials, the manufacturing processes that shape them, and the industrial engineering tools that plan and control production. Each stream has a small set of standard formulas that GATE reuses.
Materials
- BCC, FCC and HCP structures differ in packing factor and slip systems; FCC is ductile because it has twelve slip systems.
- The Fe–Fe₃C diagram has a eutectoid at 0.76% C and 727 °C and a eutectic at 4.3% C and 1147 °C. TTT and CCT curves govern whether austenite becomes pearlite, bainite or martensite.
- Annealing softens, normalizing refines grain, quenching hardens, tempering restores toughness. Hall–Petch and cold work raise strength.
Manufacturing
- Casting: Chvorinov's rule t = k(V/A)² sizes risers; the riser must solidify after the casting.
- Machining: Merchant's circle relates shear angle, rake angle and friction; Taylor's tool life VTⁿ = C.
- Forming and joining: rolling load, extrusion ratio, blanking force = shear strength × sheared area; weld defects and heat-affected zone behaviour.
Industrial engineering
- EOQ = √(2DS/H); PERT expected time = (a + 4m + b)/6, with critical path from network floats; Johnson's rule sequences n jobs on two machines; M/M/1 uses ρ = λ/μ.
Worked example
Taylor with n = 0.2: if V = 100 m/min gives 25 min life, then C = 100 × 25^0.2 = 190.4. For 100 min life, V = 190.4/100^0.2 = 190.4/2.512 ≈ 75.8 m/min. Quadrupling tool life buys only about a 24% speed reduction, which is why the exponent dominates the economics.
Traps
Leaving the exponent out of VTⁿ = C; using total area instead of volume-to-surface ratio in Chvorinov; confusing annealing with normalizing; forgetting that PERT weights the most likely time by four.