Questions
6–8 questions in major PSU papers
Difficulty
Medium-Hard
Importance
High yield for HPCL/NTPC/ONGC
Overview
Mechanical Metallurgy focuses on the macroscopic and microscopic response of engineering materials to external forces, forming the backbone of material selection in structural design. For PSU exams, mastering the stress-strain relationships, failure modes, and energy absorption criteria is vital for solving high-frequency numericals.
Deformation: Slip and Twinning
Plastic deformation in crystalline materials occurs primarily through slip or twinning. Slip involves dislocation motion across slip planes, while twinning is a reorientation of the lattice, becoming dominant at lower temperatures or in HCP structures.
- Schmid's Law: Resolved Shear Stress = Sigma * cos(phi) * cos(lambda)
- Critical Resolved Shear Stress (CRSS) is the stress required to initiate slip
- Slip systems: BCC (48), FCC (12), HCP (3)
- Twinning is significant in HCP metals like Magnesium and Zinc
- Schmid factor (m) = cos(phi) * cos(lambda)
Creep and Fatigue
Creep is the time-dependent permanent deformation under constant load at elevated temperatures, often described by the three stages: primary, secondary (steady-state), and tertiary. Fatigue failure occurs under cyclic loading, where cracks propagate even below the yield strength of the material.
- Steady-state creep rate: epsilon_dot = A * sigma^n * exp(-Q/RT)
- Endurance limit (Fatigue limit): stress level below which failure never occurs
- Goodman relationship: (sigma_a / sigma_e) + (sigma_m / sigma_u) = 1
- S-N Curve: stress amplitude vs number of cycles to failure
- Creep failure is intergranular; fatigue failure is transgranular
Fracture Mechanics
Fracture mechanics quantifies the stress required to propagate a crack in a material containing flaws. Understanding the relationship between critical crack length and fracture toughness is essential for preventing catastrophic brittle failure.
- Griffith Criterion: sigma_f = sqrt(2*E*gamma_s / pi*a)
- Stress Intensity Factor: K = Y * sigma * sqrt(pi*a)
- Fracture Toughness: K_IC = Y * sigma_c * sqrt(pi*a)
- Ductile fracture: High energy absorption, extensive plastic deformation
- Brittle fracture: Low energy absorption, rapid crack propagation
Hardness Testing
Hardness testing measures a material's resistance to localized plastic deformation. Different scales rely on specific indenters and loading conditions to correlate with ultimate tensile strength.
- Brinell Hardness Number (BHN) = 2P / (pi * D * (D - sqrt(D^2 - d^2)))
- Vickers Hardness (HV): uses diamond pyramid indenter
- Rockwell Hardness (HRC/HRB): based on depth of indentation
- Relationship: UTS (MPa) approx 3.45 * BHN
- Mohs scale: comparative hardness based on scratch resistance
Formula Sheet
Schmid Law: tau_RSS = sigma * cos(phi) * cos(lambda)
Steady-state Creep: epsilon_s = A * sigma^n * exp(-Q/RT)
Fatigue (Goodman): sigma_a / S_e + sigma_m / S_u = 1
Fracture: K_IC = Y * sigma * sqrt(pi * a)
Griffith Criterion: sigma_c = sqrt(2 * E * gamma_s / (pi * a))
Brinell Hardness: BHN = 2P / (pi * D * (D - sqrt(D^2 - d^2)))
Exam Tip
Always verify the crystal structure (BCC vs FCC vs HCP) before calculating slip systems or predicting dominant deformation modes, as this is the most common trap in PSU numericals.
Common Mistakes
- Confusing Schmid factor calculation angles (phi is angle between load and normal, lambda is angle between load and slip direction).
- Applying Goodman's relation incorrectly by mixing up mean stress and amplitude stress in fatigue problems.
- Neglecting the temperature-dependent term (exp(-Q/RT)) in creep rate calculations.
More Revision Notes
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