Materials, Strength of Materials, and Failure Analysis
Domain scope
This domain tests stress-strain behavior, elastic constants, yield and ultimate strength, ductility, hardness, fatigue, creep, fracture, corrosion, and heat treatment. Questions often ask you to predict failure mode or calculate deformation.
Core rules
- Hooke's law in tension: σ = Eε; shear: τ = Gγ.
- Axial deformation: δ = FL/(AE).
- Engineering stress uses original area; true stress uses instantaneous area.
- Ductile materials usually fail by yielding and shear; brittle materials by tensile fracture with little deformation.
- Fatigue occurs below the ultimate strength and is sensitive to stress range, surface finish, and stress concentration.
- Creep is time-dependent deformation at elevated temperature under sustained load.
- Hardness correlates only approximately with tensile strength; it is not a design strength.
Worked example
A steel rod of cross-section 500 mm² and length 2 m carries 50 kN. E = 200 GPa = 200,000 N/mm². δ = FL/(AE) = (50,000×2000)/(500×200,000) = 1.0 mm. The rod remains elastic if the stress, σ = 50,000/500 = 100 MPa, is below yield.
Traps
- Using diameter instead of radius when computing area.
- Forgetting that 1 MPa = 1 N/mm².
- Mixing engineering and true stress near necking.
- Treating hardness as a direct allowable design stress.
- Assuming a ductile material will fail in a brittle manner without low-temperature or triaxial-stress justification.