PE Metallurgical cheat sheet

Engineering stress is σ = F/A0 and engineering strain is ε = ΔL/L0; true stress σt = σ(1+ε) and true strain εt = ln(1+ε) are valid up to the onset of necking.

Considère criterion: necking begins when dσt/dεt = σt, so the true ultimate tensile strength equals the strain-hardening rate at that point.

Hooke's law σ = Eε holds below the proportional limit; Poisson's ratio ν = -εlateral/εaxial is about 0.25-0.35 for metals and approaches 0.5 for rubbery polymers.

Griffith brittle fracture: σf = sqrt(2Eγs/(πa)) for a through-thickness crack of half-length a, so fracture stress decreases as the square root of crack size increases.

Linear-elastic fracture mechanics: KI = Yσ·sqrt(πa); fracture occurs when KI >= KIC, and KIC generally falls as yield strength rises and as temperature falls.

Steady-state creep: εdot = A·σ^n·exp(-Q/RT) with n of roughly 3-8; Larson-Miller parameter P = T(C + log tR) with C near 20 for many steels.

Fatigue relations: Basquin Δσ/2 = σf'(2Nf)^b, Paris law da/dN = C(ΔK)^m, and Goodman mean-stress correction σa/σe + σm/σu = 1.

Thermal shock resistance parameter R = σf(1-ν)/(Eα); high strength, low modulus, high toughness and low thermal expansion all improve resistance to thermal shock cracking.

Fe-Fe3C diagram: eutectoid at 0.76 wt% C and 727 °C (austenite to ferrite plus cementite), eutectic at 4.3 wt% C and 1147 °C (ledeburite); maximum solubility of C in austenite is 2.11 wt% at 1147 °C.

Hall-Petch: σy = σ0 + k·d^(-1/2); refining grain size raises yield strength and usually improves toughness because boundaries block dislocation motion and cracks.

Martensite forms by a diffusionless shear transformation; it is body-centred tetragonal, hardness increases with carbon content, and Ms/Mf temperatures decrease with carbon and alloy content.

Hardenability, the depth of hardening, is ranked by the Jominy end-quench test; Mn, Mo, Cr, Ni and B increase hardenability by shifting CCT curves to longer times.

Precipitation hardening sequence: solution treatment, quench, then age; peak strength occurs with fine coherent precipitates (e.g. GP zones, θ''), and overaging follows coarsening and loss of coherency.

Austenitic stainless steels (304 is 18Cr-8Ni; 316 adds Mo for chloride resistance) sensitize between about 425 and 815 °C when Cr-rich M23C6 precipitates at grain boundaries, causing intergranular corrosion.

Ductile iron contains spheroidal graphite produced by Mg or Ce treatment; gray iron contains graphite flakes, giving high damping capacity and thermal conductivity but very low tensile ductility.

Ceramics are ionically or covalently bonded, stiff, brittle and refractory; strength is flaw-controlled and described by Weibull statistics, where a higher modulus m means less scatter in strength.

Polymers: Tg is the glass transition and Tm the crystalline melting point; increasing crystallinity raises stiffness, strength and density while reducing optical clarity and impact toughness.

Viscoelastic models: a Maxwell element (spring and dashpot in series) describes stress relaxation, while a Kelvin-Voigt element (parallel) describes retarded elastic creep.

Longitudinal isostrain composite modulus Ec = VfEf + VmEm; transverse loading follows approximately the isostress series rule 1/Ec = Vf/Ef + Vm/Em.

Critical fibre length lc = σf·d/(2τi); fibres shorter than lc pull out rather than fracture, so discontinuous composites need l much greater than lc to develop full fibre strength.

Semiconductor conductivity σ = n·e·μe + p·e·μh; Si has a band gap near 1.1 eV and GaAs near 1.42 eV, and doping shifts the Fermi level to raise conductivity by orders of magnitude.

Dielectric behaviour is set by permittivity and dielectric loss; piezoelectric ceramics such as PZT couple mechanical strain and electric polarization, while ferromagnetic and superconducting materials have their own critical temperature limits.

Chvorinov's rule: solidification time t = B(V/A)^2, where V is casting volume, A is heat-extracting surface area and B a mould constant; risers must freeze after the casting they feed.

Secondary dendrite arm spacing decreases with cooling rate as λ = a·(Ṫ)^(-n) with n near 0.3-0.5; faster cooling refines microstructure and reduces microsegregation.

Carbon equivalent for weldability: CE = C + Mn/6 + (Cr+Mo+V)/5 + (Ni+Cu)/15; CE above about 0.4 indicates a risk of hard martensite and cold cracking, requiring preheat.

Annealing after cold work proceeds through recovery, recrystallization and grain growth; the recrystallization temperature is roughly 0.4-0.5 Tm and decreases with increasing prior deformation.

Hot working above the recrystallization temperature keeps the workpiece strain-free and formable; cold working below it produces strain hardening, better surface finish and property anisotropy.

Carburizing raises surface carbon in low-carbon steel in the austenite range; nitriding forms hard nitride cases at 500-570 °C without a quench; shot peening imposes compressive residual stress to resist fatigue.

In fusion welding the heat-affected zone sees thermal cycles that can coarsen grains, dissolve precipitates or form martensite, so HAZ properties differ from both weld metal and base metal.

Ashby performance indices from the objective: light stiff tie M = E/ρ, light stiff beam M = E^(1/2)/ρ, light strong beam M = σ^(2/3)/ρ; maximizing the index selects the best material class.

Specific stiffness E/ρ and specific strength σ/ρ rank materials for weight-limited design; composites, magnesium, aluminium and titanium score well against steels.

Fatigue design converts mean stress to an equivalent fully reversed stress via Goodman or Soderberg lines, and safety factors are applied to stress, to life, or to both.

Galvanic coupling: the more active metal in the galvanic series becomes the anode and corrodes; avoid large cathode-to-anode area ratios and electrically insulate dissimilar metal joints.

Leak-before-break design requires the critical crack length computed from KIC to exceed the wall thickness, so leakage is detected before unstable fracture occurs.

Selection must weigh manufacturing route, joining and weldability, corrosion allowance, cost per unit property, embodied energy, availability and applicable codes such as ASME BPVC and ASTM standards.

Tensile testing per ASTM E8 gives 0.2% offset yield strength, UTS, elongation and reduction of area; measured values depend on strain rate, temperature and specimen orientation.

Hardness scales: Brinell (ball indenter), Rockwell (indenter plus major load), Vickers (diamond pyramid, HV = 1.854F/d^2); tensile strength roughly correlates as σu ≈ 3.3·HV in MPa.

Charpy V-notch impact testing per ASTM E23 measures absorbed energy and lateral expansion versus temperature; the ductile-to-brittle transition is sharp in BCC steels and essentially absent in FCC metals.

NDT capability: penetrant and magnetic particle methods detect surface or near-surface flaws, radiography and ultrasonics detect internal flaws, and eddy current detects surface cracks in conductive parts.

Fractography signatures: ductile fracture shows dimples, brittle fracture shows cleavage facets or intergranular separation, and fatigue shows striations plus beach marks from crack arrest.

Corrosion control includes cathodic protection, coatings, inhibitors and passive alloy selection; SCC and hydrogen embrittlement require the simultaneous presence of tensile stress and a specific environment.

Weibull analysis and statistical treatment of strength data are required for brittle materials, since measured strength depends on stressed volume and the largest flaw population.

Engineering stress is σ = F/A0 and engineering strain is ε = ΔL/L0; true stress σt = σ(1+ε) and true strain εt = ln(1+ε) are valid up to the onset of necking.

Considère criterion: necking begins when dσt/dεt = σt, so the true ultimate tensile strength equals the strain-hardening rate at that point.

Hooke's law σ = Eε holds below the proportional limit; Poisson's ratio ν = -εlateral/εaxial is about 0.25-0.35 for metals and approaches 0.5 for rubbery polymers.

Griffith brittle fracture: σf = sqrt(2Eγs/(πa)) for a through-thickness crack of half-length a, so fracture stress decreases as crack size increases.

Linear-elastic fracture mechanics: KI = Yσ·sqrt(πa), and fracture occurs when KI >= KIC; KIC generally falls as yield strength rises and temperature falls.

Steady-state creep: εdot = A·σ^n·exp(-Q/RT) with n of roughly 3-8; the Larson-Miller parameter P = T(C + log tR) uses C near 20 for many steels.

Fatigue relations: Basquin Δσ/2 = σf'(2Nf)^b, Paris law da/dN = C(ΔK)^m, and Goodman mean-stress correction σa/σe + σm/σu = 1.

Thermal shock resistance parameter R = σf(1-ν)/(Eα); high strength, high toughness, low modulus and low thermal expansion improve resistance to thermal shock cracking.