EG184 — Definitions & Diagrams

Definitions with Diagrams

Key terms illustrated. Every diagram corresponds to an exam target.

Topic 1 — Stress & Strain

Stress–Strain Curve — key features

ε σ Yield 0.2% proof UTS Fracture Slope = E 0.002 0 Elastic Strain hardening Necking
Engineering stress–strain curve — all key features labelled
Yield strength (σ_y)
Stress at which the linear elastic region ends. Start of permanent plastic deformation.
0.2% Proof stress
Stress at 0.2% permanent strain. Found by drawing a line parallel to the elastic slope starting at ε = 0.002. Always slightly greater than yield strength.
UTS
Ultimate tensile strength — peak of the engineering stress–strain curve. Onset of necking. Engineering stress falls after UTS even though true stress still rises.
Young's modulus (E)
Slope of the linear elastic region. σ = Eε. Units: GPa. Measures stiffness, not strength.
Toughness
Total area under the stress–strain curve. Units: J/m³. Combines strength AND ductility.
Plastic strain to failure
Total strain at fracture minus elastic springback (= σ_fracture/E). Always less than total strain to failure.

Topic 2 — Deformation in Crystals

Schmid's Law — angle conventions

F (tensile axis) slip plane normal slip direction φ λ τ_RSS = σ cosλ cosφ λ = angle(tensile axis, slip direction) φ = angle(tensile axis, slip plane NORMAL)
Schmid's Law — φ is to the slip plane NORMAL, not the plane itself
Resolved shear stress
τ_RSS = σ cosλ cosφ = σm. The component of the applied tensile stress that acts as shear on a specific slip system.
Schmid factor (m)
m = cosλ cosφ. Maximum 0.5 when λ = φ = 45°. Slip initiates on the system with the highest m (primary slip system).
CRSS
Critical resolved shear stress — minimum shear stress to initiate slip. Material constant. Yield when τ_RSS ≥ τ_CRSS.

Topic 3 — Dislocations

Edge vs Screw dislocation — key distinction

EDGE DISLOCATION extra half-plane ⊥ b ⊥ dislocation line. Moves parallel to b. SCREW DISLOCATION b ∥ dislocation line. Can cross-slip.
Edge: b perpendicular to line (extra half-plane). Screw: b parallel to line (helical planes).
Edge dislocation
Extra half-plane of atoms. b ⊥ dislocation line. Moves parallel to b. Can climb (T > 0.4T_m). Cannot cross-slip.
Screw dislocation
No extra half-plane; spiral atomic planes. b ∥ dislocation line. Moves ⊥ to shear direction. Can cross-slip. Cannot climb.
Hall-Petch
σ_y = σ₀ + k_y·d^(−½). Fine grain → high yield strength. Breaks down below ~10 nm. Units of d must match k_y.
Frank-Read source
Pinned segment bows → forms loop → regenerates. Critical stress: τ = Gb/l where l = pinned length (NOT grain size).

Topic 4 — Strengthening & Annealing

Precipitation hardening — strength vs aging time

Aging time σ_y peak aged under-aged (cutting) over-aged (Orowan)
Yield strength vs aging time. Peak = maximum strength. Over-aging reduces strength as particles coarsen.
Under-aged
Small coherent precipitates. Dislocations cut through them. Strength below peak.
Peak-aged
Optimum size and spacing. Maximum hardness and yield strength.
Over-aged
Coarsened incoherent particles (Ostwald ripening). Larger spacing L → lower Orowan stress τ ≈ Gb/L → strength falls.
Recrystallisation
New strain-free equiaxed grains nucleate and grow. Largest change in mechanical properties during annealing. Strength ↓↓, ductility ↑↑.

Topic 5 — Fracture

Ductile fracture
Large plastic deformation. Cup-and-cone morphology. Dimpled surface (microvoid coalescence) in SEM. High energy, slow propagation.
Brittle fracture
Little plastic deformation. Flat, granular, shiny surface. Cleavage or intergranular in SEM. Low energy, sudden catastrophic failure.
K_IC (fracture toughness)
Critical Mode I stress intensity. Material property. Units: MPa√m. Fracture when K = σ√(πa) ≥ K_IC.
DBT temperature
BCC and HCP metals only. At 50% of upper shelf Charpy energy. Fine grain → lower T_t. Larger grain / more impurities → higher T_t.
Griffith criterion
σ_f = √(2Eγ/πa). Brittle materials only. a = half-length for internal crack; full length for edge crack.

Topic 6 — Fatigue

Striations
Microscopic (SEM only). One per fatigue cycle. Stage II only. Absent in fast-fracture zone.
Beachmarks
Macroscopic (visible to naked eye). NOT one per cycle — each mark = thousands of striations. Caused by loading interruptions.
Stage I
45° to tensile axis. Crystallographic slip planes. Microstructure-dependent. PSB intrusions nucleate cracks.
Stage II
Perpendicular to tensile axis. Paris Law regime. Less microstructure-dependent. Blunting-resharpening mechanism.
Fatigue limit
Ferritic steels only. Below this stress amplitude: infinite life. ~UTS/2. Aluminium and titanium have no true fatigue limit.
Shot peening
Compressive residual stress layer opposes crack opening. Does NOT primarily work by hardening. Over-peening introduces subsurface tensile stress.

Topic 7 — Creep & SCC

Creep curve — three stages

Time ε Primary Secondary ε̇_s Tertiary Fracture ← design parameter
Creep curve. Secondary (steady-state) rate ε̇_s is the engineering design parameter.
Secondary creep rate (ε̇_s)
Constant minimum creep rate. Hardening balanced by recovery/climb. KEY design parameter for lifetime calculation.
Power Law: n ≈ 5
Dislocation creep. Dominates at engineering stresses. ε̇_s ∝ σ^5. Determined from gradient of log ε̇_s vs log σ plot.
Activation energy Q_C
Q_C = −R × (gradient of ln ε̇_s vs 1/T). The minus sign is critical. Use KELVIN in all Arrhenius calculations.
SCC — three requirements
(1) Tensile stress + (2) reactive environment + (3) susceptible material. Remove any one → SCC stops. Causes brittle failure of normally ductile metals.
Hydrogen embrittlement
Worst at intermediate temperatures (~room temperature) and LOW strain rates. BCC and HCP most susceptible. As little as 0.0001 wt% H can cause cracking.