Heat treatment — annealing, normalising, quenching, tempering; precipitation hardening: Question bank

Symbols and terms this bank uses

Before answering, make sure every symbol below is one you can read out in plain words. If any is unfamiliar, the figures further down anchor them to pictures.

Definition The vocabulary

SSSS — supersaturated solid solution: a solid that holds more dissolved solute (e.g. Cu in Al) than it comfortably would at that temperature, because a fast quench froze the solute in place before it could come out. "Super-saturated" = over-filled.
Hall–Petch symbols in $σ_{y} = σ_{0} + \frac{k}{d}$ :
- $σ_{y}$ = yield strength, the stress at which the metal starts to deform permanently.
- $σ_{0}$ = lattice-friction stress, the baseline resistance of a single crystal with no grain boundaries at all (the "floor").
- $k$ = the Hall–Petch coefficient, a material constant measuring how strongly boundaries block slip.
- $d$ = grain size (average grain diameter). Smaller grains = more boundary per volume.
Orowan symbols in $Δ τ = \frac{G b}{L}$ :
- $Δ τ$ = the extra shear stress needed to push a dislocation past precipitates.
- $G$ = the shear modulus, the metal's stiffness against shape-shearing.
- $b$ = the Burgers vector length, the size of the atomic step a dislocation carries.
- $L$ = the precipitate spacing, the gap between neighbouring obstacle particles.

Intuition Why the two formulas

look the way they do — the pictures The figures below are the visual justification the equations rely on. Refer back to them while you answer.

The CCT-style cooling map (figure above): the horizontal axis is time, the vertical axis is temperature. A slow cooling curve (cyan) crosses the pearlite "nose" → equilibrium soft phases. A fast curve (amber) misses the nose entirely, dropping below the martensite-start line → hard martensite. The critical cooling rate is the steepest curve that just misses the nose; quenching must beat it.

The Hall–Petch picture: dislocations pile up against a grain boundary. Smaller grains pack more boundaries in, so slip is blocked more often — that is why

σ_{y}

rises as

d

falls, and why the curve flattens toward the floor

σ_{0}

for huge grains.

The Orowan bowing + ageing hump: a dislocation line bows between two precipitates spaced

L

apart (left); a tighter gap needs more stress, so

Δ τ = G b / L

. As ageing proceeds, precipitates first refine (small

L

, rising strength) then coarsen (large

L

, falling strength) — giving the peak-ageing hump of strength versus time (right).

True or false — justify

True or false: quenching makes any metal harder.

False — hardening by quench needs the diffusionless FCC→BCT martensite shear plus dissolved carbon; pure aluminium has no such transformation, so a quench only traps a soft supersaturated solution until ageing builds precipitates.

True or false: slow cooling always gives the softest steel structure.

True for equilibrium steels — slow (furnace) cooling gives atoms time to diffuse to comfortable positions, forming coarse pearlite with large grains, which is the softest, most ductile arrangement.

True or false: annealing and normalising differ only in the cooling rate.

True — both austenitise identically; furnace-cooling (anneal) gives coarse pearlite and big grains, still-air cooling (normalise) gives finer pearlite and smaller grains, so the only knob turned is cooling speed.

True or false: tempering makes martensite softer than the original annealed steel.

False — tempering only trades a little hardness of the very hard martensite for toughness; the tempered product is still far harder than the fully annealed structure.

True or false: longer ageing always means a stronger precipitation-hardened alloy.

False — strength versus ageing time is a hump: past the peak, precipitates coarsen (Ostwald ripening), spacing

L

grows, the Orowan stress

G b / L

falls, and the alloy over-ages and softens.

True or false: martensite forms because carbon has time to diffuse out of the lattice.

False — it's the opposite; martensite forms because the quench is so fast that carbon has no time to leave the FCC lattice, so it is trapped and forces the lattice into a strained BCT shape.

True or false: smaller grain size lowers the yield strength.

False — Hall–Petch says

σ_{y} = σ_{0} + k / d

, so smaller grain size

d

raises

σ_{y}

because more grain boundaries block dislocation motion (see the pile-up figure).

True or false: a supersaturated solid solution (SSSS) is already hard right after quenching.

False — the SSSS is still relatively soft; the strengthening comes only during ageing when the trapped solute forms fine coherent precipitates that pin dislocations.

True or false: any cooling rate will produce martensite in steel.

False — only cooling faster than the critical cooling rate (the curve that just misses the pearlite nose on the CCT diagram) traps martensite; slower rates cross the nose and form pearlite instead.

Spot the error

"To harden Duralumin, austenitise it and quench to form martensite."

Error — aluminium alloys have no austenite and cannot form martensite; you solution-treat, quench to a supersaturated solution, then age to precipitate — a diffusion-based, not shear-based, hardening.

"Normalising is done by cooling the steel inside the furnace."

Error — furnace cooling is annealing; normalising cools in still air, which is faster and produces the finer, tougher grain structure.

"Peak hardness in age hardening comes from the largest possible precipitates."

Error — peak hardness comes from fine, closely spaced precipitates (small

L

, large

G b / L

); large coarse precipitates mean wide spacing and low strength (over-aged).

"You should always quench and then leave the part as-is for maximum performance."

Error — as-quenched martensite is glass-brittle with residual stress and will crack in service; almost all quenched steel is tempered to restore toughness.

"Ferrite (α) dissolves lots of carbon, which is why it's soft."

Error — ferrite is BCC and dissolves almost no carbon; austenite (FCC) is the phase that dissolves lots of carbon (see the Iron-Carbon Phase Diagram). Ferrite's softness comes from being nearly pure, unstressed iron.

"Grain boundaries help dislocations glide, so more boundaries make metal softer."

Error — grain boundaries stop dislocations, causing pile-ups; more boundaries mean harder deformation, hence Hall–Petch strengthening, not softening.

"Tempering re-dissolves the carbon back into austenite."

Error — tempering is done well below the austenite region; it lets some carbon precipitate as fine carbides from the martensite, relieving lattice strain — it does not re-form austenite.

"A slower quench is always safer and gives the same hardness."

Error — on the CCT map a slower curve may cross the pearlite nose and miss the martensite-start line, giving soft pearlite instead of hard martensite; hardness depends on beating the critical cooling rate.

Why questions

Why does slow cooling produce equilibrium phases but fast cooling does not?

Equilibrium phases require atoms to hop between lattice sites, which needs time and temperature; slow cooling supplies both, while a fast quench freezes atoms in place before they can diffuse.

Why is martensite so hard and brittle at the same time?

The trapped carbon severely distorts the BCT lattice, and this internal strain both blocks dislocation motion (hard) and leaves little room for plastic flow before fracture (brittle).

Why does normalising strengthen steel relative to annealing?

The faster air cool prevents grain coarsening, giving a smaller grain size

d

; by Hall–Petch

σ_{y} = σ_{0} + k / d

, smaller

d

raises yield strength.

Why do we quench before ageing in precipitation hardening?

The quench traps all the solute in a supersaturated solution so none precipitates prematurely; ageing then controls precipitation to form the desired fine, coherent particles.

Why does a smaller precipitate spacing

L

give more strengthening (Orowan)?

A dislocation must bow into a tighter arc to squeeze between closer obstacles, and the extra shear stress

Δ τ = G b / L

rises as

L

shrinks — like needing more pressure to blow a smaller bubble.

Why does the CCT diagram have a "nose"?

Transformation to pearlite needs both a driving force (grows as you cool) and atom mobility (falls as you cool); the two compete, so transformation is fastest at an intermediate temperature — that speed maximum is the nose the quench must dodge.

Why must aerospace parts use sequences of treatments rather than one cooling path?

A single path can't deliver both high strength and toughness (e.g. quench gives hard-but-brittle martensite); combining steps like quench-and-temper achieves the contradictory property set demanded.

Edge cases

What happens if you quench a plain-carbon steel that has almost no carbon?

With little carbon to trap and distort the lattice, the martensitic hardening is weak — carbon content is what strains the BCT structure, so very-low-carbon steel barely hardens on quenching.

What happens to strength if ageing time approaches zero (as-quenched)?

With no ageing, no strengthening precipitates have formed, so the alloy sits at the soft SSSS end of the hardness-versus-time hump.

What happens if ageing is carried out at too high a temperature?

High temperature gives so much atom mobility that precipitates nucleate coarsely and coarsen quickly, skipping the fine-precipitate peak and landing in the over-aged, soft regime.

Is there any benefit to tempering an alloy that was never hardened by martensite?

No — tempering exists to relax martensitic strain and form carbides from martensite; a non-martensitic (e.g. aged aluminium) alloy has no such strained phase to relieve.

What is the limiting behaviour of

σ_{y}

as grain size

d

becomes very large?

d \to \infty

, the

k / d

term vanishes and

σ_{y} \to σ_{0}

, the lattice-friction floor — a coarse-grained metal is governed almost entirely by intrinsic lattice resistance.

What cooling rate lies exactly on the critical cooling rate line?

A curve that just grazes the pearlite nose gives a mixed structure (some pearlite, some martensite); anything faster is fully martensitic, anything slower starts losing hardness to pearlite.

Recall Self-check

Quenching hardness mechanism in aluminium vs steel ::: Steel = diffusionless martensite shear; aluminium = trap-then-age precipitation. Completely different physics. The shape of strength-versus-ageing-time ::: A hump (peak-ageing), not a ramp — over-ageing softens via Orowan spacing growth. The Hall–Petch symbols ::: $σ_{0}$ = lattice floor, $k$ = boundary strength constant, $d$ = grain size; smaller $d$ ⇒ larger $σ_{y}$ . The Orowan symbols ::: $G$ = shear modulus, $b$ = Burgers vector, $L$ = precipitate spacing; smaller $L$ ⇒ larger $Δ τ$ .