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Metallurgical Engineering DISCUSSION
Textbooks state that a casting cooled quickly has finer grains than one cooled slowly, and that fine-grained steel is stronger and tougher. I can repeat both statements but I do not understand the mechanism behind either.
Why does the cooling rate control grain size, how large is the strength gain for a realistic change, say from 50 µm to 10 µm ferrite grains in mild steel, and how is grain size controlled in practice when you cannot simply cool a thick section faster?
Grain size is the result of a race between nucleation and growth. Each grain starts from one nucleus and grows until it meets its neighbours, so the more nuclei form per unit volume before the transformation is complete, the smaller the final grains.
Fast cooling takes the metal further below its equilibrium transformation temperature before much has happened. That undercooling is the driving force for nucleation: the energy barrier for forming a stable nucleus falls roughly with the square of the undercooling, so the nucleation rate rises very steeply. Growth also speeds up at first, but far less sharply, so nucleation wins and the grains end up smaller.
The strength effect is described by the Hall-Petch relation: σ_y = σ_0 + k × d^(-1/2), where d is the grain diameter. Grain boundaries block dislocations, and smaller grains mean shorter pile-ups and more boundaries to cross.
For mild steel, textbook values are σ_0 of about 70 MPa and k of about 0.74 MPa·m^(1/2). At d = 50 µm, d^(-1/2) = 141 m^(-1/2), giving 70 + 0.74 × 141 = 175 MPa. At 10 µm, d^(-1/2) = 316, giving 70 + 234 = 304 MPa. Real steels have other contributions on top, but the grain-size term alone adds about 130 MPa for that refinement.
Grain refinement is also the one common strengthening method that improves toughness at the same time. Solid solution, precipitation and work hardening all raise strength but tend to raise the ductile-to-brittle transition temperature of steel. Finer ferrite grains lower it, because a cleavage crack has to change direction at every boundary and the dislocation pile-ups that start such cracks are shorter.
This is the reason structural and pipeline steels are specified as fine-grained, and why a coarse-grained heat-affected zone beside a weld is often the least tough part of a joint.
In thick sections the cooling rate is limited, so other methods are used. In castings, inoculants or grain refiners are added to the melt to supply nuclei, for example titanium-boron master alloys in aluminium. In steel, heating into the austenite range and air cooling (normalising) replaces coarse grains with new fine ones, because every pass through the transformation nucleates fresh grains.
Aluminium-killed and microalloyed steels carry fine particles such as aluminium nitride or niobium, titanium and vanadium carbonitrides that pin austenite grain boundaries. Combined with controlled rolling at relatively low finishing temperatures, this gives fine ferrite, in the region of 5 to 10 µm, even in thick plate. Overheating undoes it: once the particles dissolve or coarsen, the austenite grains grow quickly.
