Question

What is the best way to reduce the average grain size in a metal speciman.

Answer 1

Grain-boundary strengthening is a methode of  strengthening materials by changing their average grain size in metal speciman. By changing grain size one can influence dislocation movement and yield strength.For example, heat treatment after plastic deformation and changing the rate of solidification are ways to alter grain size.

Decreasing grain size decreases the amount of possible pile up at the boundary, increasing the amount of applied stress necessary to move a dislocation across a grain boundary. The higher the applied stress needed to move the dislocation, the higher the yield strength. Thus, there is then an inverse relationship between grain size and yield strength, as demonstrated by the Hall–Petch equation.

There is an inverse relationship between delta yield strength and grain size to some power, x.

where d is the strengthening coefficient and both k and x are material specific. The smaller the grain size, the smaller the repulsion stress felt by a grain boundary dislocation and the higher the applied stress needed to propagate dislocations through the material.

The relation between yield stress and grain size is described mathematically by the Hall–Petch equation:

where σ_y is the yield stress, σ_o is a materials constant for the starting stress for dislocation movement (or the resistance of the lattice to dislocation motion), k_y is the strengthening coefficient (a constant specific to each material), and d is the average grain diameter.

Theoretically, a material could be made infinitely strong if the grains are made infinitely small. Microstructure with the highest yield strength is a grain size of about 10 nm (3.9×10⁻⁷ in), because grains smaller than this undergo another yielding mechanism.

Example - Controlling grain size in aluminum alloys is by introducing particles to serve as nucleants, such as Al–5%Ti. Grains will grow via heterogeneous nucleation; that is, for a given degree of undercooling beneath the melting temperature, aluminum particles in the melt will nucleate on the surface of the added particles. Grains will grow in the form of dendrites growing radially away from the surface of the nucleant. Solute particles can then be added (called grain refiners) which limit the growth of dendrites, leading to grain refinement. Al-Ti-B alloys are the most common grain refiner for Al alloys; however, novel refiners such as Al₃Sc have been suggested.