Grain boundary strengthening

Grain-boundary strengthening (or Hall–Petch strengthening) is a method of strengthening materials by changing their average crystallite (grain) size. It is based on the observation that grain boundaries are insurmountable borders for dislocations and that the number of dislocations within a grain have an effect on how stress builds up in the adjacent grain, which will eventually activate dislocation sources and thus enabling deformation in the neighbouring grain, too. So, by changing grain size one can influence the number of dislocations piled up at the grain boundary and yield strength. For example, heat treatment after plastic deformation and changing the rate of solidification are ways to alter grain size. Grain-boundary strengthening (or Hall–Petch strengthening) is a method of strengthening materials by changing their average crystallite (grain) size. It is based on the observation that grain boundaries are insurmountable borders for dislocations and that the number of dislocations within a grain have an effect on how stress builds up in the adjacent grain, which will eventually activate dislocation sources and thus enabling deformation in the neighbouring grain, too. So, by changing grain size one can influence the number of dislocations piled up at the grain boundary and yield strength. For example, heat treatment after plastic deformation and changing the rate of solidification are ways to alter grain size. In grain-boundary strengthening, the grain boundaries act as pinning points impeding further dislocation propagation. Since the lattice structure of adjacent grains differs in orientation, it requires more energy for a dislocation to change directions and move into the adjacent grain. The grain boundary is also much more disordered than inside the grain, which also prevents the dislocations from moving in a continuous slip plane. Impeding this dislocation movement will hinder the onset of plasticity and hence increase the yield strength of the material. Under an applied stress, existing dislocations and dislocations generated by Frank–Read sources will move through a crystalline lattice until encountering a grain boundary, where the large atomic mismatch between different grains creates a repulsive stress field to oppose continued dislocation motion. As more dislocations propagate to this boundary, dislocation 'pile up' occurs as a cluster of dislocations are unable to move past the boundary. As dislocations generate repulsive stress fields, each successive dislocation will apply a repulsive force to the dislocation incident with the grain boundary. These repulsive forces act as a driving force to reduce the energetic barrier for diffusion across the boundary, such that additional pile up causes dislocation diffusion across the grain boundary, allowing further deformation in the material. 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. However, when there is a large direction change in the orientation of the two adjacent grains, the dislocation may not necessarily move from one grain to the other but instead create a new source of dislocation in the adjacent grain. The theory remains the same that more grain boundaries create more opposition to dislocation movement and in turn strengthens the material. Obviously, there is a limit to this mode of strengthening, as infinitely strong materials do not exist. Grain sizes can range from about 100 μm (0.0039 in) (large grains) to 1 μm (3.9×10−5 in) (small grains). Lower than this, the size of dislocations begins to approach the size of the grains. At a grain size of about 10 nm (3.9×10−7 in), only one or two dislocations can fit inside a grain (see Figure 1 above). This scheme prohibits dislocation pile-up and instead results in grain boundary diffusion. The lattice resolves the applied stress by grain boundary sliding, resulting in a decrease in the material's yield strength.