Grain boundary strengthening
In materials science, grain-boundary strengthening is a method of strengthening materials by changing their average crystallite size. It is based on the observation that grain boundaries are insurmountable borders for dislocations and that the number of dislocations within a grain has 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 as well. 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.
Theory
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.
There is a limit to this mode of strengthening, as infinitely strong materials do not exist. Grain sizes can range from about to . Lower than this, the size of dislocations begins to approach the size of the grains. At a grain size of about, only one or two dislocations can fit inside a grain. 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.
To understand the mechanism of grain boundary strengthening one must understand the nature of dislocation-dislocation interactions. Dislocations create a stress field around them given by:
where G is the material's shear modulus, b is the Burgers vector, and r is the distance from the dislocation. If the dislocations are in the right alignment with respect to each other, the local stress fields they create will repel each other. This helps dislocation movement along grains and across grain boundaries. Hence, the more dislocations are present in a grain, the greater the stress field felt by a dislocation near a grain boundary:
Interphase boundaries can also contribute to grain boundary strengthening, particularly in composite materials and precipitation-hardened alloys. Coherent IPBs, in particular, can provide additional barriers to dislocation motion, similar to grain boundaries. In contrast, non-coherent IPBs and partially coherent IPBs can act as sources of dislocations, which can lead to localized deformation and affect the mechanical properties of the material.
Subgrain strengthening
A subgrain is a part of the grain that is only slightly disoriented from other parts of the grain. Current research is being done to see the effect of subgrain strengthening in materials. Depending on the processing of the material, subgrains can form within the grains of the material. For example, when Fe-based material is ball-milled for long periods of time, subgrains of 60–90 nm are formed. It has been shown that the higher the density of the subgrains, the higher the yield stress of the material due to the increased subgrain boundary. The strength of the metal was found to vary reciprocally with the size of the subgrain, which is analogous to the Hall–Petch equation. The subgrain boundary strengthening also has a breakdown point of around a subgrain size of 0.1 μm, which is the size where any subgrains smaller than that size would decrease yield strength.Types of Strengthening Boundaries
Coherent Interphase Boundaries
Coherent grain boundaries are those in which the crystal lattice of adjacent grains is continuous across the boundary. In other words, the crystallographic orientation of the grains on either side of the boundary is related by a small rotation or translation. Coherent grain boundaries are typically observed in materials with small grain sizes or in highly ordered materials such as single crystals. Because the crystal lattice is continuous across the boundary, there are no defects or dislocations associated with coherent grain boundaries. As a result, they do not act as barriers to the motion of dislocations and have little effect on the strength of a material. However, they can still affect other properties such as diffusion and grain growth.When solid solutions become supersaturated and precipitation occurs, tiny particles are formed. These particles typically have interphase boundaries that match up with the matrix, despite differences in interatomic spacing between the particle and the matrix. This creates a coherency strain, which causes distortion. Dislocations respond to the stress field of a coherent particle in a way similar to how they interact with solute atoms of different sizes. It is worth noting that the interfacial energy can also influence the kinetics of phase transformations and precipitation processes. For instance, the energy associated with a strained coherent interface can reach a critical level as the precipitate grows, leading to a transition from a coherent to a disordered interface. This transition occurs when the energy associated with maintaining the coherency becomes too high, and the system seeks a lower energy configuration. This happens when particle dispersion is introduced into a matrix. Dislocations pass through small particles and bow between large particles or particles with disordered interphase boundaries. The predominant slip mechanism determines the contribution to strength, which depends on factors such as particle size and volume fraction.
Partially-coherent Interphase Boundaries
A partially coherent interphase boundary is an intermediate type of IPB that lies between the completely coherent and non-coherent IPBs. In this type of boundary, there is a partial match between the atomic arrangements of the particle and the matrix, but not a perfect match. As a result, coherency strains are partially relieved, but not completely eliminated. The periodic introduction of dislocations along the boundary plays a key role in partially relieving the coherency strains. These dislocations act as periodic defects that accommodate the lattice mismatch between the particle and the matrix. The dislocations can be introduced during the precipitation process or during subsequent annealing treatments.Non-coherent Interphase Boundaries
Incoherent grain boundaries are those in which there is a significant mismatch in crystallographic orientation between adjacent grains. This results in a discontinuity in the crystal lattice across the boundary, and the formation of a variety of defects such as dislocations, stacking faults, and grain boundary ledges.The presence of these defects creates a barrier to the motion of dislocations and leads to a strengthening effect. This effect is more pronounced in materials with smaller grain sizes, as there are more grain boundaries to impede dislocation motion. In addition to the barrier effect, incoherent grain boundaries can also act as sources and sinks for dislocations. This can lead to localized plastic deformation and affect the overall mechanical response of a material.When small particles are formed through precipitation from supersaturated solid solutions, their interphase boundaries may not be coherent with the matrix. In such cases, the atomic bonds do not match up across the interface and there is a misfit between the particle and the matrix. This misfit gives rise to a non-coherency strain, which can cause the formation of dislocations at the grain boundary. As a result, the properties of the small particle can be different from those of the matrix. The size at which non-coherent grain boundaries form depends on the lattice misfit and the interfacial energy.