Grain boundary strengthening
For example, heat treatment after plastic deformation and changing the rate of solidification are ways to alter grain size.
[1] In grain-boundary strengthening, the grain boundaries act as pinning points impeding further dislocation propagation.
Impeding this dislocation movement will hinder the onset of plasticity and hence increase the yield strength of the material.
The theory remains the same that more grain boundaries create more opposition to dislocation movement and in turn strengthens the material.
The lattice resolves the applied stress by grain boundary sliding, resulting in a decrease in the material's yield strength.
Coherent IPBs, in particular, can provide additional barriers to dislocation motion, similar to grain boundaries.
For example, when Fe-based material is ball-milled for long periods of time (e.g. 100+ hours), subgrains of 60–90 nm are formed.
The strength of the metal was found to vary reciprocally with the size of the subgrain, which is analogous to the Hall–Petch equation.
In other words, the crystallographic orientation of the grains on either side of the boundary is related by a small rotation or translation.
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.
The predominant slip mechanism determines the contribution to strength, which depends on factors such as particle size and volume fraction.
The periodic introduction of dislocations along the boundary plays a key role in partially relieving the coherency strains.
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.
In addition to the barrier effect, incoherent grain boundaries can also act as sources and sinks for dislocations.
[6] When small particles are formed through precipitation from supersaturated solid solutions, their interphase boundaries may not be coherent with the matrix.
The size at which non-coherent grain boundaries form depends on the lattice misfit and the interfacial energy.
Annealing at specific temperatures and durations can induce atomic rearrangements, diffusion, and stress relaxation at the grain boundaries, leading to changes in the interfacial energy.
[10] There is an inverse relationship between delta yield strength and grain size to some power, x. where k is the strengthening coefficient and both k and x are material specific.
It is important to note that the H-P relationship is an empirical fit to experimental data, and that the notion that a pileup length of half the grain diameter causes a critical stress for transmission to or generation in an adjacent grain has not been verified by actual observation in the microstructure.
In the early 1950s two groundbreaking series of papers were written independently on the relationship between grain boundaries and strength.
Based on his experimental work carried out in 1946–1949, N. J. Petch of the University of Leeds, England published a paper in 1953 independent from Hall's.
By measuring the variation in cleavage strength with respect to ferritic grain size at very low temperatures, Petch found a relationship exact to that of Hall's.
The Hall–Petch relation was experimentally found to be an effective model for materials with grain sizes ranging from 1 millimeter to 1 micrometer.
Consequently, it was believed that if average grain size could be decreased even further to the nanometer length scale the yield strength would increase as well.
In Han’s work,[18] a series of molecular dynamics simulations were done to investigate the effect of grain size on the mechanical properties of nanocrystalline graphene under uniaxial tensile loading, with random shapes and random orientations of graphene rings.
Other explanations that have been proposed to rationalize the apparent softening of metals with nanosized grains include poor sample quality and the suppression of dislocation pileups.
One method for controlling grain size in aluminum alloys is by introducing particles to serve as nucleants, such as Al–5%Ti.
One common technique is to induce a very small fraction of the melt to solidify at a much higher temperature than the rest; this will generate seed crystals that act as a template when the rest of the material falls to its (lower) melting temperature and begins to solidify.
