The common tie to making a material stronger is to keep dislocations from moving freely in the material. Some techniques to strengthening a material are:
1. Precipitate Hardening: adding another material that will strain the lattice and slow dislocation movement.
2. Grain Boundaries: adding grain boundaries will slow dislocation movement.
3. Phase Boundaries: for the same reason as precipitate hardening
4. Other Dislocations: Sometimes dislocations can intersect, causing a strain in the lattice that requires more energy to break than just a single location.
For precipitate hardening, the yield strength is proportional to the spacing of the precipitates. An example of a precipitate is Cementite in steel. Too much of this precipitate and the effects of the precipitate will be a factor in strength- too much cementite, and the steel will be brittle like cementite. The spacing of the lamella in pearlite (the ferrite-cementite layers in steel) is a function of temperature at which the pearlite is formed.
The way to increase the number of dislocations and the number of grain boundaries is to cold work the material. This will decrease the grain size, and obviously, the more grains there are, the more grain boundaries.
The way to characterize the number of dislocations is by dislocation density. This can be one of two measures- an area or a volume. Dislocation density (area) is found by the number of dislocations divided by the height and width of the area of material. This can be thought of as how many dislocations intersect a cross-sectional plane. Dislocation density (volume) is found by the number of dislocations multiplied by the length of dislocations all divided by the volume of the material. This can be thought of as how much of the material is in dislocations. Average ranges are from 10^6 for a soft material to 10^13 for a heavily deformed sample.