Grain boundary hardening in a poly-crystal
When a tensile stress is applied to a poly-crystal, dislocations glide along a slip plane until they reach a grain boundary. Since the grain boundary acts as a barrier to dislocation motion, dislocations accumulate at the boundary and form a pile up.
Similar dislocations travelling on the same slip plane will repel each other. If there are n dislocations in a pile up, the stress at the grain boundary will be n times the applied stress. New slip is initiated when the stress on the neighbouring grain reaches sufficient level.
Dislocations in the neighbour grain can move along the slip plane and form a pile up again. This process is repeated until slip has initiated in all grains, so that marcroscopic yielding can occur.