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Layer 1 Layer 2

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.

Layer 1 Layer 2

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.

Layer 1 Layer 2 Layer 3

Layer 1 Layer 2 Layer 3

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.

Layer 1 D σ y σ 0 = + k √D k σ y σ 0 Hall-Petch relationship : : : Yield stress intrinsic yield stress material constant D : Grain size

Layer 1 D σ y σ 0 = + k √D k σ y σ 0 Hall-Petch relationship : : : Yield stress intrinsic yield stress material constant D : Grain size Layer 1 Layer 2