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There are generally two types of yield point - upper and lower yield points.
Some metals, such as mild steel, reach an upper yield point before dropping rapidly to a lower yield point.
If a low-carbon steel is only stressed to some point between the upper and lower yield point then the surface may develop Lüder bands.
The material response is linear up until the upper yield point, but the lower yield point is used in structural engineering as a conservative value.
After unpinning, dislocations are free to move in the crystal, which results in a subsequent lower yield point, and the material will deform in a more plastic manner.