Peierls stress (orPeierls-Nabarro stress, also known as thelattice friction stress^[1]) is the force (first described byRudolf Peierls and modified byFrank Nabarro) needed to move adislocation within a plane of atoms in theunit cell. The magnitude varies periodically as thedislocation moves within the plane. Peierls stress depends on the size and width of adislocation and the distance between planes. Because of this, Peierls stress decreases with increasing distance between atomic planes. Yet since the distance between planes increases with planar atomic density,slip of the dislocation is preferred on closely packed planes.

${\displaystyle {\tau }_{\mathrm{P}\mathrm{N}}\propto G{e}^{-2\pi W/b}}$

Where:

${\displaystyle W=\frac{d}{1-\nu }=}$ the dislocation width

${\displaystyle G}$ =shear modulus

${\displaystyle \nu }$ =Poisson's ratio

${\displaystyle b}$ = slip distance orBurgers vector

${\displaystyle d}$ = interplanar spacing

The Peierls stress also relates to the temperature sensitivity of theyield strength of material because it very much depends on both short-range atomic order and atomic bond strength. As temperature increases, the vibration of atoms increases, and thus both peierls stress and yield strength decrease as a result of weaker atomic bond strength at high temperatures.

• Hertzberg, Richard W.Deformation and Fracture Mechanics of Engineering Materials 4th Edition

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