Hall–Petch relationship otherwise Hall–Petch strengthening; grain-boundary strengthening (rus. соотношение Холла-Петча otherwise закон Холла-Петча) — Relationship between yield point  and grain size d for a polycrystalline material: , where  – a certain shear stress required to ensure gliding dislocations in a monocrystal, and K is a constant individual for each material also known as the Hall-Petch parameter.


The Hall-Petch relation (law) gives a quantitative description of an increase in the yield stress of a polycrystalline material as its grain size decreases. This relationship is based on dislocation mechanisms of plastic deformation: grain boundaries hinder the movement of dislocations. In addition to polycrystalline materials, this relation also applies to some laminated materials.

It is important to note that for nanomaterials with grain sizes of several tens of nanometres this law, to a certain extent, is not observed, giving way to the so-called inverse Hall-Petch effect, whose mechanisms are not well understood yet.


  • Mileiko Sergey T.


  1. Hall-Petch Law (nanomechanics)(in Russian). // Nanometr. — www.nanometer.ru/2008/12/18/nanoazbuka_54966.html (reference dsate: 01.08.2010).
  2. Gao H., Ji B., Jäger I. L. et al. Materials become insensitive to flaws at nanoscale: Lessons from nature // Proceedings of the National Academy of Sciences. 2003. V. 100, №10. P. 5597–5600. —www.pnas.org/content/100/10/5597.full (reference date 12.12.2011).
  3. Grain boundary strengthening // Wikipedia, the free Encyclopedia. — http://en.wikipedia.org/wiki/Grain_boundary_strengthening (reference date: 01.08.2010).
  4. Carlton C. E., Ferreira P. J. What is behind the inverse Hall–Petch effect in nanocrystalline materials? // Acta Materialia. 2007. V. 55. P. 3749–3756.

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