The Hall-Petch relationship or Hall-Petch Law is a relation in materials science that deals with the connection between the grain size, or crystallite size, and the yield point of a material. This relation says that the larger the grain size of a crystalline material, the weaker it is, that is the smaller its yield strength. The relation is described mathematically by the Hall-Petch equation which is

$\backslash sigma\_y\; =\; \backslash sigma\_0\; +\; \{k\_y\; \backslash over\; \backslash sqrt\; \{d\}\}$

where k_y is the fitting parameter (a material constant), σ_o is a materials constant for the starting stress for dislocation movement, d is the grain diameter, and σ_y is the yield stress.

History

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In the early 1950s two groundbreaking series of papers were written independently on the relationship between grain boundaries and strength.

Hall

In 1951 E.O. Hall wrote three papers which appeared in volume 64 of the Proceedings of the Physical Society. In his third paper, Hall showed that the length of slip bands or crack lengths correspond to grain sizes and thus a relationship could be established between the two. concentrated on the yielding properties of mild steels.

Petch

Based on his experimental work carried out in 1946-1949, N.J. Petch of the University of Leeds, England published a paper in 1953 independent from Hall's. Petch's paper concentrated more on brittle fracture. By measuring the variation in cleavage strength with respect to ferritic grain size at very low temperatures, Petch found a relationship exact to that of Hall's. Thus this important relationship is named after both Hall and Petch.

References

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1. Meier, Mike. The Hall-Petch Relationship. Sept. 13, 2004. Depeartment of Materials Science at UC-Davis. Nov. 6, 2005 http://www.matsci.ucdavis.edu/MatSciLT/EMS-174L/Files/HallPetch.pdf.

Materials science

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