Meyer's law

Meyer's law is an empirical relation between the size of a hardness test indentation and the load required to leave the indentation. The formula was devised by Prof. Eugene Meyer of the Materials Testing Laboratory at the Imperial School of Technology, Charlottenburg, Germany, circa 1908.

It takes the form:

${\displaystyle P\,=\,kd^{n}}$

where

n usually lies between the values of 2, for fully strain hardened materials, and 2.5, for fully annealed materials. It is roughly related to the strain hardening coefficient in the equation for the true stress-true strain curve by adding 2. Note, however, that below approximately d = 0.5 mm (0.020 in) the value of n can surpass 3. Because of this Meyer's law is often restricted to values of d greater than 0.5 mm up to the diameter of the indenter.

The variables k and n are also dependent on the size of the indenter. Despite this, it has been found that the values can be related using the equation:

${\displaystyle P=k_{1}d_{1}^{n_{1}}=k_{2}d_{2}^{n_{2}}=k_{3}d_{3}^{n_{3}}=...}$

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