Meyer's law is an
empirical
Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences and ...
relation between the size of a
hardness test indentation
__FORCETOC__
In the written form of many languages, an indentation or indent is an empty space at the beginning of a line to signal the start of a new paragraph. Many computer languages have adopted this technique to designate "paragraphs" or ot ...
and the load required to leave the indentation.
[.] The formula was devised by Eugene Meyer of the Materials Testing Laboratory at the Imperial School of Technology,
Charlottenburg
Charlottenburg () is a locality of Berlin within the borough of Charlottenburg-Wilmersdorf. Established as a town in 1705 and named after Sophia Charlotte of Hanover, Queen consort of Prussia, it is best known for Charlottenburg Palace, the la ...
, Germany, circa 1908.
Equation
It takes the form:
:
where
*''P'' is the pressure in megapascals
*''k'' is the resistance of the material to initial penetration
[S.L. Hoyt, "The Ball Indentation Hardness Test," ''Trans. Am. Soc. Steel Treating'', 6 (1924).]
*''n'' is Meyer's index, a measure of the effect of the deformation on the hardness of the material
*''d'' is the chordal diameter (diameter of the indentation)
The index ''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'' = 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:
:
Meyer's law is often used to relate hardness values based on the fact that if the weight is quartered, the diameter of the indenter is halved. For instance, the hardness values are the same for a test load of 3000 kgf with a 10 mm indenter and for a test load of 750 kgf with a 5 mm diameter indenter. This relationship isn't perfect, but its ]percent error In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared, i.e. dividing by a ''standard'' or ''reference'' or ''starting'' v ...
is relatively small.
A modified form of this equation was put forth by Onitsch:[.]
:
See also
*Meyer hardness test
The Meyer hardness test is a hardness test based upon projected area of an impression. The hardness, H, is defined as the maximum load, P_\text divided by the projected area of the indent, A_\text.
:H=\frac .
This is a more fundamental measureme ...
References
Notes
Bibliography
*{{Citation , last = Tabor , first = David , title = The Hardness of Metals , publisher = Oxford University Press , year = 2000 , url = https://books.google.com/books?id=b-9LdJ5FHXYC , isbn = 0-19-850776-3.
Hardness tests