Meyer's law is an
empirical
Empirical evidence is evidence obtained through sense experience or experimental procedure. It is of central importance to the sciences and plays a role in various other fields, like epistemology and law.
There is no general agreement on how t ...
relation between the size of a
hardness test
Indentation hardness tests are used in mechanical engineering to determine the hardness of a material to deformation. Several such tests exist, wherein the examined material is indented until an impression is formed; these tests can be performed o ...
indentation
__FORCETOC__
In the written form of many languages, indentation describes empty space ( white space) used before or around text to signify an important aspect of the text such as:
* Beginning of a paragraph
* Hierarchy subordinate concept
* Qu ...
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 Boroughs and localities of Berlin, locality of Berlin within the borough of Charlottenburg-Wilmersdorf. Established as a German town law, town in 1705 and named after Sophia Charlotte of Hanover, Queen consort of Kingdom ...
, 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'' ...
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 measurem ...
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