Often times, a pure metal is described as isotropic because the mechanical properties do not vary with direction. However, I recently learned that Young's modulus changes with direction according to the equation attached. Sxx is compliance and l,m,n are the direction cosines.
So then are any materials truly isotropic, or is that an assumption we tend to make
Dear\ Gevorg Ter-Isahakyan
pls read this article :-
- http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0327-07932007000400005
- https://msp.org/jomms/2006/1-2/jomms-v1-n2-p02-s.pdf
- http://www3.ogs.trieste.it/bgta/pdf/bgta40.1_CAVALLINI.pdf
Good luck
The known factor K (combination of three elastic stiffness parameters, see elsewhere) should equal UNITY in case of ideal isotropy, whereas most metals have this exceeding TWO and even more. Nonetheless, there are good exclusions:
W has K=1 within about 0.01 errors, Al and Mo have 0.8 and 1.2, respectively, or vice versa (check please).
Dr. Zisman has correctly pointed out the most (elastically) isotropic metals. Tungsten (W) is the closest approximation to a truly isotropic metal.
If interested, other indices to measure elastic anisotropy are described in this article:
Article Elastic anisotropy of crystals
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