TITLE:
The Probability Distribution of the Elastic Properties of Pure Metals
AUTHORS:
Clint Steele
KEYWORDS:
Elasticity, Engineering Materials, Central Limit Theorem, Pseudo-Isotropy
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.6,
April
8,
2014
ABSTRACT:
While there are many
published data on the average properties of elasticity for metals, there is little
on the expected randomness. This is despite the known randomness of the
elasticity of the grains that make up metals. It seems implicitly assumed that
due to pseudo-isotropy, the average is all that is of concern. But how does one
know if this is always the case? By creating a simple model of a metal, it is
shown that for typical metal samples the randomness is negligible. However, as
samples become smaller, it is possible to estimate the randomness based on
information about the properties of grains within the metal. Further, due to
the central limit theorem, which is implied by the model, a Gaussian
distribution can be expected. This can be used in an evolutionary approach to
generating a distribution for further probabilistic analysis of a respective
system.