The Probability Distribution of the Elastic Properties of Pure Metals

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.