The log-normal distribution: A better fitness for the results of mechanical testing of materials

Abstract

According to present regulations, the characteristic value of a property of a material is calculated assuming the population is normally distributed. Here it is shown that this assumption is only a good approximation to the real distribution of values when coefficients of variation are low, but that it fails when that coefficient is higher than 0.25, if the variable ranges between 0 and +∞. It is also shown that the log-normal distribution is an accurate approach to the true distribution of values, both for low and high coefficients of variation. An analysis of the relevant features of both the normal and log-normal distribution functions is performed. Likewise both functions are applied to six different sets of experimental results of materials tests and the characteristic values obtained are compared. An easy method developed to compute the characteristic value under the assumption of a log-normal distribution is finally presented.