Probabilistic control of materials by a simulation method

This work deals with a method to find the number of required tests so that the failure stress of a material belongs to a given rank of tolerance of cumulative probability. The method is based on the estimation of the dispersion of the Weibull’s parameters (the inferior limit tension σL, below which there is no failure, the superior limit tension σS, over which there is always failure, and the fabrication parameters m and K) by means of the optimization of a linear correlation between the cumulative probability and the failure tension. Using a property of the Fischer’s matrix and the dispersion of parameters estimated by the simulation method, the number of samples compatible with fixed values of cumulative probability of failure Fc and tolerance δF can be found and, consequently, its control. This methodology is applied to the case of a steel SAE 1020, in relation to the yield stress.