Probabilistic design and quality control in probabilistic strength of materials

A numerical simulation method is used here for the design and quality control of a material subject to normal gradual stress (sigma)or a cyclic stress (sigma), having fixed cumulative probability F and the number of cycles l; capable of achieving a given mechanical property such as yield point, elastic limit stress, fracture strength, etc., as well as the admissible tolerance (delta)F the presence of such property is to be accepted with. With F and (delta)F, the stress of the design (sigma)C can be determined, as well as the variations (sigma)m, (sigma)(sigma)0 and (delta)(sigma)L of Weibull’s parameters m, (sigma)0 and (sigma)L, respectively, that the tolerance (delta)F admits. When cyclic stresses arise, other parameters must be introduced, k1, k2 and p, which produce variations (delta)k1, (delta)k2, and (delta)p, respectively. The determination of the necessary number of samples to be tested in order to carry out the quality control of the material, with a given probability of effectiveness, is obtained with variations (delta)m, (delta)(sigma)0, (delta)(sigma)L, (delta)k1, (delta)k2 and (delta)p, with the parameter dispersion estimated by numerical simulation, and with the help of a property deduced from the Fischer’s matrix to obtain the parameter dispersion.