Is Weibull’s modulus really a material constant? Example case with interacting collinear cracks

The Weibull distribution is widely used to describe the scatter of the strength in brittle (but also quasi-brittle) materials, often assuming that the Weibull modulus is a ‘‘material constant’’. One possible motivation of this perhaps comes from the classical Freudenthal s interpretation of Weibull modulus depending on the crack size distribution, which however assumes the cracks to be at large distance one from the other. It is here found with simple numerical experiments with collinear cracks that Weibull distributions tend to be obtained also with interaction taken into account, but the Weibull modulus depends on both the crack size distribution and the distribution of ligaments. Hence, Weibull modulus should not be considered a ‘‘material constant’’ or to correspond to an ‘‘intrinsic’’ microstructure of the material, as assumed in many industrial applications and commercial postprocessors of FEM softwares, even in the case of a varying stress fields. In the limit case of a crack or sharp notch this leads to paradoxically a zero scale parameter (and the usual Weibull modulus). Hence, in the case of a blunt notch, we suggest the Weibull modulus would vary depending on the distribution of cracks, their distances, and the interaction with the geometry and stress field. Only numerical simulations where the distribution of cracks is directly included in the geometry under consideration can provide the correct scale factor and Weibull modulus.