Limits for the Application of Weibull Statistics in Brittle Materials

Limits for the Application of Weibull Statistics in Brittle Materials 

There are certain prerequisites for the occurrence of a Weibull distribution [65, 67, 71], the most important being (i) that the structure fails if one single flaw becomes critical (weakest link hypothesis) and (ii) that dangerous flaws do not interact. 

Notably, these prerequisites are not valid for ductile and fiber-reinforced materials. In the first case, stresses are accommodated by plastic deformation, whilst in the latter case the load can be transferred from the matrix into the fibers. Furthermore, a negligible interaction between flaws is only possible if the flaw density is low. Thus, Weibull theory does not apply to porous materials. 

It has also been shown that Weibull theory does not apply to very small specimens [62], in which the fracture-causing flaws are also very small. For a Weibull material (i.e., for a material with relative flaw density corresponding to g oc a P), the density of the flaws becomes so high for small flaws that an interaction between the flaws will undoubtedly occur. 

In cases where the relative frequency of flaw sizes has a shape different to that of a Weibull material, the Weibull modulus becomes stress-dependent. The same happens for bimodal and multimodal flaw distributions [70, 71]. 

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