Weibull bimodal flaw size distribution

Figure 12.13 Bimodal flaw size distribution a narrow peaked flaw population is superposed to a wide population, (a) Relative frequency of flaw sizes (bottom) and density of critical flaw sizes (top) versus the flaw size (b) Weibull plot showing the probability function (through line)...

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]. 

The use of Weibull plots for design purposes has to be handled with extreme care. As with all extrapolations, a small uncertainty in the slope can result in large uncertainties in the survival probabilities, and hence to increase the confidence level, the data sample has to be sufficiently large N > 100). Furthermore, in the Weibull model, it is implicitly assumed that the material is homogeneous, with a single flaw population that does not change with time. It further assumes that only one failure mechanism is operative and that the defects are randomly distributed and are small relative to the specimen or component size. Needless to say, whenever any of these assumptions is invalid, Eq. (11.23) has to be modified. For instance, bimodal distributions that lead to strong deviations from a linear Weibull plot are not uncommon. 

Danzer et al. have discussed the influence of other types of flaw populations (e.g. of bimodal distributions) on strength [I I, 12]. In these cases the Weibull modulus might depend on the applied load amplitude and on the size of the specimen. Then the determination of a design stress in the usual way may become problematic. A stress and size dependent modulus occurs for materials with an R-curve behaviour [11] and may also be caused by internal stress fields [ 11 ]. 

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See also in sourсe #XX -- [ ]

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