A comprehensive probabilistic fracture analysis methodology should allow data to be combined or pooled from multiple specimen sizes and geometries such that all available fracture data can be integrated into strength/probability estimates and such that size-scaling aspects of the model can be tested. Moreover, this capability must, among other things, allow for multiaxial stress states, and be be capable of providing a measure of the statistical uncertainty in estimates of strength and/or probability including confidence and tolerance bounds. Previous efforts of the authors have produced estimators for combined data, confidence and tolerance bounds on estimates, bias and bias correction of estimates and measures of statistical efficiency of the estimators. These developments have been based on Weibull's uniaxial model involving k, a dimensionless “load factor” or “structure factor.”
The results presented in this paper show that similar techniques are applicable to more comprehensive models of multiaxial failure. Building on previous work by the first author, reported elsewhere, and generalizing results recently reported in the literature, it is shown that the Batdorf-Heinisch's (B-H) flaw density distribution and the Lamon-Evans' (L-E) elemental strength approaches to weakest-link fracture statistics for multiaxial loading give equivalent probability predictions for equivalent failure criteria. A generalization is also given detailing necessary and sufficient conditions for the B-H and L-E approaches to be equivalent. This allows a general size factor to be defined that simultaneously takes into account geometry, loading, and multiaxial stresses. This general size factor replaces k in the estimators for combined data, confidence and tolerance bounds on estimates, bias and bias correction of estimates and measures of statistical efficiency previously developed by the authors. It can be applied on an elemental basis or to a component structure as a whole, and this has consequences in determining probability predictions. Also employing these results, it is indicated how a contradictory conclusion, also reported in the literature, was reached. All in all, there appear to be no obvious roadblocks in incorporating the effects of multiaxial stresses into current analysis methods. Moreover, the form of the generai size factor indicates that it may be possible to obtain generalizations that cover time and/or temperature effects. Thus, the equivalence of the B-H and L-E formulations has broad reaching implications.