Mechanics Based Statistical Prediction of Structure Size and Geometry Effects on Safety Factors for Composites and Other Quasibrittle Materials

The objective of this paper1 is a rational determination of safety factors of quasibrittle structures, taking into account their size and shape. To this end, it is necessary to establish the probability density distribution function (pdf) of the structural strength. For perfectly ductile and perfectly brittle materials, the proper pdf’s of the nominal strength of structure are known to be Gaussian and Weibullian, respectively, and are invariable with structure size and geometry. However, for quasibrittle materials, many of which came recently to the forefront of attention, the pdf has recently been shown to depend on structure size and geometry, varying gradually from Gaussian pdf with a remote Weibull tail at small sizes to a fully Weibull pdf at large sizes. This recent result is reviewed, and then mathematically extended in two ways: 1) to a mathematical description of structural lifetime as a function of applied (time-invariable) nominal stress, and 2) to a mathematical description of ∗McCormick Institute Professor and W.P. Murphy Professor of Civil Engineering and Materials Science, Northwestern University, 2145 Sheridan Road, CEE/A135, Evanston, Illinois 60208; z-bazant@northwestern.edu. Authorized republication, with minor modifications, of a paper that was presented at the 48th AIAA/ASME/ASCE/AHS/ASE Structures, Structural Dynamics and Materials Conference in Honolulu, Hawaii, and appeared in the CD of conference proceedings, American Institute of Aeronautics and Astronautics, pp. 1–15.