Mechanics based statistical prediction of structure size and geometry effects on safety factors for composites and other quasibrittle materials

Zdeněk P. Bažant

The objective of this paper 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 the statistical parameters of the pdf of structural strength as a function of structure size and shape. Experimental verification and calibration is relegated to a subsequent journal article.