This happens because the tensile properties of ceramics depend so critically on the size and geometry of the ever present flaws, there is considerable scatter in the values for the strength determined from a tensile, bending, or fatigue test. Ceramic parts produced from identical materials by identical methods fail at very different applied loads.
In order to design structural parts using ceramics, the probability that a flaw is present that will cause failure to occur at any given stress must be known.
The Weibull distribution and Weibull modulus provide one statictical approach to designing with ceramics.
The Weibull distrubition describes the fraction of samples that fail at different applied stresses. At low stresses, a small fraction of samples contain flaws large enough o cause fracture; most fail at an intermediate applied stress; and a few contain only small flaws and do not fail until large stresses and applied. To provide predictability, we prefer a very narrow distribution.
