Statistical interference of material strength and surface prestress in heat-treated glass

It is customary to assume that the characteristic design value for heat-treated glass is represented by the sum of the characteristic values of the annealed glass strength and of the heat-induced surface prestress, even though experiments have provided evidence that the resulting strength may be much higher. Here, we investigate the statistical interference between an assumed two-parameter Weibull distribution for the annealed glass strength and a Gaussian distribution for the surface prestress. We show how the compound distribution confirms the experimental findings and, in particular, that the type of stress induced by the applied loads, ie, uniaxial vs biaxial, has an important role. This effect, which is more relevant for “weak” than for “strong” glasses, is the mechanical counterpart of the well-known principle of diversification of investments in economy, and leads to a critical consideration of the design approach commonly suggested by structural standards.