Optimal cold bending of laminated glass

Abstract

Cold-bending of laminated glass panels, by forcing their contact with a constraining frame, is a promising technique for free-form glazed surfaces. Their static state varies in time due to the viscosity of the polymeric interlayer, which causes the decay of the shear-coupling of the constituent glass plies. The direct problem consists in calculating the spatial and temporal evolution of stress after cold-bending. Considering an equivalent secant elastic shear-modulus for the interlayer to account for its viscoelasticity, various conditions for cylindrical deformations are analyzed in detail. A "conjugate-beam analogy" is proposed for the inverse problem, i.e., to determine the deformed shape that, at a prescribed time, provides the desired state of stress. Remarkably, the simplest constant-curvature deformation, often used for cold bending, produces high shear stress concentrations in the interlayer with consequent risks of delamination. For the same sag, better linear or cubic distribution of shear stress are attained with slightly different deformations, compatibly with glass strength. Among the considered cases, the optimal configuration is sinusoidal, because it provides the smoothest distribution of shear stress with inappreciable geometric differences with respect to the circular shape.