The effects of high strain-rate and in-plane restraint on quasi-statically loaded laminated glass: a theoretical study with applications to blast enhancement

Abstract

Laminated glass panels are increasingly used to improve the blast resilience of glazed facades, as part of a wider effort to mitigate the threat posed to buildings and their occupants by terrorist attacks. The blast response of these ductile panels, however, is still only partially understood and requires bridging of the knowledge gap between the fundamental behaviour at material level and the response observed in full-scale blast tests. To enhance our understanding of the structural response of laminated glass and bridge this knowledge gap, this paper adopts a ‘first principles’ approach and investigates the effects of high strain-rate associated with blast loading and in-plane restraint offered by blast-resistant frames. These are studied by developing simplified analytical beam models for all stages of deformation that account for the enhanced material properties of both the glass and the interlayer at high strain-rates. The increased shear modulus of the interlayer under high strain-rates results in a composite bending response of the un-fractured laminated glass. This also enhances the residual post-fracture bending moment capacity from the combined action of the glass fragments in compression and the interlayer in tension, which is considered negligible under low strain-rates. The post-fracture resistance is significantly improved by the introduction of in-plane restraints, due to the membrane action arising from the stretching of a panel under large deflections. This was demonstrated by developing a yield condition, which accounts for the relative contributions of bending moment and membrane force, and applying the upper bound theorem of plasticity that assumes a tearing failure of the interlayer. To complement the work presented in this paper and complete the theoretical framework for the blast response of laminated glass, future work should focus on the assessment of two-way spanning plate-action and inertia effects, which were ignored to focus solely on the effects of high strain-rate and in-plane restraint.