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 efforts to mitigate the threat posed to buildings and their occupants by terrorist attacks. The blast response of these ductile panels is still only partially understood, with an evident knowledge gap between fundamental behaviour at the material level and observations from full-scale blast tests. To enhance our understanding, and help bridge this gap, this paper adopts a 'first principles' approach to investigate the effects of high strain-rate, associated with blast loading, and the 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 properties of both the glass and the interlayer at high strain-rates. The increased shear modulus of the interlayer results in a composite bending response of the un-fractured laminated glass. This also enhances the residual post-fracture bending moment capacity, arising 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 restraint, due to the membrane action associated with panel stretching under large deflections. This is demonstrated by developing a yield condition that accounts for the rela-tive contributions of bending and membrane action, and applying the upper bound theorem of plasticity, assuming a tearing failure of the interlayer. Future work aims to complete the theoretical framework by including the assessment of plate-action and inertia effects.

High strain-rate effects from blast loads on laminated glass: An experimental investigation of the post-fracture bending moment capacity based on time–temperature mapping of interlayer yield stress

“…The second objective is to investigate if the post-fracture response of laminated glass can be described using cracked elastic theory, which assumes a composite bending action of the interlayer, working in tension, together with the glass fragments working in compression. In particular, the experimental results will assist in validating the analytical models developed by Angelides et al [13], which predict the elastic bending capacity at high strain-rates using an equivalent, transformed cross-section. This elastic response was identified as Stage 3 by Angelides et al [13], with Stage 4 corresponding to the subsequent plastic response.…”

“…In particular, the experimental results will assist in validating the analytical models developed by Angelides et al [13], which predict the elastic bending capacity at high strain-rates using an equivalent, transformed cross-section. This elastic response was identified as Stage 3 by Angelides et al [13], with Stage 4 corresponding to the subsequent plastic response. Note that the terms 'elastic' and 'plastic' used here refer to the change in stiffness observed in the post-fracture stress-strain diagram.…”

“…The consistent pattern formed from small glass fragments that was observed by Hooper [5], therefore represents a yield line mechanism. As described in the analytical models developed by Angelides et al [13], the formation of plastic hinges may be attributed to a composite bending action, with the interlayer acting in tension and the compression component being provided by the glass fragments that come into contact as the panel deforms. For large deflections, the result is a combined bending and membrane response.…”

“…This paper aims to contribute to our understanding of the blast response of laminated glass by focussing on its post-fracture bending capacity at high strain-rates. Although membrane action is anticipated to dominate the response at large deflections, as demonstrated by the yield condition defined by Angelides et al [13], the investigation of the residual bending capacity is important, as it is expected that strains will accumulate along the yield lines formed during bending, dissipating energy and ultimately leading to tearing failure of the PVB. Two objectives are set for the experimental work presented here.…”

Glass engineering!

“…The paper by Botz et al (2019) experimentally investigates the time dependent behavior of PVB (polyvinyl butyral) under varying temperature and humidity conditions. The article written by Angelides et al (2019) sets up a theoretical model for evaluating the effect of high strain rates in laminated glass appli-cable to e.g. blast loads.…”