Simulating progressive failure in laminated glass beams with a layer-wise randomized phase-field solver

TL;DR

This paper tackles progressive failure in laminated glass beams, where deterministic fracture models fail to reproduce distributed cracking. It introduces a simple layer-wise phase-field model with independent Weibull-distributed strengths per glass layer and solves it on a dimensionally reduced layer-wise beam, analyzed through Monte Carlo simulations. Validation against four-point bending experiments shows the model can reproduce several progressive cracking patterns but tends to underpredict ductility, underscoring the importance of along-length strength variability. The work points to future directions involving random field strength descriptions and more extensive experiments to enhance predictive capability for safety-critical laminated glass applications.

Abstract

Laminated glass achieves improved post-critical response through the composite effect of stiff glass layers and more compliant polymer films, manifested in progressive layer failure by multiple localized cracks. As a result, laminated glass exhibits greater ductility than non-laminated glass, making structures made with it suitable for safety-critical applications while maintaining their aesthetic qualities. However, such post-critical response is challenging to reproduce using deterministic failure models, which mostly predict failure through a single through-thickness crack localized simultaneously in all layers. This numerical-experimental study explores the extent to which progressive failure can be predicted by a simple randomized model, where layer-wise tensile strength is modeled by independent, identically distributed Weibull variables. On the numerical side, we employ a computationally efficient, dimensionally-reduced phase field formulation -- with each layer considered to be a Timoshenko beam -- to study progressive failure through combinatorial analysis and detailed Monte Carlo simulations. The reference experimental data were obtained from displacement-controlled four-point bending tests performed on multi-layer laminated glass beams. For certain combinations of the glass layer strengths, results show that the randomized model can reproduce progressive structural failure and the formation of multiple localized cracks in the glass layers. However, the predicted response was less ductile than that observed in experiments, and the model could not reproduce the most frequent glass layer failure sequence. These findings highlight the need to consider strength variability along the length of a beam and to include it in phase-field formulations.

Figures (18)

• Figure 1: Subdomains in a multi-layer laminated glass beam sample occupying domain $\Omega$. The structure consists of $M$ layers $\Omega_m$, with the odd indices ($m = 1, 3, \ldots, M$) corresponding to the glass layers and even indices ($m = 2, 4, \ldots, M-1$) to the polymer interlayers.
• Figure 2: Local coordinate systems, geometrical parameters, and primary unknowns of the layer-wise beam model (left) and through-thickness distribution of normal strain in the $m$-th layer and the adopted numerical quadrature (right).
• Figure 3: Flowchart of the staggered static phase-field algorithm.
• Figure 4: Scheme of the four-point bending test on multi-layer laminated glass beams. $\overline{w}(t)$ denotes the time evolution of the prescribed displacement and $R(t)$ the corresponding reaction.
• Figure 5: Force-displacement diagrams for all laminated glass beam samples and specimens. Solid lines are used to distinguish different samples.