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.

翻译：层压玻璃通过刚性玻璃层与柔韧聚合物薄膜的复合效应，实现了渐进式层状失效（表现为多个局部裂纹）所展现的改进型临界后响应。因此，相较于非层压玻璃，层压玻璃具有更高的延展性，使其制成的结构在保持美学特性的同时适用于安全关键型应用。然而，此类临界后响应难以通过确定性失效模型复现——这类模型通常预测所有层同时局部化的单一贯穿厚度裂纹。本数值-实验研究探索了简单随机模型预测渐进失效的可行性：该模型采用独立同分布的威布尔变量对逐层抗拉强度进行建模。数值方面，我们采用计算高效的降维相场公式——将每层视为铁木辛柯梁——通过组合分析和详细蒙特卡洛模拟研究渐进失效。参考实验数据来自多层压玻璃梁的位移控制四点弯曲试验。结果表明，对于特定玻璃层强度组合，随机模型可复现玻璃层的渐进结构失效及多个局部裂纹的形成。然而，预测响应比实验观测值更脆，且模型无法复现最常见的玻璃层失效顺序。这些发现凸显了需考虑沿梁长度方向的强度变异性，并将其纳入相场公式的必要性。