Schmidt Jaroslav, Zemanová Alena, Zeman Jan, Šejnoha Michal
Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Thakurova 7, 166 29 Prague 6 - Dejvice, Czech Republic.
Materials (Basel). 2020 Nov 16;13(22):5153. doi: 10.3390/ma13225153.
A phase-field description of brittle fracture is employed in the reported four-point bending analyses of monolithic and laminated glass plates. Our aims are: (i) to compare different phase-field fracture formulations applied to thin glass plates, (ii) to assess the consequences of the dimensional reduction of the problem and mesh density and refinement, and (iii) to validate for quasi-static loading the time-/temperature-dependent material properties we derived recently for two commonly used polymer foils made of polyvinyl butyral or ethylene-vinyl acetate. As the nonlinear response prior to fracture, typical of the widely used Bourdin-Francfort-Marigo model, can lead to a significant overestimation of the response of thin plates under bending, the numerical study investigates two additional phase-field fracture models providing the linear elastic phase of the stress-strain diagram. The typical values of the critical fracture energy and tensile strength of glass lead to a phase-field length-scale parameter that is challenging to resolve in the numerical simulations. Therefore, we show how to determine the fracture energy concerning the applied dimensional reduction and the value of the length-scale parameter relative to the thickness of the plate. The comparison shows that the phase-field models provide very good agreement with the measured stresses and resistance of laminated glass, despite the fact that only one/two cracks are localised using the quasi-static analysis, whereas multiple cracks evolve during the experiment. It was also observed that the stiffness and resistance of the partially fractured laminated glass can be well approximated using a 2D plane-stress model with initially predefined cracks, which provides a better estimation than the one-glass-layer limit.
在报道的整体玻璃板和层压玻璃板的四点弯曲分析中采用了脆性断裂的相场描述。我们的目标是：（i）比较应用于薄玻璃板的不同相场断裂公式；（ii）评估问题尺寸缩减、网格密度和细化的影响；（iii）针对准静态加载验证我们最近为两种常用的由聚乙烯醇缩丁醛或乙烯-醋酸乙烯酯制成的聚合物箔推导的与时间/温度相关的材料特性。由于广泛使用的Bourdin-Francfort-Marigo模型典型的断裂前非线性响应可能导致对薄板弯曲响应的显著高估，数值研究调查了另外两种提供应力-应变图线性弹性阶段的相场断裂模型。玻璃的临界断裂能和抗拉强度的典型值导致一个在数值模拟中难以解析的相场长度尺度参数。因此，我们展示了如何确定与应用的尺寸缩减相关的断裂能以及相对于板厚度的长度尺度参数值。比较表明，尽管使用准静态分析仅定位了一/两条裂纹，而在实验过程中会出现多条裂纹，但相场模型与层压玻璃的测量应力和阻力非常吻合。还观察到，使用具有初始预定义裂纹的二维平面应力模型可以很好地近似部分断裂的层压玻璃的刚度和阻力，这比单层玻璃极限提供了更好的估计。
