Modeling of glass exposed to extreme loadings

Abstract

The interest in the load bearing capacity of glass is gradually increasing as a consequence of increased demand for transparency in buildings and vehicles and more strict safety requirements. Due to the stochastic and violent behavior of glass fracture, experimental studies on glass require many repetitions, drastically increasing the experimental cost and environmental impact. For this reason, there is a need for accurate numerical tools that can incorporate the stochastic and violent nature of glass fracture.

With that in mind, this thesis aims to increase the understanding of the mechanical behavior of glass through experimental studies and development of numerical models. The work includes an experimental study on three types of windshields using a new experimental setup that facilitates detailed extraction of important data, such as loading and deformation histories and crack propagation data. The acquired experimental database from the windshield tests was used to verify the performance of the Glass Strength Prediction Model (GSPM) for complex geometries. Furthermore, the GSPM was improved to account for sub-critical crack growth (SCG) and implemented into the commercial finite element (FE) code LS-DYNA, where it works as a fracture initiation trigger for the existing glass material model MAT_280. In relation to the crack propagation behavior of glass, an experimental setup for quasi-statically loaded L-shaped glass specimen was developed to document the crack propagation behavior in terms of propagation path and speed as well as load level. A phase-field approach to fracture was implemented into shell and solid user elements in LS-DYNA with a new crack driving force to simulate the experimental behavior. Furthermore, in collaboration with the Department of Physics at NTNU, a method for characterizing the glass surface flaws using Fourier ptychographic microscopy (FPM) is developed.

The experimental study on windshields revealed a stochastic and size-dependent component strength with varying resulting crack patterns. In addition, circumferential cracks were found to have higher average crack speeds than radial cracks. With the introduction of SCG into the GSPM, the model was shown capable of predicting both the rate- and size-dependent behavior of glass fracture. The GSPM predicted accurate fracture initiation locations on windshields close to the experimental results, and it was found that the maximum flaw depth and the depth-to-half-length ratio of the flaw were the most influential input parameters. The experiments on L-shaped glass specimens showed a positive correlation between the initial crack propagation speed and the critical load level. In addition, a correlation between the crack propagation path and the critical load level was found. An exponential decay was observed in the crack propagation speed with time. With the new crack driving force, the implemented fracture phase-field model proved capable of capturing the initial crack propagation speed for the lowest and highest critical load levels seen in the experiments. However, the crack propagation speed dropped too quickly compared to the experiments, potentially leading to deviations from the experiments in the final part of the predicted crack paths.

Overall, this work has pushed the field of glass modeling one step further, with the introduction of a solver integrated version of the GSPM which can trigger other existing fracture models. In this way, the bar is lowered for incorporating the stochastic behavior of glass fracture in modern design processes where FE simulations are involved. Furthermore, the new crack driving force for the phase-field approach to fracture proved it possible to predict the initial crack propagation speeds for varying critical load levels. Hopefully, these findings will inspire new and extended research in the field of glass modeling