Phase-field Fracture Modelling of Thin Monolithic and Laminated Glass Plates under Quasi-static Bending

TL;DR

This paper employs phase-field fracture models to analyze thin monolithic and laminated glass plates under quasi-static bending, comparing formulations, assessing dimensional effects, and validating material properties for improved fracture prediction.

Contribution

It compares different phase-field fracture models for thin glass, evaluates dimensional reduction effects, and validates material properties for accurate quasi-static fracture simulation.

Findings

Phase-field models agree well with experimental stresses and resistance.

Linear elastic models better predict crack localization in thin plates.

Partially fractured laminated glass stiffness can be approximated with a 2D plane-stress model.

Abstract

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. So, 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 localised using the quasi-static analysis, whereas multiple cracks evolved during the experiment. It has also been 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.}