The revisited phase-field approach to brittle fracture: Application to indentation and notch problems

TL;DR

This paper revisits a phase-field model for brittle fracture, validating its predictions against experimental indentation and notch tests on glass and PMMA, enhancing understanding of fracture processes in brittle materials.

Contribution

It extends and validates a comprehensive phase-field theory for brittle fracture by applying it to complex indentation and notch problems, bridging theory and experimental observations.

Findings

The phase-field model accurately predicts fracture initiation and propagation in indentation tests.

The model successfully captures crack paths in notched PMMA beams.

Validation results support the model's applicability to real-world brittle fracture scenarios.

Abstract

In a recent contribution, Kumar, Bourdin, Francfort, and Lopez-Pamies (J. Mech. Phys. Solids 142:104027, 2020) have introduced a comprehensive macroscopic phase-field theory for the nucleation and propagation of fracture in linear elastic brittle materials under arbitrary quasistatic loading conditions. The theory can be viewed as a natural generalization of the phase-field approximation of the variational theory of brittle fracture of Francfort and Marigo (J. Mech. Phys. Solids 46:1319--1342, 1998) to account for the material strength at large. This is accomplished by the addition of an external driving force -- which physically represents the macroscopic manifestation of the presence of inherent microscopic defects in the material -- in the equation governing the evolution of the phase field. The main purpose of this paper is to continue providing validation results for the theory by confronting its predictions with direct measurements from three representative types of experimentally common yet technically challenging problems: $i$) the indentation of glass plates with flat-ended cylindrical indenters and the three-point bending of $ii$) U-notched and $iii$) V-notched PMMA beams.