Universality and stability phase-diagram of two-dimensional brittle fracture

TL;DR

This paper demonstrates the universal nature of oscillatory crack instability in brittle materials and presents a comprehensive stability phase-diagram that is independent of near-tip nonlinearities.

Contribution

It reveals the universal character of crack instabilities and provides a phase-diagram for brittle fracture that is robust across different nonlinear elastic conditions.

Findings

Oscillatory crack instability is universal across different materials.

The oscillation wavelength follows a universal master curve.

High-velocity tip-splitting instability occurs with increased driving force.

Abstract

The two-dimensional oscillatory crack instability, experimentally observed in a class of brittle materials under strongly dynamic conditions, has been recently reproduced by a nonlinear phase-field fracture theory. Here we highlight the universal character of this instability by showing that it is present in materials exhibiting widely different near crack tip elastic nonlinearity, and by demonstrating that the oscillations wavelength follows a universal master curve in terms of dissipation-related and nonlinear elastic intrinsic length scales. Moreover, we show that upon increasing the driving force for fracture, a high-velocity tip-splitting instability emerges, as experimentally demonstrated. The analysis culminates in a comprehensive stability phase-diagram of two-dimensional brittle fracture, whose salient properties and topology are independent of the form of near tip nonlinearity.