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

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.

arXiv comment5 pages, 4 figures, Supplemental Material

References in corpus (20)

• Phase-Field Model of Mode III Dynamic Fracture
• Laws of crack motion and phase-field models of fracture
• Morphogenesis and propagation of complex cracks induced by thermal shocks
• Origin of Crack Tip Instabilities
• Unsteady Crack Motion and Branching in a Phase-Field Model of Brittle Fracture
• Phase field modeling of crack propagation
• The Dynamics of Rapid Fracture: Instabilities, Nonlinearities and Length Scales
• The Breakdown of Linear Elastic Fracture Mechanics near the Tip of a Rapid Crack
• Instability in dynamic fracture and the failure of the classical theory of cracks
• Phase Field Modeling of Fast Crack Propagation
• Oscillations in Rapid Fracture
• Weakly Nonlinear Theory of Dynamic Fracture
• Dynamics of Simple Cracks
• The 1/r singularity in weakly nonlinear fracture mechanics
• Study of the branching instability using a phase field model of inplane crack propagation
• Topological defects govern crack front motion and facet formation on broken surfaces
• Branching Instabilities in Rapid Fracture: Dynamics and Geometry
• Dynamic Crack Tip Equation of Motion: High-speed Oscillatory Instability
• An intrinsic nonlinear scale governs oscillations in rapid fracture
• Crack propagation as a free boundary problem

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