An assessment of phase field fracture: crack initiation and growth

Abstract

The phase field paradigm, in combination with a suitable variational structure, has opened a path for using Griffith’s energy balance to predict the fracture of solids. These so-called phase field fracture methods have gained significant popularity over the past decade, and are now part of commercial finite element packages and engineering fitness- for-service assessments. Crack paths can be predicted, in arbitrary geometries and dimensions, based on a global energy minimization—without the need for ad hoc criteria. In this work, we review the fundamentals of phase field fracture methods and examine their capabilities in delivering predictions in agreement with the classical fracture mechanics theory pioneered by Griffith. The two most widely used phase field fracture models are implemented in the context of the finite element method, and several paradigmatic boundary value problems are addressed to gain insight into their predictive abilities across all cracking stages; both the initiation of growth and stable crack propagation are investigated. In addition, we examine the effectiveness of phase field models with an internal material length scale in capturing size effects and the transition flaw size concept. Our results show that phase field fracture methods satisfactorily approximate classical fracture mechanics predictions and can also reconcile stress and toughness criteria for fracture. The accuracy of the approximation is however dependent on modelling and constitutive choices; we provide a rationale for these differences and identify suitable approaches for delivering phase field fracture predictions that are in good agreement with well-established fracture mechanics paradigms. This article is part of a discussion meeting issue ‘A cracking approach to inventing new tough materials: fracture stranger than friction’.

Thermodynamic Conditions for Consolidation of Dissimilar Materials in Bimetal and Functional Graded Structures

“…However, in PD and PF models the criteria for the crack growth is determined as a part of the solution and no external criteria is needed. (iii) Variational phase field methods for fracture are enjoying a notable success [49,50].…”

Phase field fracture predictions of microscopic bridging behaviour of composite materials

“…The composite microstructure is resolved ahead of the crack tip as an embedded cell, while the remaining ply material is homogenised as a transversely-isotropic elastic solid, see Fig. is mainly toughness-dominated due to the initial pre-crack [48]. A cohesive surface contact between fibre and matrix is defined using a quadratic traction-separation law.…”

Micromechanics-based phase field fracture modelling of CNT composites

“…However, discrete methods are limited when dealing with complex crack topologies, arbitrary crack trajectories or the interaction of multiple cracks. Phase field fracture methods have emerged as a promising alternative to discrete approaches [35][36][37]. By using an auxiliary (phase field) variable to track the interface between fractured and unbroken phases, complex cracking phenomena can be captured on the original finite element mesh.…”