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The phase field paradigm, in combination with a suitable variationalstructure, has opened a path for using Griffith's energy balance to predict thefracture of solids. These so-called phase field fracture methods have gainedsignificant popularity over the past decade, and are now part of commercialfinite element packages and engineering fitness-for-service assessments. Crackpaths can be predicted, in arbitrary geometries and dimensions, based on aglobal energy minimisation - without the need for \textit{ad hoc} criteria. Inthis work, we review the fundamentals of phase field fracture methods andexamine their capabilities in delivering predictions in agreement with theclassical fracture mechanics theory pioneered by Griffith. The two most widelyused phase field fracture models are implemented in the context of the finiteelement method, and several paradigmatic boundary value problems are addressedto gain insight into their predictive abilities across all cracking stages;both the initiation of growth and stable crack propagation are investigated. Inaddition, we examine the effectiveness of phase field models with an internalmaterial length scale in capturing size effects and the transition flaw sizeconcept. Our results show that phase field fracture methods satisfactorilyapproximate classical fracture mechanics predictions and can also reconcilestress and toughness criteria for fracture. The accuracy of the approximationis however dependent on modelling and constitutive choices; we provide arationale for these differences and identify suitable approaches for deliveringphase field fracture predictions that are in good agreement withwell-established fracture mechanics paradigms.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

An assessment of phase field fracture: crack initiation and growth