  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 minimisation - without the need for \textit{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.
