  Fracture of materials with rate-dependent mechanical behaviour, e.g.
polymers, is a highly complex process. For an adequate modelling, the coupling
between rate-dependent stiffness, dissipative mechanisms present in the bulk
material and crack driving force has to be accounted for in an appropriate
manner. In addition, the fracture toughness, i.e. the resistance against crack
propagation, can depend on rate of deformation. In this contribution, an
energetic phase-field model of rate-dependent fracture at finite deformation is
presented. For the deformation of the bulk material, a formulation of finite
viscoelasticity is adopted with strain energy densities of Ogden type assumed.
The unified formulation allows to study different expressions for the fracture
driving force. Furthermore, a possibly rate-dependent toughness is
incorporated. The model is calibrated using experimental results from the
literature for an elastomer and predictions are qualitatively and
quantitatively validated against experimental data. Predictive capabilities of
the model are studied for monotonic loads as well as creep fracture.
Symmetrical and asymmetrical crack patterns are discussed and the influence of
a dissipative fracture driving force contribution is analysed. It is shown
that, different from ductile fracture of metals, such a driving force is not
required for an adequate simulation of experimentally observable crack paths
and is not favourable for the description of failure in viscoelastic rubbery
polymers. Furthermore, the influence of a rate-dependent toughness is discussed
by means of a numerical study. From a phenomenological point of view, it is
demonstrated that rate-dependency of resistance against crack propagation can
be an essential ingredient for the model when specific effects such as
rate-dependent brittle-to-ductile transitions shall be described.
