  This paper investigates the effects of plasticity on the effective fracture
toughness. A layered material is considered as a modelling system.
  An elastic-plastic phase-field model and a surfing boundary condition are
used to study how the crack propagates throughout the material and the
evolution of the effective toughness as a function of the layer angle. We first
study three idealized situations, where only one property among fracture
toughness, Young's modulus and yield strength is heterogeneous whereas the
others are uniform. We observe that in the case of toughness and strength
heterogeneity, the material exhibits anomalous isotropy: the effective
toughness is equal to the largest of the point-wise values for any layer angle
except when the layers are parallel to the macroscopic direction of
propagation. As the layer angle decreases, the crack propagates along the
brittle-to-tough interfaces, whereas it goes straight when the layers have
different yield strength but uniform toughness. We find that smooth deflections
in the crack path do not induce any overall toughening and that the effective
toughness is not proportional to either the cumulated fracture energy or the
cumulated plastic work. In the case of elastic heterogeneity, the material is
anisotropic in the sense of the effective toughness, as the latter varies as a
function of the layer angle. Four toughening mechanisms are active: stress
fluctuations, crack renucleation, plastic dissipation and plastic blunting.
Finally, we consider a layered medium comprised of compliant-tough-weak and
stiff-brittle-strong phases, as it is the case for many structural composites.
We observe a transition from an interface-dominated to a plasticity-dominated
failure regime, as the phase constituents become more ductile. The material is
anisotropic in the sense of the effective toughness.
