  In this work, we extend the recently proposed adaptive phase field method to
model fracture in orthotropic functionally graded materials (FGMs). A recovery
type error indicator combined with quadtree decomposition is employed for
adaptive mesh refinement. The proposed approach is capable of capturing the
fracture process with a localized mesh refinement that provides notable gains
in computational efficiency. The implementation is validated against
experimental data and other numerical experiments on orthotropic materials with
different material orientations. The results reveal an increase in the
stiffness and the maximum force with increasing material orientation angle. The
study is then extended to the analysis of orthotropic FGMs. It is observed
that, if the gradation in fracture properties is neglected, the material
gradient plays a secondary role, with the fracture behaviour being dominated by
the orthotropy of the material. However, when the toughness increases along the
crack propagation path, a substantial gain in fracture resistance is observed.
