In this contribution, a variational crack phase‐field model for heterogeneous materials is used to study periodic microstructures. The discontinuity at material interfaces is taken into account by an additional static order parameter. A partial rank‐I relaxation ensures the pointwise fulfillment of the Hadamard jump condition and static equilibrium within the diffuse interface. Crack propagation is investigated for different orientations of hexagonal microstructures and various phenomena like toughening‐by‐weakening and an orientation‐dependent fracture toughness are observed.