The resistance to crack propagation of heterogeneous materials is controlled by their microstructure, which include phase arrangement, presence of inclusions and others. The estimation of the microstructure influence on the overall toughness has a significant engineering relevance, enabling the design of microstructures that maximize fracture resistance. In this work an estimate of the effective toughness of heterogeneous materials is proposed based on the Phase Field Fracture (PFF) model implemented in an FFT homogenization solver. The estimate is based on the simulation of the deformation of representative volume elements of the microstructure, controlled by a constant energy dissipation rate using an arc-length type control. The definition of the toughness corresponds to the total energy dissipated after the total fracture of the RVE —which can be accurately obtained thanks to the dissipation control [1]— divided by the RVE transverse area-. The proposed estimate accounts for both the effect of heterogeneity in toughness and elastic response on the overall fracture energy [2] First, the method is applied to obtain the effective toughness of composites and elastic polycrystals in a series of examples. In the two types of materials, it is found that both heterogeneity in elastic response and fracture energy contribute to increase the effective toughness. Microscopically, it is found that toughening mechanisms are related to the passage of the crack through tougher phases and deviation o the crack path. Then, the PPF-FFT model is extended to study the elasto-plastic fracture of polycrystals. In this case, a crystal plasticity model is used as constitutive equations of the grains and the stored energy is the driving force for crack propagation. The toughening effects due to crack deviations is also observed here, being in this case crack path controlled by the slip systems instead of cleavage planes. REFERENCES [1] P Aranda, J Segurado, A crack-length control technique for phase field fracture in FFT homogenization, International Journal of Numerical Methods in Engineering 126: e7664. 2025 [2] P Aranda, J Segurado, Effective toughness estimation by FFT based phase field fracture: application to composites and polycrystals, Mechanics Research Communications, 2005