• Developing a multi-scale method to consider the functionally interphase properties. • Using the Multi-scale strategy in order to investigate the main damage mechanisms. • Multi-scale method is able to accurately investigate the fracture energy and FCPR. • Developing the micromechanical models with consideration FG interphase properties. • The compression between analytical and experimental results shows a good agreement. • Formulation is extremely dependent of the interphase region properties effects. • Evaluating σ cr , and H with consideration functionally interphase properties. Nowadays, novel technologies like nanofillers-based nanocomposites constitute one of the most active research fields in the extremely high performance materials, caused by the fact that this nanomaterial enhances the properties of different polymers in a significant way. Using these materials in polymer structure could enhance the mechanical properties such as fracture energy and fatigue behavior, which caused by variable or cyclic loadings. In the present study, by using the hierarchical multi-scale modeling procedure the fracture toughness (resistance to cracking), fracture energy and fatigue behavior of nanofillers/epoxy nanocomposites with consideration the contributions of the toughening mechanisms of interfacial debonding and plastic void growth in dissipation energy were investigated and discussed. Afterwards, the effect of CNT/matrix interphase on the fracture toughness, fracture energy and fatigue behavior was evaluated by varying the parameters of Young's modulus and thickness of interphase. Furthermore, analysis of multi-scale modeling strategy was utilized in order to assess the influences of interphase properties and interfacial fracture energy on major parameters such as the critical stress debonding stress and radial component of the stress concentration tensor. In addition, different micromechanical models such as Halpin-Tsai and Maxwell and models were utilized to determine the Young's modulus of nanocomposite as functionally graded (FG) interphase properties. Fracture energy and fatigue behavior measurements indicated that the properties of interphase region have a crucial importance on the fracture toughness of CNTs/epoxy nanocomposites. In order to verify the model, comparisons were carried out between the results of model with those predicted by experiments. The consistency between results for most fillers show the good performance of the procedure which has been utilized in this study. [ABSTRACT FROM AUTHOR]