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Approximate Stress Intensity Factors (SIFs) for a semi-circular surface crack in arbitrary elastic finite and infinite bodies are presented. Utilizing General Point Load Weight Function (GPLWF) concept, an explicit expression is derived to determine SIFs for semi-circular cracks subjected to uniform, linear, and nonlinear loads. The presented formulation not only provides a solution for cracked bodies subjected to arbitrary two-dimensional stress distribution on the crack faces, but also could present SIFs for any point on the crack front. The results of the presented formulation for special cases, i.e. semi-circular cracks in a finite thickness plate subjected to complicated loadings, central and non-central semi-circular cracks in finite-length thick-walled cylinders subjected to a uniform internal pressure, and central semi-circular cracks in an infinite-length thick-walled cylinder subjected to a non-uniform internal pressure are compared with the available results in the literature and those obtained through FEM, indicating a very good accuracy. The proposed procedure will be generalized for semi-elliptical cracks in arbitrary structures and mixed mode loading in future. [ABSTRACT FROM AUTHOR]

• Using 2-D WF for investigation of a fully closed 2-D subsurface crack. • Growth pattern determination for an elliptical crack under moving contact pressure. • History of SIFs calculation for subsurface cracks under subsurface shear stresses. • Validating WFM as a simple tool for the engineers to evaluate fatigue life. In the present study, weight function (WF) method was used to investigate the propagation pattern of a two-dimensional parallel subsurface crack under a moving contact pressure. Under contact loading, the crack was fully closed and only shear fracture modes led to the propagation. At first, the histories of stress intensity factors (SIFs) were calculated using the available two-dimensional WFs. Then, the SIFs range for four main points along the crack front and the Paris Law were utilized to determine step by step propagation. Results revealed WF method as an efficient method for fatigue analysis of fully closed cracks. [ABSTRACT FROM AUTHOR]

• 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]