The main objective of this work is to present a numerical modeling of crack propagation path in isotropic functionally graded materials (FGMs) under mixed-mode loadings. The displacement extrapolation technique (DET) and the maximum circumferential stress (MCS) criterion are investigated in the context of crack growth in functionally graded beam subject to three and four bending conditions. Using the Ansys Parametric Design Language (APDL), the variation continues of the material properties are incorporated by specifying the material parameters at the centroid of each finite element (FE) and the crack direction angle is evaluated as a function of stress intensity factors (SIFs) at each increment of crack extension. In this paper, two applications are investigated using an initial crack perpendicular and parallel to material gradient, respectively. The developed approach is validated using available numerical and experimental results reported in the literature.

In this study, the finite element method is applied to investigate the mechanical behavior of aluminium notched structures reinforced by composite patch. In order to evaluate the efficiency of patches in the case of lateral semicircular and V-notches, it is very important to analyze the stress distribution at the notch tip and to take in consideration the influence of the geometrical and mechanical properties of the patch and the adhesive. Simple and double patch were used as reinforcement techniques. Results showed that the stress concentration factor is reduced at the notch tip by using a double patch reinforcement. This reduction becomes more noticeable when the patch thickness increases.