Graded extended finite elements for stress intensity factor of gradient composites

Graded extended finite element was proposed for fracture characteristic analysis in graded composites whose varying properties were predicted by micromechanics method. The spatially varying stiffness matrix was calculated through the linear interpolation of displacement field and a continuous gradient finite element model was established. The superiority of graded extended finite element method (XFEM) was verified through comparing the results of graded element, homogeneous element and relevant literatures. Furthermore, the influence of material properties on stress intensity factor (SIF) was discussed in detail. The results of graded XFEM can converge to the exact solutions quickly as increasing mesh density, whereas the calculation error of homogeneous XFEM cannot vanish as increasing mesh density, and it rises with the increase of crack length and property gradient. The increase of property gradient and thickness ratio of coating and substrate enlarge the SIF in coating graded material. The increase of crack length and the decrease of thickness ratio of connecting layer and substrate lead to the raise of SIF in connecting graded material.