Numerical Study on the Determination of Crack Initiation Angle, Stress Field and Stress Triaxiality at Crack Tip in a Cracked Beam of Functionally Graded Material

The purpose of this study is to determine the crack initiation angle and stress field at and around the crack tip during initial crack propagation in a cracked beam of a functionally graded material (FGM). The distribution of stresses developed in the varied elastic modulus directions is determined numerically using extended finite element method (XFEM). A complete numerical analysis has been performed using a finite element model to evaluate the level of crack angle and structural stresses in the crack tip zone, crack growth zone and crack propagation zone. Dummy thermal loads are used to represent the functionally graded material properties and different initial crack lengths are considered. An XFEM subroutine file was used to develop the enrichment function model for simulation of the crack growth process during the numerical analysis. It was seen that high crack initiation angle arises in large initial crack length and that as the initial crack length ‘a’ increases the crack initiation angle ‘ϴ’ also increases. In the crack tip region, the axial stresses are tensile and exhibit tensile behavior along the elastic modulus ratio direction up to a depth of more than 45% of the height of FGM beam, whereas the shear stresses were found to be significantly volatile in nature. The results display that the stresses produced at outer surface region of crack zones are affected due to expansion of crack tip zone. During the crack growth process, the bending effect created is principally accountable for the distribution of stresses in the crack zone.