Computational methods for fracture analysis of orthotropic functionally graded materials under thermal and hygroscopic loading

In this study, two different computational methods are proposed for the investigation of stress intensity factors, components of J?integral and energy release rate of inclined edge cracks in orthotropic functionally graded materials (FGM) and polymeric graded materials (PGM). The first method is based on Jk?integral, whereas the second is based on the utilization of J1?integral with crack tip displacement field. Accuracy of these methods is tested by a third method, Displacement Correlation Technique (DCT). Due to the inclination of the crack, mixed?mode effects are valid on the material, which is subjected to steady?state thermal and hygroscopic loadings. Analytical formulation is carried out with the use of the constitutive relations of orthotropic plane elasticity problem. Thermomechanical properties of the material models, which are namely elasticity and shear moduli, Poisson ratios, coefficients of thermal conduction and thermal expansion, are assumed to be analytical functions of global coordinates. In order to calculate these material properties at the crack tip, so?called functions are expressed in terms of local coordinates by using coordinate transformation. For the purpose of numerical calculations, Jk?integral is transformed into the Equivalent Domain Integral (EDI), which is widely preferred at fracture analyses of nonhomogeneous materials in literature. Components of J?integral are expressed in terms of finite summations with the adoption of Gauss?Legendre Quadrature. These procedures are integrated into the general purpose finite element analysis software ANSYS for the evaluation of fracture parameters. The temperature and moisture distributions formed in the material are also obtained by this software and used as an input to the structural analysis. Numerical cases are conducted by considering inclined edge cracks located in orthotropic Nickel?Alumina FGM under steady?state thermal loading and orthotropic epoxy?polyurethane PGM under steady?state hygrothermal loading. Effects of crack inclination angle, normalized crack location and normalized crack length on J1? and J2?integrals and stress intensity factors are examined in parametric analyses. As a conclusion, inspection of these computational methods revealed that they are capable of generating consistent results with each other and literature, as well as physically meaningful results for different types of materials.