Methods for calculating stress intensity factors in anisotropic materials: Part I—z = 0 is a symmetric plane

The problem of a crack in general anisotropic material under LEFM conditions is presented. In Part I, three methods are presented for calculating stress intensity factors for various anisotropic materials in which z = 0 is a plane of symmetry. All of the methods employ the displacement field obtained by means of the finite element method. The first one is known as displacement extrapolation and requires the values of the crack face displacements. The other two are conservative integrals based upon the J-integral. One employs symmetric and asymmetric fields to separate the mode I and II stress intensity factors. The second is the M-integral which also allows for calculation of K_I and K_II separately.All of these methods were originally presented for isotopic materials. Displacement extrapolation and the M-integral are extended for orthotropic and monoclinic materials, whereas the J_I- and J_II-integrals are only extended for orthotropic material in which the crack and material directions coincide. Results are obtained by these methods for several problems appearing in the literature. Good to excellent agreement is found in comparison to published values. New results are obtained for several problems.In Part II, the M-integral is extended for more general anisotropies. In these cases, three-dimensional problems must be solved, requiring a three-dimensional M-integral.