Abstract
PurposeThe purpose of this paper is to present special nine‐node quadrilateral elements to discretize the un‐cracked boundary and the inclined surface crack in a transversely isotropic cuboid under a uniform vertical traction along its top and bottom surfaces by a three‐dimensional (3D) boundary element method (BEM) formulation. The mixed‐mode stress intensity factors (SIFs), KI, KII and KIII, are calculated.Design/methodology/approachA 3D dual‐BEM or single‐domain BEM is employed to solve the fracture problems in a linear anisotropic elastic cuboid. The transversely isotropic plane has an arbitrary orientation, and the crack surface is along an inclined plane. The mixed 3D SIFs are evaluated by using the asymptotical relation between the SIFs and the relative crack opening displacements.FindingsNumerical results show clearly the influence of the material and crack orientations on the mixed‐mode SIFs. For comparison, the mode‐I SIF when a horizontal rectangular crack is embedded entirely within the cuboid is calculated also. It is observed that the SIF values along the crack front are larger when the crack is closer to the surface of the cuboid than those when the crack is far away from the surface.Research limitations/implicationsThe FORTRAN program developed is limited to regular surface cracks which can be discretized by the quadrilateral shape function; it is not very efficient and suitable for irregular crack shapes.Practical implicationsThe evaluation of the 3D mixed‐mode SIFs in the transversely isotropic material may have direct practical applications. The SIFs have been used in engineering design to obtain the safety factor of the elastic structures.Originality/valueThis is the first time that the special nine‐node quadrilateral shape function has been applied to the boundary containing the crack mouth. The numerical method developed can be applied to the SIF calculation in a finite transversely isotropic cuboid within an inclined surface crack. The computational approach and the results of SIFs are of great value for the modeling and design of anisotropic elastic structures.
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