General flat crack arbitrarily located in the transversely-isotropic body

The author published an article (Fabrikant, 2011), where the problem of a general flat crack located in the plane, perpendicular to the plane of isotropy, namely, x = 0 was solved. The case of arbitrary normal or tangential loading was considered. A more complicated case of a flat crack, related to arbitrary axes (x1,x2,x3)(x1,x2,x3) was solved in (Fabrikant, 2015). The crack is still located in the plane x1=0x1=0 perpendicular to the planes of isotropy, but the other two axes (x2,x3)(x2,x3) are rotated by angle φ   from the major axes (y,zy,z). We consider here a more complicated case of transversely isotropic body, related to the system of axes (x1,x2,x3)(x1,x2,x3), weakened in the plane x3=0x3=0 by a flat crack of arbitrary shape. We derive the governing integral equation for such general case. As illustrations, we consider the cases of elliptical crack subjected to normal and tangential tractions. We present complete solution for the fields of displacements and stresses as single contour integrals of elementary integrands. We compute stress intensity factors as well.