| Stress concentrations in Nb-Al2 O3 and Cu-Al2O 3 bicrystals caused by common geometrical discontinuities are investigated using the boundary element method in three-dimensional linear, anisotropic elasticity. The analyses are carried out for a plate with a circular hole and a double U-notch bar in tension; the geometric discontinuities being at the bicrystal interface. The material principal axes of the crystals are rotated independently in a parametric study, and the largest normal and von Mises equivalent stresses are determined a short distance away from the free edges of the interface where weak stress singularities exist. Due to the incompatibility of the elastic constants at the interface, the rotation of the material axes can cause the equivalent stress to increase by 71% to 134%, relative to the corresponding isotropic homogeneous cases, and by 28% to 82%, relative to the corresponding isotropic bimaterial cases. The largest increases observed are in the Cu-Al2O3 bicrystal, double U-notch bar problem. It is found as well that rotation of the cubic material principal axis coinciding with the load axis causes very little change in the maximum stresses when compared to other material axis rotations, and rotations of the Nb and Cu material principal axes produce opposing trends. The present work also includes an investigation of the effectiveness of introducing auxiliary holes to decrease the stress concentration for the problem of a bicrystal plate with a circular hole. This is carried out for a range of geometrical parameters. It is demonstrated in this study that a significant decrease in the maximum principal stress at the edge of the hole can be achieved. |
