Stress concentration due to a hemispherical surface inclusion

Fatigue cracks often initiate at surface inclusions, and sometimes appear at inclusions within the bulk. To clarify the relative efficiency of these crack sources, an approximate solution for the elastic stress of a hemispherical surface inclusion is provided and compared with the existing result of a spherical interior inclusion. The approximate solution is obtained from the Eshelby solution for the elastic field of an ellipsoid inclusion by introducing the Green's function of an elastic half-space. The numerical calculated results indicate that the stress concentration of a surface inclusion is higher when the inclusion is harder than the matrix, while that of an embedded inclusion is higher when the inclusion is softer than the matrix.