Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Lankford and F.N. Kusenberger, Metallurgical Transactions A 4 (1973) 553–559.
J.D. Eshelby, Proceedings Royal Society, Series A 241 (1957) 376–396.
J.D. Eshelby, Proceedings Royal Society, Series A 252 (1959) 561–569.
M. Shibata and K. Ono, Acta Metallurgica 26 (1978) 921–932.
M. Shibata and K. Ono, Materials Science and Engineering 34 (1978) 131–137.
R.D. Mindlin in Midwestern Conference on Solid Mechanics (1959) 56–59.
T. Mura in Micromechanics of Defects in Solids, 2nd rev. edn., Martinus Nijhoff Publishers, The Netherlands (1987) 112–113.
J.E. DennisJr. and R.B. Schnabel in Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, New Jersey (1983).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mei, Z., Morris, J.W. Stress concentration due to a hemispherical surface inclusion. Int J Fract 64, 43–61 (1993). https://doi.org/10.1007/BF00019624
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00019624