Abstract Boundary problems for a circular elastic insert bonded partially to the interior of an infinite medium of another material are formulated and solved in closed form. The unbonded portions of the interface may be regarded as circular arcs of discontinuities or curved cracks. By application of the complex function theory dealing with sectionally holomorphic functions, the present problem is reduced to the solution of the problem of linear relationship or Hilbert problem. Exact solutions to several examples of theoretical and practical importance are obtained. They include the cases of uni-axial tension applied at infinity and concentrated forces located in the insert and/or the surrounding material. Contact stresses are computed and compared to those for perfect bonding. It is found that the stresses near the tips of a curved crack possess the same trig-log character of singularity as those obtained for a straight crack between dissimilar media. Formulas for finding the crack-tip stress-intensity factors, employed m the Griffith-Irwin theory of fracture, are also derived.
[1]
A. H. England.
A Crack Between Dissimilar Media
,
1965
.
[2]
J. Rice,et al.
Plane Problems of Cracks in Dissimilar Media
,
1965
.
[3]
N. Muskhelishvili.
Some basic problems of the mathematical theory of elasticity
,
1953
.
[4]
P. C. Paris,et al.
Crack-Tip, Stress-Intensity Factors for Plane Extension and Plate Bending Problems
,
1962
.
[5]
John Dundurs,et al.
The Elastic Plane With a Circular Insert, Loaded by a Radial Force
,
1961
.
[6]
John R. Rice,et al.
The Bending of Plates of Dissimilar Materials With Cracks
,
1964
.
[7]
R. Salganik,et al.
The brittle fracture of cemented bodies
,
1963
.
[8]
J. Dundurs,et al.
The Elastic Plane With a Circular Insert, Loaded by a Tangentially Directed Force
,
1962
.
[9]
M. Williams.
The stresses around a fault or crack in dissimilar media
,
1959
.