Crack problems may be solved by first establishing the stress field in the crack's absence and distributing strain nuclei along the line of the crack in order to render its faces traction-free. The relationship between the different possible forms of nucleus and the kinds of singular integral equation to which they lead are explored. The merits of each are then highlighted.
BuecknerH. F.The propagation of cracks and the energy of elastic deformation. Trans. ASME, 1958, 80, 1225–1230.
2.
DundursJ.Elastic interaction of dislocations with inhomogeneities. In Mathematical theory of dislocations, 1969, pp. 70–115 (American Society of Mechanical Engineers, New York).
3.
SchmueserD.ComninouM.DundursJ.Separation and slip between a layer and a substrate caused by a tensile load. Int. J. Engng Sci., 1980, 18, 1149–1155.
4.
NowellD.HillsD. A.Open cracks at or near free edges. J. Strain Analysis, 1987, 22(3), 177–185.
5.
DundursJ.MuraT.Interaction between an edge dislocation and a circular inclusion. J. Mech. Phys. Solids, 1964, 12, 177–189.
6.
DundursJ.SendeckyjG. P.Behaviour of an edge dislocation near a bimetallic interface. J. Appl. Phys., 1965, 36, 3353–3354.
7.
WarrenW. E.The edge dislocation inside an elliptical inclusion. Mechanics of Mater., 1983, 2, 319–330.
8.
AntlasG.SantareM. H.Arbitrarily oriented crack inside an elliptical inclusion. J. Appl. Mech., 1993, 60, 589–594.
9.
BallariniR.LuoH. A.Green's functions for dislocations in strips and related crack problems, Int. J. Fract., 1991, 50, 239–262.
10.
WeeksR.DundursJ.StippesM.Exact analysis of an edge dislocation near a surface layer. Int. J. Engng Sci., 1968, 6, 365–372.
11.
MuskhelishviliN.I. Singular integral equations. Boundary problems of function theory and their application to mathematical physics, 1953 (Noordhoff, Groningen).
12.
ErdoganF.GuptaG. D.CookT. S.Numerical solution of singular integral equations. In Methods of analysis and solution of crack problems (Ed SihG. C.), 1973, pp. 368–425 (Noordhoff, Leyden).
13.
DewynneJ. N.HillsD. A.NowellD.The opening mode displacement of surface-breaking plane cracks. Comp. Meth. in Appl. Mech. and Engng, 1992, 97, 321–331.
14.
KayaA. C.ErdoganF.On the solution of integral equations with strongly singular kernels. Q. Appl. Math., 1987, XLV, 105–122.
15.
KorsunskyA. M.HillsD. A.The solution of plane crack problems by dislocation dipole procedures. J. Strain Analysis, 1995, 30(1), 21–27.
16.
TimoshenkoS. P.GoodierJ. N.Theory of elasticity, 3rd edition, 1970 (McGraw-Hill, London).
17.
MelanE.Der Spannungszustand der durch eine Einzelkraft im Innern beanspruchten Halbscheibe. Z. Angew. Mathematik und Mechanik, 1932, 12, 343–346.
18.
NisitaniH.Solution of notch problems by body force method. In Methods of analysis and solution of crack problems (Ed. SihG. C.), 1973, pp. 1–68 (Noordhoff, Leyden).
19.
SihG. C.LiebowitzH.Mathematical theories of fracture. In Fracture, an advanced treatise (Ed. LiebowitzH.), 1968, pp. 97–99 (Academic Press, New York).
