On the conditions at infinity in external crack problems

✍ Scribed by V.I. Fabrikant; T.S. Sankar; G.D. Xistris

• Publisher: Elsevier Science
• Year: 1986
• Tongue: English
• Weight: 313 KB
• Volume: 23
• Category: Article
• ISSN: 0013-7944
• DOI: 10.1016/0013-7944(86)90102-5

✦ Synopsis

The classical approach to external crack problems reduces them to the solution of some equivalent problems for a half-space. It is known that the stresses at the boundary plane z = 0 usually are not in equilibrium, which implies an existence of equilibrating forces and moments at infinity. Recently, Stallybrass published two papers claiming a new approach which makes the total force and the moments at infinity equal to zero. Now, which solution is correct'? The right decision can be made only through a thorough consideration of the conditions at infinity. It is shown that, for an axisymmetric case, the solution by Stallybrass and the classical solution present just two particular cases of an infinite number of solutions possible, each of them being correct and corresponding to some specific conditions at infinity. In the asymmetric case, the solution by Stallybrass is not self-consistent because it implies an interpenetration of the crack faces. Existence of the bending moment at infinity, prescribed by the classical approach, provides the only self-consistent solution.