Summary
The concept of path independent integrals introduced previously for homogeneous media is extended to the case of a crack in the interface between dissimilar half planes. Using any of the pathindependent integrals defined in this paper we obtain the stress intensity factor when the lips of the crack are loaded by identical distributions of stresses in both lips, or by concentrated forces or couples. The above integrals are extended in order to include the case of an arbitrary number of collinear cracks in the interface of two half planes. The case of periodic cracks may be derived from the above analysis. Finally, an interesting generalization may be obtained for the case where arbitrary cracks, inclusions or concentrated forces and couples, not necessarily applied at the lips of the crack, interact.
Übersicht
Das Konzept wegunabhängiger Integrale, welches für homogene Medien früher eingeführt wurde, wird für den Fall eines Risses in einer Grenzfläche zwischen zwei verschiedenen Halbebenen erweitert. Durch Verwendung eines der in dieser Arbeit definierten wegunabhängigen Integrale erhalten wir den Spannungsintensitätsfaktor, wenn die Eißlippen durch an beiden Lippen identisch verteilter Spannungen oder Einzelkräfte oder Momente belastet werden. Die oben genannten Integrale sind erweitert, um den Fall einer willkürlichen Zahl von kollinearen Bissen in der Grenzfläche der Halbebenen einzuschließen. Der Fall von periodischen Rissen kann aus dieser Analysis erhalten werden. Schließlich kann eine interessante Verallgemeinerung für den Fall erhalten werden, daß willkürliche Risse, Einschlüsse oder nicht unbedingt an den Rißlippen wirkende Einzelkräfte und Momente in Wechselwirkung stehen.
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Tsamasphyros, G.J., Theocaris, P.S. Path-independent integrals in inhomogeneous media. Ing. arch 52, 159–166 (1982). https://doi.org/10.1007/BF00535309
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DOI: https://doi.org/10.1007/BF00535309