Summary
The reflected shadow method of caustics was applited up to now for the study of the stress fields around isolated cracks [1]. In this paper the theory is extended to the general case of an array of collinear asymmetric internal cracks. A rigorous analysis of the interaction between neighboring cracks is developed and the influence of the intererack distance, as related to the size of neighboring cracks, is determined. It is shown that the shape and size of the caustic are dependent on the abovementioned factors. Since the dimensions of the caustic are directly related to the complex stress intensity factor,K *, it is shown that the method is effective in accurately determining the instantaneous value ofK *.
Zusammenfassung
Die Kaustikenmethode wurde bis jetzt nur zur Untersuchung des Spannungsfeldes um isolierte Risse benutzt. In dieser Arbeit wird diese Theorie auf den allgemeineren Fall einer Reihe kollinearer, asymmetrischer, innerer Risse erweitert. Eine strenge Untersuchung der gegenseitigen Beeinflussung benachbarter Risse wird durchgeführt und der Einfluß der Rißentfernung, im Vergleich zur Größe benachbarter Risse, bestimmt. Es wird gezeigt, daß Gestalt und Größe der Kaustik von diesen Faktoren abhängt. Da die Abmessungen der Kaustik in direktem Zusammenbhang zum komplexen KerbspannungsfaktorK * stehen, wird gezeigt, daß die Methode zur genauen Bestimmung des augenblicklichen Wertes vonK * geeignet ist.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Theocaris, P. S.: Local Yielding Around a Crack Tip in Plexiglas. Jnl. Appl. Mech. Trans. ASME37, 409–415 (1970).
Muskhelishvili, N. I.: Some Basic Problems of the Mathematical Theory of Elasticity, 3rd ed., pp. 496–498. (English Translation byRadok, J. R. M.) Holland: P. Noordhoff. 1953.
Irwin, G.: Analysis of Stresses and Strains Near the End of a Crack Traversing a Plate. Jnl. Appl. Mech. Trans. ASME24, 361–364 (1957).
Paris, P. C., andG. Sih: Stress Analysis of Cracks. Fracture Toughness Testing and its Applications. ASTM Spe. Techn. Publ. No 381, pp. 30–83 (1964).
Barenblatt, G. I.: Mathematical Theory of Equilibrium Cracks in Brittle Fracture. Advances in Applied Mechanics, Vol. VII, pp. 55–129. New York: Academic Press. 1962.
Bowie, O. L.: Analysis of an Infinite Plate Containing Radial Cracks Originating from the Boundary of an Internal Circular Hole. Jnl. Math. Physics25, 60–71 (1956).
Erdogan, F.: On the Stress Distribution in Plates with Collinear Cuts under Arbitrary Loads: Proc. 4th U.S. Nat. Cong. Appl. Mech., pp. 547–553 (1962).
Sih, G.: Boundary Problems for Longitudinal Shear Cracks. Proc. Second Conf. Theor. Applied Mechanics, pp. 67–73. New York: Pergamon Press. 1964.
Theocaris, P. S.: Reflected Shadow Method for the Study of Constrained Zones in Cracked Plates. Applied Optics10, 2240–2247 (1971).
Theocaris, P. S.: Interaction Between Collinear Asymmetric Cracks, J. Strain Anal.7, 186–193 (1972).
Favre, H.: Sur une nouvelle méthode d'optique de détermination des tensions interieurs. Revue d'Optique théorique et instrumentale8, 5–8 (1929).
Born, M., andE. Wolf: Principles of Optics, 4th ed., pp. 110–113. London: Pergamon Press. 1970.
Author information
Authors and Affiliations
Additional information
With 8 Figures
Rights and permissions
About this article
Cite this article
Theocaris, P.S. A theoretical consideration of the constrained zones in an array of interacting collinear and asymmetric cracks. Acta Mechanica 17, 169–189 (1973). https://doi.org/10.1007/BF01183753
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01183753