Summary
The optical method of caustics, as it has been developed by the author, was used for the study of the stress singularity at the singular corner of a bimaterial composite consisting of two materially dissimilar wedges bonded together along either one or two of their interfaces and submitted to any type of loading. The equations of the caustics were derived by putting the complex stress functions of the Muskhelishvili formulation of the plane stress problem in their asymptotic forms, which are valid at the close vicinity of the corner. By comparing the theoretically defined caustics to those obtained by the experiments the order of the elastic stress singularity in the particular cases studied was calculated. The following special cases were considered: (i) a homogeneous wedge with various values of its angle; (ii) Two dissimilar wedges bonded together along one interface to form any part of a plane; (iii) Two dissimilar wedges bonded together along both their interfaces to form a full plane; and (iv) Two dissimilar half-planes bonded together along their interface while an oblique crack is traversing either of the half-planes and terminating at the interface. The values of the elastic stress singularities, as they have been defined experimentally, corroborate the theoretical results.
Zussamenfassung
Die vom Verfasser entwickelte optische Methode der Kaustiken wird für die Untersuchung von Spannungs-Singularitäten an singulären Ecken eines aus zwei materiell verschiedenen Keilen bestehenden, längs einer oder beider Grenzflächen verbundenen Körpers unter dem Einfluss beliebiger Belastungen angewandt. Die Kaustik-Gleichungen werden unter Verwendung von Muskhelishvilis komplexen Spannungsfunktionen in ihren asymptotischen Formen hergeleitet, die in der Nähe der Ecken gültig sind. Die Ordnung der elastischen Spannungs-Singularitäten bei den untersuchten Sonderfällen wurde durch Vergleich zwischen den theoretisch bestimmten und den experimentell gewonnenen Kaustiken ermittlet. Folgende Sonderfälle wurden untersucht: (I) homogene Keile mit verschiedenen Winkeln, (II) zwei verschiedene Keile, die längs einer Grenze verbunden sind und einen Teil der Ebene überdecken, (III) zwei verschiedene Keile, die längs beider Grenzen verbunden sind und eine Ebene bilden, (IV) zwei verschiedene Halbebenen, längs ihrer Grenzen verbunden, wobei ein schräger Riss durch eine Halbebene bis an die Grenze verläuft. Die aus den Versuchen ermittelten Werte von elastischen Spannungs-Singularitäten bestätigen die theoretischen Argebnisse.
Similar content being viewed by others
References
C.J. Tranter,Integral Transforms in Mathematical Physics, 2nd Ed., Chap. V, Wiley, New York 1965.
D.B. Bogy,On the Problem of Edge-Bonded Elastic Quarter Planes Loaded at the Boundary, Int. J. Solids Struct.6, 1287–1313 (1970).
D.B. Bogy andK.C. Wang,Stress Singularities at Interface Corners in Bonded Dissimilar Isotropic Elastic Materials, Int. J. Solids Struct.7, 993–1005 (1971).
D.B. Bogy,Two Edge-Bonded Elastic Wedges of Different Materials and Wedge Angles Under Surface Tractions, J. Appl. Mech.38, 377–386 (1971).
D.B. Bogy,On the Plane Elastostatic Problem of a Loaded Crack Terminating at a Material Interface, J. Appl. Mech.38, 911–918 (1971).
J. Dundurs,Edge-Bonded Dissimilar Orthogonal Elastic Wedges under Normal and Shear Loading (discussion). J. Appl. Mech.36, 650–652 (1969).
P.S. Theocaris,The Order of Singularity at a Multi-Wedge Corner of a Composite Plate, J. Engng. Sci.12, 107–120 (1974).
P.S. Theocaris,Stress Singularities in a Bi-wedge, paper submitted for publication in J. Mech. Phys. Solids.
P.S. Theocaris Local Yielding Around a Crack Tip in Plexiglas, J. Appl. Mech.37, 409–415 (1970).
P.S. Theocaris,Reflected Shadow Method for the Study of Constrained Zones in Cracked Plates, Appl. Optics10, 2240–2247 (1971).
P.S. Theocaris andN. Joakimides,Some Properties of Generalized Epicycloids Applied to Fracture Mechanics, Z. angew. Math. Phys.22, 876–890 (1971).
P.S. Theocaris,Constrained Zones in a Periodic Array of Collinear Equal Cracks, Int. J. Mech. Sci.14, 79–94 (1972).
P.S. Theocaris,Stress Singularities at Concentrated Loads, Exp. Mech.13, 511–518 (1973).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Theocaris, P.S. Stress and displacement singularities near corners. Journal of Applied Mathematics and Physics (ZAMP) 26, 77–98 (1975). https://doi.org/10.1007/BF01596280
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01596280