Abstract
The problem of multi-material junctions composed of angularly nonhomogeneous elastic wedges in plane elasticity is addressed. For this new type of grading the governing equation for the Airy stress function is derived and, by applying the eigenfunction expansion method, a fourth-order ODE with nonconstant coefficients for the eigenequation is obtained. The solution to this ODE permits the formulation of an eigenvalue problem similar to that valid for material junctions between homogenous different materials. It is mathematically demonstrated that the angular grading influences the order of the stress-singularity. The potentials of the use of this new class of materials in joining technology are carefully investigated and some illustrative examples are deeply discussed. Comparisons with the corresponding results obtained from homogeneous materials are made.
References
D. Bogy (1968) ArticleTitleEdge-bonded dissimilar orthogonal elastic wedges under normal and shear loading ASME Journal of Applied echanics 25 460–466
D. Bogy (1971) ArticleTitleTwo edge-bonded elastic wedges of different materials and wedge angles under surface tractions ASME Journal of Applied Mechanics 38 377–386
D. Bogy (1974) ArticleTitleThe order of singularity at a multi-wedge corner of a composite plates International Journal of Engineering Science 12 107–120
Carpinteri, A. and Paggi, M. (2005a). Analytical study of the singularities arising at multimaterial interfaces in 2D linear elastic problems. Engineering Fracture Mechanics, in print.
Carpinteri, A. and Paggi, M. (2005b). Influence of the intermediate material on the singular stress field in tri-material junctions. Physico-Chemical Mechanics of Materials, in print.
A. Carpinteri (1987) ArticleTitleStress-singularity and generalized fracture toughness at the vertex of re-entreant corners Engineering Fracture Mechanics 26 143–155 Occurrence Handle10.1016/0013-7944(87)90086-5
F. Delale F. Erdogan (1983) ArticleTitleThe crack problem for a nonhomogeneous plane ASME Journal of Applied Mechanics 50 609–614 Occurrence Handle0542.73118
J. Eischen (1987) ArticleTitleFracture of nonhomogeneous materials International Journal of Fracture 34 3–22
F. Erdogan B. Wu (1997) ArticleTitleThe surface crack problem for a plate with functionally graded properties ASME Journal of Applied Mechanics 64 449–456 Occurrence Handle0900.73615
F. Erdogan (1983) ArticleTitleStress intensity factors ASME Journal of Applied Mechanics 50 992–1002 Occurrence Handle0526.73024
F. Erdogan (1995) ArticleTitleFracture mechanics of functionally gradient materials Composites Engineering 5 753–770 Occurrence Handle10.1016/0961-9526(95)00029-M
G. Golub C. Loan (1996) Matrix Computations. EditionNumber3 The John Hopkins University Press Baltimore, MD
T. Inoue H. Koguchi (1996) ArticleTitleInfluence of the intermediate material on the order of stress singularity in three-phase bonded structure International Journal of Solids and Structures 33 399–417 Occurrence Handle0900.73454
N. Konda F. Erdogan (1994) ArticleTitleThe mixed mode crack problem in a nonhomogeneous elastic plane Engineering Fracture Mechanics 47 533–545 Occurrence Handle10.1016/0013-7944(94)90253-4
S. Pageau P. Joseph S.J. Biggers (1994) ArticleTitleThe order of stress singularities for bonded and disbonded three-material junctions ASME Journal of Applied Mechanics 31 2979–2997 Occurrence Handle0943.74504
Paulino G. (ed.) (2002) Special Issue on Fracture of Functionally Graded Materials, Vol. 69. Engineering Fracture Mechanics.
I. Sneddon (1951) Fourier Transforms McGraw-Hill Book Co., Inc. New York
P. Theocaris (1974) ArticleTitleThe order of singularity at a multi-wedge corner of a composite plate International Journal of Engineering Science 12 107–120 Occurrence Handle10.1016/0020-7225(74)90011-1 Occurrence Handle0272.73038
K. Wieghardt (1907) ArticleTitleÜber das Spalten und Zerreissen elastischer Körper Z. Mathematik und Physik 55 60–103 Occurrence Handle38.0824
M. Williams (1952) ArticleTitleStress singularities resulting from various boundary conditions in angular corners of plates in extension ASME Journal of Applied Mechanics 74 526–528
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Carpinteri, A., Paggi, M. On the Asymptotic Stress Field in Angularly Nonhomogeneous Materials. Int J Fract 135, 267–283 (2005). https://doi.org/10.1007/s10704-005-4087-4
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DOI: https://doi.org/10.1007/s10704-005-4087-4