Abstract
The geometry of a thin flat plate containing a curvilinear crack of finite size is investigated. The plate is loaded by uniform bending and torsional moments at infinite distance from the crack contour, while distributed normal bending moments and torques exist at the upper and lower crack surfaces. The bending stress intensity factors for the curvilinear crack are calculated on the basis of classical plate theory. The displacements and internal moments are represented by two complex analytic functions. Extra conditions are imposed to ensure the univalence of the displacements, which is not evident because the plate comprises a multiply connected domain due to the presence of the crack. A linearization with respect to the crack-curvature function has been performed and the bending stress intensity factors are calculated as the first-order solutions for slightly curved cracks. The results are illustrated with a few examples, such as uniform loading configurations and the geometry of a crack along a circular arc. The loading of thin flat plates by a combination of tensile forces and bending moments is also investigated. In analogy with the variation of the stress components over the cross section of the plate, two combined stress intensity factors are introduced having the same dependence on the perpendicular coordinate and being related to the symmetric and anti-symmetric stress intensity factors of the separate plane-stress and bending problems. The resulting energy release rate is shown to be in full agreement with known results in the literature.
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References
S.P. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, McGraw-Hill Kogakusha, Tokyo (1959).
E. Reissner, Transactions of ASME, Journal of Applied Mechanics 12 (1945) A69-A77.
C.Y. Hui and A.T. Zehnder, International Journal of Fracture 61 (1993) 211–229.
B. Cotterell and J.R. Rice, International Journal of Fracture 16 (1980) 155–169.
N.I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen, The Netherlands (1953).
G.N. Savin, Stress Concentration around Holes, Pergamon Press, Oxford (1961).
V.A. Merkulov, Mechanics of Solids 10 (1975) 146–152.
G.C. Sih, P.C. Paris and F. Erdogan, Transactions of ASME, Journal of Applied Mechanics 29 (1962) 306–312.
F. Erdogan, O. Tuncel and P.C. Paris, Transactions of ASME, Journal of Basic Engineering 84 (1962) 542–546.
N.I. Muskhelishvili, Singular Integral Equations, Noordhoff, Groningen, The Netherlands (1953).
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van Vroonhoven, J.C.W. Stress intensity factors for curvilinear cracks loaded by bending and torsional moments. Int J Fract 68, 193–218 (1994). https://doi.org/10.1007/BF00013068
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DOI: https://doi.org/10.1007/BF00013068