Abstract
The problem of the evaluation of the stress intensity factors (SIF) at a kinked crack-tip is treated by the use of the most appropriate tool for this problem, the Mellin transform technique. The advantage of this technique lies on the validity of the solution everywhere in the stress field and for every length of the branched crack. Since in the limiting case of the kinked crack, numerical difficulties appear in the evaluation of the kernel functions of the corresponding Fredholm integral-equation system, an asymptotic development, with respect to the length of the kinked crack, is constructed for these functions and therefore for the SIFs at the kinked tip. This analysis yields the interesting result that the SIFs at the crack tip tend to vanish as the kinked crack reduces in length, a result which is similar to the already established behavior of the SIFs at an interfacial tip.
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References
BilbyB.A. and CardewG.E., The Crack with a Kinked Tip, Int. Jnl. Fract., 11 (1975), pp. 708–711.
Gupta G.D., Strain Energy Release Rate for Mixed-Mode Crack Problem, ASME-Paper No. 76-WA/PVP-7.
BilbyB.A. and CardewG.E., Stress Intensity Factors at the Tips of Kinked and Forked Cracks, Fracture 1977, editor TaplinD.M.R., Vol. 3, University of Waterloo Press, Canada, (1977), pp. 197–200.
KarihalooB.L., KeerL.M., Nemat-NasserS., OranratnachaiA., Approximate Description of Crack Kinking and Curving, Inl. Appl. Mech., 48 (1981), pp. 515–519.
HayashiK. and Nemat-NasserS., Energy Release Rate and Crack Kinking under Combined Loading, Jnl. Appl. Mech., 48 (1981), pp. 520–524.
LoK.K., Analysis of Branched Cracks, Jnl. Appl. Mech., 45 (1978), pp. 797–802.
ChatterjeeS.N., The Stress Field in the Neighborhood of a Branched Crack in an Infinite Sheet, Int. Jnl. Solid Struct., 11 (1975), pp. 521–538.
TheocarisP.S. and IoakimidisN., The Symmetrically Branched Crack in an Infinite Elastic Medium, Jnl. Appl. Math. Phys., 27 (1976), pp. 801–814.
TheocarisP.S., Asymmetric Branching of Cracks, Jnl. Appl. Mech., 44 (1977), pp. 611–618.
IoakimidisN. and P.S. Theocaris, Mode-I Stress Intensity Factors of Corner Points in Plane Elastic Media, Engng. Fract. Mech., 13 (1980), pp. 699–708.
WuC.H., Elasticity Problems of a Slender Z-Crack, Jnl. Elastic, 8 (1978), pp. 183–205.
NuismerR.J. and SendeckyjG.P., On the Changing Order of Singularity at Crack Tip, Jnl. Appl. Mech., 44 (1977), pp. 625–630.
Green G., Integral Equation Methods, Thomas Nelson Ltd., (1969), pp. 183–186.
Sneddon I.N., Fouried Transforms, Mc. Graw Hill Co., (1970), pp. 385–390.
SrivastavR.P. and PariharK.S., Dual and Triple Integral Equations Involving Inverse Mellin Transforms, SIAM Jnl. Appl. Math., 16 (1968), pp. 126–133.
MukiR. and WestmannR.A., Crack Emanating from an Open Notch, Jnl. Elastic., 4 (1974), pp. 173–186.
WestmannR.A., Geometrical Effects in Adhesive Joints, Int. Jnl. Engng. Sci., 13 (1974), pp. 369–391.
Doetch G., Guide to the Applications of the Lapalce and Z-Transforms, Van Nostrand Reinhold Co., (1967), p. 128.
VillagioP., Qualitative Methods in Elasticity, Noordhoff International publ., Leyden, (1977), p. 522.
KarpS.N. and KaralC.Jr., The Elastic Field Behaviour in the Neighborhood of a Crack of Arbitrary Angle, Comm. Pur. Appl. Math., 20 (1962), pp. 413–421.
Pogorzelski W., Integral Equations and its Applications, Vol. I., Pergamon Press, (1966), p. 181.
AtkinsonK.E., The Numerical Solution of Fredholm Integral Equations of the Second Kind, SIAM Jnl. Num. Anal., 4, (1967), pp. 337–348.
Atkinson K.E., A Survey on the Numerical Solution of the Fredholm Integral Equations of the Second Kind, SIAM, (1976).
AbramowitzA. and StegunI.A., Handbook of Mathematical Functions, Dover Publications, New York, (1969), p. 890.
KuiperG., Preliminary Design of Ship Lines by Mathematical Methods, Jnl. Ship. Res., 5 (1970), pp. 29–36.
TheocarisP.S., Secondary After-Failure Fractures Due to Transversely Reflected Waves, Engrg. Fract. Mech. 15 (1981) pp. 283–290.
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Theocaris, P.S., Makrakis, G.N. The kinked crack solved by Mellin transform. J Elasticity 16, 393–411 (1986). https://doi.org/10.1007/BF00041764
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DOI: https://doi.org/10.1007/BF00041764