Abstract
A method of calculating stress intensity factors for branched and bent cracks embedded in an infinite body has been developed. The branches are always assumed to be sharp cracks and are modelled by dislocation distributions. The original crack may be either sharp or of elliptical cross-section with finite root radius. Hence, the method which has a precision ±2%, is also applicable to the study of crack branches emanating from elliptical holes and, approximately, also from notches. The following detailed calculations have been made assuming mode I loading: branched sharp crack with branches of equal and different length, bent sharp crack, and one and two crack branches emanating from the crack with a finite root radius. Bending of a sharp crack under mixed mode loading has also been studied. The criteria of maximum tensile stress and maximum energy release rate used in the study of direction of crack propagation are discussed.
Similar content being viewed by others
References
F. Erdogan, Fracture, vol. II, ed. H. Liebowitz, Academic Press (1968) 498.
M.O. speidel, Theory of Stress corrosion Cracking, NATO Conference Ericeira (1971) 289.
C.S. Carter, Engineering Fracture Mechanics, 3 (1972) 1.
H. Kitagawa, R. Yuuki and T. Ohira, Engineering Fracture Mechanics, 7 (1975) 515.
I.M. Austen, R. Brook and J.M. West, International Journal of Fracture, 12 (1976) 253.
F. Erdogan and G.C. Sih, Transactions of ASME, Series D., Journal of Basic Engineering, 85 (1963) 519.
J.G. Williams and P.D. Ewing, International Journal of Fracture Mechanics, 8 (1972) 441.
M.A. Hussain, S.L. Pu and J. Underwood, Assoc. National Symposium on Fracture Mechanics II, ASTM Special Technical Publication 560 (1973) 2.
G.C. Sih, Transaction of ASME, Series E., Journal of Applied Mechanics, 24 (1965) 51.
E. Smith, Journal of Mechanics and Physics of Solids, 16 (1968) 329.
T. Nahayama, Transactions JSME, 39 (1973) 322.
J.R. Willis, International Journal of Fracture, 11 (1975) 489.
H. Andersson, Journal of Mechanics and Physics of Solids, 17 (1969) 405.
G.C. Sih and P.C. Paris, Transactions of ASME, Series E, 306 (1962).
N.I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Gos. Izdat, Fismatgiz, Moscow (1966) (English translation by J.R.M. Radok, Noordhoff, Leyden, 1975).
H. Andersson, Journal of Mechanics and Physics of Solids, 18 (1970) 437.
H. Kitagawa and R. Yuuki, Transactions JSME, 41 (1975) 346.
S.N. Chatterjee, International Journal of Solids and Structures, 11 (1975) 521.
E. Smith, International Journal of Fracture Mechanics, 1 (1965) 204.
J.F. Kalthoff, International Journal of Fracture Mechanics, 7 (1971) 478.
P.S. Theocaris, Journal of Mechanics and Physics of Solids, 20 (1972) 265.
R.J. Nuismer, International Journal of Fracture, 11 (1975) 245.
V. Vitek, Journal of Mechanics and Physics of Solids, 24 (1976) 67.
J.P. Hirth and J. Lothe, Theory of Dislocations, McGraw-Hill, New York-London (1968).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vitek, V. Plane strain stress intensity factors for branched cracks. Int J Fract 13, 481–501 (1977). https://doi.org/10.1007/BF00034249
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00034249