Abstract
For some time now the elastic T-term has been proposed as a secondary “biaxiality” parameter, to be used in conjunction with the stress intensity factor, K I, or the path independent integral J, as the primary parameter for the characterization of crack tip fracture states. At a recent conference a theorem due to Eshelby was presented [1]. The theorem provides a convenient method of calculating the T-term, obtained by evaluating appropriate J contour integrals. Examples of analytical, semi-analytical and numerical applications were included. Here, some additional finite element applications, using a fairly simple idealization, are presented in greater detail and comparison of the results of the different independent analyses available so far are made, giving further evidence of the practical utility of Eshelby's method. New results on double-edge notched specimens are also included.
Résumé
On a proposé depuis un certain temps déjà, que le terme T élastique soit considéré comme un paramètre de biaxialité secondaire, à utiliser de concert avec le factuer d'intensité de contraintes KI, on l'intégrale J, en tant que paramètre primaire, pour caractériser les états de la rupture à l'extrémité d'une fissure. Lors d'une conférence récente, on a présenté un théorème, dû à Eshelby, qui fournit une méthode commode pour calculer le terme T, obtenue par une évaluation des intégrales de contour J appropriées. On a inclu des exemples d'applications analytiques, semianalytiques et numériques. Dans la présente étude, on donne avec de plus amples détails quelques applications complémentaires des éléments finis, en utilisant une idéalisation assez simple, et l'on compare les résultats de diverses analyses disponibles jusqu'ici, ce qui convainc de l'utilité pratique de la méthode d'Eshelby.
On inclut également des résultats nouveaux obtenus sur des éprouvettes à double entaille latérale.
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References
G.E. Cardew, M.R. Goldthorpe, I.C. Howard and A.P. Kfouri, in Fundamentals of Deformation and Fracture, Proceedings of the Eshelby Memorial Symposium (ed.) B.A. Bilby, K.J. Miller and J.R. Willis, Sheffield 2–5 April 1984, Cambridge University Press (1985).
J.R. Rice, in Fracture, An Advanced Treatise, Vol. II (ed.) H. Liebowitz, Academic Press (1968) 191–311.
M.F.Ashby, C.Gandhi and D.M.R.Taplin, Acta Metallurgica 27 (1979) 699–729.
A.P. Kfouri and J.R. Rice, Fracture 77, Advances in Research on the Strength and Fracture of Materials, D.M.R. Taplin (ed.) Vol. I, Pergamon Press (1978) 41–60.
A.P.Kfouri and K.J.Miller, Proceedings Institute of Mechanical Engineers 190 (paper 48/76) (1976) 571–584.
A.P. Kfouri, “On Double Limits and Asymptotic Small Scale Yielding Solutions of Crack Tip Fields”, paper presented at the Symposium on Energy Release Rates and Path Independent Integrals in Defect and Fracture Mechanics, Bad Honnef, F.R.G., Jan 9–11, 1985.
P.D.Hilton, International Journal of Fracture 9 (1973) 143–156.
K.J.Miller and A.P.Kfouri, International Journal of Fracture 10 (1974) 393–404.
A.P. Kfouri and K.J. Miller, Fracture 77, Advances in Research on the Strength and Fracture of Materials, D.M.R. Taplin (ed.) Vol. 3, Pergamon Press (1978) 241–246.
K.J. Miller and A.P. Kfouri, in ASTM STP 668 (1977) 214–228.
J.Eftis, N.Subramonian and H.Liebowitz, Engineering Fracture Mechanics 9 (1977) 753–764.
P.S.Theocaris and E.Gdoutos, Engineering Fracture Mechanics 7 (1975) 331–340.
B.Cotterell, International Journal of Fracture Mechanics 2 (1966) 526–533.
P.S.Leevers, J.C.Radon and L.E.Culver, Journal of the Mechanics and Physics of Solids 24 (1976) 381–395.
H. Kitagawa and R. Yuuki, Fracture 77, Advances in Research on the Strength and Fracture of Materials, D.M.R. Taplin (ed.) 3, Pergamon Press (1978) 201–211.
B.Cotterell and J.R.Rice, International Journal of Fracture 16 (1980) 155–169.
S.G.Larsson and A.J.Carlsson, Journal of the Mechanics and Physics of Solids 21 (1973) 263–277.
J.R.Rice, Journal of the Mechanics and Physics of Solids 22 (1974) 17–26.
T.M.Edmunds and J.R.Willis, Journal of the Mechanics and Physics of Solids 25 (1977) 423–455.
M.L.Williams, Journal of Applied Mechanics 24 (1957) 109–114.
P.S.Leevers and J.C.Radon, International Journal of Fracture 19 (1982) 311–325.
J.Boussinesq, Application des Potentiels a l'Etude de l'Equilibre et du Mouvement des Solides Elastiques, Gauthier-Villars, Paris (1885).
J.H.Michell, Proceedings London Mathematics Society 32 (1900) 35.
S.P. Timoshenko and Goodier, Theory of Elasticity, 3rd edition, McGraw-Hill, Inc. (1970).
J.R.Rice and G.F.Rosengren, Journal of the Mechanics and Physics of Solids 16 (1968) 1–12.
D.P. Rooke and D.J. Cartwright, Compendium of Stress Intensity Factors, H.M.S.O. (1976).
K.J. Knott, Fundamentals of Fracture Mechanics, Butterworths (1973).
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Kfouri, A.P. Some evaluations of the elastic T-term using Eshelby's method. Int J Fract 30, 301–315 (1986). https://doi.org/10.1007/BF00019710
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DOI: https://doi.org/10.1007/BF00019710