Abstract
This paper focuses firstly on the development of a comprehensive anisotropic theory of continuum damage mechanics for brittle solids suffering progressive deterioration. The basic concept of damage parameterization is re-examined and a new set of damage variables introduced yielding a new damage effect tensor through which the effective stress and strain tensors are defined. Constitutive equations of the damaged material are established incorporating a new hypothesis on equivalence between damaged and undamaged responses of the material. The model is completed by introduction of a general damage characteristic tensor which accounts for the experimentally observed fact that the rate of damage growth depends nonlinearly on applied external loads. The established damage model is next applied to investigate the crack-tip shielding effect due to anisotropic microcracking. The ratio of near-tip to remote stress intensity factors is obtained in closed form. A moderate but definite effect of anisotropy of microcracking is observed. The case of isotropic damage is found to be the least effective in screening remote external loads and is in accord with the results obtained by other researchers using different approaches.
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References
R.G. Hoagland and J.D. Embury, Journal of American Ceramic Society 63 (1980) 404–410.
A.G. Evans and K.T. Faber, Journal of American Ceramic Society 64 (1981) 394–398.
Y. Fu and A.G. Evans, Acta Metallurgica 33 (1985) 1515–1523.
A.G. Evans and Y. Fu, Acta Metallurgica 33 (1985) 1525–1531.
M. Ortiz, Journal of Applied Mechanics 54 (1987) 54–58.
J.W. Hutchinson, Acta Metallurgica 35 (1987) 1605–1619.
M. Ortiz, International Journal of Solids and Structures 24 (1988) 231–250.
P. Charalambides and R.M. McMeeking, submitted for publication.
R.G. Hoagland, G.T. Hahn and A.R. Rosenfield, Rock Mechanics (1973) 77–106.
C.C. Wu, S.W. Freiman, R.W. Rice and J.J. Mecholsky, Journal of Materials Science 13 (1978) 2659–2670.
S. Mindess and S. Diamond, Cement and Concrete Research 10 (1980) 509.
A.R. Rosenfield and B.S. Majumdar, Metallurgical Transactions 18A (1987) 1053.
M.J. Owen, in Short Fiber Reinforced Composite Materials, B.A. Sanders (ed.), ASTM STP 772 (1982) 85.
P.T. Curtis, M.G. Bader and J.E. Bailey, Journal of Materials Science 13 (1978) 377.
E.S.M. Chim, Ph.D dissertation, University of Illinois at Urbana-Champaign (1985).
S. Jansson and U. Stigh, Journal of Applied Mechanics 52 (1985) 609.
J.R. Rice, in Fracture, H. Liebowitz (ed.), Vol. 2, Academic Press (1968) 191.
L.M. Kachanov, Izvestiya Akademia Nauk USSR Otd. Tekh. 8 (1958) 26.
Y.N. Rabotnov, Creep Problems in Structural Members, North Holland Publishing Company (1969).
F.A. Leckie and D.R. Hayhurst, Proceedings of the Royal Society of London A 340 (1974) 323–347.
S. Murakami, N. Ohno and D.R. Hayhurst, in IUTAM Symposium on Physical Nonlinearities in Structures, Springer, Berlin (1981) 422–444.
J. Lemaitre, Nuclear Engineering Design 80 (1984) 233–245.
F. Sidroff, in IUTAM Symposium on physical Nonlinearities in Structures, J. Hult and J. Lemaitre (eds.), Springer, Berlin (1981) 237–244.
J.P. Cordebois and F. Sidoroff, Journal de Mecanique Theorique et Appliquee, Numero Special (1980) 45–60.
D. Krajcinovic, Journal of Applied Mechanics 52 (1983) 829–834.
C.L. Chow and J. Wang, International Journal of Fracture 33 (1987) 3–16.
C.L. Chow and J. Wang, Engineering Fracture Mechanics 27 (1987) 547–558.
J.L. Chaboche, Journal of Applied Mechanics 55 (1988) 59–72.
J. Betten, Journal de Mecanique Theorique et Appliquee 2 (1983) 13–32.
J. Lemaitre, Journal of Engineering Materials and Technology 107 (1985) 83–89.
D. Krajcinovic, Damage Mechanics and Continuum Modelling, N. Stubbs and D. Krajcinovic (eds.), ASCE Publications, New York (1985) 39.
S. Murakami, Journal of Applied Mechanics 55 (1988) 280–286.
R. Hill, The Mathematical Theory of Plasticity, Oxford University Press, Oxford (1950).
D.R. Bland, in Proceedings of the 9th International Congress of Applied Mechanics, Bruxelles (1956).
C.L. Chow and J. Wang, Damage Mechanics in Composites, A.S.D. Wang and G.K. Haritos (eds.), The Winter Annual Meeting of ASME (1987) 1–9.
J. Lemaitre, Engineering Fracture Mechanics 25 (1984) 725.
S.S. Wang, E.S.-M. Chim and H. Suemasu, Journal of Applied Mechanics 53 (1986) 339–346.
D.J. Holcomb, Journal of Rheology 28 (1984) 725.
J.W. Hutchinson, Acta Metallurgica 31 (1983) 1079–1088.
J.B. Martin and F.A. Leckie, Journal of the Mechanics and Physics of Solids 20 (1972) 227.
E.D. Case, Journal of Materials Science 19 (1984) 3702–3712.
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Chow, C.L., Lu, T.J. A continuum damage mechanics approach to crack tip shielding in brittle solids. Int J Fract 50, 79–114 (1991). https://doi.org/10.1007/BF00035206
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DOI: https://doi.org/10.1007/BF00035206