Abstract
Mode I near-tip stress fields for elastic perfectly plastic pressure-sensitive materials under plane strain and small-scale yielding conditions are presented. A Coulomb-type yield criterion described by a linear combination of the effective stress and the hydrostatic stress is adopted in the analysis. The finite element computational results sampled at the distance of a few crack opening displacements from the tip show that, as the pressure sensitivity increases, the magnitudes of the normalized radial and hoop stress ahead of the tip decrease, the total angular span of the singular plastic sectors decreases, and the angular span of the elastic sectors bordering the crack surfaces increases. When non-singular T stresses are considered along the boundary layer of the small-scale yielding model, the near-tip stresses decrease as the T stress decreases. The plastic zone shifts toward the crack surfaces as the T stress increases. When the discontinuities of the radial stress and the out-of-plane normal stress along the border between the plastic sector and the elastic sector are allowed, the angular variations of the asymptotic crack-tip fields agree well with those of the finite element computations. Variation of the Q stresses for pressure-sensitive materials can be found from the asymptotic solutions when the plastic zone size ahead of the tip is relatively larger than the crack opening displacement. In addition the T stress is shown to have strong effects on the plastic zone sizes and shapes which could affect the toughening of pressure-sensitive materials.
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References
D. C. Drucker, Metallurgical Transactions 4 (1973) 667–673.
W. A. Spitzig and O. Richmond, Polymer Engineering and Science 19 (1979) 1129–1139.
L. M. Carapellucci and A. F. Yee, Polymer Engineering and Science 26 (1986) 920–930.
B. Budiansky, J. W. Hutchinson and J. C. Lambropoulos, International Journal of Solids and Structures 19 (1981) 337–355.
R. M. McMeeking and A. G. Evans, Journal of the American Ceramic Society 65 (1982) 242–246.
I.-W. Chen and P. E. Reyes Morel, Journal of the American Ceramic Society 69 (1986) 181–89.
P. E. Reyes Morel and I.-W. Chen, Journal of the American Ceramic Society 71 (1988) 343–353.
C.-S. Yu and D. K. Shetty, Journal of the American Ceramic Society 72 (1989) 921–928.
F. Z. Li and J. Pan, Journal of Applied Mechanics 57 (1990) 40–49.
F. Z. Li and J. Pan, Engineering Fracture Mechanics 35 (1990) 1105–1116.
J. W. Hutchinson, Journal of the Mechanics and Physics of Solids 16 (1968) 13–31.
J. W. Hutchinson, Journal of the Mechanics and Physics of Solids 16 (1968) 337–347.
J. R. Rice and G. F. Rosengren, Journal of the Mechanics and Physics of Solids 16 (1968) 1–12.
J. Pan and I. W. Chen, Crack-Tip Fields for Transformation Toughening Materials, presented at the 93rd Annual Meeting of the American Ceramic Society, Cincinnati, Ohio (1991).
P. Dong and J. Pan, International Journal of Solids and Structures 28 (1991) 1113–1127.
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.
C. Bentegón and J. W. Hancock, Journal of Applied Mechanics 58 (1991) 104–110.
A. M. Al-Ani and J. W. Hancock, Journal of the Mechanics and Physics of Solids 39 (1991) 23–43.
Z.-Z. Du and J. W. Hancock, Journal of the Mechanics and Physics of Solids 39 (1991) 555–567.
N. P. O'Dowd and C. F. Shih, Journal of the Mechanics and Physics of Solids 39 (1991) 989–1015.
N. P. O'Dowd and C. F. Shih, Journal of the Mechanics and Physics of Solids 40 (1992) 939–963.
J. R. Rice, in Mechanics of Solids: The R. Hill 60th Anniversary Volume, H. G. Hopkins and M. J. Sewell (eds.), Pergamon Press, Oxford (1982) 539–562.
D. C. Drucker and W. Prager, Quarterly of Applied Mathematics 10 (1952) 157–165.
J. W. Rudnicki and J. R. Rice, Journal of the Mechanics and Physics of Solids 23 (1975) 371–394.
A. Needleman and J. R. Rice, in Mechanics of Sheet Metal Forming D. P. Koistinen and N.-M. Wang (eds.), Plenum Publishing Co. (1978) 237-265.
H.-Y. Jeong, X.-W. Li, A. F. Yee and J. Pan, Mechanics of Materials, in press (1994).
H.-Y. Jeong, A Macroscopic Constitutive Law for Porous Solids with Pressure-Sensitive Matrices and Its Implications for Plastic Flow Localization and Crack-Tip Behavior, Ph.D. thesis, The University of Michigan, Ann Arbor, Michigan (1992).
R. Hill, The Mathematical Theory of Plasticity, Clarendon Press, Oxford (1950).
T. H. Wu, Soil Mechanics. Allyn and Bacon, Boston, Massachusetts (1966).
O. Richmond and W. A. Spitzig, International Union of Theoretical and Applied Mechanics (1980) 377-286.
A. J. Kinloch and R. J. Young, Fracture Behaviour of Polymers, Elsevier Applied Science, London and New York (1983).
I. W. Chen, Journal of the American Ceramic Society 74 (1991) 2564–2572.
P. Dong and J. Pan, Engineering Fracture Mechanics 37 (1990) 43–57.
P. Dong and J. Pan, International Journal of Fracture 45 (1990) 243–262.
J. R. Rice, Journal of Applied Mechanics 35 (1968) 379–386.
J. R. Rice and D. M. Tracey, in Numerical and Computer Methods in Structural Mechanics, S. J. Fenves et al. (eds), Academic Press (1973) 585–623.
P. S. Leevers and J. C. Radon, International Journal of Fracture 19 (1982) 311–325.
R. M. McMeeking, Journal of the Mechanics and Physics of Solids 25 (1977) 357–381.
C. F. Shih, Journal of the Mechanics and Physics of Solids 29 (1981) 305–326.
F. A. McClintock, in Fracture: An Advanced Treatise, Vol. 3, Engineering Fundamentals and Environmental Effects, H. Liebowitz (ed.) Academic Press, New York (1971) 47.
D. M. Tracey, Journal of Engineering Materials and Technology 98 (1976) 146–151.
M. Kim and J. Pan, Effects of Non-Singular Stresses on Crack-Tip Fields for Transformation Toughened Materials: Part I-Plane Strain Case, presented at the 95th Annual Meeting of the American Ceramic Society, Cincinnati, Ohio (1993).
Z. E. A. Ben-Aoun and J. Pan, Effects of Non-Singular Stresses on Crack-Tip Fields for Transformation Toughened Materials: Part II-Plane Stress Case, presented at the 95th Annual Meeting of the American Ceramic Society, Cincinnati, Ohio (1993).
J. Pan, Journal of the Mechanics and Physics of Solids 34 (1986) 263–277.
R. Hill, Proceedings of the Royal Society of London A341 (1948) 281–297.
Z. E. A. Ben-Aoun and J. Pan, Engineering Fracture Mechanics 44 (1993) 649–662.
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Kim, M., Pan, J. Effects of non-singular stresses on crack-tip fields for pressure-sensitive materials, Part 1: Plane strain case. Int J Fract 68, 1–34 (1994). https://doi.org/10.1007/BF00032323
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DOI: https://doi.org/10.1007/BF00032323