Advertisement

Applied Mathematics and Mechanics

, Volume 31, Issue 1, pp 67–76 | Cite as

Interaction between cracks and effect of microcrack zone on main crack tip

  • Xiao-zhou Xia (夏晓舟)Email author
  • Qing Zhang (章青)
  • Pi-zhong Qiao (乔丕忠)
  • Li-juan Li (李丽娟)
Article

Abstract

Mechanism interaction between cracks with different orientation angles is analyzed based on the principle of superposition and a flattening method. It is found that the maximum interaction effect does not occur when the microcrack is along the direction parallel or perpendicular to the principal tensile stress, which is different from the conclusion drawn by Ortiz (1987). The mechanism of microcrack generation and the effect of the microcrack zone on the main crack tip are studied. It is concluded that the microcrack zone has effect on the main crack tip, which increases with the increase of microcrack density and length.

Key words

principle of superposition stress intensity factor interaction effect microcrack zone 

Chinese Library Classification

O346 

2000 Mathematics Subject Classification

74R 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Ortiz, M. A continuum theory of crack shielding in ceramics. Journal of Applied Mechanics, ASME 54(3), 54–58 (1987)zbMATHGoogle Scholar
  2. [2]
    Ortiz, M. and Giannakopoulos, A. E. Maximal crack tip shielding by microcracking. Journal of Applied Mechanics, ASME 56(6), 279–283 (1989)CrossRefGoogle Scholar
  3. [3]
    Kachanov, M. Elastic solids with many cracks: a simple method of analysis. Int. J. Solids Struct. 23(1), 23–43 (1987)zbMATHCrossRefGoogle Scholar
  4. [4]
    Kachanov, M. A simple technique of stress analysis in elastic solids with many cracks. Int. J. Fracture 28(1), R11–R19 (1985)Google Scholar
  5. [5]
    Gao, Y. X., Zheng, Q. S., and Yu, S. W. Microscopic analysis and invariant description of the effective elastic properties of damaged solids-a general theoretic model accounting for interaction of micro-defects (in Chinese). Chinese Journal of Theoretical and Applied Mechanics 30(5), 552–563 (1998)Google Scholar
  6. [6]
    Ju, J. W. and Chen, T. M. Effective elastic moduli of two-dimensional brittle solids with interacting microcracks, part I: basic formulations. Journal of Applied Mechanics, ASME 61(6), 349–357 (1994)zbMATHGoogle Scholar
  7. [7]
    Ju, J. W. and Chen, T. M. Effective elastic moduli of two-dimensional brittle solids with interacting microcracks, part II: evolutionary damage models. Journal of Applied Mechanics, ASME 61(6), 358–368 (1994)CrossRefGoogle Scholar
  8. [8]
    Chen, Y. Z. General case of multiple crack problems in an infinite plate. Engineering Fracture Mechanics 20(4), 591–597 (1984)CrossRefGoogle Scholar
  9. [9]
    Feng, X. Q., Li, J. Y., and Yu, S. W. A simple method for calculating interaction of numerous microcracks and its applications. Int. J. Solids Struct. 40(2), 447–464 (2003)zbMATHCrossRefGoogle Scholar
  10. [10]
    Rose, L. R. F. Microcrack interaction with a main crack. Int. J. Fracture 31(3), 233–242 (1986)CrossRefGoogle Scholar
  11. [11]
    Rubinstein, A. A. Macrocrack interaction with semi-infinite microcrack array. Int. J. Fracture 27(2), 113–119 (1985)Google Scholar
  12. [12]
    Yan, X. Q. An effective numerical approach for multiple void-crack interaction. Journal of Applied Mechanics 73(4), 525–535 (2006)zbMATHCrossRefGoogle Scholar
  13. [13]
    Zeng, Y. S. Theory and Application of Fracture and Damage (in Chinese), Tsinghua University Press, Beijing (1992)Google Scholar

Copyright information

© Shanghai University and Springer Berlin Heidelberg 2010

Authors and Affiliations

  • Xiao-zhou Xia (夏晓舟)
    • 1
    • 2
    • 3
    Email author
  • Qing Zhang (章青)
    • 2
    • 3
  • Pi-zhong Qiao (乔丕忠)
    • 2
    • 3
    • 4
  • Li-juan Li (李丽娟)
    • 1
  1. 1.The Faculty of ConstructionGuangdong University of TechnologyGuangzhouP. R. China
  2. 2.State Key Laboratory of Hydrology-Water Resources and Hydraulic EngineeringHohai UniversityNanjingP. R. China
  3. 3.Department of Engineering MechanicsHohai UniversityNanjingP. R. China
  4. 4.Department of Civil and Environmental EngineeringWashington State UniversityPullmanUSA

Personalised recommendations