Skip to main content
SpringerLink
Log in

New description of microcrack damage based on conservation laws

  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

This paper presents a new description for brittle solids with microcracks under plane strain assumption. The basic idea is to extend the conservation laws such as theJ j-vector andM-integral analysis used in single crack problems to strongly interacting crack problems. TheM-integral contains two distinct parts. One of them is a summation from the well-known relation between theM-integral and the stress intensity factors (SIF) at both tips of each crack. The other, called as the additional contribution, is obtained from the two components of theJ j-vector and the coordinates of each microcrack center in a global system. Of great significance is the clarification of the confusion about the dependence of theM-integral on the origin selection of global coordinates, provided that the vector vanishes at infinity and that the closed contour chosen to calculate the integral and the vector encloses all the microcracks completely. TheM-integral is equivalent to the decrease of the total potential energy of the microcracking solids with the strong interaction being taken into account. TheM-integral analysis, from a physical point of view, does play an important role in evaluating the damage level of brittle solids with strongly interacting microcracks.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kachanov LM. Time of the rupture process under creep conditions.Izv Akad Nauk SSR Otd Tekh Nauk, 1958, (8): 26–31

    MATH  Google Scholar 

  2. Chaboche JL. Continuum damage mechanics: Part I, General concepts.ASME J Applied Mech, 1988, 55: 59–64

    Article  Google Scholar 

  3. Chaboche JL. Continuum damage mechanics: Part II, Damage growth, crack initiation, and crack growth.ASME J Applied Mech, 1988, 55: 65–72

    Article  Google Scholar 

  4. Christensen RM. A critical evaluation for a class of micromechanics models.J Mech Phys Solids, 1990, 38: 379–404

    Article  Google Scholar 

  5. Kachanov M. Elastic solids of many cracks and related problems.Advances of Applied Mechanics, 1993, 30: 259–428

    Article  Google Scholar 

  6. Jun JW, Lee X. On three-dimensional self-consistent micromechanical damage models for brittle solids: Part I, Tensile loadings.ASCE J Engng Mech, 1991, 117: 1495–1515

    Google Scholar 

  7. Jun JW, Chen TM. Effective elastic moduli of two-dimensional brittle solids with interacting microcracks: Part I, Stational.ASME J Appl Mech, 1994, 61: 349–357

    Google Scholar 

  8. Jun JW, Chen TM. Effective elastic moduli of two-dimensional brittle solids with interacting microcracks: Part II, Evolutionary damage models.ASME J Appl Mech, 1994, 61: 358–366

    Google Scholar 

  9. Krajcinovic D. Damage mechanics.Mechanics of Materials, 1989, 8: 117–197

    Article  Google Scholar 

  10. Budiansky B, Rice JR. Conservation laws and energy-release rates.ASME Journal of Applied Mechanics, 1973, 40: 201–203

    MATH  Google Scholar 

  11. Knowles JK, Sternberg E. On a class of conservation laws in linearized and finite elastostatics.Arch Rat Mech Anal, 1972, 44: 187–211

    Article  MATH  MathSciNet  Google Scholar 

  12. Chen YH.M-integral analysis for two-dimensional solids with strongly interacting cracks: Part I, In an infinite brittle sold.international Journal of Solids and Structures, 2001, 38(18): 3193–3212

    Article  MATH  Google Scholar 

  13. Chen YM.M-integral analysis for two-dimensional solids with strongly interacting cracks: Part II, In the brittle phase of an infinite metal/ceramic bimaterial.International Journal of Solids and Structures, 2001, 38(18): 3213–3232

    Article  Google Scholar 

  14. Gross D. Sponnuny sintensitatsfaktoren von ribsystemen (stress intensity factors of system of cracks).Ing-Arch, 1982, 51:301–310 (in German)

    Article  MATH  Google Scholar 

  15. Chen YZ. General case of multiple crack problems in an infinite body.Engineering Fracture Mechanics, 1984, 20: 591–597

    Article  Google Scholar 

  16. Suo Z. Zener's crack and theM-integral.ASME Journal of Applied Mechanics, 2000, 67: 417–418

    Article  MATH  Google Scholar 

  17. Freund LB. Stress intensity factor calculation based on a conservation integral.Int J Solids Structures, 1978, 14: 241–250

    Article  Google Scholar 

  18. Herrmann GA, Hermann G. On energy release rates for a plane cracks.ASME J Applied Mech, 1981, 48: 525–530

    Article  MATH  Google Scholar 

  19. Zhao LG, Chen YH. Further investigation of subinterface cracks.Archive of Applied Mechanics, 1997, 67: 393–406

    Article  MATH  Google Scholar 

  20. Zhao LG, Chen YH. On the contribution of subinterface microcracks near the tip of an interface crack to theJ-integral in bimaterial solids.Int J Engng Sci, 1997, 35: 387–407

    Article  MATH  Google Scholar 

  21. Chen YH, Lu TJ. Conservation laws of theJ k-vector for microcrack damage in piezoelectric materials.International Journal of Solids and Structures, 2001, 38(18): 3232–3249

    MATH  Google Scholar 

  22. King RB, Herrmann G. Nondestructive evaluation of theJ-andM-integrals.ASME J Applied Mech, 1981, 48: 83–87

    Article  MATH  Google Scholar 

  23. Kanninen MF, Popelar CF. Advanced Fracture Mechanics. New York: Oxford University Press, 1985

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Civil Engineering and Mechanics, Xi'an Jiaotong University, 710049, Xi'an, China

    Chen Yiheng

Authors
  1. Chen Yiheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The projec supported by the National Natural Science Foundation of China (19891180)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yiheng, C. New description of microcrack damage based on conservation laws. Acta Mech Sinica 18, 429–440 (2002). https://doi.org/10.1007/BF02486569

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02486569

Key Words

Search

Navigation