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Energy release rates for various defects under different loading conditions

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Abstract

It is well known that the energy release rate associated with translation, rotation and self-similar expansion of defects in solids are expressed by the path-independent integrals J, L, and M, respectively. It is shown that these integrals for a crack or a circular hole may be obtained by first considering an elliptical cavity and then performing a limiting process. This obviates dealing with singularities at the crack tip. The energy release rates for these defects under various mechanical, thermal and electromechanical loading conditions are calculated.

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References

  1. H. M. Westergard, Bearing pressures and cracks, Journal of Applied Mechanics, 49(A) (1939).

  2. J. R. Rice, A path-independent integral and the approximate analysis of strain concentration by notches and cracks, ASME Journal of Applied Mechanics 35 (1968) 379–386.

    Article  Google Scholar 

  3. W. Gunther, Über Einige Randintegrale der Elastomechanik, Abhandlungen der Braunschweigischen Wissenschaftlichen Gesellschaft, XIV, Verlag Friedr. Vieweg & sohn, Braunschweig (1962) 53–72.

    Google Scholar 

  4. J. K. Knowles and E. Sternberg, On a class of conservation laws in linearized and finite elastostatics, Archive for Rational Mechanics and Analysis, 44 (1972) 187–211.

    Article  MathSciNet  MATH  Google Scholar 

  5. L. B. Freund, Stress intensity factor calculations based on a conservational integral, International Journal of Solids and Structures, 14 (1978) 241.

    Article  Google Scholar 

  6. J. H. Park and Y. Y. Earmme, Application of conservative integrals to interfacial crack problems, Mechanics of Materials, 5(3) (1986) 261–276.

    Article  Google Scholar 

  7. Y. H. Chen, M-integral analysis for two dimensional solids with strongly interacting microcracks, Part-I: in an infinite brittle solids, International Journal of Solids and Structures, 38 (2001) 3193–3212.

    Article  MATH  Google Scholar 

  8. Y. Z. Chen, Analysis of L integral and theory of the derivative stress field in plane elasticity, International Journal of Solids and Structures, 40 (2003) 3589–3602.

    Article  MATH  Google Scholar 

  9. Y. Z. Chen and Y. L. Kang, Analysis of M integral in plane elasticity, ASME Journal of Applied Mechanics, 71 (2004) 572–574.

    Article  MATH  Google Scholar 

  10. G. A. Herrmann, Description of the plane crack in terms of local fields verses path independent integrals, in: G. C. Sih, E. Sommer, W. Dahl (Eds.), Application of Fracture Mechanics to Materials and Structures, Martinus Nijhoff Publishers (1983) 571–579.

  11. R. King and G. Herrmann, Nondestructive evaluation of the J and M integrals, ASME Journal of Applied Mechanics, 103(1) (1981) 83–87.

    Article  Google Scholar 

  12. Y. E. Pak, G. A. Herrmann and G. Hermann, Energy release rates for various defects, in: D. O. Thompson, D. E. Chimenti (Eds.), Review of progress in quantitative nondestructive evaluation 2B, Plenum Publishing Corporation (1983) 1389–1397.

  13. Y. E. Pak, Crack extension force in a piezoelectric material, Journal of Applied Mechanics 57 (1990) 647–653.

    Article  MATH  Google Scholar 

  14. Y. E. Pak, Circular inclusion problem in antiplane piezoelectricity, International Journal of Solids and Structures 29 (1992) 2403–2419.

    Article  MATH  Google Scholar 

  15. Y. E. Pak, On the use of path-independent integrals in calculating mixed-mode stress intensity factors for elastic and thermoelastic cases, Journal of Thermal Stresses 33 (2010) 661–673.

    Article  Google Scholar 

  16. Y. E. Pak, Elliptical inclusion problem in antiplane piezoelectricity: implication for fracture mechanics, International Journal of Engineering Science, 48 (2010) 209–222.

    Article  Google Scholar 

  17. B. Budiansky and J. R. Rice, Conservation laws and energy release rates, ASME Journal of Applied Mechanics, 40 (1973) 201.

    Article  MATH  Google Scholar 

  18. G. A. Herrmann and G. Herrmann, On the energy release rate for a plane crack, ASME Journal of Applied Mechanics, 48 (1981) 525–528.

    Article  MATH  Google Scholar 

  19. S. P. Timoshenko and J. N. Goodier, Theory of elasticity, Mc-Graw-Hill (1970).

  20. J. W. Eishen and G. Hermann, Energy release rates and related balance laws in linear elastic defect mechanics, Journal of Applied Mechanics, 109 (1987) 388–392.

    Article  Google Scholar 

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Authors and Affiliations

  1. Advanced Institutes of Convergence Technology, Seoul National University, Suwon, Korea

    Y. Eugene Pak

  2. Department of Mechanical Engineering, Ajou University, Suwon, Korea

    Dhaneshwar Mishra & Seung-Hyun Yoo

Authors
  1. Y. Eugene Pak
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  2. Dhaneshwar Mishra
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  3. Seung-Hyun Yoo
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Correspondence to Y. Eugene Pak.

Additional information

Recommended by Associate Editor Seong Beom Lee

Y. Eugene Pak is currently serving as Director of the Convergence Research Division at the Advanced Institutes of Convergence Technology in Seoul National University. He received his B.S. degree in Mechanical Engineering from the State University of New York at Buffalo in 1980 and M.S. and Ph.D degrees in Mechanical Engineering from Stanford University in 1982 and 1985, respectively. After obtaining his Ph.D. degree, he worked as a Senior Research Scientist at Northrup-Grumman Corporate Research Center. He worked with the Samsung Advanced Institute of Technology (SAIT) from 1995 to 2009 where he conducted research in MEMS, nano and biotechnology.

Dhaneshwar Mishra received his B.E. Degree from MNREC (presently known as MNNIT), India in 1998 and his M.E. Degree at Anna University, Chennai, India in 2003. He completed his Ph.D Degree at Ajou University, Suwon, Korea in 2011 August, and is currently working as a Post Doctoral researcher at the Research Center for Automotive Parts Technology, Ajou University. His areas of interest are computational mechanics of materials, especially defect and fracture mechanics of bio and piezoelectric materials, Design and CAE.

Seung-Hyun Yoo is a professor of the Department of Mechanical Engineering and the Director of the AUCHRD (Ajou University Center for Human Resource Development), Ajou University. He received his B.S. and M.S. degree from Seoul National University in 1977 and 1981 respectively after fulfilling military service as an artillery officer in the Korean army. He then received his Ph.D degree from Stanford University in 1987. Thereafter he worked as a Research Fellow at the University of Michigan and as a Senior Researcher at KIMM (Korea Institute of Machinery and Materials) till he moved to Ajou University in 1990. His research interests cover all aspects of mechanics of thin structures with discontinuities, biomechanics and CAI (computer aided innovation), and SI (systematic innovation) for creative engineering design.

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Eugene Pak, Y., Mishra, D. & Yoo, SH. Energy release rates for various defects under different loading conditions. J Mech Sci Technol 26, 3549–3554 (2012). https://doi.org/10.1007/s12206-012-0870-0

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  • DOI: https://doi.org/10.1007/s12206-012-0870-0

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