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Relationship between the CTOD and the J-integral for stationary and growing cracks. Closed-form solutions

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Abstract

A modified line-plasticity model, involving concept of structured nonlinear zone coupled with the final stretch criterion governing the crack propagation, is used to show the effects of material strain-hardening and the redistribution of strain caused by an advancing quasi-static crack, on the essential parameters pertinent to a mathematical description of elasto-plastic fracture process including its ductile limit. The model links micro-structural and continuum aspects of ductile fracture occurring in dissipative solids equipped with an ability to strain-harden. Attention has been focused on the crack tip opening displacement ( δ_t ) and the J-integral, both associated with either stationary of quasi-static crack contained in a power-hardening material of the Ramberg–Osgood type. The ratios of δ_t and J for a stationary and moving crack are represented via closed-form solutions and then compared against the earlier numerical results of Shih (1981), based on the finite element analyses. Expressions derived here, apart from having a theoretical merit, address an issue of significant interest to the researchers involved in the field of the Experimental Fracture Mechanics.

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References

  • Amazigo, J.C. (1979). Some mathematical problems of elastic-plastic crack-growth. Fracture Mechanics: SIAM-AMS Proceedings; Symposium on Mathematical Problems in Fracture Mechanics (Edited by R. Burridge), New York City, NY, March 28–29, 1978, 125–135.

  • Choroszynski, M. (1996). Experimental studies of CTOD and J-integral in ductile steels. Proceedings of Welding 96; Welding in Power Industry, Serbian Society of Welding, Belgrade, 170–191.

    Google Scholar 

  • Cvijovic, Z. (1997). Quantitative Fractography, Proceedings of 7th International Fracture Mechanics Summer School (Edited by S. Sedmak and A. Sedmak), IFMASS 7, Belgrade.

  • Geric, K. (1997). Final Stretch Zone Measurements, A. Sedmak), IFMASS 7, Belgrade. ibid}.

  • Gocev, J. (1997). Techniques for J-Integral Direct Measurement for Surface Cracks in Bending and Tension, A. Sedmak), IFMASS 7, Belgrade. ibid}.

  • Grabulov, V., Burzic, Z., Veljanovski, B. and Blacic, I. (1997). Laboratory experience in cracked specimens testing, A. Sedmak), IFMASS 7, Belgrade. ibid}.

  • Hutchinson, J.W. and Paris, P.C. (1979). Stability analysis of J-controlled crack growth. Elastic-Plastic Fracture, ASTM-STP 668, American Society for Testing and Materials, Philadelphia, PA, 37–64.

    Google Scholar 

  • McMeeking, R.M. and Parks, D.M. (1979). Criteria for J-dominance of crack-tip fields in large-scale yielding. Elastic-Plastic Fracture, ASTM STP 668, American Society for Testing and Materials, Philadelphia, PA, 175–194.

    Google Scholar 

  • Omidvar, B. and Wnuk, M.P. (1997). Local and global instabilities associated with continuing crack extension in dissipative solids. International Journal of Fracture 84, 237–260.

    Article  Google Scholar 

  • Petrovski, B. (1997). Fracture Toughness Evaluation in Transition Temperature Region, Proceedings of 7th International Fracture Mechanics Summer School (Edited by S. Sedmak and A. Sedmak), IFMASS 7, Belgrade.

  • Rice, J.R. (1967). Stresses due to a sharp notch in a work-hardening elastic-plastic material loaded by longitudinal shear, Trans. ASME 89. Journal of Applied Mechanics 34(2), 287–298.

    MathSciNet  Google Scholar 

  • Rice, J.R. (1968a). Mathematical analysis in the mechanics of fracture. Fracture: an Advanced Treatise (Edited by H. Liebowitz), Academic Press, New York, 191–311.

    Google Scholar 

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

    MathSciNet  Google Scholar 

  • Rice, J.R., Drugan, W.J. and Sham, T.L. (1980). Elastic-plastic analysis of growing cracks. Fracture Mechanics: 12th Conference, ASTM STP 700, 189–221.

  • Shih, C.F. (1981). Relationships between the J-integral and the crack opening displacement for stationary and extending cracks. Journal of the Mechanics and Physics of Solids 29(4), 305–326.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Shoji, T., Takahashi, H., Suzuki, M. and Kondo, T. (1981). A new parameter for characterizing corrosion fatigue crack-growth. Journal of Engineering Materials and Technology, Trans. ASME 103(4), 298–304.

    Article  Google Scholar 

  • Wnuk, M.P. (1997). Final Stretch Zone as a Fracture Mechanics Parameter, Proceedings of 7th International Fracture Mechanics Summer School (Edited by S. Sedmak and A. Sedmak), IFMASS 7, Belgrade.

  • Wnuk, M.P. and Omidvar, B. (1997). Effects of strain hardening on quasi-static fracture in elasto-plastic solid represented by modified yield strip model. International Journal of Fracture 84, 383–403.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering and Mechanics, University of Wisconsin-Milwaukee, P.O. Box 784, Milwaukee, WI, 53201

    Bijan Omidvar (Adj. Assistant Professor)

  2. Department of Civil Engineering and Mechanics, University of Wisconsin-Milwaukee, P.O. Box 784, Milwaukee, WI, 53201

    Michael P. Wnuk (Professor)

  3. Metallurgy, Analytical Process Laboratories, P.O. Box 23785, Milwaukee, WI, 53223

    M. Choroszynski (Technical Director)

Authors
  1. Bijan Omidvar
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  2. Michael P. Wnuk
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  3. M. Choroszynski
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Omidvar, B., Wnuk, M.P. & Choroszynski, M. Relationship between the CTOD and the J-integral for stationary and growing cracks. Closed-form solutions. International Journal of Fracture 87, 331–343 (1997). https://doi.org/10.1023/A:1007498909766

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  • DOI: https://doi.org/10.1023/A:1007498909766

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