Abstract
The approximate solutions for calculation of the energy J-integral of a body both with a notch and with a crack under elastic-plastic loading have been obtained. The crack is considered as the limit case of a sharp notch. The method is based on stress concentration analysis near a notch/crack tip and the modified Neuber's approach. The HRR-model and the method based on an equation of equilibrium were also employed to calculate the J-integral. The influence of the strain hardening exponent on the J-integral is discussed. New aspects of the two-parameter J * c-fracture criterion for a body with a short crack are studied. A theoretical investigation of the effect of the applied critical stress (or the crack length) on the strain fields ahead of the crack tip has been carried out.
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Ainsworth R.A., Bannister A.C. and Zerbst U. (2000) An overview of the European flaw assessment procedure SINTAP and its validation. International Journal of Pressure Vessels and Piping 77, 869–876.
Anderson T.L. (1995) Fracture Mechanics: Fundamentals and Applications. CRC Press, Boca Raton.
Atluri S.N. (ed.) (1986) Computational Methods in the Mechanics of Fracture. North-Holland Publ. Co., Amsterdam, 430 pp.
Budden P.J., Sharples J.K. and Dowling A.R. (2000) The R6 procedure: resent developments and comparison with alternative approaches. International Journal of Pressure Vessels and Piping 77, 895–903.
Cisilino A.P. and Aliabadi M.H. (1999) BEM implementation of the energy domain integral for the elastoplastic analysis of 3D fracture problems. International Journal of Fracture 96, 229–245.
Cherepanov C.P. (1979) Mechanics of Brittle Fracture. McGraw-Hill, New York.
Guo W. (2002) Theoretical investigation of elastoplastic notch fields under triaxial stress constraint. International Journal of Fracture 115, 233–249.
Hajinski G.M. (1983) Calculation of concentrators when elastic-plastic deforming. Rastchety na Prochnost 24, 41–53 (in Russian).
HutchinsonW. (1968) Singular behavior of the end of a tensile crack in hardening materials. Journal of Mechanics and Physics of Solids 16, 13–31.
Kumar V., German M.D. and Shih C.F. (1981) An Engineering Approach for Elastic-Plastic Fracture Analysis. Report EPRI NP-1931, Electric Power Research Institute, Palo Alto.
Makhutov N.A. (1981) Deformation Criteria of Fracture and Calculation of Strength of Construction Element. Mashinostroenie, Moscow (in Russian).
Makhutov N.A. and Domojirov L.1. (1989) Two-parameter failure criterion in view of refined size of plastic zone. Zavodskaya Laboratoriya N 1 54–59 (in Russian).
Makhutov N.A., Matvienko Yu.G. and Chernyakov S.V. (1993) A unified methodological approach to calculation analysis of the stages of nucleation and growth of low-cycle fatigue cracks. Materials Science 29, 109–114.
Makhutov N.A. and Matvienko Yu.G. (1998) Fracture toughness characterization. In G.P. Cherepanovq (ed.) FRACTURE: A Topical Encyclopaedia of Current Knowledge. Krieger Publ. Comp. Florida pp. 359–366.
Matvienko Yu.G. (1986) Two-parameter failure criterion and hardening of material. Zavodskaya Laboratoriya N 9 60–62 (in Russian).
Matvienko Yu.G. (1994) J-estimation formulas for non-linear crack problems. International Journal of Fracture 68, R15–R18.
Matvienko Yu.G. (1997) Aproximate solution for hardening solids with a crack. In R.K. Mahidhara, A.B. Geltmacher, K. Sadananda and P. Matic (eds.) Recent Advances in Fracture. TMS publ. Warrendale pp. 307–313.
Matvienko Yu.G. (2002) Damage process and crack propagation in materials. In A. Neimitz, I.V. Rokach, D. Kocanda and R. Golos (eds.) Proc. of the 14th European Conference on Fracture 'Fracture Mechanics beyond 2000'. EMAS Publ., UK vol. 2, pp. 467–474.
Matvienko Yu.G. and Morozov E.M. (1987) Some problems in linear and non-linear fracture mechanics. Engineering Fracture Mechanics 28, 127–138.
Matvienko Yu.G. and Morozov E.M. (1994) A method for approximate calculation of the energy integral for notched and cracked bodies. Materials Science 30, 345–349.
Morozov E.M. (1999) An ultimate crack resistance concept. Fatigue and Fracture of Engineering Materials and Structures 22, 997–1001.
Motarjemi A.K. and Kocak M. (2002) Fracture assessment of a clad steel using various SINTAP defect assessment procedure levels. Fatigue and Fracture of Engineering Materials and Structures 24, 929–939.
Rahman S. (2001) Probabilistic fracture mechanics: J-estimation and finite element methods. Engineering Fracture Mechanics 68, 107–125.
Rahman S. and Brust F.W. (1997) Approximate methods for predicting J-integral of a circumferentially surfacecracked pipe subject to bending. International Journal of Fracture 85, 111–130.
Rang B.S.I. and Kobayashi A.S. (1988) J-estimation procedure based on Moire interferometry data. Transaction of ASME, Journal of Pressure Vessel Technology 110, 291–300.
Rice J. (1968) A path-independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of Applied Mechanics 35, 379–386.
Rice J.R. and Rosengren G.F. (1968) Plane strain deformation near a crack tip in a power-law hardening materials. Journal of Mechanics and Physics of Solids 16, 1–12.
Schwalbe K.-H. and Zerbst U. (2000) The engineering treatment model. International Journal of Pressure Vessels and Piping 77, 905–918.
Webster S. and Bannister A. (2000) Structural integrity assessment procedure for Europe-of the SINTAP program overview. Engineering Fracture Mechanics 67, 481–514.
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Matvienko, Y., Morozov, E. Calculation of the energy J-integral for bodies with notches and cracks. International Journal of Fracture 125, 249–261 (2004). https://doi.org/10.1023/B:FRAC.0000022241.23377.91
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DOI: https://doi.org/10.1023/B:FRAC.0000022241.23377.91