Multiaxial fatigue of V-notched steel specimens: a non-conventional application of the local energy method
F. BERTO
Department of Management and Engineering, University of Padova, Stradella S. Nicola, 3-36100, Vicenza, Italy
Search for more papers by this authorP. LAZZARIN
Department of Management and Engineering, University of Padova, Stradella S. Nicola, 3-36100, Vicenza, Italy
Search for more papers by this authorJ. R. YATES
Department of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK
Search for more papers by this authorF. BERTO
Department of Management and Engineering, University of Padova, Stradella S. Nicola, 3-36100, Vicenza, Italy
Search for more papers by this authorP. LAZZARIN
Department of Management and Engineering, University of Padova, Stradella S. Nicola, 3-36100, Vicenza, Italy
Search for more papers by this authorJ. R. YATES
Department of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK
Search for more papers by this authorABSTRACT
The paper deals with the multi-axial fatigue strength of notched specimens made of 39NiCrMo3 hardened and tempered steel. Circumferentially V-notched specimens were subjected to combined tension and torsion loading, both in-phase and out-of-phase, under two nominal load ratios, R=−1 and R= 0, also taking into account the influence of the biaxiality ratio, λ=τa/σa. The notch geometry of all axi-symmetric specimens was a notch tip radius of 0.1 mm, a notch depth of 4 mm, an included V-notch angle of 90° and a net section diameter of 12 mm. The results from multi-axial tests are discussed together with those obtained under pure tension and pure torsion loading on plain and notched specimens. Furthermore the fracture surfaces are examined and the size of non-propagating cracks measured from some run-out specimens at 5 million cycles. Finally, all results are presented in terms of the local strain energy density averaged in a given control volume close to the V-notch tip. The control volume is found to be dependent on the loading mode.
REFERENCES
- 1 Pook, L. P. and Sharples, J. K. (1979) The mode III fatigue crack growth threshold for mild steel. Int. J. Fract. 15, R223–R226.
- 2 Pook, L. P. (1982) Mixed mode threshold behaviour of mild steel. In: Fatigue thresholds: Fundamentals and Engineering applications (Eduted by J. Backlund, A. Blom & C. J. Beevers). EMAS Ltd., West Midlands , UK , pp. 1007–1032.
- 3 Ritchie, R. O., McClintock, F. A., Nayeb-Hashemi, H. and Ritter, M. A. (1982) Mode III fatigue crack propagation in low alloy steel. Metal. Trans. 13A, 101–110.
- 4 Tschegg, E. K. (1983) Mode III and Mode I fatigue crack propagation behaviour under torsional loading. J. Mater. Sci. 18, 1604–1614.
- 5 Pook, L. P. (1985) The fatigue crack direction and threshold behaviour of mild steel under mixed mode I and III loading. Int. J. Fatigue 7, 21–30.
- 6 Tong, J., Yates, J. R. and Brown, M. W. (1986) Some aspects of fatigue thresholds under mode III and mixed mode and I loadings. Int. J. Fatigue 18, 279–285.
- 7 Yates, J. R. and Miller, K. J. (1989) Mixed mode (I + III) fatigue threshold in a forging steel. Fatigue Fract. Eng. Mater. Struct. 12, 259–270.
- 8 Yates, J. R. and Mohammed, R. A. (1996) The determination of fatigue crack propagation rates under mixed mode (I + III) loading. Int. J. Fatigue 18, 197–203.
- 9 Murakami, Y. and Takahashi, K. (1998) Torsional fatigue of a medium carbon steel containing an initial small surface crack introduced by tension-compression fatigue: crack branching, non-propagation and fatigue limit. Fatigue Fract. Eng. Mater. Struct. 21, 1473–1484.
- 10 Yu, H. C., Tanaka, K. and Akiniwa, Y. (1998) Estimation of torsional fatigue strength of medium carbon steel bars with circumferential crack by the cyclic resistance-curve method. Fatigue Fract. Eng. Mater. Struct. 21, 1067–1076.
- 11 Tanaka, K., Akiniwa, Y. and Yu, H (1999) The propagation of a circumferential fatigue crack in medium-carbon steel bars under combined torsional and axial loadings. In: Mixed-Mode Crack Behaviour 1359 (Edited by K. J. Miller & D. L. McDowell), ASTM, West Conshohocked , PA , pp. 295–311.
- 12 Makabe, C. and Socie, D. F. (2001) Crack growth mechanism in precracked torsional fatigue specimens. Fatigue Fract. Eng. Mater. Struct. 24, 607–615.
- 13 Murakami, Y., Takahashi, K. and Kusumoto, R. (2003) Threshold and growth mechanism of fatigue cracks under mode II and Mode III loadings. Fatigue Fract. Eng. Mater. Struct. 26, 523–531.
- 14 Tanaka, K., Akiniwa, Y., Kato, T. and Mikuriya, T. (2005) Fatigue crack propagation from a precrack torsional and axial loading. Fatigue Fract. Eng. Mater. Struct 28, 73–82.
- 15
Suresh, S. (1998) Fatigue of Materials. 2nd Edn. Cambridge University Press,
UK.
10.1017/CBO9780511806575 Google Scholar
- 16 Ritchie, R. O. (1988) Mechanics of fatigue crack propagation in metals, ceramics and composites: role of crack tip shielding. Mater. Sci. Eng. A103, 15–28.
- 17 Pippan, R., Hageneder, P., Knabl, W., Clemens, H., Hebesberger, T. and Taberning, B. (2001) Fatigue threshold and crack propagation in γ-TiAl sheets. Intermetallics 9, 89–96.
- 18 Pippan, R. (1991) Threshold and effective threshold of fatigue crack propagation in ARMCO iron I: the influence of grain size and cold working. Mater Sci. Eng. A138, 1–13.
- 19 Pokluda, J., Sandera, P. and Hornikova, J. (2004) Statistical approach to roughness-induced shielding effects. Fatigue Fract. Eng. Mater. Struct. 27, 141–157.
- 20 Vaziri, A. and Nayeb-Hashemi, H. (2005) The effect of crack interaction on the stress intensity factor in Mode III crack growth in round shaft. Eng. Fract. Mech. 72, 617–629.
- 21 Ellyin, F. (1997) Fatigue Damage, Crack Growth and Life Prediction, Chapman & Hall, London
- 22 Moftakhar, A., Buczynski, A. and Glinka, G. (1995) Calculation of elasto-plastic strains and stresses in notches under multiaxial loading. Int. J. Fract. 70, 357–373.
- 23 Park, J. and Nelson, D. (2000) Evaluation of an energy-based approach and a critical plane approach for predicting constant amplitude multiaxial fatigue life. Int. J. Fatigue 22, 23–39
- 24 Froustey, C., Lasserre, S. and Dubar, L. (1992) Validity of some multiaxial fatigue criteria under bending-torsion at the endurance fatigue limit. In: Proceedings of Mat-Tech ’92. IITT-International, France , pp. 79–85. (in French).
- 25 Morel, F., Palin-Luc, T. and Froustey, C. (2001) Comparative study and link between mesoscopic and energetic approaches in high cycle multiaxial fatigue. In. J. Fatigue 23, 317–327.
- 26 Pluvinage, G. (1997) Rupture and fatigue initiated from notches. Application of the notch intensity factor. Revue Francaise de Mecanique 1997–1, 53–61. (in French).
- 27 Bentachfine, S., Pluvinage, G., Gilgert, J., Azari, Z. and Bouami, D. (1999) Notch effect in low cycle fatigue. Int. J. Fatigue 21, 421–430.
- 28 Yao, W. (1993) Stress field intensity approach for predicting fatigue life. Int. J. Fatigue 15, 234–245.
- 29 Gasiak, G. and Pawliczek, R.(2003) Application of an energy model for fatigue life prediction of construction steels under bending, torsion and synchronous bending and torsion. Int. J. Fatigue 25, 1339–1346.
- 30 Banvillet, A., Palin-Luc, T. and Lasserre, S. (2003) A volumetric based high cycle multiaxial fatigue criterion, Int. J. Fatigue 25, 755–769.
- 31 Macha, E. and Sonsino, C. M. (1999) Energy criteria of multi-axial fatigue failure. Fatigue Fract. Eng. Mater. Struct. 22, 1053–1070.
- 32 Lagoda, T., Macha, E. and Będkowski, W. (1999) A critical plane approach based on energy concepts: application to biaxial random tension-compression high-cycle fatigue regime. Int. J. Fatigue 21, 431–443.
- 33 Lazzarin, P. and Zambardi, R. (2001) A finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp V-shaped notches. Int. J. Fract. 112: 275–298.
- 34 Lazzarin, P. and Lassen, T. and Livieri, P. (2003) A Notch Stress Intensity approach applied to fatigue life predictions of welded joints with different local toe geometry. Fatigue Fract. Eng. Mater. Struct. 26, 49–48.
- 35 Lazzarin, P., Sonsino, C. M. and Zambardi, R. (2004) A notch stress intensity approach to assess the multiaxial fatigue strength of welded tube-to flange joints subjected to combined loadings. Fatigue Fract. Eng. Mater. Struct. 27, 127–140.
- 36 Atzori, B., Berto, F., Lazzarin, P. and Quaresimin, M. (2006) Multi-axial fatigue behaviour of a severely notched carbon steel. Int. J. Fatigue 28, 485–493.
- 37 Lazzarin, P., Livieri, P., Berto, F. and Zappalorto, M. (2008) Local strain energy density and fatigue strength of welded joints under uniaxial and multiaxial loading. Eng. Fract. Mech. 75, 1875–1889.
- 38 Dowling, N. E. (1999) Mechanical Behaviour of Materials, 2nd Edn, Prentice Hall International, NJ .
- 39 Dowling, N. E. (2007) Mechanical Behaviour of Materials, 2nd Edn, Prentice Hall International, NJ .
- 40 Peterson, R. E. (1974) Stress Concentration Factors, John Wiley, New York . (See also W. D. Pilkey (1997) Peterson's Stress Concentration Factors, 2nd edn. John Wiley, New York .)
- 41 Agerman, E. (1960) Notch Sensitivity in Steel, ASEA research number 4 Västeras, Sweden , pp. 5–45.
- 42 Petersen, C. (1951) The processes in metal grain structures subjected to static and cyclic loading. Journal of Metallography 42, 161–170.
- 43 Ciavarella, M. and Meneghetti, M. (2004) On fatigue limit in the presence of notches: classical vs. recent unified formulations Int. J. Fatigue 28, 485–493.
- 44 Lazzarin, P. and Tovo, R. (1998) A notch intensity approach to the stress analysis of welds. Fatigue Fract. Eng. Mater. Struct. 21, 1089–1104.
- 45 Lazzarin, P. and Filippi, S. (2006) A generalised stress intensity factor to be applied to rounded V-shaped notches. Int. J. Solids Struct. 43, 2461–2478.
- 46 Davoli, P., Bernasconi, A., Filippini, M., Foletti, S. (2005) Mechanical Behaviour of Materials, McGraw-Hill, Milano . (in italian).
- 47 Kanninen, M. F. and Popelar C. H. (1985) Advanced Fracture Mechanics, Oxford University Press, New York , Clarendon Press, Oxford .
- 48
Gdoutos, E. E. (1990) Fracture Mechanics Criteria and Applications, Kluwer Academic Publishers,
Dodrecht
,
Boston
,
London
.
10.1007/978-94-009-1956-3 Google Scholar
- 49 Hult, J.A. H and McClintock, F. A. (1956) Elastic-plastic stress and strain distribution around sharp notches under repeated shear. In: 9th International Congress in Applied Mechanics, 8. Brussels .
- 50 Bilby, B. A., Cottrell, A. H. and Swinden, K. H. (1963) The spread of plastic yield from a notch. Proc. Roy. Soc. A 272, 304–314.
- 51
Koskinen, M. F. (1963) Elastic-plastic deformation of a single grooved flat under longitudinal shear.
J. Basic Eng.
85, 585–594.
10.1115/1.3656914 Google Scholar
- 52 Rice, J. R. (1966) Contained plastic deformation near cracks and notches under longitudinal shear. Int. J. Fract. Mech. 2, 426–447.
- 53 Rice, J. R (1967) Stresses due to a sharp notch in a work-hardening elastic-plastic material loaded by longitudinal shear. J. Appl. Mech. 34, 287–298.
- 54 Lazzarin, P. and Berto, F. (2008) Control volumes and strain energy density under small and large scale yielding due to tension and torsion loading. Fatigue Fract. Eng. Mater. Struct., 31 95–107.
- 55 Zappalorto, M. and Lazzarin, P. (2007) Analytical study of the elastic-plastic stress fields ahead of parabolic notches under antiplane shear loading. Int. J. Fract. 148, 139–154.
- 56 Atzori, B., Meneghetti, G. and Susmel, L. (2005) Material fatigue properties for assessing mechanical components weakened by notches and defects. Fatigue Fract. Eng. Mater. Struct. 29, 83–97.
- 57 Sih, G. C. (1974) Strain-energy-density factor applied to mixed mode crack problems. Int. J. Fract. 10, 305–321.
- 58
Sih, G. C. (1991) Mechanics of Fracture Initiation and Propagation: Surface and volume energy density applied as failure criterion, Kluwer Academic Publisher,
Dordrecht
.
10.1007/978-94-011-3734-8 Google Scholar
- 59 Gillemot, L. F. (1965) Brittle fracture of welded materials. Commonw. Weld. Conf. C7, 353–358.
- 60 Gillemot, L. F., Czoboly E. and Havas, I. (1985) Fracture mechanics applications of absorbed specific fracture energy: notch and unnotched specimens. Theor. Appl. Fract. Mech. 4, 39–45.
- 61 Sih, C. G. and Tang, X. S. (2007) Random property of micro/macro fatigue crack growth behavior predicted from energy density amplitude range. Theor. Appl. Fract. Mech. 43, 97–111.
- 62 Molski, K. and Glinka, G. (1981) A method of elastic-plastic stress and strain calculation at a notch root. Mater. Sci. Eng. 50, 93–100.
- 63 Glinka, G. (1985) Energy density approach to calculation of inelastic strain-stress near notches and cracks. Eng. Fract. Mech., 22, 485–508.
- 64 Yosibash, Z., Bussiba, A. R. and Gilad, I. (2004) Failure criteria for brittle elastic materials. Int. J. Fract. 125, 307–333.
- 65 Lazzarin, P. and Berto, F. (2005) Some expressions for the strain energy in a finite volume surrounding the root of blunt V-notches. Int. J. Fract. 135, 161–185.