SPECIAL ISSUE CONTRIBUTION
Proportional/nonproportional constant/variable amplitude multiaxial notch fatigue: cyclic plasticity, non-zero mean stresses, and critical distance/plane
N. Zuhair Faruq,
Luca Susmel,
N. Zuhair Faruq
Department of Civil and Structural Engineering, The University of Sheffield, Sheffield, UK
Search for more papers by this authorCorresponding Author
Luca Susmel
Department of Civil and Structural Engineering, The University of Sheffield, Sheffield, UK
Correspondence
Prof. Luca Susmel, Department of Civil and Structural Engineering, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK.
Email: [email protected]
Search for more papers by this authorN. Zuhair Faruq,
Luca Susmel,
N. Zuhair Faruq
Department of Civil and Structural Engineering, The University of Sheffield, Sheffield, UK
Search for more papers by this authorCorresponding Author
Luca Susmel
Department of Civil and Structural Engineering, The University of Sheffield, Sheffield, UK
Correspondence
Prof. Luca Susmel, Department of Civil and Structural Engineering, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK.
Email: [email protected]
Search for more papers by this authorAbstract
This paper deals with the formulation and experimental validation of a novel fatigue lifetime estimation technique suitable for assessing the extent of damage in notched metallic materials subjected to in-service proportional/nonproportional constant/variable amplitude multiaxial load histories. The methodology being formulated makes use of the Modified Manson-Coffin Curve Method, the Shear Strain–Maximum Variance Method, and the elasto-plastic Theory of Critical Distances, with the latter theory being applied in the form of the Point Method. The accuracy and reliability of our novel fatigue lifetime estimation technique were checked against a large number of experimental results we generated by testing, under proportional/nonproportional constant/variable amplitude axial-torsional loading, V-notched cylindrical specimens made of unalloyed medium-carbon steel En8 (080M40). Specific experimental trials were run to investigate also the effect of non-zero mean stresses as well as of different frequencies between the axial and torsional stress/strain components. This systematic validation exercise allowed us to demonstrate that our novel multiaxial fatigue assessment methodology is remarkably accurate, with the estimates falling within an error factor of 2. By modelling the cyclic elasto-plastic behaviour of metals explicitly, the design methodology being formulated and validated in the present paper offers a complete solution to the problem of estimating multiaxial fatigue lifetime of notched metallic materials, with this holding true independently of sharpness of the stress/strain raiser and complexity of the load history.
REFERENCES
- 1Stephens RI, Fatemi A, Stephens RR, Fuchs HO. Metal Fatigue in Engineering. 2nd ed. USA: John Wiley & Sons; 2001.
- 2Susmel L. Multiaxial Notch Fatigue: From Nominal to Local Stress-Strain Quantities. Cambridge, UK: Woodhead & CRC; 2009.
- 3Socie DF, Marquis GB. Multiaxial Fatigue. Warrendale, PA: SAE; 2000.
10.4271/R-234 Google Scholar
- 4Neuber H. Theory of Notch Stresses: Principles for Exact Calculation of Strength With Reference to Structural Form and Material. 2nd ed. Berlin, Germany: Springer-Verlag; 1958.
- 5Peterson RE. Notch sensitivity. In: G Sines, JL Waisman, eds. Metal Fatigue. New York, USA: McGraw Hill; 1959: 293-306.
- 6Gough HJ. Engineering steels under combined cyclic and static stresses. Proc Inst Mech Eng. 1949; 160(1): 417-440.
10.1243/PIME_PROC_1949_160_040_02 Google Scholar
- 7Tipton SM, Nelson DV. Advances in multiaxial fatigue life prediction for components with stress concentrators. Int J Fatigue. 1997; 19: 503-515.
- 8Susmel L, Lazzarin P. A bi-parametric modified Wöhler curve for high cycle multiaxial fatigue assessment. Fatigue Fract Eng Mater Struct. 2002; 25(1): 63-78.
- 9Lazzarin P, Susmel L. A stress-based method to predict lifetime under multiaxial fatigue loadings. Fatigue Fract Eng Mater Struct. 2003; 26(12): 1171-1187.
- 10Taylor D. The Theory of Critical Distances: A New Perspective in Fracture Mechanics. Oxford, UK: Elsevier; 2007.
- 11Susmel L. A unifying approach to estimate the high-cycle fatigue strength of notched components subjected to both uniaxial and multiaxial cyclic loadings. Fatigue Fract Eng Mater Struct. 2004; 27(5): 391-411.
- 12Susmel L, Taylor D. The modified Wöhler curve method applied along with the theory of critical distances to estimate finite life of notched components subjected to complex multiaxial loading paths. Fatigue Fract Eng Mater Struct. 2008; 31(12): 1047-1064.
- 13Susmel L. Multiaxial fatigue limits and material sensitivity to non-zero mean stresses normal to the critical planes. Fatigue Fract Eng Mater Struct. 2008; 31(3-4): 295-309.
- 14Carpinteri A, Spagnoli A, Vantadori S, Bagni C. Structural integrity assessment of metallic components undermultiaxial fatigue: the C–S criterion and its evolution. Fatigue Fract Eng Mater Struct. 2013; 36(9): 870-883.
- 15Atzori B, Berto F, Lazzarin P, Quaresimin M. Multi-axial fatigue behaviour of a severely notched carbon steel. Int J Fatigue. 2006; 28(5-6): 485-493.
- 16Berto F, Lazzarin P, Yates JR. Multiaxial fatigue of V-notched steel specimens: a non-conventional application of the local energy method. Fatigue Fract Eng Mater Struct. 2011; 34(11): 921-943.
- 17Branco R, Costa JD, Berto F, Antunes FV. Fatigue life assessment of notched round bars under multiaxial loading based on the total strain energy density approach. Theor Appl Fract Mec. 2018; 97: 340-348.
- 18Meneghetti G, Campagnolo A, Berto F, Tanaka K. Notched Ti-6Al-4V titanium bars under multiaxial fatigue: synthesis of crack initiation life based on the averaged strain energy density. Theor Appl Fract Mec. 2018; 96: 509-533.
- 19Manson SS. Behaviour of materials under conditions of thermal stress. National Advisory Committee for Aeronautics, NACA TN-2933, 1954.
- 20Coffin LF. A study of the effects of cyclic thermal stresses on a ductile metal. Trans ASME. 1954; 76: 931-950.
- 21Morrow JD. Cyclic plastic strain energy and the fatigue of metals. In: Internal friction, damping and cyclic plasticity, ASTM STP 378, Philadelphia, USA, pp. 45–87, 1965.
- 22Smith KN, Watson P, Topper TH. A stress-strain function for the fatigue of metal. J Mater. 1970; 5: 767-778.
- 23Neuber H. Theory of stress concentration for shear-strained prismatical bodies with arbitrary nonlinear stress-strain law. ASME J Appl Mech. 1961; 28(4): 544-550.
10.1115/1.3641780 Google Scholar
- 24Glinka G. Energy density approach to calculation of inelastic strain-stress near notches and cracks. Eng Fract Mech. 1985; 22(3): 485-508.
- 25Hoffmann M, Seeger T. A generalised method for estimating multiaxial elastic-plastic notch stresses and strains. Part 1: Theory Trans ASME, J Eng Mater Technol. 1985; 107: 250-254.
- 26Hoffmann M, Seeger T. A generalised method for estimating multiaxial elastic-plastic notch stresses and strains. Part 2: application and general discussion. Trans ASME, J Eng Mater Technol. 1985; 107(4): 255-260.
- 27Köttingen VB, Barkey ME, Socie DF. Pseudo stress and pseudo strain based approaches to multiaxial notch analysis. Fatigue Fract Eng Mater Struct. 1995; 18: 981-1006.
- 28Ince A, Glinka G. Innovative computational modelling of multiaxial fatigue analysis for notched components. Int J Fatigue. 2016; 82: 134-145.
- 29Tipton SM, Fash JW. Multiaxial fatigue life prediction for the SAE specimen using strain based approaches. In: GE Leese, DF Socie, eds. Multiaxial Fatigue: Analysis and Experiments. Warrendale, PA, USA: SAE AE-14; 1989: 67-80.
- 30Susmel L, Meneghetti G, Atzori B. A novel multiaxial fatigue criterion to predict lifetime in the low/medium-cycle fatigue regime. Part II: Notches Trans ASME, J Eng Mater Technol. 2009; 131:021010-1/8.
- 31Gates N, Fatemi A. Notched fatigue behavior and stress analysis under multiaxial states of stress. Int J Fatigue. 2014; 67: 2-14.
- 32Susmel L, Taylor D. An elasto-plastic reformulation of the theory of critical distances to estimate lifetime of notched components failing in the low/medium-cycle fatigue regime. Trans ASME, J Eng Mater Technol. 2010; 132(2):021002–1/8.
- 33Susmel L, Taylor D. Estimating lifetime of notched components subjected to variable amplitude fatigue loading according to the elasto-plastic theory of critical distances. Trans ASME, J Eng Mater Technol. 2015; 137(1):011008–1/15.
- 34Gates N, Fatemi A. Notch deformation and stress gradient effect in multiaxial fatigue. Theor Appl Fract Mec. 2016; 84: 3-25.
- 35Gates NR, Fatemi A. Multiaxial variable amplitude fatigue life analysis using the critical plane approach, part II: notched specimen experiments and life estimations. Int J Fatigue. 2018; 106: 56-69.
- 36Susmel L, Taylor D. A novel formulation of the theory of critical distances to estimate lifetime of notched components in the medium-cycle fatigue regime. Fatigue Fract Eng Mater Struct. 2007; 30(7): 567-581.
- 37Susmel L, Taylor D. The theory of critical distances to estimate lifetime of notched components subjected to variable amplitude uniaxial fatigue loading. Int J Fatigue. 2011; 33(7): 900-911.
- 38Susmel L, Taylor D. A critical distance/plane method to estimate finite life of notched components under variable amplitude uniaxial/multiaxial fatigue loading. Int J Fatigue. 2012; 38: 7-24.
- 39Louks R, Gerin B, Draper J, Askes H, Susmel L. On the multiaxial fatigue assessment of complex three-dimensional stress concentrators. Int J Fatigue. 2014; 63: 12-24.
- 40Susmel L, Meneghetti G, Atzori B. A simple and efficient reformulation of the classical Manson-Coffin curve to predict lifetime under multiaxial fatigue loading. Part I: Plain Materials Trans ASME, J Eng Mater Technol. 2009; 131(2):021009–1/9.
- 41Wang Y, Susmel L. The modified Manson-Coffin curve method to estimate fatigue lifetime under complex constant and variable amplitude multiaxial fatigue loading. Int J Fatigue. 2016; 83: 135-149.
- 42Susmel L. A simple and efficient numerical algorithm to determine the orientation of the critical plane in multiaxial fatigue problems. Int J Fatigue. 2010; 32(11): 1875-1883.
- 43Macha E. Simulation investigations of the position of fatigue fracture plane in materials with biaxial loads. Materialwiss Werkstofftech. 1989; 20(4): 132-136.
- 44Kanazawa K, Miller KJ, Brown MW. Low-cycle fatigue under out-of-phase loading conditions. Trans ASME, J Eng Mater Technol. 1977; 99(3): 222-228.
- 45Matsuishi M, Endo T. Fatigue of metals subjected to varying stress. Presented to the Japan Society of Mechanical Engineers, Fukuoka, Japan, 1968.
- 46Downing SD, Socie DF. Simple rainflow counting algorithms. Int J Fatigue. 1982; 4(1): 31-40.
- 47Kaufman RP, Topper T. The influence of static mean stresses applied normal to the maximum shear planes in multiaxial fatigue. In: A Carpinteri, M Freitas, A Spagnoli, eds. Biaxial and Multiaxial Fatigue and Fracture. Oxford, UK: Elsevier and ESIS; 2003: 123-143.
- 48Socie DF. Fatigue damage models. Trans ASME, J Eng Mater Technol. 1987; 109(4): 293-298.
- 49Susmel L, Tovo R, Lazzarin P. The mean stress effect on the high-cycle fatigue strength from a multiaxial fatigue point of view. Int J Fatigue. 2005; 27(8): 928-943.
- 50Susmel L, Tovo R, Benasciutti D. A novel engineering method based on the critical plane concept to estimate the lifetime of weldments subjected to variable amplitude multiaxial fatigue loading. Fatigue Fract Eng Mater Struct. 2009; 32(5): 441-459.
- 51Socie DF, Morrow J. In: JJ Burke, V Weiss, eds. Review of Contemporary Approaches to Fatigue Damage Analysis, Risk and Failure Analysis for Improved Performance and Reliability. New York, NY, USA: Plenum Pub. Corp; 1980: 141-194.
- 52Palmgren A. Die Lebensdauer von Kugellagern. Zeitschrift des Vereines Deutscher Ingenieure. 1924; 68: 339-341.
- 53Miner MA. Cumulative damage in fatigue. J Appl Mech. 1945; 67: AI59-AI64.
- 54Sonsino CM. Fatigue testing under variable amplitude loading. Int J Fatigue. 2007; 29(6): 1080-1089.
- 55Pilkey WD, Pilkey DF. Peterson's Stress Concentration Factors. Third ed. NY, USA: Wiley; 2017.
- 56Zappalorto M, Lazzarin P, Filippi S. Stress field equations for U and blunt V-shaped notches in axisymmetric shafts under torsion. Int J Fracture. 2010; 164(2): 253-269.
- 57Jiang Y, Sehitoglu H. Modelling of cyclic ratchetting plasticity—part I: development and constitutive relations. Trans ASME, J Appl Mech. 1996; 63(3): 720-725.
- 58Jiang Y, Sehitoglu H. Modelling of cyclic ratchetting plasticity—part II: comparison of model simulations with experiments. Trans ASME, J Appl Mech. 1996; 63: 726-733.
- 59Hoffmeyer J, Döring R, Seeger T, Vormwald M. Deformation behaviour, short crack growth and fatigue lives under multiaxial nonproportional loading. Int J Fatigue. 2006; 28(5-6): 508-520.
- 60Han C, Chen X, Kim KS. Evaluation of multiaxial fatigue criteria under irregular loading. Int J Fatigue. 2002; 24(9): 913-922.
- 61Kanazawa K, Miller KJ, Brown MW. Cyclic deformation of 1% Cr-No-V steel under out-of-phase loads. Fatigue Fract Eng Mater Struct. 1979; 2(2): 217-228.
- 62Shang DG, Sun GQ, Yan CL. Multiaxial fatigue damage parameter and life prediction for medium-carbon steel based on the critical plane approach. Int J Fatigue. 2007; 29(12): 2200-2207.
- 63Kim KS, Park JC, Lee JW. Multiaxial fatigue under variable amplitude loads. Trans ASME, J Eng Mater Technol. 1999; 121(3): 286-293.
