×

Microstructure-sensitive critical plastic strain energy density criterion for fatigue life prediction across various loading regimes. (English) Zbl 1472.74028

Summary: In the present work, we postulate that a critical value of the stored plastic strain energy density (SPSED) is associated with fatigue failure in metals and is independent of the applied load. Unlike the classical approach of estimating the (homogenized) SPSED as the cumulative area enclosed within the macroscopic stress-strain hysteresis loops, we use crystal plasticity finite element simulations to compute the (local) SPSED at each material point within polycrystalline aggregates of a nickel-based superalloy. A Bayesian inference method is used to calibrate the critical SPSED, which is subsequently used to predict fatigue lives at nine different strain ranges, including strain ratios of 0.05 and \(-1\), using nine statistically equivalent microstructures. For each strain range, the predicted lives from all simulated microstructures follow a lognormal distribution. Moreover, for a given strain ratio, the predicted scatter is seen to be increasing with decreasing strain amplitude; this is indicative of the scatter observed in the fatigue experiments. Finally, the lognormal mean lives at each strain range are in good agreement with the experimental evidence. Since the critical SPSED captures the experimental data with reasonable accuracy across various loading regimes, it is hypothesized to be a material property and sufficient to predict the fatigue life.

MSC:

74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Suresh S. 1998 Fatigue of materials. Cambridge, UK: Cambridge University Press.
[2] Socie D, Marquis G. 1999 Multiaxial fatigue. Warrendale, PA: SAE International.
[3] Basquin OH. 1910 The exponential law of endurance tests. Proc. Am. Soc. Test. Mater. 10, 625-630.
[4] Coffin LF. 1954 A study of the effects of cyclic thermal stresses on a ductile metal. Trans. Am. Soc. Mech. Eng. 76, 931-950.
[5] Manson SS. 1953 Behavior of materials under conditions of thermal stress. Cleveland, OH: National Advisory Committee for Aeronautics.
[6] Morrow JD. 1965 Cyclic plastic strain energy and fatigue of metals. In Internal friction, damping, and cyclic plasticity (ed. B Lazan), pp. 45-87. West Conshohocken, PA: ASTM International.
[7] Garud YS. 1981 A new approach to the evaluation of fatigue under multiaxial loadings. J. Eng. Mater. Technol. 103, 118-125. (doi:10.1115/1.3224982)
[8] Ellyin F, Kujawski D. 1984 Plastic strain energy in fatigue failure. J. Press. Vessel Technol. 106, 342-347. (doi:10.1115/1.3264362)
[9] Park J, 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. (doi:10.1016/S0142-1123(99)00111-5)
[10] Varvani-Farahani A. 2000 New energy-critical plane parameter for fatigue life assessment of various metallic materials subjected to in-phase and out-of-phase multiaxial fatigue loading conditions. Int. J. Fatigue 22, 295-305. (doi:10.1016/S0142-1123(00)00002-5)
[11] Łagoda T. 2001 Energy models for fatigue life estimation under uniaxial random loading. Part II: verification of the model. Int. J. Fatigue 23, 481-489. (doi:10.1016/S0142-1123(01)00017-2)
[12] Łagoda T. 2001 Energy models for fatigue life estimation under uniaxial random loading. Part I: the model elaboration. Int. J. Fatigue 23, 467-480. (doi:10.1016/S0142-1123(01)00016-0)
[13] Liu KC, Wang JA. 2001 An energy method for predicting fatigue life, crack orientation, and crack growth under multiaxial loading conditions. Int. J. Fatigue 23, 129-134. (doi:10.1016/s0142-1123(01)00169-4)
[14] Gasiak G, 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. (doi:10.1016/S0142-1123(03)00055-0)
[15] Chen X, Xu S, Huang D. 1999 Critical plane-strain energy density criterion for multiaxial low-cycle fatigue life under non-proportional loading. Fatigue Fract. Eng. Mater. Struct. 22, 679-686. (doi:10.1046/j.1460-2695.1999.t01-1-00199.x)
[16] Syed A. 2004 Accumulated creep strain and energy density based thermal fatigue life prediction models for SnAgCu solder joints. In Proc. of the 54th Electronic Components and Technology Conf. (IEEE Cat. No. 04CH37546), Las Vegas, NV, 4 June 2004, pp. 737-746. New York, NY: IEEE.
[17] Jahed H, Varvani-Farahani A. 2006 Upper and lower fatigue life limits model using energy-based fatigue properties. Int. J. Fatigue 28, 467-473. (doi:10.1016/j.ijfatigue.2005.07.039) · Zbl 1139.74337
[18] Shokrieh MM, Taheri-Behrooz F. 2006 A unified fatigue life model based on energy method. Compos. Struct. 75, 444-450. (doi:10.1016/j.compstruct.2006.04.041)
[19] Ellyin F, Golos K. 1988 Multiaxial fatigue damage criterion. J. Eng. Mater. Technol. 110, 63-68. (doi:10.1115/1.3226012)
[20] Jahed H, Varvani-Farahani A, Noban M, Khalaji I. 2007 An energy-based fatigue life assessment model for various metallic materials under proportional and non-proportional loading conditions. Int. J. Fatigue 29, 647-655. (doi:10.1016/j.ijfatigue.2006.07.017)
[21] Lee K-O, Hong S-G, Lee S-B. 2008 A new energy-based fatigue damage parameter in life prediction of high-temperature structural materials. Mater. Sci. Eng. A 496, 471-477. (doi:10.1016/j.msea.2008.07.035)
[22] Scott-Emuakpor OE, Shen H, George T, Cross C. 2008 An energy-based uniaxial fatigue life prediction method for commonly used gas turbine engine materials. J. Eng. Gas Turbines Power 130, 062504. (doi:10.1115/1.2943152)
[23] Naderi M, Amiri M, Khonsari MM. 2010 On the thermodynamic entropy of fatigue fracture. Proc. R. Soc. A 466, 423-438. (doi:10.1098/rspa.2009.0348) · Zbl 1195.74033
[24] Zhu S-P, Huang H-Z, He L-P, Liu Y, Wang Z. 2012 A generalized energy-based fatigue-creep damage parameter for life prediction of turbine disk alloys. Eng. Fract. Mech. 90, 89-100. (doi:10.1016/j.engfracmech.2012.04.021)
[25] Golos K, Ellyin F. 1988 A total strain energy density theory for cumulative fatigue damage. J. Press. Vessel Technol. 110, 36-41. (doi:10.1115/1.3265565)
[26] Ellyin F, Xia Z. 1993 A general fatigue theory and its application to out-of-phase cyclic loading. J. Eng. Mater. Technol. 115, 411-416. (doi:10.1115/1.2904239)
[27] Ellyin F, Kujawski D. 1993 A multiaxial fatigue criterion including mean-stress effect. In Advances in multiaxial fatigue (eds D McDowell, J Ellis), pp. 55-66. West Conshohocken, PA: ASTM International.
[28] Liu KC. 1993 A method based on virtual strain-energy parameters for multiaxial fatigue life prediction. In Advances in multiaxial fatigue (eds D McDowell, J Ellis), pp. 67-84. West Conshohocken, PA: ASTM International.
[29] Chu C-C, Conle FA, Bonnen JJF. 1993 Multiaxial stress-strain modeling and fatigue life prediction of SAE axle shafts. In Advances in multiaxial fatigue (eds D McDowell, J Ellis), pp. 37-54. West Conshohocken, PA: ASTM International.
[30] Glinka G, Shen G, Plumtree A. 1995 A multiaxial fatigue strain energy density parameter related to the critical fracture plane. Fatigue Fract. Eng. Mater. Struct. 18, 37-46. (doi:10.1111/j.1460-2695.1995.tb00140.x)
[31] Glinka G, Wang G, Plumtree A. 1995 Mean stress effects in multiaxial fatigue. Fatigue Fract. Eng. Mater. Struct. 18, 755-764. (doi:10.1111/j.1460-2695.1995.tb00901.x)
[32] Sangid MD. 2013 The physics of fatigue crack initiation. Int. J. Fatigue 57, 58-72. (doi:10.1016/j.ijfatigue.2012.10.009)
[33] Thompson N, Wadsworth N, Louat N. 1956 The origin of fatigue fracture in copper. Philos. Mag. 1, 113-126. (doi:10.1080/14786435608238086)
[34] Fatemi A, Socie DF. 1988 A critical plane approach to multiaxial fatigue damage including out-of-phase loading. Fatigue Fract. Eng. Mater. Struct. 11, 149-165. (doi:10.1111/j.1460-2695.1988.tb01169.x)
[35] McDowell DL. 2005 Microstructure-sensitive computational fatigue analysis. In Handbook of materials modeling (ed. Yip S), pp. 1193-1214. Berlin, Germany: Springer.
[36] Shenoy MM, Gordon AP, McDowell DL, Neu RW. 2005 Thermomechanical fatigue behavior of a directionally solidified Ni-base superalloy. J. Eng. Mater. Technol. 127, 325-336. (doi:10.1115/1.1924560)
[37] Shenoy M, Zhang J, McDowell DL. 2007 Estimating fatigue sensitivity to polycrystalline Ni-base superalloy microstructures using a computational approach. Fatigue Fract. Eng. Mater. Struct. 30, 889-904. (doi:10.1111/j.1460-2695.2007.01159.x)
[38] Xue Y, McDowell DL, Horstemeyer MF, Dale MH, Jordon JB. 2007 Microstructure-based multistage fatigue modeling of aluminum alloy 7075-T651. Eng. Fract. Mech. 74, 2810-2823. (doi:10.1016/j.engfracmech.2006.12.031)
[39] Przybyla CP, Prasannavenkatesan R, Salajegheh N, McDowell DL. 2010 Microstructure-sensitive modeling of high cycle fatigue. Int. J. Fatigue 32, 512-525. (doi:10.1016/j.ijfatigue.2009.03.021)
[40] Przybyla CP, McDowell DL. 2010 Microstructure-sensitive extreme value probabilities for high cycle fatigue of Ni-base superalloy IN100. Int. J. Plast. 26, 372-394. (doi:10.1016/j.ijplas.2009.08.001) · Zbl 1426.74274
[41] Przybyla CP, McDowell DL. 2012 Microstructure-sensitive extreme-value probabilities of high-cycle fatigue for surface vs. subsurface crack formation in duplex Ti-6Al-4 V. Acta Mater. 60, 293-305. (doi:10.1016/j.actamat.2011.09.031)
[42] Przybyla CP, Musinski WD, Castelluccio GM, McDowell DL. 2013 Microstructure-sensitive HCF and VHCF simulations. Int. J. Fatigue 57, 9-27. (doi:10.1016/j.ijfatigue.2012.09.014)
[43] Sinha S, Ghosh S. 2006 Modeling cyclic ratcheting based fatigue life of HSLA steels using crystal plasticity FEM simulations and experiments. Int. J. Fatigue 28, 1690-1704. (doi:10.1016/j.ijfatigue.2006.01.008)
[44] Kirane K, Ghosh S. 2008 A cold dwell fatigue crack nucleation criterion for polycrystalline Ti-6242 using grain-level crystal plasticity FE model. Int. J. Fatigue 30, 2127-2139. (doi:10.1016/j.ijfatigue.2008.05.026)
[45] Anahid M, Samal MK, Ghosh S. 2011 Dwell fatigue crack nucleation model based on crystal plasticity finite element simulations of polycrystalline titanium alloys. J. Mech. Phys. Solids 59, 2157-2176. (doi:10.1016/j.jmps.2011.05.003) · Zbl 1270.74185
[46] Sangid MD, Maier HJ, Sehitoglu H. 2011 A physically based fatigue model for prediction of crack initiation from persistent slip bands in polycrystals. Acta Mater. 59, 328-341. (doi:10.1016/j.actamat.2010.09.036)
[47] Sangid MD, Maier HJ, Sehitoglu H. 2011 An energy-based microstructure model to account for fatigue scatter in polycrystals. J. Mech. Phys. Solids 59, 595-609. (doi:10.1016/j.jmps.2010.12.014) · Zbl 1270.74045
[48] Yeratapally SR, Glavicic MG, Hardy M, Sangid MD. 2016 Microstructure based fatigue life prediction framework for polycrystalline nickel-base superalloys with emphasis on the role played by twin boundaries in crack initiation. Acta Mater. 107, 152-167. (doi:10.1016/j.actamat.2016.01.038)
[49] Korsunsky AM, Dini D, Dunne FPE, Walsh MJ. 2007 Comparative assessment of dissipated energy and other fatigue criteria. Int. J. Fatigue 29, 1990-1995. (doi:10.1016/j.ijfatigue.2007.01.007) · Zbl 1140.74333
[50] Wan VVC, Maclachlan DW, Dunne FPE. 2014 A stored energy criterion for fatigue crack nucleation in polycrystals. Int. J. Fatigue 68, 90-102. (doi:10.1016/j.ijfatigue.2014.06.001)
[51] Jiang J et al. 2016 Microstructurally sensitive crack nucleation around inclusions in powder metallurgy nickel-based superalloys. Acta Mater. 117, 333-344. (doi:10.1016/j.actamat.2016.07.023)
[52] Chen B, Jiang J, Dunne FPE. 2018 Is stored energy density the primary meso-scale mechanistic driver for fatigue crack nucleation? Int. J. Plast. 101, 213-229. (doi:10.1016/j.ijplas.2017.11.005)
[53] Wilson D, Zheng Z, Dunne FPE. 2018 A microstructure-sensitive driving force for crack growth. J. Mech. Phys. Solids 121, 147-174. (doi:10.1016/j.jmps.2018.07.005)
[54] Wilson D, Dunne FPE. 2019 A mechanistic modelling methodology for microstructure-sensitive fatigue crack growth. J. Mech. Phys. Solids 124, 827-848. (doi:10.1016/j.jmps.2018.11.023)
[55] Wilson D, Wan W, Dunne FPE. 2019 Microstructurally-sensitive fatigue crack growth in HCP, BCC and FCC polycrystals. J. Mech. Phys. Solids 126, 204-225. (doi:10.1016/j.jmps.2019.02.012)
[56] Cruzado A, Lucarini S, LLorca J, Segurado J. 2018 Microstructure-based fatigue life model of metallic alloys with bilinear Coffin-Manson behavior. Int. J. Fatigue 107, 40-48. (doi:10.1016/j.ijfatigue.2017.10.014)
[57] Pineau A. 2001 The randomness of fatigue and fracture behaviour in metallic materials and mechanical structures. In Mechanics of random and multiscale microstructures (eds Jeulin D, Ostoja-Starzewski M), pp. 163-219. Vienna, Austria: Springer. · Zbl 1143.74363
[58] Peralta AD, Enright M, Megahed M, Gong J, Roybal M, Craig J. 2016 Towards rapid qualification of powder-bed laser additively manufactured parts. Integr. Mater. Manuf. Innov. 5, 8. (doi:10.1186/s40192-016-0052-5)
[59] Gong J et al. 2016 Integrated thermal process optimization of alloy 718Plus® for additive manufacturing. Superalloys 2016, 1031-1040.
[60] Allegheny Technologies Incorporated. 2013 ATI 718Plus® Alloy Technical Data Sheet, UNS N07818. See https://www.atimetals.com/Products/Documents/datasheets/nickel-cobalt/nickel-based/ati_718plus_tds_en_v3.pdf.
[61] ASTM International. 2012 E606/E606M-12 standard test method for strain-controlled fatigue testing. West Conshohocken, PA: ASTM International.
[62] Bandyopadhyay R, Prithivirajan V, Sangid MD. 2019 Uncertainty quantification in the mechanical response of crystal plasticity simulations. JOM 71, 2612-2624. (doi:10.1007/s11837-019-03551-3)
[63] Groeber MA, Jackson MA. 2014 DREAM.3D: a digital representation environment for the analysis of microstructure in 3D. Integr. Mater. Manuf. Innov. 3, 1-17. (doi:10.1186/2193-9772-3-5)
[64] Chan LH. 2010 Synthetic three-dimensional voxel-based microstructures that contain annealing twins. Pittsburgh, PA: Carnegie Mellon University.
[65] Geuzaine C, Remacle JF. 2012 Gmsh: a 3-D finite element mesh generator with built-in pre- and post-processing facilities. Int. J. Numer. Methods Eng. 79, 1309-1331. (doi:10.1002/nme.2579) · Zbl 1176.74181
[66] Lee EH. 1969 Elastic-plastic deformation at finite strains. J. Appl. Mech. 36, 1-6. (doi:10.1115/1.3564580) · Zbl 0179.55603
[67] Rice JR. 1971 Inelastic constitutive relations for solids: an internal variables theory and its application to metal plasticity. J. Mech. Phys. Solids 19, 433-455. (doi:10.1016/0022-5096(71)90010-X) · Zbl 0235.73002
[68] Hutchinson JW. 1976 Bounds and self-consistent estimates for creep of polycrystalline materials. Proc. R. Soc. A 348, 101-127. (doi:10.1098/rspa.1976.0027) · Zbl 0319.73059
[69] Frederick CO, Armstrong PJ. 2007 A mathematical representation of the multiaxial Bauschinger effect. Mater. High Temp. 24, 1-26. (doi:10.3184/096034007X207589)
[70] McGinty RD. 2001 Multiscale representation of polycrystalline inelasticity. Atlanta, GA: Georgia Institute of Technology.
[71] Kocks UF. 1970 The relation between polycrystal deformation and single-crystal deformation. Metall. Mater. Trans. 1, 1121-1143. (doi:10.1007/BF02900224)
[72] Prithivirajan V, Sangid MD. 2018 The role of defects and critical pore size analysis in the fatigue response of additively manufactured IN718 via crystal plasticity. Mater. Des. 150, 139-153. (doi:10.1016/j.matdes.2018.04.022)
[73] Haldipur P, Margetan FJ, Thompson RB. 2004 Estimation of single-crystal elastic constants from ultrasonic measurements on polycrystalline specimens. AIP Conf. Proc., 700, 1061-1068. (doi:10.1063/1.1711735)
[74] Cheng J, Shahba A, Ghosh S. 2016 Stabilized tetrahedral elements for crystal plasticity finite element analysis overcoming volumetric locking. Comput. Mech. 57, 733-753. (doi:10.1007/s00466-016-1258-2) · Zbl 1382.74116
[75] Castelluccio GM, McDowell DL. 2015 Microstructure and mesh sensitivities of mesoscale surrogate driving force measures for transgranular fatigue cracks in polycrystals. Mater. Sci. Eng. A 639, 626-639. (doi:10.1016/j.msea.2015.05.048)
[76] Rovinelli A, Sangid MD, Proudhon H, Guilhem Y, Lebensohn RA, Ludwig W. 2018 Predicting the 3D fatigue crack growth rate of small cracks using multimodal data via Bayesian networks: in-situ experiments and crystal plasticity simulations. J. Mech. Phys. Solids 115, 208-229. (doi:10.1016/j.jmps.2018.03.007)
[77] Rovinelli A, Sangid MD, Proudhon H, Ludwig W. 2018 Using machine learning and a data-driven approach to identify the small fatigue crack driving force in polycrystalline materials. npj Comput. Mater. 4, 35. (doi:10.1038/s41524-018-0094-7)
[78] Nicolas A, Co NEC, Burns JT, Sangid MD. 2019 Predicting fatigue crack initiation from coupled microstructure and corrosion morphology effects. Eng. Fract. Mech. 220, 106661. (doi:10.1016/j.engfracmech.2019.106661)
[79] Bandyopadhyay R, Sangid MD. 2019 Crystal plasticity assessment of inclusion- and matrix-driven competing failure modes in a nickel-base superalloy. Acta Mater. 177, 20-34. (doi:10.1016/j.actamat.2019.07.024)
[80] Smith RC. 2013 Uncertainty quantification: theory, implementation, and applications. Philadelphia, PA: SIAM.
[81] Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E. 1953 Equation of state calculations by fast computing machines. J. Chem. Phys. 21, 1087-1092. (doi:10.1063/1.1699114) · Zbl 1431.65006
[82] Hastings WK. 1970 Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97-109. (doi:10.1093/biomet/57.1.97) · Zbl 0219.65008
[83] Yeratapally SR, Glavicic MG, Argyrakis C, Sangid MD. 2017 Bayesian uncertainty quantification and propagation for validation of a microstructure sensitive model for prediction of fatigue crack initiation. Reliab. Eng. Syst. Saf. 164, 110-123. (doi:10.1016/j.ress.2017.03.006)
[84] Cross R, Makeev A, Armanios E. 2007 Simultaneous uncertainty quantification of fracture mechanics based life prediction model parameters. Int. J. Fatigue 29, 1510-1515. (doi:10.1016/j.ijfatigue.2006.10.027) · Zbl 1194.74297
[85] Macdougall D. 2000 Determination of the plastic work converted to heat using radiometry. Exp. Mech. 40, 298-306. (doi:10.1007/BF02327503)
[86] Knysh P, Korkolis YP. 2015 Determination of the fraction of plastic work converted into heat in metals. Mech. Mater. 86, 71-80. (doi:10.1016/j.mechmat.2015.03.006)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.