3D Grain-Based Mesoscale Modeling of Short Fatigue Crack Growth for Bridge Weldments Considering Crack-Front Evolution
Publication: Journal of Engineering Mechanics
Volume 146, Issue 2
Abstract
To evaluate short crack growth and fatigue damage accumulation in steel structures, efforts have been made based on a two-dimensional (2D) grain-based model for fatigue life assessment under variable amplitude loads. However, crack arrested in a 2D field could be problematic since the arrested 2D crack might propagate toward the out-of-plane direction. In addition, the pure plane stress/plain assumption in 2D simulation could not be applied to many complex stress states. In this paper, a three-dimensional (3D) fatigue damage estimation model is proposed based on a twofold nonlinear grain-based fatigue life assessment method. The persistent slip band based short fatigue crack growth model is implemented in this model combined with Miner’s rule for grain fatigue accumulation evaluations. Rain-flow counting method and the linear damage rule in grains are employed for fatigue damage growth within each grain. Meanwhile, in the grain and subgrain regime, the crack is assumed to nucleate and grow along with persistent slip bands. Also, an adjacent persistent slip band detection algorithm is developed to locate the potential crack propagation path. Therefore, fatigue damage is calculated grain by grain until the crack length reaches the characteristic length (such as over 0.1 mm), where linear elastic fracture mechanics (LEFM) thoery becomes more reliable. Sensitivity analysis is conducted for the number of grains and the element size in statistical volume element model under constant amplitude loads. Finally, a case study is performed to demonstrate the proposed method for variable amplitude loads, and the results are compared with the 2D model results in the literature.
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Acknowledgments
This material is based on work supported by the National Science Foundation [NSF Grant Civil, Mechanical and Manufacturing Innovation (CMMI-1537121)] and Research Excellence Program (REP) from the Office of the Vice President for Research (OVPR) of the University of Connecticut. These supports are greatly appreciated. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the sponsors.
References
Agoston, M. K. 2005. Computer graphics and geometric modeling: Implementation and algorithms, 300–306. New York: Springer.
Alaoui, A. E. M., D. Thevenet, and A. Zeghloul. 2009. “Short surface fatigue cracks growth under constant and variable amplitude loading.” Eng. Fract. Mech. 76 (15): 2359–2370. https://doi.org/10.1016/j.engfracmech.2009.07.017.
ASTM. 2011. Standard practices for cycle counting in fatigue analysis. ASTM E1049-85. West Conshohocken, PA: ASTM.
Bargmann, S., B. Svendsen, and M. Ekh. 2011. “An extended crystal plasticity model for latent hardening in polycrystals.” Comput. Mech. 48 (6): 631–645. https://doi.org/10.1007/s00466-011-0609-2.
Benedetti, I., and V. Gulizzi. 2018. “A grain-scale model for high-cycle fatigue degradation in polycrystalline materials.” Int. J. Fatigue 116 (Nov): 90–105. https://doi.org/10.1016/j.ijfatigue.2018.06.010.
Bomidi, J. A. R., N. Weinzapfel, and F. Sadeghi. 2012. “Three-dimensional modelling of intergranular fatigue failure of fine grain polycrystalline metallic MEMS devices.” Fatigue Fract. Eng. Mater. Struct. 35 (11): 1007–1021. https://doi.org/10.1111/j.1460-2695.2012.01689.x.
Boungou, D., F. Guillet, M. El Badaoui, P. Lyonnet, and T. Rosario. 2015. “Fatigue damage detection using cyclostationarity.” Mech. Syst. Signal Process. 58–59 (Jun): 128–142. https://doi.org/10.1016/j.ymssp.2014.11.010.
Castelluccio, G. M., and D. L. McDowell. 2014a. “A mesoscale approach for growth of 3D microstructurally small fatigue cracks in polycrystals.” Int. J. Damage Mech. 23 (6): 791–818. https://doi.org/10.1177/1056789513513916.
Castelluccio, G. M., and D. L. McDowell. 2014b. “Mesoscale modeling of microstructurally small fatigue cracks in metallic polycrystals.” Mater. Sci. Eng. A 598 (Mar): 34–55. https://doi.org/10.1016/j.msea.2014.01.015.
Cazzulani, G., F. Ripamonti, and F. Resta. 2014. “Fatigue damage reduction for flexible structure through active control.” In Proc., 2014 IEEE Conf. on Control Applications, 1729–1734. New York: IEEE.
Farkas, D., M. Willemann, and B. Hyde. 2005. “Atomistic mechanisms of fatigue in nanocrystalline metals.” Phys. Rev. Lett. 94 (16): 165502. https://doi.org/10.1103/PhysRevLett.94.165502.
Fatemi, A., and D. F. Socie. 1988. “A critical plane approach to multiaxial fatigue damage including out-of-phase loading.” Fatigue Fract. Eng. Mater. Struct. 11 (3): 149–165. https://doi.org/10.1111/j.1460-2695.1988.tb01169.x.
Fatemi, A., and L. Yang. 1998. “Cumulative fatigue damage and life prediction theories: A survey of the state of the art for homogeneous materials.” Int. J. Fatigue 20 (1): 9–34. https://doi.org/10.1016/S0142-1123(97)00081-9.
Fricke, W. 2015. “Recent developments and future challenges in fatigue strength assessment of welded joints.” Proc., Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 229 (7): 1224–1239. https://doi.org/10.1177/0954406214550015.
Ghahremani, K., S. Walbridge, and T. Topper. 2015. “High cycle fatigue behaviour of impact treated welds under variable amplitude loading conditions.” Int. J. Fatigue 81 (Dec): 128–142. https://doi.org/10.1016/j.ijfatigue.2015.07.022.
Ghosh, S., and P. Chakraborty. 2013. “Microstructure and load sensitive fatigue crack nucleation in Ti-6242 using accelerated crystal plasticity FEM simulations.” Supplement, Int. J. Fatigue 48 (SC): 231–246. https://doi.org/10.1016/j.ijfatigue.2012.10.022.
Harati, E., L. Karlsson, L. E. Svensson, and K. Dalaei. 2015. “The relative effects of residual stresses and weld toe geometry on fatigue life of weldments.” Int. J. Fatigue 77 (Aug): 160–165. https://doi.org/10.1016/j.ijfatigue.2015.03.023.
Hemmesi, K., M. Farajian, and A. Fatemi. 2017. “Application of the critical plane approach to the torsional fatigue assessment of welds considering the effect of residual stresses.” Int. J. Fatigue 101 (Aug): 271–281. https://doi.org/10.1016/j.ijfatigue.2017.01.023.
Huang, Y. 1991. A user-material subroutine incorporating single crystal plasticity in the ABAQUS finite element program. Cambridge, MA: Harvard Univ.
Krupp, U., O. Düber, H. J. Christ, B. Künkler, P. Köster, and C. P. Fritzen. 2007. “Propagation mechanisms of microstructurally short cracks-factors governing the transition from short- to long-crack behavior.” Mater. Sci. Eng. A 462 (1–2): 174–177. https://doi.org/10.1016/j.msea.2006.03.159.
Li, Y., V. Aubin, C. Rey, and P. Bompard. 2012. “The effects of variable stress amplitude on cyclic plasticity and microcrack initiation in austenitic steel 304L.” Comput. Mater. Sci 64 (Nov): 7–11. https://doi.org/10.1016/j.commatsci.2012.05.028.
Liang, Y., and W. Chen. 2016. “A regularized miner’s rule for fatigue reliability analysis with Mittag-Leffler statistics.” Int. J. Damage Mech. 25 (5): 691–704. https://doi.org/10.1177/1056789515607610.
Lin, B., L. G. Zhao, J. Tong, and H. J. Christ. 2010. “Crystal plasticity modeling of cyclic deformation for a polycrystalline nickel-based superalloy at high temperature.” Mater. Sci. Eng., A 527 (15): 3581–3587. https://doi.org/10.1016/j.msea.2010.02.045.
Liu, Y., and S. Mahadevan. 2007. “Stochastic fatigue damage modeling under variable amplitude loading.” Int. J. Fatigue 29 (6): 1149–1161. https://doi.org/10.1016/j.ijfatigue.2006.09.009.
Liu, Y., and S. Mahadevan. 2009. “Probabilistic fatigue life prediction using an equivalent initial flaw size distribution.” Int. J. Fatigue 31 (3): 476–487. https://doi.org/10.1016/j.ijfatigue.2008.06.005.
Liu, Y.-P., C.-Y. Chen, and G.-Q. Li. 2012. “Fatigue crack growth and control of 14MnNbq welding plates used for bridges.” J. Eng. Mech. 138 (1): 30–35. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000295.
Maddox, S. J., and K. G. Richards. 1991. Fatigue strength of welded structures. 2nd ed. Cambridge, UK: Abington.
Miah, M. S., E. N. Chatzi, V. K. Dertimanis, and F. Weber. 2017. “Real-time experimental validation of a novel semi-active control scheme for vibration mitigation.” Struct. Control Health Monit. 24 (3): e1878. https://doi.org/10.1002/stc.1878.
Miller, K. J. 1987. “The behaviour of short fatigue cracks and their initiation part I: A review of two recent books.” Fatigue Fract. Eng. Mater. Struct. 10 (1): 75–91. https://doi.org/10.1111/j.1460-2695.1987.tb01150.x.
Musinski, W. D., and D. L. McDowell. 2016. “Simulating the effect of grain boundaries on microstructurally small fatigue crack growth from a focused ion beam notch through a three-dimensional array of grains.” Acta Mater. 112 (Jun): 20–39. https://doi.org/10.1016/j.actamat.2016.04.006.
Navarro, A., and E. R. de los Rios. 1988. “Short and long fatigue crack growth: A unified model.” Philos. Mag. A 57 (1): 15–36. https://doi.org/10.1080/01418618808204496.
Ngoula, D. T., H. T. Beier, and M. Vormwald. 2017. “Fatigue crack growth in cruciform welded joints: Influence of residual stresses and of the weld toe geometry.” Int. J. Fatigue 101 (Aug): 253–262. https://doi.org/10.1016/j.ijfatigue.2016.09.020.
Nishimura, K., and N. Miyazaki. 2004. “Molecular dynamics simulation of crack growth under cyclic loading.” Comput. Mater. Sci 31 (3–4): 269–278. https://doi.org/10.1016/j.commatsci.2004.03.009.
Oliver, J., M. Caicedo, E. Roubin, A. E. Huespe, and J. A. Hernández. 2015. “Continuum approach to computational multiscale modeling of propagating fracture.” Comput. Methods Appl. Mech. Eng. 294 (Sep): 384–427. https://doi.org/10.1016/j.cma.2015.05.012.
Peirce, D., R. J. Asaro, and A. Needleman. 1982. “An analysis of nonuniform and localized deformation in ductile single crystals.” Acta Metall. 30 (6): 1087–1119. https://doi.org/10.1016/0001-6160(82)90005-0.
Peirce, D., R. J. Asaro, and A. Needleman. 1983. “Material rate dependence and localized deformation in crystalline solids.” Acta Metall. 31 (12): 1951–1976. https://doi.org/10.1016/0001-6160(83)90014-7.
Pineau, A., D. L. McDowell, E. P. Busso, and S. D. Antolovich. 2016. “Failure of metals II: Fatigue.” Acta Mater. 107 (Apr): 484–507. https://doi.org/10.1016/j.actamat.2015.05.050.
Remes, H., P. Varsta, and J. Romanoff. 2012. “Continuum approach to fatigue crack initiation and propagation in welded steel joints.” Int. J. Fatigue 40 (C): 16–26. https://doi.org/10.1016/j.ijfatigue.2012.01.007.
Riemer, A., S. Leuders, M. Thöne, H. A. Richard, T. Tröster, and T. Niendorf. 2014. “On the fatigue crack growth behavior in 316L stainless steel manufactured by selective laser melting.” Eng. Fract. Mech. 120 (Apr): 15–25. https://doi.org/10.1016/j.engfracmech.2014.03.008.
Rycroft, C. H. 2009. “Voro++: A three-dimensional voronoi cell library in C++.” Chaos 19 (4): 041111. https://doi.org/10.1063/1.3215722.
Rycroft, C. H., G. S. Grest, J. W. Landry, and M. Z. Bazant. 2006. “Analysis of granular flow in a pebble-bed nuclear reactor.” Phys. Rev. E: Stat. Nonlinear Soft Matter Phys. 74 (2): 021306. https://doi.org/10.1103/PhysRevE.74.021306.
Sangid, M. D. 2013. “The physics of fatigue crack initiation.” Int. J. Fatigue 57 (Dec): 58–72. https://doi.org/10.1016/j.ijfatigue.2012.10.009.
Sangid, M. D., H. J. Maier, and H. Sehitoglu. 2011. “A physically based fatigue model for prediction of crack initiation from persistent slip bands in polycrystals.” Acta Mater. 59 (1): 328–341. https://doi.org/10.1016/j.actamat.2010.09.036.
Schijve, J. 2009. Vol. 25 of Fatigue of structures and materials, 1–622. New York: Springer.
Shang, Y.-B., H.-J. Shi, Z.-X. Wang, and G.-D. Zhang. 2015. “In-situ SEM study of short fatigue crack propagation behavior in a dissimilar metal welded joint of nuclear power plant.” Mater. Des. 88 (Dec): 598–609. https://doi.org/10.1016/j.matdes.2015.08.090.
Shenoy, M., Y. Tjiptowidjojo, and D. McDowell. 2008. “Microstructure-sensitive modeling of polycrystalline IN 100.” Int. J. Plast. 24 (10): 1694–1730. https://doi.org/10.1016/j.ijplas.2008.01.001.
Shenoy, M., J. Zhang, and D. L. McDowell. 2007. “Estimating fatigue sensitivity to polycrystalline Ni-base superalloy microstructures using a computational approach.” Fatigue Fract. Eng. Mater. Struct. 30 (10): 889–904. https://doi.org/10.1111/j.1460-2695.2007.01159.x.
Shyam, A., and W. W. Milligan. 2005. “A model for slip irreversibility, and its effect on the fatigue crack propagation threshold in a nickel-base superalloy.” Acta Mater. 53 (3): 835–844. https://doi.org/10.1016/j.actamat.2004.10.036.
Sinha, S., and S. Ghosh. 2006. “Modeling cyclic ratcheting based fatigue life of HSLA steels using crystal plasticity FEM simulations and experiments.” Int. J. Fatigue 28 (12): 1690–1704. https://doi.org/10.1016/j.ijfatigue.2006.01.008.
Smith, B. D., D. S. Shih, and D. L. McDowell. 2016. “Fatigue hot spot simulation for two widmanstätten titanium microstructures.” Int. J. Fatigue 92 (Nov): 116–129. https://doi.org/10.1016/j.ijfatigue.2016.05.002.
Stephens, R. I., A. Fatemi, R. R. Stephens, and H. O. Fuchs. 2001. Metal fatigue in engineering. 2nd ed. New York: Wiley.
Sweeney, C. A., W. Vorster, S. B. Leen, E. Sakurada, P. E. McHugh, and F. P. E. Dunne. 2013. “The role of elastic anisotropy, length scale and crystallographic slip in fatigue crack nucleation.” J. Mech. Phys. Solids 61 (5): 1224–1240. https://doi.org/10.1016/j.jmps.2013.01.001.
Tanaka, K., and T. Mura. 1981. “A dislocation model for fatigue crack initiation.” J. Appl. Mech. 48 (1): 97–103. https://doi.org/10.1115/1.3157599.
Trochidis, A., E. Douka, and B. Polyzos. 2000. “Formation and evolution of persistent slip bands in metals.” J. Mech. Phys. Solids 48 (8): 1761–1775. https://doi.org/10.1016/S0022-5096(99)00077-0.
Vatti, B. R. 1992. “A generic solution to polygon clipping.” Commun. ACM 35 (7): 56–63. https://doi.org/10.1145/129902.129906.
Vijay, A., N. Paulson, and F. Sadeghi. 2018. “A 3D finite element modelling of crystalline anisotropy in rolling contact fatigue.” Int. J. Fatigue 106 (Jan): 92–102. https://doi.org/10.1016/j.ijfatigue.2017.09.016.
Wang, Y.-R., and T.-H. Kuo. 2016. “Effects of a dynamic vibration absorber on nonlinear hinged-free beam.” J. Eng. Mech. 142 (4): 04016003. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001039.
Wei, L. W., E. R. De Los Rios, and M. N. James. 2002. “Experimental study and modelling of short fatigue crack growth in aluminium alloy Al7010-T7451 under random loading.” Int. J. Fatigue 24 (9): 963–975. https://doi.org/10.1016/S0142-1123(02)00006-3.
Wu, W., J. Owino, A. Al-Ostaz, and L. Cai. 2014. “Applying periodic boundary conditions in finite element analysis.” In Proc., Simulia Community Conf., 1–937. Vélizy-Villacoublay, France: Dassault Systemes.
Xie, C. L., S. Ghosh, and M. Groeber. 2004. “Modeling cyclic deformation of HSLA steels using crystal plasticity.” J. Eng. Mater. Technol. 126 (4): 339–352. https://doi.org/10.1115/1.1789966.
Xue, Y. 2010. “Modeling fatigue small-crack growth with confidence—A multistage approach.” Int. J. Fatigue 32 (7): 1210–1219. https://doi.org/10.1016/j.ijfatigue.2009.12.016.
Yin, X., S. Lee, W. Chen, W. K. Liu, and M. F. Horstemeyer. 2009. “Efficient random field uncertainty propagation in design using multiscale analysis.” J. Mech. Des. 131 (2): 021006. https://doi.org/10.1115/1.3042159.
Yuan, H., W. Zhang, G. M. Castelluccio, J. Kim, and Y. Liu. 2018a. “Microstructure-sensitive estimation of small fatigue crack growth in bridge steel welds.” Int. J. Fatigue 112 (Dec): 183–197. https://doi.org/10.1016/j.ijfatigue.2018.03.015.
Yuan, H., W. Zhang, J. Kim, and Y. Liu. 2017. “A nonlinear grain-based fatigue damage model for civil infrastructure under variable amplitude loads.” Int. J. Fatigue 104 (Nov): 389–396. https://doi.org/10.1016/j.ijfatigue.2017.07.026.
Yuan, H., W. Zhang, and Y. Liu. 2018b. “Quantification of time distribution to initial long crack with reduced order microstructural representation on microstructurally short fatigue crack growth model.” In Proc., 2018 AIAA Non-Deterministic Approaches Conf., 1–9. Reston, VA: American Institute of Aeronautics and Astronautics.
Zárate, B. A., J. M. Caicedo, J. Yu, and P. Ziehl. 2012. “Probabilistic prognosis of fatigue crack growth using acoustic emission data.” J. Eng. Mech. 138 (9): 1101–1111. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000414.
Zhang, K. S., J. W. Ju, Z. Li, Y. L. Bai, and W. Brocks. 2015. “Micromechanics based fatigue life prediction of a polycrystalline metal applying crystal plasticity.” Mech. Mater. 85 (Jun): 16–37. https://doi.org/10.1016/j.mechmat.2015.01.020.
Zhang, W., C. S. Cai, and F. Pan. 2013. “Nonlinear fatigue damage assessment of existing bridges considering progressively deteriorated road conditions.” Eng. Struct. 56 (Nov): 1922–1932. https://doi.org/10.1016/j.engstruct.2013.06.027.
Zhang, W., C. S. Cai, F. Pan, and Y. Zhang. 2014. “Fatigue life estimation of existing bridges under vehicle and non-stationary hurricane wind.” J. Wind Eng. Ind. Aerodyn. 133 (Oct): 135–145. https://doi.org/10.1016/j.jweia.2014.06.008.
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Journal of Engineering Mechanics
Volume 146 • Issue 2 • February 2020
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©2019 American Society of Civil Engineers.
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Received: Sep 9, 2018
Accepted: Jul 8, 2019
Published online: Dec 11, 2019
Published in print: Feb 1, 2020
Discussion open until: May 11, 2020
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