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Crystal plasticity model to predict fatigue crack nucleation based on the phase transformation theory

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Abstract

A crystal plasticity model is developed to predict the fatigue crack nucleation of polycrystalline materials, in which the accumulated dislocation dipoles are considered to be the origin of damage. To describe the overall softening behavior under cyclic loading, a slip system-level dislocation density-related damage model is proposed and implemented in the finite element analysis with Voronoi tessellation. The numerical model is applied to calibrate the stress–strain relationship at different cycles before fatigue crack nucleation. The parameters determined from the numerical analysis are substituted into a modified phase transformation model to predict the critical fatigue crack nucleation cycle. Comparing with the experimental results of Sn–3.0Ag–0.5Cu (SAC305) alloy and P91 steel, the proposed method can describe the constitutive behavior and predict the fatigue crack nucleation accurately.

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References

  1. Shim, D.J., Alderliesten, R.C., Spearing, S.M., et al.: Fatigue crack growth prediction in GLARE hybrid laminates. Compos. Sci. Technol. 63, 1759–1767 (2003)

    Google Scholar 

  2. Wen, K., Xiong, B., Zhang, Y., et al.: Over-aging influenced matrix precipitate characteristics improve fatigue crack propagation in a high Zn-containing Al–Zn–Mg–Cu alloy. Mater. Sci. Eng., A 716, 42–54 (2018)

    Google Scholar 

  3. Naderi, M., Amiri, M., Iyyer, N., et al.: Prediction of fatigue crack nucleation life in polycrystalline AA7075-T651 using energy approach. Fatigue Fract. Eng. M. 39, 167–179 (2016)

    Google Scholar 

  4. Tanaka, K., Mura, T.: A dislocation model for fatigue crack initiation. ASME J. Appl. Mech. 48, 97–103 (1981)

    MATH  Google Scholar 

  5. Chan, K.S.: A microstructure-based fatigue-crack-initiation model. Metall. Mater. Trans. A 34, 43–58 (2003)

    Google Scholar 

  6. Li, D.F., Barrett, R.A., O’Donoghue, P.E., et al.: A multi-scale crystal plasticity model for cyclic plasticity and low-cycle fatigue in a precipitate-strengthened steel at elevated temperature. J. Mech. Phys. Solids 101, 44–62 (2017)

    Google Scholar 

  7. Fine, M.E., Bhat, S.P.: A model of fatigue crack nucleation in single crystal iron and copper. Mater. Sci. Eng., A 468, 64–69 (2007)

    Google Scholar 

  8. Yao, Y., Wang, J.D., Keer, L.M.: A phase transformation based method to predict fatigue crack nucleation and propagation in metals and alloys. Acta Mater. 127, 244–251 (2017)

    Google Scholar 

  9. McDowell, D.L., Dunne, F.P.E.: Microstructure–sensitive computational modeling of fatigue crack formation. Int. J. Fatigue 32, 1521–1542 (2010)

    Google Scholar 

  10. Basinski, Z.S., Basinski, S.J.: Fundamental-aspects of low amplitude cyclic deformation in face-centered cubic-crystals. Prog. Mater Sci. 36, 89–148 (1992)

    Google Scholar 

  11. Phan, V.T., Zhang, X., Li, Y., et al.: Microscale modeling of creep deformation and rupture in Nickel-based superalloy IN 617 at high temperature. Mech. Mater. 114, 215–227 (2017)

    Google Scholar 

  12. Sweeney, C.A., Vorster, W., Leen, S.B., et al.: The role of elastic anisotropy, length scale and crystallographic slip in fatigue crack nucleation. J. Mech. Phys. Solids 61, 1224–1240 (2013)

    MathSciNet  Google Scholar 

  13. Li, L., Shen, L., Proust, G.: Fatigue crack initiation life prediction for aluminium alloy 7075 using crystal plasticity finite element simulations. Mech. Mater. 81, 84–93 (2015)

    Google Scholar 

  14. Zhang, K.S., Ju, J.W., Li, Z., et al.: Micromechanics based fatigue life prediction of a polycrystalline metal applying crystal plasticity. Mech. Mater. 85, 16–37 (2015)

    Google Scholar 

  15. Chen, B., Jiang, J., Dunne, F.P.E.: Microstructurally-sensitive fatigue crack nucleation in Ni-based single and oligo crystals. J. Mech. Phys. Solids 106, 15–33 (2017)

    Google Scholar 

  16. Brommesson, R., Ekh, M., Joseph, C.: 3D grain structure modelling of intergranular fracture in forged Haynes 282. Eng. Fract. Mech. 154, 57–71 (2016)

    Google Scholar 

  17. Bhat, S.P., Fine, M.E.: Fatigue crack nucleation in iron and a high strength low alloy steel. Mater. Sci. Eng., A 314, 90–96 (2001)

    Google Scholar 

  18. Döenges, B., Giertler, A., Krupp, U., et al.: Significance of crystallographic misorientation at phase boundaries for fatigue crack initiation in a duplex stainless steel during high and very high cycle fatigue loading. Mater. Sci. Eng., A 589, 146–152 (2014)

    Google Scholar 

  19. Chow, C.L., Wang, J.: An anisotropic theory of elasticity for continuum damage mechanics. Int. J. Fracture 33, 3–16 (1987)

    Google Scholar 

  20. Zhang, W., Jiang, W., Xu, Z., et al.: Fatigue life of a dissimilar welded joint considering the weld residual stress: experimental and finite element simulation. Int. J. Fatigue 109, 182–190 (2018)

    Google Scholar 

  21. Mounounga, T.B., Abdul-Latif, A., Razafindramary, D.: Damage induced anisotropy of polycrystals under complex cyclic loadings. Int. J. Mech. Sci. 53, 271–280 (2011)

    Google Scholar 

  22. Patra, A., McDowell, D.L.: A void nucleation and growth based damage framework to model failure initiation ahead of a sharp notch in irradiated bcc materials. J. Mech. Phys. Solids 74, 111–135 (2015)

    MathSciNet  Google Scholar 

  23. Lemaitre, J., Chaboche, J.L.: Mechanics of Solid Materials. Cambridge University Press, Cambridge (1990)

    MATH  Google Scholar 

  24. Yao, Y., He, X., Keer, L.M., et al.: A continuum damage mechanics-based unified creep and plasticity model for solder materials. Acta Mater. 83, 160–168 (2015)

    Google Scholar 

  25. Liu, J., Li, J., Dirrasa, G., et al.: A three-dimensional multi-scale polycrystalline plasticity model coupled with damage for pure Ti with harmonic structure design. Int. J. Plast 100, 192–207 (2018)

    Google Scholar 

  26. Kim, J.B., Yoon, J.W.: Necking behavior of AA 6022-T4 based on the crystal plasticity and damage models. Int. J. Plast 73, 3–23 (2015)

    Google Scholar 

  27. Abdul-Latif, A., Saanouni, K.: Damaged anelastic behavior of FCC polycrystalline metals with micromechanical approach. Int. J. Damage Mech 3, 237–259 (1994)

    Google Scholar 

  28. Abdul-Latif, A., Mounounga, B.T.: Damage-induced anisotropy with damage deactivation. Int. J. Damage Mech 18, 177–198 (2009)

    Google Scholar 

  29. Anahid, M., Samal, M.K., Ghosh, S.: Dwell fatigue crack nucleation model based on crystal plasticity finite element simulations of polycrystalline titanium alloys. J. Mech. Phys. Solids 59, 2157–2176 (2011)

    MATH  Google Scholar 

  30. Wan, V.V.C., MacLachlan, D.W., Dunne, F.P.E.: A stored energy criterion for fatigue crack nucleation in polycrystals. Int. J. Fatigue 68, 90–102 (2014)

    Google Scholar 

  31. Zhu, Y., Engelhardt, M.D., Pan, Z.: Simulation of ductile fracture initiation in steels using a stress triaxiality–shear stress coupled model. Acta Mech. Sin. (2019). https://doi.org/10.1007/s10409-018-0825-5

    Article  Google Scholar 

  32. Ashton, P.J., Harte, A.M., Leen, S.B.: A strain-gradient, crystal plasticity model for microstructure–sensitive fretting crack initiation in ferritic-pearlitic steel for flexible marine risers. Int. J. Fatigue 111, 81–92 (2018)

    Google Scholar 

  33. Fatemi, A., Socie, D.F.: A critical plane approach to multiaxial fatigue damage including out-of-phase loading. Fatigue Fract. Eng. Mater. Struct. 11, 149–165 (1988)

    Google Scholar 

  34. Manonukul, A., Dunne, F.P.E.: High- and low-cycle fatigue crack initiation using polycrystal plasticity. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 460, 1881–1903 (2004)

    MATH  Google Scholar 

  35. Huang, Y.: A user-material subroutine incorporating single crystal plasticity in the ABAQUS finite element program. [Ph.D Thesis] Harvard University, Cambridge (1991)

    Google Scholar 

  36. Hu, P., Liu, Y., Zhu, Y., et al.: Crystal plasticity extended models based on thermal mechanism and damage functions: application to multiscale modeling of aluminum alloy tensile behavior. Int. J. Plast 86, 1–25 (2016)

    Google Scholar 

  37. Kalidindi, S.R., Bronkhorst, C.A., Anand, L.: Crystallographic texture evolution in bulk deformation processing of FCC metals. J. Mech. Phys. Solids 40, 537–569 (1992)

    Google Scholar 

  38. Beyerlein, I.J., Tomé, C.N.: A dislocation-based constitutive law for pure Zr including temperature effects. Int. J. Plast 24, 867–895 (2008)

    MATH  Google Scholar 

  39. Capolungo, L., Beyerlein, I.J., Tomé, C.N.: Slip-assisted twin growth in hexagonal close-packed metals. Scr. Mater. 60, 32–35 (2009)

    Google Scholar 

  40. Madec, R., Devincre, B., Kubin, L., et al.: The role of collinear interaction in dislocation-induced hardening. Science 301, 1879–1882 (2003)

    Google Scholar 

  41. Zecevic, M., Knezevic, M.: A dislocation density based elasto-plastic self-consistent model for the prediction of cyclic deformation: application to AA6022-T4. Int. J. Plast 72, 200–217 (2015)

    Google Scholar 

  42. Kitayama, K., Tomé, C.N., Rauch, E.F., et al.: A crystallographic dislocation model for describing hardening of polycrystals during strain path changes: application to low carbon steels. Int. J. Plast 46, 54–69 (2013)

    Google Scholar 

  43. Mecking, H., Kocks, U.F.: Kinetics of flow and strain-hardening. Acta Metall. 29, 1865–1875 (1981)

    Google Scholar 

  44. Jeong, Y., Barlat, F., Tomé, C.N., et al.: A comparative study between micro- and macro-mechanical constitutive models developed for complex loading scenarios. Int. J. Plast 93, 212–228 (2017)

    Google Scholar 

  45. Bonora, N.: A nonlinear CDM model for ductile failure. Eng. Fract. Mech. 58, 11–28 (1997)

    Google Scholar 

  46. Lin, B., Zhao, L.G., Tong, J., et al.: Crystal plasticity modeling of cyclic deformation for a polycrystalline nickel-based superalloy at high temperature. Mater. Sci. Eng., A 527, 3581–3587 (2010)

    Google Scholar 

  47. Mura, T., Nakasone, Y.: A theory of fatigue crack initiation in solids. J. Appl. Mech. 57, 1–6 (1990)

    Google Scholar 

  48. Liu, L., Yao, Y., Zeng, T., et al.: A dislocation density based micromechanical constitutive model for Sn–Ag–Cu solder alloys. Mater. Res. Express 4, 106506 (2017)

    Google Scholar 

  49. Zhou, B., Bieler, T.R., Lee, T.K., et al.: Methodology for analyzing slip behavior in ball grid array lead-free solder joints after simple shear. J. Electron. Mater. 38, 2702–2711 (2009)

    Google Scholar 

  50. Brar, N.S., Tyson, W.R.: Elastic and plastic anisotropy of white tin. Can. J. Phys. 50, 2257–2264 (1972)

    Google Scholar 

  51. Wen, W., Borodachenkova, M., Tomé, C.N., et al.: Mechanical behavior of low carbon steel subjected to strain path changes: experiments and modeling. Acta Mater. 111, 305–314 (2016)

    Google Scholar 

  52. Mura, T.: Micromechanics of Defects in Solids. Springer, Amsterdam (1982)

    Google Scholar 

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Acknowledgements

The work was supported by the National Natural Science Foundations of China (Grants 11572249, 11772257 and 11602196), and Y. Yao acknowledges the Alexander von Humboldt Foundation for supporting his stay at the Max-Planck-Institut für Eisenforschung.

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Authors and Affiliations

  1. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an, 710072, China

    Lu Liu, Jundong Wang, Tao Zeng & Yao Yao

  2. Max-Planck-Institut für Eisenforschung GmbH, Max Planck Str. 1, 40237, Düsseldorf, Germany

    Yao Yao

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  1. Lu Liu
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Correspondence to Yao Yao.

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Liu, L., Wang, J., Zeng, T. et al. Crystal plasticity model to predict fatigue crack nucleation based on the phase transformation theory. Acta Mech. Sin. 35, 1033–1043 (2019). https://doi.org/10.1007/s10409-019-00876-9

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  • DOI: https://doi.org/10.1007/s10409-019-00876-9

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