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

  • Lu Liu
  • Jundong Wang
  • Tao Zeng
  • Yao YaoEmail author
Research Paper
  • 25 Downloads

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.

Keywords

Fatigue crack nucleation Damage Crystal plasticity Finite element Dislocation density 

Notes

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.

References

  1. 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)CrossRefGoogle Scholar
  2. 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)CrossRefGoogle Scholar
  3. 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)CrossRefGoogle Scholar
  4. 4.
    Tanaka, K., Mura, T.: A dislocation model for fatigue crack initiation. ASME J. Appl. Mech. 48, 97–103 (1981)CrossRefzbMATHGoogle Scholar
  5. 5.
    Chan, K.S.: A microstructure-based fatigue-crack-initiation model. Metall. Mater. Trans. A 34, 43–58 (2003)CrossRefGoogle Scholar
  6. 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)CrossRefGoogle Scholar
  7. 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)CrossRefGoogle Scholar
  8. 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)CrossRefGoogle Scholar
  9. 9.
    McDowell, D.L., Dunne, F.P.E.: Microstructure–sensitive computational modeling of fatigue crack formation. Int. J. Fatigue 32, 1521–1542 (2010)CrossRefGoogle Scholar
  10. 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)CrossRefGoogle Scholar
  11. 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)CrossRefGoogle Scholar
  12. 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)MathSciNetCrossRefGoogle Scholar
  13. 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)CrossRefGoogle Scholar
  14. 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)CrossRefGoogle Scholar
  15. 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)CrossRefGoogle Scholar
  16. 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)CrossRefGoogle Scholar
  17. 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)CrossRefGoogle Scholar
  18. 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)CrossRefGoogle Scholar
  19. 19.
    Chow, C.L., Wang, J.: An anisotropic theory of elasticity for continuum damage mechanics. Int. J. Fracture 33, 3–16 (1987)CrossRefGoogle Scholar
  20. 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)CrossRefGoogle Scholar
  21. 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)CrossRefGoogle Scholar
  22. 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)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Lemaitre, J., Chaboche, J.L.: Mechanics of Solid Materials. Cambridge University Press, Cambridge (1990)CrossRefzbMATHGoogle Scholar
  24. 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)CrossRefGoogle Scholar
  25. 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)CrossRefGoogle Scholar
  26. 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)CrossRefGoogle Scholar
  27. 27.
    Abdul-Latif, A., Saanouni, K.: Damaged anelastic behavior of FCC polycrystalline metals with micromechanical approach. Int. J. Damage Mech 3, 237–259 (1994)CrossRefGoogle Scholar
  28. 28.
    Abdul-Latif, A., Mounounga, B.T.: Damage-induced anisotropy with damage deactivation. Int. J. Damage Mech 18, 177–198 (2009)CrossRefGoogle Scholar
  29. 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)CrossRefzbMATHGoogle Scholar
  30. 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)CrossRefGoogle Scholar
  31. 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 Google Scholar
  32. 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)CrossRefGoogle Scholar
  33. 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)CrossRefGoogle Scholar
  34. 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)CrossRefzbMATHGoogle Scholar
  35. 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. 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)CrossRefGoogle Scholar
  37. 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)CrossRefGoogle Scholar
  38. 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)CrossRefzbMATHGoogle Scholar
  39. 39.
    Capolungo, L., Beyerlein, I.J., Tomé, C.N.: Slip-assisted twin growth in hexagonal close-packed metals. Scr. Mater. 60, 32–35 (2009)CrossRefGoogle Scholar
  40. 40.
    Madec, R., Devincre, B., Kubin, L., et al.: The role of collinear interaction in dislocation-induced hardening. Science 301, 1879–1882 (2003)CrossRefGoogle Scholar
  41. 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)CrossRefGoogle Scholar
  42. 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)CrossRefGoogle Scholar
  43. 43.
    Mecking, H., Kocks, U.F.: Kinetics of flow and strain-hardening. Acta Metall. 29, 1865–1875 (1981)CrossRefGoogle Scholar
  44. 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)CrossRefGoogle Scholar
  45. 45.
    Bonora, N.: A nonlinear CDM model for ductile failure. Eng. Fract. Mech. 58, 11–28 (1997)CrossRefGoogle Scholar
  46. 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)CrossRefGoogle Scholar
  47. 47.
    Mura, T., Nakasone, Y.: A theory of fatigue crack initiation in solids. J. Appl. Mech. 57, 1–6 (1990)CrossRefGoogle Scholar
  48. 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)CrossRefGoogle Scholar
  49. 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)CrossRefGoogle Scholar
  50. 50.
    Brar, N.S., Tyson, W.R.: Elastic and plastic anisotropy of white tin. Can. J. Phys. 50, 2257–2264 (1972)CrossRefGoogle Scholar
  51. 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)CrossRefGoogle Scholar
  52. 52.
    Mura, T.: Micromechanics of Defects in Solids. Springer, Amsterdam (1982)CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanics, Civil Engineering and ArchitectureNorthwestern Polytechnical UniversityXi’anChina
  2. 2.Max-Planck-Institut für Eisenforschung GmbHDüsseldorfGermany

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