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Inhomogeneous deformation growth of a metal under cyclic loading and its influence on fatigue

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Abstract

In this paper, the effects of inhomogeneous material deformation and fatigue caused by meso-mechanical inhomogeneity are investigated. A representative volume element is constructed for pure copper as a material model which features a polycrystalline Voronoi aggregation consisting of a number of crystal grains. The Chaboche model with random parameters is adopted to reflect inhomogeneous cyclic plastic behavior of grains. Key simulations are performed to model the experimental cyclic evolution of strain fatigue under symmetrical tensile–compressive loading. The simulation results show that, although the macroscopic material hysteresis curve keeps stable, the mesoscopic deformations become increasingly inhomogeneous and the statistic differences keep growing. Accordingly, further research on the underlying relation between inhomogeneous deformation and fatigue is conducted, and a systematic methodology to predict the low-cycle fatigue life is revealed.

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References

  1. Asaro, R.J., Rice, J.R.: Strain localizaion in ductile single crystals. J. Mech. Phys. Solids. 25(5), 309–338 (1977)

    Article  Google Scholar 

  2. Bennett, V.P., McDowell, D.L.: Polycrystal orientation distribution effects on microslip in high cycle fatigue. Int. J. Fatigue 25(1), 27–39 (2003)

    Article  Google Scholar 

  3. Bochenek, B., Pyrz, R.: Reconstruction methodology for planar and spatial random microstructure. In: New Challenges in Mesomechanics 2002 (2002)

  4. Chaboche, J.L.: Constitutive equations for cyclic plasticity and cyclic viscoplasticity. Int. J. Plast. 5(3), 247–302 (1989)

    Article  Google Scholar 

  5. Chan, K.S.: Roles of microstructure in fatigue crack initiation. Int. J. Fatigue 32(9), 1428–1447 (2010)

    Article  Google Scholar 

  6. Chan, K.S., Lee, Y.D.: Effects of deformation-induced constraint on high-cycle fatigue in Ti alloys with a duplex microstructure. Metall. Mater. Trans. A 39(7), 1665–1675 (2008)

    Article  Google Scholar 

  7. Ghosh, S., Anahid, M.: Homogenized constitutive and fatigue nucleation models from crystal plasticity FE simulations of Ti alloys, Part 1: macroscopic anisotropic yield function. Int. J. Plast. 47, 182–201 (2013)

    Article  Google Scholar 

  8. Hansen, A., Hinrichsen, E.L., Roux, S.: Scale-invariant disorder in fracture and related breakdown phenomena. Phys. Rev. B 43(1), 665 (1991)

    Article  Google Scholar 

  9. Hill, R., Rice, J.R.: Constitutive analysis of elastic-plastic crystals at arbitrary strain. J. Mech. Phys. Solids 20(6), 401–413 (1972)

    Article  Google Scholar 

  10. Huang, Y.: A user-material subroutine incorporating single crystal plasticity in the ABAQUS finite element program. Division of Applied Sciences, Harvard University, Report MECH-178 (1991)

  11. Hutchinson, J.W.: Bounds and self-consistent estimates for creep of polycrystalline materials. Proc. R. Soc. Lond. A Math. Phys. Sci. 348(1652), 101–127 (1976)

    MATH  Google Scholar 

  12. Kalikindi, R.S., Bronkhorst, C.A., Anand, L.: Crystallographic texture evolution in bulk deformation processing of FCC metals. J. Mech. Phys. Solids 40(3), 537–569 (1992)

    Article  Google Scholar 

  13. Liu, Y., Varghese, S., Ma, J., Yoshino, M., Lu, H., Komanduri, R.: Orientation effects in nanoindentation of single crystal copper. Int. J. Plast. 24(11), 1990–2015 (2008)

    Article  Google Scholar 

  14. Maniatty, A.M., Dawson, P.R., Lee, Y.S.: A time integration algorithm for elastoviscoplastic cubic crystals applied to modelling polycrystalline deformation. Int. J. Numer. Methods Eng. 35(8), 1565–1588 (2010)

    Article  Google Scholar 

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

    Article  Google Scholar 

  16. Mcgarry, J.P., O’Donnell, B.P., McHugh, P.E., McGarry, J.G.: Analysis of the mechanical performance of a cardiovascular stent design based on micromechanical modelling. Comput. Mater. Sci. 31(3), 421–438 (2004)

    Article  Google Scholar 

  17. Muszka, K.: Modelling of deformation inhomogeneity in the angular accumulative drawing process–multiscale approach. Mater. Sci. Eng. A 559, 635–642 (2013)

    Article  Google Scholar 

  18. Needleman, A., Asaro, R.J., Lemonds, J., Peirce, D.: Finite element analysis of crystalline solids. Comput. Methods Appl. Mech. Eng. 52(1), 689–708 (1985)

    Article  Google Scholar 

  19. Needleman, A., Tvergaard, V.: Comparison of crystal plasticity and isotropic hardening predictions for metal-matrix composites. J. Appl. Mech. 60(1), 70–76 (1993)

    Article  Google Scholar 

  20. Payne, J., Welsh, G., Christ Jr., R.J., Nardiello, J., Papazian, J.M.: Observations of fatigue crack initiation in 7075–T651. Int. J. Fatigue 32(2), 247–255 (2010)

    Article  Google Scholar 

  21. Peirce, D., Asaro, R.J., Needleman, A.: Material rate dependence and localized deformation in crystalline solids. Acta Metall. 31(12), 1951–1976 (1983)

    Article  Google Scholar 

  22. Prakash, A., Lebensohn, R.A.: Simulation of micromechanical behavior of polycrystals: finite elements versus fast Fourier transforms. Modell. Simul. Mater. Sci. Eng. 17(6), 64010–64016 (2009)

    Article  Google Scholar 

  23. Sangid, M.D.: The physics of fatigue crack initiation. Int. J. Fatigue 57, 58–72 (2013)

    Article  Google Scholar 

  24. Sarma, G., Zacharia, T.: Integration algorithm for modeling the elasto-viscoplastic response of polycrystalline materials. J. Mech. Phys. Solids 47(6), 1219–1238 (1999)

    Article  Google Scholar 

  25. Sun, C.T., Vaidya, R.S.: Prediction of composite properties from a representative volume element. Compos. Sci. Technol. 56(2), 171–179 (1996)

    Article  Google Scholar 

  26. Sweeney, C.A., Vorster, W., Leen, S.B., Sakurada, E., McHugh, P.E., Dunne, F.P.E.: The role of elastic anisotropy, length scale and crystallographic slip in fatigue crack nucleation. J. Mech. Phys. Solids 61(5), 1224–1240 (2013)

    Article  MathSciNet  Google Scholar 

  27. Tang, C.: Numerical simulation of progressive rock failure and associated seismicity. Int. J. Rock Mech. Min. Sci. 34(2), 249–261 (1997)

    Article  MathSciNet  Google Scholar 

  28. Xia, Z., Zhou, C., Yong, Q., Zhang, X.: On selection of repeated unit cell model and application of unified periodic boundary conditions in micro-mechanical analysis of composites. Int. J. Solids Struct. 43(2), 266–278 (2006)

    Article  MathSciNet  Google Scholar 

  29. Zhang, K.S., Wu, M.S., Feng, R.: Simulation of microplasticity-induced deformation in uniaxially strained ceramics by 3-D Voronoi polycrystal modeling. Int. J. Plast. 21(4), 801–834 (2005)

    Article  Google Scholar 

  30. Zhang, K., Ju, J.W., Li, Z., Bai, Y.L., Brocks, W.: Micromechanics based fatigue life prediction of a polycrystalline metal applying crystal plasticity. Mech. Mater. 85, 16–37 (2015)

    Article  Google Scholar 

  31. Zhang, K., Shi, Y., Ju, J.W.: Grain-level statistical plasticity analysis on strain cycle fatigue of a FCC metal. Mech. Mater. 64, 76–90 (2013)

    Article  Google Scholar 

Download references

Acknowledgements

This research was supported by the National Natural Scientific Foundation of China (Fund Nos. 11632077) and the Guangxi Science Research and Study Abroad Program for Excellent Ph.D. Students of Guangxi Zhuang Autonomous Region (2016). These financial supports are gratefully acknowledged. Further, we are truly grateful to the anonymous reviewer for the outstanding suggestions and guidance during our revision process. Especifically, Eqs. (1)–(3) are kindly guided by the anonymous reviewer.

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Authors and Affiliations

  1. Key Laboratory of Disaster Prevention and Structural Safety, College of Civil and Architectural Engineering, Guangxi University, Nanning, 530004, China

    Da-Wei Qin, J. Woody Ju & Ke-Shi Zhang

  2. Department of Civil and Environmental Engineering, University of California, Los Angeles, CA, 90095-1593, USA

    J. Woody Ju

  3. College of Civil Engineering, Shaoxing University, Shaoxing, 312000, China

    Ze-Shen Li

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  1. Da-Wei Qin
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Correspondence to J. Woody Ju.

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Qin, DW., Ju, J.W., Zhang, KS. et al. Inhomogeneous deformation growth of a metal under cyclic loading and its influence on fatigue. Acta Mech 231, 701–713 (2020). https://doi.org/10.1007/s00707-019-02560-2

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  • DOI: https://doi.org/10.1007/s00707-019-02560-2

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