Advertisement

Acta Mechanica

, Volume 230, Issue 12, pp 4463–4479 | Cite as

Plastic deformation of a film-substrate with inhomogeneous inclusions under contact loading

  • Jing Yang
  • Qihong Fang
  • Guozheng Kang
  • Kun ZhouEmail author
Original Paper
  • 45 Downloads

Abstract

In this paper, a semi-analytic solution is developed to investigate the plastic deformation of a film-substrate with inhomogeneous inclusions subjected to contact loading. In this solution, the surface pressure distribution and contact area can be determined by solving a set of governing equations via a modified conjugate gradient method. The inhomogeneous inclusions and the coating material are modeled as homogeneous inclusions with known initial eigenstrains plus unknown equivalent eigenstrains, according to the Eshelby’s equivalent inclusion method. A plasticity loop and an incremental loading process are used to obtain the accumulative plastic strain iteratively. This model considers not only the interactions among the contact loading body, embedded inhomogeneous inclusions and film materials, but also the plastic deformation of the film-substrate system. This solution is of great significance to understand the plastic deformation mechanism of a film-substrate with inhomogeneous inclusions under contact loading.

Notes

Acknowledgements

The authors acknowledge financial support by Singapore Maritime Institute (Grant No: SMI-2014-MA11) and the National Natural Science Foundation of China (Grant No: 11472200).

References

  1. 1.
    Askari, D., Ghasemi-Nejhad, M.N.: Effects of vacancy defects on mechanical properties of graphene/carbon nanotubes: a numerical modeling. J. Comput. Theor. Nanosci. 8(4), 783–794 (2011)CrossRefGoogle Scholar
  2. 2.
    Hao, F., et al.: Mechanical and thermal transport properties of graphene with defects. Appl. Phys. Lett. 99(4), 041901 (2011)CrossRefGoogle Scholar
  3. 3.
    Jin, M.Z., et al.: The effects of micro-defects and crack on the mechanical properties of metal fiber sintered sheets. Int. J. Solids Struct. 51(10), 1946–1953 (2014)CrossRefGoogle Scholar
  4. 4.
    Zhou, K., et al.: A fast method for solving three-dimensional arbitrarily shaped inclusions in a half space. Comput. Methods Appl. Mech. Eng. 198(9–12), 885–892 (2009)zbMATHCrossRefGoogle Scholar
  5. 5.
    Zhou, K., et al.: Multiple 3D inhomogeneous inclusions in a half space under contact loading. Mech. Mater. 43(8), 444–457 (2011)CrossRefGoogle Scholar
  6. 6.
    Zhou, K., et al.: Semi-analytic solution for multiple interacting three-dimensional inhomogeneous inclusions of arbitrary shape in an infinite space. Int. J. Numer. Methods Eng. 87(7), 617–638 (2011)zbMATHCrossRefGoogle Scholar
  7. 7.
    Zhou, K.: Elastic field and effective moduli of periodic composites with arbitrary inhomogeneity distribution. Acta Mech. 223(2), 293–308 (2012)zbMATHCrossRefGoogle Scholar
  8. 8.
    Dong, Q.B., Zhou, K.: Elastohydrodynamic lubrication modeling for materials with multiple cracks. Acta Mech. 225(12), 3395–3408 (2014)zbMATHCrossRefGoogle Scholar
  9. 9.
    Zhou, K., Wei, R.B.: Modeling cracks and inclusions near surfaces under contact loading. Int. J. Mech. Sci. 83, 163–171 (2014)CrossRefGoogle Scholar
  10. 10.
    Zhou, K., Wei, R.B.: Multiple cracks in a half-space under contact loading. Acta Mech. 225(4–5), 1487–1502 (2014)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Dong, Q.B., Zhou, K.: Multiple inhomogeneous inclusions and cracks in a half space under elastohydrodynamic lubrication contact. Int. J. Appl. Mech. 7(1), 1550003 (2015)CrossRefGoogle Scholar
  12. 12.
    Dong, Q.B., Zhou, K.: Modeling heterogeneous materials with multiple inclusions under mixed lubrication contact. Int. J. Mech. Sci. 103, 89–96 (2015)CrossRefGoogle Scholar
  13. 13.
    Dong, Q.B., et al.: Analysis of fluid pressure, interface stresses and stress intensity factors for layered materials with cracks and inhomogeneities under elastohydrodynamic lubrication contact. Int. J. Mech. Sci. 93, 48–58 (2015)CrossRefGoogle Scholar
  14. 14.
    Zhou, K., et al.: Semi-analytic solution of multiple inhomogeneous inclusions and cracks in an infinite space. Int. J. Comput. Methods 12(1), 1550002 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Dong, Q.B., et al.: Heterogeneous structures with inhomogeneous inclusions under elastohydrodynamic lubrication contact with consideration of surface roughness. Proc. Inst. Mech. Eng. Part J-J. Eng. Tribol. 230(5), 571–582 (2016)CrossRefGoogle Scholar
  16. 16.
    Fang, Q.H., Zhang, L.C.: Coupled effect of grain boundary sliding and dislocation emission on fracture toughness of nanocrystalline materials. J. Micromech. Mol. Phys. 1(2), 1650008 (2016) MathSciNetCrossRefGoogle Scholar
  17. 17.
    Long, X., et al.: Mechanical effects of isolated defects within a lead-free solder bump subjected to coupled thermal-electrical loading. J. Micromech. Mol. Phys. 1(1), 1650004 (2016)CrossRefGoogle Scholar
  18. 18.
    Markenscoff, X.: On the dynamic generalization of the anisotropic Eshelby ellipsoidal inclusion and the dynamically expanding inhomogeneities with transformation strain. J. Micromech. Mol. Phys. 1(3–4), 1640001 (2016)CrossRefGoogle Scholar
  19. 19.
    Mikata, Y.: Analytical treatment on the effective material properties of a composite material with spheroidal and ellipsoidal inhomogeneities in an isotropic matrix. J. Micromech. Mol. Phys. 1(3–4), 1640012 (2016)CrossRefGoogle Scholar
  20. 20.
    Ren, H., et al.: A new peridynamic formulation with shear deformation for elastic solid. J. Micromech. Mol. Phys. 1(2), 1650009 (2016)CrossRefGoogle Scholar
  21. 21.
    Shi, C., et al.: An interphase model for effective elastic properties of concrete composites. J. Micromech. Mol. Phys. 01(01), 1650005 (2016)CrossRefGoogle Scholar
  22. 22.
    Wei, R.B., et al.: Modeling surface pressure, interfacial stresses and stress intensity factors for layered materials containing multiple cracks and inhomogeneous inclusions under contact loading. Mech. Mater. 92, 8–17 (2016)CrossRefGoogle Scholar
  23. 23.
    Yang, S., Sharma, P.: Eshelby’s tensor for embedded inclusions and the elasto-capillary phenomenon. J. Micromech. Mol. Phys. 1(3–4), 1630002 (2016)CrossRefGoogle Scholar
  24. 24.
    Zhou, K., Dong, Q.B.: A three-dimensional model of line-contact elastohydrodynamic lubrication for heterogeneous materials with inclusions. Int. J. Appl. Mech. 8(2), 1650014 (2016)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Burbery, N.B., et al.: Dislocation dynamics in polycrystals with atomistic-informed mechanisms of dislocation–grain boundary interactions. J. Micromech. Mol. Phys. 2(1), 1750003 (2017)CrossRefGoogle Scholar
  26. 26.
    Kuroda, M.: Interpretation of the behavior of metals under large plastic shear deformations: a macroscopic approach. Int. J. Plast. 13(4), 359–383 (1997)zbMATHCrossRefGoogle Scholar
  27. 27.
    Kiritani, M., et al.: Plastic deformation of metal thin films without involving dislocations and anomalous production of point defects. Radiat. Eff. Defects Solids 157(1–2), 3–24 (2002)CrossRefGoogle Scholar
  28. 28.
    Richmond, O., Alexandrov, S.: The theory of general and ideal plastic deformations of Tresca solids. Acta Mech. 158(1–2), 33–42 (2002)zbMATHCrossRefGoogle Scholar
  29. 29.
    Bucher, A., et al.: A material model for finite elasto-plastic deformations considering a substructure. Int. J. Plast. 20(4–5), 619–642 (2004)zbMATHCrossRefGoogle Scholar
  30. 30.
    Guo, L.G., et al.: Research on plastic deformation behaviour in cold ring rolling by FEM numerical simulation. Model. Simul. Mater. Sci. Eng. 13(7), 1029–1046 (2005)CrossRefGoogle Scholar
  31. 31.
    Shi, J., et al.: Damage criteria based on plastic strain energy intensity under complicated stress state. Int. J. Appl. Mech. 7(6), 1550089 (2015)CrossRefGoogle Scholar
  32. 32.
    Chen, J., et al.: Interaction between dislocation and subsurface crack under condition of slip caused by half-plane contact surface normal force. Eng. Fract. Mech. 114, 115–126 (2013)CrossRefGoogle Scholar
  33. 33.
    Wei, R., et al.: Fatigue crack propagation in heterogeneous materials under remote cyclic loading. J. Micromech. Mol. Phys. 1(01), 1650003 (2016)CrossRefGoogle Scholar
  34. 34.
    Bo, L., et al.: Study of transformation toughening behavior of an edge through crack in zirconia ceramics with the cohesive zone model. Int. J. Appl. Mech. 10, 1850066 (2018)CrossRefGoogle Scholar
  35. 35.
    Hui, L., et al.: An implicit coupling finite element and peridynamic method for dynamic problems of solid mechanics with crack propagation. Int. J. Appl. Mech. 10(10), 1850037 (2018)Google Scholar
  36. 36.
    Mamalis, A.G., et al.: The effect of porosity and micro-defects on plastically deformed porous materials. J. Mater. Process. Technol. 96(1–3), 117–123 (1999)CrossRefGoogle Scholar
  37. 37.
    Pettermann, H.E., et al.: A thermo-elasto-plastic constitutive law for inhomogeneous materials based on an incremental Mori–Tanaka approach. Comput. Struct. 71(2), 197–214 (1999)CrossRefGoogle Scholar
  38. 38.
    von Blanckenhagen, B., et al.: Discrete dislocation simulation of plastic deformation in metal thin films. Acta Mater. 52(3), 773–784 (2004)CrossRefGoogle Scholar
  39. 39.
    Cleja-Tigoiu, S.: Elasto-plastic materials with lattice defects modeled by second order deformations with non-zero curvature. Int. J. Fract. 166(1–2), 61–75 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  40. 40.
    Ellers, J., Driessen, G.: Genetic correlation between temperature-induced plasticity of life-history traits in a soil arthropod. Evol. Ecol. 25(2), 473–484 (2011)CrossRefGoogle Scholar
  41. 41.
    Bose, T., Rattan, M.: Modeling creep analysis of thermally graded anisotropic rotating composite disc. Int. J. Appl. Mech. 10, 1850063 (2018) CrossRefGoogle Scholar
  42. 42.
    Jiang, Y.Y., et al.: Three-dimensional elastic-plastic stress analysis of rolling contact. J. Tribol.-Trans. ASME 124(4), 699–708 (2002)CrossRefGoogle Scholar
  43. 43.
    Shao, Y.F., et al.: Multiscale simulations on the reversible plasticity of Al (0 0 1) surface under a nano-sized indenter. Comput. Mater. Sci. 67, 346–352 (2013)CrossRefGoogle Scholar
  44. 44.
    Shi, S., et al.: Elastic-plastic response of clamped square plates subjected to repeated quasi-static uniform pressure. Int. J. Appl. Mech. 10(6), S1758825118500679 (2018)CrossRefGoogle Scholar
  45. 45.
    Wang, H., et al.: Effects of detwinning on the inelasticity of AZ31B sheets during cyclic loading and unloading. Int. J. Appl. Mech. 10(9), 1850095 (2018)CrossRefGoogle Scholar
  46. 46.
    Mazarei, Z., et al.: Thermo-elasto-plastic analysis of thick-walled spherical pressure vessels made of functionally graded materials. Int. J. Appl. Mech. 8(4), 1650054 (2016)CrossRefGoogle Scholar
  47. 47.
    Soyarslan, C., et al.: A thermomechanically consistent constitutive theory for modeling micro-void and/or micro-crack driven failure in metals at finite strains. Int. J. Appl. Mech. 8(1), 1650009 (2016)CrossRefGoogle Scholar
  48. 48.
    Jacq, C., et al.: Development of a three-dimensional semi-analytical elastic–plastic contact code. J. Tribol.Trans. ASME 124(4), 653–667 (2002)CrossRefGoogle Scholar
  49. 49.
    Chen, W.W., et al.: Modeling elasto-plastic indentation on layered materials using the equivalent inclusion method. Int. J. Solids Struct. 47(20), 2841–2854 (2010)zbMATHCrossRefGoogle Scholar
  50. 50.
    Mura, T.: Micromechanics of Defects in Solids. Springer, Dordrecht (1982)CrossRefGoogle Scholar
  51. 51.
    Wang, Z.J., et al.: A numerical elastic–plastic contact model for rough surfaces. Tribol. Trans. 53(2), 224–238 (2010)CrossRefGoogle Scholar
  52. 52.
    Osullivan, T.C., King, R.B.: Sliding contact stress-field due to a spherical indenter on a layered elastic half-space. J. Tribol.-Trans. ASME 110(2), 235–240 (1988)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Mechanical EngineeringZhejiang University of TechnologyHangzhouPeople’s Republic of China
  2. 2.School of Mechanical and Aerospace EngineeringNanyang Technological UniversitySingaporeSingapore
  3. 3.State Key Laboratory of Advanced Design and Manufacturing for Vehicle BodyHunan UniversityChangshaPeople’s Republic of China
  4. 4.Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and EngineeringSouthwest Jiaotong UniversityChengduPeople’s Republic of China

Personalised recommendations