Skip to main content
SpringerLink
Log in

A model and simulation strategy for fatigue damage evolution of copper films

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

A damage model and simulation strategy are developed to simulate fatigue damage evolution and predict fatigue life of metallic films. The fatigue damage model is established based on the collective effect of current all micro/nanoscale cracks within material in a homogenized way, and block cycle jump method is used in the simulation strategy, which can speed up fatigue damage evolution simulation for metallic films reasonably. Based on numerical study, fatigue damage evolution and life of the smooth and notched specimens for copper films subjected to various stress levels are numerically analyzed and compared with the corresponding experimental results. It shows that the developed damage model and simulation strategy can be used to simulate the fatigue damage evolution and predict fatigue life for metallic films reasonably.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Abbreviations

D :

Damage variable

L :

Size of the representative volume element (RVE)

d :

Size of the micro-scale element

a :

Crack length

A, \(\alpha\) :

Model parameters

\(\Delta \tilde{\sigma }\) :

Effective stress range

\(\Delta \sigma\) :

Nominal stress range

\(N\) :

Current cyclic number

\(\Delta N\) :

Cyclic number within one standard loading block

\(N_{f}\) :

Fatigue life

\(\sigma_{ij}\) :

Stress components

\(\varepsilon_{kl}\) :

Strain components

\(\Delta \sigma\) :

Stress range

\(\delta\) :

Kronecker delta

\(C_{ijkl}\) :

Elastic constants

\(E\) :

Initial elastic modulus

\(v\) :

Poisson’s ratio

References

  1. Su Y, Wang S, Huang YA et al (2015) Elasticity of fractal inspired interconnects. Small 11(3):367–373

    Article  Google Scholar 

  2. Sun B, Li Z (2019) Kinematics analysis of scissor-type inspired interconnects. Acta Mech 230(8):2979–2988

    Article  MathSciNet  Google Scholar 

  3. Sun B, Li Z (2019) An efficient computational method for curved interconnects deformation. Eur J Mech-A/Solids 75:82–92

    Article  MathSciNet  MATH  Google Scholar 

  4. Gleskova H, Cheng IC, Wagner S et al (2006) Mechanics of thin-film transistors and solar cells on flexible substrates. Sol Energy 80(6):687–693

    Article  Google Scholar 

  5. Song YM, Xie Y, Malyarchuk V et al (2013) Digital cameras with designs inspired by the arthropod eye. Nature 497(7447):95

    Article  Google Scholar 

  6. Kim J, Lee M, Shim HJ et al (2014) Stretchable silicon nanoribbon electronics for skin prosthesis. Nat Commun 5:5747

    Article  Google Scholar 

  7. Lee D, Lee J, Kim T et al (2019) Effect of the thermal annealing on the stretchability and fatigue failure of the copper film on the polymer substrate. J Electron Mater 48(7):4582–4588

    Article  Google Scholar 

  8. Tripathi PN, Ojha SK, Nazarov A (2020) Development of highly reliable BiFeO3/HfO2/Silicon gate stacks for ferroelectric non-volatile memories in IoT applications. J Mater Sci: Mater Electron 31(24):22107–22118

    Google Scholar 

  9. Sodavaram NK, Arif KM (2019) Fatigue testing of integrated thin film metal membranes for implantable biomedical pressure sensors. J Mech Sci Technol 33(7):3383–3389

    Article  Google Scholar 

  10. Bizouerne M, Pargon E, Petitetienne C et al (2018) Low damage patterning of In0.53Ga0.47As film for its integration as n-channel in a fin metal oxide semiconductor field effect transistor architecture. J Vacuum Sci Technol 36(6):061305

    Article  Google Scholar 

  11. Kim BJ, Jung SY, Cho Y et al (2013) Crack nucleation during mechanical fatigue in thin metal films on flexible substrates. Acta Mater 61(9):3473–3481

    Article  Google Scholar 

  12. Lee S, Yoo T, Han Y et al (2017) Polyimide-epoxy composites with superior bendable properties for application in flexible electronics. J Electron Mater 46(8):1–10

    Article  Google Scholar 

  13. Schnabl K, Wentlent L, Mootoo K et al (2014) Nanocopper based solder-free electronic assembly. J Electron Mater 43(12):4515–4521

    Article  Google Scholar 

  14. Zhu S, Hao Y, Liao D et al (2020) Probabilistic modeling and simulation of multiple surface crack propagation and coalescence. Appl Math Model 78:383–398

    Article  MATH  Google Scholar 

  15. Liao D, Zhu S, Correia JA et al (2020) Recent advances on notch effects in metal fatigue: a review. Fatigue Fract Eng Mater Struct 43(4):637–659

    Article  Google Scholar 

  16. Kraft O, Schwaiger R, Wellner P (2001) Fatigue in thin films: lifetime and damage formation. Mater Sci Eng, A 319:919–923

    Article  Google Scholar 

  17. Wimmer A, Heinz W, Detzel T et al (2015) Cyclic bending experiments on free-standing Cu micron lines observed by electron backscatter diffraction. Acta Mater 83:460–469

    Article  Google Scholar 

  18. Zhang GP, Sun KH, Zhang B et al (2008) Tensile and fatigue strength of ultrathin copper films. Mater Sci Eng, A 483:387–390

    Article  Google Scholar 

  19. Kondo T, Bi XC, Hirakata H et al (2016) Mechanics of fatigue crack initiation in submicron-thick freestanding copper films. Int J Fatigue 82:12–28

    Article  Google Scholar 

  20. Ostrowicki GT, Sitaraman SK (2016) Cyclic magnetic actuation technique for thin film interfacial fatigue crack propagation. Eng Fract Mech 168:1–10

    Article  Google Scholar 

  21. Kondo T, Hirakata H, Minoshima K (2017) Thickness effects on fatigue crack propagation in submicrometer-thick freestanding copper films. Int J Fatigue 103:444–455

    Article  Google Scholar 

  22. Kondo T, Shin A, Akasaka M, Hirakata H, Minoshima K (2019) Vacuum effects on fatigue crack growth in submicrometre-thick freestanding copper films. Fatigue Fract. Eng. Mater. Struct. 42(5):1118–1129

    Article  Google Scholar 

  23. Liu XD, Shang DG, Li M et al (2013) Healing fatigue damage by laser shock peening for copper film. Int J Fatigue 54:127–132

    Article  Google Scholar 

  24. Lee DY, Song JH (2012) Fatigue life and plastic deformation behavior of electrodeposited copper thin film under variable amplitude loading. Int J Fatigue 38:1–6

    Article  Google Scholar 

  25. Samet D, Rambhatla VNNT, Kwatra A et al (2017) A fatigue crack propagation model with resistance curve effects for an epoxy/copper interface. Eng Fract Mech 180:60–72

    Article  Google Scholar 

  26. Zhang B, Xiao TY, Luo XM et al (2015) Enhancing fatigue cracking resistance of nanocrystalline Cu films on a flexible substrate. Mater Sci Eng, A 627:61–64

    Article  Google Scholar 

  27. Sun B, Li Z (2014) A multi-scale damage model for fatigue accumulation due to short cracks nucleation and growth. Eng Fract Mech 127:280–295

    Article  Google Scholar 

  28. Sun B, Xu YL, Li Z (2016) Multi-scale fatigue model and image-based simulation of collective short cracks evolution process. Comput Mater Sci 117:24–32

    Article  Google Scholar 

  29. Sun B, Xu YL, Li Z (2016) Multi-scale model for linking collective behavior of short and long cracks to continuous average fatigue damage. Eng Fract Mech 157:141–153

    Article  Google Scholar 

  30. Kondo T, Shin A, Hirakata H et al (2016) Fatigue crack propagation properties of submicron-thick freestanding copper films in vacuum environment. Procedia Struct Integr 2:1359–1366

    Article  Google Scholar 

  31. Lemaitre J (2012) A course on damage mechanics. Springer, London

    MATH  Google Scholar 

  32. Sun B (2018) A continuum model for damage evolution simulation of the high strength bridge wires due to corrosion fatigue. J Constr Steel Res 146:76–83

    Article  Google Scholar 

  33. Sun B, Xu YL, Wang FY et al (2019) Multi-scale fatigue damage prognosis for long-span steel bridges under vehicle loading. Struct Infrastruct Eng 15:524–538

    Article  Google Scholar 

  34. Fish J, Yu Q (2002) Computational mechanics of fatigue and life predictions for composite materials and structures. Comput Methods Appl Mech Eng 191:4827–4849

    Article  MATH  Google Scholar 

  35. Sun B, Xu YL, Zhu Q et al (2019) Auto-adaptive multiblock cycle jump algorithm for fatigue damage simulation of long-span steel bridges. Fatigue Fract Eng Mater Struct 42(4):919–928

    Google Scholar 

  36. Sun B, Xu YL, Zhu Q et al (2019) Concurrent multi-scale fatigue damage evolution simulation method for long-span steel bridges. Int J Damage Mech 28(2):165–182

    Article  Google Scholar 

  37. Liu H, Shang DG, Ma XP et al (2009) Tension-tension fatigue properties and life prediction of electroplated copper films. J Mech Eng 45(9):261–265

    Article  Google Scholar 

Download references

Acknowledgements

The works described in this paper are financially supported by National Program on Key Research and Development Project of China (2020YFB2103500-2) and National Natural Science Foundation of China (grant no. 52008104), to which the authors are most grateful.

Author information

Authors and Affiliations

  1. Jiangsu Key Laboratory of Engineering Mechanics, Department of Engineering Mechanics, School of Civil Engineering, Southeast University, Nanjing, 210096, China

    Bin Sun

Authors
  1. Bin Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bin Sun.

Ethics declarations

Conflict of interest

We declare that we have no conflict of interest in the manuscript.

Additional information

Technical Editor: João Marciano Laredo dos Reis.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sun, B. A model and simulation strategy for fatigue damage evolution of copper films. J Braz. Soc. Mech. Sci. Eng. 43, 276 (2021). https://doi.org/10.1007/s40430-021-02996-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40430-021-02996-5

Keywords

Search

Navigation