Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T03:08:28.119Z Has data issue: false hasContentIssue false
  • English
  • Français

Multi-scale modeling of fatigue damage in a metal wire film with the thickness effect

Published online by Cambridge University Press:  16 November 2020

Xingzhen Huang ,
Bin Sun  and
Zhaoxia Li
Xingzhen Huang
Affiliation:
Department of Engineering Mechanics, Jiangsu Key Laboratory of Engineering Mechanics, Southeast University, Nanjing210096, China
Bin Sun
Affiliation:
Department of Engineering Mechanics, Jiangsu Key Laboratory of Engineering Mechanics, Southeast University, Nanjing210096, China
Zhaoxia Li*
Affiliation:
Department of Engineering Mechanics, Jiangsu Key Laboratory of Engineering Mechanics, Southeast University, Nanjing210096, China
*
a)Address all correspondence to this author. e-mail: [email protected]
Get access

Abstract

The thickness effect has a significant influence on the fatigue life of micro–nanometer thin films. Due to the increasing application of micro–nanometer thin films in the field of microelectronics, a suitable fatigue prediction model is urgently needed. To reveal the impact of the thickness effect on the fatigue life of a copper wire film, cyclic tension fatigue test of four groups of copper wire films were carried out. Based on the theory of continuous damage mechanics and damage homogenization method, a fatigue damage accumulation model that considered the film thickness was proposed. Based on the proposed fatigue damage prediction model, the damage evolution law and fatigue life of copper wire films with different thickness and strain range were predicted. Furthermore, the size effect of the copper films was analyzed. The results showed that the fatigue life of copper wire films will decrease with the increase of thickness and strain amplitude; the thinner the film, the more significant the thickness effect on the fatigue life is; with the increase of the film thickness, the film thickness effect will gradually decrease.

Keywords

fatiguedamagemetal wire filmthickness effect
Type
Article
Information
Journal of Materials Research , Volume 35 , Issue 23-24 , 14 December 2020 , pp. 3170 - 3179
Check for updates
Copyright
Copyright © The Author(s), 2020, published on behalf of Materials Research Society by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Spearing, S.M.: Materials issues in microelectromechanical systems (MEMS). Acta Mater. 48, 179–196 (2000).CrossRefGoogle Scholar
Zhang, G.P., Volkert, C.A., Schwaiger, R., Wellner, P., Arzt, E., and Kraft, O.: Length-scale-controlled fatigue mechanisms in thin copper films. Acta Mater. 54, 3127–3139 (2006).CrossRefGoogle Scholar
Bhushan, B., Kulkarni, A.V., Bonin, W., and Wyrobek, J.T.: Nanoindentation and picoindentation measurements using a capacitive transducer system in atomic force microscopy. Philos. Mag. A 74, 1117–1128 (1996).CrossRefGoogle Scholar
Zhang, G.P., Liang, F., Luo, X.M., and Zhu, X.F.: A review on cyclic deformation damage and fatigue fracture behavior of metallic nanolayered composites. J. Mater. Res. 34, 1–10 (2019).CrossRefGoogle Scholar
Liang, J., Li, L., Niu, X., Yu, Z., and Pei, Q.: Elastomeric polymer light-emitting devices and displays. Nat. Photonics 7, 817–824 (2013).CrossRefGoogle Scholar
Sekitani, T., Nakajima, H., Maeda, H., Fukushima, T., Aida, T., Hata, K., and Someya, T.: Stretchable active-matrix organic light-emitting diode display using printable elastic conductors. Nat. Mater. 8, 494–499 (2009).CrossRefGoogle ScholarPubMed
Xu, S., Zhang, Y., Cho, J., Lee, J., Huang, X., Jia, L., Fan, J.A., Su, Y., Su, J., Zhang, H., Cheng, H., Lu, B., Yu, C., Chuang, C., Kim, T., Song, T., Shigeta, K., Kang, S., Dagdeviren, C., Petrov, I., Braun, P.V., Huang, Y., Paik, U., and Rogers, J.A.: Stretchable batteries with self-similar serpentine interconnects and integrated wireless recharging systems. Nat. Commun. 4, 1543 (2013).CrossRefGoogle ScholarPubMed
Yoon, J., Baca, A.J., Park, S., Elvikis, P., Geddes, J.B.I., Li, L., Kim, R.H., Xiao, J., Wang, S., Kim, T., Motala, M.J., Ahn, B.Y., Duoss, E.B., Lewis, J.A., Nuzzo, R.G., Ferreira, P.M., Huang, Y., Rockett, A., and Rogers, J.A.: Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs. Nat. Mater. 7, 907–915 (2008).CrossRefGoogle ScholarPubMed
Baca, A.J., Ahn, J.H., Sun, Y., Meitl, M.A., Menard, E., Kim, H.S., Choi, W.M., Kim, D.H., Huang, Y., and Rogers, J.A.: Semiconductor wires and ribbons for high-performance flexible electronics. Angew. Chem. 47, 5524–5542 (2008).CrossRefGoogle ScholarPubMed
Kim, D., Song, J., Choi, W.M., Kim, H., Kim, R., Liu, Z., Huang, Y.Y., Hwang, K., Zhang, Y., and Rogers, J.A.: Materials and noncoplanar mesh designs for integrated circuits with linear elastic responses to extreme mechanical deformations. Proc. Natl. Acad. Sci. USA 105, 18675–18680 (2008).CrossRefGoogle ScholarPubMed
Chuang, W.H., Fettig, R.K., and Ghodssi, R.: An electrostatic actuator for fatigue testing of low-stress LPCVD silicon nitride thin films. Sens. Actuat. A 121, 557–565 (2005).CrossRefGoogle Scholar
Muhlstein, C.L., Brown, S.B., and Ritchie, R.O.: High-cycle fatigue of single-crystal silicon thin films. J. Microelectromech. Syst. 10, 593–600 (2001).CrossRefGoogle Scholar
Alsem, D.H., Pierron, O.N., Stach, E.A., Muhlstein, C.L., and Ritchie, R.O.: Mechanisms for fatigue of micron-scale silicon structural films. Adv. Eng. Mater. 9, 15–30 (2007).CrossRefGoogle Scholar
Kraft, O., Wellner, P., Hommel, M., Schwaiger, R., and Arzt, E.: Fatigue behavior of polycrystalline thin copper films. Z. Metallkde. 93, 392–400 (2002).CrossRefGoogle Scholar
Kraft, O., Schwaiger, R., and Wellner, P.: Fatigue in thin films: lifetime and damage formation. Mat. Sci. Eng. A: Struct. 319, 919–923 (2001).CrossRefGoogle Scholar
Wang, D., Volkert, C.A., and Kraft, O.: Effect of length scale on fatigue life and damage formation in thin Cu films. Mat. Sci. Eng. A: Struct. 493, 267–273 (2008).CrossRefGoogle Scholar
Hu, T.C., Wang, Y.T., Hsu, F.C., Sun, P.K., and Lin, M.T.: Cyclic creep and fatigue testing of nanocrystalline copper thin films. Surf. Coat. Technol. 215, 393–399 (2013).CrossRefGoogle Scholar
Kondo, T., Bi, X., Hirakata, H., and Minoshima, K.: Mechanics of fatigue crack initiation in submicron-thick freestanding copper films. Int. J. Fatigue 82, 12–28 (2016).CrossRefGoogle Scholar
Saghaeian, F., Lederer, M., Hofer, A., Todt, J., Keckes, J., and Khatibi, G.: Investigation of high cyclic fatigue behaviour of thin copper films using MEMS structure. Int. J. Fatigue 128, 105179 (2019).CrossRefGoogle Scholar
Lee, Y.S., Sim, G.D., Bae, J.S., Kim, J.Y., and Lee, S.B.: Tensile and fatigue behavior of polymer supported silver thin films at elevated temperatures. Mater. Lett. 193, 81–84 (2017).CrossRefGoogle Scholar
Yang, Y., Zhang, B., Wan, H., Liu, K., and Zhang, G.: Bilayer graphene-covered Cu flexible electrode with excellent mechanical reliability and electrical performance. J. Mater. Res. 34, 3645–3653 (2019).CrossRefGoogle Scholar
Lemaitre, J.: A Course on Damage Mechanics (Springer-Verlag, 1996). doi:10.1007/978-3-642-18255-6.CrossRefGoogle Scholar
Sun, B., Huang, X., and Li, Z.: Electro-mechanical degradation model of flexible metal films due to fatigue damage accumulation. Met. Mater. Int. 26, 501–509 (2020).CrossRefGoogle Scholar
Lemaitre, J., Chaboche, J.L., and Maji, A.K.: Mechanics of solid materials. J. Eng. Mech. 119, 642–643 (1992).CrossRefGoogle Scholar
Luo, X.M. and Zhang, G.P.: Grain boundary instability dependent fatigue damage behavior in nanoscale gold films on flexible substrates. Mater. Sci. Eng. A (2017).CrossRefGoogle Scholar
Zheng, S., Luo, X., and Zhang, G.: Cumulative shear strain-induced preferential orientation during abnormal grain growth near fatigue crack tips of nanocrystalline Au films. J. Mater. Res. 35, 372–379 (2020).CrossRefGoogle Scholar
Sun, B.: A continuum model for damage evolution simulation of the high strength bridge wires due to corrosion fatigue. J. Constr. Steel Res. 146, 76–83 (2018).CrossRefGoogle Scholar
Sun, B. and Li, Z.: A multi-scale damage model for fatigue accumulation due to short cracks nucleation and growth. Eng. Fract. Mech. 127, 280–295 (2014).CrossRefGoogle Scholar
Guo, H., Sun, B., and Li, Z.: Multi-scale fatigue damage model for steel structures working under high temperature. Acta Mech. Sin. (2019).CrossRefGoogle Scholar
Fan, C., Li, Z., and Wang, Y.: A multi-scale corrosion fatigue damage model of high-strength bridge wires. Int. J. Damage Mech. 29, 887–901 (2019).CrossRefGoogle Scholar
Hong, Y.S., Gu, Z.Y., Fang, B., and Bai, Y.L.: Collective evolution characteristics and computer simulation of short fatigue cracks. Philos. Mag. A 75, 1517–1531 (1997).CrossRefGoogle Scholar
Yu, H.L. and Hong, Y.S.: Collective evolution characteristics and computer simulation of voids near the crack tip of ductile metal. Key Eng. Mat. 183-187, 157–162 (2000).CrossRefGoogle Scholar
Wang, L., Wang, Z., Xie, W., and Song, X.: Fractal study on collective evolution of short fatigue cracks under complex stress conditions. Int. J. Fatigue 45, 1–7 (2012).CrossRefGoogle Scholar
Sun, B., Xu, Y., and Li, Z.: Multi-scale fatigue model and image-based simulation of collective short cracks evolution process. Comput. Mater. Sci. 117, 24–32 (2016).CrossRefGoogle Scholar
Qiao, Y. and Hong, Y.: A stochastic model for evolution of collective short-fatigue-cracks based on local field analysis. Acta Mech. Sin. 30, 564–571 (1998).Google Scholar
Qiao, Y. and Hong, Y.S.: An analysis of collective damage for short fatigue cracks based on equilibrium of crack numerical density. Eng. Fract. Mech. 59, 151–163 (1998).CrossRefGoogle Scholar
Wang, L., Wang, Z., and Yu, M.: Experimental study and numerical simulation on coalescence and interference of short cracks for low cycle fatigue at hight temperature. J. Mech. Strength 30, 642–646 (2008).Google Scholar
Xu, Y., Jiang, F., Newbern, S., Huang, A., Ho, C.M., and Tai, Y.C.: Flexible shear-stress sensor skin and its application to unmanned aerial vehicles. Sens. Actuat. A Phys. 105, 321–329 (2003).CrossRefGoogle Scholar
Schwaiger, R. and Kraft, O.: Size effects in the fatigue behavior of thin Ag films. Acta Mater. 51, 195–206 (2003).CrossRefGoogle Scholar
Kondo, T., Hirakata, H., and Minoshima, K.: Thickness effects on fatigue crack propagation in submicrometer-thick freestanding copper films. Int. J. Fatigue 103, 444–455 (2017).CrossRefGoogle Scholar
Zhang, J.Y., Zhang, X., Liu, G., Wang, R.H., Zhang, G.J., and Sun, J.: Length scale dependent yield strength and fatigue behavior of nanocrystalline Cu thin films. Mat. Sci. Eng. A: Struct. 528, 7774–7780 (2011).CrossRefGoogle Scholar
Bai, Y., Ke, F., and Xia, M.: Formulation of statistical evolution of microcracks in solids. Acta Mech. Sin. 7, 61–68 (1991).Google Scholar
Ke, F.J., Bai, Y.L., and Xia, M.F.: Evolution of ideal micro-crack system. Sci. China Ser. A 33, 1447–1459 (1990).Google Scholar