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.
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References
S.M. Spearing: Materials issues in microelectromechanical systems (MEMS). Acta Mater. 48, 179–196 (2000).
G.P. Zhang, C.A. Volkert, R. Schwaiger, P. Wellner, E. Arzt, and O. Kraft: Length-scale-controlled fatigue mechanisms in thin copper films. Acta Mater. 54, 3127–3139 (2006).
B. Bhushan, A.V. Kulkarni, W. Bonin, and J.T. Wyrobek: Nanoindentation and picoindentation measurements using a capacitive transducer system in atomic force microscopy. Philos. Mag. A 74, 1117–1128 (1996).
G.P. Zhang, F. Liang, X.M. Luo, and X.F. Zhu: A review on cyclic deformation damage and fatigue fracture behavior of metallic nanolayered composites. J. Mater. Res. 34, 1–10 (2019).
J. Liang, L. Li, X. Niu, Z. Yu, and Q. Pei: Elastomeric polymer light-emitting devices and displays. Nat. Photonics 7, 817–824 (2013).
T. Sekitani, H. Nakajima, H. Maeda, T. Fukushima, T. Aida, K. Hata, and T. Someya: Stretchable active-matrix organic light-emitting diode display using printable elastic conductors. Nat. Mater. 8, 494–499 (2009).
S. Xu, Y. Zhang, J. Cho, J. Lee, X. Huang, L. Jia, J.A. Fan, Y. Su, J. Su, H. Zhang, H. Cheng, B. Lu, C. Yu, C. Chuang, T. Kim, T. Song, K. Shigeta, S. Kang, C. Dagdeviren, I. Petrov, P.V. Braun, Y. Huang, U. Paik, and J.A. Rogers: Stretchable batteries with self-similar serpentine interconnects and integrated wireless recharging systems. Nat. Commun. 4, 1543 (2013).
J. Yoon, A.J. Baca, S. Park, P. Elvikis, J.B.I. Geddes, L. Li, R.H. Kim, J. Xiao, S. Wang, T. Kim, M.J. Motala, B.Y. Ahn, E.B. Duoss, J.A. Lewis, R.G. Nuzzo, P.M. Ferreira, Y. Huang, A. Rockett, and J.A. Rogers: Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs. Nat. Mater. 7, 907–915 (2008).
A.J. Baca, J.H. Ahn, Y. Sun, M.A. Meitl, E. Menard, H.S. Kim, W.M. Choi, D.H. Kim, Y. Huang, and J.A. Rogers: Semiconductor wires and ribbons for high-performance flexible electronics. Angew. Chem. 47, 5524–5542 (2008).
D. Kim, J. Song, W.M. Choi, H. Kim, R. Kim, Z. Liu, Y.Y. Huang, K. Hwang, Y. Zhang, and J.A. Rogers: 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).
W.H. Chuang, R.K. Fettig, and R. Ghodssi: An electrostatic actuator for fatigue testing of low-stress LPCVD silicon nitride thin films. Sens. Actuat. A 121, 557–565 (2005).
C.L. Muhlstein, S.B. Brown, and R.O. Ritchie: High-cycle fatigue of single-crystal silicon thin films. J. Microelectromech. Syst. 10, 593–600 (2001).
D.H. Alsem, O.N. Pierron, E.A. Stach, C.L. Muhlstein, and R.O. Ritchie: Mechanisms for fatigue of micron-scale silicon structural films. Adv. Eng. Mater. 9, 15–30 (2007).
O. Kraft, P. Wellner, M. Hommel, R. Schwaiger, and E. Arzt: Fatigue behavior of polycrystalline thin copper films. Z. Metallkde. 93, 392–400 (2002).
O. Kraft, R. Schwaiger, and P. Wellner: Fatigue in thin films: lifetime and damage formation. Mat. Sci. Eng. A: Struct. 319, 919–923 (2001).
D. Wang, C.A. Volkert, and O. Kraft: Effect of length scale on fatigue life and damage formation in thin Cu films. Mat. Sci. Eng. A: Struct. 493, 267–273 (2008).
T.C. Hu, Y.T. Wang, F.C. Hsu, P.K. Sun, and M.T. Lin: Cyclic creep and fatigue testing of nanocrystalline copper thin films. Surf. Coat. Technol. 215, 393–399 (2013).
T. Kondo, X. Bi, H. Hirakata, and K. Minoshima: Mechanics of fatigue crack initiation in submicron-thick freestanding copper films. Int. J. Fatigue 82, 12–28 (2016).
F. Saghaeian, M. Lederer, A. Hofer, J. Todt, J. Keckes, and G. Khatibi: Investigation of high cyclic fatigue behaviour of thin copper films using MEMS structure. Int. J. Fatigue 128, 105179 (2019).
Y.S. Lee, G.D. Sim, J.S. Bae, J.Y. Kim, and S.B. Lee: Tensile and fatigue behavior of polymer supported silver thin films at elevated temperatures. Mater. Lett. 193, 81–84 (2017).
Y. Yang, B. Zhang, H. Wan, K. Liu, and G. Zhang: Bilayer graphene-covered Cu flexible electrode with excellent mechanical reliability and electrical performance. J. Mater. Res. 34, 3645–3653 (2019).
J. Lemaitre: A Course on Damage Mechanics (Springer-Verlag, 1996). doi:10.1007/978-3-642-18255-6.
B. Sun, X. Huang, and Z. Li: Electro-mechanical degradation model of flexible metal films due to fatigue damage accumulation. Met. Mater. Int. 26, 501–509 (2020).
J. Lemaitre, J.L. Chaboche, and A.K. Maji: Mechanics of solid materials. J. Eng. Mech. 119, 642–643 (1992).
X.M. Luo and G.P. Zhang: Grain boundary instability dependent fatigue damage behavior in nanoscale gold films on flexible substrates. Mater. Sci. Eng. A (2017).
S. Zheng, X. Luo, and G. Zhang: 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).
B. Sun: 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).
B. Sun and Z. Li: A multi-scale damage model for fatigue accumulation due to short cracks nucleation and growth. Eng. Fract. Mech. 127, 280–295 (2014).
H. Guo, B. Sun, and Z. Li: Multi-scale fatigue damage model for steel structures working under high temperature. Acta Mech. Sin. (2019).
C. Fan, Z. Li, and Y. Wang: A multi-scale corrosion fatigue damage model of high-strength bridge wires. Int. J. Damage Mech. 29, 887–901 (2019).
Y.S. Hong, Z.Y. Gu, B. Fang, and Y.L. Bai: Collective evolution characteristics and computer simulation of short fatigue cracks. Philos. Mag. A 75, 1517–1531 (1997).
H.L. Yu and Y.S. Hong: Collective evolution characteristics and computer simulation of voids near the crack tip of ductile metal. Key Eng. Mat. 183-187, 157–162 (2000).
L. Wang, Z. Wang, W. Xie, and X. Song: Fractal study on collective evolution of short fatigue cracks under complex stress conditions. Int. J. Fatigue 45, 1–7 (2012).
B. Sun, Y. Xu, and Z. Li: Multi-scale fatigue model and image-based simulation of collective short cracks evolution process. Comput. Mater. Sci. 117, 24–32 (2016).
Y. Qiao and Y. Hong: A stochastic model for evolution of collective short-fatigue-cracks based on local field analysis. Acta Mech. Sin. 30, 564–571 (1998).
Y. Qiao and Y.S. Hong: An analysis of collective damage for short fatigue cracks based on equilibrium of crack numerical density. Eng. Fract. Mech. 59, 151–163 (1998).
L. Wang, Z. Wang, and M. Yu: 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).
Y. Xu, F. Jiang, S. Newbern, A. Huang, C.M. Ho, and Y.C. Tai: Flexible shear-stress sensor skin and its application to unmanned aerial vehicles. Sens. Actuat. A Phys. 105, 321–329 (2003).
R. Schwaiger and O. Kraft: Size effects in the fatigue behavior of thin Ag films. Acta Mater. 51, 195–206 (2003).
T. Kondo, H. Hirakata, and K. Minoshima: Thickness effects on fatigue crack propagation in submicrometer-thick freestanding copper films. Int. J. Fatigue 103, 444–455 (2017).
J.Y. Zhang, X. Zhang, G. Liu, R.H. Wang, G.J. Zhang, and J. Sun: Length scale dependent yield strength and fatigue behavior of nanocrystalline Cu thin films. Mat. Sci. Eng. A: Struct. 528, 7774–7780 (2011).
Y. Bai, F. Ke, and M. Xia: Formulation of statistical evolution of microcracks in solids. Acta Mech. Sin. 7, 61–68 (1991).
F.J. Ke, Y.L. Bai, and M.F. Xia: Evolution of ideal micro-crack system. Sci. China Ser. A 33, 1447–1459 (1990).
Acknowledgments
The works described in the present paper are financially supported by Jiangsu Province Natural Sciences Fund Subsidization Project (BK20170655), the Fundamental Research Funds for the Central Universities (3205009203), and Zhishan Youth Scholar Program of SEU, to which the authors are most grateful.
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Huang, X., Sun, B. & Li, Z. Multi-scale modeling of fatigue damage in a metal wire film with the thickness effect. Journal of Materials Research 35, 3170–3179 (2020). https://doi.org/10.1557/jmr.2020.307
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DOI: https://doi.org/10.1557/jmr.2020.307