Effective properties of metal films during uniaxial stretching

doi:10.7523/j.issn.2095-6134.2010.3.003

Abstract

Abstract:

This paper focuses on the variation in properties of the metal films under the conditions of uniaxial stretching. By employing the effective theories (i.e. Parallel, Maxwell, and Hashin-Shtrikman theories), cracks models are established to obtain the relation between effective electric-resistance and strain. The theoretical solutions are compared with the previous experimental results. It is shown that the Maxwell solution agrees well with the experimental results. Furthermore, the tensile strain energy method and the homogenous method could be used to estimate the effective Youngs modulus of films during the deformation, and the accuracies of the estimation are subsequently compared using the finite elements method. The results show that the homogenous method is better. Finally, the correlations of the effective electric-resistance with effective Youngs modulus and damage variable are established.

Key words: flexible electronics, metal films, cracks propagation, effective theories

CLC Number:

XU Wei, YANG Jin-Shui. Effective properties of metal films during uniaxial stretching[J]. , 2010, 27(3): 314-322.

References

[1] Xu W, Lu T J. Flexible electronics system and their mechanical properties
[J]. Advances in Mechanics, 2008, 38 (2): 137-150 (in Chinese). 许巍, 卢天健. 柔性电子系统及其力学性能
[J]. 力学进展, 2008, 38(2):137-150.

[2] Li T, Huang Z, Suo Z, et al. Stretchability of thin metal films on elastomer substrates
[J]. Applied Physics Letter, 2005, 85 (16): 3435-3437.

[3] Lacour S P, Jones J, Wagner S, et al. Stretchable interconnects for elastic electronic surfaces
[J]. Proceedings of the IEEE, 2005, 93 (8): 1459-1467.

[4] Wagner S, Lacour S P, Jones J, et al. Electronic skin: architecture and components
[J]. Physica E, 2004, 25: 326-334.

[5] Alaca B E, Saif M T A, Sehitoglu H. On the interface debond at the edge of a thin film on a thick substrate
[J]. Acta Materialia, 2002, 50: 1197-1209.

[6] Lacour S P, Wagner S, Huang Z, et al. Stretchable gold conductors on elastomeric substrates
[J]. Applied Physics Letters, 2003, 82: 2404-2406.

[7] Niu R M, Liu G, Wang C, et al. Thickness dependent critical strain in submicron Cu films adherent to polymer substrate
[J]. Applied Physics Letters, 2007, 90: 161907.

[8] Hommel M, Kraft O. Deformation behavior of thin copper films on deformable substrates
[J]. Acta Materialia, 2001, 49: 3935-3947.

[9] Lu N, Wang X, Suo Z, et al. Metal films on polymer substrates strained beyond 50%
[J]. Applied Physics Letters, 2007, 91: 221909.

[10] Maxwell J C. A treatise on electricity and magnetism
[M]. 3rd ed. New York: Dover publication Inc, 1954.

[11] Wang J, Carson J K, North M F, et al. A new approach to modeling the effective thermal conductivity of heterogeneous materials
[J]. International Journal of Heat and Mass Transfer, 2006, 49, 3075-3083.

[12] Gao L, Zhou X, Ding Y. Effective thermal and electrical conductivity of carbon nanotube composites
[J]. Chemical Physics Letters, 2007, 434: 297-300.

[13] Gu S, Lu T J, Hass D D, et al. Thermal conductivity of zirconia coatings with zig-zag pore microstructures
[J]. Acta Materialia, 2001, 49: 2539-2547.

[14] Hasin Z, Shtrikman S. A variational approach to the theory of the elastic behavior of multiphase materials
[J]. Journal of the Mechanics and Physics of Solids, 1963, 11: 127-140.

[15] Zhao H F, Hu G K, Lu T J. Correlation between the elastic moduli and conductivity of planar porous materials
[J]. International Journal of Fracture, 2004, 126: 11-18.

[16] Zhao H F, Hu G K, Lu T J. Cross-property raltion for two-phase planar composites
[J]. Computational Material Science, 2006, 35: 408-415.

[17] Dai G M, Zhang W H. Size effects of effective Youngs modulus for periodic cellular materials
[J]. Science in China Series G, 2009, 52(8): 1262-1270.

[18] Kachanov M, Sevostianov I, Shafiro B. Explicit cross property correlation for porous materials with anisotropic microstructures
[J]. Journal of the Mechanics and Physics of Solids, 2001, 49: 1-25.

[19] Lu T J, Hutchinson J W. Thermal conductivity and expansion of cross-ply ceramic composites with matrix cracks
[J]. Journal of the Mechanics and Physics of Solids, 1995, 43: 1175-1198.

[20] 余寿文,冯西桥. 损伤力学
[M]. 北京:清华大学出版社, 1997.