Acta Mechanica Sinica

, Volume 34, Issue 2, pp 381–391 | Cite as

Micromechanics of substrate-supported thin films

  • Wei He
  • Meidong Han
  • Shibin Wang
  • Lin-An Li
  • Xiuli Xue
Review Paper


The mechanical properties of metallic thin films deposited on a substrate play a crucial role in the performance of micro/nano-electromechanical systems (MEMS/NEMS) and flexible electronics. This article reviews ongoing study on the mechanics of substrate-supported thin films, with emphasis on the experimental characterization techniques, such as the rule of mixture and X-ray tensile testing. In particular, the determination of interfacial adhesion energy, film deformation, elastic properties and Bauschinger effect are discussed.


Thin films Deformation Adhesion Elastic property Bauschinger effect 



This work was supported by the National Natural Science Foundation of China (Grants 11472186 and 11602083) and the Natural Science Foundation of Hunan Province, China (Grant 2016JJ6044).


  1. 1.
    Crawford, G.: Flexible at Panel Displays. Wiley, Somerset (2005)CrossRefGoogle Scholar
  2. 2.
    Kim, D.-H., Xiao, J., Song, J., et al.: Stretchable, curvilinear electronics based on inorganic materials. Adv. Mater. 22, 2108–2124 (2010)CrossRefGoogle Scholar
  3. 3.
    Ko, H.C., Stoykovich, M.P., Song, J., et al.: A hemispherical electronic eye camera based on compressible silicon optoelectronics. Nature 454, 748–753 (2008)CrossRefGoogle Scholar
  4. 4.
    Brand, J., Kok, M., Koetse, M., et al.: Flexible and stretchable electronics for wearable health devices. Solid-State Electron. 113, 116–120 (2015)CrossRefGoogle Scholar
  5. 5.
    Forrest, S.: The path to ubiquitous and low-cost organic electronic appliances on plastic. Nature 428, 911–918 (2004)CrossRefGoogle Scholar
  6. 6.
    Fewster, P.: X-ray analysis of thin films and multilayers. Rep. Prog. Phys. 59, 1339 (1996)CrossRefGoogle Scholar
  7. 7.
    Cotton, D., Graz, I., Lacour, S.: Stretchable touch sensitive keypad. Proc. Chem. 1, 152–155 (2009)CrossRefGoogle Scholar
  8. 8.
    Rogers, J., Someya, T., Huang, Y.: Materials and mechanics for stretchable electronics. Science 327, 1603–1607 (2010)CrossRefGoogle Scholar
  9. 9.
    Kim, D.-H., Ahn, J.-H., Choi, W.M., et al.: Stretchable and foldable silicon integrated circuits. Science 320, 507–511 (2008)CrossRefGoogle Scholar
  10. 10.
    Freund, L., Suresh, S.: Thin Film Materials: Stress, Defect Formation and Surface Evolution. Cambridge University Press, Cambridge (2004)zbMATHCrossRefGoogle Scholar
  11. 11.
    Hohlfeld, E., Davidovitch, B.: Sheet on a deformable sphere: wrinkle patterns suppress curvature-induced delamination. Phys. Rev. E 91, 012407 (2015)CrossRefGoogle Scholar
  12. 12.
    Bella, P., Kohn, R.V.: Wrinkling of a thin circular sheet bonded to a spherical substrate. Philos. Trans. R. Soc. A 375, 2093 (2017)CrossRefGoogle Scholar
  13. 13.
    Hure, J., Roman, B., Bico, J.: Stamping and wrinkling of elastic plates. Phys. Rev. Lett. 109, 054302 (2012)CrossRefGoogle Scholar
  14. 14.
    Kim, D.-H., Song, J., Choi, W., et al.: Materials and noncoplanar mesh designs for integrated circuits with linear elastic responses to extreme mechanical deformations. Proc. Nat. Acad. Sci. 105, 18675–18680 (2008)CrossRefGoogle Scholar
  15. 15.
    Song, J., Feng, X., Huang, Y.: Mechanics and thermal management of stretchable inorganic electronics. Natl. Sci. Rev. 3, 128–143 (2016)CrossRefGoogle Scholar
  16. 16.
    Toth, F., Rammerstorfer, F., Cordill, M., et al.: Detailed modelling of delamination buckling of thin films under global tension. Acta Mater. 61, 2425–2433 (2013)CrossRefGoogle Scholar
  17. 17.
    Li, B., Cao, Y., Feng, X., et al.: Mechanics of morphological instabilities and surface wrinkling in soft materials: a review. Soft Matter 8, 5728–5745 (2012)CrossRefGoogle Scholar
  18. 18.
    Xue, X., Wang, S., Zeng, C., et al.: Buckling-delamination and cracking of thin titanium films under compression: experimental and numerical studies. Surf. Coat. Technol. 244, 151–157 (2014)CrossRefGoogle Scholar
  19. 19.
    Huang, H.S., Pei, H.J., Chang, Y.C., et al.: Tensile behaviors of amorphous-zrcu/nanocrystalline-cu multilayered thin film on polyimide substrate. Thin Solid Films 529, 177–180 (2013)CrossRefGoogle Scholar
  20. 20.
    Djaziri, S., Renault, P.-O., Le Bourhis, E., et al.: Comparative study of the mechanical properties of nanostructured thin films on stretchable substrates. J. Appl. Phys. 116, 093504 (2014)CrossRefGoogle Scholar
  21. 21.
    Hommel, M., Kraft, O.: Deformation behavior of thin copper films on deformable substrates. Acta Mater. 49, 3935–3947 (2001)CrossRefGoogle Scholar
  22. 22.
    Xiang, Y., Vlassak, J.: Bauschinger effect in thin metal films. Scr. Mater. 53, 177–182 (2005)CrossRefGoogle Scholar
  23. 23.
    Xiang, Y., Li, T., Suo, Z., et al.: High ductility of a metal film adherent on a polymer substrate. Appl. Phys. Lett. 87, 161910 (2005)CrossRefGoogle Scholar
  24. 24.
    Lu, N., Wang, X., Suo, Z., et al.: Metal films on polymer substrates stretched beyond 50%. Appl. Phys. Lett. 91, 221909 (2007)CrossRefGoogle Scholar
  25. 25.
    Niu, R.M., Liu, G., Wang, C., et al.: Thickness dependent critical strain in submicron cu films adherent to polymer substrate. Appl. Phys. Lett. 90, 161907 (2007)CrossRefGoogle Scholar
  26. 26.
    Marx, V., Cordill, M., Tbbens, D., et al.: Effect of annealing on the size dependent deformation behavior of thin cobalt films on flexible substrates. Thin Solid Films 624, 34–40 (2017)CrossRefGoogle Scholar
  27. 27.
    Graudejus, O., Jia, Z., Li, T., et al.: Size-dependent rupture strain of elastically stretchable metal conductors. Scr. Mater. 66, 919 (2012)CrossRefGoogle Scholar
  28. 28.
    Suo, Z., Vlassak, J.J., Wagner, S.: Micromechanics of macroelectronics. China Particuol. 3, 321–328 (2005)CrossRefGoogle Scholar
  29. 29.
    Jia, H., Wang, S., Li, L., et al.: Application of optical 3d measurement on thin film buckling to estimate interfacial toughness. Opt. Lasers Eng. 54, 263–268 (2014)CrossRefGoogle Scholar
  30. 30.
    Mittal, K.: Adhesion measurement of thin films. Act. Passive Electron. Compon. 3, 21–42 (1976)Google Scholar
  31. 31.
    Gerberich, W., Cordill, M.: Physics of adhesion. Rep. Prog. Phys. 69, 2157 (2006)CrossRefGoogle Scholar
  32. 32.
    Chen, J., Bull, S.: Indentation fracture and toughness assessment for thin optical coatings on glass. J. Phys. D Appl. Phys. 40, 5401 (2007)CrossRefGoogle Scholar
  33. 33.
    Hutchinson, J.W., Suo, Z.: Mixed mode cracking in layered materials. Adv. Appl. Mech. 29, 63–191 (1991)zbMATHCrossRefGoogle Scholar
  34. 34.
    Cordill, M., Fischer, F., Rammerstorfer, F., et al.: Adhesion energies of cr thin films on polyimide determined from buckling: experiment and model. Acta Mater. 58, 5520–5531 (2010)Google Scholar
  35. 35.
    Faurie, D., Zighem, F., Garcia-Sanchez, A., et al.: Fragmentation and adhesion properties of cofeb thin films on polyimide substrate. Appl. Phys. Lett. 110, 721 (2017)CrossRefGoogle Scholar
  36. 36.
    Wu, K., Zhang, J.Y., Liu, G., et al.: Buckling behaviors and adhesion energy of nanostructured Cu/\(x\) (\(x\) = Nb, Zr) multilayer films on a compliant substrate. Acta Mater. 61, 7889 (2013)CrossRefGoogle Scholar
  37. 37.
    Wu, D., Xie, H., Yin, Y., et al.: Micro-scale delaminating and buckling of thin film on soft substrate. J. Micromech. Microeng. 23, 03540 (2013)Google Scholar
  38. 38.
    Mohri, M., Nili-Ahmadabadi, M., PouryazdanPanah, M., et al.: Evaluation of structure and mechanical properties of Ni-rich NiTi/Kapton composite film. Mater. Sci. Eng. A 668, 13–19 (2016)CrossRefGoogle Scholar
  39. 39.
    Kirsch, B., Chen, X., Richman, E., et al.: Probing the effects of nanoscale architecture on the mechanical properties of hexagonal silica/polymer composite thin films. Adv. Funct. Mater. 15, 1319–1327 (2005)CrossRefGoogle Scholar
  40. 40.
    Geandier, G., Renault, P.-O., Le Bourhis, E., et al.: Elastic-strain distribution in metallic film-polymer substrate composites. Appl. Phys. Lett. 96, 041905 (2010)CrossRefGoogle Scholar
  41. 41.
    Hommel, M., Kraft, O., Arzt, E.: A new method to study cyclic deformation of thin films in tension and compression. J. Mater. Res. 14, 2373–2376 (1999)CrossRefGoogle Scholar
  42. 42.
    Schadler, L., Noyan, I.C.: Experimental Determination of the Strain Transfer Across a Flexible Intermediate Layer in Thin Film Structures as a Function of Flexible Layer Thickness//MRS Proceedings. Cambridge University Press, Cambridge (1991)Google Scholar
  43. 43.
    Schadler, L., Noyan, I.: Experimental determination of the strain transfer across a flexible intermediate layer in thin-film structures. J. Mater. Sci. Lett. 11, 1067–1069 (1992)CrossRefGoogle Scholar
  44. 44.
    Yin, H., Prieto-Munoz, P.: Stress transfer through fully bonded interface of layered materials. Mech. Mater. 62, 69–79 (2013)CrossRefGoogle Scholar
  45. 45.
    Faurie, D., Renault, P.-O., Le Bourhis, E., et al.: Determination of elastic constants of a fiber-textured gold film by combining synchrotron X-ray diffraction and in situ tensile testing. J. Appl. Phys. 98, 093511 (2005)CrossRefGoogle Scholar
  46. 46.
    Wojciechowski, P., Mendolia, M.: Fracture and cracking phenomena in thin films adhering to high-elongation substrates. Phys. Thin Films 16, 271–340 (1991)CrossRefGoogle Scholar
  47. 47.
    Yanaka, M., Tsukahara, Y., Nakaso, N., et al.: Cracking phenomena of brittle films in nanostructure composites analysed by a modified shear lag model with residual strain. J. Mater. Sci. 33, 2111–2119 (1998)CrossRefGoogle Scholar
  48. 48.
    Huang, H., Spaepen, F.: Tensile testing of free-standing Cu, Ag and Al thin films and Ag/Cu multilayers. Acta Mater. 48, 3261–3269 (2000)CrossRefGoogle Scholar
  49. 49.
    Belrhiti, Y., Gallet-Doncieux, A., Germaneau, A., et al.: Application of optical methods to investigate the non-linear asymmetric behavior of ceramics exhibiting large strain to rupture by four-points bending test. J. Eur. Ceram. Soc. 32, 4073–4081 (2012)CrossRefGoogle Scholar
  50. 50.
    Wu, D., Xie, H., Dai, X., et al.: A novel method to fabricate microgratings applied for deformation measurement around a crack in a thin film. Meas. Sci. Technol. 25, 025012 (2014)CrossRefGoogle Scholar
  51. 51.
    Hild, F., Roux, S.: Digital image correlation: from displacement measurement to identification of elastic properties—a review. Strain 42, 69–80 (2006)CrossRefGoogle Scholar
  52. 52.
    Duprfie, J., Doumalin, P., Husseini, H., et al.: Displacement discontinuity or complex shape of sample: assessment of accuracy and adaptation of local dic approach. Strain 51, 391–404 (2015)CrossRefGoogle Scholar
  53. 53.
    Barranger, Y., Doumalin, P., Duprfie, J., et al.: Strain measurement by digital image correlation: influence of two types of speckle patterns made from rigid or deformable marks. Strain 48, 357–365 (2012)CrossRefGoogle Scholar
  54. 54.
    Welzel, U., Ligot, J., Lamparter, P., et al.: Stress analysis of polycrystalline thin films and surface regions by X-ray diffraction. J. Appl. Crystallogr. 38, 1–29 (2005)CrossRefGoogle Scholar
  55. 55.
    Noyan, I., Huang, T., York, B.: Residual stress/strain analysis in thin films by X-ray difiraction. Crit. Rev. Solid State Mater. Sci. 20, 125–177 (1995)CrossRefGoogle Scholar
  56. 56.
    Stoney, G.: The tension of metallic films deposited by electrolysis. Containing papers of a mathematical and physical character. Proc. R. Soc. Lond. Ser. A 82, 172–175 (1990)CrossRefGoogle Scholar
  57. 57.
    Chou, T.-L., Yang, S.-Y., Chiang, K.-N.: Overview and applicability of residual stress estimation of film-substrate structure. Thin Solid Films 519, 7883–7894 (2011)CrossRefGoogle Scholar
  58. 58.
    Janssen, G., Abdalla, M., Van Keulen, F., et al.: Celebrating the 100th anniversary of the stoney equation for film stress: developments from polycrystalline steel strips to single crystal silicon wafers. Thin Solid Films 517, 1858–1867 (2009)CrossRefGoogle Scholar
  59. 59.
    Zhu, J., Xie, H., Hu, Z., et al.: Residual stress in thermal spray coatings measured by curvature based on 3d digital image correlation technique. Surf. Coat. Technol. 206, 1396–1402 (2011)CrossRefGoogle Scholar
  60. 60.
    Kim, C., Lee, T.-I., Kim, M., et al.: Warpage analysis of electroplated cu films on fiber-reinforced polymer packaging substrates. Polymers 7, 985–1004 (2015)CrossRefGoogle Scholar
  61. 61.
    Culity, B.: Elements of X-ray Diffraction. Addition-Wesley, London (1978)Google Scholar
  62. 62.
    Hauk, V.: Structural and Residual Stress Analysis by Nondestructive Methods: Evaluation-Application-Assessment. Elsevier, Amsterdam (1997)zbMATHGoogle Scholar
  63. 63.
    Noyan, I., Cohen, J.: Residual Stress: Measurement by Diffraction and Interpretation. Springer, New York (1987)CrossRefGoogle Scholar
  64. 64.
    Martinschitz, K., Daniel, R., Mitterer, C., et al.: Elastic constants of fibre-textured thin films determined by X-ray diffraction. J. Appl. Crystallogr. 42, 416–428 (2009)CrossRefGoogle Scholar
  65. 65.
    Faurie, D., Castelnau, O., Brenner, R., et al.: In situ diffraction strain analysis of elastically deformed polycrystalline thin films, and micromechanical interpretation. J. Appl. Crystallogr. 42, 1073–1084 (2009)CrossRefGoogle Scholar
  66. 66.
    Clemens, B., Bain, J.: Stress determination in textured thin films using X-ray diffraction. MRS Bull. 17, 46–51 (1992)CrossRefGoogle Scholar
  67. 67.
    Krottenthaler, M., Schmid, C., Schauer, J., et al.: A simple method for residual stress measurements in thin films by means of focused ion beam milling and digital image correlation. Surf. Coat. Technol. 215, 247–252 (2013)CrossRefGoogle Scholar
  68. 68.
    Zhu, J.G., Xie, H.M., Li, Y.J., et al.: Interfacial residual stress analysis of thermal spray coatings by miniature ring-core cutting combined with DIC method. Exp. Mech. 54, 127–136 (2014)CrossRefGoogle Scholar
  69. 69.
    Korsunsky, A., Sebastiani, M., Bemporad, E.: Focused ion beam ring drilling for residual stress evaluation. Mater. Lett. 63, 1961–1963 (2009)CrossRefGoogle Scholar
  70. 70.
    Zhu, R.H., Xie, H.M., Zhu, J.G., et al.: A microscale strain rosette for residual stress measurement by SEM Moire method. Sci. China Phys. Mech. Astron. 57, 716–722 (2014)CrossRefGoogle Scholar
  71. 71.
    Bemporad, E., Brisotto, M., Depero, L., et al.: A critical comparison between xrd and fib residual stress measurement techniques in thin films. Thin Solid Films 572, 224–231 (2014)CrossRefGoogle Scholar
  72. 72.
    Doerner, M.F., Nix, W.D.: Stresses and deformation processes in thin films on substrates. Crit. Rev. Solid State Mater. Sci. 14, 225–268 (1988)CrossRefGoogle Scholar
  73. 73.
    Janssen, G.: Stress and strain in polycrystalline thin films. Thin Solid Films 515, 6654–6664 (2007)CrossRefGoogle Scholar
  74. 74.
    Lu, N., Suo, Z., Vlassak, J.J.: The effect of film thickness on the failure strain of polymer-supported metal films. Acta Mater. 58, 1679–1687 (2010)CrossRefGoogle Scholar
  75. 75.
    Oliver, W., Pharr, G.: Measurement of hardness and elastic modulus by instrumented indentation: advances in understanding and refinements to methodology. J. Mater. Res. 19, 3–20 (2004)CrossRefGoogle Scholar
  76. 76.
    Zhu, J.G., Xie, H.M., Hu, Z., et al.: Cross-sectional residual stresses in thermal spray coatings measured by Moire interferometry and nanoindentation technique. J. Therm. Spray Technol. 21, 810–817 (2012)CrossRefGoogle Scholar
  77. 77.
    Zhu, J.G., Wei, C., Xie, H.M.: Simulation of residual stresses and their effects on thermal barrier coating systems using finite element method. Sci. China Phys. Mech. Astron. 58, 1–10 (2015)Google Scholar
  78. 78.
    Javed, H., Merle, B., Prei, E., et al.: Mechanical characterization of metallic thin films by bulge and scratch testing. Surf. Coat. Technol. 289, 69–74 (2016)CrossRefGoogle Scholar
  79. 79.
    Djaziri, S., Faurie, D., Renault, P.O., et al.: Yield surface of polycrystalline thin films as revealed by non-equibiaxial loadings at small deformation. Acta Mater. 61, 5067–5077 (2013)CrossRefGoogle Scholar
  80. 80.
    Denis, Y., Spaepen, F.: The yield strength of thin copper films on kapton. J. Appl. Phys. 95, 2991–2997 (2004)CrossRefGoogle Scholar
  81. 81.
    Choi, Y., Lee, Y.-K.: Elastic modulus of amorphous Ge\(_2\)Sb\(_2\)Te\(_5\) thin film measured by uniaxial microtensile test. Electron. Mater. Lett. 6, 23–26 (2010)CrossRefGoogle Scholar
  82. 82.
    Chen, X., Kirsch, B., Senter, R., et al.: Tensile testing of thin films supported on compliant substrates. Mech. Mater. 41, 839–848 (2009)CrossRefGoogle Scholar
  83. 83.
    He, W., Goudeau, P., Bourhis, E.L., et al.: Study on young’s modulus of thin films on kapton by microtensile testing combined with dual DIC system. Surf. Coat. Technol. 308, 273–279 (2016)CrossRefGoogle Scholar
  84. 84.
    Faurie, D., Renault, P.-O., Bourhis, E.Le, et al.: Study of texture effect on elastic properties of au thin films by X-ray diffraction and in situ tensile testing. Acta Mater. 54, 4503–4513 (2006)CrossRefGoogle Scholar
  85. 85.
    Thomasov, M., Sedlk, P., Seiner, H., et al.: Youngs moduli of sputter-deposited niti films determined by resonant ultrasound spectroscopy: austenite, r-phase, and martensite. Scr. Mater. 101, 24–27 (2015)CrossRefGoogle Scholar
  86. 86.
    Lpez-Puerto, A., Avils, F., Gamboa, F., et al.: A vibrational approach to determine the elastic modulus of individual thin films in multilayers. Thin Solid Films 565, 228–236 (2014)CrossRefGoogle Scholar
  87. 87.
    Slima, M., Alhusseinb, A., Billard, A., et al.: On the determination of Young’s modulus of thin films with impulse excitation technique. J. Mater. Res. 32, 1–15 (2016)Google Scholar
  88. 88.
    Bauschinger, J.: Ueber die veranderung der elasticitatagrenze und der elasticitatamoduls verschiadener metalle. Zivilingenieur 27, 289–348 (1881)Google Scholar
  89. 89.
    Baker, S., Keller-Flaig, R.-M., et al.: Bauschinger effect and anomalous thermomechanical deformation induced by oxygen in passivated thin cu films on substrates. Acta Mater. 51, 3019–3036 (2003)CrossRefGoogle Scholar
  90. 90.
    Xiang, Y., Vlassak, J.J.: Bauschinger and size effects in thin-film plasticity. Acta Mater. 54, 5449–5460 (2006)CrossRefGoogle Scholar
  91. 91.
    Brugger, C., Coulombier, M., Massart, T., et al.: Strain gradient plasticity analysis of the strength and ductility of thin metallic films using an enriched interface model. Acta Mater. 58, 4940–4949 (2010)CrossRefGoogle Scholar
  92. 92.
    Zhou, C., LeSar, R.: Dislocation dynamics simulations of the bauschinger effect in metallic thin films. Comput. Mater. Sci. 54, 350–355 (2012)CrossRefGoogle Scholar
  93. 93.
    Rajagopalan, J., Rentenberger, C., Karnthaler, H., et al.: In situ tem study of microplasticity and bauschinger effect in nanocrystalline metals. Acta Mater. 58, 4772–4782 (2010)CrossRefGoogle Scholar
  94. 94.
    Rajagopalan, J., Han, J., Saif, M.: Bauschinger effect in unpassivated freestanding nanoscale metal films. Scr. Mater. 59, 734–737 (2008)CrossRefGoogle Scholar
  95. 95.
    Shishvan, S., Nicola, L.Van, der Giessen, E.: Bauschinger effect in unpassivated freestanding thin films. J. Appl. Phys. 107, 093529 (2010)CrossRefGoogle Scholar
  96. 96.
    Guruprasad, P., Carter, W., Benzerga, A.: A discrete dislocation analysis of the bauschinger effect in microcrystals. Acta Mater. 56, 5477–5491 (2008)CrossRefGoogle Scholar
  97. 97.
    Liu, Z.-L., Zhuang, Z., Liu, X.-M., et al.: Bauschinger and size effects in thin-film plasticity due to defect-energy of geometrical necessary dislocations. Acta. Mech. Sin. 27, 266–276 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  98. 98.
    Davoudi, K., Nicola, L., Vlassak, J.J.: Bauschinger effect in thin metal films: discrete dislocation dynamics study. J. Appl. Phys. 115, 013507 (2014)CrossRefGoogle Scholar
  99. 99.
    Xu, S., Yan, Z., Jang, K.-I., et al.: Assembly of micro/nanomaterials into complex, three-dimensional architectures by compressive buckling. Science 347, 154–159 (2015)CrossRefGoogle Scholar
  100. 100.
    Song, J., Jiang, H., Liu, Z., et al.: Buckling of a stiff thin film on a compliant substrate in large deformation. Int. J. Solids Struct. 45, 3107–3121 (2008)zbMATHCrossRefGoogle Scholar
  101. 101.
    Khang, D.-Y., Jiang, H., Huang, Y., et al.: A stretchable form of single crystal silicon for high-performance electronics on rubber substrates. Science 311, 208–212 (2006)CrossRefGoogle Scholar
  102. 102.
    Renault, P.-O., Faurie, D., Le Bourhis, E., et al.: Deposition of ultra-thin gold film on in situ loaded polymeric substrate for compression tests. Mater. Lett. 73, 99–102 (2012)CrossRefGoogle Scholar
  103. 103.
    Faurie, D., Renault, P.-O., Le Bourhis, E., et al.: X-ray elastic strain analysis of compressed au thin film on polymer substrate. Surf. Coat. Technol. 215, 322–326 (2013)CrossRefGoogle Scholar
  104. 104.
    He, W., Renault, P.-O., Le Bourhis, E., et al.: Cyclic testing of thin Ni films on a pre-tensile compliant substrate. Mater. Sci. Eng. A 695, 112–119 (2017)CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Wei He
    • 1
  • Meidong Han
    • 1
  • Shibin Wang
    • 1
  • Lin-An Li
    • 1
  • Xiuli Xue
    • 2
  1. 1.Department of MechanicsTianjin UniversityTianjinChina
  2. 2.Department of Engineering MechanicsHunan University of Science and TechnologyXiangtanChina

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