Evaluation of Poisson’s ratio for thin soft material by multiplex procedure of spherical indentation mechanics
Source abstract
Abstract
The Poisson’s ratio plays a significant role in material science and manufacturing, and it should be effectively identified for thin soft materials. In this study, a theoretical multiplex procedure is proposed with spherical indentation to identify the Poisson’s ratio of thin soft materials. First, the spherical indentation theories of full contact, fundamental and extended Hertzian are functional separated. By analyzing the sensitivity of the separated terms in each theory, the multiplex procedure is developed. Then, computational simulations are performed to observe the indentation behavior of same thin soft material tested by each theory. The numerical results are approximately fitted by each theory under initial and large indentation depth. Both extended Hertzian and full contact theories show high feasibility to fit the numerical results, while the fundamental theory is applied in the initial contact region. Subsequently, the multiplex procedure is conducted to identify the Poisson’s ratio by the full contact theory with fundamental and extended Hertzian theories. The result indicates that the multiplex theory developed herein is depending on the contact theories and indentation depth. Consequently, by using the multiplex theory, the accurate identification of Poisson’s ratio for thin soft materials can be realized in the case of large Poisson’s ratio, extended Hertzian theory and initial indentation depth.
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Research context
OpenAlex topics: Metal and Thin Film Mechanics · Advanced Surface Polishing Techniques · Adhesion, Friction, and Surface Interactions
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (57)
Show source-provided references
1. Alfano, M., Pagnotta, L.: Measurement of the dynamic elastic properties of a thin coating. Rev. Sci. Instrum. 77(5), 056,107 (2006)10.1063/1.2198747 ↗
2. Badawi, K., Villain, P., Goudeau, P., Renault, P.O.: Measuring thin film and multilayer elastic constants by coupling in situ tensile testing with x-ray diffraction. Appl. Phys. Lett. 80(25), 4705–4707 (2002)10.1063/1.1488701 ↗
3. Baumeister, P.: Optical Coating Technology, vol. 137. SPIE Press (2004)10.1117/3.548071 ↗
4. Bradby, J., Williams, J., Wong-Leung, J., Swain, M.V., Munroe, P.: Mechanical deformation in silicon by micro-indentation. J. Mater. Res. 16(5), 1500–1507 (2001)10.1557/JMR.2001.0209 ↗
5. Chang, K.H.: e-Design: Computer-aided Engineering Design. Academic Press (2016)
6. Cheng, Y.T., Cheng, C.M.: Relationships between hardness, elastic modulus, and the work of indentation. Appl. Phys. Lett. 73(5), 614–616 (1998)10.1063/1.121873 ↗
7. Christensen, N.I.: Poisson’s ratio and crustal seismology. J. Geophys. Res.: Solid Earth 101(B2), 3139–3156 (1996)10.1029/95JB03446 ↗
8. Chudoba, T., Schwarzer, N., Richter, F.: Determination of elastic properties of thin films by indentation measurements with a spherical indenter. Surf. Coat. Technol. 127(1), 9–17 (2000)10.1016/S0257-8972(00)00552-1 ↗
9. Doerner, M.F., Nix, W.D.: A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1(4), 601–609 (1986)10.1557/JMR.1986.0601 ↗
10. Du, B., Tsui, O.K., Zhang, Q., He, T.: Study of elastic modulus and yield strength of polymer thin films using atomic force microscopy. Langmuir 17(11), 3286–3291 (2001)10.1021/la001434a ↗
11. Dudney, N.J., et al.: Thin film micro-batteries. Electrochem. Soc. Interface 17(3), 44 (2008)10.1149/2.F04083IF ↗
12. Ewing, J.A., Rosenhain, W.: Viii. the crystalline structure of metals. (second paper.). Philos. Trans. R. Soc. Lond. Ser. A Contain. Papers of a Mathematical or Physical Character 195(262-273), 279–301 (1900)10.1098/rsta.1900.0029 ↗
13. Fischer-Cripps, A.: A review of analysis methods for sub-micron indentation testing. Vacuum 58(4), 569–585 (2000)10.1016/S0042-207X(00)00377-8 ↗
14. Greaves, G.N.: Poisson’s ratio over two centuries: challenging hypotheses. Notes Rec. R. Soc. 67(1), 37–58 (2013)10.1098/rsnr.2012.0021 ↗
15. Greaves, G.N., Greer, A., Lakes, R.S., Rouxel, T.: Poisson’s ratio and modern materials. Nat. Mater. 10(11), 823–837 (2011)10.1038/nmat3134 ↗
16. Harris, D.C.: Nonlinear least-squares curve fitting with microsoft excel solver. J. Chem. Educ. 75(1), 119 (1998)10.1021/ed075p119 ↗
17. Hay, J., Wolff, P.: Small correction required when applying the Hertzian contact model to instrumented indentation data. J. Mater. Res. 16(5), 1280–1286 (2001)10.1557/JMR.2001.0179 ↗
18. Herbert, E., Pharr, G., Oliver, W., Lucas, B., Hay, J.: On the measurement of stress-strain curves by spherical indentation. Thin Solid Films 398, 331–335 (2001)10.1016/S0040-6090(01)01439-0 ↗
19. Hertz, H.: Über die beriihrung fester elastischer korper (on the contact of elastic solids). J. für die reine und angewandte Math. 92, 146–162 (1881)
20. Hertz, H.R.: Uber die beruhrung fester elastischer korper und uber die harte. Verhandlung des Vereins zur Beforderung des GewerbefleiBes, Berlin p. 449 (1882)10.1515/9783112342404-004 ↗
21. Huber, M.T.: Zur theorie der berührung fester elastischer körper. Ann. Phys. 319(6), 153–163 (1904)10.1002/andp.19043190611 ↗
22. Ilic, B., Krylov, S., Craighead, H.G.: Young’s modulus and density measurements of thin atomic layer deposited films using resonant nanomechanics. J. Appl. Phys. 108(4), 044,317 (2010)10.1063/1.3474987 ↗
23. Johnson, K.L.: One hundred years of hertz contact. Proc. Inst. Mech. Eng. 196(1), 363–378 (1982)10.1243/PIME_PROC_1982_196_039_02 ↗
24. Katardjiev, I., Yantchev, V.: Recent developments in thin film electro-acoustic technology for biosensor applications. Vacuum 86(5), 520–531 (2012)10.1016/j.vacuum.2011.10.012 ↗
25. Köster, W., Franz, H.: Poisson’s ratio for metals and alloys. Metall. Rev. 6(1), 1–56 (1961)10.1179/095066061790425893 ↗
26. Krottenthaler, M., Schmid, C., Schaufler, J., Durst, K., Göken, M.: 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)10.1016/j.surfcoat.2012.08.095 ↗
27. Lakes, R.: Advances in negative poisson’s ratio materials (1993)10.1002/adma.19930050416 ↗
28. Larsen, U.D., Signund, O., Bouwsta, S.: Design and fabrication of compliant micromechanisms and structures with negative poisson’s ratio. J. Microelectromech. Syst. 6(2), 99–106 (1997)10.1109/84.585787 ↗
29. Lu, C., Sakuma, A.: Formulation method of ball indentation process for ultra-thin elastic body with mechanics poisson effect. In: COMPLAS XV: Proceedings of the XV International Conference on Computational Plasticity: Fundamentals and Applications, pp. 402–410. CIMNE (2019)
30. Moram, M., Barber, Z., Humphreys, C.: Accurate experimental determination of the poisson’s ratio of gan using high-resolution x-ray diffraction. J. Appl. Phys. 102(2), 023,505 (2007)10.1063/1.2749484 ↗
31. Nielsen, L.E.: Generalized equation for the elastic moduli of composite materials. J. Appl. Phys. 41(11), 4626–4627 (1970)10.1063/1.1658506 ↗
32. Novikov, V., Sokolov, A.: Poisson’s ratio and the fragility of glass-forming liquids. Nature 431(7011), 961–963 (2004)10.1038/nature02947 ↗
33. Ohring, M.: Materials Science of Thin Films. Elsevier, Amsterdam (2001)
34. Oliver, W.C., Pharr, G.M.: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7(6), 1564–1583 (1992)10.1557/JMR.1992.1564 ↗
35. Parejo, P.G., Zayat, M., Levy, D.: Highly efficient UV-absorbing thin-film coatings for protection of organic materials against photodegradation. J. Mater. Chem. 16(22), 2165–2169 (2006)10.1039/b601577h ↗
36. Pharr, G.M., Herbert, E.G., Gao, Y.: The indentation size effect: a critical examination of experimental observations and mechanistic interpretations. Annu. Rev. Mater. Res. 40, 271–292 (2010)10.1146/annurev-matsci-070909-104456 ↗
37. Poisson, S.D.: Traité de mécanique 2, 476 (1811)
38. Poisson, S.D.: Ann. Chim. Phys. (eds Gay-Lussac, L. J. & Arago, F.) 36, 384–385 (1827)
39. Raphael, B., Smith, I.F.: Fundamentals of Computer-aided Engineering. Wiley, London (2003)
40. Read, W.T., Shockley, W.: Dislocation models of crystal grain boundaries. Phys. Rev. 78(3), 275 (1950)10.1103/PhysRev.78.275 ↗
41. Sakuma, A.: Softness measurement technics of human skin by indentation devices imitating palpation. In: ASME International Mechanical Engineering Congress and Exposition, vol. 56222, p. V03BT03A062. American Society of Mechanical Engineers (2013)10.1115/IMECE2013-66258 ↗
42. Sakuma, A.: Handy-device development of softness measurement by indentation imitating palpation for evaluation of elasticity and visco-elasiticity. In: ASME International Mechanical Engineering Congress and Exposition, vol. 57380, p. V003T03A025. American Society of Mechanical Engineers (2015)10.1115/IMECE2015-51589 ↗
43. Sakuma, A., Igarashi, K.: Behavior evaluation of deformation, damage and fracture of biological soft tissue by using indentation test. In: ASME International Mechanical Engineering Congress and Exposition, vol. 50534, p. V003T04A037. American Society of Mechanical Engineers (2016)10.1115/IMECE2016-66672 ↗
44. Sakuma, A., Shirai, Y.: Palpation-like devices of ball indentation for softness evaluation of biological tissue. In: International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol. 58158, p. V003T13A001. American Society of Mechanical Engineers (2017)
45. Sharpe, W., Yuan, B., Edwards, R.: A new technique for measuring the mechanical properties of thin films. J. Microelectromech. Syst. 6(3), 193–199 (1997)10.1109/84.623107 ↗
46. Shirai, Y., Li, Z., Sakuma, A.: Position identification of inclusions in soft objects by indentation testing. In: ASME International Mechanical Engineering Congress and Exposition, vol. 58363, p. V003T04A074. American Society of Mechanical Engineers (2017)10.1115/IMECE2017-70546 ↗
47. Sit, A.J., Lin, S.C., Kazemi, A., McLaren, J.W., Pruet, C.M., Zhang, X.: In vivo non-invasive measurement of young’s modulus of elasticity in human eyes: a feasibility study. J. Glaucoma 26(11), 967 (2017)10.1097/IJG.0000000000000774 ↗
48. Swadener, J., George, E., Pharr, G.: The correlation of the indentation size effect measured with indenters of various shapes. J. Mech. Phys. Solids 50(4), 681–694 (2002)10.1016/S0022-5096(01)00103-X ↗
49. Tani, M., Sakuma, A.: Applicability evaluation of Young’s modulus measurement using equivalent indentation strain in spherical indentation testing for soft materials. Trans. Jpn. Soc. Mech. Eng. Ser. A 76(761), 102–108 (2010)10.1299/kikaia.76.102 ↗
50. Tani, M., Sakuma, A., Shinomiya, M.: Evaluation of thickness and young’s modulus of soft materials by using spherical indentation testing. Trans. Jpn. Soc. Mech. Eng. Ser. A 75(755), 901–908 (2009)10.1299/kikaia.75.901 ↗
51. Thomas, H.R.: Stresses due to the pressure of one elastic solid upon another. Univ. Illinois Bull. 212, 14–22 (1930)
52. Vlassak, J., Nix, W.: A new bulge test technique for the determination of Young’s modulus and Poisson’s ratio of thin films. J. Mater. Res. 7(12), 3242–3249 (1992)10.1557/JMR.1992.3242 ↗
53. Vossen, J.L., Kern, W., Kern, W., et al.: Thin Film Processes II, vol. 2. Gulf Professional Publishing (1991)
54. Weppelmann, E., Field, J., Swain, M.: Observation, analysis, and simulation of the hysteresis of silicon using ultra-micro-indentation with spherical indenters. J. Mater. Res. 8(4), 830–840 (1993)10.1557/JMR.1993.0830 ↗
55. Zandt, G., Ammon, C.J.: Continental crust composition constrained by measurements of crustal Poisson’s ratio. Nature 374(6518), 152–154 (1995)10.1038/374152a0 ↗
56. Zarudi, I., Zhang, L., Cheong, W., Yu, T.: The difference of phase distributions in silicon after indentation with Berkovich and spherical indenters. Acta Mater. 53(18), 4795–4800 (2005)10.1016/j.actamat.2005.06.030 ↗
57. Zhou, B.L.: The biomimetic study of composite materials. JOM 46(2), 57–62 (1994)10.1007/BF03222561 ↗