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On the determination of Young’s modulus of thin films with impulse excitation technique

  • M.F. Slim (a1), A. Alhussein (a1), A. Billard (a2), F. Sanchette (a1) and M. François (a3)...

The purpose of this paper is to propose a critical assessment of Young’s modulus determination of coated materials using Impulse Excitation Technique (IET). In this technique, the coated substrate is excited by an impulse and the acoustic vibrations are recorded. The frequency of the first bending mode is then used in a mechanical model to obtain the Young’s modulus of the coating. The existing models are based on two different theories: the flexural rigidity of a composite beam and the Classical Laminated Beam Theory (CLBT). The aim of the present paper is to assess the accuracy (trueness and precision) of the technique. For this, different models proposed in the literature are compared with a finite element model of the specimen for various conditions. The trueness and precision of models were evaluated and the best model was identified. Then a detailed uncertainty budget is performed to identify and quantify the most influent factors on the global uncertainty.

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1. Lopes C., Vieira M., Borges J., Fernandes J., Rodrigues M.S., Alves E., Barradas N.P., Apreutesei M., Steyer P., Tavares C.J., Cunha L., and Vaz F.: Multifunctional Ti–Me (Me = Al, Cu) thin film systems for biomedical sensing devices. Vacuum 122, 353359 (2015).
2. Makhlouf A.S.H.: Protective coatings for automotive, aerospace and military applications: Current prospects and future trends. In Handbook of Smart Coatings for Materials Protection, Makhlouf A.S.H., ed. (Woodhead Publishing, Cambridge, 2014); pp. 121131.
3. Tait J.G., Worfolk B.J., Maloney S.A., Hauger T.C., Elias A.L., Buriak J.M., and Harris K.D.: Spray coated high-conductivity PEDOT:PSS transparent electrodes for stretchable and mechanically-robust organic solar cells. Sol. Energy Mater. Sol. Cells 110, 98106 (2013).
4. Billard A. and Perry F.: Pulvérisation cathodique magnétron. Techniques de l’Ingénieur, M1654 (2005).
5. Thornton J.A.: Influence of apparatus geometry and deposition conditions on the structure and topography of thick sputtered coatings. J. Vac. Sci. Technol. 11, 666670 (1974).
6. Bellan C. and Dhers J.: Evaluation of Young modulus of CVD coatings by different techniques. Thin Solid Films 469–470, 214220 (2004).
7. Radovic M., Lara-Curzio E., and Riester L.: Comparison of different experimental techniques for determination of elastic properties of solids. Mater. Sci. Eng., A 368, 5670 (2004).
8. Tan Y., Shyam A., Choi W.B., Lara-Curzio E., and Sampath S.: Anisotropic elastic properties of thermal spray coatings determined via resonant ultrasound spectroscopy. Acta Mater. 58, 53055315 (2010).
9. Sedmák P., Seiner H., Sedlák P., Landa M., Mušálek R., and Matějíček J.: Application of resonant ultrasound spectroscopy to determine elastic constants of plasma-sprayed coatings with high internal friction. Surf. Coat. Technol. 232, 747757 (2013).
10. Thomasová M., Sedlák P., Seiner H., Janovská M., Kabla M., Shilo D., and Landa M.: Young’s moduli of sputter-deposited NiTi films determined by resonant ultrasound spectroscopy: Austenite, R-phase, and martensite. Scr. Mater. 101, 2427 (2015).
11. Gadaud P. and Pautrot S.: Application of the dynamical flexural resonance technique to industrial materials characterisation. Mater. Sci. Eng., A 370, 422426 (2004).
12. López-Puerto A. and Oliva A.I.: A vibrational approach to determine the elastic modulus of individual thin films in multilayers. Thin Solid Films 565, 228236 (2014).
13. Gadaud P., Milhet X., and Pautrot S.: Bulk and coated materials shear modulus determination by means of torsional resonant method. Mater. Sci. Eng., A 521–522, 303306 (2009).
14. Mazot P. and Pautrot S.: Détermination du module d’young de dépôts par flexion dynamique: Application aux systèmes bicouche et tricouche. Ann. Chim. Sci. Mat. 23, 821827 (1998).
15. Pickett G.: Equations for computing elastic constants from flexural and torsional resonant frequencies of vibration of prisms and cylinders. Am. Soc. Test. Mater., Proc. 45, 846865 (1945).
16. Tefft W.E.: Numerical solution of the frequency equations for the flexural vibration of cylindrical rods. J. Res. Natl. Bur. Stand., Sect. B 64B, 237242 (1960).
17. Spinner S., Reichard T.W., and Tefft W.E.: A comparison of experimental and theoretical relations between Young’s modulus and the flexural and longitudinal resonance frequencies of uniform bars. J. Res. Natl. Bur. Stand., Sect. A 64A, 147155 (1960).
18. Spinner S. and Valore R.C.: Comparison of theoretical and empirical relations between the shear modulus and torsional resonance frequencies for bars of rectangular cross section. J. Res. Natl. Bur. Stand. 60, 459464 (1958).
19. Tefft W.E. and Spinner S.: Torsional resonance vibrations of uniform bars of square cross section. J. Res. Natl. Bur. Stand., Sect. A 65A, 167171 (1961).
20. ASTM E1876–15: Standard test method for dynamic Young’s modulus, shear modulus, and Poisson’s ratio by impulse excitation of vibration (2015).
21. Atri R.R., Ravichandran K.S., and Jha S.K.: Elastic properties of in-situ processed Ti–TiB composites measured by impulse excitation of vibration. Mater. Sci. Eng., A 271, 150159 (1999).
22. Berry B.S. and Pritchet W.C.: Vibrating reed internal friction apparatus for films and foils. IBM J. Res. Dev. 19, 334343 (1975).
23. Peraud S., Pautrot S., Villechaise P., Mazot P., and Mendez J.: Determination of Young’s modulus by a resonant technique applied to two dynamically ion mixed thin films. Thin Solid Films 292, 5560 (1997).
24. Etienne S., Ayadi Z., Nivoit M., and Montagnon J.: Elastic modulus determination of a thin layer. Mater. Sci. Eng., A 370, 181185 (2004).
25. Rao S.S.: Vibration of Continuous Systems (John Wiley & Sons, Inc., Hoboken, 2006).
26. Pagnotta L. and Stigliano G.: Elastic characterization of isotropic plates of any shape via dynamic tests: Practical aspects and experimental applications. Mech. Res. Commun. 36, 54161 (2009).
27. Gere J.: Mechanics of Materials (Cengage Learning, Independence, 2003).
28. François D.: Essais mécaniques et lois de comportement (Éditions Lavoisier, Cachan, 2001).
29. Lord J.D. and Morrell R.: Measurement Good Practice Guide No. 98, Elastic Modulus Measurement (National Physical Laboratory, Middlesex, UK, 2007).
30. Abaqus Analysis User’s Manual (6.12).
31. JCGM 200:2012: International vocabulary of metrology—Basic and general concepts and associated terms (VIM) (2012).
32. JCGM 100:2008(E): Evaluation of measurement data—Guide to the expression of uncertainty in measurement (2008).
33. Bullough C.K.: The determination of uncertainties in Dynamic Young’s Modulus. Standards Measurment & Testing Project No. SMT4-CT97-2165 (2000).
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Journal of Materials Research
  • ISSN: 0884-2914
  • EISSN: 2044-5326
  • URL: /core/journals/journal-of-materials-research
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