PSI - Issue 43

Stanislav Žák et al. / Procedia Structural Integrity 43 (2023) 23 – 28 Stanislav Žák and Alice Lassnig / Structural Integrity Pr ocedia 00 (2022) 000 – 000

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such evaluation of mode I adhesion energy is still a common practice, therefore, presented results and the differences when assuming the elastic mismatch correctly are a good representation of possible ways of introducing large errors by small simplifications. It should be noted that for material systems with high α -value, a more complex calculation of Γ ( Ψ ), including the real substrate deformation, has to be used (Yu and Hutchinson, 2002). However, since the presented work aims at changes in mode-mixity due to elastic mismatch and the approach with included substrate deformation has no effect on the mode-mixity (Yu and Hutchinson, 2002), only the simplified, original calculation of Γ ( Ψ ) is presented. Conclusions In this work, extended dependence of the mode-mixity on the elastic mismatch between thin film and substrate was used to reveal the changes in evaluated G I, c in contrast to simplified cases assuming no elastic mismatch. Regardless of the type of semi-empirical Γ ( Ψ ) function, the use of correctly characterized elastic mismatch lead to revealing the error of the simplified approach in the range between 10% and 20% for the three model material systems. Such results show the indisputable importance of using the correct value of phase factor ω and mode -mixity angle Ψ when assessing the practical work of adhesion Γ I or mode I critical crack driving force G I, c . Acknowledgements This research was funded by the Austrian Science Fund (FWF), grant no. ESP 41-N. A. Lassnig acknowledges funding from the FWF under the grant number T891-N36. P. Kreiml from Erich Schmid Institute of Materials Science, Austrian Academy of Sciences and K.-H. Pichler from the Department of Materials Science, Montanuniversität Leoben are gratefully acknowledged for depositing used Mo films on PI substrate. References Aranda, M.T., García, I.G., Reinoso, J., Mantič, V., 2022. Experimental eval uation of the similarity in the interface fracture energy between PMMA/epoxy/PMMA and PMMA/epoxy joints. Eng. Fract. Mech. 259, 1 – 19. Bang, J., Coskun, S., Pyun, K.R., Doganay, D., Tunca, S., Koylan, S., Kim, D., Unalan, H.E., Ko, S.H., 2021. Advances in protective layer coating on metal nanowires with enhanced stability and their applications. Appl. Mater. Today 22, 100909. Banks-Sills, L., Ashkenazi, D., 2000. A note on fracture criteria for interface fracture, International Journal of Fracture. Beom, H.G., 1995. Generalized Dundurs Parameters and the Bimaterial Anisotropic Interfacial Crack, in: Batra, R.C. (Ed.), Contemporary Research in Engineering Science. pp. 66 – 83. Charalambides, M., Kinloch, A.J., Wang, Y., Williams, J.G., 1992. On the analysis of mixed-mode failure. Int. J. Fract. 54, 269 – 291. Cordill, M.J., Bahr, D.F., Moody, N.R., Gerberich, W.W., 2004. Recent Developments in Thin Film Adhesion Measurement. IEEE Trans. Device Mater. Reliab. 4, 163 – 168. Dundurs, J., 1967. Effect of Elastic Constants on Stress in a Composite under Plane Deformation. J. Compos. Mater. 1, 310 – 322. Euler, L., 1952. Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes sive solutio problematis isoperimetrici latissimo sensu accepti, 1st ed. Htwe, Y.Z.N., Mariatti, M., 2022. Printed Graphene and Hybrid Conductive Inks for Flexible, Stretchable, and Wearable Electronics: Progress, Opportunities, and Challenges. J. Sci. Adv. Mater. Devices 100435. Hutchinson, J.W., Suo, Z., 1992. Mixed Mode Cracking in Layered Materials. Adv. Appl. Mech. 29, 63 – 191. Lassnig, A., Terziyska, V.L., Zálešák, J., Jörg, T., Többens, D.M., Griesser, T., Mitterer, C., Pippan, R., Cordill, M.J., Al ., E., 2021. Microstructural Effects on the Interfacial Adhesion of Nanometer-Thick Cu Films on Glass Substrates: Implications for Microelectronic Devices. ACS Appl. Nano Mater. 4 (1), 61 – 70. Oldroyd, P., Malliaras, G.G., 2022. Achieving long-term stability of thin-film electrodes for neurostimulation. Acta Biomater. 139, 65 – 81. Suo, Z., Hutchinson, J.W., 1990. Interface crack between two elastic layers. Int. J. Fract. 43, 1 – 18. Volinsky, A.A., Moody, N.R., Gerberich, W.W., 2002. Interfacial toughness measurements for thin films on substrates. Acta Mater. 50, 441 – 466. Yu, H.H., Hutchinson, J.W., 2002. Influence of substrate compliance on buckling delamination of thin films. Int. J. Fract. 113, 39 – 55. Žák, S., Lassnig, A., Hrstka, M., Cordill, M.J., 2022. Buckling -induced delamination: connection between mode mixity and Dundurs parameters. Theoretical and Appl. Frac. Mech. (submitted).