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Cylindrical lateral depth-sensing indentation testing of thin anisotropic elastic films. (English) Zbl 1406.74484

Summary: A two-dimensional frictionless contact problem for a parabolic indenter pressed against an orthotropic elastic strip resting on a frictionless rigid substrate is studied. The sixth-order asymptotic solution is obtained in the case of a relatively small contact zone with respect to the elastic strip thickness. The so-called cylindrical lateral indentation test, which utilizes lateral contact of a cylindrical indenter, is developed for indentation testing of a thin transversely isotropic film with the symmetry plane orthogonal to the contact plane under the assumption that the film thickness is small compared to the cylinder indenter length. The presented testing methodology is based on a least squares best fit of the second-order asymptotic model to the depth-sensing indentation data.

MSC:

74K35 Thin films
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
74M15 Contact in solid mechanics
74E10 Anisotropy in solid mechanics
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[1] Aleksandrov, V. M., Two problems with mixed boundary conditions for an elastic orthotropic strip, J. Appl. Math. Mech., 70, 128-138, (2006)
[2] Aleksandrov, V. M., The integral equations of plane contact problems for high values of the parameter, J. Appl. Math. Mech., 75, 711-715, (2011) · Zbl 1272.74492
[3] Andrianov, I. V.; Awrejcewicz, J.; Barantsev, R. G., Asymptotic approaches in mechanics: new parameters and procedures, Appl. Mech. Rev., 56, 87-110, (2003)
[4] Argatov, I. I., Solution of the plane Hertz problem, J. Appl. Mech. Tech. Phys., 42, 1064-1072, (2001) · Zbl 1078.74627
[5] Argatov, I. I., Frictionless and adhesive nanoindentation: asymptotic modeling of size effects, Mech. Mater., 42, 807-815, (2010)
[6] Argatov, I. I., Depth-sensing indentation of a transversely isotropic elastic layer: second-order asymptotic models for canonical indenters, Int. J. Solids Struct., 48, 3444-3452, (2011)
[7] Argatov, I.; Daniels, A. U.; Mishuris, G.; Ronken, S.; Wirz, D., Accounting for the thickness effect in dynamic spherical indentation of a viscoelastic layer: application to non-destructive testing of articular cartilage, Eur. J. Mech. A Solids, 37, 304-317, (2013) · Zbl 1347.74070
[8] Argatov, I. I.; Sabina, F. J., Asymptotic analysis of the substrate effect for an arbitrary indenter, Quart. J. Mech. Appl. Math., 66, 75-95, (2013) · Zbl 1291.74141
[9] Batra, R. C.; Jiang, W., Analytical solution of the contact problem of a rigid indenter and an anisotropic linear elastic layer, Int. J. Solids Struct., 45, 5814-5830, (2008) · Zbl 1381.74162
[10] Borodich, F. M.; Keer, L. M.; Korach, ChS., Analytical study of fundamental nanoindentation test relations for indenters of non-ideal shapes, Nanotechnology, 14, 803-808, (2003)
[11] Choi, S. T.; Jeong, S. J.; Earmme, Y. Y., Modified-creep experiment of an elastomer film on a rigid substrate using nanoindentation with a flat-ended cylindrical tip, Scr. Mater., 58, 199-202, (2008)
[12] Delafargue, A.; Ulm, F.-J., Explicit approximations of the indentation modulus of elastically orthotropic solids for conical indenters, Int. J. Solids Struct., 41, 7351-7360, (2004) · Zbl 1124.74316
[13] Dimitriadis, E. K.; Horkay, F.; Maresca, J.; Kachar, B.; Chadwick, R. S., Determination of elastic moduli of thin layers of soft material using the atomic force microscope, Biophys. J., 82, 2798-2810, (2002)
[14] Ding, H. J.; Chen, W. Q.; Zhang, L., Elasticity of transversely isotropic materials, (2006), Springer Dordrecht · Zbl 1101.74001
[15] Ebenstein, D. M.; Pruitt, L. A., Nanoindentation of biological materials, Nanotoday, 1, 26-33, (2006)
[16] Erbaş, B.; Yusufoğlu, E.; Kaplunov, J., A plane contact problem for an elastic orthotropic strip, J. Eng. Math., 70, 399-409, (2011) · Zbl 1254.74088
[17] Fischer-Cripps, A. C., Nanoindentation, (2004), Springer-Verlag New York
[18] Giannakopoulos, A. E., Elastic and viscoelastic indentation of flat surfaces by pyramid indentors, J. Mech. Phys. Solids, 54, 1305-1332, (2006) · Zbl 1120.74656
[19] Greenwood, J. A.; Barber, J. R., Indentation of an elastic layer by a rigid cylinder, Int. J. Solids Struct., 49, 2962-2977, (2012)
[20] Hayes, W. C.; Keer, L. M.; Herrmann, G.; Mockros, L. F., A mathematical analysis for indentation tests of articular cartilage, J. Biomech., 5, 541-551, (1972)
[21] Huang, N. F.; Okogbaa, J.; Lee, J. C.; Jha, A.; Zaitseva, T. S.; Paukshto, M. V.; Sun, J. S.; Punjya, N.; Fuller, G. G.; Cooke, J. P., The modulation of endothelial cell morphology, function, and survival using anisotropic nanofibrillar collagen scaffolds, Biomaterials, 34, 4038-4047, (2013)
[22] Jin, H.; Lewis, J. L., Determination of Poisson’s ratio of articular cartilage by indentation using different-sized indenters, J. Biomech. Eng., 126, 138-145, (2004)
[23] Korhonen, R. K.; Saarakkala, S.; Töyräs, J.; Laasanen, M. S.; Kiviranta, I.; Jurvelin, J. S., Experimental and numerical validation for the novel configuration of an arthroscopic indentation instrument, Phys. Med. Biol., 48, 1565-1576, (2003)
[24] Lekhnitskii, S. G., Theory of elasticity of an anisotropic body, (1981), Mir Publishing Moscow · Zbl 0467.73011
[25] Liao, Q.; Huang, J.; Zhu, T.; Xiong, C.; Fang, J., A hybrid model to determine mechanical properties of soft polymers by nanoindentation, Mech. Mater., 42, 1043-1047, (2010)
[26] Nayak, L.; Johnson, K. L., Pressure between elastic bodies having a slender area of contact and arbitrary profiles, Int. J. Mech. Sci., 21, 237-247, (1979) · Zbl 0397.73091
[27] Pandolfi, A.; Vasta, M., Fiber distributed hyperelastic modeling of biological tissues, Mech. Mater., 44, 151-162, (2012)
[28] Pelletier, H.; Krier, J.; Mille, P., Characterization of mechanical properties of thin films using nanoindentation test, Mech. Mater., 38, 1182-1198, (2006)
[29] Stolz, M.; Gottardi, R.; Raiteri, R.; Miot, S.; Martin, I.; Imer, R.; Staufer, U.; Raducanu, A.; Düggelin, M.; Baschong, W.; Daniels, A. U.; Friederich, N. F.; Aszodi, A.; Aebi, U., Early detection of aging cartilage and osteoarthritis in mice and patient samples using atomic force microscopy, Nat. Nanotechnol., 4, 186-192, (2009)
[30] Sveklo, V. A., Boussinesq type problems for the anisotropic half-space, J. Appl. Math. Mech., 28, 1099-1105, (1964) · Zbl 0151.36302
[31] Vlassak, J. J.; Ciavarella, M.; Barber, J. R.; Wang, X., The indentation modulus of elastically anisotropic materials for indenters of arbitrary shape, J. Mech. Phys. Solids, 51, 1701-1721, (2003) · Zbl 1077.74589
[32] Vlassak, J. J.; Nix, W. D., Indentation modulus of elastically anisotropic half spaces, Philos. Mag. A, 67, 1045-1056, (1993)
[33] Vlassak, J. J.; Nix, W. D., Measuring the elastic properties of anisotropic materials by means of indentation experiments, J. Mech. Phys. Solids, 42, 1223-1245, (1994)
[34] Vorovich, I. I.; Aleksandrov, V. M.; Babeshko, V. A., Non-classical mixed problems of the theory of elasticity, (1974), Nauka Moscow, [in Russian]
[35] Willis, J. R., Hertzian contact of anisotropic bodies, J. Mech. Phys. Solids, 14, 163-176, (1966) · Zbl 0145.22103
[36] Willis, J. R., Boussinesq problems for an anisotropic half-space, J. Mech. Phys. Solids, 15, 331-339, (1967) · Zbl 0153.56604
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