A method for determining the local mechanical properties using nanoindentation in oscillating mode

Authors

  • Роман Игоревич Изюмов (Roman I. Izyumov) Institute of continuous media mechanics UB RAS
  • Антон Юрьевич Беляев (Anton Yu. Belyaev) Institute of continuous media mechanics UB RAS
  • Александр Львович Свистков (Aleksander L. Svistkov) Perm State University

DOI:

https://doi.org/10.17072/1994-3598-2020-3-39-47

Keywords:

nanoindentation, atomic force microscopy, dynamic model of interaction, force modulation

Abstract

A new method of processing of data obtained using atomic force microscopy (AFM) in the oscil-lating nanoindentation mode is proposed. The model of the AFM probe on elastic beam (canti-lever) interaction with a sample is developed. In addition to the static load, applied on a base of the cantilever, a force modulation, according to a harmonic law, is set. This approach makes possible to take into account not only the force of the probe-material interaction but also the phase shift of the cantilever oscillations with respect to a given harmonic signal on the cantilever base as well as the amplitudes ratio of these oscillations. This information allows the presence of the viscosity in the material evaluating. The advantage of the oscillatory regime over quasistatic indentation was shown. It consists in the possibility to exclude the influence of irreversible pro-cesses (plastic, brittle fracture in the material) on the result of the experiment and to reveal the presence of the time dependent behavior. It is shown that the model contains a small amount of constants; methods for their determination are proposed. The calculations, performed using the developed model, made it possible to make a number of recommendations on choosing the can-tilever stiffness to obtain the most informative experimental results. This approach seems per-spective in studying materials with a high degree of stiffness inhomogeneity, including the deter-mination of the local properties of filled nanocomposites near filler particles.

Author Biographies

Роман Игоревич Изюмов (Roman I. Izyumov), Institute of continuous media mechanics UB RAS

м.н.с. лаборатории микромеханики структурно-неоднородных сред

Антон Юрьевич Беляев (Anton Yu. Belyaev), Institute of continuous media mechanics UB RAS

м.н.с. лаборатории микромеханики структурно-неоднородных сред

Александр Львович Свистков (Aleksander L. Svistkov), Perm State University

доктор физико-математических наук; профессор

References

Garcia R., Perez R. Dynamic atomic force microscopy methods. Surface Science Reports, 2002, vol. 47, pp. 197–301.

Anselmetti D. et al. Imaging of biological materials with dynamic force microscopy. Nanotechnology, 1994, vol. 5, pp. 87–94.

Sader J.E., Pacifico J., Green C.P., Mulvaney P. General scaling law for stiffness measurement of small bodies with applications to the atomic force microscope. Journal of Applied Physics, 2005, vol. 97. 124903.

Haviland D. B. Quantitative force microscopy from a dynamic point of view. Current Opinion in Colloid and Interface Science, 2017, vol. 27, pp. 74–81.

Maivald P., et al. Using force modulation to image surface elasticities with the atomic force microscope. Nanotechnology, 1991, vol. 2, pp. 103–106.

Killgore J.P., et al. Viscoelastic Property Mapping with Contact Resonance Force Microscopy. Langmuir, 2011, vol. 27, pp. 13983–13987.

Stana G. and Price W. Quantitative measurements of indentation moduli by atomic force acoustic microscopy using a dual reference method. Review of Scientific Instruments, 2006, vol. 77. 103707.

Hertz H. On the contact of rigid elastic solids and on hardness, in Miscellaneous Papers. London: MacMillan, 1882/1896.

Caron A., Arnold W. Observation of local internal friction and plasticity onset in nanocrystalline nickel by atomic force acoustic microscopy. Acta Materialia, 2009, vol. 57, pp. 4353–4363.

Yuya P. A., Hurley D. C., Turner J. A. Contact-resonance atomic force microscopy for viscoelasticity. Journal of Applied Physics, 2008, vol. 104. 074916.

Stan G., Cook R. F. Mapping the elastic properties of granular Au films by contact resonance atomic force microscopy. Nanotechnology, 2008, vol. 19. 235701.

Radmacher M., Tillmann R. W., Gaub H. E. Imaging viscoelasticity by force modulation with the atomic force microscope. Biophysical Journal, 1993, vol. 64, pp. 735–742.

Muraoka M., Arnold W. A method of evaluating local elasticity and adhesion energy from the non-linear response of AFM cantilever vibrations. JSME International Journal Series A, 2001, vol. 44 (3), pp. 396–405.

Hurley D. C., et al. Mapping substrate/film adhesion with contact-resonance-frequency atomic force microscopy. Applied Physics Letters, 2006, vol. 89, 021911.

Morozov I. A., Svistkov A. L., Heinrich G., Lauke B. Structure of the carbon-black-particles framework in filled elastomer materials. Polymer Science Series A, 2007, vol. 49 (3), pp. 292–299.

Lauke B. Effect of particle size on fracture toughness of polymer composites. Composites Science and Technology, 2008, vol. 68 (15–16), pp. 3365–3372.

Yao H., et al. Effect of silane coupling agent on the fatigue crack propagation of silica-filled natural rubber. Journal of Applied Polymer Science, 2015, vol. 132 (20). 41980.

Johnson K. L., Kendall K., Roberts A. D. Surface energy and the contact of elastic solids. Proc. R. Soc. A, 1971, vol. 324 (1558), pp. 301–313.

Derjaguin B. V., Muller V. M., Toporov Y. P. Effect of contact deformations on the adhesion of particles. Journal of Colloid and Interface Science, 1975, vol. 53 (2), pp. 314–326.

Maugis D. Adhesion of spheres. The JKR-DMT transition using a Dugdale model. Journal of Colloid and Interface Science, 1992, vol. 150 (1), pp. 243–269.

Izyumov R. I., Belyaev A. Yu., Garishin O. K. Investigation of the interaction of nanoindenter with elastomer using a dynamic model of probe movement. Bulletin of Perm University. Physics, 2019, vol. 2. pp. 46–54.

Tipsnano. AFM Probes and Accessories: [Electronic resource]. URL: ttps://www.ntmdt-tips.com/products/view/nsg30 (access date: 10.03.2020).

Sader J.E., Larson I., Mulvaney P., White L.R. Method for the calibration of atomic force microscope cantilevers. Review of Scientific Instruments, 1995, vol. 66 (7), pp. 3789–3798.

Cook S. M., Schäffer T. E., Chynoweth K. M., et al. Practical implementation of dynamic methods for measuring atomic force microscope cantilever spring constants. Nanotechnology, 2006, vol. 17, pp. 2135.

Published

2020-09-23

How to Cite

Изюмов (Roman I. Izyumov) Р. И., Беляев (Anton Yu. Belyaev) А. Ю., & Свистков (Aleksander L. Svistkov) А. Л. (2020). A method for determining the local mechanical properties using nanoindentation in oscillating mode. Bulletin of Perm University. Physics, (3). https://doi.org/10.17072/1994-3598-2020-3-39-47

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