Comparing Nano and Macroindentation in Search of Microfibril Angle in Spruce

Comparing Nano and Macroindentation in Search of Microfibril Angle in Spruce

L. Kucíková J. Vorel V. Hrbek J. Němeček M. Šejnoha

Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mechanics

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The present paper describes experimental measurements of wood stiffness and analytical homogenization to provide estimates of the Micro-fibril angle (MFA). It is known that the orientation of fiber-like aggregates of crystalline cellulose in S2 layer of the wood cell with respect to the alignment of lumens considerably influences the overall stiffness of wood. Recently an inverse approach exploiting the results of nanoindentation at the level of wood cell and analytical homogenization has been proposed as a suitable tool for the MFA determination. A simpler methodology based on the results of indentation at the structural level using the Pilodyn 6J testing device has also been advocated as an alternative appealing particularly to engineering practice. Comparison of the two approaches suggesting their advantages as well as drawbacks is the principal objective of this contribution. As an example, an application to spruce as the most common type of wood used in building structures is considered.


homogenization, micro-fibril angle, nanoindentation, pilodyn 6J


[1] Kettunen, P.O., Wood Structure and Properties, Trans Tech Publications Ltd: Enfield, N.H, 2006.

[2] Fujita, M. & Harada, H., Ultrastructure and Formation of Wood Cell Wall, Marcel Dekker: New York, second revised edition, 2001.

[3] Donaldson, L., Microfibril angle: measurement, variation and relation - a review. IAWA Journal, 29(4), pp. 345–386, 2008.

[4] Hofstetter, K., Hellmich, C. & Eberhardsteiner, J., Development and experimental validation of a continuum micromechanics model for the elasticity of wood. European Journal of Mechanics - A/Solids, 24(6), pp. 1030–1053, 2005.

[5] Sejnoha, M. & Zeman, J., Micromechanics in Practice, WIT Press, Southampton, Boston, 2013.

[6] Vlassak, J., Ciavarella, M., Barber, J. & Wang, X., The indentation modulus of elastically anisotropic materials for indenters of arbitrary shape. Journal of the Mechanics and Physics of Solids, 51(9), pp. 1701–1721, 2003.

[7] Gindl, W. & Schoberl, T., The significance of the elastic modulus of wood cell walls obtained from nanoindentation measurements. Composites Part A: Applied Science and Manufacturing, 35(11), pp. 1345–1349, 2004.

[8] Tze, W.T.Y., Wang, S., Rials, T.G., Pharr, G.M. & Kelley, S.S., Nanoindentation of wood cell walls: continuous stiffness and hardness measurements. Composites: Part A, 38, pp. 945–953, 2007.

[9] Jager, A., Bader, T., Hofstetter, K. & Eberhardsteiner, J., The relation between indentation modulus, microfibril angle, and elastic properties of wood cell walls. Composites Part A: Applied Science and Manufacturing, 42(6), pp. 677–685, 2011.

[10] Melzerová, L. & Šejnoha, M., Interpretation of results of penetration tests performed on timber structures in bending. Applied Mechanics and Materials, 486, pp. 347–352, 2014.

[11] Gamstedt, E.K., Bader, T.K. & de Borst, K., Mixed numerical-experimental methods in wood micromechanics. Wood Science and Technology, 47, pp. 183–202, 2013.

[12] Melzerová, L., Kucíková, L., Janda, T. & Šejnoha, M., Estimation of orthotropic mechanical properties of wood based on non-destructive testing. Wood Research, 2016. Under review.

[13] Konnerth, J., Gierlinger, N., Keckes, J. & Gindl, W., Actual versus apparent within cell wall variability of nanoindentation results from wood cell walls related to cellulose microfibril angle. Journal of Material Science, 44, pp. 4399–4406, 2009.

[14] Šejnoha, M., Janda, T., Melzerováa, L. & Nežerka, V., Stochastic model of laminated timber beam. Engineering Structures, 2016. Submitted.

[15] Oliver, W. & Pharr, G., An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. Journal of Materials Research, 7(06), pp. 1564–1583, 1992.

[16] Benveniste, Y., A new approach to the application of Mori-Tanaka theory in composite materials. Mechanics of Materials, 6, pp. 147–157, 1987.

[17] Vorel, J. & Šejnoha, M., Evaluation of homogenized thermal conductivities of imperfect carbon-carbon textile composites using the Mori-Tanaka method. Structural Engineering and Mechanics, 33(4), pp. 429–446, 2009.

[18] Milton, G.W., The Theory of Composites, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, 2002.