Skip to main content
SpringerLink
Log in

Key parameters controlling stiffness variability within trees: a multiscale experimental–numerical approach

  • Original Paper
  • Published:
Trees Aims and scope Submit manuscript

Abstract

Microstructural properties of wood vary considerably within a tree. Knowledge of these properties and a better understanding of their relationship to the macroscopic mechanical performance of wood are crucial to optimize the yield and economic value of forest stocks. This holds particularly for the end-use requirements in engineering applications. In this study the microstructure–stiffness relationships of Scots pine are examined with a focus on the effects of the microstructural variability on the elastic properties of wood at different length scales. For this purpose, we have augmented microstructural data acquired using SilviScan-3™ (namely wood density, cell dimensions, earlywood and latewood proportion, microfibril angle) with local measurements of these quantities and of the chemical composition derived from wide-angle X-ray scattering, light microscopy, and thermogravimetric analysis, respectively. The stiffness properties were determined by means of ultrasonic tests at the clear wood scale and by means of nanoindentation at the cell wall scale. In addition, micro-mechanical modeling was applied to assess the causal relations between structural and mechanical properties and to complement the experimental investigations. Typical variability profiles of microstructural and mechanical properties are shown from pith to bark, across a single growth ring and from earlywood to latewood. The clear increase of the longitudinal stiffness as well as the rather constant transverse stiffness from pith to bark could be explained by the variation in microfibril angle and wood density over the entire radial distance. The dependence of local cell wall stiffness on the local microfibril angle was also demonstrated. However, the local properties did not necessarily follow the trends observed at the macroscopic scale and exhibited only a weak relationship with the macroscopic mechanical properties. While the relationship between silvicultural practice and wood microstructure remains to be modeled using statistical techniques, the influence of microstructural properties on the macroscopic mechanical behavior of wood can now be described by a physical model. The knowledge gained by these investigations and the availability of a new micromechanical model, which allows transferring these findings to non-tested material, will be valuable for wood quality assessment and optimization in timber engineering.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Alteyrac J, Cloutier A, Ung C-H, Zhang SY (2006) Mechanical properties in relation to selected wood characteristics of black spruce. Wood Fiber Sci 38(2):229–237

    CAS  Google Scholar 

  • Auty D (2011) Modelling the effects of forest management on the wood properties and branch characteristics of UK-grown Scots pine. PhD Thesis, University of Aberdeen

  • Auty D, Gardiner BA, Achim A, Moore JR, Cameron AD (2012) Models for predicting microfibril angle variation in Scots pine. Ann For Sci. doi:10.007/s13595-012-0248-6

  • Bader TK, Hofstetter K, Hellmich C, Eberhardsteiner J (2011) The poroelastic role of water in cell walls of the hierarchical composite ‘softwood’. Acta Mech 217:75–100

    Article  Google Scholar 

  • Bader TK, Hofstetter K, Eberhardsteiner J, Keunecke D (2012) Microstructure-stiffness relationships of Common yew and Norway spruce. Strain 48(4):306–316

    Google Scholar 

  • Bucur V (2006) Acoustics of wood, 2nd edn. Springer, Berlin

    Google Scholar 

  • Cave ID (1966) Theory of X-ray measurement of microfibril angles in wood. Forest Prod J 16(10):37–43

    Google Scholar 

  • Cave ID, Walker JCF (1994) Stiffness of wood in fast-grown plantation softwoods: the influence of microfibril angle. Wood Sci Technol 31:225–234

    Article  Google Scholar 

  • Eder M, Jungnikl K, Burgert I (2009) A close-up view of wood structure and properties across a growth ring of Norway spruce (Picea abies [L] Karst.). Trees Struct Funct 23:79–84

    Article  Google Scholar 

  • Eriksson D, Lindberg H, Bergsten U (2006) Influence of silvicultural regime on wood structure characteristics and mechanical properties of clear wood in Pinus sylvestris. Silva Fenn 40:743–762

    Google Scholar 

  • Evans R (1999) A variance approach to the X-ray diffractometric estimation of microfibril angle in wood. Appita J 52:283–294

    Google Scholar 

  • Evans R (2006) Wood stiffness by X-ray diffractometry. In: Stokke DD, Groom LH (eds) Characterization of the cellulosic cell wall. Blackwell Publishing, Ames, pp 138–146

    Chapter  Google Scholar 

  • Fengel D, Wegener G (2003) Wood—chemistry, ultrastructure, reactions. Kessel, Remagen

    Google Scholar 

  • Grønli MG, Varhegyi G, Di Blasi C (2001) Thermogravimetric analysis and devolatilization kinetics of wood. Ind Eng Chem Res 41(17):4201–4208

    Article  Google Scholar 

  • Hofstetter K, Hellmich C, Eberhardsteiner J (2005) Development and experimental validation of a continuum micromechanics model for the elasticity of wood. Eur J Mech A Solids 24:1030–1053

    Article  Google Scholar 

  • Hofstetter K, Hellmich C, Eberhardsteiner J (2007) Micromechanical modeling of solid-type and plate-type deformation patterns within softwood materials: a review and an improved approach. Holzforschung 61:343–351

    Article  CAS  Google Scholar 

  • Jäger A, Bader TK, Hofstetter K, Eberhardsteiner J (2011) The relation between indentation modulus, microfibril angle and elastic properties of wood cell walls. Compos Part A Appl S 42:677–685

    Article  Google Scholar 

  • Jakes JE, Frihard CR, Beecher JF, Moon RJ, Resto PJ, Melgarejo ZH, Suarez OM, Baumgart H, Elmustafa AA, Stone DS (2009) Nanoindentation near the edge. J Mater Res 24(3):1016–1031

    Article  CAS  Google Scholar 

  • Kohlhauser C, Hellmich C, Vitale-Brovarone C, Rota A, Eberhardsteiner J (2009) Ultrasonic characterization of porous biomaterials across different frequencies. Strain 45:34–44

    Article  Google Scholar 

  • Kollmann F (1982) Technologie des Holzes und der Holzwerkstoffe (Technology of wood and wood products), vol 1, 2nd edn. Springer, Berlin (in German)

    Google Scholar 

  • Konnerth J, Harper D, Lee SH, Rials TG, Gindl W (2008) Adhesive penetration of wood cell walls investigated by scanning thermal microscopy (SThM). Holzforschung 62:91–98

    CAS  Google Scholar 

  • Konnerth J, Gierlinger N, Keckes J, Gindl W (2009) Actual versus apparent within cell wall variability of nanoindentation results from wood cell walls related to cellulose microfibril angle. J Mater Sci 44:4399–4406

    Article  CAS  Google Scholar 

  • Koponen T, Karppinen T, Hæggström E, Saranpää P, Serimaa R (2005) The stiffness modulus in Norway spruce as a function of year ring. Holzforschung 59:451–455

    Article  CAS  Google Scholar 

  • MacDonald E, Hubert J (2002) A review of the effects of silviculture on timber quality of Sitka spruce. Forestry 75:107–138

    Article  Google Scholar 

  • Mäkinen H, Mäkelä A, Hynynen J (2009) Predicting wood and branch properties of Norway spruce as a part of a stand growth simulation system. USDA Forest Service, pp 15–21. General Technical Report PNW-GTR 791

  • Meylan BA (1967) Measurement of microfibril angle by X-ray diffraction. For Prod J 17(5):51–58

    Google Scholar 

  • Moore JR, Lyon AJ, Searles GJ, Vihermaa LE (2009) The effects of site and stand factors on the tree and wood quality of Sitka spruce growing in the United Kingdom. Silva Fenn 43:383–396

    Google Scholar 

  • Oliver WC, Pharr GM (1992) An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res 7:1564–1583

    Article  CAS  Google Scholar 

  • Sedighi-Gilani M, Sunderland H, Navi P (2005) Microfibril angle non-uniformities within normal and compression wood tracheids. Wood Sci Technol 29:419–430

    Article  Google Scholar 

  • Senft JF, Bendtsen BA (1985) Measuring microfibrillar angles using light microscopy. Wood Fib Sci 17(4):564–567

    Google Scholar 

  • Suquet P (1987) Elements of homogenization for inelastic solid mechanics. In: Sanchez-Palencia E, Zaoui A (eds) Homogenization techniques for composite media. Springer, Wien, pp 109–143

    Google Scholar 

  • Vihermaa LE (2010) Influence of site factors and climate on timber properties of Sitka spruce. PhD Thesis, University of Glasgow

  • Wimmer R, Lucas BN (1997) Comparing mechanical properties of secondary wall and cell corner middle lamella in spruce wood. IAWA J 18(1):77–88

    Google Scholar 

  • Zaoui A (2002) Continuum micromechanics: survey. J Eng Mech ASCE 128:808–816

    Article  Google Scholar 

  • Zhang B, Fei B, Yu Y, Zhao R (2007) Microfibril angle variability in Masson pine (Pinus massoniana Lamb.) using X-ray diffraction. For Stud China 9(1):33–38

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to acknowledge Prof. Herwig Peterlik (University of Vienna) and Dr Thomas Koch (Vienna University of Technology) for providing the equipment for the WAXS and TGA measurements, respectively. The SilviScan-3™ work was undertaken as part of the David Auty’s PhD thesis, which was jointly funded by Corporate and Forestry Services, Forestry Commission, UK, and the Scottish Forestry Trust. Additional funding was provided by the European Cooperation in Science and Technology (COST) program, under the Short Term Scientific Mission initiative under COST Actions E50 and FP0802.

Author information

Author notes

  1. David Auty

    Present address: Département des sciences du bois et de la forêt, Pavillon Gene-H.-Kruger, Université Laval, 2425, rue de la Terrasse, Quebec, QC, G1V 0A6, Canada

Authors and Affiliations

  1. Institute for Mechanics of Materials and Structures, Vienna University of Technology, Karlsplatz 13/202, 1040, Vienna, Austria

    Leopold Wagner & Thomas K. Bader

  2. University of Aberdeen, Cruickshank Building, St Machar Drive, Aberdeen, AB24 3UU, Scotland, UK

    David Auty

  3. School of Engineering, University of Glasgow, Rankine Building, Glasgow, G12 8LT, Scotland, UK

    Karin de Borst

Authors
  1. Leopold Wagner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Thomas K. Bader
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. David Auty
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Karin de Borst
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Leopold Wagner.

Additional information

Communicated by M. Adams.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wagner, L., Bader, T.K., Auty, D. et al. Key parameters controlling stiffness variability within trees: a multiscale experimental–numerical approach. Trees 27, 321–336 (2013). https://doi.org/10.1007/s00468-012-0801-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00468-012-0801-9

Keywords

Search

Navigation