In the present study, the pure viscoelastic behaviour of European beech wood is analysed in the longitudinal direction at three different moisture contents. The moisture-dependent creep compliance is identified using a four-point bending test device. The viscoelastic behaviour is ascertained to be linear with moisture content and quantified by means of a Kelvin-Voigt model approac

Hering, Stefan

Niemz, Peter

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Eur. J. Wood Prod. (2012) 70:667–670DOI 10.1007/s00107-012-0600-4O R I G I NA L S O R I G I NA L A R B E I T E NMoisture-dependent, viscoelastic creep of European beech woodin longitudinal directionStefan Hering · Peter NiemzReceived: 6 June 2011 / Published online: 3 February 2012© Springer-Verlag 2012Abstract In the present study, the pure viscoelastic be-haviour of European beech wood is analysed in the longi-tudinal direction at three different moisture contents. Themoisture-dependent creep compliance is identified using afour-point bending test device. The viscoelastic behaviour isascertained to be linear with moisture content and quantifiedby means of a Kelvin-Voigt model approach.Viskoelastisches Kriechverhalten von Rotbuchein longitudinaler Richtung bei verschiedenenHolzfeuchtenZusammenfassung In dieser Arbeit wird das viskoelasti-sche Verhalten von Rotbuchenholz in longitudinaler Rich-tung bei drei verschiedenen Holzfeuchten untersucht. MitHilfe eines Vierpunktbiegeprüfstandes wurde die feuchte-abhängige Kriechnachgiebigkeit bestimmt. Ein linearer Zu-sammenhang zwischen der Holzfeuchte und der Kriech-nachgiebigkeit wird nachgewiesen und anhand eines verall-gemeinerten Kelvin-Voigt Ansatzes quantifiziert.1 IntroductionFor a numerical simulation of the time-dependent behaviourof wood, viscoelastic material properties are required. Nu-merous scientific investigations have been carried out con-sidering the time-dependent characteristics of wood andwood composites (Ranta-Maunus 1975; Bazant 1985; Huntand Shelton 1987; Holzer et al. 1989; Toratti 1992; LiuS. Hering () · P. NiemzInstitute for Building Materials (Wood Physics), ETH Zurich,8093 Zurich, Switzerlande-mail: shering@ethz.ch1994; Hanhijärvi and Hunt 1998). While basic informationabout viscoelasticity is given in Nowacki (1965) and Lock-ett (1972) for example, bending creep tests can be foundin Zhou et al. (1999) and Bengtsson and Kliger (2003) orunder tensile and compressive load in Toratti and Svens-son (2000). Theoretical investigations concerning constitu-tive laws and models were studied in Kaliske (2000), Svens-son and Toratti (2002), Hanhijärvi and Mackenzie-Helnwein(2003) or Fortino et al. (2009).Moreover, the creep phenomenon can be divided intothree types of wood-creep behaviour: the pure, simple vis-coelastic or time-dependent creep, the mechano-sorptivecreep and the pseudo creep and recovery phenomenon.The latter manifests during continued moisture cycling, themechano-sorptive is associated with transient moisture con-tent changes and the pure viscoelastic part is a well knownphenomenon, however, for wood it requires constant cli-matic conditions although it depends on the moisture con-tent (Hunt 1999).Due to the large increase in long-term deformationscaused by the interaction of moisture content variations andmechanical loads as well as the increased amount of com-putational complexity, which is required to solve the time-dependent hereditary integral formulation, the pure vis-coelastic creep is usually neglected in numerical models.Thus, the consequence is a lack of systematic experimentaldata (Liu 1993).However, the pure viscoelastic creep component is need-ed not only for a full description of its time-dependent ma-terial behaviour in constant climatic conditions, but alsofor the determination of the mechano-sorptive component.Hence, in this study, the pure viscoelastic creep mechanismsof European beech wood were determined at three differentconstant moisture contents. The influence of the moisture668 Eur. J. Wood Prod. (2012) 70:667–670Table 1 Specimen properties of the viscoelastic creep tests at differentmoisture contentsTab. 1 Prüfkörpereigenschaften der Kriechversuche bei unterschied-lichen HolzfeuchtenNumber of specimenn [–]Moisture contentω [%]Density ρ[kg/m3]8 x¯ 8.14 780CoV [%] 1.55 2.265 x¯ 15.48 700CoV [%] 1.87 7.997 x¯ 23.20 760CoV [%] 2.82 2.64x¯ mean value, CoV coefficient of variationcontent on the pure creep strain is analysed and quantifiedby means of a linear regression.2 Material and methods2.1 Wood samplesIn the present study, the time-dependent deformation be-haviour of European beech wood samples (Fagus sylvat-ica L.) from stands near Zurich was analysed.Samples containing red heartwood, tension wood, knotsand other defects were omitted. Cuboid-shaped specimenswith dimensions 250 mm × 20 mm × 5 mm (longitudinal–radial–tangential) and orthogonal principal material direc-tions parallel to the edges were chosen with a number n ≥ 6annual rings to ensure sufficient reproducibility of mate-rial properties in the cross-sectional area. After preparation,the specimens were divided into three groups (Table 1) andclimatised at different relative humidities (35%, 80%, and95%) and at a temperature of 20 °C.2.2 Experimental setupAfter the specimens reached equilibrium moisture content,viscoelastic creep tests were performed on a four-pointbending device positioned in a climate chamber.The bending device was designed for eight specimenswith 200 mm distance between the supports. Figure 1 il-lustrates a section of the experimental design for a singlespecimen.The load was applied by means of weights, distributed30 mm from the centre of the specimen, symmetrically andsimultaneously for all eight specimens. Compared to liter-ature references (e.g., Niemz 1993), the average loading ofthe specimens was approximately 25% of the ultimate bend-ing strength.Fig. 1 Arrangement of the specimen in the four-point bending testdevice (section of a single specimen)Abb. 1 Probenanordnung im Vier-Punkt Biegeversuch (Ausschnitt ei-ner Probe)To reduce the influence of friction, the supports wereequipped with radial bearings realised by Teflon bushings.The deflections were measured at the deformation maximumby displacement transducers with an accuracy of 0.01 mm.Additionally, the climatic conditions were monitored bya combined temperature/humidity measuring sensor.2.3 Compliance analysisTo identify the viscoelastic material characteristic, the mea-sured time-dependent deformations v have to be convertedinto the stress-strain domain using the compliance func-tion J . Considering the boundary conditions of the four-point bending device, the differential equation for the elasticcurve is given byIv′′(x,ω, t)J (ω, t)= −Mb(x) (1)including the bending moment Mb and the moment of in-ertia I , which are used to calculate the total complianceJ (ω, t). It has to be noted that this simplified approach isused with the specimen slenderness taken into account, ap-parent shear stresses neglected and with only small gradientsin the displacement expected.For a characterisation of the viscoelastic material proper-ties, the total compliance function J (ω, t) was determinedat three different moisture conditions. Subtracting the initialpure elastic part of the compliance J0 and fitting the data toa generalised Kelvin-Voigt model with a term for a linearmoisture dependencyEur. J. Wood Prod. (2012) 70:667–670 669Fig. 2 Measurement data of themoisture-dependent creepcompliance of European beechwood in the longitudinaldirectionAbb. 2 Messdaten derholzfeuchteabhängigenKriechnachgiebigkeit vonRotbuchenholz in longitudinalerRichtungJve(ω, t) = J (ω, t) − J0(ω)=m∑r=1(Jr1ω + Jr0)(1 − e−t/λr ) (2)yields the viscoelastic compliance function Jve.3 Results and discussionThe measurement data with mean and standard deviationcurves and the corresponding fitted creep compliance func-tion are visualised in Figs. 2 and 3. The approximation, ex-cept for some minor deviations at the beginning, is in goodagreement with the mean values of the measurement data.Hence, results from the measurements of this study suggesta linearly increasing viscoelastic compliance function withincreasing moisture content.Table 2 provides the parameters of (2), which were deter-mined using m = 6 Kelvin-Voigt elements with the methodof least squares.However, such a compliance function is thermody-namically admissible if thermodynamic laws are satis-fied (Dubois et al. 2005). Besides positive values of thecompliance function J (ω, t) ≥ 0 as well as its derivative∂J (ω, t)/∂t ≥ 0, every Kelvin-Voigt element has to fulfilspecific thermodynamic restrictions. On the one hand, therelaxation times λr obviously have to be positive, whichis given without exception. On the other hand, the elementcompliances Jr1ω + Jr0 have to be positive as well, whichcannot be achieved for all six elements and moisture con-tents (cf. Mohager and Toratti 1992; Liu 1994). A regres-sion analysis performed on the constraint of positive ele-ment compliances, however, yields (even with an increasednumber of Kelvin-Voigt elements (m = 20)) no results com-Fig. 3 Measurement data vs. fitted creep compliance function depend-ing on time and moisture content for European beech wood in the lon-gitudinal directionAbb. 3 Vergleich der Messdaten mit dem Regressionsmodell der zeit-und feuchteabhängigen Kriechnachgiebigkeitsfunktion für Rotbuchen-holz in longitudinaler Richtungparable to the latter. Hence, the proposed approach is used,even though it is more descriptive than a mechanical ap-proach. Nevertheless, the results allow for a representationof the measured material behaviour and comparison againstother species and other creep components.Here, it has to be noted that a different number of spec-imens are assigned to inner defects of the specimen, dueto the fact that arising outliers show no significant dif-ferences in density, ultrasound velocity, number of annualrings, orientation of the principle axes and moisture con-tent.The obtained material parameters are determined formoisture contents in between ω ∼= 8, . . . ,23% and up to atime t ∼= 200 h. For this reason, terms and conditions of us-age and even extrapolation should be handled with care.670 Eur. J. Wood Prod. (2012) 70:667–670Table 2 Regression coefficients of the moisture- and time-dependentcreep compliance J (ω, t) of European beech wood in the longitudinaldirectionTab. 2 Regressionskoeffizienten der feuchte- und zeitabhängigenKriechnachgiebigkeit J (ω, t) in longitudinaler Richtung für Rotbu-chenholzr [–] Jr1 [MPa−1] Jr0 [MPa−1] λr [h]1 −7.69e-7 3.74e-6 1.112 1.11e-6 −4.99e-6 0.823 9.84e-7 −5.22e-6 60.864 8.51e-7 −5.97e-6 8.905 2.82e-6 1.03e-5 3427.656 5.06e-7 −2.90e-5 7039.804 ConclusionThe presented material data not only indicates viscoelas-tic creep behaviour linear to the moisture content, but alsoprovides a moisture-dependent set of input data for sub-sequent time-dependent numerical analyses of Europeanbeech wood structures. Moreover, essential material param-eters for further quantification of the mechano-sorptive ma-terial behaviour were obtained and a promising equation fordescriptive material characterisation was introduced.Acknowledgements This work was funded by the State Secretariatfor Education and Research of Switzerland (SER) and supported by theEuropean Cooperation in the field of Scientific and Technical Research(COST, Action E53).ReferencesBazant ZP (1985) Constitutive equation of wood at variable humidityand temperature. Wood Sci Technol 19:159–177Bengtsson C, Kliger R (2003) Bending creep of high-temperature driedspruce timber. Holzforschung 57:95–100Dubois F, Randriambololona H, Petit C (2005) Creep in wood undervariable climate conditions: Numerical modeling and experimen-tal validation. Mech Time-Depend Mater 9:173–202Fortino S, Mirianon F, Toratti T (2009) A 3D moisture-stress FEManalysis for time dependent problems in timber structures. MechTime-Depend Mater 13:333–356Hanhijärvi A, Hunt D (1998) Experimental indication of interac-tion between viscoelastic and mechano-sorptive creep. Wood SciTechnol 32:57–70Hanhijärvi A, Mackenzie-Helnwein P (2003) Computational analysisof quality reduction during drying of lumber due to irrecoverabledeformation. I: Orthotropic viscoelastic-mechanosorptive-plasticmaterial model for the transverse plane of wood. J Eng Mech129:9 :996-1004Holzer SM, Loferski JR, Dillard DA (1989) A review of creep in wood:concepts relevant to develop long-term behavior predictions forwood structures. Wood Fiber Sci 21(4):376–392Hunt DG (1999) A unified approach to creep of wood. Proc R SocLond A:4077–4095Hunt DG, Shelton CF (1987) Progress in the analysis of creep in woodduring concurrent moisture changes. J Mater Sci 22:313–320Kaliske M (2000) A formulation of elasticity and viscoelasticity forfibre reinforced material at small and finite strains. Comput Meth-ods Appl Mech Eng 185(2–4):225–243Liu T (1993) Creep of wood under a large span of loads in con-stant and varying environments—Part 1: Experimental observa-tions and analysis. Holz Roh- Werkst 51:400–405Liu T (1994) Creep of wood under a large span of loads in constant andvarying environments—Part 2: Theoretical investigations. HolzRoh- Werkst 52:63–70Lockett FJ (1972) Nonlinear viscoelastic solids. Academic Press, NewYorkMohager S, Toratti T (1992) Long term bending creep of wood incyclic relative humidity. Wood Sci Technol 27(1):49–59Niemz P (1993) Physik des Holzes und der Holzwerkstoffe. DRW-Verlag Weinbrenner GmbH & Co, Leinfelden-EchterdingenNowacki W (1965) Theorie des Kriechens. Franz Deuticke, WienRanta-Maunus A (1975) The viscoelasticity of wood at varying mois-ture content. Wood Sci Technol 9:189–205Svensson S, Toratti T (2002) Mechanical response of wood perpendic-ular to grain when subjected to changes of humidity. Wood SciTechnol 36:145–156Toratti T (1992) Creep of timber beams in a variable environment.Helsinki University of TechnologyToratti T, Svensson S (2000) Mechano-sorptive experiments perpen-dicular to grain under tensile and compressive loads. Wood SciTechnol 34(4):317–326Zhou Y, Fushitani M, Kubo T, Ozawa M (1999) Bending creep be-haviour of wood under cyclic moisture changes. J Wood Sci45:113–119

Moisture-dependent, viscoelastic creep of European beech wood in longitudinal direction

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Moisture-dependent, viscoelastic creep of European beech wood in longitudinal direction

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