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COST Action FP0802 Experimental and Computational Characterization Techniques
in Wood Mechanics
Thematic workshop
Mixed numerical and experimental methods applied to the mechanical characterization of bio‐based materials
April 27‐28, 2011 Vila Real, Portugal
Book of Abstracts
Organisers and venue: José Morais, José Xavier, João Pereira, Lígia Pinto
Centre for Research and Technology of Agro‐ Environmental and Biological Sciences ‐ CITAB University of Trás‐os‐Montes e Alto Douro – UTAD Quinta de Prados, Apartado 1013 5001‐801 Vila Real, Portugal Tel.: +351 259 350 475 Fax: +351 259 350 629 Email: [email protected] web: http://www.citab.utad.pt/
Advisory Committee: Karin Hofstetter Action Chair, Vienna University of Technology, Austria
Lennart Salmén Action Vice‐Chair, STFI‐Packforsk, Sweden
Lisbeth Thygesen WG1 Leader, University of Copenhagen, Denmark
Michaela Eder WG2 Leader, MPI of Colloids and Interfaces, Germany
Kristofer Gamstedt WG3 Leader, KTH ‐ Royal Institute of Technology, Sweden
COST Action FP0802
The main objective of the COST Action FP0802 “Experimental
and Computational Characterization Techniques in Wood
Mechanics” is to increase the understanding of the wood
microstructure and micromechanics by exploring and
evaluating emerging techniques in the fields of physics,
chemistry, materials and computer science in order to
provide a strong basis for the development of innovative
wood‐based products in the future and for enhancing the use
of the natural resource wood.
Workshop Objectives
The objective of the workshop is to present and discuss the benefits and problems of combined numerical/ experimental methods for the study of wood and possibly also more general to bio‐based materials (e.g. micro‐spectroscopy, mechanical tests in ESEM, full‐field measurements of deformation, Finite Element simulation and optimization methods). The workshop will provide a forum to communicate current ideas and strategies in this field.
iii
Table of contents Program at a glance vii
Keynotes
Full‐field measurements and identification for biological soft tissuesStéphane Avril
p. 1
Characterising and modeling structural disorder in microfibrils of sitka spruce wood Michael Jarvis
p. 3
Oral Presentations
Analysis of latewood/earlywood coupling effects on swelling/shrinkage by synchrotron radiation phase contrast X‐ray tomographic microscopy and 3d image analysis
Alessandra Patera, M.Griffa, D.Derome, J.Carmeliet p. 5
Multiscale computational homogenization for the hygro‐mechanical analysis of growth rings in softwoods
Ahmad Rafsanjani, D. Derome, H. Herrmann, J. Carmeliet p. 7 On the variability of transverse elastic properties of p. pinaster at the cellular level
João Pereira, José Xavier, Pedro Couto, José Morais, José Lousada, Pedro Melo‐Pinto p. 9 High spatial resolution measurement of wood density using hyperspectral imaging and neural networks
Armando Fernandes, José Lousada, José Morais, José Xavier, João Pereira, Pedro Melo‐Pinto p. 11
Novel characterization of methacrylate impregnated woodOliver Hudson, Michelle Oyen p. 13
Water vapour sorption ‐ the parallel exponential kinetics model and cell wall viscoelasticity
Callum Hill p. 15 Finite element modelling of interfacial stresses of asymmetrical laminated wood products subjected to moisture changes
Ling Li, Meng Gong, Y.H. Chui, Dagang Li p. 17 Combined experimental and numerical investigation of water transport in wood below the fiber saturation point
Johannes Eitelberger, S. Dvinskikh, K. Hofstetter p. 19 Effectiveness of parameter identification for modeling the transient bound water diffusion in wood
Wieslaw Olek, J. Weres, P. Perré p. 21 Analysis of external and internal mass transfer resistance at steady state diffusion experiments on small clear wood specimens
Aleš Straže, Ž. Gorišek p. 23 Particle modeling of dynamic fracture in fiber‐based materials
Johan Persson, P. Isaksson p. 25 Some design principles of biomimetic actuators
Sébastien Turcaud, L. Guiducci, P. Fratzl, Y.J.M. Bréchet, J.W.C. Dunlop p. 27 Effects of fibre agglomeration on strength of wood‐fibre composites
Thomas Joffre, Kristofer Gamstedt, Arttu Miettinen, Erik Wernersson p. 29 Strain analysis in dried green wood: experimentation and modeling approaches
Rostand Moutou Pitti, F. Dubois, N. Sauvat p. 31
v
Poster Presentations
Analyzing size, form and distribution of particles for WPCAndreas Krause, Marcus Müller, Kim‐Christian Krause
p. 33
Optical measurement of local strains development in finger‐jointed wood subjected to static and sustained loads
Boris Clouet, Lech Muszynski, Régis Pommierp. 35
Structural characterization of different hardwoods using infrared spectroscopyCarmen‐Mihaela Popescu, Maria‐Cristina Popescu
p. 37
Estimation of stiffness of microfibrillated cellulose based on nanostructure characterized by transmission electron microscopy
Gabriella Josefsson, E.K. Gamstedt, B.S. Tanemp. 39
The dependency of shear zone length on the shear strength profiles in paperboard Hui Huang, Mikael Nygårds
p. 41
The response of growth ring in wood to microclimate changeLeszek Krzemien, Michal Lukomski
p. 43
Swelling gel‐filled honeycombs, a model for the anisotropic actuation in the iceplant seed capsule
Lorenzo Guiducci, Khashayar Razghandi, Lucas Bertinetti, Matthew Harrington, Ingo Burgert, Peter Fratzl, John Dunlop
p. 45
Thermal behaviors of some hardwood and softwood species evaluated by thermogravimetry
Maria‐Cristina Popescu, Carmen‐Mihaela Popescup. 47
Fibre‐fibre bond strength – experimental and numerical evaluation of normal and shear loading components
Mikael Magnusson, S. Ostlund p. 49
Determination of the thuja burr material symmetries by direct contact ultrasonic method on spherical specimens
Mohammed El Mouridi, Thierry Laurent, Tancrède Almeras, Olivier Arnould, Abdelillah Hakam, Joseph Gril
p. 51
Calculating mechanical properties of wood using computer modeling via indentation Vasiliki Gountsidou, H.M. Polatoglou
p. 53
List of participants p. 55
vi
Wednesday, 27 April 08:30‐09:00 Registration
09:00‐09:15 Workshop opening
09:15‐12:30 Section I – Chair: Karin Hofstetter
09:15‐10:00
Keynote: FULL‐FIELD MEASUREMENTS AND IDENTIFICATION FOR BIOLOGICAL SOFT TISSUES: Stéphane Avril, Ecole Nationale Supérieure des Mines, France
10:00‐10:25 ANALYSIS OF LATEWOOD/EARLYWOOD COUPLING EFFECTS ON SWELLING/SHRINKAGE BY SYNCHROTRON RADIATION PHASE CONTRAST X‐RAY TOMOGRAPHIC MICROSCOPY AND 3D IMAGE ANALYSIS: Alessandra Patera, M.Griffa, D.Derome, J.Carmeliet, Laboratory of Building Science and Technology, EMPA, Switzerland
10:25‐10:50 MULTISCALE COMPUTATIONAL HOMOGENIZATION FOR THE HYGRO‐MECHANICAL ANALYSIS OF GROWTH RINGS IN SOFTWOODS: Ahmad Rafsanjani, D. Derome, H. Herrmann, J. Carmeliet, Wood Laboratory, EMPA, Switzerland
10:50‐11:15 Coffee break
11:15‐11:40 ON THE VARIABILITY OF TRANSVERSE ELASTIC PROPERTIES OF P. PINASTER AT THE CELLULAR LEVEL: João Pereira, José Xavier, Pedro Couto, José Morais, José Lousada, Pedro Melo‐Pinto, CITAB/UTAD, Portugal
11:40‐12:05 HIGH SPATIAL RESOLUTION MEASUREMENT OF WOOD DENSITY USING HYPERSPECTRAL IMAGING AND NEURAL NETWORKS: Armando Fernandes, José Lousada, José Morais, José Xavier, João Pereira, Pedro Melo‐Pinto, CITAB/UTAD, Portugal
12:05‐12:30 NOVEL CHARACTERIZATION OF METHACRYLATE IMPREGNATED WOOD: Oliver Hudson, Michelle Oyen, Cambridge University, Engineering Department, United Kingdom
12:30‐14:00 Lunch (restaurant “Panorânico” at the UTAD campus)
14:00‐15:00 Poster Section, Chair: José Xavier
ANALYZING SIZE, FORM AND DISTRIBUTION OF PARTICLES FOR WPC: Andreas Krause, Marcus Müller, Kim‐Christian Krause, Department Wood Biology and Wood Products, Georg‐August‐University, Germany
OPTICAL MEASUREMENT OF LOCAL STRAINS DEVELOPMENT IN FINGER‐JOINTED WOOD SUBJECTED TO STATIC AND SUSTAINED LOADS: Boris Clouet, Lech Muszynski, Régis Pommier, I2M/GCE, Université Bordeaux 1, France
STRUCTURAL CHARACTERIZATION OF DIFFERENT HARDWOODS USING INFRARED SPECTROSCOPY: Carmen‐Mihaela Popescu, Maria‐Cristina Popescu, Romanian Academy, Petru Poni Institute of Macromolecular Chemistry, Romania
vii
ESTIMATION OF STIFFNESS OF MICROFIBRILLATED CELLULOSE BASED ON NANOSTRUCTURE CHARACTERIZED BY TRANSMISSION ELECTRON MICROSCOPY: Gabriella Josefsson, E.K. Gamstedt, B.S. Tanem, Uppsala University, Angstrom Laboratory, Division of applied mechanics, Norway
THE DEPENDENCY OF SHEAR ZONE LENGTH ON THE SHEAR STRENGTH PROFILES IN PAPERBOARD: Hui Huang, Mikael Nygårds, BiMaC Innovation, KTH Solid Mechanics, Sweden
THE RESPONSE OF GROWTH RING IN WOOD TO MICROCLIMATE CHANGE: Leszek Krzemien, Michal Lukomski, Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, Poland
SWELLING GEL‐FILLED HONEYCOMBS, A MODEL FOR THE ANISOTROPIC ACTUATION IN THE ICEPLANT SEED CAPSULE: Lorenzo Guiducci, Khashayar Razghandi, Lucas Bertinetti, Matthew Harrington, Ingo Burgert, Peter Fratzl, John Dunlop, Max Planck Institute of Colloids and Interfaces, Department of Biomaterials, Germany
THERMAL BEHAVIORS OF SOME HARDWOOD AND SOFTWOOD SPECIES EVALUATED BY THERMOGRAVIMETRY: Maria‐Cristina Popescu, Carmen‐Mihaela Popescu, Romanian Academy, Petru Poni Institute of Macromolecular Chemistry, Romania
FIBRE‐FIBRE BOND STRENGTH – EXPERIMENTAL AND NUMERICAL EVALUATION OF NORMAL AND SHEAR LOADING COMPONENTS: Mikael Magnusson, S. Ostlund, BiMaC Innovation, Department of Solid Mechanics, KTH, Royal Institute of Technology, Sweden
DETERMINATION OF THE THUJA BURR MATERIAL SYMMETRIES BY DIRECT CONTACT ULTRASONIC METHOD ON SPHERICAL SPECIMENS: Mohammed El Mouridi, Thierry Laurent, Tancrède Almeras, Olivier Arnould, Abdelillah Hakam, Joseph Gril, Laboratoire de Mécanique et de Génie Civil, Université de Montpellier 2, France
CALCULATING MECHANICAL PROPERTIES OF WOOD USING COMPUTER MODELING VIA INDENTATION: Vasiliki Gountsidou, H.M. Polatoglou, Aristotle University of Thessaloniki, Greece
15:00‐18:00 Section II – Chair: Michael Jarvis
15:00‐15:25 WATER VAPOUR SORPTION – THE PARALLEL EXPONENTIAL KINETICS MODEL AND CELL WALL VISCOELASTICITY: Callum Hill, Forest Products Research Institute, Edinburgh Napier University, Edinburgh, UK
15:25‐15:50 FINITE ELEMENT MODELLING OF INTERFACIAL STRESSES OF ASYMMETRICAL LAMINATED WOOD PRODUCTS SUBJECTED TO MOISTURE CHANGES: Ling Li, Meng Gong, Y.H. Chui, Dagang Li, Faculty of Forestry and Environmental Management, University of New Brunswick, Canada
15:50‐16:15 Coffee break
16:15‐16:40 COMBINED EXPERIMENTAL AND NUMERICAL INVESTIGATION OF WATER TRANSPORT IN WOOD BELOW THE FIBER SATURATION POINT: Johannes Eitelberger, S. Dvinskikh, K. Hofstetter, Institute for Mechanics of Materials and Structures, Vienna University of Technology, Austria
16:40‐17:05 EFFECTIVENESS OF PARAMETER IDENTIFICATION FOR MODELING THE TRANSIENT BOUND WATER DIFFUSION IN WOOD: Wieslaw Olek, J. Weres, P.
viii
Perré, Faculty of Wood Technology, Poznań University of Life Sciences, Poland
17:05‐17:30 ANALYSIS OF EXTERNAL AND INTERNAL MASS TRANSFER RESISTANCE AT STEADY STATE DIFFUSION EXPERIMENTS ON SMALL CLEAR WOOD SPECIMENS: Aleš Straže, Ž. Gorišek, University of Ljubljana, Biotechnical Faculty, Slovenia
18:00‐19:00 Visit to Mateus Palace
20:00‐23:00 Dinner at the restaurant “Hotel Régua Douro”
Thursday, 28 April
09:30‐12:30 Section III – Chair: Michaela Eder
09:30‐10:15 Keynote 2 – CHARACTERISING AND MODELING STRUCTURAL DISORDER IN MICROFIBRILS OF SITKA SPRUCE WOOD: Michael Jarvis, Chemistry Department, Glasgow University, Scotland, UK
10:15‐10:40 PARTICLE MODELING OF DYNAMIC FRACTURE IN FIBER‐BASED MATERIALS:
Johan Persson, P. Isaksson, Division of Applied Mechanics, Mid Sweden
University, Sweden
10:40‐11:05 SOME DESIGN PRINCIPLES OF BIOMIMETIC ACTUATORS: Sébastien Turcaud,
L. Guiducci, P. Fratzl, Y.J.M. Bréchet, J.W.C. Dunlop, Max Planck Institute of
Colloids and Interfaces, Department of Biomaterials, Germany
11:05‐11:30 Coffee break
11:30‐11:55 EFFECTS OF FIBRE AGGLOMERATION ON STRENGTH OF WOOD‐FIBRE COMPOSITES: Thomas Joffre, Kristofer Gamstedt, Arttu Miettinen, Erik Wernersson, Uppsala University, Division of applied mechanics, Sweden
11:55‐12:20 STRAIN ANALYSIS IN DRIED GREEN WOOD: EXPERIMENTATION AND MODELING APPROACHES: Rostand Moutou Pitti, F. Dubois, N. Sauvat, Laboratoire GEMH, Centre Universitaire Génie Civil, France
12:20‐12:30 Workshop closing
12:30‐14:00 Lunch (restaurant “Panorânico” at the UTAD campus)
ix
Full-Field Measurements and Identification for Biological Soft Tissues
Stéphane Avil
Ecole Nationale Supérieure des Mines, 158 cours Fauriel, 42023 SAINT-ETIENNE cedex 2, France
Key words: full-field optical methods, Biological soft tissues, material parameter characterisation
ABSTRACT
Biological soft tissues appear to develop, grow, remodel, and adapt so as to maintain particular mechanical metrics (e.g., stress) near target values. To accomplish this, tissues often develop regionally varying stiffness and anisotropy. The goal of this work is to develop and implement hybrid experimental - computational method to quantify regional variations in properties in situ.
To this end, we combine video based measurements of the finite displacements experienced by sets of speckle patterns that are placed on the surface of the sample with a custom inverse method to infer, using nonlinear regression, the best-fit material parameters within a postulated form of the stored energy function. Diverse applications will be noted, but the method will be illustrated primarily for results from arteries and skin. Extension of the approach to medical-imaging based data will also be discussed.
1
2
Characterising and Modeling Structural Disorder in Microfibrils of Sitka Spruce Wood
Lynne H. Thomas† and Michael C. Jarvis‡*
†Chemistry Department, Bath University, Bath BA2 7AY, England, UK
‡Chemistry Department, Glasgow University, Glasgow G12 8QQ, Scotland, UK [email protected]
Key words: micromechanics, wood, experimental characterization, material behaviour
ABSTRACT
Multiscale modeling of mechanical deformation in wood, if it is to start from processes at the molecular scale and immediately above, must take account of structure at these scales and of the way in which the structural elements are interconnected. There is limited experimental evidence about the interconnection of cellulose microfibrils in wood cell walls [1,2]. This has led to uncertainty concerning the mechanism of slippage between cellulose microfibrils during tensile deformation in wood with high microfibril angle (MFA), such as compression wood and juvenile wood in conifers [3-5]. In wood with low MFA, the high aspect ratio of the microfibrils might suggest that slippage between them should not occur. Nevertheless, irreversible tensile deformation of low-MFA wood at high moisture content [6] suggests that some such mechanism exists [7], or that the microfibrils themselves can extend in an unknown way. These uncertainties make modeling difficult when it extends to the nanoscale.
Mature Sitka spruce wood with very low MFA (<5°) was subjected to tensile deformation under controlled humidity. On halting the extension at strains of 0.5-1% stress relaxation occurred with a time constant of the order of 10s, and the extension became partially irreversible.
Wide-angle X-ray scattering (WAXS) experiments on 37 mm gauge length x 2 mm x 0.3 mm strips of the same material were carried out on a Rigaku image-plate diffractometer under controlled tensile strains of up to 1.5%, although many samples fractured at lower strain. The distribution of cellulose orientations was determined from the tangential profile of the equatorial 200 reflection. There was a small amount of reorientation of the microfibrils towards the direction of the strain, but only enough to explain about one-tenth of the macroscopic strain on a cosine basis: the remaining strain must therefore result from either linear stretching of the microfibrils or slippage between them.
The unit cell of cellulose (when indexed as cellulose I) was measurably extended in length under tension. The crystallographic strain shown by the crystalline fraction of the cellulose was linearly correlated to the macroscopic strain up to the point of fracture but was always less than the macroscopic strain. The discrepancy was too large to be accounted for by reorientation of the microfibrils. There being no sign of shear between cells (i.e. slippage at the micro-scale), it seems most likely that nanoscale slippage between microfibrils or between microfibril aggregates was responsible. The more diffuse scattering component associated with oriented but less ordered components of the microfibrils behaved in a way that was qualitatively similar to crystalline cellulose.
The apparent presence of this form of nanoscale tensile deformation in wood with very low MFA is difficult to reconcile with extreme length of the microfibrils, generally assumed to be of the order of 1
3
m or more. Whether it might take the form of shear at microfibril surfaces or within the matrix between microfibril aggregates is uncertain.
These results present challenges for computational modeling. It is certainly possible to subsume this unidentified form of nanoscale shear within a shear modulus for the matrix material [8], but that approach does not answer the question of mechanism at the molecular level.
References [1] Sedighi-Gilani, M. and P. Navi, Experimental observations and micromechanical modeling of
successive-damaging phenomenon in wood cells' tensile behavior. Wood Science and Technology, 41 (2007), 69-85.
[2] Fratzl, P., I. Burgert, and H.S. Gupta, On the role of interface polymers for the mechanics of natural polymeric composites. Physical Chemistry Chemical Physics, 6 (2004), 5575-5579.
[3] Kojima, Y. and H. Yamamoto, Effect of microfibril angle on the longitudinal tensile creep behavior of wood. Journal of Wood Science, 50 (2004), 301-306.
[4] Xu, P., et al., Dual-axis electron tomography: a new approach for investigating the spatial organization of wood cellulose microfibrils. Wood Science and Technology, 41 (2007), 101-116.
[5] Donaldson, L.A. and A.P. Singh, Bridge-like structures between cellulose microfibrils in radiata pine (Pinus radiata D. Don) Kraft pulp and holocellulose. Holzforschung, 52 (1998), 449-454.
[6] Altaner, C.M. and M.C. Jarvis, Modelling polymer interactions of the 'molecular Velcro' type in wood under mechanical stress. Journal of Theoretical Biology, 253 (2008), 434-445.
[7] Fratzl, P., I. Burgert, and J. Keckes, Mechanical model for the deformation of the wood cell wall. Zeitschrift Fur Metallkunde, 95 (2004), 579-584.
[8] Saavedra Flores, E.I., A large strain computational multi-scale model for the dissipative behaviour of wood cell-wall. Computational Materials Science, 50 (2011), 1202-1211.
4
Analysis of Latewood/Earlywood Coupling Effects on Swelling/Shrinkage by Synchrotron Radiation Phase Contrast X-ray Tomographic Microscopy and
3D image analysis
A.Pateraa*, M.Griffaa, D.Deromeb, J.Carmelieta,c
aLaboratory of Building Science and Technology, EMPA, Überlandstrasse 129, Dübendorf, Switzerland, 8600 bWood Laboratory, EMPA, Überlandstrasse 129, Dübendorf, Switzerland, 8600
cChair of Building Physics, ETHZ,Wolfgang-Pauli-strasse 15, Zürich, Switzerland, 8093
Key words: wood, cellular scale measurements, swelling/shrinkage
1. Introduction and methods
We investigate wood swelling/shrinkage, due to varying environmental relative humidity (RH). This study is performed at the cellular scale by combining synchrotron radiation-based Phase Contrast X-ray Tomographic Microscopy (srPCXTM) and 3D image registration. The analysis of previous measurements on specimens of pure latewood and pure earlywood led to the conclusion that swelling/shrinkage strains are within the same range in tangential and radial directions for latewood, while in earlywood the radial strain is much smaller than the tangential one. This result indicates that earlywood may be susceptible to the influence of local mi-crostructural features and that rays may play a restraining role [1]. To look further at wood structural heterogeneity effects on its hygromechanical behavior, we performed si-milar srPCXTM measurements on specimens containing both earlywood and latewood. Figure 1(a) shows an example of a srPCXTM cross-sectional image of a specimen of Picea Abies [L. Karst] containing both latewood and earlywood, that we acquired at the TOMCAT beamline of the Swiss Light Source, Paul Scherrer Institute. Figure 1(b) describes the experimental protocol used during the measure-ments, when the specimen was tomographed after achieving moisture content equilibrium at different relati-ve humidity levels, in adsorption, from a starting point of 20%RH, to 40-60-75 and 88% RH , and in desorp-tion, through the same steps.
Figure 1: (a) srPCXTM cross-sectionial image of a Picea Abies spe-cimen sample containing both earlywood and latewood. (b) Hygro-mechanical load experimental protocol adopted during the srPCXTM scanning. F
Figure 2: Superposition of two srPCXTM ima-ges acquired at two different relative humidity levels (20%RH, white,88% RH, red) during the adsorption stage of the hygromechanical load protocol.
2. Data analysis
The sample undergoes important swelling and local deformation as shown in Figure 2. With the goal of quantitatively estimating the swelling/shrinkage strains of the specimens containing both latewood and ear-lywood at the cellular scale, we use three image analysis methods: (i) we quantify volumetric swelling/shrinkage strain using segmentation algorithms based on voxel value
thresholding; (ii) we perform a pattern analysis that allows us to estimate dimensional changes of specific anatomical fea-
tures along the two cross-sectional directions, e.g., change of lumen radial and tangential size. This analy-sis is performed in 2D, on single cross-sectional XTM images;
(iii) in order to determinate quantitatively the swelling/shrinkage strains along the tangential, radial and lon-gitudinal directions, we perform 3D affine registration on sub-regions of the srPCXTM datasets. An affi-ne deformation model is a first approximation in describing the actual swelling/shrinking deformations going on during. It allows for global estimation of the average strain tensor over the overall sub-region.
5
3. Results
A preliminary segmentation of one srPCXTM dataset and count of voxels (method i) allowed us to estímate the volumetric strain at the different relative humidity levels of the hygroscopic load cycle, shown in Figure 3. These preliminary results show hygromechanical hysteresis, and maybe non-closing of the loop, at least for the chosen Region of Interest (ROI).
Figure 3: Volumetric strain estimated by voxel value-based segmentation for a sub-volume across the boundary between earlywood and latewood, in adsorption (solid line) and desorption (dash line). Figure 4 shows the strains, in tangential and radial directions, as obtained by method (ii). We observe that the radial swelling in earlywood is smaller than in latewood, while the tangential swelling almost the same for both halves of the specimen. Preliminary 3D affine registration shows that the results strongly vary with the sub-region of interest considered. Preliminary results show less hysteresis than the volumetric analysis and non-closed loops, except for the earlywood where the behavior is similar to the volumetric one. Work is on-going towards better identifying the magnitude and origin of this behaviour.
Figure 3: Strain vs RH for subROI of earlywood in radial (a) and in tangential (b) directions and latewood in radial (c) and in tangential (d) directions
References: [1] Derome, D., Griffa, M., Koebel, M., Carmeliet, J. Hysteretic swelling of wood at cellular scale probed by phase contrast X-ray tomography, J. Struct. Biol., 173, 180-190 (2001), DOI:10.1016/j.jsb.2010.08.011.
6
Multiscale Computational Homogenization for the Hygro-Mechanical
Analysis of Growth Rings in Softwoods
A. Rafsanjani†*
, D. Derome†, Hans J. Herrmann
‡, and J. Carmeliet
‡‡
† Wood Laboratory, EMPA
Überlandstrasse 129, CH-8600 Dübendorf, Switzerland [email protected], [email protected]
‡ Computational Physics for Engineering Materials,
IfB, HIF E12, ETH Hönggerberg, Schafmattstr. 6, CH-8093 Zürich, Switzerland [email protected]
‡‡Laboratory for Building Science and Technology, EMPA,
Überlandstrasse 129, CH-8600 Dübendorf, Switzerland ‡‡ Chair of Building Physics, ETH Zürich,
HIL E46.3, Wolfgang-Pauli-strasse 15, CH-8093 Zürich, Switzerland [email protected]
Key words: multiscale modeling, softwood, homogenization, swelling coefficient
ABSTRACT
This paper presents a two-scale micro-mechanical analysis framework [1] for growth rings in softwoods based on a computational homogenization technique. In this method, the evolution of the mechanical fields at the macroscopic level (growth ring) is resolved through the incorporation of the micro-structural (cellular structure) response. Applying this method to wood, an orthotropic cellular material, the variation of cross-sectional cell dimensions under mechanical/hygric loading is solved at the micro-scale. These results are averaged and transferred to the macro level problem where the mechanical response and swelling behavior of an individual growth ring is computed. This method has the major benefit that no explicitly determined homogenized material properties (e.g. stiffness, swelling coefficients) are required, since no constitutive equations are required for the macroscopic stresses at the macro level. The finite element simulations are performed based on explicit meshing of the microstructures on honeycomb RVEs, with different boundary conditions. The necessary and sufficient condition (so-called Hill condition) for equivalence between the energetically and mechanically defined properties is that the average of the product of the stress σ and strain tensors ε (micro level) equals the product of their averages (macro level). This condition is satisfied by three different types of boundary conditions for random media: kinematic uniform (KUBC), periodicity compatible mixed uniform (PMUBC) and periodic boundary conditions (PBC) [2]. The overall swelling coefficients also can be calculated by adding a load case that constrains the change of the volume of RVE, and applies a uniform moisture content increment. This allows evaluating the volume averaged swelling stress tensor, from which the apparent swelling coefficients can be obtained. A general PYTHON script is written in the scripting interface in ABAQUS to carry out the scale bridging. The modeling procedure is described here in details. In the first step, according to the distribution of early- and latewood cells in a specific growth ring the domain is discretized using a biased structured mesh which is finer in latewood and is coarser in earlywood. In the second step, at each integration point a boundary value problem is defined. A honeycomb RVE is generated and parameterized with five geometric dimensions: height and thickness of lateral walls and length, thickness and angle of inclined walls. A simplified periodic partitioning pattern is employed to
7
distinguish the lateral walls from inclined ones. The geometric parameters and partitioning pattern of the honeycomb RVE is depicted in figure 1. The material properties of the cell wall are assumed to be orthotropic and three orthogonal direthe thickness and normal to the plane.
Figure 1. (a) honeycomb The unit cell dimensions can be determined by[3]. When the unit cell model is generatedthe effective (or apparent) stiffnesscalculated and transferred to the macro scale analysis. distribution for a sample unit cell with PBC boundary conditions for different loading testsbe used for calculation of effective properties.
(a)
Figure 2. Stress distribution for a sample unit cell with PBC boundary conditions: tangential tensile test (b), in-plane shear test (c) and swelling due to a uniform moisture increment The proposed multiscale approachtechniques at different scales and upscaling with rich informationorientation, early- and latewood interaction, influence of morphological and environmental effects on effective (or apparent) properties (stiffness, swelling, etc.) in soft
References [1] Yuan, Z. and J. Fish, Toward realization of computational homogenization in practice.
International Journal for Numerical Methods in Engineering
[2] D. Pahr, and P. Zysset: Influence of of cancellous bone. Biomechanics and Modeling in Mechanobiology
[3] W. Zillig, Moisture transport in wood using a multi scale approach, Ph.D. Thesis, KULeuven, May, 2009.
distinguish the lateral walls from inclined ones. The geometric parameters and partitioning pattern of the honeycomb RVE is depicted in figure 1. The material properties of the cell wall are assumed to be orthotropic and three orthogonal directions are selected to be oriented along the cell walls, along the thickness and normal to the plane.
(a) honeycomb dimensions and (b) partitioning pattern
can be determined by statistical analysis of microscopy images, e.g. SEMis generated, the above mentioned boundary conditions are applied
apparent) stiffness matrix and swelling coefficients at each intecalculated and transferred to the macro scale analysis. To illustrate the approach, figuredistribution for a sample unit cell with PBC boundary conditions for different loading tests
fective properties.
(b) (c)
Stress distribution for a sample unit cell with PBC boundary conditions: plane shear test (c) and swelling due to a uniform moisture increment
multiscale approach provides a powerful tool which incorporates at different scales and upscaling with rich information (geometry, material properties and
and latewood interaction, etc.) embedding. This model can be used influence of morphological and environmental effects on effective (or apparent) properties (stiffness, swelling, etc.) in softwoods and also other wood based products.
Yuan, Z. and J. Fish, Toward realization of computational homogenization in practice. International Journal for Numerical Methods in Engineering 73(2008): 361-D. Pahr, and P. Zysset: Influence of boundary conditions on computed apparent elastic properties
Biomechanics and Modeling in Mechanobiology 7(2008): 463W. Zillig, Moisture transport in wood using a multi scale approach, Ph.D. Thesis, KULeuven,
t1
h
t2
l
θ
(a) (b)
distinguish the lateral walls from inclined ones. The geometric parameters and partitioning pattern of the honeycomb RVE is depicted in figure 1. The material properties of the cell wall are assumed to
ctions are selected to be oriented along the cell walls, along
pattern
statistical analysis of microscopy images, e.g. SEM the above mentioned boundary conditions are applied and
and swelling coefficients at each integration point are , figure 2 shows stress
distribution for a sample unit cell with PBC boundary conditions for different loading tests which can
(d)
Stress distribution for a sample unit cell with PBC boundary conditions: radial tensile test (a), plane shear test (c) and swelling due to a uniform moisture increment (d)
provides a powerful tool which incorporates appropriate modeling (geometry, material properties and
. This model can be used for studying the influence of morphological and environmental effects on effective (or apparent) hygro-mechanical
woods and also other wood based products.
Yuan, Z. and J. Fish, Toward realization of computational homogenization in practice. -380.
boundary conditions on computed apparent elastic properties (2008): 463-476.
W. Zillig, Moisture transport in wood using a multi scale approach, Ph.D. Thesis, KULeuven,
8
On the Variability of Transverse Elastic Properties of P. pinaster at the Cellular Level
João Pereira†,‡, José Xavier†, Pedro Couto†, José Morais†, José Lousada† and Pedro Melo-Pinto
†CITAB - Centre for the Research and Technology of Agro-Environmental and Biological Sciences
University of Trás-os-Montes e Alto Douro, Apartado 1013
5001-801 Vila Real, Portugal {jmcx, jmorais, jlousada}@utad.pt
‡Escola Superior de Tecnologia e Gestão de Viseu
Departamento de Engenharia de Madeiras Campus Politécnico de Repeses
3504-510 Viseu, Portugal [email protected]
Key words: transverse elastic properties, wood, unit cellular models, image processing
ABSTRACT
Wood is a bio-based composite polymer formed by trees. Historically, it has always played an important role as a structural material, namely in construction. Still nowadays, wood represents an important engineering material, namely because it is renewable and recyclable, there are important forest resources in earth and takes itself as an efficient way of CO2 sequestration, the transformation processes have a low cost, and it has a good stiffness/weight ratio. Besides, in the last decades, new wood engineering products (e.g., particle-based or fibre based panels), have been developed in order to fulfil structural requirements. More recently, wood and other natural-fibre reinforced polymers have caught more attention in the development of new bio-composites, replacing fossil carbohydrates as raw material. Thus, in order to reach an increased, efficient and ecological utilisation, not only the bulk mechanical properties of wood species but also their spatial variation at several hierarchical length scales (from the stem to the cellular levels), must be accurately characterised by suitable methodologies. Studies on wood characterisation have however addressed most preferentially mechanical properties parallel to the grain (longitudinal direction). Thus, an effort still remains to be done for representative evaluation of spatial variability of wood properties perpendicular to the grain [1]. This work aims at assessing the spatial variation of transverse elastic properties within individual growth rings, as well as along the radius of the stem, by analysing the local variation of geometry and shape of the P. pinaster cellular structure.
The anatomical characterisation (morphometrical analysis) of the tracheids cross-section was carried out using xylological samples with nominal dimensions of 15(R)x10(L)x8(T) (mm). Samples were taken at several positions along the radius of the stem in order to study spatial variation effects. Firstly, the samples were boiled in autoclave with alcohol and glycerin. This preliminary treatment is useful for accurate cutting. Transverse slices were cut of about 25 m thick, using a microtome of sliding knife. Finally, they were dehydrated and mounted on microscope slides with Entellan®, for microscope observation and geometrical characterization.
Images were taken by an Olympus BX50 fluorescence microscope, at a magnification of 200x (Figure 1). The conversion factor was 0.46 m/pixel. The pixel resolution of individual images were
9
1280(width)x960(height) pixel. Images were recorded by successively shifting the samples with increments inferior to the image width. Adjacent images were then superimposed in order to reconstruct the complete growth ring. Image processing, consisting in segmentation and morphological operations, were then applied in order to enhance the geometry and shape of the wood cells. The output images were then processed using AutoCAD® 2010 in order to characterise the parameters of the wood cells (Figure 1a). Typical cell arrangement and geometry for both earlywood and latewood of P. pinaster are shown in Figure 1b and 1c, respectively.
The wood cellular structure has a huge variability, even within individual earlywood or latewood regions (Figure 1b, 1c). The approach described about, coupling image processing with CAD tools, for the cellular parameter characterisation can therefore be very time consuming, because a large number of cells has to be considered for representative evaluation. In order to overcome this drawback, the evaluation of cellular parameters (Figure 1a) by automatic or semi-automatic image processing by combining multilevel thresholding with fuzzy logic [2] is under current investigation.
The wood cell parameters (Figure 1a) can then be input into unit cell models of the aggregate of wood cells in order to estimate stiffness parameters of wood at the cellular level [3]. Besides, finite element analyses can also be performed in order to simulate wood behaviour at the annual ring scale taking into account the actual cell geometry [4].
(a) (b) (c)
Figure 1: (a) geometrical parameters of the hexagonal unit cell model; (b) P. pinaster earlywood cells; (c) P. pinaster latewood cells.
References [1] J. Xavier, S. Avril; F. Pierron, J. Morais. Variation of transverse and shear stiffness properties of wood in a
tree. Composites Part A: Applied Science and Manufacturing, 40(12): 1953-1960, 2009. [2] P. Couto, M. Pagola, H. Bustince, E. Barrenechea, P. Melo-Pinto. Uncertainty in multilevel thresholding
using atanassov's intuitionistic fuzzy sets. In IEEE World Congress on Computational Intelligence, p. 330-335, Hong Kong, China, 2008.
[3] L.J. Gibson, M.F. Ashby. Cellular solids: Structure and properties. Pergamon Press, 1988. [4] H. Qing, L. Mishnaevsky Jr. 3D multiscale micromechanical model of wood: From annual rings to
microfibrils International Journal of Solids and Structures, 47(9): 1253-1267, 2010.
10
High Spatial Resolution Measurement of Wood Density Using Hyperspectral Imaging and Neural Networks
Armando Fernandes, José Lousada, José Morais,
José Xavier, João Pereira and Pedro Melo-Pinto
CITAB - Centre for the Research and Technology of Agro-Environmental and
Biological Sciences
University of Trás-os-Montes e Alto Douro,
Apartado 1013
5001-801 Vila Real, Portugal
[email protected], [email protected],
{jlousada,jmorais,jmcx,pmelo}@utad.pt
Keywords: Wood, Hyperspectral Imaging, Neural Networks, Density
ABSTRACT
In this work a preliminary study is presented aiming to apply hyperspectral imaging and neural
networks to the measurement of wood density profiles at the growth ring scale. Hyperspectral
imaging is a spectroscopy technique that allows gathering information on how samples absorb or
reflect light. This information is dependent of the samples chemical composition and physical
structure. The type of information we are interested in is reflectance. Reflectance is a measure of the
percentage of light that is reflected by a sample relatively to the light that is incident on the sample.
With hyperspectral imaging it is possible to measure, simultaneously, reflectance values for various
wavelengths of incident light and for various sample points that are only 75µm apart from each other.
All the measured reflectance values are used to compose a single image (see Figure 1a).
To use hyperspectral imaging in density measurements, it is necessary to transform the reflectance
values measured into density values. This was done creating a calibration based on neural networks
which are biologically inspired mathematical processors capable of modeling any function to any
required degree of accuracy [1]. In our case, the neural network inputs are the principal components
of the hyperspectral data [1]. The principal components are uncorrelated variables that result from the
linear combination of the reflectance values. The most relevant principal components represent most
of the variability of the reflectance values.
Since hyperspectral imaging allows measuring density with high spatial resolution it can be employed
instead of the conventional X-ray microdensitometry technique. The creation of a new technique for
density measurements is relevant because X-ray microdensitometry has a major disadvantage: it
requires the use of ionizing radiation that is harmful for health. Another disadvantage of X-ray
microdensitometry is that it measures density for only one sample point at a time.
In scientific literature we did not find any work where hyperspectral imaging was used for wood
density measurement, there are however, various previous works where conventional spectroscopy is
employed with this purpose [2-4]. Our work has several advantages over these previous works. First
of all, we measure 75µm wide regions while in previous works the density is measured in regions a
few millimeters wide. Secondly, we can measure hundreds of positions simultaneously while in
previous works only one position of the sample is measured each time. Thirdly, our wavelength
range, 400-1000 nm, allows our equipment to be cheaper than the equipment that is required to do
measurements in the wavelength band of the previous works which is between 1000-2500 nm.
The best neural network that we created has five principal components as input, two hidden layers
with four neurons each and an output layer with one neuron. The neural network was trained with the
11
Levenberg-Marquardt algorithm. Our work was done using only one sample of Pinus pinaster. A total
of 150 and 365 density points were used to train and validate the neural network, respectively (see
Figure 1b). The training points correspond to six years of growth of the tree and the validation points
to seven years. For the validation points, the squared correlation coefficient (r2) and the mean absolute
error (MAE) between the density values measured by X-ray microdensitometry and the values
obtained with the neural networks with hyperspectral information as input are 0.96 and 0.041 g/cm3,
respectively. The Partial Least Squares (PLS) algorithm, that is frequently used to create calibrations
that convert spectroscopy data into sample density values [2-4], achieved an r2 of 0.91 and a MAE of
0.064 g/cm3 for the validation set points of our sample. Therefore, the neural network result is better
than PLS. As future work, we are developing calibrations using samples from different trees.
Wa
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Hyperspectral Training
Hyperspectral Validation
Den
sit
y (
g/c
m3)
Position on the sample (mm)
a)
b)
Figure 1: a) Hyperspectral image with 75µm and 0.6 nm of spatial and spectral resolution, respectively. The
image has 1040 rows and 515 columns. b) Density values adjusted to the hyperspectral image. The gray line
corresponds to the ground truth values measured by X-ray microdensitometry, the stars and circles are the result
of the neural network whose input is the hyperspectral image shown in a).
References
[1] C.M. Bishop: Neural networks for pattern recognition, Clarendon Press ,Oxford University Press, (1995).
[2] P.D. Jones, L.R. Schimleck, G.F. Peter, R.F. Daniels, and A. Clark III: Nondestructive estimation of Pinus
taeda L. wood properties for samples from a wide range of sites in Georgia. Canadian Journal of Forest
Research-Revue Canadienne De Recherche Forestiere 35 (2005), 85-92.
[3] L. Thygesen: Determination of dry matter content and basic density of Norway spruce by near infrared
reflectance and transmittance spectroscopy. Journal of near infrared spectroscopy 2 (1994), 127-135.
[4] B.K. Via, C.L. So, T.F. Shupe, M. Stine, and L.H. Groom: Ability of near infrared spectroscopy to monitor
air-dry density distribution and variation of wood. Wood and Fiber Science 37 (2005), 394-402.
12
Novel Characterization of Methacrylate Impregnated Wood
Oliver T. Hudson†* and Michelle L. Oyen†
†Cambridge University Engineering Department
Trumpington Street Cambridge CB2 1PZ
United Kingdom [email protected], [email protected]
Key words: wood, impregnation modification, nanoindentation, FTIR, characterization.
ABSTRACT Fast growing, porous wood species are receiving significant research interest due to the potential for modification to add significant commercial value. Practical methods for determining, understanding and predicting modification effectiveness are needed. The complementary use of nanomechanical property mapping, computational FTIR spectra analysis and computational image analysis are presented as a methodology for determining polymer impregnation effectiveness over a spatial area that is large enough to demonstrate the limitations of the modification to diffuse through the sample. Experimental
Willow (Salix Viminalis) was subjected to a heat initiated polymerisation impregnation treatment with polymer blends containing 2-Hydroxyethyl methacrylate (HEMA), methyl methacrylate (HEMA), ethylene dimethacrylate (EDMA) developed from the impregnation methodology detailed by Zhang et al. [1]. Density measurements were made before and after impregnation modification. Displacement-controlled nanoindentation testing (Hysitron Inc., MN, USA) was used to map variations in nanomechanical properties. FTIR spectroscopy (PerkinElmer, Waltham, MA, USA) was performed on at known locations across the impregnated samples. Scanning electron microscopy (Carl Zeiss, Jena, Germany) images from across impregnated samples were also collected. Control samples (unmodified wood and solid cured polymer blocks) were also subjected to the same investigative regime.
Numerical
A specially developed MATLAB curve fitting code was used to normalise FTIR spectra and manipulate a least squares fit methodology to combine individual component spectra to produce a match for impregnated composite spectra. The least squares fit methodology uses a minimization strategy that is specific to the optimisation algorithm, which in this case is the subspace trust region method and is based on the interior-reflective Newton method [2]. This analysis produces predicted polymer and wood proportions for each FTIR spectra taken from impregnated samples, calculated from the best match that the MATLAB code is able to achieve. An analysis in ImageJ [3] of optical microscope images taken from impregnated samples to determine mean pixel grey value in specific regions was developed as a further indicator of impregnation effectiveness. A model, based on the most applicable form of the Kozeny-Carmen equation [4], for pre-polymerisation impregnation fluid flow is presented. The cellular structure of wood is simplified to a block packed with hollow tubes of identical diameter while the impregnation fluid flow is driven by a pressure gradient. Experimental values are shown to be c. 60% of theoretical values. The model is shown to be useful for determining required impregnation conditions for specific impregnation depths.
13
Results
An example of the data achieved through the complementary use of nanomechanical property mapping and the computational analyses previously detailed is shown in Figure 1. The distinct colour change in the impregnated samples highlights the step change in nanomechanical response and FTIR based predicted polymer proportion.
Figure 1: Methacrylate impregnated willow samples displaying reduced modulus (indicated by circle size relative to scale bar) and FTIR predicted polymer proportion for the same location (detailed as a percentage).
SEM images of specific regions and an example of the spectra match achieved are also shown.
Conclusions
It is shown that the effectiveness of the impregnation process can be relatively rapidly characterised using nanoindentation, FTIR spectroscopy (with a least squares fit methodology) and ImageJ [3] based optical microscope image analysis. This methodology is carried out across a spatial region that is large enough to show the limitations of the impregnator's diffusion through a sample, the findings are cross-validated by SEM. The methodology and results have been validated with a second wood species (Populus Nigra Italica). The ability of the methodologies detailed to predict and determine impregnation effectiveness form valuable tools for researchers developing impregnated modified woods. References [1] Y. Zhang, S. Y. Zhang, Y. H. Chui, H. Wan: Effect of impregnation and in-situ polymerization of
methacrylates on hardness of sugar maple wood. Journal of Applied Polymer Science, 99 (2004), 1674-1683.
[2] M. Galli, M. L. Oyen: Fast identification of poroelastic parameters from indentation tests.
Computer Modeling in Engineering and Sciences, 48 (2009), 241-268. [3] W. S. Rasband: ImageJ. U. S. National Institutes of Health, Bethesda, Maryland, USA,
http://rsb.info.nih.gov/ij/, 1997-2011. [4] J. Dvorkin. Kozeny-Carmen Equation Revisited. Department of Geophysics, Stanford University,
Stanford, CA, USA, 2009.
14
Water Vapour Sorption – the Parallel Exponential Kinetics Model and Cell Wall Viscoelasticity
Callum Hill
Forest Products Research Institute, Edinburgh Napier University, Edinburgh, EH10 5DT, UK
Key words: micromechanics, wood, experimental characterization, water vapour sorption, kinetics
ABSTRACT
It has been recently demonstrated that the water vapour sorption kinetics of the plant cell wall can be accurately described by the so-called parallel exponential kinetics (PEK) model, which has the mathematical form:
MC = MC0 + MC1[1 – exp(-t/t1)] + MC2[1 – e(-t/t2)] (1)
Where MC is the moisture content after infinite time of exposure of the sample to a constant relative humidity (RH), MC0 is the moisture content of the sample at time zero. The sorption kinetic curve is composed of two exponential terms which represent a fast and slow process having characteristic times of t1 and t2 respectively. The terms MC1 and MC2 are the moisture contents at infinite time associated with the fast and slow processes respectively. There has been speculation as to what physical phenomena the two processes represent and there is no clear view on this at the present time. Using such a function, it is possible to obtain highly accurate curve fits, as illustrated in Figure 1, which also shows the adsorption curve deconvoluted into fast and slow sorption processes.
0 5 10 15 20 25 30 35 40 451.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
'slow'
'fast'
Mo
istu
re c
on
ten
t (%
)
Time (minutes)
Figure 1: Adsorption curve with PEK curve fit also showing fast and slow components
The fast and slow components of the PEK equation have a mathematical form that is identical with that describing the dynamic response of a Kelvin-Voigt element when subjected to an instantaneous stress increase (σ0):
ε = (σ0 /E)[1 – exp(-t/φ)] (2)
15
Where ε is the strain at time t, E is the elastic modulus and φ is a time constant which is defined as the ratio η/E, where η is the viscosity [5]. In the case of a plant fibre subjected to a change in relative humidity (RH), there is a change in the swelling pressure (Π –equivalent to σ0) exerted within the cell wall when the atmospheric water vapour pressure is raised from an initial value pi to a final value pf given by Equation 3:
Π = - (ρ/M)RT.ln(pi/pf) (3)
Where ρ is the density and M is the molecular weight of water, R is the gas constant and T is the isotherm temperature in kelvin. In the model described herein, the strain of the system is assumed to be equivalent to the volume change of the cell wall as a result of water vapour adsorption or desorption. This volume change is further assumed to be linearly related to the change in the mass fraction of the water present in the cell wall. The appropriate mechanical analogue comprises two Kelvin-Voigt elements arranged in series (Fig. 2) with E1, E2 being the moduli associated with the fast and slow processes respectively and η1 and η2 being the equivalent matrix viscosities.
Figure 2: Adsorption curve with PEK curve fit also showing fast and slow components
Using such a model, the sorption kinetics data of various wood species has been analysed. The results are presented at the workshop, but some illustrative examples are given in Figure 3.
Figure 3: Examples of cell wall moduli calculated for the fast (E1) and slow (E2) sorption processes and viscosities for the fast (η1) and slow (η2) sorption processes.
0
5
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15
20
25
30
35
E1 (
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adsorption desorption
Cotton
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E2 (
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Cotton
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Cotton
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Cotton
16
Finite Element Modelling of Interfacial Stresses of Asymmetrical Laminated Wood Products Subjected to Moisture Changes
Ling Li 1,2, Meng Gong1, Y.H. Chui1, and Dagang Li2
1Faculty of Forestry and Environmental Management,
University of New Brunswick, Fredericton, N.B., E3B 3B1, Canada
[email protected] , [email protected], [email protected] 2 Nanjing Forestry University, Nanjing, Jiangsu, 210037, China
Keywords: Asymmetrical laminated wood; Finite element modelling; Interfacial stresses; Moisture changes.
Abstract
Asymmetrical two-layer wood products are adhesively made using thermo-mechanically densified wood as surface layer and untreated wood as substrate. Such laminated wood products show a great potential for wood flooring, stairs and desktops. However, interfacial stresses of this type of laminated products may result from the different wood movements and mechanical properties of densified and untreated wood subjected to moisture in their service. The interfacial stresses existing in the adhesive layer could result in delamination along bondline of laminated products once they exceed the bond strength. The studies on the interfacial stresses of laminated wood products are very limited due to the complex in interfacial structures, a combination of wood and adhesive, and difficulty in measuring the physical and mechanical properties of an adhesive [1,2]. The aims of this study were to develop a finite element model (FEM) to predict the interfacial stresses and to study the influence of thickness ratio of densified wood and untreated wood on the magnitude of interfacial stresses.
Balsam fir (Abies balsamea (L.) Mill.) was test material. Two configurations of laminated wood products were bonded using polyurethane adhesive in the parallel-to-the-grain direction. One was made of 3-mm-thick densified wood and 16-mm-thick untreated wood (3mm-D-16mm-UD) and the other included 7-mm-thick densified wood and 12-mm-thick untreated wood (7mm-D-12mm-UD). The physical and mechanical properties of densified wood, untreated wood and adhesive were taken from literature or determined from experiments. The moisture content at test varied from 7% to 2% for densified wood and from 15% to 5% for untreated wood. After treatment, the deformations of laminated wood products were obtained via image processing techniques to verify the results predicted by FEM. Then the interfacial stresses and the influence of thickness ratio on them were analysed by FEM.
17
Figure 1: Deformation of a 7mm-D-12mm-UD specimen after treatment
Figure 2: Deformation of a 7mm-D-12mm-UD specimen (ABAQUS)
Figure 3: Distribution of interfacial normal stress
Figure 4: Distribution of interfacial shear stress
It was found that the maximum interfacial normal and shear stresses were mostly distributed at the two edges of bondline and the values of them increased with the increase of the thickness ratio of densified wood and untreated wood.
References
[1] P. Blanchet, G. Gendron, A. Cloutier, and R. Beauregard: Numerical prediction of engineered wood flooring deformation. Wood and Fiber Science, 37(3), 2005, 484-496.
[2] J. Deteix, P. Blanchet, A. Fortin, and A. Cloutier: Finite element modelling of laminate wood composites hygromechanical behaviour considering diffusion effects in the adhesive layers, Wood and Fiber Science, 40(1), 2008, 132-143.
18
Combined Experimental and Numerical Investigation of Water Transport in Wood Below the Fiber Saturation Point
J. Eitelberger†*, S. Dvinskikh‡, and K. Hofstetter†
†Institute for Mechanics of Materials and Structures, Vienna University of Technology
Karlsplatz 13/202, A-1040 Vienna, Austria [email protected]
‡Division of Physical Chemistry and Industrial NMR Centre, Royal Institute of Technology Teknikringen 36, SE-10044 Stockholm, Sweden
Key words: transient water transport, nuclear magnetic resonance imaging (MRI), continuum micro-mechanics, coupled problems, finite element method
ABSTRACT
The interaction of wood and water affects almost each field in wood material science. With respect to the transport behavior of water in wood, transient transport processes were of particular interest in the last years. Therein, new models allow for suitable predictions of such processes [1,2,3], and new non-destructive experimental methods [4,5] provide enhanced insight into the processes inside a wood sample during a test. A further increase in knowledge by combining theoretical and experimental approaches was aimed at in the framework of the European WoodWisdom-Net project “Improved moisture”.
The main interest of the experimental part was the determination of moisture profiles of a wood sample after changing the external climatic conditions. For this purpose, three specimens of Norway spruce wood were prepared, one for investigating transport in each principal material direction of wood (radial, tangential, longitudinal). They were sealed on all sides except for one, at which they were exposed to different saturated salt solutions controlling the relative humidity in an NMR glass tube as shown in Fig. 1.
Figure 1: Experimental setup and its representation with a finite element model
19
After equilibration of the samples at a relative humidity of 65 %, relative humidity was changed in three steps by changing the salt solution in the NMR tube: first up to 95 % RH, then down to 35 % RH, and finally back to 65 % RH again (the temperature remained constant at 23 °C). For each step, the evolution of the moisture profile in the sample over time was studied until the sample reached equilibrium again. In particular, moisture profiles were measured using proton magnetic resonance imaging (MRI) as described in [4].
To characterize the samples as well as possible, their dry densities and their sorption isotherm were determined. In addition, SilviScan measurements were performed for the sample with moisture transport in radial direction, yielding morphological data of cell shapes and dimensions and informat-ion about the density profile throughout the investigated area.
Based on these informations, material parameters were estimated using continuum micromechanics [1,2]. The experimental setup was reproduced within a finite element model, which was subjected to the same boundary conditions as in the test (see Fig. 1). Finally, measured and calculated moisture profiles were compared at different time instances; the results for the radial sample are shown in Fig. 2. A good agreement of experiment and model is observed, both for different material directions and for different humidity steps.
Figure 2: Comparison of experimentally determined moisture concentration profiles (solid lines) and accord-ing modeling results (dashed lines). Spruce sample, radial direction, average dry density 379 kg/m³. External change in relative humidity from 95 % down to 35 % at a temperature of 23 °C.
The good agreement serves as validation of the modeling approach. Important aspects like the bound-ary conditions for the sample and the correct material parameters could be identified. Furthermore, some phenomena observed in the experiment such as low internal moisture gradients in the sample with moisture transport in the longitudinal direction could be explained on a physical background.
References
[1] J. Eitelberger, K. Hofstetter: Prediction of transport properties of wood below the fiber saturation point – A multiscale homogenization approach and its experimental validation. Part I: Thermal conductivity. Composites Science and Technology 71 (2011), 134-144.
[2] J. Eitelberger, K. Hofstetter: Prediction of transport properties of wood below the fiber saturation point – A multiscale homogenization approach and its experimental validation. Part II: Steady state moisture diffusion coefficient. Composites Science and Technology 71 (2011), 145-151.
[3] J. Eitelberger, et al.: Theory of transport processes in wood below the fiber saturation point. Physical background on the microscale and its macroscopic description. Holzforschung, accepted for publication.
[4] S. V. Dvinskikh et al.: A multinuclear magnetic resonance imaging (MRI) study of wood with adsorbed water: Estimating bound water concentration and local wood density. Holzforschung 65 (2011), 103-107.
[5] D. Mannes et al.: Non-destructive determination and quantification of diffusion processes in wood by means of neutron imaging. Holzforschung 63 (2009), 589-596
20
Effectiveness of Parameter Identification for Modeling the Transient Bound Water Diffusion in Wood
W. Olek†*, J. Weres‡, P. Perr釆
†Faculty of Wood Technology, Poznań University of Life Sciences
ul. Wojska Polskiego 28, 60-637 Poznań, Poland [email protected]
‡Faculty of Agriculture and Bioengineering, Poznań University of Life Sciences
ul. Wojska Polskiego 28, 60-637 Poznań, Poland [email protected]
‡† Laboratoire de Génie des Procédés et Matériaux, Ecole Centrale Paris
Grande Voie des Vignes - 92295 Châtenay-Malabry Cedex, France [email protected]
Key words: water transport in wood, finite element modeling, inverse coefficient problem, optimization algorithms
ABSTRACT
Parameter identification procedures were developed and assessed to increase accuracy of mathematical modeling of the transient bound water diffusion in wood. Reliable coefficient values for the mathematical model [6] were estimated by minimizing differences between data measured in experiments and results of computer simulations. Several problems decreasing effectiveness of the parameter identification procedures were analyzed:
1. Unreliability of some data measured in experiments and used in parameter identification.
Experimental data unreliabilities occur frequently in a process of data acquisition, and are due to limitations in experimental procedures and measuring equipment. The flaws concerning two general approaches were emphasized:
a) a loss of sample material continuity and a small number of time instants of the investigated process, but a satisfactory distribution of the moisture content in the spatial direction of the process [3, 4],
b) average values of the moisture content in space, but the sample material continuity is preserved, and a huge number of time instants is possible [1, 8]. For this approach we depicted a problem of disturbances caused by continuous, long duration measurement of mass, and a need of taring a balance.
2. Uncertainties of the mathematical model and its numerical representation in computing simulation results.
Model uncertainties play a crucial role in parameter identification at the stage of direct modeling, i.e. during obtaining predictions. A role of the boundary condition of the third kind was analyzed, and a modified form of the condition was proposed [7]. Also several features strongly affecting uncertainty of the numerical model were discussed. The original numerical approach was based on the finite element method with the use of 3D curvilinear isoparametric elements to represent geometry of investigated objects, and with two-point, absolutely stable recurrence schemes in
21
time [9]. To deal with the quasi-linearity of equations an iterative procedure was developed. Numerical description of eventual non-homogeneity, anisotropy and geometric irregularity of investigated object was also taken into account, and any form of initial and boundary conditions is acceptable. The FEM model was enhanced with original procedures to control accuracy, stability, susceptibility to oscillations and efficiency. The final model for solving direct problems was composed of the recurrence scheme of algebraic equations, input data representing conditions of the investigated process, and empirical equations to calculate the equilibrium moisture content. The original numerical model was implemented in the software tool PES (Parabolic Equation Solver).
3. Adequateness of an optimization procedure developed to identify model coefficients.
Several bound-constrained optimization methods [2, 5] were used to identify coefficients of the mathematical model by minimizing differences between experimental data and simulation results. The detailed algorithms (simulated annealing, tabu search, genetic algorithm, variable metric algorithm and trust region algorithm) were developed and implemented in the original information system Identix and its subsystem IPS (Inverse Problem Solver) [10]. The algorithms were compared with respect to their performance, and due to high computational complexity of the problem only the trust region algorithm was recommended.
References [1] Y. Chen, E.T. Choong, D.M. Wetzel: A numerical analysis technique to evaluate the moisture-
dependent diffusion coefficient on moisture movement during drying. Wood and Fiber Science, 28(3), 338-345, 1996.
[2] A.R. Conn, N.I.M. Gould, P.L. Toint: Trust-Region Methods. SIAM, Philadelphia, PA, USA 2000.
[3] P. Koc, M. Houška, B. Štok: Computer aide identification of the moisture transport parameters in spruce wood. Holzforschung, 57(5), 533-538, 2003.
[4] J.Y. Liu, W.T. Simpson, S.P. Verrill: An inverse moisture diffusion algorithm for the determination of diffusion coefficient. Drying Technology, 19(8), 1555-1568, 2001.
[5] J. Nocedal, S. Wright: Numerical Optimization, 2nd ed. Springer-Verlag, Berlin, 2006. [6] W. Olek, J. Weres: Effects of the method of identification of the diffusion coefficient on accuracy
of modeling bound water transfer in wood. Transport in Porous Media, 66(1-2), 135-144, 2007. [7] W. Olek, P. Perré, J. Weres: Implementation of a relaxation equilibrium term in the convective
boundary condition for a better representation of the transient bound water diffusion in wood. Wood Science and Technology, DOI 10.1007/s00226-010-0399-2, 2011.
[8] W.T. Simpson, J.Y. Liu: An optimization technique to determine red oak surface and internal moisture transfer coefficients during drying. Wood and Fiber Science, 29(4), 312-318, 1997.
[9] J. Weres, W. Olek: Inverse finite element analysis of technological processes of heat and mass transport in agricultural and forest products. Drying Technology, 23(8), 1737-1750, 2005.
[10] J. Weres, W. Olek, S. Kujawa: Comparison of optimization algorithms for inverse FEA of heat and mass transport in biomaterials. Journal of Theoretical and Applied Mechanics, 47(3), 701-716, 2009.
22
Analysis of External and Internal Mass Transfer Resistance at Steady State Diffusion Experiments on Small Clear Wood Specimens
A. Straže†*, Ž. Gorišek†
†University of Ljubljana, Biotechnical Faculty Rožna dolina, C. VIII/34, SI 1000 Ljubljana Slovenia
Key words: diffusion, external mass transfer, cup method, moisture content, wood.
ABSTRACT
The bound water transport and the related properties have been studied extensively using Fick’s first law of diffusion with data from steady-state experiments, traditionally called the cup method, and with unsteady-state experiments and Fick’s second law of diffusion [1-3].
The credibility of the cup method for determination of the diffusion coefficient (D) is often questioned since it has been experimentally proved that the wood surface moisture content differs significantly from the equilibrium moisture content (EMC) [4]. Therefore correction of the relative humidity (RH) at the surface of the tested specimen was calculated [5]. Additionally, the physical interpretation of the Fick’s first law equation means that moisture content (MC) of wood surface has to be immediately equal to the EMC. The consequence of this assumption is neglecting the so called external resistance of moisture transfer (Rs), which is questionable for small size wood specimens, especially for the longitudinal moisture transport determination.
The water mass flow ( m ) in the diffusion cup method experimentation can be determined in the wood specimen and also at the surface boundary layer:
21 cAS
L
cADm
, where (1)
A represent cross section of the specimen, L = thickness of the specimen, D = diffusion coefficient, S = surface emission coefficient, Δc1 and Δc2 are moisture concentration difference between two surfaces of the specimen and between surface of the specimen and the surroundings, respectively.
Similar to electrical circuits, resistances in moisture transport circuits can also be simply added up in accordance with the way they are connected. In the case of diffusion cup method, there are in addition to basic diffusion resistance of the specimen (RD=L/(D×A)) – also two external, surface resistances (Rs=1/(S×A)), which can either be equal or different. The total mass transfer resistance (Rt) can therefore be written as a function of the thickness of specimen (L) having constant parameter, which represent two external resistances (2/S):
D
L
SARRAR Dst
122
(2)
Steady state diffusion cup experiments where made on spruce wood (Picea abies Mill.) in radial (R), tangential (T) and longitudinal direction (L) at various thicknesses, 2 to 6 mm in radial direction and 4 to 18 mm in longitudinal direction. Specimens were at 20 °C successively exposed to difference in relative humidity of 18% (RH1), 44% (RH2), 65% (RH3), 87% (RH4) and 97% (RH5).
23
Total mass transfer resistance increased with thickness of wood specimen and with reduction of average MC, at all anatomical directions. The share of external mass transfer resistance was the highest at the lowest thickness of specimens, and exponentially decreased at higher thicknesses. Oppositely to total mass transfer resistance, external mass transfer resistance decreased with reduction of average wood MC.
Rt = 178,139.70L + 2,047,519.96R² = 1.00
Rt = 7532.1L + 360901R² = 0.991.0E+05
1.0E+06
1.0E+07
1.0E+08
0 5 10 15 20
(Rt)L[s/m
]
L [mm]
y = 0.8747e‐0.046x
R² = 0.98
y = 0.9854e‐0.017x
R² = 0.99
0.0
0.2
0.4
0.6
0.8
1.0
0 5 10 15 20
(2Rs/ Rt)L[ ]
L [mm]
Rt = 7,762,740.49L + 17,391,446.33R² = 0.99
Rt = 77953L + 389818R² = 0.90
1.0E+05
1.0E+06
1.0E+07
1.0E+08
0 1 2 3 4 5 6 7
(Rt)R[s/m
]
L [mm]
y = 0.794x‐0.583
R² = 0.9842
y = 0.909e‐0.12x
R² = 0.883
0.0
0.2
0.4
0.6
0.8
1.0
0 1 2 3 4 5 6 7
(2Rs/ Rt)R[ ]
L [mm]
Rt = 9,400,198.29L + 21,061,065.36R² = 1.00
Rt = 70538L + 510978R² = 0.97
1.0E+05
1.0E+06
1.0E+07
1.0E+08
0 1 2 3 4 5 6 7
(Rt)T[s/m
]
L [mm]
y = 0.8132x‐0.608
R² = 0.9999
y = 0.9263e‐0.088x
R² = 0.9816
0.0
0.2
0.4
0.6
0.8
1.0
0 1 2 3 4 5 6 7
(2Rs/ Rt)T[ ]
L [mm]
Figure 1 Dependence of total mass transfer resistance (Rt) (left) and share of external mass transfer resistance (2Rs/Rt) (right) on thickness of specimen (L) in longitudinal- (top), radial- (middle) and tangential direction (bottom) ( - low average MC (RH1, RH2); - high average MC (RH4, RH5)).
References 1. Comstock, G.L. Moisture diffusion coefficients in wood as calculated from adsorption, desorption, and steady state data. Forest Products Journal 1963, 13, 97-103. 2. Choong, E.T. Diffusion coefficients of softwoods by steady-state and theoretical methods. Forest Products Journal 1965, 15, 21-27. 3. Olek, W. Analysis of the cup method application for determination of the bound water diffusion coefficient in wood. Folia Forestalia Polonica 2003, 34, 15-25. 4. Shmulsky, R.; Kadir, K.; Erickson, R. Effect of air velocity on surface EMC in the drying of red oak lumber. Forest Products Journal 2002, 52, 78-80. 5. Siau, J.F. Transport processes in wood; Springer-Verlag, Berlin, 1984.
24
Particle Modeling of Dynamic Fracture in Fiber-Based Materials
J. Persson, P. Isaksson*
Division of Applied Mechanics Mid Sweden University Sundsvall, Sweden
Key words: micromechanics, experimental characterization, material behaviour, modeling,
ABSTRACT
We propose a new way to model rapid deformation in fibrous materials. Deformation and fracture in fiber-based materials are very complex processes that depend strongly on the microstructure (the geometrical arrangement of fiber-material, connectivity, thickness, etc.), the mechanical properties of material constituents and the rates of applied loads. Due to its complex nature, the understanding of dynamic deformation processes in network structures is still in its infancy [1]. Rapid stress and deformation is the cause for a multitude of fractures, from paper in paper machines [1] to fabrics and human tissue and bone [2].
To model this rapid deformation we propose a particle-based method, where each fiber is represented by a series of discrete particles. Relevant interactions are included in the model such as longitudinal elastic stiffness, bending stiffness and their corresponding viscous damping. Where two fibers are joined, appropriate force and torsion are added to counteract change of relative position and orientation of the joined fiber segments.
Figure 1: Two crossing fibers and a fiber to fiber joint
Any fiber-network can be represented including initial- and boundary conditions. The system then evolves and at every time step dt, all the usual mechanical properties can be evaluated, (both on a micro and macro level) since the particles are interacting in a well-defined way through Newton’s equations of motion, including all relevant interactions, and possesses unique characteristics that permit a significantly more realistic representation of deforming dynamic network materials than has been reported earlier in literature, this mainly because we can use billions of particles over billions of time steps.
Due to arised stress waves in the net the local strain energy may momentarily be sufficiently high to fracture bonds or fibers and the subsequent evolving deformation is computed by cancelling interactions with the broken elements whereupon the process of fracture accumulation is modeled as a continuous evolution of particle states in time. In this way, the evolution of fracture in the network is characterized and qualitative observations regarding the dynamic fracture process are deduced. Hence, the microscopic fracture nucleation and propagation is described by distinct processes. The nucleated micro fractures are anticipated to generate new “baby” stress waves and interference phenomena may take place. The stress wave driven micro fractures may continue to nucleate until steady-state of the system is reached. A final stage of fracture evolution may occur if the micro fractures coalesce and form a propagating macroscopic crack,
The model is compared to results from micromechanical experiments performed on network materials and numerically judged with Silling’s peridynamical particle model [3,4]. The numerical agreement is excellent and the experimental results strongly support the derived particle model.
25
References [1] Niskanen, K., 2007. Paper Physics. Revised edition. Fapet OY, Helsinki, Finland.
[2] Parkkari, J., Kannus, P., Palvanen, M., Natri, A., Vainio, J., Aho, H., Vuori, I., Järvinen, M., 1999. Majority of hip fractures occur as a result of a fall and impact on the greater trochanter of the femur: a prospective controlled hip fracture study with 206 consecutive patients. Calcified Tissue Int. 65, 183–187.
[3] Silling SA, 2000. Reformulation of elasticity theory for discontinuities and long- range forces. J Mech Phys Solids 48, 175–209.
[4] Silling SA, Askari E., 2005. A meshfree method based on the peridynamic model of solid mechanics, Comput. Struct. 83, 1526–1535.
26
Some Design Principles of Biomimetic Actuators
S. Turcaud†*, L. Guiducci†, P. Fratzl†, Y. J. M. Bréchet ‡, and J. W. C. Dunlop†
† Max Planck Institute of Colloids and Interfaces, Department of Biomaterials,
Potsdam, Germany [email protected]
‡ SIMaP-Grenoble Institute of Technology,
Saint Martin d'Hères, France [email protected]
Key words: actuation, eigenstrain, finite element method, design space
ABSTRACT
Natural hygromorph actuators, such as those found in the pine cone [1] or in the awns of wheat [2][3] and the storksbill, achieve complex motions powered by differential swelling of tissues due to changes in external humidity. The global swelling capacity of their constitutive tissues mostly depends on geometrical considerations, such as the cell shape and the orientations of the stiff cellulose fibres within the soft swellable hemi-cellulose matrix making up the cell wall [4]. A fundamental design parameter is the microfibril angle (MFA), between cellulose fibres of a given cell wall layer and the main axis of the cell, which allows different tissues to controlling the swelling behavior. By combining tissues with different MFAs it is possible to introduce differential swelling which leads to controlled shape changes of the plant organ. This structure-function relationship observed in the biological world, namely the control of swellability (via the MFA) in different regions, can lead to an interesting design principle translatable to the engineering world [5][6][7].
We investigate this problem in the context of continuum mechanics, in which the generic notion of eigenstrain [8] enables us to look at the effect of such nonelastic strain distributions in elastic bodies in a more general manner. Indeed, eigenstrains can be created by humidity as well as temperature, magnetic, chemical and electrical fields, if coupled with the right material properties. One simple way of looking at eigenstrain distributions is to achieve differential swelling inside a structure made of two elastic phases with different expansion properties under a uniform expansion field. The resultant motion depends on the geometric distribution of the two phases and the cross section of the structure. In this contribution we use the finite element method to explore how the geometry and symmetry of the initial structure (containing swellable and non-swellable elements) controls the range of motion available [9]. Figure 1, shows several examples from [9], in which the actuation of biphasic extrudable beams is modeled. We demonstrate that actual actuation patterns, while restricted by symmetry considerations, are also dependent on other geometrical parameters such as the ratio of free outer surface to inner volume. For example the introduction of a mirror symmetry (Fig. 1a) leads to bending, rotation symmetry for example leads to twisting only when the outer boundary is sufficiently open and flexible (Figs. 1b,c). The final goal of this work is to develop a set of design rules for developing actuators with a given motion, which could find application in micromechanical systems as well as in further understanding the mechanisms behind actuation in plant tissues.
27
Figure 1: Actuation patterns of biphasic extrudable actuators for different cross sections (from [9])
References [1] C. Dawson, J.F.V. Vincent, A.-M. Rocca: How pine cones open. Nature 390(6661) (1997), 668-
668. [2] R. Elbaum, S. Gorb, P. Fratzl: Structures in the cell wall that enable hygroscopic movement of
wheat awns. Journal of Structural Biology 164(1) (2008), 101-107.
[3] R. Elbaum, L. Zaltzman, I. Burgert, P. Fratzl: The role of wheat awns in the seed dispersal unit. Science 316(5826) (2007), 884-886.
[4] I. Burgert, M. Eder, N. Gierlinger, P. Fratzl: Tensile and compressive stresses in tracheids are induced by swelling based on geometrical constraints of the wood cell. Planta 226(4) (2007), 981-987.
[5] J.W.C. Dunlop, Y.J.M. Brechet: Architectured Structural Materials: A Parallel Between Nature and Engineering. Architectured Multifunctional Materials 1188(2009) 15-25 241.
[6] I. Burgert, P. Fratzl: Actuation systems in plants as prototypes for bioinspired devices. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 367(1893) (2009): 1541-1557.
[7] E. Reyssat, L. Mahadevan: Hygromorphs: from pine cones to biomimetic bilayers. Journal of The Royal Society Interface, (2009).
[8] T. Mura: Micromechanics of Defects in Solids. Kluwer Academics, 1987. [9] S. Turcaud, L. Guiducci, P. Fratzl, Y.J.M. Brechet, J.W.C: Dunlop: An excursion into the design
space of biomimetic architectured biphasic actuators. IJMR, Accepted.
28
Effects of Fibre Agglomeration on Strength of Wood-Fibre Composites
Thomas Joffre *1, Kristofer Gamstedt 1, Arttu Miettinen 2 and Erik Wernersson3
1 Uppsala University, Division of applied mechanics
Ångströmlaboratoriet Box 524 751 20 Uppsala, Sweden [email protected]
2 University of Jyväskylä, Department of Physics P.O. Box 35 (YFL) FI-40014
3 Swedish University of Agricultural Sciences Centre for Image Analysis Box 337 SE-751 05 Uppsala
Key words: micromechanics, wood fibre composite, experimental characterization, agglomerations
ABSTRACT
The micromechanical models used to predict strength of composites, e.g. Fukuda-Chou model [1], have their origin in elastic micromechanical models based solely on the elastic properties of the constituents, fibre orientation and fibre content. In contrast, strength of heterogeneous brittle materials is also controlled by the distribution of defects, since failure is initiated locally at the weakest link of the material. Thus the idea of this project is to use the weaknesses and flaws in the material as a starting point for the micromechanical model, aiming for improved predictive strength models accounting for fibre dispersion.
The Achilles heel of the cellulose pulp fibre composites is agglomerations of the fibres. The fibres aggregate or are not adequately separated during the manufacturing process which in turn generate a composite filled with agglomerated fibres. With microcomputed tomography, we can characterize size and orientation of these fibre bundles (mm length scale) as in Figure 1. Experience tells us that agglomerations are not completely wetted by the matrix polymer, as in Figure 2 and because of that the agglomeration-matrix interface is very likely to debond and the agglomerations will act as cavities inside the material [2].
Two models were used in this study to investigate stress fields in heterogeneous materials, stress concentration factor (SCF) and stress intensity factor (SIF). The SCF caused by triaxial ellipsoidal inclusions was solved by the equivalent inclusion method [3]. The SCF does not consider the size of the inclusion but only its shape. To employ a length scale parameter the SIF was evaluated for slanted ellipsoidal inclusion.
The experiment shows the correlation between SIF of the critical agglomeration and ultimate tensile strength (UTS): big agglomerations with high SIF reduce the UTS. SCF of the inclusion does not control the UTS. One reason could be the size of the high stressed volume is more important than the stress in the maximum point.
29
Fig. 1 Agglomerations in a biocomposite Fig. 2 Agglomeration with voids at matrix interface
References
[1] Fukuda, H. A probabilistic theory of the strength of short-fibre composites with variable fibre length and orientation. Journal of materials science. 1982, Vol. 17, 4. [2] Kohler, Andreas. Agglomerations in Cellulose Fibre Reinforced Plastic Composite Stockholm KTH : s.n., 2010. [3] Mura, T. Micromechanics of defects in solids. Evanston, IL, U.S.A.: Martinus Nijhoff Publishers, 1987.
30
Strain Analysis in Dried Green Wood: Experimentation and Modeling Approaches
Moutou Pitti R. ‡, Dubois F.†*, and Sauvat N. †
†University of Limoges
Laboratoire GEMH, Centre Universitaire Génie Civil, 19300, Egletons, France [email protected]; [email protected]
‡Blaise Pascal University
Clermont Université, Université Blaise Pascal, LaMI EA 3867, BP 206, 63000 Clermont Ferrand, France
Key words: green wood drying, experimental characterization, finite element method
ABSTRACT
The natural or artificial shrinkage due to drying is commonly responsible of crack appears in wood peaces [1]. These defects are even more marked on the logs pieces cut up and stored in the open air during a long time. In this fact, it is essential to understand the different processes that lead to these phenomena in the green woods.
In the literature, the deformations and the evolution of drying-induced stresses in wood are studied based on a finite element model which takes into account the alteration of mechanical properties of wood during drying phase [2]. Also, several authors have presented a model of drying that permits evaluation of moisture content distribution in dried wood during the drying rate periods with the moisture content at the body surface reaches the fibre saturation point (FSP) [2]. In this last work, the acoustic emission method (AE) is used for monitoring the state of stress in dried wood.
Support cameras
Green wood Slice
Scales
Cameras
L = 150 mm
Hc = 150mm
Woodscrew
Srtresswood
Normal wood
Figure 1: Experimental device [3]
31
In this work, the radial and tangential strains due to the natural drying of a green wood slice are studied by analytical, experimental and numerical methods [3]. The analytical method applied is based on a mathematical model coming from cylindrical strain calculations [2,4] integrating the orthotropy in the swelling-shrinkage tensor. The finite element calculation is limited, in this paper, at an elastic behavior integrating a mechano-sorptive effect. Moreover, the model assumes a plane stress configuration and an homogeneity of the moisture content. The experimental device is based on the mark tracking method composed of an acquisition system date recording the displacement of target posted on the wood slice during the drying phase, Figure 1. Simultaneously, the sample is placed on an electronically balance providing the weight measure versus time.
strain radial
(mm)center todistance
strain tengential
(mm)center todistance
(b)
(a) Localisation of crack initiation
Figure 2: (a) Evolution of tangential and radial strain versus the distance to the center pf slice; (b) Localisation of crack initiation by finite element method during drying
In Figure 2 (a), it posted the evolution of tangential and radial strains versus the distance to the center of the slice for different moisture content. Radial strains are computed by defining local orthotropic referential. During the evolution of moisture content between the FSP level and its critical value inducing the crack initiation (w=11,48%) the numerical and experimental results illustrate a very good agreement. In the same time, the finite element model allows the localization of the crack initiation during drying process, Figure 2 (b).
References [1] Kowalski S.J, W. Molinski, G. Musielak: The identification of fracture in dried wood based on
theoretical modeling and acoustic emission. Wood Sci Technol, 38 (2004) 35–52. [2] S.J. Kowalski, A. Smoczkiewicz-Wojciechowska: Stresses in dried wood. Modeling and
experimentation. Transp Porous Med, 66 (2007), 145-158. [3] R. Moutou Pitti: Deformations lors du séchage d’une rondelle de bois vert: modélisation et
expérimentation, Egletons 2005. [4] I.D. Cave: A theory of the shrinkage of wood. Wood Sci Technol, 6 (1972), 284-292.
32
Analyzing Size, Form and Distribution of Particles for WPC
Andreas Krause†*, Marcus Müller and Kim-Christian Krause†
†Department Wood Biology and Wood Products, Georg-August-University Göttingen
Büsgenweg 4, D-37077 Göttingen [email protected]
Key words: particle analytics, WPC, size distribution, form distribution, fiber-matrix-theory
ABSTRACT
Wood plastic composites (WPC) are a composite material consisting of a thermoplastic matrix and wood particles [1]. In dependence of the wooden particles the wood is mainly considered a filler or fiber. Some authors reported a reinforcement effect and consider wood particles as fiber, whereas others showed a reduction in strength (mainly in impact bending), which is typical for fillers [2-4]. To distinguish between the functions fiber or filler and its effect on the composite, knowledge about size, form and distribution of the particles is essential. An image analysis method measuring particles at dispersion in air, is applied to investigate wood particles for WPC. Main benefit of this system is the high number of measured particles in combination with detailed information about size and form. Form is calculated for each particle individually. Particles used for WPC (< 2 mm) were measured and evaluated.
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
Acc
umu
late
d fr
act
ion
of
par
ticle
, a
sse
sse
d b
y le
ng
th [
%]
0 200 400 600 800 1000 1200 1400 1600 1800 2000Length of particle [µm]
Figure 1: Accumulated fraction of particle length, assessed by length.
Results for spruce particles (n=339 136) show that the particle length and diameter (not shown) have a wide distribution (Figure 1), however the aspect ratio (Table 1) is somewhat consistent. The mean fiber length is 129 µm at an aspect ration of 4.5. Using the theory of reinforced duroplastics, it is possible to calculate a critical fiber length. The critical fiber length gives a maximum active fiber length in the composite. Longer fibers will not cause a higher reinforcement, whereas shorter fibers lead to a reduced reinforcement effect [5]. Since wood particles have a wide distribution in diameter, the formula is changed to calculate a critical
33
aspect ration (1). Tension strength of fiber was assumed as 800 N/mm2 [6] and shear strength of polymer as 40 N/mm2 [7]. The resulting critical aspect ratio (ARc) is 10. This value is higher than the mean aspect ratio of the particles, but the longest 10% proportion of particles are in the same range. The calculation is estimated excluding the following parameters: Risk of low interfacial adhesion between particle and matrix, random particle orientation in matrix, anisotropic strength of particles. Tensile strength of particle differs from findings reported by Eder et al. [6].
Table 1: Dimensions and aspect ratio of particles for smallest 10% fraction, mean value (50%) and largest 10% fraction (90%)
Accumulated fraction
Length [µm]
Width [µm]
Aspect ratio
10% 26 1.8 50% 129 4.5 90% 569 9.5
B
fB
f
cc d
lAR
*2
(1)
• ARc = critical aspect ratio • lc = critical fiber length • σfB = tensile strength of fiber • df = fiber diameter • τB = shear strength of matrix
The presented method of image analysis provides detailed information about particle size and form of wood particles for WPC. From these results it can be concluded, that using wood particles in thermoplastic matrixes potentially causes certain reinforcement. The reinforcement potential is relatively low because of the low aspect ratio and strength of particles compared to other fibers such as glass or carbon fiber. Optimizing aspect ratio, particle orientation and interfacial adhesion can lead to high mechanical properties in WPC.
References 1. Klyosov, A.A., Wood-plastic composites. 2007, Hoboken, NJ: Wiley. XXVII, 698 S. 2. Guo, G., et al., Influence of wood fiber size on extrusion foaming of wood fiber/HDPE
composites. Journal of Applied Polymer Science, 2008. 107(6): p. 3505-3511. 3. Migneault, S., et al., Effect of fiber length on processing and properties of extruded wood-
fiber/HDPE composites. Journal of Applied Polymer Science, 2008. 110(2): p. 1085-1092. 4. Mirbagheri, J., et al., Tensile properties of wood flour/kenaf fiber polypropylene hybrid
composites. Journal of Applied Polymer Science, 2007. 105(5): p. 3054-3059. 5. Ehrenstein, G., Faserverbundkunststoffe - Werkstoff Verarbeitung Eigenschaften. 2. Auflage.
2006, München: Hanser Verlag. 6. Eder, M., et al., The effect of (induced) dislocations on the tensile properties of individual
Norway spruce fibres. Holzforschung, 2007. 62(1): p. 77-81. 7. Hellerich, W., G. Harsch, and E. Baur, Werkstoff-Führer Kunststoffe. Eigenschaften,
Prüfungen, Kennwerte. 10. Aufl. ed. 2010, München: Hanser. XV, 588 S.
34
Optical Measurement of Local Strains Development in Finger-Jointed Wood Subjected to Static and Sustained Loads
Boris Clouet1, Lech Muszynski2, and Régis Pommier3
1I2M – GCE
Université Bordeaux 1 – Talence, 33405 – FRANCE [email protected]
2Dept of Wood Science & Engineering
Oregon State University – Corvallis, Oregon 97331 – U.S.A [email protected]
2I2M – GCE
Université Bordeaux 1 – Talence, 33405 – FRANCE [email protected]
Key words: green wood adhesion, Timber structure, Digital Image Correlation
ABSTRACT
In this study the full field optical measurement techniques based on the digital image correlation (DIC) were applied to investigate the local strains development in wet formed finger joints in French Maritime Pine logs. Wood is a natural composite, characterized by fairly complex multi-level anisotropic, heterogeneous cellular structure, and high affinity to water. To various extents this nature is inherited by all wood-based composites. These materials when subjected to loads often reveal non-uniform deformation and strain patterns, and complex failure modes. About 50% of wood products present on the world markets today are manufactured as adhesive bonded or composites finished products with adhesive joints. Adhesive bonding is often used in order to obtain products of desired dimensions and geometries. It also provides an efficient way of utilizing low quality wood in value added products. French Maritime Pine is an example of relatively abundant wood, which despite of favorable mechanical properties of clear material is generally considered unfit for structural applications due to presence of large number of knots and other undesirable features. One way of utilizing this secondary resource, which otherwise would become waste or fuel, is by removing the undesirable zones and re-constituting the relatively homogeneous clear wood sections into longer solid members by adhesive bonding. However cross-grained sections of wood do not bond easily. Currently finger jointing is considered the most efficient way of creating durable structural grade end joints in wood. Finger joints created in carefully conditioned dry wood are capable of retaining of up to 90% of the original tensile strength of the clear wood. However the micromechanics of finger joints in wood is not fully understood. Of particular interest is the load transfer at and around the finger tips, where the joint failure is typically initiated [1]. New promising technology of creating finger joints in wet wood developed at Laboratory of Wood Rheology in Bordeaux is expected to reduce the effect of strain concentrations around the finger tips and thus improve the overall strength of the bond [2]. In this study finger joints created in wet Maritime Pine logs according to European Standard EN385 using a new one-component polyurethane adhesive formula are investigated. The general approach is to measure development of strain concentrations in wet formed finger joints subjected to static and sustained loads. Small specimens of finger jointed sections (cross sections of 18 mm x 5 mm) are acquired from larger joint samples manufactured in wet Maritime Pine logs according to European
35
Standard EN385 using a new one-component polyurethane adhesive formula. The specimens were then divided into two random groups. The first group was subjected to benchmark static tensile tests to failure. The second group has been subjected to a sustained load at 10% of the ultimate tensile load level (creep tests), after which the residual tensile strength in the joints will be determined in static tensile tests. The static tensile tests were performed in a regular universal testing machine. The creep tests are performed in a special static loading frame that allows testing four specimens at once in a way, which allows optical measurement of the deformations. Tests are performed in a controlled climate room at 23° C and 65% Relative humidity. In addition reference static tensile strength will be determined on specimens of clear Maritime Pine wood. Limited reference static and creep tests were also performed on traditional dry-formed finger joint specimens created in the same material. The morphology of the joints is being examined in high resolution x-ray computed tomography (CT) scanner. This will allow morphology based modeling of the joint in the further stage of the project. In tests with finger joints all deformations are measured with a full field optical measurement system VIC3D (by Correlated Solutions). Description of a 3-D measurement principles, calibration procedures, and sample applications may be found in [3, 4]. Development of local strain concentrations in, and around the adhesive bond was investigated. Results reveal severe strain concentrations indicating poor load transfer at the finger tips. Accuracy of the measurement is evaluated from initial images of undeformed scene.
Figure 1: Specimen of a green formed finger joint and sample strain concetration maps: eyy, exx and exy REFERENCES [1] J. Konnerth, A. Valla, W. Gindl and U. Müller, “Measurement of strain distribution in timber finger joints”, Wood Sci Technol., 40 (8), 631-636, (2006). [2] R. Pommier and G. Elbez, “Finger-jointing green softwood: Evaluation of the interaction between polyurethane adhesive and wood”, Wood Material Science and Engineering. 1(3), 127-137, (2006). [3] T. Schmidt, J. Tyson and K. Galanulis, “Full-Field Dynamic Displacement and Strain Measurement Using Advanced 3-D Image Correlation Photogrammetry”, Part I. Experimental Techniques, 27(3), 47-50, (2002). [4] T. Schmidt, J. Tyson and K. Galanulis, “Full-Field Dynamic Displacement and Strain Measurement Using Advanced 3-D Image Correlation Photogrammetry”, Part II. Experimental Techniques, 27(4), 44-47, (2002).
36
Structural Characterization of Different Hardwoods Using Infrared Spectroscopy
Carmen-Mihaela Popescu†*, Maria-Cristina Popescu†
†Romanian Academy, “Petru Poni” Institute of Macromolecular Chemistry, Physical Chemistry of
Polymers Laboratory 41A Gr. Ghica Voda Alley, Ro.700487, IASI, Romania
[email protected], [email protected]
Key words: wood, structural characterization, infrared spectroscopy
ABSTRACT
Wood is a natural composite consisting of cellulose, hemicelluloses and lignin, along with smaller proportions of polysaccharides, fats, water, etc. [1]. Cellulose is a linear polymer of glucose units which can form intra- and interchain bonds forming a crystalline macromolecule. It is relatively rigid with a high degree of dimensional stability in the direction of the cellulose fibers. Hemicelluloses have a more irregular structure with side groups, substituent groups and sugars present along the length of the chain. Lignin is a randomised condensed polymer with many aromatic groups and is much more hydrophobic than cellulose or hemicelluloses [2]. The ability to identify a particular wood species has its benefits in a number of situations.
The aim of this study is to find the most convenient procedure to make an easy differentiation between various kinds of wood. The wood samples used were: poplar (Populus tremula), lime (Tillia cordata), sweet cherry (Prunus avium), hornbeam (Carpinus betulus), beech (Fagus sylvatica), oak (Quercus robur). FT-IR and 2D IR correlation spectroscopy are very useful techniques for analyzing the structure of wood components and the chemical changes in wood induced by different factors.
Figure 1: FT-IR spectra hardwood samples (PT – Populus tremula, TC – Tillia cordata, PA – Prunus avium, FS – Fagus sylvatica, QR – Quercus robur, CB – Carpinus betulus)
37
The FT-IR spectra of different wood species are shown in Figure 1. The hydroxyl stretching region (3800–2700 cm-1 region) of the spectrum is particularly useful for elucidating hydrogen-bonding patterns because, in favorable cases, each distinct hydroxyl group gives a single stretching band at a frequency that decreases with an increasing strength of the hydrogen-bonding. These H-bonds are considered to be responsible for various properties of native cellulose, lignin and of course wood itself. Thus, a mixture of intermolecular and intramolecular hydrogen bonds is considered to cause the broadening of the OH band in the IR spectra.
The spectra of wood samples are very complex in the ‘‘fingerprint’’ region (1900– 800 cm-1). Here we can find bands assigned to different stretching vibrations of the groups from the main wood components. Despite many similarities across all spectra, analysis of peak ratios, which reflect relative shifts in chemical wood composition, revealed site-specific features.
By FT-IR spectroscopy, was observed that the ratio values of lignin/carbohydrate IR bands for wood decreases with increasing the average wood density, showing a decrease in lignin content. Also, the calculated values of lignin percentage from the FT-IR spectra are in very good correlation with the values from literature. 2D correlation IR spectroscopy was able to evidence differences which were not obtained from normal IR spectra.
References [1] S. Dammström, L. Salmén, P. Gatenholm: BioResources, 4 (2009), 3 [2] M.A. Hubbe, L.A. Lucia: Biomaterials 2 (2007), 534.
38
Estimation of Stiffness of Microfibrillated Cellulose Based on Nanostructure Characterized by Transmission Electron Microscopy
G. Josefsson*1, E. K. Gamstedt1 and B. S. Tanem2
1 Uppsala University, Angstrom Laboratory, Division of applied mechanics 2 SINTEF Materials and Chemistry, Trondheim, Norway
The cellulose microfibrils (MFC) in the wood cell wall contribute to the mechanical properties of the wood fibres, and are today the focus of extensive research due to a combination of improved production methodology and foreseen application areas. Basic knowledge of the structure and properties of the crystalline- and amorphous domains in MFC is essential to understand and be able to predict the properties of MFC-based materials, as well as to understand the properties of the wood cell wall. The present work combines structural information of MFC from high resolution transmission electron microscopy (HRTEM) with micromechanical modelling using a Mori-Tanaka scheme. The elastic properties, predicted from the nanostructure characterized by HRTEM and elastic modelling is compared to and discussed in relation to literature data from nanoscale three point bending tests performed by atomic force microscopy. The microscopy shows that the reinforcing crystalline domains have considerably smaller axial dimensions in industrial MFC, than what is anticipated in the native state in the cell-wall. Simulations show that crystallite aspect ratio is a key parameter which controls the axial stiffness. Strategies for milder fibrillation routes should therefore be considered, where the high native crystallite aspect ratio can be retained to a larger extent.
(a) (b)
Figure: (a) Predicted elastic modulus for a crystalline volume fraction of 0.77, and (b) high‐
resolution transmission electron micrograph of MFC.
0
20
40
60
80
100
120
0 5 10 15 20 25 30 35
Young'smodulus, EMFC(GPa)
Aspect ratio, a
Rule of mixtures asymptote
a = 1
39
40
The Dependency of Shear Zone Length on the Shear Strength Profiles in Paperboard
Hui Huang
†*, Mikael Nygårds
†
†BiMaC Innovation,
KTH Solid Mechanics,
SE-100 44 Stockholm,
Sweden
Key words: out-of-plane, shear test, tilted double notched, lamination, paperboard
ABSTRACT
Out-of-plane properties are the key factors for the mechanics behavior materials, especially for
converting operations, such as creasing and folding. However, traditional shear testing method has its
limitations. To improve the shear test technique, a notched shear test (NST) was proposed by Nygårds
et al. [1, 2]. For NST, two grooves are ground on the paper material, one on each side. The paper
material is also strengthened by plastic foil which is gently laminated on the two sides of notched
sample to improve shear test performance. In this study, the NST was modified by the use of titled
notches. This enables us to measure shear strength profiles efficiently. Besides, the local character of
the shear strength profiles was also investigated by a study where the shear zone length L is varied.
Figure 1 and Figure 2 show the paper material sample from in-plane direction and thickness direction.
Paper material sample was cut into strips with width w= 15.0 mm after grinding and lamination, as
illustrated by the lines in Figure 1. Then, the shear test was done by using a tensile test machine
(Lorentzen & Wettre Allwetron TH1). During the test, tensile force with corresponding displacement
was measured. The shear strength τ was calculated based on the tested force by equation 1,
wL
F
, (1)
where F is the tensile force, w is the width of the test sample and L is the shear zone length (as illustrated in
Figure 2).
Figure 1: Two sides of after-ground paper sample
Figure 2: Paper sample sandwich structure demonstration
41
The experiments were done in both the machine direction (MD) test and cross machine direction
(CD) test, i.e. the grooves ran in CD for the MD tests, in MD for the CD tests. Five sheets for each
length L = 1.5, 2.5, 5.0, 10.0, 15.0, 20.0 and 25.0 mm were tested. Figure 3 exhibits the box plot of
shear stress with different shear zone length L. Figure 4 shows the microscopic picture of shear
failure comparison between the sample of long shear zone test and short shear zone test.
Figure 3: Box plots of shear stress with different shear zone length for (a) MD tests, and (b) CD tests
Figure 4: The microscopic picture of 25.0 mm sample (above) and 2.5 mm sample (down)
According to the results, the shear strength measurements were size dependent. For all measurements
with different shear zone length, bonds were broken and the fibre network was deformed. The reason
different strengths were measured was due to the fact that different mechanisms were activated, e.g.
fibre bridging and localization of the test. In different applications, different kind of out-of-plane
strength data is desired. In applications where delamination is of concern, measurements with large L
are important, since delamination failure will occur along the weakest point, and also can split a paper
sheet. On the other hand, processes that rely on local damage, such as creasing and folding, local
failure at certain positions are desired. Hence, it is necessary to measure local shear strengths with
respect to both shear length as well as position in the thickness direction
References [1] M. Nygårds, C. Fellers and S. Östlund. Development of the notched shear test. Adv. In Pulp and
Paper Res. Oxford. 887-898, 2009.
[2] M. Nygårds, J. Malnory. Measuring the out-of-plane shear strength profiles in different paper
qualities. Nord. Pulp Paper Res. J. In press, 2010.
42
The Response of Growth Ring in Wood to Microclimate Change
Leszek Krzemień, Michał Łukomski
† Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences
ul Niezapominajek 8 [email protected]
Key words: heritage science, panel paintings, growth rings, structural response, relative humidity;
ABSTRACT
The mechanical properties of wood vary spatially on the growth rings scale. The inhomogeneous response of this material to external factors leads to a complex deformation of wood containing objects. It is particularly important for art objects exposed to temperature and relative humidity variations as deformation can result in damage of both wood structure and design layer in case of panel painting or polychromy. The position and size of the damage on the surface of painted wood is strongly correlated with the growth ring structure of the wooden support. Therefore the knowledge of the local response of wood to climatic variations is necessary to establish the safe range of humidity fluctuations in the vicinity of panel paintings.
In order to measure the response of wood on the growth rings scale to both climatic change and external load the Digital Speckle Pattern Interferomentry (DSPI) was utilized. The strain field generated while the specimen was subjected to external factors was reconstructed from the displacement map obtained by DSPI. Thanks to high precision and spatial resolution of the method applied the strain of early and late wood was determined separately in the same experiment. Systematic measurements performed on the lime wood samples show that maximal and minimal local strains have the same value in mechanical and humidity tests. In both cases the maximal value of strain is 25% above the average displacement.
Further tests on different wood species important for the cultural heritage preservation are planned.
Acknowledgements
The research was supported by a grant from the Polish Ministry of Science and Higher Education supporting activities of COST Action IE0601 Wood science for conservation of cultural heritage. The authors would like to thank Henk Schellen and Eric Wijen from University of Technology, Eithoven for . their invaluable help.
43
44
Swelling gel-filled honeycombs, a model for the anisotropic actuation in the iceplant seed capsule
Lorenzo Guiducci†, Khashayar Razghandi†*, Lucas Bertinetti, Matthew J. Harrington, Ingo
Burgert, Peter Fratzl and John W. C. Dunlop‡
† Max Planck Institute of Colloids and Interfaces, Department of Biomaterials
Science Park Golm, Potsdam, Germany. [email protected]
Key words: swelling, anisotropy, cellular material, biphasic, material behaviour
ABSTRACT
The plant kingdom provides many examples of systems showing actuation capabilities in the absence of metabolic energy, such as the pine cone [1] and the wheat awn [2]. Such systems may provide rich landscape for the bioinspired design of artificial actuators, as complex actuation, due to hygroscopic swelling, is controlled by the architectural arrangement of the different swellable tissues. Among these systems we consider the seed capsule of the ice-plant Delosperma nakurense, which opens its valves upon wetting to allow for seed dispersal [3]. The valves are opened by a ridge-like keel consisting of an anisotropic honeycomb of cells filled with a swellable matrix reminiscent of the tension wood G-layer. In this contribution we present a mechanical model to describe the anisotropic swelling of the keel-cells as a function of relative humidity.
We model the tissue of the keels as a two-dimensional infinite cellular structure (Fig. 1). The morphology of the cellular solid can be described as a diamond honeycomb, with four inclined walls joining in a rigid node. Main geometrical features of the honeycomb (angle, wall length and thickness) are derived from ESEM cross-section images of the keels tissue in the dry state. The material of the walls is considered to be isotropic and linear elastic with a Young’s modulus of 10 GPa. In the humidity range (RH>95%) in which the unfolding process happens, the G-layer is highly swollen; therefore we “neglect” it as a structural component and model it as a hydrostatic pressure acting against the cell (Fig. 2). The cell walls are considered as rigidly connected bars and withstand the deformation mainly under bending meaning shear can be neglected [4]. We treat the swelling of such a polymer in terms of the well known Flory theory [5], which provide an explanation for swelling as a process driven by an entropic energy gain. Under isothermal and quasi-static conditions, this energy gain is translated into mechanical work done by the G-layer to deform the honeycomb walls. The model is able to reproduce the high anisotropy of the swelling eigenstrain observed in the biological system and gives good estimates for the longitudinal strains. The model however predicts small negative strains in the transverse direction, that are not observed experimentally, suggesting that swelling of the cell walls themselves needs to be included in further versions of the model.
45
Figure 1. Schematic of the honeycomb in the undeformed (dry) state.
Figure 2. Schematic of the honeycomb in the deformed (wet) state upon swelling of the G-layer
References [1] Dawson, C., Vincent, J. and Rocca, A.-M. How pine cones open. Nature 390, (1997).668-668. [2] Elbaum, R., Zaltzman, L., Burgert, I. and Fratzl, P. The Role of Wheat Awns in the Seed
Dispersal Unit. Science 316, (2007) 884-886. [3] Harrington, M. Razghandi, K., Ditsch, F., Guiducci, L., Rueggeberg, M., Dunlop, J., Fratzl, P.,
Neinhuis, C. and Burgert I., Nature's actuated origami: hydro-responsive unfolding of ice plant seed capsules, under review (2011).
[4] Gibson, L. and Ashby, M., Cellular Solids Structure and Properties, (1997) Cambridge University Press.
[5] Flory, Principles of Polymer Chemistry, Cornell University Press, 1992.
46
Thermal Behaviors of Some Hardwood and Softwood Species Evaluated by Thermogravimetry
Maria-Cristina Popescu†*, Carmen-Mihaela Popescu †
†Romanian Academy, “Petru Poni” Institute of Macromolecular Chemistry, Physical Chemistry of
Polymers Laboratory 41A Gr. Ghica Voda Alley, Ro.700487, IASI, Romania
[email protected], [email protected]
Key words: wood, structural characterization, infrared spectroscopy
ABSTRACT
Each of three major components (cellulose, lignin and hemicelluloses) of the wood has its own characteristic properties with respect to thermal degradation, which are based in polymer composition. The three-dimensional nature and microstructure of wood are variables that play important roles in terms of their effects on combustion behavior. Thus, the individual chemical components of wood behave differently if they are isolated or if they are intimately combined within each single cell of the wood structure.
During the thermal decomposition process of wood, small molecules, often flammable or toxic, are eliminated, and eventually a charred mass is left. Noncombustible products, such as carbon dioxide, traces of inorganic compounds, and water vapor are produced between 30 and 150 oC. At about 170 oC, some components begin to break down chemically; low temperature degradation at low rate occurs in lignin and hemicelluloses; the hemicelluloses are lost in 190–380 oC temperature interval, while lignins decomposition starts at very low temperature of only 170 oC and mass loss is low but it occurs on a very wide interval with large maxima in DTG curve extended up to more than 600 oC. Cellulose decomposes in a narrow 280–400 oC temperature range. This means that in complex material as wood, the thermogravimetric processes of all components overlap, the predominant being that of cellulose which has a high rate of mass loss in its decomposition interval [1, 2].
Figure 1 shows the results of thermogravimetric tests performed on the different wood species. Water loss is observed below 140 oC, and the further thermal degradation takes place as a two-step process. In particular, it is seen that the water desorption percent is different for every wood species.
For the first step, the temperature corresponding to the maximum mass loss rate varies for each wood species between 62 and 73 oC. Also the mass loss for this process varies between 6.3 and 8.8 wt%. This may be explained by the devolatilization of different low molecular compounds from wood samples.
Decomposition is a complex process both because the studied samples have many components and each of them decompose in several stages and also the thermal behavior is determined by operational conditions especially heating rate, final temperature of heating, heat transfer, degradation/decomposition occurs by competitive and/or consecutive reactions. For the hardwood samples, the temperatures corresponding to the maximum decomposition rate (Tm) decrease linearly with increasing the wood density, while the onset temperatures (Ti) and to the end of the stage (Tf) are almost the same for all studied wood species. The differences appear for the fir wood sample; in this case the temperature corresponding to the maximum decomposition rate is the lowest from the wood series studied. This may be explained by the different structure of the softwood versus
47
hardwood samples. The mass loss occurring during the decomposition process shows an exponential decrease with increasing the wood density for hardwood samples.
Figure 1: DTG curves for different wood samples (PT – Populus tremula, TC – Tillia cordata, PA – Prunus avium, FS – Fagus sylvatica, QR – Quercus robur, CB – Carpinus betulus)
Because the temperature intervals of hemicelluloses, cellulose and lignin decomposition partially overlap each other; the hemicelluloses and/or amorphous cellulose decomposition step usually appears as a more or less pronounced shoulder instead of a well defined peak. This shoulder is better evidenced for the sweet cherry, hornbeam and oak wood.
The mass loss occurring during the decomposition process shows an exponential decrease, while the residual mass increases with increasing the wood density for hardwood samples. The thermal parameters are particular for each kind of wood.
References [1] L. Helsen, E.J. Van den Bulck, Journal of Analitical & Applied Pyrolysis 53 (2000), 51. [2] J.J.M. Orfao, F.J.A. Antunes, J.L. Figueiredo, Fuel 78 (1999) 349.
48
Fibre-Fibre Bond Strength – Experimental and Numerical Evaluation of Normal and Shear Loading Components
M. S. Magnusson†* and S. Östlund†
BiMaC Innovation
Department of Solid Mechanics KTH, Royal Institute of Technology
SE-100 44 Stockholm, Sweden [email protected] and [email protected]
Key words: fibre-fibre bond strength, micromechanics, pulp fibre, experimental characterization
ABSTRACT
In order to tailor the properties of paper based materials, the deformation and damage mechanism in
the fibre-fibre bonds must be understood and especially how biochemical and/or mechanical
modifications of fibre wall and fibre surface influence the properties at the microscopic level. This
paper reports on the development of a method for making, testing and evaluation of fibre-fibre cross
test pieces.
Direct measurements of fibre-fibre bond strengths were first reported by McIntosh et. al. [1] and
Mayhood [2], independently, in 1962. Several studies ([3-6]) has since then been made to evaluate
bond shear strengths from dried fibres, shives or cellophane film test pieces, typically in
perpendicular cross or lap joint configurations. In this paper, kraft pulp fibre-fibre crosses were
prepared by press-drying fibres suspended in droplets of depolarized water between Teflon covered
steel plates. The fibre-fibre crosses were tested in a tensile stage using a miniature load cell of
capacity 0.5 N. In the subsequent evaluation, the load-deformation responses of the fibre-fibre crosses
(Figure 1) together with information of the particular fibre-fibre cross geometry was used to estimate
the normal and shear tractions in the bonded area.
0 0.02 0.04 0.06 0.08 0.1 0.120
5
10
15
20
25Structural Response
Displacement [mm]
Forc
e [m
N]
Experimental structural response
FEM structural response
Figure 1: Force-displacement curve for three fibre-fibre crosses experiencing three different modes of failure.
The experimental data (blue) is compared to data from FEM calculations (green) as well as the point used for
calibration of the numerical results (red circle).
49
Here, variations in fibre-fibre cross geometry, such as natural curvature, position of the bond and fibre
lengths has been taken into account by using microscopic image analysis to model each test piece
with 8-node continuum linear brick elements. The yield stress of the fibres in the study was
significantly higher than the shear strengths of the bonds; hence the deformations in the fibres could
to a good approximation be considered as elastic until bond failure. A relatively simple finite element
model was shown to model the experimental load-displacement curves as shown in Figure 1, when
calibrating the model data to the point in the experimental load-displacement curves where a sudden
drop in stiffness occurred.
The deformations of the fibres give rise to different combinations of normal and shear loading in the
bonded region. A first approximation of the normal and shear traction distributions can be obtained
from the FEM-analysis (Figure 2). These can then be used to evaluate the influence of fibre wall and
fibre surface modifications on the strength properties of the bond.
Figure 2: Interface shear (top) and normal (bottom) tractions in the bonded region from finite element
simulation, with high stresses depicted in red. The pulled fibre is opaque to visualize the interface traction
distributions.
References [1] D. C. McIntosh: Tensile and Bonding Strengths of Loblolly Pine Kraft Fibers Cooked to Different
Yields, Tappi, 46, No. 5, 273-277, 1963
[2] C. H. Mayhood, JR., O. J. Kallmes, and M. M. Cauley, The Mechanical Properties of Paper - Part
II: Measured Shear Strength of Individual Fiber to Fiber Contacts, Tappi, 45, No. 1, 69-73, 1962
[3] A. P. Schniewind, L. J. Nemeth, and D. L. Brink, Fiber and Pulp Properties - 1. Shear Strength of
Single-Fiber Crossings, Tappi, 47, No. 4, 244-248, 1964
[4] A. F. Button, Fiber-Fiber Bond Strength – A Study of a Linear Elastic Model Structure, Doctoral
Dissertation, The Institute of Paper Science and Technology, Atlanta, Georgia.
[5] R. A. Stratton and N. L. Colson, ”Fibre wall damage during bond failure.” Nordic Pulp and Paper
Research Journal, 8 (No. 2), 245-257, 1993
[6] A. Torgnysdotter, Fibre/fibre joints; Their characterization and influence on different paper
strength properties, Department of Fibre and Polymere Technology, Stockholm, Sweden, KTH,
Doctoral Thesis: 71, (2006)
50
Determination of the Thuja Burr Material Symmetries by Direct Contact Ultrasonic Nethod on Spherical Specimens
Mohammed El Mouridi1,2*, Thierry Laurent1, Tancrède Almeras1, Olivier Arnould1, Abdelillah Hakam2, Joseph Gril1
1Laboratoire de Mécanique et de Génie Civil, Université de Montpellier 2, CNRS UMR 5508, CC 048 Place Eugène Bataillon, 34095 Montpellier, France
{mohamed.el-mouridi, thierry.laurent, tancrede.almeras, olivier.arnould, joseph.gril}@univ-montp2.fr 2 Faculté des Sciences de Rabat, Équipe des Sciences et Technologie du Bois : 4, Avenue Ibn Battouta
B.P. 1014 Agdal-Rabat, Maroc [email protected]
Key words: Material symmetry, anisotropy, ultrasonic method, direct contact, sphere, burr, wood, thuja.
Abstract
Thuja (Tetraclinis articulata (Vahl.) Master) is a species endemic to the South-western coast of the Mediterranean Sea and especially Maghreb. The thuja burr is an outgrowth found at the collar of thuja trees. The burr wood of thuja is composed of dark growths of high density, mixed in a "matrix" of woody tissue of density close to that of thuja. When properly worked, the wood of thuja burr reveals a remarkable speckled pattern, leading to a real aesthetic value (Figure 1). In order to document the physical and mechanical properties behaviour of burr wood of thuja, we developed a method for determining the material symmetries for any material with unknown anisotropy, by combining ultrasonic experimental methods and numerical computation.
Figure 1a : Thuja burr Figure 1b : A machined plate
from the wood burr of thuja
An ultrasonic experimental device was developed to measure the elastic stiffness of a test specimen in a particular direction. Usually, the sample geometry used for direct contact ultrasonic methods is cubic or polyhedral allowing to obtain, on a single specimen of anisotropic material, 3 (cube) to 13 (polyhedron) measurements in different directions [1,2]. This number of measurements is not enough to determine the material symmetries on a single specimen. To overcome this limitation, an ultrasonic experimental device in direct contact on spherical specimens has been developed and improved (Figure 2). Using this geometry, the stiffness of the material can be measured in any number of directions on the same specimen. The result of this procedure is a “stiffness map”, giving stiffness as a function of specimen orientation.
51
The material symmetries can be computed from this stiffness map. The method consists in expressing the theoretical relation between a stiffness matrix given in any coordinate system and the resulting stiffness map, and then performing a reverse identification of these parameters using a least square method.
Figure 2: Experimental device
To qualify this experimental device and test its robustness, a test campaign was done on homogeneous material with known axes of orthotropy (beech wood), showing that the procedure is able to find the principal directions of material symmetry with an accuracy of less than 6°. Then, the method was applied to the burr wood of thuja in order to identify its principal axes of anisotropy, and its anisotropy ratio. This revealed that the burr wood, unlike normal wood, is transverse isotropic. The anisotropy ratio between the main direction and the second direction is less than 2. X-ray tomography was used to observe the structure of this material and explain its specific low ratio of anisotropy (Figure 3).
Figure 3: Experimental results: X-ray scan combined with stiffness map
References
[1] D. Keunecke W. Sonderegger; K. Pereteanu; T. Lüthi; P. Niemz. 2007. Determination of Young’s and shear moduli of common yew and Norway spruce by means of ultrasonic waves. Wood Sci Technol 41:309–327.
[2] BUCUR, V. 2006. Acoustics of wood, Springer series in wood sciences, Editors : T.E. Timell, R. Wimm.
52
Calculating Mechanical Properties of Wood Using Computer Modeling Via Indentation
V.Gountsidou, and H.M.Polatoglou
Aristotle University of Thessaloniki,
Thessaloniki,Greece [email protected]
Key words: nanoindentation, wood, orthotropic
ABSTRACT
When we calculate the mechanical properties of an homogenous and isotropic material, we must have in mind that two of its three material properties are independent. Wood is a commomly used engineering material. It is composite and consists of a complex array of cellulose cells, reinforced by organic compounds, primarily by lignin. It can be modelled as an orthotropic material, having three mutually perpendicular planes of material symmetry, one parallel to the grain, one tangential to the grain and one radial. Hofstetter et al employ anisotropic indentation theory to study the influence of elastic stiffness components, on the indentation modulus. The indentation modulus is a function of longitutional, traverse and shear modulus of the cell wall material. This theory instead of the commonly used isotropic allows using nanoindentation for quantitative studies.
Studying bibliography it seems that nanoinentation of wood is in its initial phase. Using depth-sensing indentation Wimmer investigates in spruce wood the hardness and the Young modulus of the cell corner middle lamella and of the S2 and examines their differences and trends. Two data sets were taken. The first one has to do with Young modulus and hardness of radial and tangential S2 walls, CCML and also Spurr’s resin as a control. The second one comparison is made for Young modulus and hardness of cell corner middle lamella and of the S2 along a 250μm distance in a tree ring.
Johannes Konnerth et al using pyramid diamond indenter tip and a cone diamond tip in a load-controlled node, estimated elastic modulus and hardness, from the load-indentation depth curves. Regions with high and low modulus were found in S2. It is interesting that regions of high modulus in one cell wall are often accompanied by low moduli in the neighbouring cell wall. On the other had the variability in hardness of cells only partly correlates with the distribution of the modulus.
Pharr et al used continuous nanoindentation technique to measure the mechanical properties of individual native wood fibers. Samples from the same growth ring were received. A series of hardness and modulus values as a function of indentation depth were produced. The obtained stiffness values are less than the value of the tensile modulus and the data are influenced from the penetration size effect. Also a predictable pattern of Eu values was found as a function of MFA, but these were lower than the corresponding moduli estimated from the cell-wall models.
Since computerized procedure is a nondestructive method, there is a variety of models that can be done using it and study the calculated Young modulus, Poison ratio, etc. During
53
the nanoindentation procedure the properties of the material can be probed in the nanoscale and sections can be received. Finally nanoindentation gives us the opportunity to measure the mechanical properties in the submicron level, which is of enormous significance for forest products.
We made orthotropic models (conical, cubes and axisymmetric ones) in bulk form and examined their material properties, under the influence of stress in different directions and compared the values with the theoretical ones. Initially the geometry is that the cell wall is a cylinder parallel to the y-axis. The core can be filled or empty.Taken also into account that the unit cell is a cylinder with the outer layer consisting of matrix material and the fiber of lumen (empty or filled with matrix) and the cell wall, and using the indentation process, we tried to analyze the effect of the constituent properties and the importance of microgeometry on the material properties.
The aim of this paper is to study orthotropic materials in bulk form, using finite element analysis. In a second level we will examine F.E.A. of indentation in orthotropic materials.
References [1] E. Marklund, J. Varna, R. C. Neagu and E .C. Gamstedt: Stiffness of Aligned Wood Fiber
Composites. Journal of Composite Materials, 42 (2008) [2] W. T. Y. Tze, S. Wang, T. G. Rials, G. M. Pharr, S. S. Kelley: Nanoindentation of wood cell
walls: Continuous stiffness and hardness measurements. ScienceDirect Composites: Part A 38 (2007), 945-953
[3] R. Wimmer, B. N. Lucas: Comparing mechanical properties of secondary wall and cell corner middle lamella in spruce wood. IAWA Journa, 18(1), (1977), 77-88
54
List of participants
Ahmad Rafsanjani Abbasi
Swiss Federal Laboratory for Materials Science and Technology, EMPA, Switzerland
Aleš Straže University of Ljubljana, Biotechnical Faculty, Dept. of Wood Science and Technology, Slovenia
[email protected]‐lj.si
Alessandra Patera ETH Zürich, EMPA, Switzerland [email protected]
Tancrède Almeras Université Montpellier 2, CNRS, LMGC, France
tancrede.almeras@univ‐montp2.fr
Ana Isabel Carvalho IBB/Centro de Genómica e Biotecnologia (CGB)‐UTAD, Portugal
Andreas Krause Georg‐August‐Universität Göttingen, Germany
Armando Fernandes
CITAB/ UTAD, Portugal [email protected]
Bernard Kurek Institut National de la Recherche Agronomique, France
Boris Clouet Université Bordeaux 1, France [email protected]
Callum Hill Edinburgh Napier University, Forest Products Research Institute, Edinburgh
Carmen‐Mihaela Popescu
Petru Poni Institute of Macromolecular Chemistry, Physical Chemistry of Polymers, Romania
Gabriella Josefsson Uppsala University, Sweden [email protected]
Hui Huang KTH Royal Institute of Technology, Sweden
Jerzy Weres Poznan University of Life Sciences, Faculty of Agriculture and Bioengineering, Poland
João Pereira CITAB/UTAD [email protected]
Johan Persson Mid Sweden University, Sweden [email protected]
Johannes Eitelberger
Vienna University of Technology, Austria
José Morais CITAB/UTAD, Portugal [email protected]
José Xavier CITAB/UTAD, Portugal [email protected]
Karin Hofstetter Institute for Mechanics of Materials and Structures, Vienna University of Technology, Vienna
Khashayar Razghandi
Max‐Planck‐Institute of Colloids and Interfaces, Department of Biomaterials, Germany
Kristina Ukvalbergiene
Kaunas University of Technology, wood Technology, Lithuania
Leszek Krzemien Polish Academy of Sciences, Poland [email protected]
55
Ling Li University of New Brunswick, Faculty of Forestry and Environmental Management , Canada
Lorenzo Guiducci Max Planck Institute of Colloids and Interfaces, Department of Biomaterials, Germany
Maria‐Cristina Popescu
Petru Poni Institute of Macromolecular Chemistry, Physical Chemistry of Polymers, Romania
Michael Jarvis University of Glasgow, Scotland, UK [email protected]
Michaela Eder Max‐Planck‐Institute of Colloids and Interfaces, Biomaterials, Germany
Mikael Magnusson KTH, Royal Institute of Technology, Sweden
Mohammed El‐Mouridi
Montpellier 2, France [email protected]‐montp2.fr
Oliver Hudson University of Cambridge, Cambridge, UK
Rostand Mmoutou Pitti
Blaise Pascal University, France rostand.moutou.pitti
@polytech.univ‐bpclermont.fr
Rastislav Lagaňa Technical University in Zvolen, Department of Wood Science, Slovakia
Sébastien Turcaud MPIKG, Biomaterials, Germany [email protected]
Stéphane Avril Ecole Nationale Supérieure des Mines, Center for Health Engineering, France
Thomas Joffre Uppsala, Sweden [email protected]
Vasiliki Gountsidou Aristotle University of Thessaloniki, Greece
Vilija Pranckeviciene
Kaunas University of Technology, Wood Technology, Lithuania
Wieslaw Olek Poznan University of Life Sciences, Poland
56
Financiamento comparticipado pelo Fundo Social Europeu e por fundos nacionais do MCTES – através do POPH‐QREN ‐
Tipologia 4.2
