On the origin of growth stresses in trees

Summary The mechanics of growth stress generation in a tissue of developing wood cells is studied by means of a continuum-mechanical model which assumes that the stresses which accumulate in the cells are induced by growth strains in the newly formed cell wall increments as they are laid down. The feasibility of the model is examined by using cell parameters both anatomical and physical to predict the variation of growth stresses with microfibril angle. In particular the measured change from tensile to compressive stresses with increasing microfibril angle for conifers is compared with the results predicted by the model.     

Tree growth stresses — Part V: Evidence of an origin in differentiation and lignification

Summary An important relationship has been shown between measurements of expansion of the radial dimension of cells during the lignification phase of differentiation, widely reported swelling of the thickness of cell walls during lignification, the fundamental mechanics of strain interactions in the three cardinal directions in materials generally, and a theory linking anisotropic behaviour of wood to its microfibril arrangement and the effect of encrusting substances in the cell wall. As a consequence, it has been deduced that tangential, longitudinal and radial stresses of substantial magnitude are generated in wood tissues as a result of lignification. In comparisons with measured growth stresses, it has been concluded that they are probably identical with the stresses that would develop as a result of lignification of the cell walls.     

Variations in physical and mechanical properties between tension and opposite wood from three tropical rainforest species

Growth strains were measured in situ in nine trees of three species from a French Guiana tropical rainforest in a clearly active verticality restoration process. The aim was to detect tension wood within the samples. Wood specimens were cut in the vicinity of the growth strain measurements in order to determine the microfibril angle and some mechanical and physical properties. As suspected, tensile growth strain was much higher in tension wood zones, as shown by the slightly higher longitudinal modulus of elasticity. Conversely, tension wood showed reduced compression strength. Longitudinal shrinkage was much higher in tension wood than in opposite wood. Clear relationships between the microfibril angle and longitudinal properties were noted in comparison (i) with those observed in gymnosperm compression wood and (ii) with expected relationships from the organization of wood fibres cell wall structure.     

Growth stress generation: a new mechanical model of the dimensional change of wood cells during maturation

A new mechanical model was developed to introduce the maturation process of wood cells theoretically. Using mechanical and physical properties of the two components of the cell wall, namely, a matrix reinforced by oriented cellulose microfibrils, it is possible to predict the relation between the anisotropic released strains and the microfibril angle. The model used in this study is based on the unified hypothesis combining the compressive stress generated in the cell wall matrix and the tensile stress originating in the cellulose microfibril as a framework. It is simple compared to the previously derived multilayered model, but it does not strictly fulfill all conditions of static equilibrium. Nevertheless, an excellent fit with observations can be obtained through varying a limited number of parameters.     

Mechanical interaction between cellulose microfibril and matrix substance in wood cell wall determined by X-ray diffraction

We investigated mechanical interactions between the cellulose microfibril and the matrix substance in wood cell walls. X-ray diffraction measurements showed that the peak positions of (200) and (004) from cellulose crystals in wood cell walls tended to shift lower and higher toward 2θ, respectively, during water desorption in wood. From our simulations, it is shown that the peak shift of (200) during water desorption is not due to changes in the scattering pattern of the amorphous substance or to lateral expansion of the cellulose crystals due to the Poisson effect in the cellulose microfibril, which is compressed in the molecular chain direction as the amorphous substance shrinks. This suggests that the cellulose microfibril expands transversely during water desorption in the wood cell wall, and that there is a mechanical interaction between the cellulose microfibril and the matrix substance.     

Generation process of growth stresses in cell walls: Relation between longitudinal released strain and chemical composition

Summary To advance the discussion on the evolution mechanism of tree growth stresses, the relation between released strain and the chemical components was investigated experimentally. The expansive released strain in the longitudinal direction assumed large values as the lignin content increased in the compression wood, but there was no relation between released strain and lignin content in the normal wood region. The contractive released strain assumed large values as the cellulose content and its crystallinity increased. Their correlation was very high and clear. From these facts, it is considered that the lignin deposition plays an important role in the generation of the growth stresses in compression wood but is not important in normal or tension wood regions. Cellulose microfibrils contract along their longitudinal axis during cell maturation, and the stress included by the contraction creates a longitudinal growth stress in normal and tension woods.The authors thank Prof. R. R. Archer, University of Massachusetts, for his valuable advice. A part of this research was supported by a grant under the Monbusho International Scientific Research Program     

Micromechanics of wood subjected to axial tension

Summary The behaviour of a small group of wood fibers of Sitka spruce during tensile loading is investigated. The load-extension curves for both early and late wood fibers consist of three distinct segments. The first segment is almost a straight line, at some stage of loading a yield point is observed. Beyond this point the specimen becomes less stiff and undergoes a large, mainly irreversible deformation. As the load is increased further, the curve exhibits the third segment showed by a significant change in slope. These curves look different from those obtained on thick specimens. In this respect, the behaviour of a thin wood specimen subjected to cyclic type tensile loading along its longitudinal direction is also illustrated. Based on wood microstructure, a model is presented to interpret the evolution of the Young's modulus of a wood fiber during tensile loading. The model considers wood as an assembly of cylindrical fibers pasted together in a longitudinal direction. We have assumed the cell wall to comprise only an S₂ layer made of a composite material consisting of a lignin and hemicellulose matrix reinforced by helical microfibrils along the fiber. Furthermore, it is assumed that the microfibril angle a in the S₂ layer is not uniform along the fiber axis and matrix degradation occurs in the zones where the microfibril angles are bigger. The validity of this assumption is verified by using holographic interferometry to visualize the displacement field of the specimen's surface under tension.The work reported in this paper is supported by a grant from the Swiss National Science Foundation, and its support is gratefully acknowledged     

Mechanical behavior of the crystal lattice of natural cellulose in wood under repeated uniaxial tension stress in the fiber direction

This study investigated the relationship between the cellulose crystal lattice strain (crystalline region) and the macroscopic surface strain in specimens of Chamaecyparis obtusa wood under repeated uniaxial tension stress in the fiber direction. Changes in the strain of the crystal lattice were measured from the peak of (004) reflection using the transit X-ray method. The macroscopic surface strain of each specimen was measured with a strain gauge. In both loading and unloading, the surface strain changed linearly with changes in stress. However, crystal lattice strain was not linear but exhibited changes along a curve with changing stress. Under stressed conditions, the crystal lattice strain was always less than the surface strain, regardless of the frequency of repetition in the loading and unloading cycle. The ratio of the crystal lattice strain to the surface strain showed a negative correlation for stress in both loading and unloading. That is, the ratio decreased with increasing stress, and finally tend to converge to a specific value. The ratio (I/I ₀) between the diffracted intensity (I ₀) in the (004) plane in the unloaded condition and the diffracted intensity (I) in the (004) plane in the loaded condition tend to converge on a specific value with increasing frequency of repetition. When the substantial tension Young’s modulus of the wood in the longitudinal direction decreased, the ratio of the strain of the crystal lattice to the surface strain also decreased. Moreover, the ratio decreased with increasing microfibril angle of the specimen.     

Modelling moisture-related mechanical properties of wood Part II: Computation of properties of a model of wood and comparison with experimental data

Starting with simple concepts of the molecular structure and models of the stiffness and swelling behaviour of lignin, hemi-cellulose and cellulose and building up through the various levels of organisation in the wood cell wall a model has been constructed that simultaneously predicts the variation with moisture content change of both the longitudinal Young's modulus and longitudinal shrinkage of wood. The model closely predicts both longitudinal shrinkage and Young's modulus as they vary with the moisture content of the wood. The model also takes into account structural variations in the form of changes in cell wall layer thicknesses and mean cellulose microfibril orientation.     

Helical fissures in compression wood cells: Causative factors and mechanics of development

Summary There is evidence showing that lignification causes both an increase in the thickness of the walls, and changes in the overall width or circumference of wood cells. Although data are not available on changes in length during lignification, it can be deduced that these must also tend to occur. As lignin occupies sites in the cell walls corresponding to those occupied by water, the theory of anisotropic shrinkage of wood may be used to predict the proportional dimensional changes tending to occur as each wall layer in a compression wood cell is lignified. Taking account of the microfibril angles in those layers, it is shown that if the angle for S₂ is more than about 45°, inevitably S₂ will tend to develop deep helical fissures or splits of the form of those reported in the literature.     

Effects of the lateral growth rate on wood quality parameters of Eucalyptus grandis from different latitudes in Brazil and Argentina

Climate change resulting from increased atmospheric carbon dioxide (CO₂) and shortages of fossil fuels such as petroleum are major problems worldwide. Under these conditions, demand for woody biomass resources is increasing. We investigated the feasibility of using fast-growing Eucalyptus grandis for material production. Samples of E. grandis were collected from four plantations in different latitude divisions, including tropical and subtropical Brazil and subtropical Argentina. Various xylem qualities were measured and related to the lateral growth rate. Lateral growth rate did not significantly affect the longitudinal released strain of the surface growth stresses or the xylem density at any of the sampling sites. Higher lateral growth rate, higher values of xylem density, and lower absolute values of the released strain were observed in plantations closer to the equator. Higher growth rates in tropical climate promote longer fiber length. In subtropical plantations, smaller diameter trees will produce tension wood with smaller microfibril angles. Planting E. grandis closer to the equator thus produces higher quality wood than in plantations at lower latitudes.     

Theory of X-ray measurement of microfibril angle in wood

Summary The property of fibre symmetry as exhibited by wood cellulose can be used to derive an explicit relationship between the orientation of a cellulose microfibril and the orientation of the X-ray beam diffracted by any of its crystallographic planes. The solution applies to a microfibril of any orientation and so is well suited to evaluating the microfibril angle distribution in wood containing cells of any cross-sectional shape. The (002) and (040) reflections of cellulose have complementary properties that could be exploited to enable current problems associated with the use of each individually for evaluating the mean microfibril angle of the S2 layer to be overcome. It is expected that it will be possible to measure the microfibril angle distribution throughout the whole cell wall and also measure the average cell cross-section of a wood sample, by analysing (002) and (040) diffraction profiles in conjunction with each other.This work is supported by the NZ Foundation for Research, Science and Technology under contract # UOC 401     

Variation pattern of wood properties of naturalCunninghamia lanceolata

In this paper, the variation pattern of wood properties was studied for naturalCunninghamia lanceolata. The mathematical models of property parameters were obtained on tracheid length, microfibril angle, late wood percentage, growth ring width and growth ring density in the radial direction. The interrelation were analyzed between tracheid length and microfibril angle. The result can provide scientific theory basis for wood utilization and early prediction of wood properties.     

Creep and stress relaxation behavior for natural cellulose crystal of wood cell wall under uniaxial tensile stress in the fiber direction

We investigated the temporal changes in creep and stress relaxation behavior in both microscopic crystalline cellulose and macroscopic strain of wood specimen using Japanese cypress (Chamaecyparis obtusa Endl.) to understand the viscoelastic properties of wood cell walls. Specimens 600 µm in thickness were observed by the X-ray diffraction and submitted to tensile load. The crystal lattice strain of (004) plane and macroscopic strain of specimen were continuously detected during creep and stress relaxation tests. It was found that the creep compliance based on macroscopic strain showed a gradual increase after instantaneous deformation due to loading and then the parts of creep deformation remained as permanent strain after unloading. On the other hand, crystal lattice strain showed a different behavior for macroscopic strain; it kept a constant value after instantaneous deformation due to loading and then increased gradually after a certain period of time. These differences between macroscopic and microscopic levels were never found in the stress relaxation tests in this study. Relaxation modulus at the macroscopic level only showed a decreasing trend throughout the relaxation process. However crystal lattice strain kept a constant value during the macroscopic relaxation process. In addition, the microfibril angle (MFA) of wood cell wall has a role of mechanical behavior at microscopic level; crystal lattice strains were smaller with increasing MFA at both creep and relaxation processes. Creep compliance and stress relaxation modulus at the macroscopic level decreased and increased with increasing MFA, respectively. Our results on the viscoelastic behavior at microscopic level evidenced its dependency on MFA.     

VARIATION PATTERN OF WOOD PROPERTIES OF NATURALCUNNINGHAMIA LANCEOLATA

m0DUCYIONCunninghaniahaceolataisoneofmalnusedwoodspeciesinSouthernChina.ItPOs-sessesthecharactenshcsofhighadaPabilityandwideuhlity.WoodscienhstshavedonemorereaearchingworkonthegrOwingcharac-tenshcsandwoodPhysicalPropeniesofPlantedCunninghamiaboceolata,butlessonthewoodPropeniesvanahonpatternofnatUralCunninghtzmiahaceolata.ThewoodpropeniesandtheircorrelahonofCunn~oriahaceolatainnatUralforestwerestudiedinordertoProviderelevamtech-mqueparametersofitsPeffochonanduhliza-tion.nsThunSAunare…     

Mechano-sorptive creep mechanism of wood in compression and bending

Summary A model is introduced which links the mechano-sorptive behaviour of wood subjected to moderate and high compression or bending stresses parallel to grain to the formation of slip planes in the cell wall. Slip plane formation is dependent on the breaking of hydrogen bonds, which process is directly related to the amount of moisture change. The dramatic change of microfibril orientation in slip plane zones cause an increase of the longitudinal shrinkage/swelling and a decrease of the modulus of elasticity. These features of slip plane formation account for both the magnitude and the oscillation of the excessive mechano-sorptive creep associated with compression and bending parallel to grain. A summary is given of the characteristics of the mechano-sorptive effects, and the model is discussed in the light of these effects.The paper is one of the results of a project on the influence of changing moisture content on the mechanical behavior of wood, currently underway in a co-operation between College of Environmental Science and Forestry, State University of New York, and the Technical University of Denmark. Support for this project is provided by the Danish Technical Research Council and by the USDA C--operative Research Program (proj. 85-FSTY-9-0112). The support is gratefully acknowledged     

Hydrostatic pressure and temperature dependence of wood moisture sorption isotherms

By expressing wood moisture content data as a function of adsorption energy, an interesting scaling capability is obtained, wherefrom the general hydrostatic pressure and temperature dependence of wood moisture content is determined. The scaling law is fully consistent with the thermodynamics of swelling. It can be used to transform room condition sorption isotherms to other temperatures and hydrostatic pressures, provided that the wood matrix is not irreversibly modified. A special procedure is suggested for the case of an irreversibly changing wood matrix, as in thermal modification and thermo-hydro-mechanical treatments. Using the present scaling theory, several fundamental aspects of wood moisture sorption are explained, such as the absence of a significant quantity of strongly bound wood moisture, the internal stress generation by sorption hysteresis in the wood cell wall, and the reason for the reversible disappearance of the sigmoid shape of the sorption isotherm at higher temperature. The results of this research may be useful (a) for transformation of known sorption data to other conditions, notably where in situ moisture measurements are difficult to perform and (b) to quantify the effects of internal stresses in the ultrastructure of the cell wall on moisture content.     

木材细胞壁与木材力学性能及水分特性之间关系研究进展

阐述了木材细胞壁微纤丝角、结晶度、纹孔和化学组分等对木材力学性能的影响规律,针对木材的水分特性重点归纳了纹孔和抽提物对木材渗透性的影响机制,并对未来细胞壁微观研究发展趋势进行了总结,旨在为木材细胞壁相关研究提供借鉴。     

Radial variation in partial compression properties perpendicular to the grain of Japanese larch (Larix kaempferi)

This study investigated the densities, average width of annual rings, and partial compression stresses at 5 % strain perpendicular to the grain of air-dried wood specimens, which were continuous in the radial direction from the pith and were obtained from Japanese larch (Larix kaempferi) trees with different diameters at breast height in the same stand, to evaluate the radial variations in partial compression properties perpendicular to the grain. The air-dried densities of the wood increased with the distance from the pith. The average width of annual rings of the wood tended to decrease with increasing distance from the pith and those of medium- and large-diameter trees seemed to increase near the pith. The partial compression stresses at 5 % strain in the tangential loading direction tended to increase with the distance from the pith and with air-dried wood density. However, in the radial loading direction, this tendency was not observed. The partial compression stresses at 5 % strain in the radial loading direction tended to be low in wood with a small average width of annual rings. These results indicate that the factors affecting the radial variations in the partial compression stress at 5 % strain differ depending on the loading directions.     

Properties of cell wall constituents in relation to longitudinal elasticity of wood

 To predict the origin of longitudinal elasticity of the solid wood in relation to the composite structure of the wood cell wall, an analytical procedure was developed on the basis of the idea of “the reinforced-matrix hypothesis” originally introduced by Barber and Meylan (1964). A multi-layered circular cylinder, having the CML, the S1, and the S2 layers, was used as a model of the ligno-cellulosic (wood) fiber, and the elastic properties of an isolated wood fiber were formulated mathematically. In the formulation, not only the structural factors, such as the microfibril angle and the thickness of each layer, but also the environmental condition, e.g. the moisture content, were taken into consideration. The effects of the moisture content and the microfibril angle upon the longitudinal Young's modulus and the Poisson's ratio of the wood fiber were simulated by using the newly derived formulae. It is anticipated to give a start to estimate the fine structure and the internal properties of the cell wall constituents in relation to the macroscopic behaviors of the wood through simulating the mechanical behaviors of the wood fiber. Received 17 August 1999