Modelling elastic and shrinkage properties of wood based on cell structure

Summary In a previous article of the authors a model was developed for estimating elastic and shrinkage properties of a softwood cell-wall. In the present article this model is enlarged to simulate the elastic properties of defect-free softwoods. The wood model consists of earlywood, latewood and ray cells, each of which have a different cell-wall structure. In the model the ratio of earlywood to latewood is defined by a given wood density. The calculated elastic properties are in good agreement with test results.     

针叶树木材细胞力学及纵向弹性模量计算——纵向弹性模量的理论模型

本文是关于针叶树木材弹性特性研究的理论分析。设定针叶树木材细胞主要由管胞和射线组成 ,根据管胞和射线细胞的解剖构造特征 ,建立了两端劈尖、矩形截面、中空的管胞模型与长方体状、中空的射线细胞模型。沿用MP层 (胞间层 初生壁 )内与 3S层 (次生壁的S1、S2、S3层 )内力学性质相同 ,而MP与 3S层间力学性质相异的假定 ,利用管胞和射线细胞模型 ,导出了管胞和射线细胞纵向弹性模量的计算公式。同时 ,根据管胞和射线细胞在针叶树木材中的排列规律 ,结合线形弹性体串并联的特性 ,进一步给出了计算针叶树木材试件宏观纵向弹性模量的方法。本项研究从木材细胞的结构和弹性特性出发 ,分析研究针叶树木材的宏观弹性行为 ,一方面可以获得关于针叶树木材弹性特性的认识 ,另一方面可以用于针叶树木材纵向弹性模量的计算和预测。     

针叶树木材细胞力学及纵向弹性模量的计算--试件纵向弹性模量的预测

依据针叶树木材管胞和射线细胞的结构模型。使用计算机抽样模拟解剖结构参数。以及使用针叶树木材纵向弹性模量计算公式和方法,计算人工林杉木,马尾松幼龄材和成熟材试件纵向弹性模量,计算结果与常温条件下气干试件测定结果十分符合。在试件晚材率和管胞解剖结构参数改变的条件下。计算预测了人工林杉木,马尾松幼龄材和成熟材纵向弹性模量的变化。结果表明：试件纵向弹性模量随晚材率,管胞长度,管胞壁厚度的增加而增加,而试件纵向弹性模量随管胞直径增加而减小。本文提出的纵向弹性模量计算的预测方法,对于运用现代生物技术控制和改变针叶树木材的材质,材性有实际意义。     

Predicting anisotropic shringkage of softwood Part 1: Theories

 The phenomenon of wood shrinkage by losing moisture can be analysed at four levels: molecular, ultrastructural, microstructural and macrostructural levels. To predict the shrinkage of wood cells, the model of Barber and Meylan is modified in the current work to reflect combined effects of shrinkage of the cell wall, changes of the lumen shape and effects of rays and bordered pits. Where a piece of wood contains a multi-layer of earlywood and latewood or multi-layer of normal and defect wood with variable properties, a model is proposed to relate the total, measurable shrinkage to the shrinkage of each layer. The model can be applied to a specimen with asymmetric properties through the thickness. In such a board, bow (or crook), cup and twist are often observed. The modified and proposed models involve several mechanical properties of the cell wall which are difficult to measure. These properties vary with wood types, such as earlywood, late wood, compression wood, or wood with spiral grain. However, an alternative method may be used to obtain these properties from experimentally measured shrinkage data, and this method will be presented in a subsequent paper. Received 25 January 1999     

An analysis of elastic and plastic fruit growth of mango in response to various assimilate supplies

Changes in elastic and plastic components of mango (Mangifera indica L. cv 'Cogshall') fruit growth were analyzed with a model of fruit growth over time and in response to various assimilate supplies. The model is based on water relations (water potential and osmotic and turgor pressures) at the fruit level. Variation in elastic fruit growth was modeled as a function of the elastic modulus and variation in turgor pressure. Variation in plastic fruit growth was modeled using the Lockhart (1965) equation. In this model, plastic growth parameters (yield threshold pressure and cell wall extensibility) varied during fruit growth. Outputs of the model were diurnal and seasonal fruit growth, and fruit turgor pressure. These variables were simulated with good accuracy by the model, particularly the observed increase in fruit size with increasing availability of assimilate supply. Shrinkage was sensitive to the surface conductance of fruit peel, the elasticity modulus and the hydraulic conductivity of fruit, whereas fruit growth rate was highly sensitive to parameters linked to changes in wall extensibility and yield threshold pressure, regardless of the assimilate supply. According to the model, plastic growth was generally zero during the day and shrinkage and swelling were linked to the elastic behavior of the fruit. During the night, plastic and elastic growths were positive, resulting in fruit expansion.     

Measurement of free shrinkage at the tissue level using an optical microscope with an immersion objective: results obtained for Douglas fir (Pseudotsuga menziesii) and spruce (Picea abies)

Shrinkage at the tissue level has been evaluated satisfactorily using relatively simple equipment, comprising an optical microscope equipped with reflected light, a standard objective, a water immersion objective of same magnification and a digital camera connected to a computer. Shrinkage is calculated from pairs of images taken at the same magnification, one collected during immersion in water and the other in air-dry state. A novel software program has been developed to determine shrinkage based on a closed chain of reference points chosen from the anatomical markers at the external part of the zone of interest. Measurements were performed on earlywood, latewood and compression wood zones from two softwood species (Douglas fir and spruce), isolated from the rest of the annual ring with the aid of a diamond wire saw. As main results, reference should be made to the low degree of shrinkage and high anisotropy factor of earlywood, the marked and practically isotropic shrinkage in latewood and the low shrinkage (with respect to cell wall thickness) and inverse anisotropy ratio in compression wood.     

纳米压痕技术测量管胞次生壁S2层的纵向弹性模量和硬度

重点研究和详细介绍了利用纳米压痕技术测试管胞次生壁S2 层纵向弹性模量以及硬度的实验技术 ,并测试了人工林杉木早晚材管胞S2 层的纵向弹性模量和硬度。结果表明 :杉木晚材管胞S2 层的平均纵向硬度为0 390GPa ,弹性模量的平均值为 1 4 84 4GPa ;早材管胞S2 层的硬度和模量则小于晚材 ,平均值分别为 0 30 6GPa和9 82 3GPa。     

On the origin of growth stresses in trees

Summary A mechanism for growth stress generation is studied which involves a contractive strain in the microfibril direction and swelling strain in the transverse direction in the developing wall of wood cells. A cylindrically anisotropic elastic model is used to calculate the accumulation of residual stresses in the S₂ wall as it is formed. An explicit relation between the shrinkage/swelling strains in the growth increment of the cell wall and the resulting axial and circumferential stresses induced in the cell is derived. For gymnosperm cells the transition from tensile stress in normal wood cells to compressive stress in compression wood cells is found with increasing microfibril angle.     

Eucalypt Wood Anatomical and Physical Properties and Their Effects on Plywood Veneer Quality

In order to better understand the reasons why eucalypt veneer checks easily and severely, wood samples of three eucalypt species were selected, and their anatomical and physical properties were examined according to conventional methods and the national standards. The effects of variances in cell wall thickness of wood fibre and vessel, and diameter of the cell lumen as well as the tissue ratio on the quality of plywood veneer were analysed. The results show that： 1） There is a great difference in fibre cell wall thickness and diameter of the cell lumen between early wood and late wood of Eucalyptus delegatensis. 2） E. obliqua has a high wood fibre tissue ratio and the thickest fibre cell wall, but the difference inthe fibre cell wall thickness between early wood and late wood is the smallest. 3） The wood fibre tissue ratio of E. regnans is smaller than that of E. obliqua, and its wood fibre cell wall isthe thinnest and there is only a very small difference in fibre cell wall thickness between early wood and late wood. The difference inthe diameter of wood fibre cell lumen among early wood, transition area and late wood is also small： 4） E. delegatensis has the highest tangential shrinkage rate and radial-tangential shrinkage rate, andE. obliqua has the lowest. It is the variability of wood anatomical properties of these species that cause the difference in the veneer shrinkagei and then affects plywood veneer quality.     

Nanostructural assembly of cellulose,hemicellulose, and lignin in the middle layer of secondary wall of ginkgo tracheid

Physical, chemical, and biological properties of wood depend largely on the properties of cellulose, noncellulosic polysaccharides, and lignin, and their assembly mode in the cell wall. Information on the assembly mode in the main part of the ginkgo tracheid wall (middle layer of secondary wall, S2) was drawn from the combined results obtained by physical and chemical analyses of the mechanically isolated S2 and by observation under scanning electron microscopy. A schematic model was tentatively proposed as a basic assembly mode of cell wall polymers in the softwood tracheid as follows: a bundle of cellulose microfibrils (CMFs) consisting of about 430 cellulose chains is surrounded by bead-like tubular hemicellulose-lignin modules (HLM), which keep the CMF bundles equidistant from each other. The length of one tubular module along the CMF bundle is about 16 ± 2 nm, and the thickness at its side is about 3–4 nm. In S2, hemicelluloses are distributed in a longitudinal direction along the CMF bundle and in tangential and radial directions perpendicular to the CMF bundle so that they are aligned in the lamellae of tangential and radial directions with regard to the cell wall. One HLM contains about 7000 C₆-C₃ units of lignin, and 4000 hexose and 2000 pentose units of hemicellulose.     

基于纳米压痕技术的木材胶合界面力学行为

【目的】研究木材胶合界面的静态和动态力学行为,探讨树脂渗透对木材管胞壁层力学性能的影响,为木质复合材料制造工艺优化和增强改性提供理论依据。【方法】采用纳米压痕静态和动态力学测试技术(Nano-DMA),对针叶材火炬松与酚醛树脂(PF)、脲醛树脂(UF)胶黏剂所形成胶合界面区域各相材料的静态弹性模量、硬度、蠕变性能以及储能模量和损耗模量等力学行为进行分析。【结果】静态力学行为方面,在界面区域,PF和UF渗透进入管胞壁层后,木材管胞壁的弹性模量( E r)和硬度( H )提高;经PF渗透后,木材管胞壁的 E r和 H 分别增加7%和26%;Burgers蠕变力学模型可有效描述胶合界面区域管胞壁的纳米压痕蠕变特性,经树脂渗透后,木材管胞壁的瞬时弹性模量增加,黏弹性模量和黏性系数减小;在保载初期,PF界面区域木材管胞壁的蠕变柔量约下降60%,UF界面区域木材管胞壁的蠕变柔量约下降58%。动态力学行为方面,随着加载频率增加,界面材料的储能模量( E ′ r)逐渐增大,而损耗模量( E ″ r)和损耗因子(tan δ)呈减小趋势;当加载频率为10 Hz时,PF和UF树脂渗透使得管胞壁层的储能模量分别增加16%和29%。【结论】胶合界面区域胶黏剂进入管胞壁层,对木材管胞的静态力学性能具有增强作用,同时胶黏剂可提高管胞壁的短期抗蠕变能力;木材管胞壁具有较高的储能模量和损耗模量,而树脂的储能模量和损耗模量较低,经树脂渗透后,木材管胞壁的储能模量增加,但损耗模量和损耗因子呈下降趋势,可能对界面传递和分散应力产生不利影响。     

Relationships of anatomical characteristics versus shrinkage and collapse properties in plantation-grown eucalypt wood from China

To explore the influence of the basic density on collapse-type shrinkage properties and to quantify the relationships of the main anatomical features with shrinkage and collapse properties, all above-mentioned parameters were determined and analyzed for three species of collapse-susceptible eucalypts, Eucalyptus urophylla, Eucalyptus grandis, and E. urophylla × E. grandis, planted in South China. The correlation coefficients were also determined and the corresponding regression equations were established with the anatomical parameters measured by using multiple linear regression. The results indicated that: (1) basic density was strongly positively linearly related to both unit tangential shrinkage (r = 0.970) and unit radial shrinkage (r = 0.959), weakly positively related to total shrinkage (r = 0.656 and 0.640 for tangential and radial, respectively), and weakly negatively related to residual collapse (r = 0.632 and 0.616 for tangential and radial, respectively). (2) The main factors affecting unit shrinkage were cell wall proportion (WP), microfibril angle (MFA), and double fiber cell wall thickness (DWT); factors playing an important role in total shrinkage were WP, ray parenchyma proportion (RP), and MFA, while RP had the highest effect on residual collapse (r = 0.949 and 0.860 for tangential and radial, respectively). (3) All corresponding regression models obtained were very suitable for the evaluation of relationships between the anatomical parameters and unit shrinkage, total shrinkage, and residual collapse, as measured using a moisture content of 28% as the fiber saturation point for all specimens.     

对防腐处理前后遭细菌侵蚀的木材超微构造研究

用透射电镜观察了隧道式细菌在未经防腐剂处理的素材和处理过的木材[欧洲白桦(Betula pendula),欧洲赤松(Pinus silvestris)和挪威云杉(Picea abies)]中形成的腐朽现象,研究了细菌入侵木材细胞壁的过程。侵蚀是从木材细胞腔内开始,通过S_3层后,细菌在细胞壁的S_1层、S_2层及胞间层内移动并且分裂,引起木材细胞壁的降解。还观察了隧道式细菌、隧道的形态和超微结构。本研究表明具缘纹孔和单纹孔的纹孔膜比纹孔缘对细菌活动更有抗性。细菌可以侵入低浓度防腐剂(0.5％Tanalith NCA)处理过的木材,表明细菌具一定解毒能力。     

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.     

Mechanistic study of microstructural deformation and stress in steam-exploded softwood

Steam explosion pretreatment results in the formation of microcracks in the cell walls of wood. In the present study, steam explosion experiments were performed and structural changes in Norway spruce were identified using scanning electron microscopy. The cellular structure of the softwood spruce was simulated using the finite element method, and the effects of pressure generated during the steam explosion pretreatment on the deformation of the cells were investigated. The simulated model included earlywood, latewood, and ray cells. The effects of bordered and cross-field pits on the stresses in the cell wall were studied as well. Many similarities were observed between the microcracks in the steam-exploded wood and the high-stress regions predicted by the model. The experimental and simulation results showed that the radial cell walls in the earlywood cells experienced major deformation. The presence of the pits created stress localization and facilitated the formation of microcracks in the cell walls.     

Micropores and mesopores in the cell wall of dry wood

To investigate micropores and mesopores in the cell walls of dry wood, CO₂ gas and N₂ gas adsorption onto dry wood were measured at ice-water temperature (273 K) and liquid nitrogen temperature (77 K). CO₂ gas adsorption isotherms obtained were used for determining micropore volumes smaller than 0.6 nm by the HK method (Horvath-Kawazoe method), and N₂ gas adsorption isotherms obtained were used for determining the mesopore volume between 2 nm and 50 nm by the Barrett-Joyner-Halenda (BJH) method. Micropores and mesopores existed in cell walls of dry wood, and the cumulative pore volume was much larger for micropores than for mesopores. Micropores in the cell wall of dry wood decreased with elevating heat treatment temperature, and the decreased micropore was reproducible by wetting and drying. Mesopores did not decrease so much with elevating heat treatment temperature. Micropore volumes for the softwood Hinoki and the hardwood Buna were compared. A larger amount of micropores existed in hardwood Buna than in softwood Hinoki, and this relationship was considered to correspond to the difference in thermal softening properties for lignin in water-swollen Hinoki and Buna. This result probably indicates that micropores in the cell walls of dry wood relate to the structure of lignin.     

The longitudinal Young's modulus of Pinus radiata

Summary The variation of the longitudinal Young's modulus with mean cellulose microfibril angle of the wood substance of the earlywood of a softwood has been determined from small clear samples.The longitudinal Young's modulus falls steeply as the angle between the longitudinal axis and the mean microfibril direction in the cell walls increases. The variation has been explained in both form and magnitude by applying the elastic theory of a fibre composite material with distributed fibre directions to a model of the experimental material. It confirms the two phase concepts of the plant cell wall, as far as the elastic properties are concerned, of rigid crystalline microfibrils embedded in an isotropic matrix of amorphous and paracrystalline materials.

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Zusammenfassung Die Änderung des Young-Moduls in longitudinaler Richtung mit dem mittleren Winkel der Cellulose-Mikrofibrillen in der Frühholzsubstanz von Nadelholz wurde an kleinen, fehlerfreien Proben bestimmt.Der longitudinale Young-Modul fällt mit zunehmendem Winkel zwischen Längsachse und mittlerer Mikrofibrillen-Richtung in der Zellwand steil ab.Die Änderung wurde nach Form und Größe durch Anwendung der Elastizitätstheorie für ein faseriges Material mit wechselnden Faserrichtungen auf ein Modell aus dem Versuchsmaterial erklärt. Das Zwei-Phasen-Modell der Pflanzenzellwand wird damit bestätigt, soweit es sich um die elastischen Eigenschaften von starren, kristallinen Cellulose-Mikrofibrillen handelt, die in einer isotropen Matrix aus amorphem, parakristallinen Material eingebettet sind.

     

Role of the gelatinous layer on the origin of the physical properties of the tension wood

To discuss the role of the gelatinous layer (G-layer) on the origins of the physical properties peculiar to the tension wood fiber (TW fiber), the deformation process of an isolated TW fiber caused by a certain biomechanical state change was formulated mathematically. The mechanical model used in the present formulation is a four-layered hollow cylinder having the compound middle lamella (CML), the outer layer of the secondary wall (S1) and its middle layer (S2), and the G-layer (G) as an innermost layer. In the formulation, the reinforced matrix mechanism was applied to represent the mechanical interaction between the cellulose microfibril (CMF) as a framework bundle and the amorphous substance as a matrix skeleton in each layer. The model formulated in the present study is thought to be useful to investigate the origins of extensive longitudinal drying shrinkage, large tensile growth stress, and a high axial elastic modulus, which are rheological properties peculiar to the TW. In this article, the detailed process of the mathematical formulation is described. In a subsequent article, some TW properties from a 70-year-old Kohauchiwakaede (Acer sieboldianum Miq.) will be analyzed using the newly developed model.     

Longitudinal hardness and Young's modulus of spruce tracheid secondary walls using nanoindentation technique

Summary Using a mechanical properties microprobe, measurements of hardness and elastic modulus of tracheid walls in the longitudinal direction of spruce wood were obtained by continuously measuring force and displacement as a diamond indenter impressed a cell wall. Maximum mechanical properties were found at the edges of the walls of angular shaped tracheids. Both the hardness and elastic modulus of latewood cell walls were higher than cell walls in the earlywood. The high spatial resolution of this new concept of mechanical testing allows a direct comparison with ultrastructural and microchemical parameters of lignified cells which opens a wider area of applications for the understanding of intrinsic wood properties.This work was conducted while the senior author was a Visiting Scientist at the Oak Ridge National Lab, Oak Ridge, TN 37831, USA partly with joint fundings from the Austrian Science Foundation (Schrödinger scholarship J799-BIO)     

Predicting the effect of specific gravity,moisture content,temperature and strain rate on the elastic properties of softwoods

Summary Rational utilization of wood highes on adequate knowledge of its behavior under a wide range of conditions. Based on a literature survey, a unified system of approximate equations and correction factors is proposed. These enable one to adjust all elastic properties of wood for variations in specific gravity, moisture content, temperature and strain rate. Predicted values should be considered as useful guides to typical softwood behavior.