Cantilever experimental setup for rheological parameter identification in relation to wood drying

Wood exhibits a pronounced time dependent deformation behavior which is usually split into ‘viscoelastic’ creep at constant moisture content (MC) and ‘mechano-sorptive’ creep in varying MC conditions. Experimental determination of model rheological parameters on a material level remains a serious challenge, and diversity of experimental methods makes published results difficult to compare. In this study, a cantilever experimental setup is proposed for creep tests because of its close analogy with the mechanical behavior of wood during drying. Creep measurements were conducted at different load levels (LL) under controlled temperature and humidity conditions. Radial specimens of white spruce wood [Picea glauca (Moench.) Voss.] with dimensions of 110 mm in length (R), 25 mm in width (T), and 7 mm in thickness (L) were used. The influence of LL and MC on creep behavior of wood was exhibited. In constant MC conditions, no significant difference was observed between creep of tensile and compressive faces of wood cantilever. For load not greater than 50% of the ultimate load, the material exhibited a linear viscoelastic creep behavior at the three equilibrium moisture contents considered in the study. The mechano-sorptive creep after the first sorption phase was several times greater than creep at constant moisture conditions. Experimental data were fitted with numerical simulation of the global rheological model developed by authors for rheological parameter identification.     

Mechanical response of wood perpendicular to grain when subjected to changes of humidity

This paper describes the deformations caused by stress and humidity interaction, mechano-sorption, in the cross grain directions of wood and the relaxation or accumulation of internal stresses caused by these deformations. Long-term tests on small clear specimens in cyclic climates with both tensile and compressive loads were carried out. The development of internal stresses in timber was measured indirectly at different times during the adsorption and desorption processes. Released deformations were measured from cross-sections after cutting them to small slices. These deformations were used to estimate the internal stresses caused by the humidity variations. Tests with constant loads and multiple humidity cycles show a mechano-sorptive strain that is ten times higher than the elastic strain. It is shown that existing models for describing mechano-sorption perpendicular to grain are inaccurate when applied to multiple humidity cycles. The present results demonstrate that if the mechano-sorptive behaviour and the moisture gradients in wood can be accurately described, it is possible to predict the stress distribution in a timber cross-section by knowing the climate history.     

A numerical study of the shape stability of sawn timber subjected to moisture variation Part 1: Theory

A three-dimensional theory for the numerical simulation of deformations and stresses in wood during moisture variation is described. The constitutive model employed, assumes the total strain rate to be the sum of the elastic strain rate, the moisture-induced strain rate and the mechano-sorption strain rate. Wood is assumed to be an orthotropic material with large differences between the longitudinal, radial and tangential directions in the properties found. The influence of the growth rings, the spiral grain and the conical shape of the log on the orthotropic directions in the wood is taken account of in the model. A finite element formulation is used to describe the deformation process and the stress development during drying.The research presented in this paper is a part of the national research programme in Sweden concerning wood physics and drying. It was financially supported by the Research Foundation of Swedish Sawmills and the Swedish Council for Forestry and Agricultural Research.     

Finite element study of growth stress formation in wood and related distortion of sawn timber

Lack of straightness in timber is the most frequent complaint regarding solid (and laminated) timber products worldwide. Nowadays, customers demand higher quality in the shape stability of wood products than they did earlier. The final distortion of timber boards is mostly caused by moisture-related stresses in wood (drying distortions) and growth-related stresses (distortions appearing when logs are split up to timber boards by sawing). To get more knowledge on how these distortions can be reduced in wooden products, there is a need for improved understanding of this material behaviour through good numerical tools developed from empirical data. A three-dimensional finite element board distortion model developed by Ormarsson (Doctoral thesis, Publ. 99:7, 1999) has been extended to include the influence of growth stresses by incorporating a one-dimensional finite element growth stress model developed here. The growth stress model is formulated as an axisymmetric general plane strain model where material for all new annual rings is progressively added to the tree during the analysis. The simulation results presented include how stresses are progressively generated during the tree growth, distortions related to the redistribution of growth stresses during log sawing, and distortions and stresses in drying reflecting the effects of growth stresses. The results show that growth stresses clearly vary during tree growth and also form a large stress gradient from pith to bark. This in itself can result in significant bow and crook deformations when logs are sawn into timber boards. The distortion results from the simulations match well with the results observed in reality. The parametric study also showed that the radial growth stress distribution is highly influenced by parameters such as modulus of elasticity, micro fibril angle and maturation strain.     

Simple analytical methods to predict one- and two-dimensional drying stresses and deformations in lumber

This study was conducted to develop analytical models for the prediction of drying stresses and defomations in lumber. Both one- and two-dimensional analytical models were developed with two assumptions: the visco-elastic creep could be neglected, and the diffusion coefficient is constant with moisture changes. The method developed in this study showed that the drying stress of lumber with symmetric moisture profile could be approximately predicted using one-dimensional (1D) and two-dimensional (2D) models. In the case of the 1D model, drying deformations could be determined rather easy and the drying stress can even be predicted by hand calculation. The results of this study might be used for lumber with an asymmetric moisture profile. In order to predict more accurately drying stress and deformation across overall moisture changes, however, this procedure should be incorporated with the other moisture transport models and might be extended to a 3D model.     

The variable parameter rheological model of wood

How to establish the rheological model to simulate creep behavior of wood and wood-based composites under change-load has not been solved in research of wood rheology. This paper presents a new model—variable parameter rheological model. The bending creep behavior of small clear poplar specimens under different constant load levels were examined. The load levels within 50% of rupture load of the specimens, and the experimental creep behavior were simulated by the variable parameter Maxwell model. The results show that using only one model of variable parameters may simulate the creep behavior of wood under different constant load levels very well. Applying the generalized Boltzmanns superposition principle, the variable parameter rheological model can be used to simulate the creep behavior of wood under change-loads conveniently and accurately.     

The modelling of time-dependant deformation in wood using chemical kinetics

Summary The development of rheological models to predict creep has led to the derivation of quite complex equations that can predict creep reasonably accurately. However, these models are conceptual and are not based on a fundamental understanding of the actual deformation processes occurring within the material. The concept of modelling creep using a chemical kinetic approach is one that attempts to understand creep in wood at a molecular level and, from this, to develop models that more accurately predict creep deflections.This paper presents two models developed from chemical kinetic theory, that describe the time-dependant deformation of wood. The validity of applying these models to experimental data has been assessed by stress relaxation tests on thin samples of Sequoia sempervirens. Two stages of experimentation were carried out. In stage 1, both models were applied to the results of stress relaxation tests on 6 samples. Similar values of activation energy and activation volume were calculated by both models and a single energy barrier was found to dominate the deformation process.In stage 2, the effect of varying the initial applied stress on activation energy and activation volume was assessed by carrying out stress relaxation tests at stress levels of 25%, 30% and 35% of the short-term strength. Values of activation energy and activation were found to increase as the applied stress level decreased.Both models describe the time-dependent behaviour of wood well, however their ability to predict long-term creep deflections may be limited. Future work will develop these models further in order to improve long-term creep prediction and then apply them to the results of both creep and stress relaxation tests at a variety of stress levels and moisture contents in order to test their validity.     

Use of Leicester's “rheological model for mechano-sorptive deflections of beams”

Summary The model for mechano-sorptive deformation proposed by Leicester is used to predict stress relaxation of wood drying under constraint from apparent creep of drying wood under constant load. The predictions are compared with measurements on four pairs of beams, one beam in each pair being tested under constant load, the other at constant deflection. Agreement was sufficiently close to demonstrate the value of the model.     

Numerical and experimental analysis of a wood drying process

 Experimental investigation and computational analysis were performed to evaluate the influence of the ambient air parameters during the drying process on the temperature, moisture and resulting deformations and stresses in wood samples. The numerical procedure uses the Finite Volume Method to discretise the equations governing heat, mass and momentum balance and takes into account the anisotropic nature of wood. The comparison of the numerical and experimental results shows very good agreements, implying that the proposed numerical algorithm can be used as a useful tool in designing wood drying schedules. Received 31 March 1999     

Modeling wood pole failure

Summary This is the first of two papers designed to describe the most recent efforts in using contemporary technology to predict strength and failure location in wood poles. In this report, a three-dimensional finite element model is presented which was developed to provide a rational stress analysis tool for wood poles. Due to practical considerations, only critical pole segments were subjected to stress analyses. Twelve-inch (30.5 cm) segments were selected for analysis which contained knots or knot clusters deemed consequential.The linear elastic model assumes small-deflection theory, and exploits linear strain, 15-node wedge and 20-node parallelepiped, isoparametric finite elements. Element geometry was selected to reflect knot size distribution found in full-size wood poles used in North America. Boundary conditions represented both applied loading and support considerations.Model verification studies were conducted on poles with isotropic (steel) and anisotropic (wood) material properties with and without spiral grain and variable longitudinal elastic properties along the pole radius. The results showed excellent agreement between theoretical and numerically-predicted pole stresses. The effect of boundary conditions on predicted stress distribution was defined, and the element geometry was appropriately modified. The developed model proved to be a rational basis for a more enhanced version to predict the mechanical behavior of wood poles with several inherent growth characteristics.     

Deformation kinetics based rheological model for the time-dependent and moisture induced deformation of wood

Summary A new general rheological model for the calculation of the creep of wood is presented. The flow equation derived in the theory of molecular deformation kinetics is adjusted to account for creep flow, moisture content change induced swelling/shrinkage and their combined effect by making an assumption that both of these processes activate the same bond breaking and reforming process. The rheological model is built by making the dashpots in a generalised Maxwell material model to obey the adjusted flow equation and by placing an additional swelling/shrinkage component to each parallel Maxwell element. Two calculated examples of the performance of the model with comparisons to experiment results are given. It seems that an explanation for the mechano-sorptive effect can be found at the coupling of the creep deformation process and moisture swelling/shrinkage and the non-linearity of the phenomena.This work has been financed by the Academy of Finland and VTT (Technical Research Centre of Finland)     

A microwave applicator for on line wood drying: Temperature and moisture distribution in wood

Summary An especially designed open microwave applicator was analysed using wood as the material to be heated and dried. The idea was to develop an on line microwave construction consisting of several small open applicators, each fed by a small standard magnetron (for example 1.4 kW main power). The process was analysed by measuring the wood temperature during heating using an IR-camera and detecting the moisture distribution during drying by CT-scanning. Pine and birch wood samples were used in the experiments, mainly 40 mm in thickness. The experiments show that the power distribution differs between dry wood and moist wood. The analysis of the temperature fields captured by the IR-camera during the first minutes allows a rather accurate determination of the MW power. Consequently, the drying proceeds unevenly in the wood specimens, especially in the longitudinal direction. The dimensions of the applicator and its relation to the wood dimension are very important. However, the wood was not destroyed, the temperature and moisture gradients did not affect the wood in terms of checks or deformations. The drying rate in different positions of the specimen varied between 0.30 and 0.80 percentage moisture content/min. The uneven energy, meaning temperature and field distribution, is to be compensated in the future by a moving wood load and by alternating the position of each applicator in a larger scale microwave pilot plant. Received 25 February 1997     

Identification of moisture-induced stresses in cross-laminated wood panels from beech wood (Fagus sylvatica L.)

The crosswise bonding of the layers in laminated solid wood panels results in internal stresses when the humidity varies. The layers hinder one another as a result of the anisotropy of wood. The purpose of this study was to determine the internal stress state in free and constrained swelling. The expansion properties in the three panel directions were measured. Furthermore, the swelling of samples was constrained while the resulting forces were recorded. Hygroscopic warping experiments were carried out inducing a climate gradient within the panels. Afterwards the stresses were calculated from released deformations and non-destructive measurements of the Young’s modulus. The materials used were untreated and heat-treated beech wood, the latter modified in two levels. In addition to homogenously structured panels, treated top layers were combined with an untreated middle layer. Swelling, swelling pressure, warping and internal stresses considerably decreased from untreated to treated wood. If layers from treated and untreated material were combined, stresses and deformations increased as compared to the variants produced only from treated wood. It was concluded that the lower equilibrium moisture content of heat-treated beech wood improves its dimensional stability, which results in smaller deformation differences between the layers. Hence, the stresses were less distinctive.     

Modeling of cell wall drying stresses in wood

All applications of wood involve drying the material from the green state. The cell wall may be viewed as a laminate consisting of different layers. The layers have different orientations and therefore different moisture expansion characteristics. As a result, stresses will develop in the layers due to drying. Micromechanical models for fibre composite materials were used in combination with a laminate analogy in order to calculate these drying stresses in the cell wall layers S1, S2 and S3. Resulting stresses were very high. In reality viscoelastic effects will significantly reduce stresses at high moisture content. However, at lower moisture content irreversible cell wall damage is likely to form as a result of the stresses computed by the model. Received 20 October 1998     

Cooling and steam conditioning after high-temperature drying of Pinus radiata board: experimental investigation and mathematical modelling

 Steam conditioning of softwood boards after kiln drying is of critical importance for relief of residual drying stresses and to improve distribution of final moisture content. The conditioning practice in New Zealand includes two steps: immediately after high temperature (HT) drying the load is cooled until the core wood temperature is 75 to 90°C, and then the stack is steam conditioned for a period of 1 to 4 hours depending on the lumber thickness and moisture content after drying. In this work, experimental and theoretical studies were performed to better understand the conditioning process and to investigate factors which influence its effectiveness. In the experiment, 50 mm thick Pinus radiata sapwood boards were first dried at 120/70°C for 11, 12, 13, 16 and 18 hours, respectively, to varying moisture contents, and then cooled and steam conditioned for 1 hour. To assess the effectiveness of conditioning, moisture pick-up, moisture gradient, and transverse residual drying stress (indicated by cup and strain) were measured. It was found that drying wood to a low moisture content (below 6%) increased the conditioning effectiveness. A separate matched stack was conditioned for 4 hours after 13 hours drying which showed better results than 1 hour conditioning. A mathematical model for wood drying was extended to include both the cooling and conditioning phases. The model was numerically solved to examine the wood temperature and moisture content changes during the whole process of drying, cooling and final steam conditioning. Increase in wood temperature, moisture pickup and moisture gradient during steam conditioning were predicted and validated by the experimental data. This information is currently being used at the New Zealand Forest Research Institute in simulation of stress development and relief for drying of Pinus radiata lumber. Received 6 July 1998     

Mechano-sorptive creep in wood fibres

In order to investigate the way in which fibre properties affect the mechano-sorptive creep phenomenon in paper, single wood fibres were exposed to tensile stresses at a constant humidity of 80% relative humidity (RH) and in a cyclic humidity environment varying between 80 and 30% RH. Contrary to earlier claims, it was demonstrated that single wood fibres exposed to a cyclic RH show a considerably higher creep than that corresponding to the highest RH experienced in the cycle, i.e., a mechano-sorptive behaviour. The creep strain rate at cyclic humidity was shown to be a function of the creep rate at constant climate, and to be an apparent linear function of the applied stress.     

Transient moisture effects on wood creep

To gain insight into the physical nature of the coupling between mechanical stress and humidity variations, the behaviour of thin wood strips was studied using specially developed apparatus for creep/recovery and relaxation/blotting-out tests in a controlled humidity environment. The load time and the rate of viscoelastic creep were found to have little influence on mechano-sorptive creep. Moreover, creep trajectory curves for specimens with continuous and interrupted humidity cycles indicated divergence from simple creep-limit behaviour. The effect of transient moisture was also modelled numerically at the molecular level using an idealized cellulose-based composite. Preliminary results suggest that: (i) during free shrinkage, the cellulose chains in elementary fibrils may bend perpendicular to the planes of the hydrogen bonded sheets which form the crystalline lattice; (ii) transient hydrogen bonding between the crystalline cellulose and amorphous polymer owing to the introduction or removal of water may accelerate shear slip between the two phases in the presence of an external load. Received 6 July 2000 The financial support of the Swiss Federal Office for Education and Science is gratefully acknowledged.     

Modelling and simulation of deformation behaviour during drying using a concept of linear difference method

This study deals with the development of a two-dimensional model to simulate the deformations in wood samples during the wood drying process for the evaluation of the drying quality. The samples cut from sapwood of beech were used to analyse the moisture content distribution of the samples at two different drying conditions. A new concept based on a linear difference method was developed to use the moisture content distribution of the samples for the simulation process to predict deformation due to casehardening. The real deformations of the prongs were compared with the simulated ones for further improvements. The results show that the model can be used to simulate the deformations independently from different drying times and drying conditions. A good comparison between real and simulated changes in deformation was found for the drying process at constant climate conditions. The results provide a useful basis for further investigations on the modelling and simulation of the deformation of the samples due to different drying processes.     

Wood as a natural smart material

The dominant feature of artificial smart materials is the “shape memory” effect. This phenomenon is based on frozen strains (FS). They were detected in wood fastened specimens during drying in the early 1960s. The integral law of wood deforming under loading and moisture content and/or temperature changes was subsequently formulated. This law takes into account the forming of FS. It was applied for the calculation of wood drying stresses. Stress memory and strain memory effects for wood were discovered. Wood has the ability to recollect the type of loading (tension or compression) which it had undergone. The difference between the free and restrained shrinkage is named “frozen shrinkage” (FSh). In calculations of drying stresses, it is more justified to use the FSh concept than “mechano-sorptive creep” (MSC). The MSC phenomenon is observed at cyclical change of moisture content in loaded wood. “Hygrofatigue” that reduces wood stiffness plays the main role in this process.     

木材静曲蠕变成套测试系统的研发

为解决木材变湿蠕变测试普遍存在的环境参数(温湿度和风速)控制方式和控制精度不足、蠕变变形量测试灵敏度和精度不足、数据智能采集和处理以及系统安全防护不足等问题,在集成现有技术的基础上研发出一套木材蠕变测试系统。该系统包括环境气候箱、蠕变测试机架、木材蠕变变形量及干缩湿胀测试单元、荷载同时装卸单元、数据采集和处理单元、系统保障和防护单元6个部分。该系统可在温度为0~70℃、相对湿度为10%~98%、风速为0.3~5.6 m/s时对木材或木基材料的普通蠕变和机械吸附蠕变进行长时间稳定的测试、记录,蠕变变形量及木材厚度方向的干缩湿胀检测精度为±0.01 mm,数据采样间隔在1 s~24 h范围内可调。与现有木材蠕变测试系统相比,本系统在多参数自动同步获取、数据采样精度、运行稳定性、安全性和环境风速可调性等方面有独特优势。通过前期对木材112 d循环变湿蠕变量、干缩湿胀量及环境温湿度参数的观测和测试结果分析,证实该套检测系统可对木材的蠕变挠度、干缩湿胀量、环境温湿度等参数进行长期连续稳定的检测、记录和显示,所有测试指标均能达到设计预期。同时,由于该系统具有多参数协同检测和精度较高等特性,使得实测木材变湿蠕变比采用喷蒸变湿处理试件所获蠕变测试结果在局部地方存在明显差异,如吸湿过程中的木材静曲挠度并不都是反向减小,而是取决于吸湿速率和外荷载的竞争关系,从而为木材静曲变湿蠕变机理的揭示提供了有力证据。该系统的研制为精确可控变温变湿环境下木材蠕变机理的研究提供了新的平台。