Modeling and simulation of viscoelastic behavior (tensile strain) of wood under moisture change*

Transcription

1 Wood Sci. Technol. 20: (1986) VVood Science and Technollogy 9 Springer-Verlag 1986 Modeling and simulation of viscoelastic behavior (tensile strain) of wood under moisture change* J. Mukudai and S. Yata, Kyoto, Japan Summary. A hypothesis was proposed on the mechanism of the characteristic viscoelastic behavior of wood under moisture change. The hypothesis was based on the inference in which the characteristic behavior might be attributed to the looseness of the interface between the S 1 and $2 layers in a cell wall. A mechanical model representing the behavior of a single cell wall on basis of the hypothesis and the results of simulation by the use of the mechanical model with the computer were shown in this repo~ The characteristics of the viscoelastic strain obtained from the simulation agreed well with those of published experimental results. ntroduction The viscoelastic behavior of wood under moisture change has been the subject of many reports. t has been shown that the viscoelastic behavior under moisture change and constant load differed characteristically from the behavior under constant moisture and constant load: the strain resulting from a constant load during one or more cycles of humidity change was far larger than the strain produced by the constant load at the equilibrium moisture content corresponding to the minimum or maximum relative humidity, and the strain increased during the drying part of the cycles and decreased during wetting. t has been hypothesized in explanation of this behavior that a stress bias makes for slippage between molecular chains during breaking and remaking of hydrogen bonds resulting from moisture changes (Gibson 1965; Eriksson, Nor6n 1965; Schniewind 1966; Takahashi, Schniewind 1974; Arima 1974). Leicester proposed a model consisting of a Maxwell model, Voigt models and a mechanosorptive model in series, but did not explain the details of the mechano-sorptive model (Leicester 1971). Another model representing a limited aspect of viscoelastic behavior under moisture change was proposed by considering the effect of diffusion of moisture within a loaded specimen (Schaffer 1972). These conceptual hypothesis and models can not be applied directly to predict viscoelastic behaviors * The authors are indebted to Professor Arno P. Schniewind, Forest Products Laboratory, University of California, for reviewing the manuscript

2 336 J. Mukudai and S. Yata over a period of creep and recovery under moisture change. Then, an empirical equation was proposed and predictions by use of the equation were carried out for viscoelastic behavior over a period of creep and recovery under moisture change, but without clarifying the mechanism of such viscoelastic behavior (Ranta- Maunus 1975). The purpose of this report was to propose an interpretation and a model of viscoelastic behavior under moisture change, and to simulate by computer the behavior of a single cell wall over a period of a creep and recovery under moisture change cycles to prove the correctness of the interpretation and suitability of the model. Hypothesis for devising the model The authors presumed that the characteristic behavior was derived from the inherent microstructure of the wood cell wall consisting of the intercellular layer (), the primary wall (P), and the outer layer (S1), the middle layer ($2) and the inner layer ($3) of the secondary wall, as follows: The layer is composed of lignin forming a three dimensional molecular structure of relatively low hygroscopicity, and transmits external forces to neighboring cells. t is well known that lignin, hemicellulose and cellulose are softened by water molecules. A recent study of chemical processing has shown that wood could be heat-softened or heat-melted by introducing the acyl group into wood components (Shiraishi 1983). This appears to show that lignin has high flexibility because of low crosslinking density. The orientation of microfibrils composed of hygroscopic cellulose determines differential swelling and shrinkage within cell wall layers: swelling and shrinkage are far larger perpendicular than parallel to microfibrils. n the P layer, fine microfibrils form a netlike structure, and the lignin content is high and the cellulose content is low. n the $1 layer, the microfibril orientation is perpendicular to the longitudinal axis of the cell, and swelling and shrinkage are negligible perpendicular to the axis i.e., in circumference, and large parallel to the axis. n the $2 layer, the orientation of microfibrils is nearly parallel to the longitudinal axis of the cell, and swelling and shrinkage are far larger perpendicular than parallel to the axis. Any swelling and shrinkage in the $2 layer will dominate the total dimensional change of the cell wall perpendicular to the longitudinal axis because the $2 layer is thicker than the others. The flexibility of the Sz layer appears to be far less than that of the outer, P and S 1 layers because the $2 layer is rich in cellulose and in crystallites in which cellulose chains are arranged regularly and bonded tightly by hydrogen bonds. n the $3 layer, the orientation of microfibrils is perpendicular to the longitudinal axis of cell, and the swelling and shrinkage perpendicular are far smaller than in parallel. The observation that there is almost no change in the diameter of the lumen after drying and wetting proves that there is very little swelling and shrinkage of the $3 layer in circumference (Stature 1964a). Therefore, the $2 layer swells towards the $1 layer in wetting, and shrinks towards the $3 layer in drying. The, P, and S1 layers appear to have a very high flexibility, because the diameters of the, P and S 1 layers increase or decrease rapidly in response to the swelling and shrinkage strain of the $2 layer, which is very much in comparison to the mechanical strain of the proportional limit produced in short-time loading test

3 Viscoelastic behavior of wood under moisture change 337 under constant moisture content, during drying and swelling. Also, at high equilibrium moisture contents, although water molecules play the role of plasticizer, these layers, especially the $1 layer, appear to work as a hoop restraining the swelling of the $2 layer (Stamm 1964b).'The outer layers resist external forces as a unit fitting tightly on the $2 layer by sufficient friction, and at low equilibrium moisture contents these layers appear to resist as a unit bonded tightly to the $2 layer by completion of remaking of the hydrogen bonds. n the drying process from a high to a low equilibrium moisture content, dried air in the lumen causes the $3 layer to shrink first, followed by the $2 layer. Molecular chains of the shrunk portion in the $2 layer are pulled successively towards the $3 layer as shrinkage proceeds, and looseness (the word "looseness" implies a state so that slippage between two surfaces can take place easily by external force during water desorption, but that the two surfaces can be bonded by remaking of the hydrogen bond after water desorption and can then act as a unit) between molecular chains of the inner dried portion and the outer wet portion results from the movement of molecular chains. f an external force is applied to the cell wall at a high equilibrium moisture content and then the cell wall is dried, the looseness causes a redistribution of the resulting stress from the dried portion to the outer wet portion of the cell wall. As a result, stress bias is produced between the dried portion and the wet portion. t seems obvious that the slippage between molecular chains by such a stress bias takes place rapidly in the initial period of moisture change at the boundary between the $1 and $2 layers rather than in the $2 layer moving gradually towards the Sl layer. This is inferred from the following: a large increase of strain observed in the initial period of drying of experimental results shows rapid stress increase and high flexibility. Firstly, since the $2 layer has low flexibility, it appears that it can not deform rapidly and not very much, while the +P+S layer can do so. Secondly, the sustaining force of the thin inner layer, which dries in the initial period of drying, decreases by the looseness, and the decreased sustaining force is redistributed to the far thicker outer layer, which does not yet dry. f the looseness that is produced is moving with drying in the $2 layer, the increase of stress of the outer layer will be small in the initial period and then will become larger gradually. On the contrary, if it is produced immediately between the $1 and the $2 layers by drying, the increase of stress of the +P+S1 layer will be large in the initial period and then will be small, because the + P + $1 layer is thin. At the final period of drying of the cell wall, the stress in the outer +P+S~ layer reaches a maximum and the stress in the $2+ $3 layer becomes a minimum. At the same time, the slippage due to the stress bias reaches a maximum at the boundary between the $2 and S~ layers. The magnitude of such a stress bias depends on the range of moisture content change. n the final period, at low equilibrium moisture content, both layers $2+$3 and +P+S1 are tightly bonded by completion of hydrogen bonding and act as a unit, fixing the difference in strain between the layers produced by the stress bias. When unloaded at a low equilibrium moisture content, the fixing of the difference in strain between the layers produces "drying set" by converting the stresses of the external force into balanced internal tensile and compressive stresses in the layers.

4 338 J. Mukudai and S. Yata On the contrary, in the rewetting process from the final low to the initial high moisture content, initially the $3 layer and then the $2 layer swells. Again there is a redistribution of stress to the swollen portion from the outer shrunk portion. Finally, the +P+S1 and S2+S 3 layers resist the external force as a unit by sufficient friction at the interface resulting from the completed hoop effect on the $2 layer, and the stress in each layer becomes equal to the initial stress distributed in each layer by the loading at the initial high equilibrium moisture content. The strain increase at the first moisture increase during cyclic moisture changes appears to be entirely the result of the slippage of molecular chains by the looseness produced previously between the $1 and $2 layers by drying prior to loading. The observed strain is equal to the sum of the swelling or shrinkage strain and the mechanical strain mentioned above which is the strain of the outer layer of the cell wall; presumably the + P + Sl layer. The authors studied previously the distribution of metallic ions in the cell wall of wood impregnated with salt solution and observed that a larger amount of ions was deposited in the outer zone of the $2 layer adjoining the $ layer than in the other portions of the cell wall, while such a tendency did not appear on the boundary of the $2 and the $3 layers (Yata, Mukudai, Kajita 1979). This result appears to show that the outer zone of the $2 layer adjoining the S~ layer is porous and that the contact points (the hydrogen bond points) between the S~ and the $2 layers are the fewest in a cell wall, and this appears to be supporting evidence for the hypothesis. Viscoelastic model under moisture change A simplified model based on the above hypothesis is shown in Fig. 1. The model consists of two parallel sub-models and (hereafter, sub-models and are called shortly model and model, respectively) which are each composed of a Maxwell model, a Voigt model and a swelling and shrinkage element A1 or A 2 having swelling and shrinkage coefficient ~1 or c~2. Running block B moves on bar C and transmits a load to models and 11 through bar E. Bar D is composed of a hygroscopic material and is able to swell and shrink under moisture change. The running block B moves on bar C in proportion to the swelling and shrinkage of bar D, and can change the portion of load applied to models and 1. The running block positions a and b are those of a high equilibrium moisture content and a low equilibrium moisture content, respectively. Values of the viscoelastic model constants change depending on the humidity conditions in the chamber. Connections F1 and F2 are pin connections rotating freely while molecular chains slip by moisture changes, but become fixed so that the inclination of the bar C is constant, while the moisture content of bar D and elements Al and A 2 are in equilibrium. After bar D and the elements A and A2 reach a high or a low equilibrium moisture content, models and act as a unit, fixing the difference in strain between the two models produced up to the time when the hoop effect or hydrogen bonding is completed.

5 Viscoelastic behavior of wood under moisture change 339-2,0, L F z-~"- J ~...~...J ~r 2 c _~ t," E D i 0" 1 a Wet b Dry Air conditioned chamber Fig. 1. Model representing viscoelastic behavior of wood under moisture change. h Model ($2+$3 layer); lh Model 0+P+S layer); A, A2: Hygroscopic materials having swelling and shrinkage coefficient cq, e2, respectively; B: Running block; D: Hygroscopic material adjusting stress bias by swelling and shrinkage; F1, F2: Pin connections n this model, the strain observed by a researcher is that of model corresponding to the outer layer; presumably the +P+S~ layer. Also, connections F~ and F2 are fixed so that the strain of model can't exceed that of model because the inner layer (model ) is wrapped into the outer layer (model ). Simulation of viscoelastic behavior under moisture change Finite difference approximations for calculation of strain The following are the governing equations for the Maxwell and Voigt models, respectively: de 1 da a dt E dt r/ and ds a = E e + ~/-dt. (2) The above equations must be satisfied by substituting values of element constants changing with moisture content and values of stress changing with a stress bias at each time during moisture change. For calculation of viscoelastic strain, numerical (1)

6 34O J. Mukudai and S. Yata [(t.~t) b 6" t Time t*~t Fig. 2. Diagrams of the finite difference approximation equations were derived from Eqs. (1) and (2) by a finite difference approximation as shown in Fig. 2. For the strain of the spring in a Maxwell model, O" e (t +At) =~ (3) and for the strain of the dashpot in the same model, O" e (t +At) = e(t) +--'At. (4) q0 For the strain of a Voigt model, a.st (1-/~) e(t+at) e ( t ). - - (5) t/l (1 +fl) (1 +fl) where, fl= E1 2r/i 9 At. As a check on the accuracy of this approximation, strains were calculated by this approximation in the case of constant moisture content and constant load. The results agreed well with strains obtained by the integration of Eqs. (1) and (2). Also, in the case of constant rate of stress increase at constant moisture content, the calculated values agreed well with values obtained by integration~ The value of 0.1 min was used for At for the simulation. While the inner layer (model ) and the outer layer (model ) act as a unit by completion of the hydrogen bonding or by completion of the hoop effect of the S 1

7 Viscoelastic behavior of wood under moisture change 341 layer, the following equation is applicable: (0" + Acr)/E (1, 0) + em (t) + (cq +Aa) "At/~ (1,0) + evl (t)' (1 -fl (1))/(1 + fl(1)) where, + (0-1 + A0-)'At/(rl(1, 1)" (1 + fl(1))) + cz + Ae = (a2-d0-)/e (2,0) + em2 (t) + (0"2--Aer) 9 At/r/(2,0) + ev2 (t) 9 (1--fl(2))/(1 +/?(2)) + (0"2-Aa) "At/(q(2, 1)" (1 + fl (2))) + ~2 (6) E(1, 1) E(2, ) b'(1)- 2-~(1,1).at, fl(2)- 2"r/(2,1).3t. r 0" 2 Aa em1 (t), 8M2 (t) evl (t), ev2 (t) Ae ~1~ ~2 Stresses in models and, and ~r~ = - a2 during recovery Additive internal stress to hold difference of strain Ae in time interval At Residual strains of models and 1 produced up to time t Strains of Voigt models of models and 1 produced until time t Difference of strain between models and l~ at the time when the hydrogen bond or the hoop effect is completed. When the strains of the two models are equal, A e = 0 Swelling and shrinkage strains of models and up to time t +At/2 Conditions assumed for the simulation This report is confined to simulation of the tensile viscoelastic strain of the cell walt parallel to the longitudinal axis of the cell because it has more comprehensible features than other types of loading. The assumed range of moisture change was from the maximum of the fiber saturation point (F,S.P.) of 30% to the minimum of 0% moisture content. A moisture change cycle consisted of drying for 100 rain and wetting for 10O rain. Model was regarded as the $2+$3 layer and model 1 as the +P+S1 layer. Since experimental data on the viscoelastic constants and shrinkage coefficients of the two composite layers was unknown, the following conditions for determining these constants were assumed on the basis of limited knowledge of the properties of the two layers: 1. The elastic moduli parallel to grain of spruce were used for the values of E (1,0) at 0% moisture content and the fiber saturation point. 2. E(1,0) > E (2, 0) 3. E(1,1)>E(2,1) and r/(l,l) > r/(2,1) 4. ct 2 > e~ 5. r/(1,0) > q(2,0) Three assumed regimes of creep and recovery under moisture change cycles were simulated as shown in Figs Changes in moisture content, stress bias, viscoelastic constants, and swelling and shrinkage strains are given by the following equation: fl(t) = fir(1 - exp (-Z" t)) (7)

8 342 J. Mukudai and S. Yata where, fl (t) = moisture content, stress bias, element constants or shrinkage strains at time t; fir = range of change; Z = constant; t = time. The value of fir of the stress bias shows the stress transferred from model to by the looseness during drying and from model 1 to by the hoop effect during wetting. n this equation, the value of Z was 0.5 in the case of stress bias because of rapid slippage by adsorption and desorption of few water molecules and 0.06 in the others. The hydrogen bond and the hoop effect were completed when the moisture content of the specimen reached 99.2% of the total moisture change, in each case 80 min after the start of either drying or wetting. Results and discussion An example of a set of element constants, shrinkage coefficients and other constants are shown in Table 1. Results of simulation by the use of these constants are shown in Figs The features of viscoelastic tensile strain of creep under moisture change cycles in these figures are similar to experimental results in tension (Eriksson, Norrn 1965), but the features of apparent strain differ from those of the experimental results: apparent strain (viscoelastic strain plus swelling and shrinkage strain) in these experimental results decreases in drying and increases in wetting. When lower stress or larger swelling and shrinkage strain was used in the simulation, similar results were obtained. Also, the creep curve under moisture change cycles in these experimental results shows a more gently Table 1. Constants of the viscoelastic model and other constants used for the simulation 0% Moisture content Model Model ] l/e(1,0) 6.0xl0-rkg-l.cm 2 l/e(2,0) 6.0 5kg-l'cm2 r/(1,0) kg 1. cm -2' min 1 t/(2, 0) 1.2 x 109 kg 9 cm -2' min i l/e(1,1) Z0xl0-rkg-l'cm 2 l/e(2,1) 7.5xl0-Skg-l-cm 2 t/(1, 1) 1.5 x 108 kf 9 cm -2' min i r/(2, 1) 2.7 x 105 kg 9 cm -2. min i 30% Moisture content Model Model 11 l/e(1,0) 8.0xl0-rkg-l.cm 2 l/e(2,0) 8.0xl0-Skg-l.cm 2 t/(1,0) 1.2xl09kgl.cm 2"mini t/(2,0) 6.0xl08kg~-cm-2.mJn 1 l/e(1,1) 2.67x10-rkg-].cm 2 l/e(2,1) 1.0xl0-4kg-l.cm 2 r/(1,1) 1.125x108kgl'cmT2"min r/(2,1) 1.5 i Swelling and shrinkage strain parallel to the longitudinal axis of cells between 0 and 30% moisture content: Model : , Model 1: External stress: 800 kg/cm 2. Stress bias: 120 kg/cm 2. The Z value in Eq. (7) for stress bias: 0.5. The Z value for moisture content, viscoelastic constants, swelling and shrinkage: 0.06.

9 Viscoelastic behavior of wood under moisture change D r... E ;f e- B t- -J A Su rface B C Center r''" i~! i :,J,l~tz Jo....!! ~B E~3 343 Oo ~~ o b Fig. 3. Schematic illustration of restraint of strain resulted from moisture gradient in specimen C g- b 15 X T[ / L~ o i2/f L~ ~ L~ H~_ of) 10,? <#'~k# ;, ~' 4 o ~- 0 ~E Xsoo ~x 0 30 %~ 0 i L ---- ~--.~ f LFL/h/LFL FL f [ 200 / Time (rain) r f Fig. 4. Tensile strains under moisture change cycles by the use of the model. -- Model 11; --- Model ; 9 Creep at constant moisture content of 30%; o Creep at constant moisture content of 0%

10 344 J. Mukudai and S. Yata increasing curve than that in the simulation over the whole period of creep. These differences may be interpreted by the following cause illustrated schematically by Fig. 3. n this figure, A, B and C show wood layers consisting of some cells and arranged in parallel from the surface to the center of the specimen. For example, in the case of tension and drying, firstly, although strain es resulted from stress bias is added to layer A by moisture change, the elongation of layer A becomes etl by restraint of layers B and C, and elongations of layers B and C become the same etl, at time t~ from the start of drying (Fig. 3a). Then, when layer Bis dried, strain es also is added to layer B, but elongations of layers A, B and C become 8t2 by restraint of layers A and C at time t2 (Fig. 3 b). Elongations of these layers then become et3 at time t3 (Fig. 3 c). Therefore, taking account of such restraint by the inner layers and swelling and shrinkage strain, it seems that the apparent strain decreases during drying and increases during wetting in each dry-wet cycle as shown in the published experimental results, and experimental creep strain becomes larger more gradually over the whole period of creep under the dry-wet cycles than the strain obtained by simulation. ncrease of apparent strain during drying, which is similar to the simulation, also is shown in the experimental result with individual pulp fibers (Jentzen 1964). t is inferred that such a restraint of strain affects the apparent viscoelastic strain in tension more than deflection in bending, which is affected largely by strain of surfaces being easily subjected to moisture change. Figure 4: q-he results are explained according to the features in Figs. 4-6, as follows: OA: The specimen conditioned at the equilibrium moisture content of 30% was stressed 800 kg/cm 2, and stresses produced by loading were and 72.7 kg/cm 2 for models and, respectively. nstantaneous elastic strain of models and lff was x Creep under the same and constant moisture condition for 100 min was started from poin t A. AB: Models and 1 were acting as a unit holding the same strain during creep, and stresses of models and 1 at point B were and 37.6 kg/cm 2, respectively, by stress relaxation of model 1. BC: Drying of the first step of moisture change cycles started after creep at constant moisture content, and stresses of models and lff recovered immediately to the initial stresses produced by loading in the wet state by release of the hoop effect. Each model acted independently without restraining each other. Then the stress of model increased by stress bias of 120kg/cm 2 resulting from the looseness and that of model decreased at the same time by the stress bias, by Eq. (7). Point a: Hydrogen bonding was completed at this point by drying, and thereafter both models acted as a unit holding the difference in strain between them constant until point C. Hydrogen bonding was always completed at the same time after the start of each drying period. Point C: Stresses of models and were and kg/cm 2, respectively, at the end of drying. CD: After the drying period, the first wetting period started, and at this time both models acted independently. Stress of model increased with increase of resistance of the $2 + $3 layer to external force by wetting, and at the same time, the stress of model decreased.

11 Viscoelastic behavior of wood under moisture change 345 Point b: The hoop effect was completed at this point of wetting, and thereafter both models acted as a unit holding the difference of strain between them constant until point D. The hoop effect always was completed at the same time after the start of wetting period. Point D: Stresses at the end of the wetting period were and 80.3 kg/cm 2 for models and 11, respectively. DE: After the second drying period started, both models acted independently until the completion of hydrogen bonds. Strain of model increased by stress bias of 120 kg/cm 2, that of model decreased at the same time, by Eq. (7). Stresses of model and 11 were and kg/cm z, respectively, at the end of drying. Models and then acted similarly to what was mentioned above following each drying and wetting period. Point G: Stresses of models and 1 were and kg/cm 2, respectively, at the end of drying and at the end of creep under moisture change cycles (1200 rain). GH: nstantaneous recovery strain by unloading of models and was 4.364x nternal stresses produced by unloading were and kg/cm 2 for models and, respectivelyl and the difference in strain between models and was x H: After unloading, recovery at constant moisture content of 0% started. Models and 11 acted as a unit holding the difference of strain between them constant until point L nternal stresses of models and were and kg/cm 2, respectively, after recovery for 1200 rain. The creep curves at equilibrium moisture contents of 30% and 0%, which were calculated by use of the constants of Table 1, are also shown in Fig. 4. n either case, the stresses distributed elastically in each model at loading changed with time: the stress in model decreased with time, the difference being added to the stress of model at the same time. The stresses in the two models after 1200 rain of creep were as follows: in the case of 30% moisture content, and 48.1 kg/cm 2 in models and 1, respectively, and in the case of 0%, and 47.0 kg/cm 2 in models and 11, respectively. Figure 5: The features from point O to point H are the same as in Fig. 4. HK: mmediately after models and recovered elastically to point H by unloading, recovery by wetting started. When the internal stresses were released by, breaking of hydrogen bonds, the strain of model recovered immediately to point J. Then, the strain of model recovered largely in a short time. Point b: The hoop effect was completed and after this point models and recovered as a unit holding the difference in strain between the models constant. Figure 6: The features from point O to point H are the same as in Fig. 4. H: The behavior of models and is the same as during recovery for 400 rain from point H of H in Fig. 4. nternal stresses of models and were and kg/cm 2, respectively, at point. Point J: This point is similar to point J in Fig. 5. K: Wetting recovery started. The behavior of models and l was similar to HK in Fig. 5, but residual strain ofmodel at point K was somewhat larger than that in Fig.5. The viscoelastic behavior under an external tensile force applied in various angles to the longitudinal cell axis may be simulated in a similar manner to that described above.

12 346 J. Mukudai and S. Yata 25 2O,H b 15 X C lo 5 ~ me 0 -;8ool ~ ol 30 ol o o 1 / l 1 /, i k_ ~ r i \ f 2 f 2 flf\[ 2# 1 r r Time (mln) Fig. 5. Tensile strains under moisture change cycles by the use of the model Model Model 1; K The viscoelastic behavior under a compressive load and moisture changes may be simulated with a similar model on the basis of the hypothesis presented. The hypothesis of the looseness between the $1 and Sz layers appears to be supported by the following experimental results: 1. t is well known that in static bending tests at constant moisture content, owing to lower strength in compression than in tension, failure appears first on the compression side of beams followed later by failure on the tension side. n studies on failure in bending under moisture change cycles, many failures took place on the tension side of beams at a larger deflection and a lower load than during creep at constant moisture content (Schniewind 1967; Schniewind, Lyon 1973). According to the present hypothesis, in the case of compression, a compression stress bias similar to the above mentioned tensile stress bias takes place during moisture changes, but, since the $2 + $3 layer is able to sustain an external compressive force because of the close contact of the two layers by compressive deformation of the +P+S] layer, failure may be more difficult in compression than in tension. On the other hand, tension failure may occur easily by a larger strain of the + P + $1 layer at a lower tensile stress during the drying period in moisture change cycles. 2. Observations of failure surfaces of wood cell walls from short-time failure tests with the electron microscope showed that, in many cases, failure took place at or near the boundary of the $1 and the $2 layers (Saiki, Furukawa, Harada 1972; C6t6, Hanna 1983). Also, observations with the electron microscope of surface

13 Viscoelastic behavior of wood under moisture change X c" 15 ~ sg me 0 9oo ~ 0 %~ 01 ' 0 f~ /-n fl.*'q,,-n " ',,,' i. ',,,' ',,,,,._.,,,._] -_J ' \f\[\f\;\;\ [ T T 200 / Time (rain) Fig. 6. Tensile strains under moisture change cycles by the use of the model Model Model 1]; K checks of wood produced by natural drying showed that many failure surfaces of drying checks exposed the $1 and $2 layers (Fujita 1974). 3. The tensile strength parallel to grain shows a maximum at a moisture content of about 8 to 10% and decreases clearly at lower moisture contents. Kollmann cited two reasons for this decrease (Kollmann 1951). According to the present hypothesis, it is inferred that the decrease in tensile strength is due to greater looseness because of larger shrinkage of the $2 layer at lower moisture contents. Since viscoelastic tensile strain under moisture changes could be obtained as shown above, characteristics of viscoelastic bending deflections of creep and recovery under moisture change cycles may be obtained by a model consisting of the same tension and compression models, and the result of the simulation may be checked with many published experimental results, in more detail. References Arima, T. 1974: Studies on rheological behavior of wood under hot pressing. 11]. Mokuzai Gakkaishi 20: C6t6, W. A.; Hanna, R. B. 1983: Ultrastructural characteristics of wood fracture surfaces. Wood Fiber 15: Eriksson, L.; Nor6n, B. 1965: Der EinfluB yon Feuchtigkeitsgnderungen auf die Verformung yon Holz bei Zug in Faserrichtung. Holz Roh-Werkst. 23:

14 348 J. M~i and S. Yata Fujita, S. 1974: The study on the mechanism of drying check of wood. Doctoral thesis of Kyoto University Gibson, E. J. 1965: Creep of wood: Role of water and effect of a changing moisture content. Nature 206: Jentzen, C. A. 1964: Effect of stress applied during drying on some properties of individual pulp fibers. For. Prod. J. 14: Kollmann, F. 1951: Technologie des Holzes und der Holzwerkstoffe. Bd. 1, pp Berlin, G6ttingen, Heidelberg: Springer-Verlag Leicester, R. L 1971: A rheological model for mechano-sorptive deflections of beams. Wood Sci. Technol. 5: Ranta-Maunus, A. 1975: The viscoelasticity of wood at varying moisture content. Wood Sci. Technol. 9: Saiki, H.; Furukawa, L; Harada, H. 1972: An observation on tensile fracture of wood by scanning electron microscope. Bulletin of Kyoto University Forests 43: Schaffer, E. L. 1972: Modeling the creep of wood in a changing moisture environment. Wood Fiber 3: Schniewind, A. P. 1966: Ober den EinfluB yon Feuchtigkeitsiinderungen auf das Kriechen von Buchenholz quer zur Faser unter Beriicksichtigung yon Temperatur und Temperaturgmderungen. Holz Roh-Werkst. 24: Schniewind, A. P. 1967: Creep-rupture life of Douglas-fir under cyclic environmental conditions. Wood Sci. Technol. 1: Schniewind, A. P.; Lyon, D. E. 1973: Further experiments on creep-rupture life under cyclic environmental conditions. Wood Fiber 4: Shiraishi, N. 1983: Plasticization of wood. n: mmamura, H.; Goto, T.; Yasue, Y.; Yokota, T.; Yoshimoto, T. (Eds.): Chemistry for wood utilization, pp Tokyo: Kyoritsu- Shuppan (in Japanese) Stamm, A. J. 1964a: Wood and cellulose science, pp New York: Ronald Press Stature, A. J. 1964b: Wood and cellulose science, pp. 22. New York: Ronald Press Takaliashi, A.; Schniewind, A. P. 1974: Deformation and drying set during cyclic drying and wetting under tensile loads. Mokuzai Gakkaishi 20: 9-14 Yata, S.; Mukudai, J.; Kajita, H. 1979: Morphological studies on the movement of substances into the cell wall of wood. 1. Mok~xi Gakkaishi 25: (Received May 13, 1985) Dr. J. Mukudai Dr. S. Yata Department of Forestry, Faculty of Agriculture Kyoto Prefectural University Nakaragi-cho, Shimogamo Sakyo-ku, Kyoto 606 Japan

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