AN ABSTRACT OF THE THESIS OF. to the Process of Drying. 2724LI/1 Z2. Michael R. Milota. as elastic, plastic, creep, shrinkage and mechano-sorptive

Transcription

1 AN ABSTRACT OF THE THESIS OF Oinglin Wu for the degree of Dotor of Philosophy in Forest Produts presented on July 1,1993. Title : Rheologial Behavior of Douglas-fir as Related to the Proess of Drying. Abstrat approved : 2724LI/1 Z2 Mihael R. Milota Large inelasti strain ours inside a piee of lumber during drying. The strain onsists of several omponents suh as elasti, plasti, reep, shrinkage and mehano-sorptive effet. The mehanial behavior of the whole board during drying is determined by the behavior of individual strain omponents and their interations. Whereas limited investigations have been made on those strains under moderate onditions, there is a lak of omprehensive researh aimed at examining the behavior at elevated temperatures and inorporating various strain omponents into a proess model. This researh provides experimental data for various strain omponents of small wood samples and an analytial tool for evaluating the drying behavior of full-size boards. Small test speimens of Douglas-fir were loaded tangentially in both tension and ompression under onstant and varying moisture onditions at different temperatures. Experiments were onduted using a small testing mahine

2 ontained within a pressure vessel. The strain fields for loaded and unloaded test samples were measured using a high resolution video amera. The required moisture hange at ontrolled temperatures was ahieved by ontrolling the total pressure in absene of air with saturated steam. Moisture ontent was monitored by a quartz spring sorption balane. The total deformation due to loading and moisture hange was deomposed into instantaneous, reep, shrinkage and mehano-sorptive omponents. Constitutive equations for eah omponent were developed as a funtion of stress, temperature, moisture, time and moisture hange. These equations were inorporated into a proess model to simulate the development of stress and strain in large piees of lumber during drying. A sliing method was used to measure the distribution of moisture and strain through the thikness of full-size boards at different stages of drying. The proess model was used to predit drying stress and strain based on the measured moisture distribution and material properties. The effet of drying onditions and types of wood on the development of drying stress was demonstrated. The predited drying strains under different drying onditions were ompared with the orresponding measurements.

3 RHEOLOGICAL BEHAVIOR OF DOUGLAS-FIR AS RELATED TO THE PROCESS OF DRYING by Qinglin Wu A THESIS Submitted to Oregon State University in partial fulfillment of the requirements for the degree of Dotor of Philosophy Completed July 1, 1993 Commenement June, 1994

4 APPROVED: Assistant Professor of Forest Produts in harge of major -<I4tM0J-AI - Head of Depa tment of Forest Produts Date thesis is presented July 1, 1993 Typed by Qinglin Wu for - - inglin Wu

5 ACKNOWLEDGEMENTS I would like to give my sinere gratitude and appreiation to the following: Dr. Mihael R. Milota, my major professor, for his guidane and full support throughout this study; Dr. E. Wolff, Dr. T. MLain, Dr. R. Lehiti, and Dr. J.R. Baggett for their advie as ommittee members. My sinere appreiation is also extended to Dr. P.E. Humphrey, Dr. J.W. Funk and Dr. C.C. Brunner for allowing me to use their sanning equipment and software during my researh. Speial thanks are given to A.R. Oliver, Emeritus Professor of Civil Tasmania, drying. and Mehanial Engineering, University of Australia for leading me to the field of wood Lastly, this thesis is dediated to my wife, Junqing Zhu, and my daughter, Rhonna Fan Wu, for their unfailing love and support of my efforts, without whih I wouldn't have aomplished my goals. This researh was funded by the USDA ooperative state researh servie under grant number

6 TABLE OF CONTENTS I. INTRODUCTION 1 II. LITERATURE REVIEW Stress Development in Drying of Lumber Wood Properties Related to Drying Stresses Experimental Findings Constitutive Modeling Modeling of Stresses in Drying of Lumber 26 III. ANALYTICAL APPROACH Stress-Strain Relation of Small Wood Samples Basi Conept and Definitions Constitutive Modeling Distribution of Moisture and Temperature Assumptions Data Fitting Stresses and Strains in Drying of Lumber Method of Analysis Method of Solution 49 IV. EXPERIMENTAL TECHNIQUES Equipment Design and Funtions Load Appliation Moisture Content Monitoring Environmental Control Deformation Monitoring Experimental Design Material Seletion and Preparation Tests of Wood Properties Lumber Drying Experiments 89 V. RESULTS AND DISCUSSION Stress-Strain Relation of Small Wood Samples Deformation under Load at Constant Moisture Contents Deformation under Load during Moisture Change Distribution of Moisture and Temperature Results of Measurement Results of Data Fitting 163

7 5.3 Stresses and Strains in Drying of Lumber Material Properties Drying Stress and Strain 170 VI. CONCLUSION AND RECOMMENDATIONS Conlusion Reommendations 195 REFERENCES 196 APPENDICES A: Nomenlature 202 B: Priniple of Strain and Time Hardening 206 C: Proedure for Fitting Creep Data 211 D: Proedure for Isolating Mehano-sorptive Strain from the Measured Total Strain 213 E: Computer Programs 215

8 LIST OF FIGURES Figure Page 2.1. Stress-strain relation of wood under the short-term loading Creep urve of wood Shrinkage-moisture ontent relation of wood for nonollapsing speies (CSIRO, 1965) Generalized 8-element Kelvin model for mehanial reep from Martensson (1988) Deomposition of total strain ( ) into instantaneous and mehano-sorptive (EM) strain omponents. (a) load funtion, (b) moisture funtion, and () strain. (E ), reep (E), sirinkage (ES), Physial aspet of proess model. (a) lumber board, (b) one-dimensional mesh, and () Crank- Niholson finite differene sheme Solution proedure for alulating stress and strain in lumber drying Shemati of overall equipment layout Pressure vessel and tensile devie. (a) side view and (b) front view Loading devie for ompression. (a) side view and (b) front view Unit for monitoring moisture ontent Control system for the apparatus Control signals. (a) PID temperature ontroller and (b) PID pressure ontroller Unit for eliminating the ondensed water from pressure vessel Flow hart of sanning system (Irving, 1989) Speimen arrangement in tests. (A) tension and (B) ompression

9 LIST OF FIGURES, CONTINUED Figure page Connetivity analysis of sanning program Setup for sanning program alibration Calibration urve of sanning program Test speimens. (a) tension and (b) ompression Shemati of experimental dry kiln Results of reep tests at 150 F and 10% MC. (a) temperature history and (b) pressure history Tensile reep of Douglas-fir in the tangential diretion at 10% MC. (a) a funtion of stress and (b) a funtion of temperature Compressive reep of Douglas-fir in the tangential diretion at 10% MC. (a) a funtion of stress and (b) a funtion of temperature Tangential MOE of Douglas-fir as a funtion of temperature at 10% MC Creep parameter in tension and ompression as a funtion of temperature at 10% MC. (a) parameter K/a and (b) parameter n Comparison of reep ompliane under tension and ompression at 10% MC and different temperatures Test onditions for drying under load at 150 F. (a) temperature history and (b) pressure history Strain variation during initial onditioning in drying tests at 150 F Results from drying under tension at 150 F. (a) moisture-time relation and (b) strain-time relation Variability of measurement for drying under tension at 150 F Results from drying under ompression at 150 F. (a) moisture-time relation and (b) strain-time relation. 115

10 LIST OF FIGURES, CONTINUED Figure Page Moisture (a) and strain (b) data from drying under ompression at 80 psi stress level. (A) 90 F, (B) 120 F, (C) and (D) 180 F Tangential shrinkage and moisture ontent relation of Douglas-fir from drying at 150 F Tangential shrinkage oeffiient of Douglasfir as a funtion of temperature Net strain from drying under tension at 150 F and 40, 60, 90, and 120 psi stress levels Net strain from drying under ompression at 150 F and 40, 60, and 80 psi stress levels Net strain from drying under ompression at 80 psi stress level. (a) 90 F, (b) 120 F, () and (d) 180 F Predited reep strain for drying under tension at 150 F and 40, 60, 90, and 120 psi stress Predited reep strain for drying under ompression. (a) 150 F and 40, 60, and 80 psi stress and (b) 90, 120, 150, and 180 F and 80 psi stress MS strain and moisture ontent relation from drying under tension at 150 F, lines showing fitted values with Equation (a) 40 psi, (b) 60 psi, () 90 psi, and (d) 120 psi stress MS strain and moisture ontent relation from drying under ompression at 150 F, lines showing fitted values with Equation (a) 40 psi, (b) 60 psi, and () 80 psi stress MS strain and moisture ontent relation from drying under ompression at 80 psi stress level, lines showing fitted values with Equation (a) 90 F, (b) 120 F, () and (d) 180 F MS parameter km as a funtion of temperature from drying under ompression at 80 psi stress

11 LIST OF FIGURES, CONTINUED Figure Page Fitted net strain from drying under tension at 150 F. (a) 40 psi, (b) 60 psi, () 90 psi, and (d) 120 psi stress Fitted net strain from drying under ompression at 150 F. (a) 40 psi, (b) 60 psi, and () 80 psi stress Fitted net strain from drying under ompression at 80 psi stress. (a) 90 F, (b) 120 F, () and (d) 180 F Test onditions for wetting under tension at 150 F. (a) temperature history and (b) pressure history Results from wetting under tension at 150 F. (a) moisture-time relation and (b) strain-time relation Variability of repeated measurements from wetting under tension at 150 F and 80 psi stress level Tangential swelling and moisture ontent relation of Douglas-fir from wetting at 150 F Net strain from wetting under tension at 150 F and 40, 80, 120, and 180 psi stress levels Instantaneous strain as a funtion of stress from wetting tests at 5% MC and 150 F Predited reep strain for wetting under tension at 150 F and 40, 80, 120, and 180 psi stress levels MS strain and moisture ontent relation from wetting under tension at 150 F, lines showing fitted values with Equation (a) 40 psi, (b) 80 psi, () 120 psi, and (d) 180 psi stress Fitted net strain from wetting under tension at 150 F. (a) 40 psi, (b) 80 psi, () 120 psi, and (d) 180 psi stress. 158

12 LIST OF FIGURES, CONTINUED Figure Page Results of lumber drying from harge I. (a) temperature profile and (b) moisture profile Results of lumber drying from harge II. (a) temperature profile and (b) moisture profile Results of lumber drying from harge III. (a) temperature profile and (b) moisture profile Fitted diffusion oeffiient as a funtion of moisture ontent for drying of Douglas-fir heartwood in omparison with Siau's data (1984) Fitted and measured moisture profiles as a funtion of time from drying harge I Fitted and measured moisture profiles as a funtion of time from drying harge II Fitted and measured moisture profiles as a funtion of time from drying harge III Predited stress distributions. (a) NRB in harge I, (b) NRB in harge II, () NRB in harge III, and (d) WRB in harge III Predited strain profiles for NRB in harge I, numbers showing nodes from board surfae (0) to enter (5). (a) instantaneous, (b) reep, () shrinkage, and (d) MS strain Predited strain profiles for NRB in harge II, numbers showing nodes from board surfae (0) to enter (5). (a) instantaneous, (b) reep, () shrinkage, and (d) MS strain Predited strain profiles for NRB in harge III, numbers showing nodes from board surfae (0) to enter (5). (a) instantaneous, (b) reep, () shrinkage, and (d) MS strain Predited strain profiles for WRB in harge III, numbers showing nodes from board surfae (0) to enter (5). (a) instantaneous, (b) reep, () shrinkage, and (d) MS strain. 179

13 LIST OF FIGURES, CONTINUED Figure Page Measured drying strains for NRB in harge I. (a) released strain and (b) total shrinkage Measured drying strains for NRB in harge II. (a) released strain and (b) total shrinkage Measured drying strains for NRB in harge III. (a) released strain and (b) total shrinkage Measured drying strains for WRB in harge III. (a) released strain and (b) total shrinkage Comparison of predited and measured net strains. (a) NRB in harge I, (b) NRB in harge II, () NRB in harge III, and (d) WRB in harge III Comparison of predited and measured board shrinkage. (a) NRB in harge I, (b) NRB in harge II, () NRB in harge III, and (d) WRB in harge III. 91

14 LIST OF TABLES Table page 4.1. Speifiations for quartz spring Speifi gravity, rings per inh, and mean moisture ontent of wood at green Stress and temperature onditions for reep tests at 10% moisture ontent Stress and range of MC hange for drying under tension and ompression at 150 F Stress and range of MC hange for drying under ompression at 90, 120, 150, and 180 F Stress and range of MC hange for wetting under tension at 150 F Variation of wet bulb temperature in lumber drying Instantaneous strain as a funtion of stress from reep tests at 150 F and 10% MC Instantaneous strain as a funtion of temperature from reep tests at 10% MC Creep parameters in tension and ompression as a funtion of stress at 150 F and 10% MC Creep parameters in tension and ompression as a funtion of temperature at 10% MC Tangential shrinkage oeffiients of Douglasfir from drying at 150 F Instantaneous strain from drying tests under tension and ompression at 150 F and 25% MC Instantaneous strain from drying tests under 80 psi ompressive stress at 90, 120, 150, and 180 F Fitted MS parameter as a funtion of stress from drying under tension and ompression at 150 F. 138

15 LIST OF TABLES, CONTINUED Table Page 5.9. Fitted MS parameter as a funtion of temperature from drying under ompression at 80 psi stress Fitted MS parameter as a funtion of stress from wetting under tension at 150 F Summary on predited drying stress from three drying harges. 171

16 LIST OF APPENDICES FIGURES Figure Page B.1. Priniple of strain-hardening. (a) approximation of the smooth stress-time urve by steps, and (b) reep strain-time urve for various stress levels aording to strain-hardening rule. 207 B.2. Priniple of time-hardening. (a) approximation of the smooth stress-time urve by steps, and (b) reep strain-time urve for various stress levels aording to time-hardening rule. 209

17 RHEOLOGICAL BEHAVIOR OF DOUGLAS-FIR AS RELATED TO THE PROCESS OF DRYING I. INTRODUCTION Wood, as a naturally ourring material, has many desirable harateristis whih have made it popular for shelter, furnishing, and artisti works. In a living tree, moisture ontent an vary from 25% to well above 200% depending on the speies and part of the tree. Although undried wood is used suessfully in many appliations, drying of wood to the equilibrium moisture ontent (EMC) is neessary from the point of view of servieability. wood dries it shrinks. Unfortunately, as The differential shrinkage aross the thikness of a lumber board reates stresses, the magnitudes of whih depend on the physial properties of the wood, drying onditions, and the time of exposure to these onditions. As wood relieves itself of these stresses, the material may take on two forms of degrade, warpage and physial defets. This degrade diminishes the usefulness of the dried lumber and thus dereases its market value. It has been reognized for many years that a key to improve drying quality and a redution of drying time lies in understanding and ontrolling internal stress development (Tiemann, 1917). Several experimental and theoretial investigations have been made to determine the distribution of

18 drying strains, and to model the stresses during lumber drying. Those studies have led to the qualitative establishment of the general stress pattern. However, a quantitative understanding of drying stress and its dependene 2 on the physial properties of wood and drying onditions is still not omplete. It is well established that wood ats as a visoelasti material when subjeted externally applied or self-indued. to a stress whih an be either In the proess of drying, the rheologial properties of wood perpendiular to the grain, inluding mehanial reep and mehano-sorptive (MS) effet, at to relieve stress and redue faults whih an arise from high internal stresses. purely elasti approah ould not Numerial studies have proven that a be used even as a first approximation in determining the drying stresses (Salin, 1987; Salin, 1992). Thus, a better understanding of the rheologial properties would ertainly lead to a more aurate estimate of drying stresses, a more aurate seletion of the drying shedule, and less lumber value loss. The investigation presented in this thesis has been onduted to develop both analytial and experimental approahes for quantifying various aspets of the rheologial behavior of wood under the onditions that are likely to our during drying. The speifi objetives were as follows.

19 1. Develop a material property model for haraterizing wood deformation under ombined mehanial and moisture loading of small wood samples. 2. Develop a proess model for evaluating stresses during drying of the full-size lumber boards, inluding the effets of mehano-sorptive and mehanial reep deformation. 3. Develop an appropriate experimental tehnique for studying wood deformation under load during moisture hange at 3 the environmental onditions generally enountered in the proess of drying lumber. 4. Assess the auray of the material property model and proess model by atually testing of small wood samples and drying of large lumber boards.

20 4 II. LITERATURE REVIEW 2.1 Stress Development in Drying of Lumber A general onept of how the stresses develop inside wood as it dries is well-doumented in the forest produts literature (MMillen, 1955a; 1955b; Kawai et al, 1979). Under the normal drying onditions, the surfae of sawn boards tends to approah the equilibrium moisture ontent of the prevailing onditions and the outer zones of the wood dry below the fiber saturation point (FSP). Thus, the fibers at surfae tend to shrink, but are restrained by the fibers at the inner zones whih are in a relatively green ondition and have not begun to shrink signifiantly. Beause of this restraint, the outer zones are stressed in tension, and as a reation, the interior zones are in ompression. When the tensile stress exeeds the proportional limit, tensile set takes plae in the outer zones. The tensile stress in the outer zones and the ompressive stress in the enter zone reah the maximum values, then derease. As the drying ontinues, suessive inner zones tend to shrink and thus hange from ompression to tension. When the tensile stresses in the surfae zones redue to zero, there is nearly always some tensile set left in these zones. outer zones shrink further. As drying still ontinues, the enter and Due to the tensile set left in

21 5 the outer zones, the outer zones hange from tension to ompression (stress reversal). After stress reversal, the outside zones gradually proeed to a maximum ompressive stress and the enter zones to a maximum tensile stress. The development of drying stresses in a softwood differs somewhat from that in a hardwood. This differene is primarily the omparatively low moisture ontent at whih reversal of the stress ours. In drying of 2-inh ponderosa pine, MMillen (1968) showed that stress reversal in both heartwood and sapwood speimens did not our until the average moisture ontent was 20% or below. Resh et al (1989) demonstrated experimentally that the stress reversal for Douglas-fir heartwood dried with a ommerial kiln shedule ourred between 15% and 17% moisture ontent. Although softwoods are dried in a short time ompared to hardwoods, ontrol and elimination of surfae heks in drying wide boards and honeyomb in drying large thik boards of dense softwood speies like Douglas-fir still require the detailed knowledge of the development of internal stresses. 2.2 Wood Properties Related to Drying Stresses Experimental Findings Under the prolonged ation of ombined stress and moisture hange in the drying proess, wood undergoes a large inelasti deformation. The deformation an be usually

22 deomposed into three major parts: instantaneous, timedependent, and moisture hange-dependent. The magnitude of eah omponent and its ontribution to the development of drying stresses depend on the related physial properties of wood. Although the importane of those properties has been reognized for a long time, omparatively little work related to drying has been done Instantaneous Elastiity and Plastiity Under short-term loading onditions, wood demonstrates a straight line relationship between stress and strain up to a yield point or proportional limit (Bodig and Jayne, 1982). If the stress is removed prior to reahing the yield point, ay (Figure 2.1), the strain returns to zero and the behavior is said to be linearly elasti. Beyond the yield stress, however, the relationship is no longer linear sine progressively less stress is required to produe a given strain hange. This ontinues up to the ultimate stress, u. If the load is removed when the stress reahes a point (a,e1) between the yield and ultimate stress, the wood unloads along a line that is approximately parallel to the initial elasti line. When strained beyond the yield point, the strain does not return to zero after the stress reahes zero. Rather a plasti strain or set (et'p) is left in the wood. It is this

23 7 (S W Instantaneous Strain Figure 2.1. Stress-strain relation of wood under the short-term loading.

24 amount of set whih ontributes the stress reversal in the proess of drying lumber (MMillen, 1955a; Oliver, 1984). The stress-strain relationship desribed above does not depend on time. As soon as the stress hanges, the strain hanges. This behavior is said to be "instantaneous". Experimental data desribing the effet of temperature and moisture ontent on suh a relationship provide basi information about the onditions at whih surfae and internal heking may our during the lumber drying. For hardwoods, several authors have investigated the hange in Young's modulus (initial slope of the instantaneous stress-strain urve), stress and strain at the proportional limit, and maximum stress and strain with hanges in temperature and moisture ontent of wood (Greenhill, 1936; Ellwood, 1954; Youngs, 1957). Among those, Greenhill's (1936) investigation was made on Amerian beeh and was restrited to an examination of tensile strength and elasti properties in the tangential diretion. Test results showed that both maximum stress and Young's modulus were dereased with inreases in temperature and moisture ontent below the FSP. Ellwood (1954) also tested Amerian beeh in both tension and ompression. He overed wider ranges of temperature (from 80 to 160 F) and moisture ontent (from 6% to green) than Greenhill. The maximum tensile stress, stress at the proportional limit in ompression, elastiity and tangential modulus of in tension and ompression all dereased with 8

25 inreasing temperature and moisture ontent. There was little differene in Young's modulus between the results from the tensile and ompressive tests. The strain at the proportional limit was almost onstant with temperature, moisture ontent, and loading mode (tension or ompression). Youngs (1957) evaluated the effets of moisture ontent and temperature on the ross grain properties of Northern red 9 oak. His study inluded strength and modulus of elastiity in tension, ompression, and shear. He demonstrated that all properties varied signifiantly with moisture ontent and temperature. The funtional relationships between the strength properties and moisture and temperature ould not be represented by the exponential funtions (Wilson, 1932). a result, Youngs established a different empirial equation to desribe both strength and modulus of elastiity for red oak. This equation ontains a quadrati relationship for moisture ontent and a linear relationship for temperature. Comprehensive testing on a native softwood speies at various levels of temperature and moisture ontent is not available. Palka (1973) summarized test results from the literature and proposed a unified system of equations for prediting the elasti properties of softwoods in terms of speifi gravity, moisture rate. As ontent, temperature, and strain Those equations are of the following form for eah of the four variables:

26 (1). Speifi gravity (0.1 < SG < 0.8): 10 Y (SG) = Yo ( ) a SG0 Y1 (2.1) (2). Moisture ontent (0% < M < 30%): Y(SG,M) = Y1 [1 + CMC(M - M1) ] (3). Temperature (T < 160 F): = Y2 (2.2) Y(SG,M, T) = Y2 [1 + C (T - T2) ] (4). Strain rate ( V > 0 feet per minute): Y3 (2.3) Y(SG,M, T, V) = Y3 [1 + CSR (Log V - Log V3) ] = Y4 (2.4) The equations involve the simplest, linearized funtions for eah of the four variables and are thus only an approximation of the real wood behavior. Considering the large natural variability of wood, the proposed system of equations and orretion fators may be aepted as a first approximation for most softwoods. Only a relatively small portion of the total stressstrain urve ours below the proportional limit. In pratie, it is impossible to dry wood without developing set and the stress-strain relation above the proportional limit is of great importane during drying when limiting onditions for defets are onsidered. Researh into the nonlinear portion of the instantaneous stress-strain urve at high moisture ontent and elevated temperatures is, however, very limited for both hardwood and softwood speies.

27 Time-Dependent Mehanial Creep Drying of wood is not an instantaneous proess. Time exerts a signifiant influene on the drying harateristis by introduing reep and stress relaxation (Youngs, 1957). These effets influene the shrinkage of wood and development of plasti deformation perpendiular to the grain, thus affeting stress development during drying. A typial reep strain versus time urve for wood is shown in Figure 2.2 (Bodig and Jayne, 1982). Primary Seondary Tertiary C C VI Q Q) Q) k U Frature Time Figure 2.2. Creep urve of wood. 1. Mehanial reep is defined throughout the text as the time-dependent deformation at a onstant moisture ontent only.

28 The first part of this urve is known as the primary reep, a large portion of whih is reoverable after 12 unloading. The seond part is identified as the steady or seondary reep, whih possesses a linear reep strain-time relationship. The last part of this urve is alled the tertiary reep where the strain rate inreases until frature ours. Extensive experiments have been onduted to investigate reep behavior of wood under tension, ompression, bending and torsion parallel to the grain. Several literature studies in this area have been published (Shniewind, 1968; Grossman et al 1969; Holzer et al, 1988). The major experimental findings regarding the effet of moisture ontent, temperature and stress on reep may be summarized as follows: 1). Moisture in wood ats as a plastizer. An inrease in moisture ontent usually leads to an inrease in reep (Bah, 1965; Gnanaharan and Haygreen, 1979). The dependene of reep on moisture ontent, however, an be onsiderably redued by expressing the reep deformation as a fration of the instantaneous deformation: RC(t) = ET(t) -e_(to) EC(t) (2.5) e,(to) ei(to) where, RC(t) is known as relative reep (Dinwoodie, 1981).

29 The relative 13 reep is almost independent of moisture ontent provided the moisture ontent does not hange (Grossman et al, 1969). Thus, the reep funtion at a given moisture ontent ould be approximately expressed as a produt of the time-dependent relative reep measured at a referene moisture ontent and an instantaneous modulus of elastiity whose dependene on the moisture ontent is known from other tests (Grossman et al, 1969). 2). An inrease in temperature leads to an aeleration of the reep (Davidson, 1962; Shaffer, 1972b). Timetemperature superposition priniple, whih states that the influene of hanges in temperature is equivalent to shifts in the time sale (Findley et al, 1976), appears to be only valid for the ompletely dry wood (Shaffer, 1972b). 3). The effet of stress level on the linearity of reep varies with wood speies and testing onditions. Under low moisture and temperature onditions, the linearity between reep and applied stress has been found with stress level up to 50% of the stati strength (Kingston and Budgen, 1972; Kingston and Clake, 1961; Grossman and Kingston, 1963). At higher moisture and temperature, however, nonlinearity appears at the stress level as low as 20% of the ultimate strength (Bah and Pentoney, 1968). The very limited evidene indiates that wood reeps at a muh greater rate perpendiular to the grain than it does parallel to the grain (Gnanaharan and Haygreen, 1979;

30 Shniewind and Barrett, 1972). 14 For Amerian beeh at 80 F and 6% moisture ontent in tension and ompression perpendiular to the grain, Ellwood (1954) noted that at a stress level of 90% of the ultimate strength, reep ourred relatively rapidly in both tension and ompression with the magnitude in ompression being more than twie that in tension. His results also showed that an inrease in temperature and moisture ontent results in a onsiderable inrease of reep. Youngs (1957) with tensile and tangential diretion. green) studied the reep and reovery of red oak ompressive stresses applied along the He used two moisture levels (12% and and two temperatures (80 F and 180 F) with the stress ranging from 40 to 80% of the ultimate stati strength. Creep and reovery were found to be inreased with inreases in both moisture ontent and temperature. The effet of raising the temperature from 80 F to 180 F at 12% moisture ontent leads to a onsiderable inrease in nonreoverable reep. Diffiulty in studying reep perpendiular to the grain under diret tension and ompression lies in the fat that a large dimensional movement due to hange in the moisture ontent exists in those material diretions. For example, the published shrinkage or swelling oeffiients for Douglas-fir are per perent moisture hange in tangential diretion and in radial diretion (Forest Produts Laboratory, 1987). Thus, the ability to maintain the steady-state testing environments over a sustained period of time for those tests

31 is extremely important. Otherwise shrinkage or swelling due to hange in moisture ontent would onfound the reep measurements. Both Youngs (1957) and Rie and Youngs (1987) enountered this problem in their measurements on red oak using onventional methods to ontrol the surrounding humidity. As ommented by Youngs (1957), the atual moisture ontent for his reep data at 180 F was signifiantly lower than the nominal value of 12% Moisture Change-Dependent Shrinkage and MS Effet Tests with wood under load during moisture hange always indiate an aelerated deformation due to the existene of MS effet (Armstrong and Kingston, 1962; Hearmon and Paton, 1964). Under tension or ompression, the effet is seen as an derease or inrease in the amount of shrinkage or swelling assoiated with a moisture ontent hange. Thus, the additional deformation under those loading onditions onsists of two parts: inherent shrinkage or swelling due to losing or gaining moisture in the hygrosopi range; and MS effet due to stress and its interation with moisture ontent hange. 1. Inherent Shrinkage The inherent shrinkage is the dimensional hange of wood whih would our as a result of moisture loss in absene of

32 any restraint. This unrestrained ondition an be approximately satisfied in the slow drying of thin wood slies, where the thikness is the moisture flow diretion and 16 the moisture gradient in this diretion an be negleted. Figure 2.3 shows a typial shrinkage-moisture ontent relationship for nonollapsing wood speies (CSIRO, 1965). Green w Q) Loss of moisture with little hange in dimension Loss of moisture aompanied by shrinkage % range at whih shrinkage starts Shrinkage proportional to hange in moisture ontent 10 Dimensional Change Figure 2.3. Shrinkage-moisture ontent relation of wood for nonollapsing speies (CSIRO, 1965).

33 As indiated by the almost vertial alignment of the urve at the left-hand side of the graph, during the early stages of drying green wood, the moisture is lost without any appreiable hange in dimension. However, as the moisture ontent falls below about 30%, the amount of shrinkage progressively inreases until a moisture ontent of about 20% has been reahed. It then attains a fairly onstant rate and the graph beomes a straight line Mehano-Sorptive Effet Mehano-sorptive effet was oined to onvey suintly that mehanial influenes ombine with moisture sorption to produe a response that annot be predited from the response to eah influene separately (Grossman, 1976). The strain so indued differs from mehanial reep strain in a variety aspets. For example, reep depends on the duration of loading, while the mehano-sorptive deformation at a onstant stress is not diretly dependent on the time. When the moisture ontent of the loaded wood hanges rapidly, deformation inreases rapidly, but the final deformation depends on the moisture step and is little affeted by the duration of the proess. Experiments indiate that the mehano-sorptive effet is seen in hardwood speies prone to ollapse from the green state to the air-dry ondition. For softwoods, there appears

34 to be almost no hange from green to the FSP, then it is almost linearly related to moisture ontent between the FSP and air-dry onditions (Armstrong, 1983). No reasonable explanation has been advaned for this differene in behavior between the two types of speies. The mehano-sorptive effet is found to vary with the loading diretion (parallel or perpendiular to the grain) and loading modes (tension, ompression, or shear). In the diretion of the grain, ompression auses more mehanosorptive deformation than tension. 18 When the moisture ontent of wood under stress is yled, exept the inrease in deformation when the wood is initially subjeted to a rise or derease in moisture ontent, eah redution in moisture ontent leads to an inrease in deformation, and eah inrease in moisture ontent leads to some redution in deformation. The final deformation at the end of eah yle gradually inreases in magnitude (Armstrong and Kingston, 1962). Subsequent tests indiate that beams rept to failure at about 1/3 ultimate load after several omplete yles in humidity (Hearmon and Paton, 1964). The bulk of mehano-sorptive strain is retained after the removal of stress. A large part of the strain is, however, reoverable after removal of the primary ativating fore when the wood is taken through another moisture yle (Armstrong and Kingston, 1962). Temporary breaking and reforming of hydrogen bonds, allowing moleular hains to move while a polymer is under

35 stress are often advaned as the mehanism for the mehanosorptive effet. Supporting these onepts, Armstrong (1972) showed that the MS effet is assoiated with moisture ontent hanges (and hene volume hanges), not a steady-state moisture movement. In ompression, slip-plane formation (Hoffineyer and Davidson, 1989) in the wood ell wall may ontribute to the MS effet.this may be why the magnitude of the MS effet is greater in ompression than tension. During lumber drying, development of the MS effet perpendiular to the grain ats to relieve stress and redue faults whih an arise from high internal stresses. The effet is similar to normal reep. However, sine MS effet may be many times larger than the reep deformation, it has a more profound influene on the stress development. Limited studies have been onduted to investigate the effet in the diretions perpendiular to the grain. Takahashi and Yamada (1966) studied the effet with Japanese Hinoki-wood. Test speimens (about 0.8 inhes thik), loaded in tension at several stress levels, were dried from a moisture ontent of 140% to 3% at 176 F. 19 For both radially and tangentially loaded speimens, the drying set or redued shrinkage under tension (ontaining mostly the MS effet) was inreased with an inrease in the applied load. speimens were involved in those tests, Sine large whih ertainly resulted in a onsiderable moisture gradient aross speimen thikness, it is diffiult to establish the quantitative

36 relationships hange in wood. between the set strain and moisture ontent For beeh at 68 F and 30% of ultimate tensile strength in the tangential diretion, Shniewind (1966) demonstrated a large inrease of the reep strain when the moisture ontent was hanged. He showed that the inrease in the strain appears to be linearly related to the extent of moisture ontent hange. With equal moisture ontent steps, the strain inrease was independent of the position of the hange within the hygrosopi range, the rate of hange, a onstant moisture ontent. Erikson 20 previous reep at (1989) reported test results on red oak under both tensile and ompressive loading onditions. At a onstant stress level of about 10% of green tensile strength, the drying sets under tension and ompression were shown to inrease with temperature. However, his data suggested that the set under tension was signifiantly larger than that under ompression at the same temperature, whih seems to be ontraditory to many published studies. Rie and Youngs (1987) at 110 F under tension. studied the MS effet with red oak A large inrease in tensile strain was observed with moisture ontent hange, but the effet of inreasing stress levels was shown to be small. Further systemati study of this phenomenon at elevated temperatures and different levels of stress is highly desirable for modeling the proess of drying lumber. However,

37 the omplex nature of shrinkage and swelling of wood under diret tension and ompression during moisture hange requires speial onsiderations in the experimental tehniques: As temperature inreases, inreasing diffiulty is expeted in ontrolling the speified humidity over a sustained period of time using the onventional methods. would be omparatively easier, however, to arry out tests in absene of air and to ontrol and measure the pressure of water vapor alone. In suh a way, the boundary layer problems assoiated with air flow are eliminated, sine the water vapor flows unimpeded to the surfae of the speimen and into wood apillaries under its own pressure gradient and not by diffusion (Christensen, 1962). Also, hange of the surrounding humidity as required for moisture hange and mathing the moisture sorption histories among different tests ould be more easily ahieved. 2. Most of the eletrial strain measuring devies would not work properly under the ondition of high temperature and humidity. As a result, the development of nonontating tehniques for strain measurement is highly desired. It In suh a way, a reliable strain measurement ould be made for tensile and ompressive tests with small thin speimens, in whih moisture ontent hanges may be effeted without introduing appreiable moisture ontent gradients.

38 2.2.2 Constitutive Modeling Parallel to the experimental efforts on the wood deformation under ombined mehanial and moisture loading, onstitutive equations for suh a proess have been proposed by a number of researhers. Leiester (1971) 22 proposed a first rheologial model for the defletion of beams under bending during moisture hange. The model onsists of an elasti element onneted in series with an mehano-sorptive element. The total defletion of the beam is related to the applied load as: S = K P + f [P f(m) &ii (2.6) where, f(m) is a material onstant whih may vary with range of moisture ontent hange. Experimental verifiation of this model indiated that the model ontributed about 85% of the total defletion of the beams in drying under load over a two-week period. The study is one of the first attempts to mathematially model the MS effet. The model in this form, however, ignores the mehanial reep omponent and predits zero reovery after unloading. Shaffer (1972a) onsidered the effet of the atual moisture ontent and effet of diffusion of moisture past a point on the strain rate. He proposed that moisture ats as a swelling agent and has a similar effet as the temperature in reduing the energy needed to strain a solid. Also, the

39 migration of water moleules into and out of a gel substane weakens the ohesive fores of the gel, thereby promoting moleular position hange in the diretion of an applied load. Additional terms were thus added to the temperature and stress-indued strain rate equation for the moisture effet: dt = A [1+ IdMI P ] EXP[- --+B *r+c M] (2.7) where, A, B and C are the material onstants; T is in K. Equation 2.7 desribes the effet in qualitative agreement with the experimental findings. However, it involves several onstants whih are diffiult to evaluate experimentally. A simplified form of Equation 2.7 was used to model the proess of press drying (Tang and Simpson, 1990). Ranta-Maunus (1975) extended the multiaxial onstitutive equation for a linear visoelasti material: = fjijkl(tt) dokl(t) 0 (2.8) into a multiple integral polynomial aording to Voltera- Frehet theory. The extended equation is simplified for an isothermal ondition by only taking the linear terms for stress and moisture as well as the first and seond order terms for stress-moisture oupling. He proposed to use a dimensionless "hygrovisoelasti onstant" to quantify the ratio of hange of ompliane to hange of moisture ontent. In order to desribe the phenomenon, three different values of the onstant are needed : a" quantifying the effet of 23

40 moisture redution; a++ quantifying the effet of first moisture inrease at any moisture level, and a+ quantifying any subsequent moisture inrease at the same moisture level. When ompared to published experimental results, the model is apable of prediting the strain response to stress in the linear range under hanging and even under yling moisture ontent. Bazant (1985) proposed a model based on thermodynamis of water diffusion in wood for the effets of moisture ontent and temperature on reep. It is proposed that pores (or voids) in wood are subdivided into maropores (ell lumen) and miropores (in the ell wall). 24 A steady-state marosopi diffusion of water through wood has no effet on reep and only mirosopi diffusion of water through the miropores aelerates reep, regardless of the diretion of diffusion. The model reflets qualitatively some experimental results. Quantitative fitting of test data was not attempted. Martensson (1988) measured the tensile deformation of hardboard under load during moisture hange, from whih a onstitutive model is suggested and quantified on the basis of test data. In the formulation, the strain rate is taken to be a funtion of stress, moisture and their time derivatives: de do _ dt = F(a, dt,m, d ) (2.9) a + 1 do + [f(m) +k(m)al dm 11 (M) E(M) dt dt

41 where q,e,f, and k are the material onstants varying with moisture ontent of wood at a given temperature. To predit the material behavior, Martensson uses a eight-element Kelvin hain (Figure 2.4) to replae the dashpot and expresses the onstants as a funtion of moisture ontent. In handling the MS effet, the author assumed that the parameter k is nonzero only for the first hange in moisture ontent. Subsequent hanges in moisture ontent lead to the MS effet only when the moisture reahes values not earlier attained. Sine the MS effet is of major importane only during the first moisture yle, the model desribes the tensile satisfatorily. deformation of hardboard at room temperature quite 25 K, K2 K3 K8 Q I F%_1 'r' Figure 2.4. Generalized 8-element Kelvin model for mehanial reep from Martensson (1988).

42 Modeling of Stresses in Drying of Lumber A qualitative understanding of stress development during wood drying was formulated as early as 1917 by Tiemann, and by 1940 a sliing tehnique for measuring drying strains was developed by Pek (1940). Sine that time, perhaps 30 researhers have attempted to mathematially model the stresses. From the above disussion of the mehanial properties of wood, it should be lear that a purely elasti onstitutive relation annot be applied to wood drying. Thus, only those investigations addressing the plasti and/or rheologial properties of wood are overed below. Lesse (1972) and Lesse and Kingston (1972) examined the problem of drying stress development in terms of the similarity between thermal- and moisture-related stresses. The thermal stress equations, whih are developed from energy and moment balanes, are interpreted in terms of moisture loss. The resulting stress is responsible for the development of elasti and plasti strain during drying. The Lesse and Kingston model is a purely theoretial approah to the omputation of stress in terms of thermal onditions and moisture gradients. Some attempts are made to ompare the model output to the data for oak reported by MMillen (1955a). Ashworth (1979) for the drying of softwoods. developed a one-dimensional stress model The model follows a linear elasti stress-strain relation up to a pre-set yield point,

43 beyond whih a plasti strain begins to appear and ats to relieve the stress. Both elasti and plasti strains are oupled using elasti/plasti parameters, whih result from the temperature and moisture distributions during drying. The model of Ashworth has no experimental basis and elements suh as reep and MS effet are not onsidered. Material onstants used in the simulation are taken from literature, apparently 27 without regard to speies or drying onditions under whih they were determined. Kawai et al (1979) developed a method for evaluating drying stresses for a two-dimensional stress state. For simplifiation, moisture movement was assumed to be onedimensional along the longitudinal diretion and a plane stress state in the transverse plane was used. It needs to be pointed out here that both assumptions are not valid when drying long lumber boards. The alulations were done using a linear elasti onstitutive equation for the orthotropi materials. The required elasti strain omponents were impliitly expressed through relationships among the observed shrinkage (i.e. board shrinkage), basi shrinkage, and inelasti strains. Those relationships were developed from the speifi experiments by relating the strains to moisture ontent or time. The inelasti strain was taken to be a ombination of mehano-sorptive and reep strains and was measured using beams stressed parallel to the grain within the linear range. Graphs of stress produed by the model agree

44 well with the expeted stress pattern. However, the model requires the board shrinkage aross the thikness as one of the input funtions, whih is related to speifi testing onditions and is not known until the wood is dried. the model 28 Thus, has no general appliation in terms of limiting drying related defets. Lessard et al (1982) developed a one-dimensional model for drying red oak. The model assumes that the total strain onsists of an elasti, a plasti and shrinkage strain. An elasto-plasti fore deformation relationship is used to onnet three strain omponents. The determination of the total strain at any given time is as follows. First, the elasti strain is determined using the stiffness given by Youngs (1957) as a funtion of temperature and moisture ontent. If the alulated stress does not exeed the elasti limit for the given moisture and temperature onditions, the strain is assumed to be entirely elasti. If the alulated stress exeeds the elasti limit, the next step is to alulate a stress relieving plasti strain. The graphs whih ompare the model predition with experimental results show a good agreement with MMillen's experimental data (MMillen, 1955b) after onsiderably adjusting the plasti flow term. However, the model is only based on an elasto-plasti fore deformation relationship, in whih the reep and MS effet omponents are ignored. This simplifiation leads to an overestimate of the stress in the early stage of drying. An

45 attempt has been made to inlude reep into the model, but an unrealisti estimate of the stress after stress reversal is obtained. Morgan et al (1982) established a onstitutive model on the basis of an elasto-visoplasti stress strain relationship under a plane strain state. The total strain is taken to be the sum of elasti, plasti, and initial (i.e. shrinkage) strains. Elasti strains are produed on the first appliation of a load and their rates are linearly related to the total stress rate by the matrix of elasti onstants. Visoplasti strains take plae when the stress levels exeed some previously defined yield stress. The relationship between the various strain omponents is related by a plasti potential, whose gradient gives the diretion of straining. The model is used to investigate stress reversal as affeted by rate of moisture loss and the variation of model parameters with moisture ontent. After a onsiderable adjustment of the model parameters, moisture distributions 29 the urves presented show the general and overall patterns of stress and strain whih are expeted during drying. The finite-element solution in this model an offer ertain advantages for a material with more omplex geometries. Also, the use of the oupled heat and mass transfer equations of Luikov (Luikov, 1966) represented a major advanes in the determination of the moisture distributions. However, the assumption of the model is that wood is isotropi. Also, the MS effet is ignored.