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Wood shrinkage response to tensile stresses in convective drying Lazarescu, Ciprian 2009

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Wood Shrinkage Response to Tensile Stresses in Convective Drying  by  Ciprian Lazarescu  M.Sc., Transilvania University of Bra ov, 2001  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  in  THE FACULTY OF GRADUATE STUDIES (Forestry)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) May 2009 © Ciprian Lazarescu, 2009  ABSTRACT This study intends to investigate the effect of tensile stresses, moisture content and air engineering parameters on shrinkage behavior of short thin and thick western hemlock specimens. The main goal is to increase the quality of dried wood products. The experimental design was structured on two levels: study the effect of tensile stresses on artificially restrained small wood strips and correlate these experiments with drying tests made on short pieces of lumber. Four matched wood strips specimens were subjected to different restraints during a drying process: zero restraint (free shrinkage), two static restrains of 3daN and 6daN, respectively and a dynamic restraint controlled by the drying process. The resulting shrinkage was dynamically measured by pairs of resistive transducers located on the middle part of each specimen. The same type of transducers was positioned around short pieces of lumber dried to similar drying conditions. The results allowed correlating the amount and rate of moisture loss depending on air parameters, determining the fiber saturation point, and studying the elastic and viscoelastic components of the restrained shrinkage process. Interconnected variables like temperature and moisture content were also shown to significantly impact the desorption process. The derived mechano-sorption analytical fit yielded high coefficients of determination (R2=0.83-0.85, p<0.05) for both structural directions tangential and radial, respectively. The results demonstrated that a temperature as high as 80ºC combined with a low humidity could reduce the tensile stresses generated in the early stages of the drying process. Overall the tangential stresses in quarter-sawn specimens are reduced to half compared with flat-sawn specimens.  ii  TABLE OF CONTENTS ABSTRACT........................................................................................................................ ii TABLE OF CONTENTS................................................................................................... iii LIST OF TABLES .............................................................................................................. v LIST OF FIGURES ........................................................................................................... vi ACKNOWLEDGEMENTS................................................................................................ x I. INTRODUCTION ........................................................................................................... 1 II. LITERATURE REVIEW............................................................................................... 3 1. Moisture-shrinkage relationship ................................................................................. 3 1.1 Fiber saturation point ............................................................................................ 3 1.2 Free shrinkage....................................................................................................... 5 1.3 Restrained shrinkage ............................................................................................. 8 1.4 Moisture content ................................................................................................. 10 2. Drying stresses .......................................................................................................... 12 2.1 General considerations........................................................................................ 12 2.2 Elastic strain........................................................................................................ 15 2.3 Creep strain ......................................................................................................... 17 2.4 Mechano-sorptive strain...................................................................................... 19 III. MATERIAL AND METHODS .................................................................................. 21 1. Small size specimens ................................................................................................ 21 1.1 Specimen preparation.......................................................................................... 21 1.2 Density and micro-fibril angle ............................................................................ 25 1.3 Instrumentation ................................................................................................... 27 1.4 Preliminary experiments ..................................................................................... 32 1.5 Moisture content measurement and fitting ......................................................... 34 1.6 Drying strain and stress calculations................................................................... 36 2. Full size specimens ................................................................................................... 39 2.1 Specimen preparation.......................................................................................... 39 2.2 Drying strains...................................................................................................... 43 IV. RESULTS AND DISCUSSION................................................................................. 44 1. Material properties .................................................................................................... 44 1.1 Density ................................................................................................................ 44 1.2 Micro-fibril angle................................................................................................ 47 2. Drying strains in small specimens ............................................................................ 49 2.1 Free shrinkage..................................................................................................... 49 2.2 Fiber saturation point .......................................................................................... 59 2.3 Moisture content ................................................................................................. 60 2.4 Restrained shrinkage ........................................................................................... 70 2.4.1 Shrinkage force ............................................................................................ 70 2.4.2 Strain components........................................................................................ 76 3. Drying strains in full-size specimens ........................................................................ 87 3.1 Strain and moisture profiles ................................................................................ 87 3.2 Key moisture contents during the drying process............................................... 91 3.3 Tensile stress calculations................................................................................... 95 V. CONCLUSIONS.......................................................................................................... 97 iii  VI. FUTURE RESEARCH............................................................................................... 99 REFERENCES ............................................................................................................... 100 APPENDIX A................................................................................................................. 111 APPENDIX B ................................................................................................................. 116  iv  LIST OF TABLES Table 1. Average oven-dry density values for each structural direction and density differential (juvenile or mature)........................................................................................ 47 Table 2. Analysis of variance for free tangential and radial data. .................................... 51 Table 3. Stress-free shrinkage: theoretical and practical results for two structural directions and three moisture contents 17, 11 and 5%...................................................... 57 Table 4. Analysis of variance for free tangential and radial data. .................................... 58 Table 5. Analysis of variance for the dependent variable β ............................................ 61 Table 6. Average values of β for each structural direction. ............................................ 62 Table 7. Weighted average values of β . .......................................................................... 62 Table 8. Analysis of variance for α . ................................................................................ 63 Table 9. Average M values of SIP and ECW ................................................................ 68 Table 10. Ultimate stress values for tangential and radial specimens. ............................. 74 Table 11. Analysis of variance for the “Shrinkage” component. ..................................... 80 Table 12. Analysis of variance for the final shrinkage value. .......................................... 86 Table 13. Moisture range for each point of interest (I, II and III) for different temperatures (40, 60 and 80ºC)......................................................................................... 94 Table 14. Shell stress range results based on set values developed during the tensile period in flat and quarter-sawn specimens........................................................................ 95  v  LIST OF FIGURES Fig. 1. The structure of the cell wall (Jozsa and Middleton 1994). .................................... 7 Fig. 2. Distribution of residual stresses at various stages of drying throughout the thickness of a drying board (McMillen 1958). ................................................................. 14 Fig. 3. Typical linear relationship between log mechanical properties and moisture content (a) and predicted relationship between MOE and different temperatures and moisture contents (b) (Bodig and Jayne 1982). ................................................................ 16 Fig. 4. Mechano-sorptive strain plot as function of cumulative moisture content (Muszynski et al. 2003). ................................................................................................... 20 Fig. 5. Average ring density from pith to bark in some second-growth woods (Jozsa et al. 1998). ................................................................................................................................ 22 Fig. 6. Volumetric shrinkage of old-growth western hemlock compared with 18 other Canadian old-growth softwoods, from green condition to 12% Memc (Jozsa et al. 1998). 22 Fig. 7. Cutting and numbering protocol for the first log: T - tangential, R - radial, M mature, J - juvenile, N - North, S - South, E - East, W – West......................................... 23 Fig. 8. Side view of the tangential (up) and radial (low) wood strips............................... 23 Fig. 9. Final step in wood strip cutting: NC table router (left) and a processed strip positioned inside the pneumatic jig (right). ...................................................................... 24 Fig. 10. Final shape and dimensions (mm) of the tested specimen. ................................. 24 Fig. 11. Density measurement from pith (left side) to the 34th annual ring...................... 25 Fig. 12. MFA measurement for a single annual ring......................................................... 26 Fig. 13. PGC cabinet: outside-inside look and computer interface (from left to right). ... 27 Fig. 14. Tangential test specimen with mounted sensors.................................................. 28 Fig. 15. Upper sensor holder: 1 – aluminum body; 2 – spherical threaded tack; 3 – sharp threaded tack; 4 – threaded hole for connecting screws; 5 – threaded hole for sensor fixture................................................................................................................................ 28 Fig. 16. Experimental test frame: 1 – rigid steel frame; 2 – free wood specimen; 3 – spring return linear motion position sensor; 4 – L-shape reference holder; 5 – upper sensor holder; 6 – load cell; 7 – steel rod; 8 – aluminum plate; 9 – threaded rod; 10 – nut; 11 – additional stud; 12 – restraining weight; 13 – frame sole. ........................................ 29 Fig. 17. Data acquisition system and lab software............................................................ 30 Fig. 18. LMP transducer (left) and load cell calibration................................................... 31 Fig. 19. Calibration results for load cell (left) and one of the LMP transducers (right). .. 31 Fig. 20. The overall moisture content of five similar specimens during the preliminary experiments. ...................................................................................................................... 33 Fig. 21. The evolution of the moisture gradient inside the specimens during drying....... 33 Fig. 22. Experimental and curve fitted moisture (using eq. 3.8) for three different relative humidity levels (76, 56 and 21%, respectively) and the same temperature (40ºC). The arrow indicates the portion of the graph where equation (3.7) could not fit well the experimental data. ............................................................................................................. 35 Fig. 23. Experimental and curve fitted shrinkage (using eq. 3.14) for radial (R) and tangential (T) at 40ºC targeting 17% moisture content..................................................... 38 Fig. 24. Experimental design of set measurements: 1- wood piece, 2- aluminum support, 3- LMP sensor, 4- core temperature sensor, 5- core moisture meter; 6- aluminum frame; 7-shell temperature sensor. ............................................................................................... 39 vi  Fig. 25. Detail of the clamping system: 1- shell moisture meter; 2- nut; 3- threaded rod; 4wide washer; 5- compression spring; 6- bar. .................................................................... 40 Fig. 26. Experimental setup for full size timbers.............................................................. 42 Fig. 27. Selected pictures of the free lumber during different drying stages: 24, 96 hours and end of the drying process (from left to right). ............................................................ 43 Fig. 28. Within ring density distribution........................................................................... 44 Fig. 29. The influence of density over ring width. Numbers adjacent to points are the corresponding ring numbers. ............................................................................................ 45 Fig. 30. Density distribution inside the radial specimens. The area were the sensors were fixed is represented with a small diagonal stripe filled rectangle. .................................... 46 Fig. 31. Density distribution inside the tangential specimens. ......................................... 46 Fig. 32. MFA variation in cross-section. The demarcation line represents the boundary between juvenile and mature wood................................................................................... 48 Fig. 33. Free shrinkage pattern in tangential specimens targeting 17, 11 and 5% moisture content at constant temperature 40ºC................................................................................ 49 Fig. 34. Free shrinkage pattern in radial specimens targeting 17, 11 and 5% moisture content at constant temperature 40ºC................................................................................ 50 Fig. 35. Experimental and curve fitted free radial and tangential shrinkage (60ºC); T and R letters stand for tangential and radial, respectively. ...................................................... 53 Fig. 36. Latewood distributions in the tested area: 1 – earlywood; 2 – latewood; 3 – sensor. ............................................................................................................................... 53 Fig. 37. Fitted and existing empirical models for tangential specimens drying from Mfsp to 0% moisture content. ........................................................................................................ 55 Fig. 38. Fitted and existing empirical models for radial specimens drying from Mfsp to 0% moisture content................................................................................................................ 56 Fig. 39. Experimental S r values for different temperatures: 40, 60 and 80oC................. 57 Fig. 40. The influence of moisture content and temperature over shrinkage rate for radial (dotted lines) and tangential (solid lines) specimens. ....................................................... 58 Fig. 41. Fitted and existing empirical models for volumetric shrinkage from Mfsp to 0% moisture content. Both empirical models were calculated for a temperature of 20ºC...... 60 Fig. 42. Experimental and curve fitted moisture for three different relative humidities (76, 56 and 21%) and the same temperature (40ºC)................................................................. 61 Fig. 43. The influence of the drying variables over the statistical coefficient β used to fit the dehydration process..................................................................................................... 62 Fig. 44. Temperature and moisture content influence over the statistical coefficient α used to fit the drying process. ........................................................................................... 64 Fig. 45. Exemplification of M Start and shrinkage time calculations for a radial specimen targeting 10% moisture content. ....................................................................................... 65 Fig. 46. M Start values for different temperatures (40, 60 and 80ºC)................................. 66 Fig. 47. M Start values separated for tangential and radial specimens. .............................. 66 Fig. 48. Shrinkage-moisture plots of specimens targeting 60ºC and 10%: fast (I), intermediate (II) and slow transition (III). ........................................................................ 67 Fig. 49 Mean SIP and ECW values (± 1SD) for the specimens which followed a type I or II transition for different temperatures (40, 60 an 80ºC). Number over bar indicates sample size. ....................................................................................................................... 68 vii  Fig. 50. Mean M Start values (± 1SD) for the specimens which followed a type III and targeted 5% for different temperatures (40, 60 an 80ºC). Number over bar indicates sample size. ....................................................................................................................... 69 Fig. 51. Shrinkage force curves for tangential specimens targeting 17% moisture content at different temperatures (40, 60 and 80ºC). ..................................................................... 70 Fig. 52. Shrinkage force curves for tangential specimens targeting 11% moisture content at different temperatures (40, 60 and 80ºC). ..................................................................... 71 Fig. 53. “Fully restrained” shrinkage force developed in tangential specimens targeting 5% moisture content at different temperatures (40, 60 and 80ºC).................................... 72 Fig. 54. “Fully restrained” shrinkage force developed in radial specimens targeting 5% moisture content at different temperatures 40, 60 and 80ºC............................................. 72 Fig. 55. Shrinkage force rate (dS/dt) in tangential specimens targeting 5% moisture content at different temperatures 40, 60 and 80ºC (same specimens from Fig. 53). ........ 73 Fig. 56. Ultimate stress values in tangential and radial direction at different temperatures (40, 60 and 80ºC). ............................................................................................................. 74 Fig. 57. Maximum stress attained in “fully restricted” tangential specimens. ................. 75 Fig. 58. Maximum stress attained in “fully restricted” radial specimens. ........................ 75 Fig. 59. Restrained and free shrinkage strain for tangential specimens targeting 17% moisture content at 40ºC. .................................................................................................. 77 Fig. 60. Restrained and free shrinkage strain for radial specimens targeting 17% moisture content at 40ºC. ................................................................................................................. 77 Fig. 61. Relationship between the external force and the total strain for different restraining levels targeting 17% moisture content at 40ºC. .............................................. 78 Fig. 62. Distribution of the strain components due to different restrained levels for tangential specimens targeting 17% moisture content at 40ºC – same specimen from Fig. 60....................................................................................................................................... 79 Fig. 63. Elastic (upper) and recoverable components for tangential specimens targeting 17% at different temperatures (40, 60 and 80ºC).............................................................. 82 Fig. 64. Elastic (upper) and recoverable components for tangential specimens targeting 5% at different temperatures (40, 60 and 80ºC)................................................................ 83 Fig. 65. Final strain results for all the experiments preformed in tangential (upper graph) and radial direction. .......................................................................................................... 84 Fig. 66. Temperature influence over final strain results for the tangential (upper graph) and radial specimens restrained by 60N. .......................................................................... 85 Fig. 67. Shrinkage strain plots along the tangential direction for flat-sawn full size specimens down to 11% moisture content at different temperatures (40, 60 and 80ºC). . 87 Fig. 68 Shrinkage strain plots along the radial direction for quarter-sawn full size specimens down to 11% moisture content at different temperatures (40, 60 and 80oC). . 88 Fig. 69 Comparison between shrinkage values for specimens having the annual rings oriented at 45º and a flat-sawn specimen while drying at 80ºC........................................ 89 Fig. 70. Difference between average moisture measurements recorded with resistance pins (Lignomat) and oven-dry method (Control) for different temperatures (40, 60 and 80ºC). ................................................................................................................................ 90 Fig. 71. Sample of individual moisture readings for each resistive pin while targeting 5% at 80ºC............................................................................................................................... 90 Fig. 72. Key points during shell shrinkage process. ......................................................... 92  viii  Fig. 73. Shrinkage rates in tangential and radial direction of a flat-sawn timber ............. 93 Fig. 74. Shrinkage rates in tangential and radial direction of a quarter-sawn timber targeting 5% at 40ºC. ........................................................................................................ 93  ix  ACKNOWLEDGEMENTS My deepest gratitude goes to my supervisor Dr. Stavros Avramidis who made all this possible for me. His advice, guidance and patience to correct and return within hours all my manuscripts throughout this whole period were remarkable (  ).  My sincere gratitude also goes to Dr. Luiz Oliveira for his continuous support and advise during this project. My many thanks to the other steering committee members Dr. Frank Lam and Dr. Greg Smith for their advise and guidance during my studies. I am grateful to Dr. Tony Kozak, for his help with statistical analysis of the data, and Mr. Bob Myronuck, whose technical assistance was invaluable – both of you made my life a lot easier. Thank you for the financial support from Natural Sciences and Engineering Research Council of Canada (NSERC), FP Innovations (Western Forintek Division) and University of British Columbia. A very personal thank you goes to my parents and wife; without your support and love none of this would have been possible. To all my Romanian and Canadian friends who are making my life richer. Thank you Katrin, Zoran, Slobodan and Prasad for guiding me during my early efforts to integrate in the university environment. Last, but not least, to Radu and Mihaela for helping me to make a smooth transition between home and abroad.  x  I. INTRODUCTION Wood is a colloidal, porous, non-homogeneous and anisotropic material that is quite challenging in processing and utilization. Due to the numerous interactions that take place within the wood-moisture-heat-environment system, drying is considered one of the most complex processing operations. Optimum drying processes entail short drying times, high product quality and reasonable costs. The central concern is represented by drying stresses, responsible for warping, checking and collapse, which are induced by the uneven moisture distribution during the dehydration process. The level of these defects is also a strong function of the shrinkage, elastic and visco-elastic parameters of wood as well as grain deviations, density variations and sawing pattern. The manifestation and development of wood stresses are governed by moisture content differences between two adjoining parts, within the same material, after one of them reduces below the fiber saturation point. With most of the water transport in a piece of lumber taking place in the cross sectional plane, material properties along this direction will have a high influence over drying stresses. In such configuration (rectangular crosssection) and mode of drying, the shrinkage of the surface layers is restrained by the wet (more plastic) inner layers which show no tendency to shrink, thus producing a tensile force exerted over the surface layers. High drying rates correlated with the strong tendency of wood to creep, particularly across the grain, leads to a lower shrinkage strain (tension set) in the outer layers. As internal forces are balancing, a compensating compression stress appears on the inner layers. The compression stress from the interior is slower and, as drying proceeds and the tension stresses advance inward, a decreasing amount of material is subjected to them. Once the core has reached the fiber saturation point, and it starts to shrink, a reversed restraining phenomenon happens – the shell is now restraining the core. During this phase tensile stresses develop at the interior and compression stresses on the exterior. Moisture removal, stresses and set formation are so interconnected that researchers named the completion of stress reversal process “a way to transform a moisture differential in set caused by stresses”. Therefore, a quantitative knowledge of the set and moisture content may estimate the stresses during the drying process. 1  Today there is little information about the quantitative aspect of permanent set especially on softwoods. The results are harder to interpret because the drying strains in softwoods are considerably smaller than in hardwoods. Exploratory studies are based on smallsample designs which are later extended to larger specimens. Often these results are blurred even by an imperfect mimic of the drying process or due to the variability of the material. The purpose of this research is to investigate the restrained perpendicular-to-grain shrinkage effect of western hemlock during drying. Drying tests on small wooden strips subjected to different restraining levels were compared with free-to-restrain specimens having similar wood structure. The experimental work led to empirical equations used to quantify the tensile stresses based on set formation and moisture content. The results were correlated with drying experiments made on short pieces of lumber having a similar anatomical structure. The free shrinkage rate or the shrinkage expected to occur without any restraints was compared with the actual shrinkage rate of the outer layers. The results obtained from this project will lead to a better understanding of the factors associated with restrained shrinkage as well as the relationship between material properties and the stresses developed during wood drying. Furthermore, the shrinkage differential might find commercial application as a lumber dry kiln control parameter.  2  II. LITERATURE REVIEW 1. Moisture-shrinkage relationship 1.1 Fiber saturation point The intimate relationship between wood and moisture (M) determined the implementation of two specific terms: equilibrium moisture content (Memc) and fiber saturation point (Mfsp). The former defines the moisture content of wood in dynamic equilibrium with the relative humidity (H) and air temperature. The latter, first defined by Tienmann in 1906, represents a particular Memc, a balance between the solution pressure within the swollen cell wall and the mechanical rigidity of the wall (Walker et al. 1993). Wood shrinkage, strongly connected with the water from the cell wall (bound water), is supposed to start at values close to Mfsp. There are several methods perfected to determine the Mfsp including finding discontinuities in electrical conductivity measurements (Myer and Rees 1926, Stamm 1929), extrapolations of sorption isotherms (plots of Memc against H at constant temperature) to values close to unit relative humidity (Spalt 1958, Wangaard and Granados 1967), shrinkage/moisture content technique (Kelsey 1956, Stamm 1929), heat of sorption measurements (Stamm and Loughborough 1935) and several others. The methodology and accuracy of nine different methods were discussed by Stamm (1971). Amongst all these methods, the shrinkage/moisture content technique will be studied in more detail in this chapter. Extrapolations of the volumetric shrinkage-moisture plots to zero shrinkage give moisture content intercepts close to Mfsp (Stamm 1929). Separate plots of tangential or radial shrinkage would give different intercept points because the directional shrinkage is affected by stress differentially (Kelsey 1956). Most of the previous work showed that the tangential intersection point is greater than the one determined on the radial specimens. The main reason is considered to be the fact that the tangential/radial ratio varies at different stages of drying (Stamm 1971). Others consider that the basic concept of Mfsp should not permit two levels of Mfsp inside the cell wall and the tangential values should  3  be the only one taken into account (Wangaard 1957). The correlation with mechanical tests was good only for mean values of modulus of rupture and elasticity versus mean tangential and radial shrinkage. Mfsp is a function of several factors, among them temperature, mechanical restraint (microtome sections of wood or pulped fibers have higher Mfsp compared with large wood specimens), wood species, extractives content, drying history and static pressure. Even among the same wood species variations are present: shrinkage measurements of cell walls in California redwood summerwood indicated an effective Mfsp of 25% and in springwood walls 19.5% (Ellwood and Wilcox 1962). Temperature influences the percentage of water molecules which could overcome the energy barrier of desorption. This effect was noticed and quantified on diffusion rate measurements (Stamm and Nelson 1961, Koumoutsakos and Avramidis 2002). Kollmann (1959) indicate a 1.3% decrease per 10˚C increase between 20˚ and 80˚C. Weichert (1963) reported a 1.2% decrease per 10˚C between 20˚ and 100˚C. There is also a considerable variation with species and specific gravity. Feist and Tarlow (1967) found that Mfsp tends to increase as specific gravity decreases probably due to decreased mechanical restraint within the cell wall. Lack of restraint may also explain the high Mfsp’s (up to 53% for Pseudotsuga mensiessi or 40% for Picea mariana) obtained by Ahlgren et al. (1972) and Stone and Scallan (1967) who made their experiments with microtome sections of wood or pulped fibers. The removal of extractives results in higher Mfsp for species having a low initial Mfsp; the effect is smaller for species already having a high initial Mfsp (Wangaard and Grenados 1967). As a rule of thumb, for temperatures between 20˚C and 120˚C, Mfsp decreases 0.1% when temperature raises 1˚C (Stamm and Nelson 1961):  M fsp = M fsp 20 − 0.1(T − 20)  (2.1)  where T is the temperature (in ˚C) and Mfsp is in %.  4  Comparable statistical analysis of Mfsp at room temperature for Douglas-fir, western hemlock and southern pines was done by Wood and Soltis (1964) and Comstock (1965); all investigators found the value of Mfsp for western hemlock at around 28%. A comprehensive research was done by Stamm (1964) for 52 softwoods and 107 hardwoods. The average value for softwoods was 26% while the hardwoods reached 27%. Slightly higher values of 31% were obtained for western hemlock while redwood went down to 25% due to the large amount of extractives. The results were summarized by Green (1989) whose equations assumed an Mfsp of 28% for most softwood species with a value of 22% for redwood, western red cedar and northern white cedar. For an Mfsp of 28% around 29.5% of the swollen cell wall is occupied by water and 69.5% is occupied by the cell wall constituents.  1.2 Free shrinkage Wood hygro-contraction (aka shrinkage) is a percent dimensional reduction that occurs as cell-wall bound water molecules escape from the amorphous areas of its cellulose chains allowing them to move closer. The primary shrinkage of the wood cell-walls in combination with the resistance offered by wood’s gross structure, determines the overall change in its dimensions (Stamm 1964). Although shrinkage cannot be described as a stress-free process, the drying stresses could be minimized by using specimens having small dimensions that can be dried in such a manner that the contained moisture remained throughout the process be as uniformly distributed as possible. Shrinkage values obtained in these conditions were named “free shrinkage” (Stamm 1929, Stevens 1938). For wood the lumen and the pores are very little or not at all affected by the shrinkage process (Beiser 1933). Permeability of thin cross sections of wood showed no significant change with increased relative vapor pressure and accompanying increase in swelling (Stamm 1935). The answer for this characteristic pattern of wood shrinkage lies within the anatomical structure of the cell wall. The structural positioning of cellulose chains inside the largest layer of the cell wall (S2) causes most of the shrinkage to happen along a direction  5  perpendicular to the tree stem and just a small amount along its length (~0.3%). The fibrils making up the primary part of the cell wall tend to be oriented spirally, almost at right angles to the fiber length, fitting tightly around a water-swollen fiber. Any gain or loss in moisture content will be restrained by these fibril wrappings. During a desorption process, at high moisture contents the restraining action is very efficient but further drying determines the non-crystalline region of these fibrils to begin to shrink. The restraining is proportional with the microfibril angle (Abe 2006). It is a fortunate feature because it limits the amount of swelling and shrinkage but in the same time creates stresses at cell wall level (Stamm 1964). The crystalline structure and orientation inside the cell walls are the main causes why shrinkage occurs mostly in tangential and radial directions (Fig. 1). The anatomical features/restraining forces at cell level also determine wood to shrink one third more in the tangential direction than radial. Gross anatomic structure, particularly the alignment of the rays, was found to be the primary cause of the transverse anisotropy (McIntosh 1954, Schniewind 1959, Koponen et al. 1991). Another interesting aspect of the shrinkage phenomenon is that minor shrinkage values are recorded before the wood reaches the Mfsp. Recent research in this domain explains this early shrinkage either by a large range of free-bound water coexistence (the loss of bound water starts before all the liquid water is removed Hernández and Bizon 1994) or the slight change of cell shape during the water removal process (Almeida et al. 2007, Perré 2007). The controversy of free-bound water coexistence was approached by splitting the term Mfsp into two parts: hygroscopicity limit and the cell wall saturation limit (Babiak 1995). The former was defined as the Memc of a relative humidity slightly lower than 100% (to avoid full saturation Stamm 1959) while the latter was determined to be proportional with the ratio of shrinkage and specific gravity of wood. The numerical model used in the dynamics simulations of the free shrinkage process developed by Navi et al. (2002) showed that the cellulose chains in elementary fibrils may bend perpendicular to the planes of the hydrogen bonded sheets which form the crystalline lattice. The effect is smaller for specimens dried under a tensile force and greater for compression. Free shrinkage values appear to be influenced by the drying rate and temperature: high shrinkage values occur in specimens dried relatively slowly at high 6  temperatures while low values are obtained for high temperatures and drying rates (Stevens 1963).  Fig. 1. The structure of the cell wall (Jozsa and Middleton 1994).  The shrinkage-moisture rate is strongly correlated i.e. the amount of shrinkage is proportional to the amount of removed water molecules. Density also influences the rate and the final shrinkage value in a relationship where the higher the density the lower the shrinkage rate and the higher the final shrinkage value (Stamm 1964, Skaar 1988). The overall shrinkage value is influenced by that of the denser latewood which forces the earlywood to shrink to a higher amount. Non-uniformity and large variations in surface deformation were also determined by field measurements of wood during drying (Kifetew et al. 1997). The asymmetric distribution of shrinkage properties was also studied by Pang (2002); the asymmetric stress distribution was considered equivalent to an external bending moment which is the main source of bow, crook, cup and twist. Corresponding tangential and radial shrinkage values may be calculated using the following empirical relations (Stamm 1935, Stamm and Loughborough 1942):  7  2 sT = G2 ( M 2 − M 1 ) 3  (2.2)  1 s R = G2 ( M 2 − M 1 ) 3  (2.3)  where G x (dimensionless) represents the specific gravity at M x (%), sT and sR are the shrinkage coefficients along tangential and radial direction (%), M 2 > M 1 . Estimated values of shrinkage are also given in Table 3-5 of Wood Handbook (USDA 1999). The following empirical equation may be used: SM = S0 (  30 − M ) 30  (2.4)  where S M (%) is the shrinkage from green conditions to M < 30 , and S 0 (%) is the total shrinkage for a particular structural direction ( S 0 = 7.8 and S 0 = 4.2 for western hemlock tangential and radial, respectively). Other equations were developed by Comstock (1965) and Green (1989). Both give relatively close numbers to Wood Handbook for the radial direction but underestimate the tangential shrinkage with almost 1%.  1.3 Restrained shrinkage As previously stated, drying stresses are minimized when small wood specimens are dried. Thick and long specimens are affected by the moisture gradient set up between shell and core. In this case, the surface fibers will start to shrink and the overall volume of the piece will be reduced even though the average moisture content is above Mfsp. The shrinkage of the surface layers is restrained by the wet (more plastic) inner layers which show no tendency to shrink; these conditions determine a less-than-free shrinkage value called tensile set. Besides less shrinkage, the tensile force will also tend to increase the size of the cell lumen (Stamm 1964) and modify Memc to a higher value (Shmulsky 2004).  8  Cracks generally occur during this early drying stage (Schniewind 1963). The destruction of xylem may also result from the value of the deformation, rather then failure stress (Kass 1965). The conclusion was suggested after observations made on stress value in externally restrained wood. As internal forces are balancing, a compensating compression stress appears on the inner layers. As drying proceeds, the tension stresses advance inward, while a decreasing amount of material is subjected to increasing compression stresses in the core. The tensile stresses developed in the adjacent layers are smaller than the one developed in the outer slices (McMillen 1958). The compression stress from the interior develops more slowly and, as drying proceeds and the tension stresses advance inward, a decreasing amount of material is subjected to them. Once the core has reached the Mfsp, and it starts to shrink, a reversed restraining phenomenon happens – the shell is now restraining the core. During this phase tensile stresses develop at the interior and compression stresses on the exterior. Similarly, the compression stress determines the apparition of compression set which represents a higher than normal shrinkage value. The phenomenon is more complicated because the set appears simultaneously in different parts of a single piece of wood same as the moisture gradient changes (Stamm 1964). As an analogy, trees are subjected to similar stresses during their lifetime as a result of adjustments made to maintain an upright position. The shortening of the fibers near the pith at all ages will result in central core of the tree under compressive stresses and the outer layers under tensile stresses (Jozsa and Middleton 1994, Zobel 1998). As the tree becomes older and larger the inner zone will come under greater compression. Another source of stress is represented by the “chemical forces” generated by the developing of the cell wall (Archer and Amherst 1987). A plant subjected all its life to these stresses has developed defensive mechanisms and therefore drying should be just an extension of this well-known living condition. Unfortunately, conventional drying implies cutting in small parts before drying and consequently a totally different distribution of material properties according  to  the  sawing  pattern.  Among  these  properties,  wood  density,  latewood/earlywood proportion, juvenile and mature wood, heartwood and sapwood are important factors with a significant influence over the quality of the final product. 9  1.4 Moisture content The moisture content represents the weight of moisture contained in a piece of wood expressed as a percentage of its oven dry weight. It can be mathematically calculated as:  M =  Wg − Wod Wod  ⋅ 100%  (2.5)  where Wg is the green weight of wood and Wod represents the oven-dry weight of wood, in grams. The moisture content in trees may range from about 30% to more than 200% of the weight of wood substance. It can be held in wood as liquid, ice or water vapor in cell lumens and cavities (free water) and as chemically bound water within cell walls. Wood may hold a maximum amount of moisture content when both the cell lumens and cell walls are completely saturated with water. The value is a function of the specific gravity of wood cell walls and basic density of wood (based on oven-dry weight and green volume). The moisture content of wood below Mfsp point is a function of both relative humidity and temperature of the surrounding air. During lumber drying two main periods can be distinguished: a constant rate period and a falling rate period (Treybal 1980). The constant rate period characterizes the beginning of the drying process and is little influenced by the air temperature but is proportional to the relative humidity. This is because evaporation is sustained by the rate of heat transfer, and the rate of heat transfer from the warm air to the moist wood surface is proportional to the temperature difference between the air and the wood surface which is at the wetbulb temperature (Walker et al. 1993). When all the water evaporates from the surface, the falling rate period starts. During the falling rate period the evaporation plane recedes into the interior of a board and diffusion is the controlling mechanism for moisture movement. The moisture content drops below the Mfsp and the surface temperature tends to equalize the dry-bulb temperature.  10  The moisture content loss for boards/timbers can be fitted using the thin-layer drying equation (Marinos-Kouris and Maroulis 1995). The drying rate is assumed to be directly proportional to the moisture content of the board and the Memc provided by the drying environment:  M (t ) = M emc + ( M i − M emc ) ⋅ e − kt  (2.6)  where k is the drying rate coefficient (1/min) and Mi is the initial moisture content, in %. Further correlations with the diffusion coefficients resulted in predictions about the drying rate (Berberovic 2007, Milota 2008). These functions might be used to fit the overall moisture content evolution during drying. Actual measurements at different depths reveal internal moisture content profiles which are a direct consequence of the diffusion coefficients. Among the modern methods used to measure these profiles specific studies include CT-scanning (Computer Tomography) and MRI (Magnetic Resonance Imaging). Other methods include measuring the electrical resistance of wood at different depths with resistance pins during the drying process (Riley and van Wyk 2005). If the probes are insulated with only the tips exposed, the moisture profile through the wood might be estimated as the needles are pushed further into the lumber (Walker et al. 1993). Resistance meters are calibrated for a particular species and correction factors are applied for calculations. The accuracy of these devices is high only for moisture contents below Mfsp because the electrical resistance drops dramatically (million times) with moisture content (Forrer and Vermass 1987).  11  2. Drying stresses 2.1 General considerations For more comprehensive stress model, total strain ( ε ) rate is assumed to be composed of thermal expansion/contraction strain ( ε T ), free shrinkage and swelling ( ε α ), elastic strain ( ε e ) and visco-elastic strain ( ε ve ) with its two components ‘creep’ ( ε c ) and ‘mechano-sorptive’ ( ε ms ). Strain components are generally assumed to be conceptually separable and the total strain can be written as: ∂ε / ∂t = ∂ (ε T + ε α + ε e + ε c + ε ms ) / ∂t  (2.7)  Wood expands if the temperature increases and shrinks if the temperature decreases. During the drying process, shrinkage caused by moisture loss is greater than thermal expansion, so the net dimensional change on heating will be negative (USDA 1999). Also, if the temperature is held constant or the variation interval is very small, thermal expansion/contraction may be neglected ( ε T = 0 ). Any stress extended over a period of time will develop an additional strain named creep. Wood, with its complicated structure at macroscopic, microscopic and molecular level, develops two types of creep strains during drying, namely, time-dependent creep and mechano-sorptive creep. The time-dependent creep appears in materials subjected to a constant load and it is typically characterized by a family of stress-strain diagrams. For wood, these stress-strain diagrams can be developed under constant temperature and moisture content. The mechano-sorptive creep, also interpreted as an accelerated creep due to moisture content changes, is the result of transient redistribution of stresses and it is associated with moisture content changes that cause the rupture of hydrogen bonds. These bonds will reform in a different location under the bias of the applied stress. Under sufficiently low moisture content and temperature, wood behaves much like a brittle material (linear elastic manner). Under intermediate moisture content and temperature wood exhibits visco-elastic behaviour. At higher stress levels, or in  12  fluctuating environmental conditions wood will have a non-linear visco-elastic behavior with considerable plastic deformation (Whale 1988). Recent research in developing constitutive models of drying stresses was done by Rice and Youngs (1990), Salin (1992), Ranta-Maunus (1993), Wu (1993), Svensson (1997), Ormansson (1999), Haque et al. (2000), Dahlblom et al. (2001), Pang (2001), Moutee, et  al. (2007). Most of the authors built Burger, Kelvin, N Kelvin or Maxwell models based on series or parallel combinations of spring and dashpot elements. An original approach was done by Moutee et al. (2007) who built a rheological model of wood cantilever for modeling the creep behavior and stress in various moisture content conditions and various load levels. Others carried their research by starting from models made on small specimens which were later used to characterize the drying stresses in full boards. This approach implied the study of the drying process under an imposed stress, either tensile or compression, which was applied in green specimens at the beginning of the test. The major inconvenience of this approach was the relaxation which took place before the shrinkage occurred and the limited number of specimens tested for a given combination of stress-moisture content. A second part of the test implied slicing of full size specimens to analyze the released deformation. Drying stresses measured either by slicing and curvature measurements were initiated by Peck (1940) and latter perfected by Kuebler (1960). Recently the released deformation was measured with transducers positioned against the end of the tested specimens (Svensson 1997). The stress is calculated as the product of the strain and Young’s modulus at a particular temperature and moisture content level. A stress diagram obtained by these methods will look, more or less, like the one illustrated in Fig. 2. After five days of drying the outer layers of the wood are under severe tensile stress. The long duration of drying process will develop a tensile set and wood will shrink less-than-free shrinkage value. Often these stresses create small surface checks which may cause problems if the surface is to be coated with paint or clear finishes. Further shrinkage in the adjoining layers will diminish the stress in the outer layers and the compressive stress inside the material increases. Severe set in the outer layers will  13  determine a reverse of stresses and the lumber will end the drying in a “casehardened” state. As underlined by Skaar (1988), this term does not indicate that the surface is any harder than wood which is not casehardened. However the stiffness is affected if measurements are made right after drying. The methods proved to be very reliable. The only impediment is the destructive nature of the testing method and the impossibility to know stresses on a continuous basis. Section width has also been shown to influence the effect of drying stresses on shrinkage: the smaller the cross section the smaller the influence of stresses over shell shrinkage (Stohr  Compression Tension  Stress  1988).  Days Drying 5 77 Mean M (%) Kiln EMC (%) 18  10 64 17  18 50 13  28 35 8  36 17 2  50 10 2  Fig. 2. Distribution of residual stresses at various stages of drying throughout the thickness of a drying board (McMillen 1958).  14  2.2 Elastic strain Under short term loading, stresses below a certain limit (called the proportional limit) produce strains which substantially disappear when the load is released (directly recoverable). This strain is called the elastic strain. Although no material is perfectly elastic, even for small deformations a slight molecular flow might occur, the spring elements (Hooke) may be used to model glass rods, ropes, wood (even wood fibers) or metal bars. The region of elastic behavior is determined experimentally through direct evaluation of stress – strain diagrams. The slope of the straight portion of the stress-strain curve is called modulus of elasticity (MOE). Beyond the proportional limit the strain will increase at a faster rate and the upper limit of the curvilinear region is the ultimate stress. The highest stress experienced within the material at its moment of rupture is termed modulus of rupture (MOR). Wood has independent mechanical properties along three mutually perpendicular axes: longitudinal (L), radial (R), and tangential (T). Twelve constants (nine are independent) are needed to describe the elastic behavior of wood: three moduli of elasticity (L,R,T), three moduli of rigidity (indicates the resistance to deflection of a member caused by shear stresses - in the LR, LT, and RT planes, respectively), and six Poisson’s ratios (ratios of the transverse to axial strain). The elasticity moduli are usually obtained from compression tests and data for radial and tangential directions are not very extensive. The modulus of elasticity of wood is approximately 1.5 to 2 times higher in the radial than in the tangential direction. For instance in order to approximate MOE in radial and tangential  direction  the  following  ratios  are  used  for  western  hemlock  MOET/MOEL=0.031 and MOER/MOEL=0.058 (USDA 1999). The cause of this difference could only be found in a high radial modulus of elasticity of the rays and of the prosenchyma cells (Price 1928, Barkas 1941).  15  2  50  Change in MOE [%]  4  MOE (10 MPa)  1.75 1.5 1.25 1 0.75 0.5 0.25  40  23%  30 20 10  12%  0  12%  -10  23%  -20  0 0  5  10  15  20  25  Moisture content (%)  30  -40  35  -20  0  20  40  Temperature [oC]  60  80  (a) (b) Fig. 3. Typical linear relationship between log mechanical properties and moisture content (a) and predicted relationship between MOE and different temperatures and moisture contents (b) (Bodig and Jayne 1982).  Both MOE and MOR decline until a moisture content slightly in excess of 20% is reached (Bodig and Jayne 1982). Neither property changes significantly at higher moisture contents. Two linear functions can be used to represent MOE and MOR - moisture content data: one for data below the Mfsp and one for data at higher levels of moisture. The intersection of the two curves may be considered as one of the methods used to determine Mfsp (Fig. 3). Guitard (1987) has quantified the effect of moisture content over MOE using the following formulation:  MOEM = MOE12 [1 − 0.015 ⋅ ( M − 12)]  (2.8)  where MOEM represents the elastic modulus for a particular moisture content ( M ≤ 30 ) and MOE12 is the elastic modulus at 12% moisture content, both in MPa. Ultimate tensile stress (UTS) parallel-and perpendicular-to-the-grain appears to reach a maximum between 10% and 12% moisture content (Kretschmann 1996). The effect of temperature on mechanical properties is widely presented in the literature. Two effects are reflected when wood temperature is increased: a transitory change in internal energy levels and permanent structural reorganizations. Temperature level, the  16  effect of sustained levels of elevated temperatures and the combination of moisture temperature are issues described in several papers. As a general rule MOE has the highest value for low temperatures (0 - 60˚C) following a linear decline with increasing temperature (up to 100˚C). For green lumber between 66 to -18oC a linear relationship may be used to describe the increase of MOE with the decrease of temperature (Green and Evans 2008). The effect of temperature on modulus of elasticity of wet wood is larger than of dry wood. Carrington (1996) attained the effect of temperature on the modulus of elasticity perpendicular to grain for softwood species with finite element model:  MOET = MOE M [1 − (50 + M )  (T − 20) ] 7000  (2.9)  where MOET (MPa) is the elasticity modulus at a particular T (ºC), T ≥ 20 , MOEM (MPa) is the elasticity modulus at a particular M (%), M ≤ 30 The state of deformation also affects the quantity of moisture held in wood and therefore temperature and moisture effect over MOE are closely interrelated. New data (Moraes et  al. 2004) shows nonlinear trends when moisture contents approach saturation and continue with high temperatures.  2.3 Creep strain Creep is defined as a time-dependent strain exhibited by a material under constant load and sometimes is the cause of failure for loadings smaller than the ultimate static load (Bodig and Jayne 1982). Recent studies support the idea that creep strain rate in wood, especially during drying is a function of strain accumulation rather than time (Hanhijarvi and Hunt 1998); it is also highly dependent on the structural direction, the magnitude and type of stress, the rate and/or duration of load, level of moisture content and temperature. Creep is very fast at the beginning (primary creep) and then slows down appearing to stabilize quickly (constant rate of creep). The third kind of creep which happens after the two previous ones is studied in terms of duration of load or creep rupture. Primary  17  suggests creep stabilization while tertiary may lead to failure. Load removal will lead to an instantaneous recovering of the elastic deformation. As time elapses more deformation will be recovered, but the recovery is not complete and residual deformation remains. The quantification of this mechanism was done using mathematical models of rheology (from the Greek “  ”) - the study of the time-dependent stress-strain behavior of  materials. Moisture in wood acts as a plasticizer. Therefore, creep in wood increases with moisture content due to the elastic softening (Schniewind 1968, Gerhards 1982). At constant high moisture content, creep increases rapidly i.e. creep at 22% is 32 times faster compared with creep at 10% moisture content. The acceleration of creep due to increase or decrease of moisture content may be explained by the micro-diffusion mechanism - the transport of water through the smallest micropores ~0.1 m in radius (Bazant 1985). Thus, creep becomes equivalent with stress-induced shrinkage and stress-induced thermal expansion. At low stresses, creep has a linear relationship with stress. For compression and bending, the limit of this linearity depends on compressive buckling of the tubular cell walls of the wood (Dinwoodie 1984). Hunt (1999) studied the creep and mechano-sorptive in European spruce (Picea abies). His results suggested that the effect of humidity over visco-elastic parameters could be represented by using simple exponential equations. Another parameter which influences creep is temperature, namely, an increase in temperature will generally reduce the stiffness of timber in bending, tension and compression (Davidson 1962, Kingston and Budgen 1972), especially above 55˚C. The interaction of creep with variable temperature results in a complex behavior that may be difficult to predict from constant temperature creep tests (Schniewind 1968). The breaking and reforming of the cross links from the amorphous regions of the wood microfibrils depends on temperature according to the activation energy theory (Bazant 1985). The activation energy is used to describe the slope of the temperature shift factor. Using Arrhenius’ law, Genevaux and Guitard (1988) provided an interpretation of creep tests performed under linearly increasing temperatures. The creep rate exhibited different peaks, each of them being attributed to a different creep mechanism. Recent studies  18  include the work done by Passard and Perré (2005) who realized an experimental set-up capable of performing creep tests on water-saturated samples up to 120°C.  2.4 Mechano-sorptive strain The phenomenon of mechano-sorptive strain could be summarized as an increased deflection of wood under load during moisture changes. During moisture cycling, there is an ‘exhaustion’ process, the creep increases per cycle slowly decreasing and tending towards a limiting value beyond which it will not progress (Hearmon and Paton 1964). This behavior depends on the load level and the size of the moisture step and is little affected by its duration (Hunt 1999, Zhou et al. 2000). Altogether it has been established that the following variables are involved: wood characteristics (density, microfibril angle, elastic modulus, shrinkage rate, etc.), stress, stress history, time, moisture content, moisture-content change, moisture content history, temperature, temperature history. Many different theories have been suggested for explaining the mechano-sorptive phenomenon. The studies reported prior to 1994 were summarized by Morlier (1994). Often the following explanation is taken into account: moisture changes cause the rupture of hydrogen bonds that can then be reformed in a different location under the bias of the applied stress. During the interval period, the material is more subjected to creep under an applied load. This explanation has been modified to fit in with the theory of physical aging of polymers (Hunt and Gril 1996). The theory of physical aging is based on the concept that amorphous solids are not in thermodynamic equilibrium at temperatures below their glass transition, but are analogous to super-cooled liquids whose volume, enthalpy and entropy are greater than they would be in equilibrium state (Hunt 1999). The original concept of physical aging was developed by McCrum (1992) into a more general theory of sequential aging. Mechano-sorptive strain in paper has also been studied intensively in the past years. It may be the result of transient stresses produced by heterogeneous hygro-expansion at the fiber-fiber bond in paper in combination with creep behavior that depends non-linearly on 19  stresses (Alfthan 2000). The major advantage of this theory is that mechano-sorptive creep seems to be a natural consequence of regular time-dependent creep. Other evidences also showed a close inter-relationship of viscoelastic creep rate and mechanosorptive creep accumulation during the intermediate cyclic-humidity periods (Hanhijarvi and Hunt 1998). The mechano-sorptive creep accumulation decreased viscoelastic creep rate and mechano-sorptive recovery decreased viscoelastic recovery rate. Lagana (2005) and Muszynski et al. (2005) illustrated the importance of measuring mechano-sorptive properties in simple loading models and established that mechanosorptive is a material property of wood. The mechano-sorptive component was extracted from the total deformation determined in course of creep tests under cycling climate conditions by subtracting the free shrinkage/swelling, and the viscoelastic deformations (including the immediate component) adjusted for current moisture. The mechanosorptive deformations were presented more conveniently against a monotonic measure of the cumulative moisture content change (Fig. 4).  Fig. 4. Mechano-sorptive strain plot as function of cumulative moisture content (Muszynski et al. 2003).  20  III. MATERIAL AND METHODS The methods of experimental design concentrate on the behavior of artificially and naturally restrained wood during the drying process. The tested specimens were divided into two groups having different dimensions: small wood strips and short pieces of lumber. The latter were named “full size specimens”, the former were referred as “small size specimens”.  1. Small size specimens 1.1 Specimen preparation Western hemlock (called simply “hemlock” throughout this thesis) is the species of interest in this project. The reasons for choosing Tsuga heterophylla, over other softwood species, are the following: •  hemlock is one of the most important export species in British Columbia;  •  high pith-to-bark density variation (Fig. 5) makes it a perfect candidate, particularly for studies where density and micro-fiber angle are among the independent variables;  •  compared to other softwood species, with similar density, hemlock has a higher shrinkage tendency (Fig. 6);  •  green hemlock contains a lot of water, it requires long kiln drying times and distorts a lot during drying;  All wood specimens were taken from a single, freshly cut 80-year old hemlock stem, grown in an experimental second-growth plantation from British Columbia (Malcolm Knapp Research Forest) with a stocking density of 300-400 stems/ha and a species composition of 70% hemlock, 20% western red cedar and 10% Douglas-fir. This way material variability was significantly reduced and the interdependencies between the drying factors could be statistically evaluated taking into account wood quality information for each sample (Pearson and Evans 2005).  21  Fig. 5. Average ring density from pith to bark in some second-growth woods (Jozsa et al. 1998).  Fig. 6. Volumetric shrinkage of old-growth western hemlock compared with 18 other Canadian old-growth softwoods, from green condition to 12% Memc (Jozsa et al. 1998). The stem, having a diameter at breast height of 700 mm, was sectioned in four 1 m-long logs; the first two were used for small size specimens (185x30x6 mm3) and the other two for full-size specimens (320x100x50 mm3). The first step in processing the small size specimens was to saw the two logs into boards having a thickness of 60 mm and a width of 185 mm (Fig. 7). The numbering system of the boards included log number (from 1 to  22  4 ), structural direction ( T - tangential or R - radial), wood density information ( M -  mature or J - juvenile) and geographic location ( N , S , E or W ).  Fig. 7. Cutting and numbering protocol for the first log: T - tangential, R - radial, M mature, J - juvenile, N - North, S - South, E - East, W – West.  The boards were wrapped in plastic bags, stored in a cold room at -10˚C (to prevent water loss and stain/decay) and then cut in clear, knot-free blocks of 30x60x185 mm3. Each block was cut into 6-6.5 mm thick strips having the tangential or the radial direction parallel to the length of the specimen (Fig. 8). The strips were positioned in a pneumatically operated support jig which kept them aligned in relationship with a template. The predetermined shape was done by a routing positioned within and guided by the slot in the template (Fig. 9).  Fig. 8. Side view of the tangential (up) and radial (low) wood strips.  23  Fig. 9. Final step in wood strip cutting: NC table router (left) and a processed strip positioned inside the pneumatic jig (right). The final dimensions of the small wood specimens were 185x6 mm2 in cross-section (tangential or radial direction) and 30 mm necked down to 16 mm in the central 110 mm (gauge region) in longitudinal direction (Fig. 10). The thickness was chosen to be less than double the tracheid length of hemlock (4.2 mm) in order to minimize moisture gradients.  Fig. 10. Final shape and dimensions (mm) of the tested specimen.  The shrinkage of the small size specimens was studied while drying at 40, 60 and 80ºC, in environments corresponding to 17, 11 and 5% target moisture contents. Three replicates were chosen for each case for a total number of 144 experimental runs. Each specimen had its own identification number, which was used later for matching purposes. An exemplification of the matrix numbering procedure is shown below:  24  40°C  60°C  80°C  S1,1...S1,5  S1,6 ...S1,11  S1,12 ...S1,17  S1TMN = 11% S 2,1...S 2,5  S 2,6 ...S 2,11  S 2,12 ...S 2,17  S3,6 ...S1,11  S3,12 ...S1,17  17% 5%  S3,1...S1,5  (3.1)  where S ij ( i = 1...3 , j = 1...17 ) represent the wood specimens from board S1TMN (Fig. 7); during a test five matched specimens are used at a time i.e. S1,1...S1,5 were tested at 40ºC while targeting 17% equilibrium moisture content.  1.2 Density and micro-fibril angle Two small wood strips (5x5 mm2 in cross section and containing 51 annual rings) were Soxhlet-extracted with acetone for 24 hours, oven-dried for 12 hours and then cut with a twin-blade pneumatic saw; the final thickness of the measured specimens was 1.68 mm. Ring width and oven-dry density were measured on a computerized Direct Reading XRay densitometer (QMS, Knoxville, TN, USA) with a resolution of 0.0254 mm (Fig. 11). All density values were reported as oven-dry density values.  Fig. 11. Density measurement from pith (left side) to the 34th annual ring.  The micro-fiber angle (MFA) of each annual ring was determined by measuring the relative width of a diffracted X-ray arc. The diffraction arc T-values were collected using 25  a Bruker D8 Discover X-Ray diffraction unit equipped with an area array detector (GADDS) on the radial face of each earlywood portion of individual growth rings. The measurements were performed with CuK 1 radiation ( = 1.54 A°), and the X-ray source fit with a 0.5 mm collimator and the scattered photon collected by the GADDS detector. The procedure used was perfected by Meylan (1967) and later used by many others (ElOsta et al. 1972, Lindeberg 2004). The specimen was placed in a holder with the tangential face perpendicular to the X-ray beam. The scattered intensity of the diffracted beam from the specimen was recorded by the area detector and plotted for different corresponding intensities (Fig. 12). Tangents were then drawn at the inflection points for the two sides of the curve and the relative peak width measured as the distance between the two tangent intersections with the baseline. This distance was referred to as the parameter 2T. The average T value ( T ) of the two peaks was determined using SAS/STAT® software – the source code is presented in A1 from Appendix A. Relative peak width values were then converted to actual fibril angle values by using a calibration equation developed from samples measured by light microscopy:  MFA = 0.5106 (T ) + 4.8875  (3.2)  Fig. 12. MFA measurement for a single annual ring  26  1.3 Instrumentation Accurate measurements of shrinkage values depend on the precise generation of temperature and relative humidity conditions. In this investigation, the equipment used to generate the air parameters was a conditioning chamber (PGC 9130) that controls air temperature and relative humidity to ±0.10ºC and ±0.1%, respectively (Fig. 13). In addition to the sensors of the climate chamber, two thermocouples, acting as dry and wetbulbs, were installed inside to double-monitor air parameters.  Fig. 13. PGC cabinet: outside-inside look and computer interface (from left to right).  The shrinkage of the small size specimens was measured in continuous 60 second intervals during drying by a pair of LMP (Linear Motion Position) sensors located on the middle part of the specimen. The transducers were fixed on both sides of the specimens and the average value was computed in order to remove the small bending effects (Fig 14). The LMP sensors can withstand temperatures up to 130˚C and each unit consists of a 5k  variable resister over which 1.5V is applied. The upper sensor holder is equipped  with two spherical tacks and a conical tack which can penetrate wood surface. The connecting screws between the plates were equipped with springs to maintain the contact between the tacks and wood during the shrinkage process. A lower L-shape aluminum profile, having a similar wood – holder connection system, was used as a reference for the sensor extendable rod (Fig. 15).  27  Tested specimen  Upper sensor holder Spring return linear motion position sensor L-shape reference holder  Fig. 14. Tangential test specimen with mounted sensors. 1  2  4 3 5 Fig. 15. Upper sensor holder: 1 – aluminum body; 2 – spherical threaded tack; 3 – sharp threaded tack; 4 – threaded hole for connecting screws; 5 – threaded hole for sensor fixture.  Four small size specimens having approximately the same annual ring pattern were subjected to different restraints, namely, zero restraint (free shrinkage), 30N, 60N and total restraint. The totally restrained sample has a load cell attached on the upper part consisting of 4 strain gauges connected in a Wheatstone bridge configuration. A fifth matched free-of-transducers specimen was weighed at different time intervals to determine the moisture change. The restraining system is shown in Fig. 16. 28  10 9 6 8 5 7 3 2 4 1 60N  30N  12  11  13  Fig. 16. Experimental test frame: 1 – rigid steel frame; 2 – free wood specimen; 3 – spring return linear motion position sensor; 4 – L-shape reference holder; 5 – upper sensor holder; 6 – load cell; 7 – steel rod; 8 – aluminum plate; 9 – threaded rod; 10 – nut; 11 – additional stud; 12 – restraining weight; 13 – frame sole.  The connection between the wood and the restraining system utilized threaded steel rods and aluminum plates. At the beginning of the experiment, the loads were placed on the frame sole and very little (initial clamping) stress was induced in the samples. The tensile forces generated by the restrained drying process led to compression in the outer part of the specimen holes. A compression load applied perpendicular to grain produced stresses that deformed the wood cells perpendicular to their length. After the hollow cell cavities were collapsed, wood became quite strong because no void space existed (twice as strong in compression than in tension perpendicular to grain). The ultimate strength in tension 29  determined the break point of the specimen as opposed to failure at the specimen clamp holes. The shrinkage starting time (in the restrained specimens) was delayed by the little compression which appeared in the outer part of the fixing holes. The same effect happened with the totally restrained specimen just at a higher magnitude level since the force was continuously increasing and therefore, with an unattainable 100% restrained shrinkage the term “totally restrained” was replaced with the maximum recorded value by the load cell during the drying process. In order to record the dimensional changes in the “totally restrained” specimen, two similar strain transducers were added. After the specimens reached M emc and no significant strain change could be recorded, the dead-loads and the locking mechanism for the specimen with the load cell were removed and the experiment continued with a conditioning step by exposing the sample to the same drying conditions until no significant dimensional change was recorded. This experimental design allowed a realistic simulation since the stress is practically induced by the drying process. The voltage supplied by the transducers was recorded in a computer through a data acquisition system and processed with Labtech (Fig. 17).  Fig. 17. Data acquisition system and lab software.  Both the load cell and the LMP transducers were designed, according to the manufacturers, to work properly at temperatures up to 100ºC. The change in electrical resistance with temperature, considered to be 200parts/millionºC, induced a maximum  30  reading error of 1.2% when tests at 80ºC were performed. The calibration and measurement error range of all LMP transducers and the load cell were done at room temperature using a universal testing machine and a digital pair of calipers (Fig. 18). The calibration tests showed a good correlation with the 1% maximum linearity error stipulated by the technical documentation (Fig. 19). Three more accuracy measurement tests were performed, throughout the eighteen month period necessary to complete all the experiments, and each time no significant changes in measuring accuracy could be determined.  Fig. 18. LMP transducer (left) and load cell calibration. 10 9 8 7 6 5 4 3 2 1 0  12 y = 0.0883x - 0.0021 R2 = 1  8 6 4 2 0 0  25  50 75 Weight [Kg]  y = -0.7984x + 8.9854 2 R = 0.9998  Volts [V]  Volts [V]  10  100  125  0  2  4 6 8 Mechanical travel [mm]  10  12  Fig. 19. Calibration results for load cell (left) and one of the LMP transducers (right).  The relationship between relative humidity and target moisture content was calculated with Hailwood–Horrobin single hydrate equation using parameters determined by Simpson (1973): 31  M=  0.018 K1 K 2 h K2h + W 1 + K1 K 2 h 1 − K 2 h  (3.3)  where h is the relative vapor pressure, in kPa and W, K1, K2 are temperature (T in ºC) function parameters:  W = 0.2234 + 0.0007 ⋅ T + 0.000019 ⋅ T 2  (3.4)  K1 = 4.73 + 0.048 ⋅ T − 0.0005 ⋅ T 2  (3.5)  K 2 = 0.706 + 0.0017 ⋅ T − 0.000006 ⋅ T 2  (3.6)  1.4 Preliminary experiments A limited number of preliminary experiments were done in order to evaluate the Memc of the specimens after drying and the testing protocol. During these experiments, a small difference of initial overall moisture content between similar specimens was detected. This raised some questions about the existence of a moisture gradient along the length of the specimen which could influence the shrinkage and stress distribution. Therefore a few drying experiments, without transducers, were carried out in order to determine the evolution of the moisture gradient during the drying process. The experimental procedure consisted of drying simultaneously five specimens having a similar structure and, at different time intervals, remove one of them, weight it and then cut in 5 pieces which were individually weighed and then oven-dried. The first specimen was cut at the very beginning of the experiment (11-2-23 from Fig. 20). The overall moisture content before cutting proved to be similar for all specimens and during the drying process the specimens follow the same moisture loss pattern (Fig. 20). On the other hand, the drying for regions near the core was quite different that is, core moisture contents were 30 to 40% higher when compared to other regions. During the drying process this difference decreased reaching values of 20% after 6 hours of drying and 0.5% at the end of the drying process (Fig. 21).  32  160 140 Moisture content [%]  120 11-2-23 11-2-24 11-2-25 11-2-26 11-2-27  100 80 60 40 20 0 0  2  4  6 Time [hrs]  8  10  12  Fig. 20. The overall moisture content of five similar specimens during the preliminary experiments.  160  Moisture content [%]  140 120 100  A-1 A-2 A-3 A-4 A-5  80 60 40 20 0 0  2  4  6 8 Time [hrs]  10  12  14  Fig. 21. The evolution of the moisture gradient inside the specimens during drying.  A moisture gradient inside the samples was an undesired feature and therefore preceding experimentation, all specimens were conditioned to full saturation by immersion in cold 33  water until sinking; the initial moisture content was around 200%. Some of the moisture content (5 to 25%) was lost at the beginning of the experiment, partly because of the time required to mount the sensors and partly due to the time necessary for the conditioning chamber to reach the required parameters. The exact value could be determined by weighing and then subtracted for curve fitting purposes. Other preliminary experiments consisted of establishing if drying under a tensile force had an influence over final moisture content. Restrained and free matched specimens were weighted at the end of the drying process and then left in the same environment for another 6 hours for conditioning. A small difference of ~1% was detected only for the specimens subjected to high restraining forces; the difference was lost after the conditioning step.  1.5 Moisture content measurement and fitting The moisture content was measured by weighing the free-of-transducer specimen at different time intervals. The conditioning chamber was equipped with an additional Plexiglas door having three iris openings, which allowed access to the experimental frame without relative humidity and temperature changes. Initially, the moisture content loss was fitted using the thin-layer drying equation (Marinos-Kouris and Maroulis 1995). The drying rate was assumed to be directly proportional to the moisture content of the board and the Memc provided by the drying environment:  dM = − k ( M − M emc ) dt  (3.7)  where k is the slope of the drying rate function (1/min) and t is time (min). The experimental results showed this equation fits well only if the dehydration process is very intense (low moisture contents are targeted) i.e., 40ºC and 21% relative humidity as seen in Fig. 22. A slightly different trend was noticed for milder drying conditions,  34  respectively the early drying rate did not drop so suddenly, but gradually i.e., 40ºC and 76% relative humidity from Fig. 22. The same trend was observed for the other tested temperatures. The effect was also pointed out by Xiao (2005) in his review of the drying rate models. Other equations, such as the one developed by Crank (1975), might provide better estimations: dM = α ⋅ β ⋅ t β −1 ⋅ ( M emc − M ) dt  (3.8)  where α and β are regression coefficients. This nonlinear function yielded high R2 coefficients under conditions of normality and equal variance.  210 17% 11% 5% Analytical fit  Moisture content [%]  180 150 120 90 60 30 0 0  500  1000  1500 2000 Time [min]  2500  3000  Fig. 22. Experimental and curve fitted moisture (using eq. 3.8) for three different relative humidity levels (76, 56 and 21%, respectively) and the same temperature (40ºC). The arrow indicates the portion of the graph where equation (3.7) could not fit well the experimental data. Between the two regression coefficients, α characterizes the slope of fitting function while β compensates for the beginning of the process. High values for α results in sharp curves which ends in a small period of time while small values represent a smooth dehydration process. The two regression coefficients were determined using a non-linear 35  fitting (A2 from Appendix A).  1.6 Drying strain and stress calculations An initial offset value for each transducer was subtracted from each reading and thus the reading values represented the difference between two consecutive positions. The strain was calculated by dividing the values given by the strain sensors ( dL , in mm) to the initial gauge distance between the conic tacks ( L = 25.4 mm):  ε=  dL ⋅ 100 [%] L  (3.9)  The shrinkage percentage for the restrained specimens was calculated as a ratio between the strain developed in the restrained specimen ( ε r ), divided by the strain developed in the free-to-shrink specimen ( ε f ):  Shrinkage =  εr ⋅ 100 [%] εf  (3.10)  The elastic percentage was calculated as the difference between the values recorded at the end of the drying process and one minute later after load release ( ε 1rmin ). The value was converted to a percentage by dividing it by ε f :  Elastic =  ε 1rmin ⋅ 100 [%] εf  (3.11)  Similarly, the recovered percentage was calculated as the ratio between the combined creep and mechano-sorptive strain ( ε ve - calculated as the difference between the final value recorded in the restrained specimens and the value recorded after the elastic percentage was released) and ε f :  Recovered =  ε ve ⋅ 100 [%] εf  (3.12)  36  The creep component was not separated from the mechano-sorptive component in this experimental design. For a rapid drying process (small specimens) the mechano-sorptive strain usually exceeds by far the creep strain (Wu 1993) and since the load was induced close to the Mfsp, during a period of intense water removal, its influence was significantly diminished (Hanhijarvi 1997). Another difficulty to separate the two components is represented by the fact that even during a constant environment loading condition both flexural stresses and its associated axial strain in tension influence wood M emc (Shmulsky 2004) and consequently a small mechano-sorptive effect will appear. Svensson (1997) has also preferred to introduce a simplified description of creep by using a reduced elastic modulus. The “set” or plastic percentage was the unrecoverable strain which resulted as a consequence of visco-elastic strain:  Plastic =  ε f − ε r − ε 1rmin − ε ve ⋅ 100 [%] ε  (3.13)  Previous research (Svensson 1997, Maska 2004, Lazarescu and Avramidis 2008) has shown that the shrinkage pattern in small specimens follows a logistic curve. In order to interpolate the experimental free shrinkage results a well known logistic differential equation (Verhulst 1838) was adapted to this case:  εf dε f f f = S r ⋅ ε ⋅ (1 − f ) , lim ε f (t ) = ε max t → ∞ dt ε max  (3.14)  f where S r defines the shrinkage rate coefficient and ε max is the maximum free shrinkage  that could be attained by the drying process. Experimental and curve fitted values are depicted in Fig. 23. Preliminary to curve fitting all null values were eliminated.  37  5 Experimental Analytical fit  4  T  [%]  3  R  2 1 0 0  500  1000 Time [min]  1500  2000  Fig. 23. Experimental and curve fitted shrinkage (using eq. 3.14) for radial (R) and tangential (T) at 40ºC targeting 17% moisture content.  The restraining forces were applied at the end of the specimen and consisted in dead weights having a value of 30.25 and 59.16 N, respectively. Stress distribution, in the area where the transducers were located, was not uniform due to the stress concentrator represented by the reduced section. The maximum stress ( σ max , in MPa) was related to the average stress of the net cross section, the nominal stress σ nom (MPa), by using a stress-concentration factor (K):  K=  σ max σ nom  (3.15)  K nominal value is directly related to the ratio between the radius of the shoulder fillet (r=3 mm), the dimension of the narrower portion (d=16.5 mm) and the dimension of the wider portion (D=29.5 mm). Using all these constants and a digitized graphic (Pilkey 1997), K value was determined to be 1.989. The nominal stress was calculated using the following relation:  38  σ nom =  P d  where  (3.16) represents the thickness of the specimen – individually determined by  measurements for each specimen, in mm and P is the restraining force, in N.  2. Full size specimens 2.1 Specimen preparation As previously stated, the other two logs (from the same tree) were used for full size specimens. In this way, the empirical equations developed on small size specimens may be used to study the stresses in boards (Wu 1993). The exact dimensions of full size specimens were 50x100 mm2 in cross section and 320 mm in length. The same type of transducers (LMP sensors) was positioned around the tested specimen using a frame connected with screws and nuts to a support body (Fig. 24). 7  6  5  4  1  3  2  Fig. 24. Experimental design of set measurements: 1- wood piece, 2- aluminum support, 3- LMP sensor, 4- core temperature sensor, 5- core moisture meter; 6- aluminum frame; 7-shell temperature sensor.  39  A realistic simulation of a drying process implies a fixed position of the lumber, the pressure of the adjacent layers being transmitted through the stacking stickers. Therefore, the tested lumber was restrained at both ends by a flexible system (to compensate for decreasing dimensions or the specimen during the drying process) composed of two bars connected with threaded rods. Contact and continuous pressure, during the drying process, was achieved through high compression springs mounted on the top bar. At the beginning of the experiment the springs were compressed using wide washers and nuts (Fig. 25). 1  2 3  4  6  5  Fig. 25. Detail of the clamping system: 1- shell moisture meter; 2- nut; 3- threaded rod; 4wide washer; 5- compression spring; 6- bar.  A wireless moisture and temperature monitoring system (Lignomat LMS-YM) was used to monitor wood moisture and temperature changes. The moisture profiles were determined using insulated pin electrodes positioned at different depths: shell (5 mm from the surface), core (25 mm from the surface) and two intermediary positions at 10 and 15 mm, respectively. The pins were designed and calibrated, by the manufacturer, to do the readings only across the grain. In this way, the influence of the water pockets running with the grain was minimized and more accurate readings above Mfsp could be done. Two separate equations, above and below Mfsp, were used to increase the accuracy 40  of the readings:  M w = B ⋅ M w1 + A  (3.17)  M fsp = B ⋅ M u + A  (3.18)  where M w is the true moisture contents of the wet board according to an oven dry test,  M w1 is the reading delivered by the transmitter (both in %), A and B are correction factors applicable above Mfsp (assume 30%) and M u =  30 − Au is the adjusted moisture Bu  reading, Au and Bu being the correction factors for readings below Mfsp. Each sensor was connected to a battery-powered transmitter station which sent the readings, by radio waves, to a receiver station located inside the conditioning chamber. The receiver was connected with a Teflon-coated cable to a computer which recorded the values. Not one, but two matched pieces of lumber were tested at a time, one having moisture, temperature and strain sensors around it and one free. The free-of-transducer lumber was used as a “Control” to double check the data provided by the sensors – at different intervals of time, it was manually measured and weighted. A dry and a wet-bulb thermometer were improvised using two temperature sensors connected to the Lignomat system. One of the sensors was wrapped in a cotton wick which was dipped into a distilled water container and a small fan was used to raise air movement to around 3 m/s. These transmitters have a rated accuracy of ±1°C at temperatures below 55°C and ±1.5°C at temperatures above 55°C. The data collector has a rated accuracy of ±1°C or better throughout the entire range of -20°C to 85°C. The accuracy of the collected data was compared with readings done with a recently calibrated microprocessor thermocouple. The same conditioning chamber was used to simulate the drying environment and the drying conditions covered the same temperatures used in the first phase of the project 40, 60 and 80˚C, respectively. The relative humidity was set to provide an environment for a  41  target moisture content of 5%. The experiment was stopped when the average indications of all moisture sensors was around 10%. A photo of the experimental setup is illustrated in Fig. 26.  Fig. 26. Experimental setup for full size timbers.  Before testing, the lumber specimens were kept in cold water in order to have a wet and fresh wood surface and diminish the risk of surface checking development (Rosenkilde et al. 2004). This way the formation of the dry shell, which controlled the drying rate when the wood was above Mfsp, was delayed for a short period of time. The cross section was either flat, quarter sawn or at a 45 degrees angle. Two replicates were chosen for each case for a total number of 36 experimental runs. The ends were coated with epoxy to avoid fast longitudinal moisture transfer. The sealing method proved to be so efficient that the evolution of the moisture front could be photographed on the end of the free lumber (Fig. 27). When the lumber reached an average moisture value of 10%, according to the moisture sensors, the experiment was stopped and the tested lumber was immediately weighted with a digital balance to 0.01g and measured with a caliper to 0.01mm at both ends and in 42  the tested region. Similar measurements were also done before starting the experiment. Specimens were then oven-dried at 103±2oC until constant weight was achieved for two similar measurements separated by 12 hours. The moisture content was calculated as oven dry-basis. The comparable results showed that the system was very accurate in terms of strain and final moisture content, but less accurate in terms of initial moisture content – more details are provided in the third chapter of the “Results and discussion” section.  Fig. 27. Selected pictures of the free lumber during different drying stages: 24, 96 hours and end of the drying process (from left to right). 2.2 Drying strains The strain was calculated by dividing the values given by the strain sensors ( dL , in mm) to the initial thickness or width (determined by measurements for each particular experiment):  ε=  dL ⋅ 100 [%] L  (3.19)  43  IV. RESULTS AND DISCUSSION 1. Material properties 1.1 Density The average diameter of the logs (including bark) was 700 mm, each log had around 69 annual rings, the first 44 annual rings being heartwood (visually identified due to the slight change in color). The first 47 annual rings were included in either pure tangential or radial specimens. The within ring density distribution is illustrated in Fig 28 (numerical values are included in Table B.1 from Appendix B). Overall the tested material was clear of decay, abnormal discoloration and mold or defects produced by natural or processing causes.  3  Oven-dry density [kg/m ]  600 550 500 450 400 350 300 0  4  8  12 16 20 24 28 32 36 40 44 48 52 Annual ring [years] Fig. 28. Within ring density distribution.  Density measurements of the first two annual rings were particularly high, slightly over 500 kg/m3, the average oven-dry density value for all annual rings being 413 kg/m3 with a standard deviation of 44 kg/m3. This value is smaller than the one reported by Jozsa et al. (1998) for a similar stocking density – 436 kg/m3 with a standard deviation of 61 kg/m3. The difference was represented by the high value of the diameter at breast height, 700 mm compared with 496 mm in Jozsa’s study and the small amount of juvenile wood 44  (discussed in the following section). Three other researchers reported hemlock density range between 407 (Jessome 1977) to 427 kg/m3 (Kennedy and Swann 1969). Hemlock ring width was found to be positively correlated with lower density values (Josza et al. 1998, Fabris 2000). A slight trend could be noticed for this particular tree (Fig. 29); the exception was the widest annual ring (23) which had a density value close to the average.  3  Oven-dry density [kg/m ]  600 3&4  550 500  23  450 400 350 300 0  1  2  3  4 5 6 Ring width [mm]  7  8  9  10  Fig. 29. The influence of density over ring width. Numbers adjacent to points are the corresponding ring numbers.  Each radial specimen contained around 33 annual rings, the juvenile specimens including annual rings starting with the second and ending close to the 33rd annual ring (interrupted contour from Fig. 30), and the mature specimens started with the 16th annual ring and ended at number 47 (continuous contour from Fig. 30). The linear displacement sensors were fixed between 5 annual rings located close to the geometric center of the specimen; the area were the sensors were fixed is depicted in Fig. 30 with a small diagonal stripe filled rectangle. Each tangential specimen usually had 15 annual rings with only one annual ring in the testing region (Fig. 31). One may notice that the tangential specimens were cut starting from the 16th annual ring in order to get annual rings straight enough for  45  pure tangential strain measurements. Another helping aspect was the width of the annual rings - the average width of the first 15th annual rings was 4.11mm while all the other annual rings had values around 5.79mm (close to the thickness of the tested specimens).  3  Oven-dry density [kg/m ]  600  Measured density Trend Sensors juvenile Sensors mature  Juvenile  550 500  Mature 450 400 350 300 0  4  8  12 16 20 24 28 32 36 40 44 48 52 Annual ring [years]  Fig. 30. Density distribution inside the radial specimens. The area were the sensors were fixed is represented with a small diagonal stripe filled rectangle.  3  Oven-dry density [kg/m ]  600 550  Trend  500 Juvenile  Mature  450 400 350 300 0  4  8  12 16 20 24 28 32 36 40 44 48 52 Annual ring [years]  Fig. 31. Density distribution inside the tangential specimens. 46  The general density trend is a declining one from pith to the 19th annual ring which usually marks the end of the juvenile zone (a well known characteristic from hemlock density profile). A rapid increase in ring density is evident from rings 20 to 29 followed by a sudden drop in rings 34 to 38 and a rise in annual rings 39 to 47. The second drop in density profile density area was caused by a low proportion of late wood which might have been the result of shorter growing seasons during those years. The difference in density value between the two structural directions is revealed in Table 1. Table 1. Average oven-dry density values for each structural direction and density differential (juvenile or mature) Tangential Radial Juvenile Mature Juvenile Mature 3 Oven-dry density [kg/m ] 420 370 440 400 3 Standard deviation [kg/m ] 20.2 33.4 35.8 25.7 (Juvenile-Mature) [%] 10 10 1.2 Micro-fibril angle Micro-fibril angle measurements, one of the most reliable methods to determine juvenile wood spread (Zobel and Sprague 1998), was measured for the first 52 annual rings (Fig. 32). The first seven annual rings had values between 33 and 29 degrees, the eighth annual ring was 25 and the ninth reached a value of 18 degrees. All the other annual rings had values between 14 and 16 degrees with an average value of 15.67 degrees and a standard deviation of 0.6. High values of MFA were found to be positively correlated with ring width (Zobel and Sprague 1998) which is in agreement with these measurements.  47  Micro-fibril angle [degrees]  40  Juvenile  35  Mature  30 25 20 15 10 5 0 0  5  10  15  20  25 30 35 Annual ring  40  45  50  55  Fig. 32. MFA variation in cross-section. The demarcation line represents the boundary between juvenile and mature wood.  The relatively small number of annual rings with high MFA (first nine) shows that the initial density drop, identified to continue up to the 19th annual ring (Fig. 28), is a poor estimator of the actual juvenile period (Middleton and Munro 2001). Long periods of juvenile wood in hemlock, usually attributed to shade tolerance (Jozsa and Middleton 1994), were not the case here due to the low stocking density from Malcolm Knapp Research Forest. The sum of the width of first nine annual rings was 30 mm (see Table B.1) and they could be included only in some of the juvenile radial samples. Since the sensors could not be fixed around the juvenile area, located at the end of the radial samples, no actual measurements could be performed for pure juvenile specimens. The terms of “mature” and “juvenile” continued to be used to describe the two density classes.  48  2. Drying strains in small specimens 2.1 Free shrinkage Typical time-shrinkage curves for free tangential specimens exposed at constant temperature (40oC) and targeting different moisture contents (17, 11 and 5%) are illustrated in Fig. 33. The amount and rate of moisture loss depend on the relative humidity of the surrounding environment, in this example 76, 56 and 21%. The first water molecules to be desorbed are the ones contained in capillaries. They are followed by water molecules adjacent to the capillary walls bounded by chemisorption, and lately by the water molecules located inside the cell walls. The process stops after the moisture content inside the wood specimen becomes sufficiently low to be in equilibrium with the ambient environment. All the shrinkage curves plotted versus time, obtained during this experimental phase, have the characteristics of a logistic or “S shape” curve with four distinct phases: initial slow increase, exponential growth, slow decrease and zero growth rate.  8  5%  Free shrinkage [%]  7  11%  6 5 17%  4 3 2 1 0 0  500  1000 1500 Time [min]  2000  2500  Fig. 33. Free shrinkage pattern in tangential specimens targeting 17, 11 and 5% moisture content at constant temperature 40ºC  49  6  5%  Free shrinkage [%]  5 4  11%  3  17%  2 1 0 0  500  1000 1500 Time [min]  2000  2500  Fig. 34. Free shrinkage pattern in radial specimens targeting 17, 11 and 5% moisture content at constant temperature 40ºC. The introductory phase represents a transitory slow accommodation to water loss; it may also contain the so called “abnormal shrinkage” explained by other researchers as a consequence of a transitory coexistence of free-bound water (Hernández and Bizon 1994), stresses induced by free water removal (Almeida et al 2007 and Perré 2007) or collapse due to capillary tensions at meniscus which determine capillary tensions in liquid (Stamm 1964). Hemlock is a species susceptible to collapse due to its small pit openings (Siau 1995), but with the specimens cut sufficiently short along the grain (in this case 16.5 mm in the measuring region) collapse should not occur (Greenhill 1938). The transition to a relative constant desorption rate (straight-line of the S profile) is faster if the partial vapor pressure is smaller. The slowing of the shrinkage rate (upper part of the S profile) reflects the increasing amount of energy required to eliminate water molecules at a continuously decreasing pressure gradient. The point of stabilization called also the “carrying capacity” represents the maximum amount of shrinkage that might be attained for a given equilibrium. Similar shrinkage patterns could be identified for the radial specimens (Fig. 34). The time-shrinkage function has two asymptotes one represented by the horizontal axis  50  and the other one determined by several material properties among which density and micro-fibril angle play important roles. Earlier starting points could be associated with low relative humidity values which set higher capillary forces inside the wood structure during the free water elimination stage. Points of interest from this data are represented by the starting moment, strain (free shrinkage) rate, time required to reach the carrying capacity and maximum shrinkage that can be attained. Strain rate and maximum free shrinkage will be discussed here, the other variables will be discussed with moisture coefficients. Free radial and tangential shrinkage values are illustrated in Fig 35 (numerical values are included in Table B.2 from Appendix B). Both groups tangential (T) and radial (R) were individually analyzed using SAS. Strain, the dependent variable, was plotted versus the independent variables moisture and temperature as well as their common transformations: power (quadratic and cubic), logarithmic, square root and inverse. Plot assessment eliminated the influence of most transformations excepting the quadratic transformation which showed a high linearity especially for tangential data. A binary variable (Z) was used to test the density effect over the analytical fit; the mature or juvenile specimens were coded with Mt and Jv letters. The program started by analyzing the significance of each variable in the presence of all the other variables and continued by dropping “step-wise” the ones having F-values below the 0.05 significance level (A3 from Appendix A). The analysis of variance is shown in Table 2. Table 2. Analysis of variance for free tangential and radial data. Source DF Mean Square F Value Probability Tangential Model 3 29.82 121.97 < .05 Error 70 0.24 Radial Model 3 23.44 264.33 < .05 Error 71 0.09 The output of the regression analysis was two equations:  ε Tf = 7.06 − 0.01 ⋅ M 2 − 0.014 ⋅ T ⋅ Z + 0.86 ⋅ Z , R 2 = 0.84 51  (4.1)  ε Rf = 5.98 − 0.2 ⋅ M − (0.015 − 0.007 ⋅ Z ) ⋅ T , R 2 = 0.92  (4.2)  Z is null for juvenile and unity for mature specimens, both equations are valid only for 0 ≤ M ≤ FSP . Individual equations for each density class are: f ε TMt = 7.93 − 0.01 M 2 − 0.014 T  (4.3)  f ε TJv = 7.06 − 0.01 ⋅ M 2  (4.4)  f ε RMt = 5.98 − 0.2 M − 0.008 T  (4.5)  f ε RJv = 5.98 − 0.2 M − 0.015 T  (4.6)  The binary variable was significant at the 0.05 level for both fits and therefore the two populations, generically called juvenile and mature, had their own distinctive equations. Plots of the experimental and interpolated tangential and radial shrinkage for both mature and juvenile specimens are shown in Fig. 35. The analytical fit was calculated for a temperature of 60ºC. The data shows that shrinkage depends both on moisture content and temperature, the only exception being the tangential juvenile group. The maximum shrinkage value that could be attained in tangential specimens decreases proportionally with the square value of moisture content and temperature (for mature wood only). This non-linear relationship is probably the result of the uneven distribution of the denser latewood, which is the controlling factor of the tangential shrinkage (Panshin and Zeeuw 1980). Multiple layers of wood (earlywood, latewood or compression wood) with variable shrinkage properties tend to generate constraints and stresses in each layer (Pang 2002). The shrinkage of the denser and stronger latewood causes the compression of the early-wood which is forced to shrink more than if it were allowed to shrink independently. Specimen cutting could not follow the shape of an annual ring and therefore latewood in the gauge area could have an ideal distribution, like the ones illustrated in Group A (Fig. 36), or it may encounter distributions like the ones from Group B. With an average annual ring width of  52  5.34 mm and 6 mm thick specimens, Group B, which tends to shrink less than Group A, was better represented in the statistical population.  8  Mature Juvenile T R  7 6 [%]  5 4 3 2 1 0 0  3  6  9 12 15 Moisture content [%]  18  21  24  Fig. 35. Experimental and curve fitted free radial and tangential shrinkage (60ºC); T and R letters stand for tangential and radial, respectively. 1  2  a  b  c  3  d  e  Group B  Group A  Fig. 36. Latewood distributions in the tested area: 1 – earlywood; 2 – latewood; 3 – sensor.  53  The density of the annual rings from the tangential juvenile area was higher than the one from the mature area (Table 1) and it was expected to shrink more (Stamm and Loughborough 1942) however, equations (4.1) and (4.2) show exactly the opposite. Two reasons might explain this irregular situation: first, recent studies show that relation between shrinkage and basic density is non-significant and insufficient for providing an accurate prediction of shrinkage (Dumail and Castera 1997) and second, the average ring width value was 6.44 mm for juvenile and 5.88 mm for mature which means that more juvenile specimens fall into the lower-shrinkage Group B. Lower radial and tangential shrinkage values in wide-ringed open-grown ponderosa pine compared with narrowerringed forest grown wood were also found by Cockrell and Howard (1968). A comparison between juvenile and mature (calculated for a temperature of 40ºC) tangential and radial results and other publish data is shown in Figs. 37 and 38. The following well-known empirical equations were used for comparison purposes: 2 sT = G2 ( M 2 − M 1 ) (Stamm and Loughborough 1942) 3  (4.7)  1 s R = G2 ( M 2 − M 1 ) 3  (4.8)  sV = G2 ( M 2 − M 1 )  (4.9)  G2 =  G0 (Siau 1995) 1 + 0.01MG0  sT , R ,V = s0 (  (4.10)  28 − M ) (USDA 1999) 28  (4.11)  where G2 (dimensionless) represents the specific gravity at M 2 (%) M 2 > M 1 , G0 is the basic specific gravity of hemlock ( G0 = 0.395 for tangential and G0 = 0.42 for radial, Table 1), sT , R ,V (%) is the shrinkage from green conditions to M < 28 (%) and s0 (%) is the total shrinkage for a particular structural direction ( s0 = 7.8 , s0 = 4.2 and s0 = 12.4 for western hemlock tangential (T), radial (R) and volumetric (V), respectively.  54  9 8  USDA 1999 Stamm 1942 Juvenile Mature  7  [%]  6 5 4 3 2 1 0 0  3  6  9  12  15  18  21  24  27  30  Moisture content [%] Fig. 37. Fitted and existing empirical models for tangential specimens drying from Mfsp to 0% moisture content.  Beginning and final parts of the curves are very close to the other two models while intermediate values showed a difference of up to 1.5%. The difference is a direct consequence of the way the shrinkage data was gathered. The measurements were done inside a specimen (Fig. 16) which had a ratio between the tangential/radial dimensions of 1:28 or 28:1. In contrast, Stamm (4.7 to 4.9) and USDA models (4.11) were built based on measurements made on small blocks with a tangential/radial ratio of 1:1. In other words, the lack of restraint allowed the tested specimens to shrink more in the tested direction. Targeting lower moisture contents meant an increase in the drying rate and the experimental curves approached the empirical models. The amorphous areas of the cellulose chains, forced to move closer at a higher rate, attained incomplete equilibrium positions i.e., there was more free volume remaining than the equilibrium case. The overall tangential shrinkage value which is controlled by the denser latewood makes the tangential specimens more prone to this effect. Higher drying rates combined with high temperatures have also decreased the final tangential shrinkage value with more than 30% in a study performed on tangential matched specimens by Stevens (1963).  55  The radial specimens followed a straight line, the shrinkage value being proportional with moisture content and temperature. This time latewood distribution inside the samples did not influence final shrinkage value and the higher density group (juvenile) shrunk more than the other one. The drying rates did not appear to influence the radial fit. The same trend was observed by Stevens (1963), whose experiments on radial specimens were little influenced by temperature and drying speed. Actually the only influence was obtained for drying runs performed at 100oC. The additive effect of latewood – early wood interaction generates equilibrium on the deformation rate whose pace is disturbed by the drying rate only for very high temperatures. Nonetheless, the temperature gradient proved to have an influence over shrinkage value for different density classes. The radial specimens having a higher density (juvenile group) shrank less as the temperature increased (eq. 4.6).  6 USDA 1999 Stamm 1942 Juvenile Mature  5  [%]  4 3 2 1 0 0  3  6  9  12  15  18  21  24  27  30  Moisture content [%] Fig. 38. Fitted and existing empirical models for radial specimens drying from Mfsp to 0% moisture content.  The intercept points with moisture axis were slightly higher for the tangential plots in agreement with previous research (Kelsey 1956, Stamm 1971). A summary of the results is illustrated in Table 3. The numbers do not represent the value calculated with the analytical fit but the average experimental value for each moisture group.  56  Table 3. Stress-free shrinkage: theoretical and practical results for two structural directions and three moisture contents 17, 11 and 5%. Moisture Tangential shrinkage [%] Radial shrinkage [%] content [%] Stamm This Stamm This USDA* USDA* (1964) Study (1964) Study 17 2.71 3.06 3.93 1.44 1.65 1.91 11 4.29 4.73 5.82 2.27 2.55 3.09 5 5.94 6.40 6.80 3.15 3.45 4.19 * Wood Handbook The next parameter to be analyzed was the shrinkage rate coefficient ( S r ) which may provide valuable information about the dynamics of the process. Shrinkage rate coefficient plotted versus moisture content lead to the identification of two obvious and expected trends, namely, either low moisture content targets or high temperatures determine an increase in shrinkage rate (Fig. 39). It was calculated using relation 3.15. Numerical radial and tangential S r values are included in Table B.3 from Appendix B.  0.07 0.06  40oC 60oC o 80 C  Sr [1/min]  0.05 0.04 0.03 0.02 0.01 0 0  3  6  9  12  15  18  21  Moisture content [%] Fig. 39. Experimental S r values for different temperatures: 40, 60 and 80oC.  57  24  A similar technique with the one used to fit the free shrinkage value was used in this case too (A4 from AppendixA). The analysis of variance is shown in Table 4. Table 4. Analysis of variance for free tangential and radial data. Source DF Mean Square F Value Probability Model 4 0.0028 88.09 < .05 Error 129 3.23e-5 The output of the regression analysis with an added interaction term (Z) for structural direction was the following equation: S r = 0.022 + (0.00034 − 0.00013 ⋅ Z ) ⋅ T − (0.0017 − 0.0003 ⋅ Z ) ⋅ M , R 2 = 0.73  (4.12)  where Z is null for tangential and unity for radial specimens, the equation is valid only for 0 ≤ M ≤ FSP . Individual equations for each structural direction are: S rT = 0.022 + 0.00034 ⋅ T − 0.0017 ⋅ M  (4.13)  S rR = 0.022 + 0.00021 ⋅ T − 0.0014 ⋅ M  (4.14)  0.06  o  40 C 60oC 80oC  Sr [1/min]  0.05 0.04 0.03 0.02 0.01 0 0  3  6  9  12  15  18  21  24  27  30  Moisture content [%] Fig. 40. The influence of moisture content and temperature over shrinkage rate for radial (dotted lines) and tangential (solid lines) specimens.  58  Slower rates determined for the radial specimens (Fig. 40) is an expected trend since permeability and moisture flow are higher in radial direction (Booker and Evans 1994, McCurdy and Keey 2002, Pang and Haslett 2002) which is the direction of drying for tangential cut specimens. It seems that an increase in temperature determined a proportional increase of the shrinkage rate for extrapolations to 0% moisture content: S rmax 40 S rmax 60 S rmax 80 ≅ ≅ =k 40 60 80  (4.15)  where S rmax t represents the maximum shrinkage rate attained for a particular temperature t =40, 60 or 80oC and k is the proportionality constant ( k = 1.33e − 4 for tangential and k = 1.26e − 4 for radial). This effect is similar with the influence of temperature over Mfsp; a higher percentage of water molecules are able to overcome desorption energy barrier. The difference between the three rates becomes higher for extrapolations to  S r = 0 . The presence of a higher number of water molecules enhances the effect of temperature over desorption rate.  2.2 Fiber saturation point The Mfsp was calculated using extrapolations of the volumetric shrinkage-moisture plots to zero shrinkage. The volumetric shrinkage was approximated from the linear shrinkages to which it is related (Greenhill 1940, Kelsey 1953): sV = sT + s R + s L −  sT s R 100  (4.16)  where sV and s L are the volumetric and longitudinal shrinkage, both in %. Since neglecting the longitudinal shrinkage does not induce appreciable errors (Greenhill 1940) the relationship may be simplified to: sV = sT + s R −  sT s R 100  (4.17)  59  or if the cross product may be neglected (Walker et al. 1993) sV = sT + s R  (4.18)  The experimental volumetric shrinkage (Fig. 41) was calculated for two temperatures 20 and 80ºC using equations (4.3), (4.5) and (4.17). The combined effect of both tangential and radial shrinkage values reduced the curvature produced by the tangential data. For a temperature of 20ºC a Mfsp of 27.7% was obtained. Temperature increase reduced the Mfsp value with 2.4%.  Volumetric shrinkage [%]  14 20oC 80oC USDA 1999 Stamm 1942  12 10 8 6 4 2 0 0  3  6  9  12  15  18  21  24  27  30  Moisture content [%] Fig. 41. Fitted and existing empirical models for volumetric shrinkage from Mfsp to 0% moisture content. Both empirical models were calculated for a temperature of 20ºC. 2.3 Moisture content Green wood subjected to constant temperature drying will change its moisture content at a rate directly proportional with the vapor pressure of the surrounding environment. Typical time-moisture curves for free radial specimens exposed at constant temperature (40oC) and variable relative humidity (76, 56 and 21%) are illustrated in Fig. 42. The initial moisture content is slightly different for each experiment due to the time lag required to reach the drying conditions.  60  210  76% RH 56% RH 21% RH Analytical fit  Moisture content [%]  180 150 120 90 60 30 0 0  500  1000  1500 2000 2500 3000 Time [min] Fig. 42. Experimental and curve fitted moisture for three different relative humidities (76, 56 and 21%) and the same temperature (40ºC). Plots of the dependent variable β (calculated with relation 3.8) versus temperature and moisture content (Fig. 43) showed that β does not appear to be influenced by both variables. The covariance analysis of the four structural variables (tangential, radial, mature and juvenile) showed that the interaction between moisture and structural direction is not significant at the 0.05 level (the source code is presented in A5 from Appendix A). The program was run again in the absence of the interaction term. The structural direction does have a small effect on β the probability values being very close to 0.05 level (Table 5). Table 5. Analysis of variance for the dependent variable β . Source DF Mean Square F Value Probability Moisture 1 0.10 7.85 < .05 Structural 3 0.037 2.87 0.04 A post hoc statistical test (Bonferroni multiple comparison test) indicated that two means were significantly different: radial and tangential juvenile. The results are shown in Table 6.  61  Table 6. Average values of β for each structural direction. Tangential Mature Juvenile  β  1.34a  *  1.38ab  Radial Mature  Juvenile  1.42b  1.40ab  *any two numbers not having the same subscript are significantly different.  2 1.8 1.6  Beta  1.4 1.2 1 0.8  Tangential Radial  0.6 0.4 0.2 0 0  3  6  9 12 15 Moisture content [%]  18  21  Fig. 43. The influence of the drying variables over the statistical coefficient β used to fit the dehydration process.  The weighted means used for further calculations are shown in Table 7; the tangential and radial mature groups were combined and analyzed again. All numerical α and β values are illustrated in Table B.4 (Appendix B). Table 7. Weighted average values of β . Juvenile Mature Tangential Radial Weighted mean 1.42 1.34 1.39 SD 0.019 0.021 0.014  β  62  The α , which characterizes the slope of the drying process appears to be influenced by both variables temperature and moisture content. This coefficient becomes 7 to 29 times higher when the environment conditions target 5% moisture content compared with 17%. The variability of the experimental data increases with the decrease of targeted moisture content. A similar coding and statistical analyses was used to analyze this variable (A6 from Appendix A). The analysis of variance is shown in Table 8. Table 8. Analysis of variance for α . Source DF Mean Square F-Value Probability Model 2 70.5 133.88 < .05 Error 126 0.53  The statistical assumptions, particularly equal variance of errors, could be met only by natural logarithm transformations of the dependent variable. The output of the regression analysis was a single equation, the binary variable and its interaction with temperature and moisture content did not pass the 0.05 significance level: ln α = a + b ⋅ M + c ⋅ T , I 2 = 0.71  (4.19)  where a, b and c are regression coefficients, a = −4.58, b = −0.205, c = −0.012 and I 2 is the squared correlation index which estimates the R 2 values for non-linear equations, F (2, 126) = 133.88, p < .05 . The structural effect over moisture loss was not significant probably because of the small thickness (less than double the tracheid length of hemlock) of the tested specimens. The analytical expression fitted for two temperatures (40 and 80ºC) and the experimental data are shown in Fig. 44. The decrease of α coefficient with temperature is an obvious and expected trend since smaller coefficients characterizes a faster drying process. Temperature increases the activity of the water molecules, raising the number of molecules able to overcome the bounding energy. Consequently, the desorption rate becomes proportional with that extra energy provided. 63  0  Moisture content [%] 6 9 12  3  15  18  21  0 Ln (Alpha in 1/min)  -2  Tangential Radial  40oC  -4 -6 -8 -10  o  80 C  -12 -14 Fig. 44. Temperature and moisture content influence over the statistical coefficient α used to fit the drying process. The study of shrinkage-moisture content interaction could provide one more valuable variable, namely, the moisture content associated with the starting point of the shrinkage process (MStart). The point was calculated as the intersection point between moisture curve and the beginning of the dehydration process. Data analysis revealed a wide variety of starting points from 26% to 125%; the temperature or the cutting pattern had no influence over the starting point (Figs. 46 and 47). The explanations for this early start could be the fact that the first millimeter of the surface, where the sensors were fixed, has dropped fast below Mfsp in the first hours earlier than the rest of the specimen creating a steep moisture gradient and presumably a small set. Other reasons might include stresses set by the hydrostatic tensile stress developed within fully saturated tissues (Kass 1965, Perré 2007) or the presence of meta-stable liquid water retained in less permeable tissues(Almeida and Hernandez 2006).  64  200  3.5  150  2.5  Shrinkage time  2  100  1.5 MStart  50  Strain [%]  Moisture content [%]  3  1 0.5  0 0  500  1000 1500 Time [min]  2000  0 2500  Fig. 45. Exemplification of M Start and shrinkage time calculations for a radial specimen targeting 10% moisture content. Further analyses focused on shrinkage-moisture plots aiming to eliminate the false shrinkage and determine shrinkage intersection point (SIP) and end of capillary water (ECW). SIP is defined as the intersection point between the extended linear portion of the moisture-shrinkage curve and zero shrinkage (Wilson 1932, Kelsey 1956) whereas ECW is the point where the linear portion starts and separates the coexistence of bound and free capillary water (Almeida et al. 2007).  65  150  40oC 60oC 80oC  MStart [%]  125 100 75 50 25 0 0  5 10 15 Equilibrium moisture content [%]  20  Fig. 46. M Start values for different temperatures (40, 60 and 80ºC).  150  Tangential Radial  MStart [%]  125 100 75 50 25 0 0  5 10 15 Equilibrium moisture content [%]  Fig. 47. M Start values separated for tangential and radial specimens.  66  20  Using shrinkage-moisture content plots three different types of transitions (dehydrations from initial to target moisture content) were identified for each group (Fig. 48): (I) – slow transition: the specimen started to shrink from high moisture contents and SIP and ECW could be clearly identified; (II) – intermediate transition: the specimen started to shrink from moisture contents close to the theoretical Mfsp; SIP and ECW could still be identified, the straight line of the plot usually continued until the end of the drying process; (III) – fast transition: the specimen started to shrink at Mfsp and no SIP or ECW could be identified using these techniques, the transition from free to bound water desorption is very fast and both points appear to coincide.  7  Shrinkage [%]  6 5 4  ECW SIP  I II  3 2  III  1 0 0  5  10  15  20  25 30 35 40 45 Moisture content [%]  50  55  60  65  Fig. 48. Shrinkage-moisture plots of specimens targeting 60ºC and 10%: fast (I), intermediate (II) and slow transition (III).  This behavior shows that the anatomical structure, especially the presence of less permeable tissues like ray cells (Almeida and Hernandez 2006), plays an important role  67  in bound-free water coexistence; a range of diffusion coefficients inside the sample might also result in a possible moisture gradient which explain the difference between type I and III transitions. One interesting aspect which was observed for type I and II transitions was that only specimens belonging to the group targeting either 17 or 11% moisture content followed it; Fig. 49 displays both SIP and ECW as cumulative values for different temperatures. The exact values of SIP and ECW are shown in Table 9.  50  Moisture content [%]  45 40 35 30  25  SIP ECW 23 21  25 20 15 10 5 0 40  60 Temperature [oC]  80  Fig. 49 Mean SIP and ECW values (± 1SD) for the specimens which followed a type I or II transition for different temperatures (40, 60 an 80ºC). Number over bar indicates sample size.  Table 9. Average M values of SIP and ECW Average M, % T, ºC No. SIP ECW Mean SD* Mean 40 21 27.60 4.43 24.26 60 23 31.20 6.87 27.41 80 25 41.07 7.30 35.54 * SD – standard deviation  68  .  SD 3.77 5.51 6.05  SIP values are considered to be moisture points above which wood properties are invariable (Kelsey 1956). At low temperatures these values approached the theoretical Mfsp and previous calculations measured for samples slowly dried at room temperature (Kelsey 1956) but for higher temperatures it escalates to 41%. Average values of 36% were also obtained by Almeida et al. 2007 but in this case the measurements were carried out on micro samples and at 30oC. Water potential tends to increase with temperature especially at 40-50% (Fortin 1979, Trembley et al. 1996) and this could determine an early start of the shrinkage process. It appears to be a direct consequence since the values are also related to wood hygroscopicity (Kelsey 1956). The results show the importance of temperature during a drying process. ECW points are 3.5 to 5.5% smaller than SIP values and follow a similar pattern. The results show that at high temperatures ECW, determined with this technique, attains large values and a clear distinction between free and capillary water could not be done. Every specimen targeting 5% and a third of the ones targeting 17 and 11% followed a type III transition. Again an increase in temperature created an earlier start of the shrinkage process. The results for the specimens targeting 5% are shown in Fig. 50.  60  16  50  Mstart [%]  40  14  15  30 20 10 0 40  60 o Temperature [ C]  80  Fig. 50. Mean M Start values (± 1SD) for the specimens which followed a type III and targeted 5% for different temperatures (40, 60 an 80ºC). Number over bar indicates sample size. 69  2.4 Restrained shrinkage 2.4.1 Shrinkage force The system designed for the “fully restrained” specimen could not totally restrain the specimen partly because of the reasons described in the “Materials and Methods” section and partly because there are different shrinkage coefficients along the sample together with a small moisture distribution. Nonetheless, even if all these mechanical and anatomical features allowed the “fully restrained” specimen to shrink, the drying was carried out while wood was subjected to a continuously increasing tensile force, labeled as shrinkage force in Figs. 51 to 54. An increase in temperature considerably reduced the shrinkage force in “fully restrained” specimens because the material could flow (relax) more easily (Figs. 51 and 52); this is in good agreement with polymer relaxation at higher temperatures. The attainment of maximum stress coincided with reaching the Memc; slow relaxations occurred after reaching the Memc when lower moisture contents were targeted (Fig. 51). The same trends were observed in restrained aspen (Populus tremuloides) by Kass (1965) or Scots pine (Pinus sylvestris) by Svenssson (1997).  120 o  40 C  Shrinkage force [N]  100 o  60 C  80 60  o  80 C  40 20 0 0  500  1000 1500 Time [min]  2000  2500  Fig. 51. Shrinkage force curves for tangential specimens targeting 17% moisture content at different temperatures (40, 60 and 80ºC).  70  140 o  40 C  Shrinkage force [N]  120 o  60 C  100  o  80  80 C  60 40 20 0 0  300  600  900 1200 Time [min]  1500  1800  Fig. 52. Shrinkage force curves for tangential specimens targeting 11% moisture content at different temperatures (40, 60 and 80ºC).  Eighty percent of “fully restrained” tangential and 15% of the “fully restrained” radial specimens targeting 5% moisture content broke in the first 10 hours of drying. This high number of failures, especially in tangential direction, emphasizes the importance of controlling the drying stresses especially during the early period. Usually, these stresses are relieved through a number of exterior checks which reduce the quality of the product. Typical failure behavior in the tangential direction is shown in Fig. 53. The radial specimens which did not break showed that a slight relaxation occurred after reaching Memc when lower M were targeted (Fig. 54). It is a direct consequence of the creep relaxation which tends to oppose the high stresses; the amount of relaxation is a combination of temperature and vapor pressure. Besides creep, an increase in temperature might also produce changes in wood components (Stamm 1956). No major changes were expected to occur for the range of tested temperatures, a small modification might occur for hemicelluloses at 80ºC (Goring 1963, Kollman and Fengel 1965, Sivonen et al. 2002) and a moderate influence for extractives (Charrier et al. 1995).  71  160 40oC  Shrinkage force [N]  140 120  60oC  o  80 C  100 80 60 40 20 0 0  100  200  300 Time [min]  400  500  600  Fig. 53. “Fully restrained” shrinkage force developed in tangential specimens targeting 5% moisture content at different temperatures (40, 60 and 80ºC).  210 o  40 C  Shrinkage force [N]  180 150  o  60 C  120 90  o  80 C  60 30 0 0  300  600 900 Time [min]  1200  1500  Fig. 54. “Fully restrained” shrinkage force developed in radial specimens targeting 5% moisture content at different temperatures 40, 60 and 80ºC. The magnitude and the faster shrinkage rate in tangential direction did not allow creep to hinder the development of stresses. The shrinkage force started to build slowly, then at a  72  higher non-linear rate, reached a peak and then decreased slowly. The failure was determined by the drying rate which was able to raise up to 2 N/min (Fig. 55). The moment of rupture was either early for high temperature drying processes or later for small temperature tests. The highest number of “survivors” in tangential direction was recorded for 60ºC which represented a compromise between the ways failure was reached.  2.5 40oC 60oC 80oC  dS/dt [N/min]  2 1.5 1 0.5 0 0  100  200  300 Time [min]  400  500  600  Fig. 55. Shrinkage force rate (dS/dt) in tangential specimens targeting 5% moisture content at different temperatures 40, 60 and 80ºC (same specimens from Fig. 53). The ultimate stress values for the different drying conditions and the two structural directions are shown in Fig. 56. Average ultimate stress values for the tangential and radial specimens at different temperatures are shown in Table 10. Failure occurred usually when the specimens attained relatively low moisture contents excepting some of the specimens dried at 60oC which failed at approximately 18%. The maximum stress reached in tangential specimens before breaking was between 1.9 MPa and 1.53 MPa which might be compared with static tensile strength of hemlock at 12% moisture content which is between 2.3 MPa and 1.6 MPa at 20ºC and 50ºC, respectively (USDA 1999). The comparison values were calculated as the average of radial and tangential observations. Since just three radial specimens failed, the results 73  from Table 10 have no statistical significance. Table 10. Ultimate stress values for tangential and radial specimens. Ultimate stress value [MPa] M**, % T, ºC Tangential/No/SD* Radial/No 40 1.9/5/0.23 3.9/1 7-10 60 1.73/8/0.3 4.68/1 7-18 80 1.53/9/0.24 4.74/1 5-10 * Average value /Number of specimens/Standard deviation ** Moisture content range attained before breaking  Ultimate stress [MPa]  5  Radial  40oC 60oC 80oC  4 3 2 1 0 0  1  2  3  4  5  6  7  8  9  10  11  12  13  Moisture content [%] Fig. 56. Ultimate stress values in tangential and radial direction at different temperatures (40, 60 and 80ºC).  For the other two targeted moisture contents, with a few exceptions, no failures were recorded. The results for tangential and radial specimens are illustrated in Figs. 57 and 58.  74  Maximum stress [MPa]  3.0  o  40 C o 60 C o 80 C  2.5 2.0 1.5 1.0 0.5 0.0 0  2  4  6  8 10 12 14 Moisture content [%]  16  18  20  Fig. 57. Maximum stress attained in “fully restricted” tangential specimens.  4.5  40oC 60oC 80oC  Maximum stress [MPa]  4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0  2  4  6  8  10  12  14  16  18  20  Moisture content [%] Fig. 58. Maximum stress attained in “fully restricted” radial specimens.  Predictions of these values, based on the several independent variables which influenced the drying process, are hard especially when total restrain could not be attained. It just 75  shows the magnitude of stress levels which might be reached during a highly restrained drying process. Totally restraining from shrinkage values will be obtained by studying the reduced shrinkage values (see next chapter). Obvious trends are higher stress levels with a decrease in temperature and moisture content. This is not surprisingly considering the effect of temperature over creep and mechano-sorptive behavior of wood (Davidson 1962; Kingston and Budgen 1972, Kitahara and Yukawa 1964). 2.4.2 Strain components The strain results for all three restraining cases in radial and tangential direction at 40ºC targeting 17% moisture content are shown in Figs. 59 and 60. Interestingly, all restrained specimens swelled between 0.17% restrained shrinkage when restrained by 30 N, to 0.4% when restrained by 77 N. The slow relaxation close to the surface, where the transducers were fixed, is a result of the restraining level and temperature whereby the higher the temperature and the restraining level, the higher the relaxation. The main reason for this swelling is the fact that the transducers were fixed in the middle region of the specimen and unless the shrinkage would start simultaneously in the whole body, a non realistic phenomenon, the middle part ends up in tension. Specific experiments with two sets of transducers fixed close to the end parts of the specimen revealed a significant time delay in shrinkage with respect to the position where these transducers were fixed. In radial direction these phenomenon seems to be correlated with the size of the annual rings: large annual rings start to contract faster than the narrow ones, but the final contraction value is indirectly proportional to size. Less shrinkage in wider annual rings was also obtained for Douglas-fir by Wu (1993). Temperature appears to have no influence over this phenomenon. In the tangential direction, the early wood – latewood distribution along the length influences shrinkage initiation and maximum value. Swelling continued until the shrinkage force in the middle region of the sample became higher than the tensile force exerted by the ends and the wood started to lift the weight. The positive tensile force value, indicated by the load cell readings during the swelling process, confirms this hypothesis.  76  5  Free  Shrinkage strain [%]  4  30N  3  60N  2  96N  1 0 0  500  1000  1500  2000  2500  3000  3500  -1 Time [min] Fig. 59. Restrained and free shrinkage strain for tangential specimens targeting 17% moisture content at 40ºC.  4  Free 30N  Shrinkage [%]  3  2  60N  1 114N 0 0 -1  500  1000  1500  2000  2500  3000  Time [min]  Fig. 60. Restrained and free shrinkage strain for radial specimens targeting 17% moisture content at 40ºC.  77  The small swelling experienced by the middle part of the sample was considered to be an elastic deformation which was totally recovered during the shrinkage process. Fig. 61 illustrates how the restraint force is related to the final restrained shrinkage strain for radial and tangential structural directions. Usually a linear trend between the restraining level and final shrinkage was obtained, even though in two of the cases the specimens had to lift a dead weight and in one case the force was continuously applied by the restraining system.  Restraining shrinkage force [N]  120 Radial Tangential  100 80 60 40 20 0 0.0  1.0  2.0  3.0  4.0  5.0  Shrinkage [%] Fig. 61. Relationship between the external force and the total strain for different restraining levels targeting 17% moisture content at 40ºC.  An example of strain components for different restraining levels in tangential specimens targeting 17% moisture content at 40ºC is given in Fig. 62. The first column from the left represents the maximum amount of shrinkage that could be attained during a particular experiment (100%) – it was recorded on the free specimen and since the specimens were matched to have the same wood structure, it represents the control value. The other three columns contain information about instantaneously released strain (elastic) delayed viscoelastic and mechano-sorptive strain (released) and set value (plastic). The percentages were calculated using relations (3.10) to (3.14). All the numerical values for radial and tangential specimens are illustrated in Tables B.5 and B.6 (Appendix B). Each 78  component will be separately analyzed and discussed in the following paragraphs.  100% Plastic Released  75%  Elastic Shrinkage  50%  25%  0% UnRestr'  Restr'30N  Restr'60N  Restr'96N  Fig. 62. Distribution of the strain components due to different restrained levels for tangential specimens targeting 17% moisture content at 40ºC – same specimen from Fig. 60.  The “shrinkage” component of the restrained specimens from Fig. 62 provides information about wood drying under either a continuously growing or a constant tensile stress. This situation is unlikely to occur since, as it has already been proven by numerous researches in this domain, the tensile stresses are slowly vanishing reaching null value at one point of the drying process. Of course inside a stack there are always pieces of lumber/timber which either start at a very high moisture content or have reduced permeability or diffusion coefficients and might end up in this particular stage at the end of the day. These pieces are called “wets” and they may be numerous in new drying strategies when high moisture contents are targeted aiming to avoid a high number of oven-dried pieces. The re-drying is done usually by unconventional drying. The amount of deformation that could not be recovered is represented by the “plastic” component. The situation is similar with a spring subjected to tensile forces for a long period of time which absorbed some of the deformation energy. The “Shrinkage” component from Fig. 61 calculated as a percentage from the free shrinkage value was symbolized with STI or R 79  according to the structural direction. It is a function of stress value ( σ ), moisture (M) and temperature (T). Common transformations of these variables were dropped “step-wisely” (see program A7 from Appendix A); the binary variable (Z), used to test density effect over the analytical fit, was significant only for the radial direction: STI = 130.42 − 33.44 ⋅ σ T − 0.1 ⋅ M 2 − 0.5 ⋅ T , R 2 = 0.71  (4.20)  S RI = 129.41 − (23.82 + 23.44 ⋅ Z ) ⋅ σ T − (1.39 + 1.69 ⋅ Z ) ⋅ M − 0.69 ⋅ T , R 2 = 0.67  (4.21)  both equations are valid only for 0 ≤ M ≤ FSP . Individual equations for radial direction are: I = 129.41 − 47.26 ⋅ σ T − 3.08 ⋅ M − 0.69 ⋅ T S RMt  (4.22)  I S RJv = 129.41 − 23.82 ⋅ σ T − 1.39 ⋅ M − 0.69 ⋅ T  (4.23)  The analysis of variance is shown in Table 11. Table 11. Analysis of variance for the “Shrinkage” component. Source DF Mean Square F Value Probability Tangential Model 3 11868 91.93 < .05 Error 112 129.09 Radial Model 4 14997 55.22 < .05 Error 194 271.59  STI or R can take values from 100% to 0% (total restrain). Equations 4.20 to 4.23 can provide the maximum stress that could be attained by totally restrained specimens ( STI or R ), unable to be attained by the experimental design. As an example, it can be calculated that for tangential specimens in the 40ºC series the maximum stress drops from 3.23 MPa to 2.44 MPa, at 60ºC from 2.93 to 2.14 MPa and at 80ºC from 2.63 MPa to 1.84 MPa in the 5%-17% moisture range. These values are exceeding by far the maximum stress values of the tangential specimens which survived during a 5% moisture target tests. Recorded numerical values were between 2.74 MPa and 1.9 MPa for 40 and  80  80ºC, respectively. These values correspond to approximately ST ,R ≈ 20% any value below this number could result in several checks and/or severe warping. Hemlock is a species prone to severe checking and the conditioning step, necessary to relieve the transversal stresses during early drying, is a must (Kozlik 1981, Kozlik and Ward 1981, Avramidis and Oliveira 1993, Bradic and Avramidis 2007, Rohrbach 2008). Final stages of softwoods drying also require higher relative humidity for the same reasons (Simpson 1991). One would expect that instantaneous elastic and recovered strain increases with stress as in a regular strength or creep test. As illustrated in Fig. 63, the instantaneously released and recovered strain shows an increase with the increase of stress for high moisture contents but at lower targeted moisture content both components are not even correlated with stress (Fig. 64). The large and continuous changes in moisture content during the test had a major influence over both components. The specimens accommodated at a variable rate with the imposed load very slow at the beginning and at a faster rate as the drying continued. Some of the force was absorbed and stored as elastic and time recoverable energy but some of it was counteracted by the shrinkage process and material flow especially at higher temperatures. Moisture contents higher than 20% have little or no influence over the elastic modulus (Bodig and Jayne 1982) and this feature together with longer drying times allowed the specimen targeting 17% to have a better rheological response. Lower moisture content targets, proved to be critical in understanding wood moisture-property relationships in clear wood (Green et al. 1990), may result in complex elastic derivations due to the progressive increase of the modulus of elasticity. Under this conditions less rheological response is expected (Kass 1965). Since the results follow a trend only for high moisture contents, no correlation between elastic and recoverable components and drying variables was attempted to be established.  81  1.6  o  40 C 60oC o 80 C  1.4  Stress [MPa]  1.2 1.0 0.8 0.6 0.4 0.2 0.0 0  5  10 15 Elastic strain [%]  20  25  1.6  o  40 C 60oC o 80 C  1.4  Stress [MPa]  1.2 1.0 0.8 0.6 0.4 0.2 0.0 0  5  10 15 20 Recoverable strain [%]  25  30  Fig. 63. Elastic (upper) and recoverable components for tangential specimens targeting 17% at different temperatures (40, 60 and 80ºC).  82  3.0 o  40 C o 60 C 80oC  Stress [MPa]  2.5 2.0 1.5 1.0 0.5 0.0 0  2  4 6 Elastic strain [%]  8  10  3.0 o  40 C o 60 C o 80 C  Stress [MPa]  2.5 2.0 1.5 1.0 0.5 0.0 0  2  4 6 Recoverable strain [%]  8  10  Fig. 64. Elastic (upper) and recoverable components for tangential specimens targeting 5% at different temperatures (40, 60 and 80ºC).  With both elastic and recoverable components unusable for lower moisture contents the research focused on the combined action of the two components in absolute values. The results show a strong correlation between shrinkage value and moisture content for all 83  restraining levels and moisture contents (Fig. 65). Numerical radial and tangential absolute values recorded after recovering the elastic and visco-elastic components values are shown in Table B.7 and B.8 (Appendix B).  9 Free 30N 60N  8  Shrinkage [%]  7 6 5 4 3 2 1 0 0  3  6  9  12  15  18  21  24  27  30  Moisture content [%]  6 Free 30N 60N  Shrinkage [%]  5 4 3 2 1 0 0  3  6  9  12  15  18  21  24  27  30  Moisture content [%] Fig. 65. Final strain results for all the experiments preformed in tangential (upper graph) and radial direction.  84  Higher drying temperatures combined with higher stresses caused larger plastic deformations mainly because of the increased room and mobility in polymers from the amorphous regions and correlated with a decrease in relaxation time (reduced drying time). The results for 60 N restrain in tangential and radial directions are shown in Fig. 66.  7  Shrinkage [%]  6  40oC 60oC 80oC  5 4 3 2 1 0 0  3  6  9  12  15  18  21  24  27  30  Moisture content [%] 4 o  40 C 60oC o 80 C  Shrinkage [%]  3  2  1  0 0  3  6  9  12  15  18  21  24  27  30  Moisture content [%] Fig. 66. Temperature influence over final strain results for the tangential (upper graph) and radial specimens restrained by 60N.  85  A similar technique with the one used for free shrinkage value was used in this case too. This final shrinkage value was symbolized by STIIor R and is a function of stress value ( σ ), moisture (M) and temperature (T). Common transformations of these variables were dropped “step-wise” (A7 from Appendix A); the binary variable (Z), used to test density effect over the analytical fit, was significant only for the radial direction: STII = 8.32 − 0.01 ⋅ M 2 − 0.023 ⋅ T − 1.42 ⋅ σ , R 2 = 0.83  (4.24)  S RII = 5.96 − 0.16 ⋅ M − 0.023 ⋅ T − (0.65 + 0.58 ⋅ Z ) ⋅ σ + 0.41 ⋅ Z , R 2 = 0.85  (4.25)  both equations are valid only for 0 ≤ M ≤ FSP . Individual equations for radial direction are: II S RMt = 5.96 − 0.16 ⋅ M − 0.023 ⋅ T − 1.23 ⋅ σ + 0.41  (4.26)  II S RJv = 5.96 − 0.16 ⋅ M − 0.023 ⋅ T − 0.65 ⋅ σ  (4.27)  The analysis of variance is shown in Table 12. Table 12. Analysis of variance for the final shrinkage value. Source DF Mean Square F-Value Probability Tangential Model 3 159.07 385.62 < .05 Error 243 0.41 Radial Model 5 53.57 299.81 < .05 Error 270 0.18  The maximum shrinkage value, which could be attained in tangential and radial specimens, decreases proportionally with the square or linear value of moisture content, temperature and stress value. The high values of the regression coefficients show how interconnected these variables are. Equations (4.24) to (4.27) are intended to be used to predict stress values based on reduced shrinkage values measured on full size specimens. If the stress factor becomes null, these equations become equivalent with equations (4.1) to (4.6) used to predict free shrinkage values. For instance by replacing  86  σ = 0, M = 0, T = 40 in equations (4.24) and (4.26) it results in a free shrinkage value of 7.37% for tangential and 5.45% for radial comparable with 7.4% and 5.66% calculated with equations (4.3) and (4.5).  3. Drying strains in full-size specimens 3.1 Strain and moisture profiles Typical time-shrinkage curves for flat and quarter-sawn full size specimens exposed at different temperatures (40, 60 and 80ºC) and a relative humidity corresponding to 5% moisture content (21, 25 and 30%) are illustrated in Figs. 67 and 68. The curves were plotted for matched specimens; the average value of the sensors located along one structural direction is plotted.  7  o  40 C o 60 C o 80 C  Shrinkage starin [%]  6 5 4 3 2 1 0 0  100  200 300 Time [min]  400  500  Fig. 67. Shrinkage strain plots along the tangential direction for flat-sawn full size specimens down to 11% moisture content at different temperatures (40, 60 and 80ºC).  The full-size specimens started to shrink from the very moment they were exposed to the drying condition even if the average moisture content was over 100% and they were kept in cold water to delay for a short time the formation of dry shell. A high amount of surface water was rapidly removed from the surface and the dry shell developed. The 87  phenomenon has been intensively studied using different techniques (Tremblay et al. 2000, Wiberg et al. 2000, Rosenkilde 2002, Salin 2008). Specific measurements showed that the first layer of fibers has a more open structure than the rest due to the anatomic elements present here. CT-scanning measurements revealed that no more than 9 min are necessary for this layer to reach a flat moisture profile provided by the environment (Rosenkilde and Glover 2002). Consequently the shrinkage of the shell started very early and, as it will be shown below, at a high rate.  40oC 60oC 80oC  3  Shrinkage starin [%]  2.5 2 1.5 1 0.5 0 0  100  200 300 Time [min]  400  500  Fig. 68 Shrinkage strain plots along the radial direction for quarter-sawn full size specimens down to 11% moisture content at different temperatures (40, 60 and 80oC).  Shrinkage appears to be influenced by temperature, higher values being associated with higher temperatures. Similar results were obtained by Espenas (1971) who with experiments made on three softwood species showed that hemlock is more prone to this effect. Direct and uniform relationships between temperature and shrinkage values were also obtained by McMillen (1958) on his red oak experiments. All shrinkage values for specimens having the annual rings oriented at 45º were between the values obtained for tangential and radial directions in a flat-sawn specimen (Fig. 69).  88  6 Tg  5  Strain [%]  4  45  o  3 Rd  2 1 0 0  30  60  90 120 Time [hrs]  150  180  210  Fig. 69 Comparison between shrinkage values for specimens having the annual rings oriented at 45º and a flat-sawn specimen while drying at 80ºC.  As it was described in section III the moisture content was measured directly using insulated pin electrodes positioned at different depths and indirectly by weighting a matched specimen at different periods of time. The difference between the two measurement systems is shown in Fig. 70. The results show that there is an error: false readings are obtained for high moisture contents – the system was supposed to provide accurate measurements for moisture contents lower than 100% and no readings for higher moisture contents. Overall, starting with 50% the difference between the readings using both methods is becoming insignificant and shell –core readings could be assessed. Individual readings for each sensor during a dehydration process at 80ºC are shown in Fig. 71. Little difference was recorded between adjacent shell or core sensors.  89  180  Moisture content [%]  160  Lignomat Control  140 120 100 80 60 40 20  o  0 0  100  o  60 C  o  80 C 200  300 Time [min]  40 C 400  500  600  Fig. 70. Difference between average moisture measurements recorded with resistance pins (Lignomat) and oven-dry method (Control) for different temperatures (40, 60 and 80ºC).  90  Moisture content [%]  80 70 60 50  Core  40 Shell  30 20 10 0 0  15  30  45  60 75 90 Time [hrs]  105  120  135  150  Fig. 71. Sample of individual moisture readings for each resistive pin while targeting 5% at 80ºC.  90  Up to a point, shell moisture loss pattern is similar with the one from small specimens: a lot of moisture is dropped very fast at a constant rate at the beginning of the drying process – this period is commonly called constant rate period (CRP). The process starts to slows down at ~20% when the first falling rate period (1FRP) is supposed to occur (Treybal 1980); during this period the diffusion is combined with bulk fluid flow from the core. As the drying process advances the core start to lose massively moisture content and when it reaches 30% the second falling rate period (2FRP) occurs; during this period the diffusion controls the drying process. The beginning of the 2FRP also triggers the shrinkage process in the entire body of the specimen.  3.2 Key moisture contents during the drying process Since the experiments on small specimens characterize wood drying under tensile stresses only CRP and 1FRP will be analyzed. Several key points could be identified during shell shrinkage process using the theoretical knowledge about the process (Fig. 72). The following trends are expected to occur: •  from 0 to I: the continuously increased stress determines a decreased shrinkage rate; at the beginning of the interval high shrinkage rate values are expected since there is little or no restraint, point I has the lowest shrinkage rate;  •  from I to II: the stress is decreasing gradually and an increased shrinkage rate is expected; the core is still at moisture contents below Mfsp until it reaches point II;  •  from II to III: the shell is under compressive stress and the shrinkage rate is accelerated by core shrinkage reaching a peak point in III;  •  from III to IV: the compressive stress started to diminish and a slower shrinkage rate is expected to occur;  91  II  III  IV  Stress  Tension  I  Compression  Time  Fig. 72. Key points during shell shrinkage process.  Sample flat-sawn and quarter-sawn shrinkage rates for tangential and radial directions are displayed in Fig. 73 and 74. Without exception the tangential rates from flat-sawn specimens followed the predicted trend from Fig. 72 while the radial rates did not exhibit any significant changes. Quarter-sawn or specimens having the annual rings oriented at 45º did not show any particular trend either. It is a direct proof that the restraining forces are too small in radial direction and the shrinkage pattern is controlled by the tangential shrinkage.  92  III  I  0.035  Tg Rd  Shrinkage rate [%/hr]  0.03 0.025 0.02 0.015 0.01 0.005 0 0  50  100 150 200 250 300 350 400 450 500 Time [hrs]  Fig. 73. Shrinkage rates in tangential and radial direction of a flat-sawn timber targeting 5% at 40ºC.  0.06 Tg Rd  Shrinkage rate [%/hr]  0.05 0.04 0.03 0.02 0.01 0 0  50  100 150 200 250 300 350 400 450 500 Time [hrs]  Fig. 74. Shrinkage rates in tangential and radial direction of a quarter-sawn timber targeting 5% at 40ºC.  93  The beginning of the shrinkage process shows some up and down periods which are suggesting an alternating restraining-relaxing process. Micro-cracks, which are forming and developing during this period, are probably responsible for this variation. Two points could be clearly identified in every tangential rate plot of flat-sawn timbers: the lowest rate point which corresponds to point I and the highest rate point which corresponds to the moment when the stresses are completely reversed (III). The second point could be identified by extrapolation – it was considered to be the point when the core started to shrink. The Mfsp corresponding to that temperature was identified from Fig. 40. Time values were correlated with moisture contents. A summary of the results is shown in Table 13. Table 13. Moisture range for each point of interest (I, II and III) for different temperatures (40, 60 and 80ºC). M in point I, % M in point II, % M in point III, % T, C 40 60 80 40 60 80 40 60 80 Shell 19-24 13-16 17-19 21-16 10-14 15-16 13-16 9-11 13-14 Core 32-56 56-58 53-56 27 26.2 25.4 16-21 16-17 20-21 Average 27-38 35-37 35-37 21-22 18-19 19-20 15-17 13-14 16.5-17  The results show that the tensile stresses in shell persist quite a long time. Stress reversal values were between 21 and 22% for 40ºC and between 18 and 20% for 60 and 80ºC. Low stress reversal values are considered to be dangerous due to time considerations. Slightly smaller stress reversal moisture contents were obtained for higher temperatures probably because the process was more intense, the diffusion coefficients increasing exponentially with temperature (Stamm and Loughborough 1942). The results are comparable with the ones obtained by McMillen (1958) whose stress reversal values for ponderosa pine, white fir, and Engelmann spruce were around 18%. Other researches situated stress reversal value for Douglas-fir either between 15–17% (Resch et. al 1989) or 19–21%. (Wu 1993). The information is particularly valuable because after this moisture content the drying schedule may become harsher.  94  3.3 Tensile stress calculations Tensile stress values were calculated with relations 4.24 to 4.27. The calculations were done for point II shell moisture intervals (Table 13) for both flat and quarter-sawn specimens (Table 14). Table 14. Shell stress range results based on set values developed during the tensile period in flat and quarter-sawn specimens. Flat-sawn Quarter-sawn T, C Tangential Radial Tangential Radial 40 1.91 – 2.06 0.62 – 0.90 0.78 – 0.83 1.21 – 1.57 60 2.42 – 2.81 0.72 – 1.24 0.90 – 1.02 0.82 – 1.04 80 0.60 – 1.20 0.17 – 0.38 0.08 – 0.54 0.21 – 0.77  As one may notice from Table 14, the stresses are approaching the failure level for tangential direction in flat-sawn specimens dried at 60oC. The temperature is particularly important because it was reported to be the lower limit of the glass transition temperature interval for lignin and hemicelluloses (Irvine 1984, Kelley et. al 1987, Nakano 2006). Other researchers situate the value of hemicelluloses and lignin leaching at values between 70 and 74ºC (Goring 1963, Salmen 1984). Temperature increase over this value triggers the visco-elastic creep which acts as a stress reliever (Rémond and Perré 2008). That the stress values obtained for 40ºC are smaller than the ones for 60ºC is easy to understand. The diffusion rate is obviously higher at 60 compared to 40ºC so the drying occurred faster but a temperature of 60ºC was not sufficient to increase the relative mobility of wood components and hence reduce the drying stresses. High reductions in stress level were obtained for 80ºC which appears to be the right temperature for this drying step. The use of higher temperatures tends to minimize the tension set even more but the danger of excessive compression set has to be taken into account (McMillen 1958). The stresses in radial direction in flat-sawn specimens are reduced to a magnitude order of 3. The water is eliminated along the radial direction at a faster rate partly because of the anatomical features (increased permeability) and partly because a larger surface is  95  exposed to the drying environment (McCurdy and Keey 2002, Pang and Haslett 2002). This feature determines a slower drying rate along the tangential direction and consequently lowers the restraining forces. Overall the tangential stresses in quarter-sawn specimens are reduced to half compared to flat-sawn specimens. Interestingly, the stresses along the radial direction in quarter-sawn specimens are slightly higher than the ones in tangential direction. The effect appears to be a consequence of the decreased size along the tangential direction. Similar results were found by Stohr (1988) who found a positive correlation between section width and shrinkage value. The results are less significant with an increase in temperature.  96  V. CONCLUSIONS This investigation aimed to study the relationship between shrinkage, moisture content and the tensile stress developed at the beginning of the drying process of hemlock. Stress values were calculated based on the restrained shrinkage values simulated on small specimens. The following conclusions could be drawn from this research: 1. The shrinkage strain in small specimens follows a non-linear pattern with the moisture loss being the driving force. The shrinkage is correlated with the square value of moisture content for tangential specimens in all simulations while linear moisture values may be used to describe the behavior in radial direction. 2. The comparison between previous shrinkage models and this study showed that early and later stages of the curves are very close while intermediate values showed a difference of up to 1.5%. The difference is a direct consequence of the way shrinkage data was gathered: the measurements were done inside a specimen which had a ratio between the tangential/radial dimensions of 1:28 or 28:1. The other theoretical models were built based on measurements made on small blocks with a tangential/radial ratio of 1:1. 3. Extrapolations of shrinkage rate parameter to 0% moisture content indicate a proportional increase with temperature. Fiber saturation point determined from extrapolations of shrinkage moisture curve to null shrinkage value was 27.7% for a reference temperature of 20ºC. 4. Three different types of shrinkage-moisture transitions could be identified. Shrinkage intersection points and end of capillary water values are increasing with temperature. The distinction between the two could not be made all the time. 5. The shrinkage force started to build slowly, then at a higher non-linear rate, reached a peak and then decreased slowly. The experiments indicated that tangential green hemlock usually cannot be dried to 5% moisture content under high restraints without failure. The failure was determined by the drying rate which was able to raise up to 2 N/min. The moment of rupture was either early for high temperature drying processes or later for small temperature tests. The highest number of “survivors” in tangential direction was 97  recorded for 60ºC which represented a compromise between the ways failure was reached. 6. The magnitude and the faster shrinkage rate in tangential direction did not allow creep to hinder the development of stresses. The shrinkage force started to build slowly, then at a higher non-linear rate, reached a peak and then decreased slowly. 7. Individual instantaneous elastic and recovered strain increased with the increase of stress for high moisture contents but at lower targeted moisture content both components could not be correlated with drying stresses. 8. Shrinkage value obtained after the tensile stress was released and all the visco-elastic strain was recovered is a function of stress value, moisture (or squared moisture for tangential) and temperature. This multiple regression correlation yielded high R values under conditions of independence, normality and equal variance. 9. Several key moisture-strain values could be identified by studying the drying rate along tangential direction in flat-sawn specimens and using the theoretical knowledge about the process. The lowest rate was associated with peak tensile stress values while the highest one might be considered to be the moment when the compression is at a maximum. The radial rates or other directions in quarter-sawn or specimens having the annual rings oriented at 45º did not show any particular trend. 10. High stress values were obtained for specimens dried at 60ºC and a low relative humidity while a high reduction in stress level could be obtained for 80ºC. The findings might help to test at laboratory scale the tensile stresses generated during several drying schedules and build models based on strain values.  98  VI. FUTURE RESEARCH This investigation was focused on tensile stresses developed during early stages of the drying process. The results proved that a temperature as high as 80ºC combined with a low relative humidity could reduce the tensile stresses generated in the early stages of the drying process. The experimental work should be extended to include tests at higher temperatures and in closer to industrial drying circumstances, namely, under different air velocities and variable drying conditions. In the current project air circulation was minimal inside the conditioning chamber used to generate the drying conditions (temperature and relative humidity) which in turn were kept constant throughout each experiment. An experimental apparatus has to be designed and constructed in order to provide these real drying conditions. Although the tensile stresses persist long into the drying cycle of softwoods the compression stress is another important component which can be modeled in a similar way. Other interesting variables that can be included in the experimental design are different cross section dimensions. Probably few of the softwood species would exhibit a different shrinkage behavior than hemlock and therefore similar patterns are expected to occur, however replicated tests on a dissimilar material like Western red-cedar or even hardwoods might provide valuable knowledge.  99  REFERENCES Abe K. and Yamamoto H. 2006. Behavior of the cellulose microfibril in shrinking woods. J. Wood Sci. 52:15-19. Ahlgren, P.A., Wood, J.R. and Goring, D.A.I. 1972. The fiber saturation point of various morphological subdivisions of Douglas-fir and aspen wood. Wood Sci. Technol. 6(2):8184. Alfthan, J. 2000. Micro-mechanically based modeling of mechano-sorptive creep in paper. Ph.D. thesis KTH Solid Mechanics Royal Institute of Technology, Sweden, 20p. Almeida G., Assor C. and Perré, P. 2007. The dynamic of shrinkage/moisture content behavior determined during the drying of micro-samples. In Proceedings of the 10th IUFRO International Wood Drying Conference, Orono, Maine, USA, August 26-30, 2007: 16-22. Almeida, G and Hernandez, R. 2006. Changes in physical properties of tropical and temperate hardwoods below and above the fiber saturation point. Wood. Sci. Technol. 40(7): 599-613. Archer, R.R. and Amherst M.A. 1987. On the origin of growth stresses in trees Part 1: Micro mechanics of the developing cambial cell wall. Wood Sci. Technol. 21(2):139-154. Avramidis, S. and Oliveira L. 1993. Influence of presteaming on kiln drying of thick Pacific coast hemlock. Forest Prod. J. 43(11):7-12. Babiak, M. and Kudela, J. 1995. A contribution to the definition of the fiber saturation point. Wood Sci. Technol. 29(3):217-226. Barkas, W.W. 1941. Wood-water relationships.VI. The influence of ray cells on shrinkage of wood. Trans. Faraday Soc. 37:535-541. Bazant, Z. P. 1985. Constitutive equation of wood at variable humidity and temperature Wood Sci. Technol. 19(3):159-177. Beiser, W. 1933. Mikrophotographische Quellungsuntersuchungen Fichten- und Buchenholz an Mikrotomschnitten im durchfallenden Licht und an Holzklötzchen im auffallenden Licht. Kolloid Z. 65: 203–211. Berberovic, A. 2007. Numerical simulation of wood drying. MSc. thesis, Oregon State University, Corvallis, Oregon. 143p. Bodig, J. and Jayne, B.A. 1982. Mechanics of wood and wood composites. Van Nostrand Reinhold Publishing. Canada. 712p. Booker, R.E. and Evans, J.M. 1994. The effect of drying schedule on the radial permeability of Pinus radiate. Holz als Roh- und Werkstoff 52(1): 150-156. 100  Bradic S. and Avramidis S. 2007. Impact of juvenile wood on hemlock timber drying characteristics. Forest Prod. J. 57 (1/2): 53-59. Carrington, A.M. 1996. High-temperature seasoning of softwood boards: determination of mechanical properties at elevated temperatures. M.E. Thesis, Department of Chemical and Process Engineering, University of Canterbury, New Zealand. Charrier, B. Haluk, J.P. and Metche, M. 1995. Characterization of European oakwood constituents acting in the brown discoloration during kiln drying. Holzforschung 49(2): 168-172. Cockrell R. A. and Howard, R. A. 1968. Specific Gravity and Shrinkage of Open Grown Ponderosa Pine. Wood Sci. Technol. 2(4): 292-298. Comstock, G.L. 1965. Shrinkage of coast-type Douglas-fir and old-growth redwood boards. Research Paper FPL 30. Madison, WI: U.S. Forest Service, Forest Products Laboratory. Crank, J. 1975. The mathematics of diffusion. Oxford University Press. Dahlblom, O., Petersson, H and Omarsson, S. 2001. Full 3-D FEM-simulations of drying distortions in spruce boards based on experimental studies. In: Proceedings of the 7th international IUFRO wood drying conference. Tsukuba, Japan: 246-251. Davidson, R.W. 1962. The influence of temperature on creep in wood. Forest Prod. J. 12(8):377-381. Dinwoodie, J.M., Pierce, C.B. and Paxton, B.H. 1984. Creep in chipboard (Par IV) Wood Sci. Technol. 18(3):377-381. Dumail J.F. and Castera P. 1997. Transverse shrinkage in juvenile wood. Wood Sci. Technol 31(4):251-264. Ellwood E. L. 1953. Properties of Beech in Tension Perpendicular to the Grain and Their Relation to Drying. Forest Prod. J. 3(5):202-209. Ellwood E. L. and Wilcox W. W. 1962. The Shrinkage of Cell Walls and Cell Cavities in Wood Microsections, Forest Prod. J. 12 (5):235-242. El-Osta, M.L.M., Wellwood, R.W., Butters, R.G. 1972. An improved X-ray technique for measuring microfibril angle of coniferous wood. Wood Sci. 5(2): 113-117. Espenas, L.D. 1971. Shrinkage of Douglas-Fir, Western Hemlock, and Red Alder as Affected by Drying Conditions. Forest Prod. J. 21(6): 44-46. Fabris, S. 2000. Influence of cambial ageing, initial spacing, stem taper and growth rate on the wood quality of three costal conifers. Ph.D. thesis, University of British Columbia, Vancouver, BC, Canada.  101  Feist, W.C. and H. Tarlow. 1967. A new procedure for measuring fiber saturation points. Forest Prod. J. 17(10):65-68. Forrer, J.B. and Vermass, H.F. 1987. Development of an improved moisture meter for wood. Forest Prod. J. 37(2):67-71. Fortin, Y. 1979. Moisture content-water potential relationship and water flow properties of wood at high moisture contents. Ph.D. thesis, The University of British Columbia, Vancouver, 187p. Genevaux, J.M. and Guitard, D. 1988. Anisotropie du comportement diffère; essai de fluage a température croissante d’un bois de peuplier. Colloque Mechanical behaviour of Wood, Bordeaux, France. Gerhards, C.C. 1982. Effect of moisture content and temperature on the mechanical properties of wood: an analysis of immediate effects. Wood Fiber Sci. 14(1):4–36. Goring, D.A. 1963. Thermal softening oflignin, hemicellulose and cellulose. Pulp and Paper Mag. 64(12): 517-527. Green D.W. and Evans J.W. 2008. The immediate effect of temperature on the modulus of elasticity of green and dry lumber. Wood Fiber Sci. 40(3):374-384. Green D.W., Evans J.W. and Kretsch-Mann D.E. 1990. Moisture content and tensile strength of Douglas fir dimension lumber. Res. Pap. FPL-RP-497. USDA Forest Serv., Forest Prod. Lab., Madison, WI. Green, D.W. 1989. Moisture content and shrinkage of lumber. Res. Pap. FPL-RP-489. Madison, WI: US Department of Agriculture, Forest Service, Forest Products Laboratory, 11p. Greenhill, W.L. 1938. Collapse and its removal: Some recent investigations with Eucalyptus regnans C.S.I.R. Pamphlet No. 75, Melbourne, Australia. Greenhill, W.L. 1940. The Shrinkage of Australian timbers: Part II. C.S.I.R. Australia. Melbourne. Pamphlet No. 97. Guitard, D. 1987. Mecanique du materiau bois et composites. Edited by CEPADUES, Toulouse, France, 238 p. Hanhijarvi A. 1997. Perpendicular-to-grain creep of Finnish softwoods in high temperature drying conditions. Experiments and modeling in temperature range 95125˚C. Technical Research Centre of Finland, VTT Publications 301. Hanhijarvi, A. and Hunt, D. 1998. Experimental indication of interaction between viscoelastic and mechano-sorptive. Wood Sci. Technol 32(1):57-70.  102  Haque, M.N., Langrish, T.A.G., Keep, L.B. and Keey, R.B. 2000. Model fitting for viscoelastic creep of Pinus radiata during kiln drying. Wood Sci. Technol. 34(5):447-457. Hearmon, R.F.S. and Paton, J M. 1964. Moisture Content Changes and Creep of Wood Forest Prod. J. 14(8):357-359. Hernández, R. E. and M. Bizon. 1994. Changes in shrinkage and tangential compression strength of sugar maple below and above the fiber saturation point. Wood Fiber Sci. 26(3):360-369. Hunt, D. 1999. A unified approach of creep in wood. Proc. R. Soc. Lond. A. 455: 40774095. Hunt, D. and Gril, J. 1997. Creep in wood and cell-wall properties. In COST E9 International Conference on Wood-Water Relations, Copenhagen, Denmark: 195-308. Jessome, A.P. 1977. Strength and related properties of woods grown in Canada. Eastern Forest Product Lab, Ottawa, Ontario, Technical Report 21. Jozsa, L.A. and Middleton, G.R. 1994. A discussion on wood quality attributes and their practical implications, Forintek Canada Corp. Special Publication No. Sp-34. Jozsa, L.A., Munro B.D. and Gordon J.R. 1998. Basic wood properties of second-growth Western Hemlock. Forintek Canada Corporation. Special Publication SP-38. Kass, A. J. 1965. Shrinkage stresses in externally restrained wood. Forest Prod. J. 15 (6):225-232. Keckés J., Burgert I., Frühmann K., Müller M., Kölln K., Hamilton M., Burghammer M., Stanzl-Tschegg S.E. and Fratzl P. 2003. Cell-wall recovery after irreversible deformation of wood. Nature Materials 2:811-814. Kelley S.S., Timothy G.R. and Glasser W.G. 1987. Relaxation behaviour of the amorphous components of wood. J. Mater. Sci. 22:617–624 Kelsey, K.E. 1956. The Shrinkage Intersection Point-Its Significance and the Method of Its Determination. Forest Prod. J. 6(10):411-417. Kennedy, R.M. and Swann, G.W. 1969. Comparative specific gravity and strength of amabilis fir and western hemlock grown in British Columbia. Forest Prod. Lab., Vancouver B.C. Rep. VP-X-50. Kifetew G., Lindberg, H. and Wiklund M. 1997. Tangential and radial deformation field measurements on wood during drying. Wood Sci. Technol. 31(1):35-44. Kingston, R.S.T. and Budgen, B. 1972. Some aspects of the rheological behaviour of wood. Wood Sci. Technol. 6(2):156-165.  103  Kitahara, R. and Yukawa, K. 1964. The influence of the changes of temperature in creep in bending. J. Jap. Wood Res. Soc. 10:169-175. Kollman, F. and Fengel, D. 1965. Changes in the chemical composition of wood by thermal treatment. Holz Roh-Werkst 23(12):461-468. Kollmann F.F.P. 1959. Uber die Sorption von Holz und ihre exacte Bestimmung. Holz Roh- Werkst 9(6):165-171. Koponen, S., Toratti T. and Kanerva, P. 1991. Modelling elastic and shrinkage properties of wood based on cell structure. Wood Sci. Technol. 25(1):25-32. Koumoutsakos A. and Avramidis S. 2002. Mass Transfer Characteristics of Western Hemlock and Western Red Cedar. Holzforschung 53(2):185-190. Kozlik C.J. and Ward, J.C. 1981. Properties and Kiln-Drying Characteristics of YoungGrowth Western Hemlock Dimension Lumber. Forest Prod. J. 31(6): 45-53. Kozlik, C.J. 1981. Shrinkage of western hemlock heartwood after conventional andhigh temperature kiln drying. Forest Prod. J. 31(12): 45-50. Kretschmann D. E. and Green D.W. 1996 Modeling moisture content-mechanical property relationship for clear Southern pine. Wood Fiber Sci. 28(3):320-337. Kuebler H. 1960. Drying stresses and stress relief in thin sections of wood. Forest Products Laboratory Report No. 2164. Lagana, R. 2005. Development of small scale experimental protocol and multi-physics model to predict the complex hygro-mechanical behaviour of wood under varying climates. PhD thesis The University of Maine, US. Lazarescu, C., Wu, H., and Avramidis, S. 2006. Shrinkage strain in wood under kilndrying conditions. PRO Ligno Scientific Journal in the Field of Wood Engineering, 2(2): 19-28. Lindeberg, J. 2004. X-ray Based Tree Ring Analyses. PhD Thesis, Swedish University of Agricultural Sciences, Umeå, 25p. lrvine, G.M. 1984. The glass transitions oflignin and hemicellulose and their measurement by differential thermal analysis. Tappi 67 (5): 118-121. Majka, J. 2004. Stress development in dependence of the wood drying rate. Electronic J. Polish Agricultural Uni., Wood Technol. 7(1). Available online at: http://www.ejpau.media.pl/volume7/issue1/wood/art-04.html. Marinos-Kouris, D. and Maroulis, Z.B. 1995. Transport properties in the drying of solids. Handbook of Industrial Drying, 2nd Ed., New York, Vol. 1, 137 p.  104  McAlister, R.H. and Clark A. III. 1992. Shrinkage of juvenile and mature wood of Ioblolly pine from three locations Forest Prod. J. 42(7/8):25-28. McCurdy M.C. and Keey R.B. 2002. Influence of sawing orientation on moisture movement through softwood boards. Maderas. Ciencia y Tecnología. 4(1):26-39. McIntosh D. C. 1954. Some Aspects of the Influence of Rays on the Shrinkage of Wood Forest Prod. J. 4(1):39-42. McMillen J. M. 1958. Stresses in wood during drying. Revised For. Prod. Lab. Report No. 1652, 53p. Meylan, B. A. 1967. Measurement of microfibril angle by X-ray diffraction. Forest Prod. J. 17(5):51-58. Middleton, G.R. and Munro, B.D. 2001. Second-Growth Western Hemlock product yields and attributes related to stand density. Forintek Canada Corporation. Special Publication SP-41. Milota, M. 2008. Drying rate correlation for Douglas-fir lumber. Forest Prod. J. 58 (7/8):37-40. Moraes, P.D., Rogaume Y. and Triboulot P. 2004. Influence of temperature on the modulus of elasticity (MOE) of Pinus sylvestris. Holzforschung 58(1):143-147. Morlier, P. 1994. Creep in timber structures. Rilem Report 8. E&Fn Spon, 149p. Moutee, M., Fortin Y.and Fafard. M. 2007. A global rheological model of wood cantilever as applied to wood drying. Wood Sci. Technol. 41(3):209-234. Muszynski, L., Lagana R., Shaler M.P. 2003. An optical method for characterization of basic hygro-mechanical properties of solid wood in tension. In: Proceedings of the 8th International IUFRO Wood Drying Conference, Brasov, Romania: 77-82. Muszynski, L., Lagana, R., Shaler, S.M. and Davids, W. 2005. Comments on the experimental technology for determination of the hygro-mechanical properties of wood. Holtzforschung 59(2):232-239. Myer, J.E. and L.W. Rees. 1926 Electrical resistance of wood with special reference to the fiber saturation point, NY State College of Forestry, Syracuse, Technical Bulletin 19, 22p. Nakano T. 2006. Analysis of the temperature dependence of water sorption for wood on the basis of dual mode theory. J. Wood Sci. 52:490–495. Navi, P., Pittet, V. and Plummer C.J.G. 2002. Transient moisture effects on wood creep Wood Sci. Technol. 36(6):447-462.  105  Ormarsson S. 1999. Numerical analysis of Moisture-Related distortions in sawn timber. PhD thesis. Publication 99:7, Chalmers University of Technology, Goteborg, Sweden, 214p. Pang, S and Haslett, A.N. 2002. Effects of sawing pattern on drying rate and residual drying stresses of Pinus radiata lumber. Maderas. Ciencia y tecnología. 4(1):40-49. Pang, S. 2001. Modeling of stresses and deformation of Radiata Pine lumber during drying. In: Proceedings of the 7th International IUFRO Wood Drying Conference. Tsukuba, Japan. 238–245. Pang, S. 2002. Predicting anisotropic shringkage of softwood Part 1: Theories. Wood Sci. Technol. 36(1):75–91. Pang, S. and Haslett, A.N. 2002. Effects of sawing pattern on drying rate and residual drying stresses of Pinus radiata lumber. Paper submitted to Maderas Ciencia y Tecnologia. 4(1):40-49. Panshin A.J. and de Zeeuw C. 1980. Textbook of wood technology. McGraw-Hill Book Co. New York, 722p. Passard, J. and Perré, P. 2005. Viscoelastic behaviour of green wood across the grain. Part I. Thermally activated creep tests up to 120°C. Annals Forest Sci. 62:707-716. Pearson, H. and Evans, R. 2005. Wood quality assessment for stress modeling project. Wood Processing, Issue no. 36, July Newsletter, 5-7. Peck, E. C. 1940. A new approach to the formulation of hardwood dry-kiln schedules. Southern Lumberman 161 (2033):136-137. Perré, P. 2007. Experimental device for the accurate determination of wood-water relations on micro-samples. Holzforschung, 61(4):419-429. Pilkey, W. D. 1997. Peterson's Stress Concentration Factors (2nd Edition). John Wiley & Sons Third Avenue, New York, 524p. Price, A. T. 1928. A mathematical discussion on the structure of wood in relation to its elastic properties. Philos.Trans. Royal Soc. London. Series A 228:1-62. Ranta-Maunus, A. 1993. Rheological behaviour of wood in directions perpendicular to the grain. Mater. Struct. 26:362-369. Rémond R. and Perré P. 2008. Drying strategies capable of reducing the stress level of a stack of boards as defined by a comprehensive dual scale model. Maderas. Ciencia y tecnología 10(1): 3-18. Resch, H., Kang, H. and Hoag, M.L. 1989. Drying Douglas-fir lumber: a computer. Wood Fiber Sci. 21(3):207-218.  106  Rice R.W. and Youngs R.L. 1990. The mechanism and development of creep during drying of red oak. Holz Roh-Werkst 48:73-79. Riley S. and L. van Wyk 2005. Measuring MC profiles with insulated pin electrodes Wood Processing, Issue no. 36, July 2005 Newsletter, 1-4. Rohrbach K. 2008. Schedule and Post-Drying Storage Effects on Western Hemlock Squares Quality. MSc. Thesis, University of British Columbia, 139p. Rosenkilde A. 2002. Moisture content profiles and surface phenomena during drying of wood. PhD thesis, Kungliga Tekniska Hogskolan, Stockholm. Oregon State University, 36p. Rosenkilde A. and Glover P. 2002. High resolution measurement of the surface layer moisture content during drying of wood using a novel magnetic resonance imaging technique. Holzforschung 56(3): 312 – 317. Rosenkilde A., Gorce J.-P. and Barry A. 2004. Measurement of moisture content profiles during drying of Scots pine using magnetic resonance imaging. Holzforschung, 58(2):138-142. Salin J.G. 1992. Numerical prediction of checking during timber drying a new mechanosorptive creep model. Holz Roh-Werkst 50:195–200. Salin, J.G. (2008) Drying of liquid water in wood as influenced by the capillary fiber network. Drying Technol. 26(5): 560-567. Salmen, L. 1984. Viscoelastic properties of in situ lignin under water-saturated conditions. J. Mater. Sci. 19(9):3090-3096. Schniewind, A. 1968. Recent progress in the study of the rheology of wood. Wood Sci. Technol. 2(3):188-206. Schniewind, A. P. 1959. Transverse anisotropy of wood: A function of gross anatomic structure. Forest Prod. J. 9(10):350-358. Schniewind, A.P. 1963. Mechanism of check formation. Forest Prod. J. 13(11): 475-480. Shmulsky, R. 2004. EMC response along the tensile face of small wood beams Wood Sci. Technol. 37(5):447-449. Siau, F. 1995. Wood: Influence of moisture on physical properties. Department of Wood Science and Forest Products, Virginia Polytechnic Institute and State University, 227p. Simpson T. W. 1973. Predicting equilibrium moisture content of wood by mathematical models. Wood Fiber Sci. 5(1): 41-49.  107  Simpson, W. T. 1991. Dry Kiln Operator's Manual. Agric. Handbook #188. USDA Forest Prod. Lab., Madison, WI, 274 pp. Sivonen, H., Maunu, S.L. Sundholm, F., Jamsa, S. and Viitaniemi, P. 2002. Magnetic resonance studies of thermally modified wood. Holtzforschung 56(2): 648-654. Skaar, C. 1988. Wood-water relations. Springer series in wood science. Springer-Verlag New York, 274p. Spalt, H.A. 1958. The fundamentals of water vapor sorption by wood. For. Prod. J. 8(10): 288–295. Stamm, A.J. 1929. The Fiber-Saturation Point of Wood as Observed from Electrical Conductivity Measurements. Ind. Eng. Chem. 1:94-97. Stamm, A.J. 1935. The effect of changes in the equilibrium relative vapour pressure upon the capillary structure of wood. Physics 6:334-342. Stamm, A.J. 1956. Thermal degradation of wood and cellulose. J. Ind. Eng. Chem. 48 (3): 413-417. Stamm, A.J. 1959. Bound-water diffusion into wood in the fiber direction. Forest Prod. J. 9(1):227-232. Stamm, A.J. 1964. Wood and Cellulose Science. Ronald Press, New York. 509p. Stamm, A.J. 1971. Review of nine methods for determining the fiber saturation point of wood and wood products. Wood Sci. 4(2):114-128. Stamm, A.J. and Loughborough W.K., 1935. Thermodynamics of the swelling of wood. J. Phys. Chem. 39:379-386. Stamm, A.J. and Loughborough, W.K. 1942. Variation in shrinking and swelling of wood. Trans. Amer. Soc. Mech. Eng. 64:379-386. Stamm, A.J. and Nelson, R.M. 1961. Comparison Between Measured and Theoretical Drying Diffusion Coefficients for Southern Pine. Forest Prod. J. 11(11):536-543. Stevens W.C. 1938. The shrinkage and expansion of wood. Forestry 12:38-43. Stevens W.C. 1963. The Transverse Shrinkage of Wood. Forest Prod. J. 13(9):386-389. Stohr H.P. 1988. Shrinkage differential as a measure for drying stress determination Wood Sci. Technol. 22(2):121-128. Stone, J.E. and Scallan, A.M. 1967. The effect of component removal upon the porous structure of the wall of wood. II. Swelling in water and the fibre saturation point. Tappi 50(10): 496–501.  108  Svensson, S. 1997. Internal Stresses in Wood Caused by Climatic Variation. PhD thesis, Lund Institute of Technology Sweden, 110p. Svensson, S. 1997. Stress-Strain Relationship of Drying Wood. Holzforschung 51: 472478. Tiemann, H.D. 1906. Effect of moisture upon the strength and stiffness of wood. U.S.D.A Forest Service Bulletin 70, 144pp. Tremblay, C., Cloutier, A. and Fortin Y. 1996. Moisture content-water potential relationship of red pine sapwood above the fiber saturation point and determination of the effective pore size distribution Wood Sci. Technol. 30(5): 361-371. Tremblay, C., Cloutier, A. and Fortin, Y. 2000. Experimental determination of the convective heat and mass transfer coefficients for wood drying. Wood Sci. Technol. 34(3): 253-276. Treybal, R.E. 1980. Mass-transfer operations. McGraw-Hill, New York, 784p. USDA. 1999. Wood Handbook. Wood as an Engineering material U.S. Dept. Agric. General Technical Report FPL-GTR-113. 486pp. Verhulst, P.F. 1838. 'Notice sur la loi que la population poursuit dans son accroissement. Correspondance mathématique et physique 10:113–121. Walker, J.C.F., Butterfield, B.G., Langrish, T.A.G., Harris, J.M. and Uprichard, J.M. 1993. Primary Wood Processing. Chapman and Hall, London, 595p. Wangaard F.F. 1957. A New Approach to the Determination of Fiber Saturation Point from Mechanical Tests. Forest Prod. J. 7(11):410-416. Wangaard, F.F. and Granados, L.A. 1967. The effect of extractives on water-vapour sorption of wood. Wood Sci. Technol. 1(4):253-277. Weichert, L. 1963. Untersuchugen uber das Sorptions- und Quellungsverhalten von Holz verschiedener Rohdichte in Abhangigkeit vom Feuchtigkeitsgehalt. Holz Roh- Werkst 21:290-300. Whale, L.R.J. 1988. Deformations characteristics of nailed or bolted timber joints subjected to irregular short or medium term lateral loading. PhD Dissertation. South Bank Polytechnic, London, U.K, 189p. Wilberg, P., Sehlstedt-P. S.M.B. and Moren, T.J. 2000. Heat and mass transfer during sapwood drying above the fibre saturation point. Drying Technol. 18(8): 1647-1664. Wilson, T.R.C. 1932. Strength-moisture relations for wood. U.S. Dept. of Agric. Tech. Bull. No. 282.  109  Wood, L.W. and Soltis, L.A. 1964. Stiffness and shrinkage of green and dry joists. Research Paper FPL 15. Madison, WI: U.S. Forest Service, Forest Product Laboratory. Wu, Q. 1993. Rheological behavior of Douglas-fir as related to the process of drying. PhD thesis, Oregon State University, 228p. Xiao, C.D. 2005. A Discussion on a Generalized Correlation for Drying Rate Modeling. Drying Technol. 23(3): 415-426. Zhou, Y., Fushitani, M. and Kubo, T. 2000. Effect of stress level on bending creep behaviour of wood during cyclic moisture changes. Wood Fiber Sci. 32(1):20-28. Zobel, B. J. and Sprague, J.R. 1998. Juvenile wood in forest trees. Springer series in wood science. Springer-Verlag, New York, 243p.  110  APPENDIX A List of Publications Lazarescu, C. and Avramidis S. (2009). Modeling Shrinkage Response to Tensile Stresses in Wood Drying II. Stress - Shrinkage Correlation in Restrained Specimens. Submitted for publication in Drying Technology. Lazarescu, C. and Avramidis S. (2009). Modeling Shrinkage Response to Tensile Stresses in Wood Drying, I. Shrinkage-Moisture Interaction in Stress Free Specimens. Accepted for publication in Drying Technology Vol. 27, No.10. Lazarescu, C. and Avramidis S. (2008). Drying Related Strain Development in Restrained Wood. Drying Technology, 26(6): 544–551. Lazarescu, C. and Avramidis, S. (2007). Evaluation of Hygrothermal Shrinkage Strain in Tsuga heterophylla. International Conference on Wood Industry in the Third Millennium – 6th edition, June 20-27 Brasov, Romania: 58-65. Lazarescu, C., Wu, H. and Avramidis, S. (2006). Shrinkage Strain in Wood under KilnDrying Conditions. PRO Ligno 2(2): 19-28. Lazarescu, C. and Avramidis, S. (2006). The Evaluation of Moisture Content Gradient using CT-scanning Technique. 60th International Convention of Forest Products Society, June 25-28, Newport Beach California. Lazarescu, C., Wu, H. and Avramidis, S. (2006). Drying Strains of Tsuga Heterophylla Lumber. 60th International Convention of Forest Products Society, June 25-28, Newport Beach California.  111  A1. SAS Source code for MFA calculation proc import datafile="C:\Folder Name\File Name.xls" out=Output File Name; sheet="Worksheet Name"; run; proc sort data=Output File Name; by sample; run; goptions reset=all ftext="Helvetica-Bold" hby=0 dev=pdfc gsfname=output gsfmode=replace; filename output 'File Name.pdf'; title1 height=22pt "#byval1"; symbol1 i=join c=blue; proc gplot data=Output File Name; plot int*chi/haxis=-200 to 200 by 10 vaxis=0 to 80 by 10 hminor=4; by sample; run; quit; A2. SAS Source code for  α  and  β  calculation  Example: Equilibrium moisture content = 17.94, Initial moisture content =81.7. Proc import datafile="C:\Folder Name\File Name.xls" out=Output File Name; sheet="Worksheet Name"; run; data Mdata2; set Mdata; y=moisture; x1=time; run; PROC NLIN iter=200 method=marquardt data=Mdata2; parms b1=0.0012 b2=1.2; model y=17.94+81.7*exp(-b1*(x1**b2)); der.b1=-81.7*(x1**b2)*exp(-b1*(x1**b2)); der.b2=-81.7*b1*(x1**b2)*log(x1)*exp(-b1*(x1**b2)); output out=pout1 r=resid1 p=yhat1; run; proc plot data=pout1; plot resid1*yhat1='*'; run; PROC univariate data=pout1 plot normal; Var resid1; Run; A3. SAS Source code for the free shrinkage fitting PROC IMPORT OUT=WORK.RDATA DATAFILE=" C:\Folder Name\File Name.xls " DBMS=EXCEL2000 REPLACE; SHEET="Structural"; GETNAMES=YES; RUN; DATA RDATA; SET RDATA; IF Density='M' THEN Z=1; IF Density='J' THEN Z=0; MoistureZ=Moisture*Z; Msquare=Moisture**2; MsquareZ=Msquare*Z; TemperatureZ=Temperature*Z;  112  RUN; PROC REG corr simple DATA=RDATA; TITLE1 'REGRSSION ANALYSIS'; OPTIONS LINESIZE=80 PAGESIZE=60; model Strain = Moisture MoistureZ Temperature TemperatureZ Msquare MsquareZ Z/SELECTION = BACKWARD SLSTAY = 0.05; OUTPUT OUT = OUT1 P = PRED1 r = RESI1; RUN; PROC PLOT DATA = OUT1; PLOT RESI1*PRED1 ='*'; RUN; PROC univariate data=out1 plot normal; var RESI1; RUN; A4. SAS Source code for shrinkage rate calculation PROC IMPORT OUT=WORK.RDATA DATAFILE=" C:\Folder Name\File Name.xls " DBMS=EXCEL2000 REPLACE; SHEET="All"; GETNAMES=YES; RUN; DATA RDATA; SET RDATA; z1=0; z2=0; z3=0; IF Structural='TJ' THEN Z1=1; IF Structural='RM' THEN Z2=1; IF Structural='RJ' THEN Z3=1; Temperaturez1=Temperature*z1; Temperaturez2=Temperature*z2; Temperaturez3=Temperature*z3; Moisturez1=Moisture*z1; Moisturez2=Moisture*z2; Moisturez3=Moisture*z3; PROC REG corr simple DATA=RDATA; TITLE1 'REGRESSION ANALYSIS'; OPTIONS LINESIZE=80 PAGESIZE=60; model Srate =Temperature Temperaturez1 Temperaturez2 Temperaturez3 Moisture Moisturez1 Moisturez2 Moisturez3 z1 z2 z3/SELECTION = BACKWARD SLSTAY = 0.05; OUTPUT OUT = OUT1 P = PRED1 r = RESI1; RUN; PROC PLOT DATA = OUT1; PLOT RESI1*PRED1 ='*'; RUN; PROC univariate data=out1 plot normal; var RESI1; RUN; A5. SAS Source code for the covariance analysis of  β  PROC IMPORT OUT=WORK.DATA1 DATAFILE=" C:\Folder Name\File Name.xls " DBMS=EXCEL2000 REPLACE; SHEET="Name"; GETNAMES=YES; RUN; OPTIONS LINESIZE=78 PAGESIZE=60; PROC GLM DATA=DATA1; CLASS Structural; MODEL Beta=Moisture Structural Moisture*Structural/SS3; LSMEANS Structural/STDERR TDIFF; RUN; OUTPUT OUT=RES1 PREDICTED=PREDICT RESIDUAL=RESID; PROC UNIVARIATE DATA=RES1 PLOT NORMAL; VAR RESID;  113  RUN; PROC ANOVA DATA=RES1; CLASS Structural; MODEL RESID = Structural; MEANS Structural/HOVTEST=BARTLETT; RUN; A6. SAS Source code for the analysis of  α  PROC IMPORT OUT=WORK.RDATA DATAFILE=" C:\Folder Name\File Name.xls " DBMS=EXCEL2000 REPLACE; SHEET="Name"; GETNAMES=YES; RUN; DATA RDATA; SET RDATA; z1=0; z2=0; z3=0; IF Structural='TJ' THEN Z1=1; IF Structural='RM' THEN Z2=1; IF Structural='RJ' THEN Z3=1; RecM=1/Moisture; RecMz1=RecM*z1; RecMz2=RecM*z2; RecMz3=RecM*z3; RUN; PROC REG corr simple DATA=RDATA; TITLE1 'REGRSSION ANALYSIS'; OPTIONS LINESIZE=80 PAGESIZE=60; model Alfa=RecM RecMz1 RecMz2 RecMz3 z1 z2 z3 /SELECTION = BACKWARD SLSTAY = 0.05; OUTPUT OUT = OUT1 P = PRED1 r = RESI1; RUN; PROC PLOT DATA = OUT1; PLOT RESI1*PRED1 ='*'; RUN; PROC univariate data=out1 plot normal; var RESI1; A7. SAS Source code for the analysis of restrained shrinkage values PROC IMPORT OUT=WORK.RDATA DATAFILE=" C:\Folder Name\File Name.xls " DBMS=EXCEL2000 REPLACE; SHEET="Structural"; GETNAMES=YES; RUN; DATA RDATA; SET RDATA; IF Structural='TM' THEN Z=1; IF Structural='TJ' THEN Z=0; Msquare=Moisture**2; MsquareZ=Msquare*Z; MoistureZ=Moisture*Z; StressZ=Stress*Z; TemperatureZ=Temperature*Z; RUN; PROC REG corr simple DATA=RDATA; TITLE1 'REGRSSION ANALYSIS'; OPTIONS LINESIZE=80 PAGESIZE=60; model Strain= Moisture MoistureZ Msquare MsquareZ Temperature TemperatureZ Stress StressZ Z /SELECTION = BACKWARD SLSTAY = 0.05; OUTPUT OUT = OUT1 P = PRED1 r = RESI1; RUN; PROC PLOT DATA = OUT1; PLOT RESI1*PRED1 ='*'; RUN;  114  PROC univariate data=out1 plot normal; var RESI1; RUN;  115  APPENDIX B Table B.1. Within ring density distribution Ring no.  Ring width [mm]  Latewood [%]  3  1.76  4  1.96  5 6  Density [Kg/m3] Earlywood  Latewood  Ring average  56.22  421.3  621.1  533.6  58.33  417.1  597.3  522.1  2.52  57.14  414.3  495.6  460.7  5.32  37.59  389.5  554.4  451.5  7  5.88  33.33  401.9  593.1  465.6  8  4.84  38.84  365.3  561.5  441.5  9  3.32  43.37  397.3  548.8  463  10  3.96  45.45  390.3  571.1  472.5  11  3.76  44.68  370.7  562.2  456.3  12  3.92  37.76  377.3  597  460.2  13  4.88  26.23  370.8  583.4  426.6  14  6.48  29.01  384.7  545.7  431.4  15  4.88  29.51  376.7  537  424  16  7.16  37.43  348.5  514.4  410.6  17  6.44  34.16  341.6  536.3  408.5  18  4.84  22.31  340.5  599.7  397.9  19  7.4  15.14  348  583.5  383.7  20  6.48  17.9  348.7  561  386.7  21  6.32  41.14  366.1  518.8  428.9  22  4.48  51.79  361.9  539.8  454  23  9.28  24.14  377.1  556.9  420.5  24  4.6  46.96  361.8  513.3  433  25  7.6  38.42  338  550.7  419.7  26  6.88  40.12  321.5  507.8  396.2  27  6.44  34.16  350.6  590.1  433  28  6.16  22.73  359.9  588.6  411.5  29  7.04  32.95  383.4  556.4  440.4  30  6.12  37.91  347.4  565  429.9  31  6.2  43.23  363.9  536.7  438.6  32  6.08  34.21  371.8  612.9  454.3  33  5.76  38.89  359.5  534.5  427.6  34  5.04  34.13  336.5  527.2  401.6  35  5.8  12.41  327.8  550.7  355.5  36  6.4  8.75  320  537.3  339  37  5  8.8  287.4  565.2  311.9  38  6.04  11.92  310.9  573.5  342.2  39  6.24  17.31  307.8  523.8  345.1  40  6.36  22.64  303.7  513.1  351.1  41  5.68  29.58  310.8  520  372.7  42  6.6  14.55  346.8  540.5  375  43  6.16  17.53  343.8  564.7  382.6  44  4.68  21.37  313.2  627.5  380.3  45  4.16  20.19  317.2  628.7  380.1  116  Ring no.  Ring width [mm]  Latewood [%]  46  3.96  47  5.44  Density [Kg/m3] Earlywood  Latewood  Ring average  26.26  317.4  573.7  384.7  29.41  314.5  532.1  378.9  48  3.64  26.37  314.6  618.9  394  Average  5.34  32.8  334.39  557.86  413.18  Table B.2. Free radial and tangential shrinkage values for hemlock at different temperatures and EMC ’s. Tangential Radial No  M, %  T, ºC  Density*  Strain, %  No  M, %  T, ºC  Density*  Strain, %  1  17.24  40  M  4.07  1  17.37  40  M  2.38  2  17.63  40  M  4.02  2  17.60  40  M  2.11  3  17.26  40  M  3.41  3  17.60  40  M  2.28  4  17.24  40  M  4.31  4  17.29  40  M  2.17  5  17.15  60  M  3.56  5  18.02  40  M  1.95  6  17.18  60  M  3.64  6  17.15  60  M  1.97  7  17.03  60  M  3.98  7  17.63  60  M  1.93  8  15.64  80  M  4.31  8  17.48  60  M  1.79  9  15.74  80  M  4.29  9  17.60  60  M  1.59  10  15.58  80  M  5.05  10  17.61  60  M  1.75  11  14.66  80  M  5.43  11  15.76  80  M  2.19  12  11.77  40  M  6.57  12  15.56  80  M  2.20  13  11.85  40  M  6.54  13  16.08  80  M  2.13  14  11.92  40  M  6.77  14  15.63  80  M  2.32  15  11.58  40  M  6.04  15  15.54  80  M  2.19  16  10.94  60  M  5.59  16  15.86  80  M  2.03  17  11.36  60  M  5.57  17  11.79  40  M  3.74  18  11.35  60  M  6.08  18  12.03  40  M  3.52  19  10.52  60  M  6.18  19  11.92  40  M  3.58  20  10.27  80  M  5.93  20  11.89  40  M  3.33  21  11.27  80  M  5.12  21  12.04  40  M  3.07  22  9.54  80  M  6.59  22  10.60  60  M  3.50  23  5.73  40  M  7.44  23  10.74  60  M  2.97  24  5.76  40  M  6.46  24  11.01  60  M  3.11  25  5.63  40  M  6.99  25  10.74  60  M  3.96  26  5.99  40  M  7.48  26  11.02  60  M  2.99  27  5.24  60  M  7.52  27  10.58  80  M  3.09  28  5.28  60  M  7.24  28  10.26  80  M  4.13  29  5.06  60  M  6.38  29  10.51  80  M  3.09  30  4.82  60  M  6.42  30  10.57  80  M  3.17  31  4.71  80  M  6.77  31  11.33  80  M  3.05  32  4.59  80  M  5.67  32  5.80  40  M  5.37  33  4.05  80  M  6.18  33  5.73  40  M  3.94  34  17.72  40  J  3.62  34  6.03  40  M  3.92  35  17.68  40  J  4.41  35  5.82  40  M  4.27  36  17.87  40  J  3.84  36  5.40  40  M  4.35  37  17.72  40  J  4.39  37  5.02  60  M  4.37  38  17.66  40  J  4.69  38  5.06  60  M  4.47  117  Tangential  Radial  No  M, %  T, ºC  Density*  Strain, %  No  M, %  T, ºC  Density*  Strain, %  39  17.95  60  J  3.86  39  5.28  60  M  4.02  40  17.58  60  J  3.07  40  5.30  60  M  4.69  41  16.73  60  J  4.35  41  4.66  80  M  4.41  42  18.14  60  J  3.64  42  4.59  80  M  4.45  43  17.99  60  J  4.35  43  4.61  80  M  4.98  44  15.69  80  J  4.65  44  4.61  80  M  4.33  45  14.73  80  J  4.45  45  4.80  80  M  4.41  46  15.72  80  J  4.94  46  16.98  40  J  2.28  47  15.72  80  J  4.61  47  18.05  40  J  1.73  48  17.66  80  J  4.69  48  17.61  40  J  1.93  49  12.11  40  J  5.06  49  17.61  40  J  1.85  50  12.07  40  J  5.77  50  17.59  60  J  1.61  51  11.89  40  J  4.80  51  17.43  60  J  1.59  52  12.32  40  J  5.81  52  17.50  60  J  1.52  53  11.07  60  J  5.47  53  15.81  80  J  1.97  54  10.93  60  J  5.45  54  15.66  80  J  1.99  55  10.34  60  J  6.24  55  15.86  80  J  1.69  56  10.98  60  J  6  56  11.62  40  J  2.87  57  10.48  80  J  6.71  57  11.54  40  J  2.80  58  10.63  80  J  6.04  58  11.70  40  J  2.87  59  10.95  80  J  4.80  59  10.71  60  J  3.11  60  9.71  80  J  6.18  60  10.81  60  J  2.97  61  10.81  80  J  6.02  61  10.92  60  J  2.76  62  6.07  40  J  6.93  62  10.81  80  J  2.461  63  5.89  40  J  6.73  63  11.27  80  J  2.54  64  5.84  40  J  6.61  64  10.43  80  J  2.81  65  6.03  40  J  6.50  65  10.55  80  J  2.91  66  5.32  60  J  6.18  66  5.70  40  J  4.00  67  5.29  60  J  5.94  67  5.91  40  J  5.26  68  5.30  60  J  6.85  68  5.89  40  J  4.33  69  5.18  60  J  7.60  69  4.80  60  J  4.04  70  5.17  60  J  6.30  70  5.37  60  J  4.09  71  4.77  80  J  7.24  71  5.07  60  J  4.53  72  5.14  80  J  6.95  72  4.94  80  J  3.58  73  4.62  80  J  7.58  73  4.69  80  J  3.31  74  4.59  80  J  6.67  74  4.55  80  J  3.46  75 4.72 80 * M and J represent mature and juvenile  J  3.94  Table B.3. Radial and tangential shrinkage rate values for hemlock at different temperatures and EMC ’s. Tangential  Radial  No  M, %  Sr  T, C  No  M, %  Sr  T, C  1  17.67  0.010  40  1  17.66  0.008  40  2  18.09  0.006  40  2  18.40  0.005  40  3  17.63  0.008  40  3  17.97  0.006  40  4  11.79  0.011  40  4  12.01  0.011  40  5  12.12  0.009  40  5  12.04  0.017  40  118  Tangential  Radial  No  M, %  Sr  T, C  No  M, %  Sr  T, C  6  11.91  0.020  40  6  11.90  0.017  40  7  5.67  0.027  40  7  5.72  0.017  40  8  5.64  0.013  40  8  5.88  0.019  40  9  5.98  0.034  40  9  5.78  0.018  40  10  17.85  0.007  40  10  18.22  0.008  40  11  18.36  0.006  40  11  18.30  0.007  40  12  17.99  0.009  40  12  17.93  0.007  40  13  17.80  0.012  40  13  17.53  0.012  40  14  18.02  0.008  40  14  17.89  0.007  40  15  12.24  0.014  40  15  12.20  0.012  40  16  12.31  0.015  40  16  12.53  0.013  40  17  11.98  0.017  40  17  12.27  0.010  40  18  11.61  0.018  40  18  12.12  0.016  40  19  6.08  0.023  40  19  12.33  0.010  40  20  5.78  0.022  40  20  5.72  0.016  40  21  5.83  0.020  40  21  6.08  0.017  40  22  5.81  0.022  40  22  5.90  0.015  40  23  18.35  0.014  60  23  5.90  0.018  40  24  17.65  0.013  60  24  5.57  0.022  40  25  11.14  0.016  60  25  18.23  0.009  60  26  11.81  0.014  60  26  18.28  0.008  60  27  11.68  0.028  60  27  18.58  0.009  60  28  5.23  0.029  60  28  10.98  0.014  60  29  5.48  0.028  60  29  11.10  0.022  60  30  5.34  0.024  60  30  11.38  0.017  60  31  18.53  0.008  60  31  5.13  0.025  60  32  17.99  0.007  60  32  5.50  0.028  60  33  18.48  0.020  60  33  5.08  0.028  60  34  18.46  0.016  60  34  18.43  0.010  60  35  18.29  0.010  60  35  18.70  0.007  60  36  11.22  0.017  60  36  18.56  0.013  60  37  11.34  0.015  60  37  18.81  0.010  60  38  11.15  0.032  60  38  18.21  0.010  60  39  11.31  0.038  60  39  11.37  0.017  60  40  5.30  0.033  60  40  11.49  0.016  60  41  5.49  0.025  60  41  11.40  0.023  60  42  5.50  0.045  60  42  11.11  0.017  60  43  5.34  0.041  60  43  11.12  0.011  60  44  5.14  0.030  60  44  5.28  0.034  60  45  17.29  0.013  80  45  4.99  0.036  60  46  17.32  0.014  80  46  5.38  0.024  60  47  16.88  0.013  80  47  5.43  0.026  60  48  11.25  0.031  80  48  5.43  0.025  60  49  11.53  0.026  80  49  17.57  0.009  80  50  11.49  0.031  80  50  16.01  0.018  80  51  4.56  0.048  80  51  17.29  0.015  80  119  Tangential  Radial  No  M, %  Sr  T, C  No  M, %  Sr  T, C  52  17.11  0.010  80  52  11.27  0.022  80  53  17.01  0.015  80  53  11.75  0.031  80  54  16.51  0.018  80  54  11.19  0.015  80  55  17.06  0.013  80  55  11.56  0.021  80  56  11.35  0.024  80  56  5.17  0.034  80  57  11.56  0.023  80  57  4.97  0.034  80  58  11.55  0.025  80  58  4.82  0.022  80  59  10.94  0.044  80  59  4.96  0.039  80  60  5.04  0.059  80  60  17.56  0.015  80  61  4.92  0.056  80  61  14.36  0.011  80  62  17.99  0.012  80  63  17.40  0.010  80  64  17.82  0.012  80  65  11.41  0.022  80  66  10.98  0.016  80  67  11.83  0.023  80  68  11.22  0.024  80  69  11.35  0.017  80  70  5.17  0.040  80  71  4.66  0.040  80  72  5.12  0.041  80  73  4.98  0.031  80  Table B.4. Statistical coefficients  α  and  β  used to fit the moisture content during the dehydration process.  No  M, [%]  β  α  T, ºC  Structural  1  17.67  1.461047  0.000169  40  TM  2  18.09  1.353889  0.000205  40  TM  3  17.63  1.389901  0.000156  40  TM  4  11.79  1.311621  0.000691  40  TM  5  12.12  1.390917  0.000412  40  TM  6  11.91  1.35224  0.000881  40  TM  7  5.67  1.346379  0.001096  40  TM  8  5.64  1.432358  0.000822  40  TM  9  5.98  1.415655  0.001327  40  TM  10  18.35  1.218495  0.000554  60  TM  11  17.65  1.382105  0.000242  60  TM  12  11.14  1.501997  0.000311  60  TM  13  11.81  1.2223  0.001097  60  TM  14  11.68  1.158182  0.0016  60  TM  15  5.23  1.293204  0.002286  60  TM  16  5.48  1.262693  0.002276  60  TM  17  5.34  1.454263  0.001091  60  TM  18  17.29  1.509681  7.06E-05  80  TM  19  17.32  1.642172  2.37E-05  80  TM  20  16.88  1.526969  5.04E-05  80  TM  21  11.25  1.418576  0.000432  80  TM  22  11.53  1.661959  7.72E-05  80  TM  120  No  M, [%]  β  α  T, ºC  Structural  23  11.49  1.462274  0.000293  80  TM  24  4.56  1.389242  0.003042  80  TM  25  17.85  1.376577  0.000156  40  TJ  26  18.36  1.376577  0.000156  40  TJ  27  17.99  1.227464  0.000548  40  TJ  28  18.02  1.181051  0.000569  40  TJ  29  12.24  1.315227  0.000562  40  TJ  30  12.31  1.340791  0.00049  40  TJ  31  11.98  1.342091  0.000705  40  TJ  32  11.61  1.650939  9.46E-05  40  TJ  33  6.08  1.385986  0.000837  40  TJ  34  5.78  1.309298  0.001186  40  TJ  35  5.83  1.504031  0.000517  40  TJ  36  5.81  1.617799  0.000271  40  TJ  37  18.53  1.561683  4.71E-05  60  TJ  38  17.99  1.645233  2.44E-05  60  TJ  39  18.48  1.459948  0.000208  60  TJ  40  18.46  1.605633  4.02E-05  60  TJ  41  18.29  1.226216  0.000519  60  TJ  42  11.22  1.513111  0.000222  60  TJ  43  11.34  1.498445  0.000255  60  TJ  44  11.15  1.358068  0.001168  60  TJ  45  11.31  1.309354  0.000723  60  TJ  46  5.30  1.432104  0.001065  60  TJ  47  5.49  1.328868  0.001742  60  TJ  48  5.50  1.436428  0.001152  60  TJ  49  5.34  1.610784  0.000807  60  TJ  50  5.14  1.28659  0.003514  60  TJ  51  17.11  1.453448  0.0001  80  TJ  52  17.01  1.516524  6.89E-05  80  TJ  53  16.51  1.508882  6.84E-05  80  TJ  54  17.06  1.329272  0.000237  80  TJ  55  11.35  1.477059  0.000248  80  TJ  56  11.56  1.336925  0.000468  80  TJ  57  11.55  1.40875  0.000327  80  TJ  58  10.94  1.42325  0.000467  80  TJ  59  5.04  1.4113  0.002567  80  TJ  60  4.92  1.511685  0.001546  80  TJ  61  18.22  1.425299  0.000117  40  RM  62  18.30  1.446187  0.000128  40  RM  63  17.93  1.430969  0.000155  40  RM  64  17.53  1.458066  0.000111  40  RM  65  12.20  1.265659  0.000639  40  RM  66  12.53  1.373927  0.000361  40  RM  67  12.27  1.25046  0.000871  40  RM  68  12.12  1.429119  0.000342  40  RM  69  12.33  1.300562  0.000584  40  RM  121  No  M, [%]  β  α  T, ºC  Structural  70  5.72  1.257161  0.001395  40  RM  71  6.08  1.228831  0.001722  40  RM  72  5.90  1.29315  0.001561  40  RM  73  5.90  1.210981  0.001893  40  RM  74  5.57  1.378954  0.000739  40  RM  75  18.43  1.431006  0.000162  60  RM  76  18.70  1.519226  6.57E-05  60  RM  77  18.56  1.431279  0.000106  60  RM  78  18.81  1.383845  0.00017  60  RM  79  11.37  1.437514  0.0004  60  RM  80  11.49  1.42002  0.000428  60  RM  81  11.40  1.312996  0.001382  60  RM  82  11.11  1.476675  0.000487  60  RM  83  11.12  1.300562  0.000584  60  RM  84  5.28  1.35211  0.001806  60  RM  85  5.38  1.449979  0.00136  60  RM  86  5.43  1.361185  0.001748  60  RM  87  5.43  1.377472  0.001172  60  RM  88  17.56  1.736394  8.07E-06  80  RM  89  14.36  1.397973  0.000131  80  RM  90  17.99  1.47362  5.92E-05  80  RM  91  17.40  1.387486  0.000236  80  RM  92  17.82  1.447902  0.000147  80  RM  93  11.41  1.493902  0.000246  80  RM  94  10.98  1.38171  0.000464  80  RM  95  11.83  1.13886  0.002833  80  RM  96  11.22  1.523783  0.000294  80  RM  97  11.35  1.492139  0.00032  80  RM  98  5.17  1.345609  0.002979  80  RM  99  4.66  1.438143  0.002015  80  RM  100  4.98  1.303826  0.003682  80  RM  101  17.66  1.394144  0.000136  40  RJ  102  18.40  1.335404  0.000187  40  RJ  103  17.97  1.305468  0.00034  40  RJ  104  12.01  1.233861  0.00084  40  RJ  105  12.04  1.216021  0.000952  40  RJ  106  11.90  1.218542  0.000899  40  RJ  107  5.72  1.14179  0.002567  40  RJ  108  5.88  1.215583  0.001801  40  RJ  109  5.78  1.080927  0.003603  40  RJ  110  18.23  1.346255  0.000208  60  RJ  111  18.28  1.35607  0.000157  60  RJ  112  18.58  1.400222  0.000178  60  RJ  113  10.98  1.476367  0.000325  60  RJ  114  11.10  1.202503  0.001147  60  RJ  115  11.38  1.368875  0.000496  60  RJ  116  5.13  1.282792  0.002446  60  RJ  122  No  M, [%]  β  α  T, ºC  Structural  117  5.50  1.271482  0.002381  60  RJ  118  5.08  1.300479  0.002013  60  RJ  119  17.57  1.384925  0.000111  80  RJ  120  16.01  1.469592  7.13E-05  80  RJ  121  17.29  1.661827  1.5E-05  80  RJ  122  11.27  1.321749  0.000533  80  RJ  123  11.75  1.431359  0.000255  80  RJ  124  11.19  1.389523  0.000425  80  RJ  125  11.56  1.461649  0.000425  80  RJ  126  5.17  1.378033  0.001735  80  RJ  127  4.97  1.316397  0.002367  80  RJ  128  4.82  1.393956  0.001911  80  RJ  129  4.96  1.447297  0.001911  80  RJ  Table B.5. Strain components of tangential specimens. No T, ºC M, % Shrinkage* Elastic Released Plastic F, N Stress, MPa Structural 1  40 17.36  73  5  9  13  30.25  0.45  TM  2  40 17.36  53  10  14  24  59.16  0.89  TM  3  40 17.36  28  15  19  38  96.41  1.44  TM  4  40 17.36  61  4  7  28  30.25  0.46  TM  5  40 17.36  50  6  10  33  59.16  0.91  TM  6  40 17.36  38  15  19  28  77.94  1.15  TM  7  40 17.36  52  10  13  24  59.16  0.91  TM  8  40 17.36  43  13  16  29  76.31  1.18  TM  9  60 17.13  60  9  16  15  30.25  0.44  TM  10  60 17.13  27  15  22  36  59.16  0.87  TM  11  60 17.13  48  13  18  21  54.59  0.82  TM  12  60 17.13  67  6  10  17  30.25  0.45  TM  13  60 17.13  42  16  14  28  59.16  0.90  TM  14  60 17.13  35  15  18  31  69.25  1.05  TM  15  80 15.46  61  9  14  16  30.25  0.45  TM  16  80 15.46  13  13  26  47  59.16  0.89  TM  17  80 15.46  23  14  27  36  51.88  0.76  TM  18  80 15.46  69  9  16  6  30.25  0.46  TM  19  80 15.46  28  19  24  30  59.16  0.91  TM  20  80 15.46  56  13  21  9  44.82  0.68  TM  21  80 15.46  41  3  5  51  30.25  0.44  TM  22  80 15.46  31  3  9  57  59.16  0.89  TM  23  40 11.79  69  1  3  27  30.25  0.45  TM  24  40 11.79  53  3  4  39  59.16  0.83  TM  25  40 11.79  38  6  7  49  123.55  1.87  TM  26  40 11.79  81  5  2  12  30.25  0.47  TM  27  40 11.79  63  4  2  31  59.16  0.91  TM  28  40 11.79  47  7  4  43  111.07  1.66  TM  29  40 11.79  78  3  3  15  30.25  0.48  TM  30  40 11.79  55  3  3  39  59.16  0.93  TM  123  No T, ºC M, % Shrinkage* Elastic Released Plastic F, N Stress, MPa Structural 31  40 11.79  26  8  7  59  156.13  2.39  TM  32  60 11.08  73  4  6  18  30.25  0.45  TM  33  60 11.08  43  5  7  45  59.16  0.91  TM  34  60 11.08  16  10  11  63  111.61  1.69  TM  35  60 11.08  58  7  2  34  30.25  0.45  TM  36  60 11.08  39  7  4  50  59.16  0.89  TM  37  60 11.08  10  10  7  73  126.81  1.90  TM  38  60 11.08  76  2  3  19  30.25  0.46  TM  39  60 11.08  50  6  6  38  59.16  0.88  TM  40  60 11.08  10  9  10  71  146.90  2.24  TM  41  80 10.39  68  5  4  23  30.25  0.45  TM  42  80 10.39  37  5  6  52  59.16  0.89  TM  43  80 10.39  78  10  8  4  30.25  0.45  TM  44  80 10.39  57  7  4  32  59.16  0.89  TM  45  80 10.39  75  3  5  16  30.25  0.45  TM  46  80 10.39  55  5  5  35  59.16  0.91  TM  47  80 10.39  35  9  7  49  102.38  1.53  TM  48  40  5.79  98  1  1  0  30.25  0.46  TM  49  40  5.79  78  2  1  19  59.16  0.87  TM  50  40  5.79  86  3  2  9  30.25  0.47  TM  51  40  5.79  71  1  1  27  59.16  0.91  TM  52  40  5.79  67  2  2  29  59.16  0.91  TM  53  60  5.13  76  4  2  18  30.25  0.46  TM  54  60  5.13  72  4  3  21  59.16  0.90  TM  55  60  5.13  78  3  2  17  30.25  0.45  TM  56  60  5.13  49  2  3  46  59.16  0.88  TM  57  60  5.13  76  1  2  21  30.25  0.47  TM  58  60  5.13  71  1  2  26  59.16  0.93  TM  59  80  4.45  84  2  2  11  30.25  0.45  TM  60  80  4.45  53  2  3  42  59.16  0.91  TM  61  80  4.45  88  3  5  3  30.25  0.47  TM  62  80  4.45  71  3  5  22  59.16  0.89  TM  63  40 17.72  91  5  5  0  30.25  0.45  TJ  64  40 17.72  39  17  16  27  87.17  1.32  TJ  65  40 17.68  81  5  8  5  30.25  0.44  TJ  66  40 17.68  52  7  12  30  59.16  0.88  TJ  67  40 17.68  32  15  21  31  66.00  0.97  TJ  68  60 17.95  63  6  7  24  30.25  0.46  TJ  69  60 17.95  39  7  10  44  59.16  0.88  TJ  70  60 17.95  20  11  8  60  50.25  0.78  TJ  71  60 17.58  54  20  15  12  30.25  0.45  TJ  72  60 17.58  25  17  16  42  59.16  0.88  TJ  73  60 17.58  36  12  14  38  43.19  0.64  TJ  74  80 15.69  48  17  14  22  59.16  0.87  TJ  75  80 15.69  67  7  9  17  33.26  0.50  TJ  76  80 14.73  41  7  9  43  30.25  0.46  TJ  77  80 14.73  28  12  5  55  59.16  0.89  TJ  124  No T, ºC M, % Shrinkage* Elastic Released Plastic F, N Stress, MPa Structural 78  80 14.73  42  7  10  41  31.53  0.47  TJ  79  40 12.11  96  1  2  0  30.25  0.46  TJ  80  40 12.11  86  3  5  7  59.16  0.87  TJ  81  40 12.11  60  16  12  12  109.44  1.62  TJ  82  40 12.07  77  1  4  17  30.25  0.45  TJ  83  40 12.07  57  4  7  32  59.16  0.88  TJ  84  40 12.07  40  9  8  44  110.81  1.67  TJ  85  60 11.07  83  3  4  11  30.25  0.45  TJ  86  60 11.07  60  4  4  32  59.16  0.91  TJ  87  60 11.07  50  6  7  37  105.09  1.60  TJ  88  60 10.93  66  5  4  25  30.25  0.41  TJ  89  60 10.93  55  6  8  31  59.16  0.79  TJ  90  60 10.93  44  9  9  38  86.63  1.17  TJ  91  80 10.48  65  3  5  27  59.16  0.89  TJ  92  80 10.48  56  5  7  33  81.29  1.22  TJ  93  80 10.63  47  9  6  38  59.16  0.91  TJ  94  80 10.63  44  8  6  42  63.12  0.94  TJ  95  80 10.95  51  4  7  39  30.25  0.46  TJ  96  80 10.95  25  13  13  49  59.16  0.88  TJ  97  80 10.95  36  8  10  46  58.69  0.87  TJ  98  40  6.07  91  1  2  6  30.25  0.45  TJ  99  40  6.07  82  1  2  14  59.16  0.88  TJ  100 40  6.07  38  9  8  45  161.56  2.46  TJ  101 40  5.89  89  1  1  8  30.25  0.46  TJ  102 40  5.89  73  3  3  22  59.16  0.93  TJ  103 60  5.32  79  2  1  18  30.25  0.45  TJ  104 60  5.32  53  4  2  41  59.16  0.89  TJ  105 60  5.32  22  6  3  70  131.70  2.00  TJ  106 60  5.29  92  1  3  4  30.25  0.48  TJ  107 60  5.29  84  3  4  9  59.16  0.93  TJ  108 60  5.29  54  4  3  38  115.95  1.80  TJ  109 60  5.30  63  2  1  34  30.25  0.47  TJ  110 60  5.30  49  5  3  44  59.16  0.93  TJ  111 60  5.30  28  6  2  64  103.55  1.66  TJ  112 80  4.77  64  5  1  31  30.25  0.45  TJ  113 80  4.77  53  4  1  42  59.16  0.90  TJ  114 80  5.14  88  3  3  6  30.25  0.46  TJ  115 80  5.14  56  3  3  38  59.16  0.88  TJ  116 80 5.14 32 7 5 56 109.92 1.70 TJ * All the values for Shrinkage, Elastic, Released and Plastic are percentages from free shrinkage. Table B.6. Strain components of radial specimens. No T, ºC M, % Shrinkage* Elastic Released Plastic F, N 9  12  40  17.37 57  2  40  17.37 26  18  19  37  59.16 0.88  RM  3  40  17.37 9  25  22  44  68.96 1.03  RM  4  40  17.60 68  3  8  21  30.25 0.44  RM  5  40  17.60 36  13  15  36  59.16 0.87  RM  125  22  Stress, MPa Structural  1  30.25 0.46  RM  No T, ºC M, % Shrinkage* Elastic Released Plastic F, N  Stress, MPa Structural  6  40  17.60 16  23  25  36  76.31 1.17  7  40  17.60 62  4  9  25  30.25 0.46  RM RM  8  40  17.60 35  16  12  36  59.16 0.89  RM  9  40  17.60 22  16  15  47  68.17 1.02  RM  10 40  17.29 54  11  14  22  30.25 0.44  RM  11 40  17.29 25  20  22  34  59.16 0.89  RM  12 40  17.29 21  24  22  34  56.77 0.84  RM  13 40  18.02 92  5  3  0  30.25 0.45  RM  14 40  18.02 65  9  11  15  59.16 0.87  RM  15 60  17.15 28  15  18  39  30.25 0.46  RM  16 60  17.15 7  23  24  46  59.16 0.92  RM  17 60  17.63 48  9  14  29  30.25 0.44  RM  18 60  17.63 16  14  24  45  59.16 0.90  RM  19 60  17.63 20  18  21  40  52.96 0.79  RM  20 60  17.48 30  16  11  43  30.25 0.44  RM  21 60  17.48 9  20  22  49  59.16 0.87  RM  22 60  17.48 24  22  20  34  45.91 0.70  RM  23 60  17.60 54  21  15  10  30.25 0.47  RM  24 60  17.60 30  23  23  23  59.16 0.90  RM  25 60  17.61 63  9  8  20  30.25 0.46  RM  26 60  17.61 12  16  10  62  59.16 0.89  RM  27 80  15.76 0  7  9  84  30.25 0.47  RM  28 80  15.76 0  23  6  71  59.16 0.90  RM  29 80  15.76 0  17  12  71  27.98 0.41  RM  30 80  15.56 18  15  15  52  30.25 0.47  RM  31 80  15.56 0  13  19  68  59.16 0.92  RM  32 80  15.56 31  12  13  44  20.39 0.31  RM  33 80  16.08 10  14  12  64  30.25 0.44  RM  34 80  16.08 0  18  8  74  59.16 0.87  RM  35 80  16.08 2  17  12  69  22.56 0.33  RM  36 80  15.63 33  21  8  37  30.25 0.46  RM  37 80  15.63 13  6  13  69  59.16 0.89  RM  38 80  15.63 14  12  14  61  32.88 0.49  RM  39 80  15.54 0  5  23  72  59.16 0.95  RM  40 80  15.54 0  6  43  50  35.59 0.56  RM  41 80  15.86 36  5  8  51  30.25 0.45  RM  42 80  15.86 6  10  17  68  59.16 0.90  RM  43 40  11.79 52  5  6  36  30.25 0.46  RM  44 40  11.79 33  8  8  51  59.16 0.87  RM  45 40  11.79 12  17  14  58  90.43 1.36  RM  46 40  12.03 80  3  3  13  30.25 0.45  RM  47 40  12.03 53  6  4  37  59.16 0.88  RM  48 40  12.03 16  13  8  64  120.04 1.82  RM  49 40  11.92 76  5  6  12  30.25 0.45  RM  50 40  11.92 38  8  8  46  59.16 0.93  RM  51 40  11.92 16  18  13  53  111.61 1.69  RM  52 40  11.89 80  2  5  13  30.25 0.48  RM  126  No T, ºC M, % Shrinkage* Elastic Released Plastic F, N  Stress, MPa Structural  53 40  11.89 63  5  5  27  59.16 0.90  RM  54 40  11.89 13  12  12  63  118.67 1.80  RM  55 40  12.04 77  2  3  19  30.25 0.46  RM  56 40  12.04 65  4  5  26  59.16 0.88  RM  57 60  10.60 70  2  1  28  30.25 0.46  RM  58 60  10.60 22  10  3  66  59.16 0.89  RM  59 60  10.60 0  19  4  77  79.03 1.19  RM  60 60  10.74 71  5  6  18  30.25 0.48  RM  61 60  10.74 44  8  10  38  59.16 0.92  RM  62 60  10.74 11  20  16  53  102.92 1.61  RM  63 60  11.01 61  6  4  29  30.25 0.47  RM  64 60  11.01 26  13  9  52  59.16 0.98  RM  65 60  11.01 1  20  17  61  89.34 1.39  RM  66 60  10.74 58  1  4  37  30.25 0.47  RM  67 60  10.74 19  10  5  65  59.16 0.91  RM  68 60  10.74 14  14  9  62  83.92 1.34  RM  69 60  11.02 83  3  3  12  30.25 0.45  RM  70 60  11.02 57  7  4  32  59.16 0.86  RM  71 80  10.58 32  13  4  51  30.25 0.48  RM  72 80  10.58 0  18  17  66  59.16 0.89  RM  73 80  10.58 0  31  10  59  58.93 0.90  RM  74 80  10.26 11  11  11  67  30.25 0.51  RM  75 80  10.26 0  17  14  69  59.16 1.03  RM  76 80  10.26 0  18  15  68  47.00 0.77  RM  77 80  10.51 43  2  4  52  30.25 0.48  RM  78 80  10.51 0  19  17  64  59.16 0.96  RM  79 80  10.51 0  22  12  66  52.42 0.84  RM  80 80  10.57 42  9  4  45  30.25 0.46  RM  81 80  10.57 0  0  0  100  59.16 0.92  RM  82 80  10.57 0  17  10  73  65.45 0.97  RM  83 80  11.33 48  1  2  49  30.25 0.46  RM  84 80  11.33 12  12  7  70  59.16 0.91  RM  85 40  5.80 70  3  3  25  30.25 0.46  RM  86 40  5.80 34  6  3  56  59.16 0.88  RM  87 40  5.80 0  15  6  78  96.94 1.53  RM  88 40  5.73 97  2  0  1  30.25 0.45  RM  89 40  5.73 72  3  2  24  59.16 0.91  RM  90 40  5.73 19  13  5  64  114.32 1.76  RM  91 40  6.03 97  2  1  1  30.25 0.48  RM  92 40  6.03 72  3  2  23  59.16 0.93  RM  93 40  6.03 19  13  5  63  203.37 3.18  RM  94 40  5.82 84  1  2  12  30.25 0.48  RM  95 40  5.82 77  2  2  18  59.16 0.93  RM  96 40  5.40 93  2  1  4  30.25 0.46  RM  97 40  5.40 69  4  2  25  59.16 0.88  RM  98 60  5.02 68  5  2  26  30.25 0.48  RM  99 60  5.02 19  9  4  68  59.16 0.92  RM  127  No T, ºC M, % Shrinkage* Elastic Released Plastic F, N  Stress, MPa Structural  100 60  5.02 0  16  5  79  81.74 1.33  RM  101 60  5.06 66  5  3  27  30.25 0.46  RM  102 60  5.06 48  5  5  41  59.16 0.93  RM  103 60  5.06 0  15  10  75  94.23 1.52  RM  104 60  5.28 94  0  2  3  30.25 0.47  RM  105 60  5.28 73  3  2  22  59.16 0.93  RM  106 60  5.28 20  16  9  55  231.07 3.70  RM  107 60  5.30 76  1  2  21  30.25 0.46  RM  108 60  5.30 53  3  3  42  59.16 0.91  RM  109 60  5.30 0  0  0  100  147.99 2.28  RM  110 60  5.23 82  2  2  13  30.25 0.47  RM  111 60  5.23 67  1  2  30  59.16 0.91  RM  112 80  4.66 63  3  4  30  30.25 0.47  RM  113 80  4.66 31  7  5  57  59.16 0.95  RM  114 80  4.66 0  17  9  74  107.06 1.68  RM  115 80  4.59 50  6  1  43  30.25 0.49  RM  116 80  4.59 24  8  4  64  59.16 0.98  RM  117 80  4.59 0  15  5  79  88.26 1.47  RM  118 80  4.61 60  3  3  34  30.25 0.47  RM  119 80  4.61 48  5  6  41  59.16 0.93  RM  120 80  4.61 0  13  11  76  94.78 1.59  RM  121 80  4.61 74  2  1  23  30.25 0.45  RM  122 80  4.61 47  6  3  43  59.16 0.95  RM  123 80  4.80 84  1  1  14  30.25 0.47  RM  124 80  4.80 57  1  2  40  59.16 0.93  RM  125 40  16.98 67  3  9  21  30.25 0.45  RJ  126 40  16.98 52  5  7  36  59.16 0.88  RJ  127 40  16.98 59  6  9  27  57.85 0.84  RJ  128 40  18.05 65  6  11  18  59.16 0.89  RJ  129 40  18.05 81  6  6  8  34.79 0.53  RJ  130 40  17.61 59  12  6  22  30.25 0.45  RJ  131 40  17.61 28  21  13  38  59.16 0.89  RJ  132 40  17.61 58  7  9  26  36.68 0.55  RJ  133 60  17.59 57  11  11  21  30.25 0.46  RJ  134 60  17.59 38  20  15  28  59.16 0.89  RJ  135 60  17.59 59  12  9  21  44.28 0.66  RJ  136 60  17.43 52  16  14  19  30.25 0.46  RJ  137 60  17.43 38  17  15  30  59.16 0.87  RJ  138 60  17.43 46  14  15  26  26.90 0.40  RJ  139 60  17.50 73  13  10  4  30.25 0.46  RJ  140 60  17.50 52  14  19  14  59.16 0.94  RJ  141 60  17.50 75  12  10  3  36.13 0.55  RJ  142 80  15.81 52  6  14  28  30.25 0.44  RJ  143 80  15.81 30  14  18  38  59.16 0.88  RJ  144 80  15.81 50  4  17  29  35.05 0.52  RJ  145 80  15.66 31  15  8  47  30.25 0.47  RJ  146 80  15.66 4  21  16  59  59.16 0.90  RJ  128  No T, ºC M, % Shrinkage* Elastic Released Plastic F, N  Stress, MPa Structural  147 80  15.66 19  16  10  55  29.62 0.45  RJ  148 80  15.86 37  13  12  38  30.25 0.46  RJ  149 80  15.86 29  7  7  57  59.16 0.92  RJ  150 80  15.86 38  12  8  42  32.33 0.49  RJ  151 40  11.62 88  1  5  6  30.25 0.45  RJ  152 40  11.62 75  3  5  16  59.16 0.89  RJ  153 40  11.62 48  10  12  30  160.48 2.42  RJ  154 40  11.54 75  6  6  13  30.25 0.46  RJ  155 40  11.54 39  12  12  37  59.16 0.97  RJ  156 40  11.54 19  20  13  48  81.20 1.24  RJ  157 40  11.70 90  3  5  3  30.25 0.46  RJ  158 40  11.70 66  5  6  23  59.16 0.92  RJ  159 40  11.70 56  12  13  19  106.72 1.61  RJ  160 60  10.71 94  2  3  1  30.25 0.46  RJ  161 60  10.71 36  10  6  47  59.16 0.90  RJ  162 60  10.71 41  10  7  42  133.33 2.00  RJ  163 60  10.81 68  12  5  15  30.25 0.47  RJ  164 60  10.81 30  15  10  45  64.37 0.99  RJ  165 60  10.92 80  6  2  11  30.25 0.46  RJ  166 60  10.92 59  11  3  27  59.16 0.95  RJ  167 60  10.92 38  16  9  37  93.69 1.48  RJ  168 80  11.27 44  22  12  22  30.25 0.48  RJ  169 80  11.27 0  28  28  44  59.16 0.97  RJ  170 80  11.27 0  19  14  67  51.63 0.81  RJ  171 80  10.43 80  2  6  12  30.25 0.46  RJ  172 80  10.43 48  2  3  47  59.16 0.91  RJ  173 80  10.43 33  8  8  51  96.41 1.47  RJ  174 80  10.55 64  15  4  17  30.25 0.47  RJ  175 80  10.55 16  18  9  58  74.69 1.15  RJ  176 40  5.70 71  4  1  24  59.16 0.98  RJ  177 40  5.70 44  7  5  43  190.89 2.75  RJ  178 40  5.91 62  2  1  34  30.25 0.49  RJ  179 40  5.91 52  6  4  37  59.16 0.93  RJ  180 40  5.89 73  3  2  22  30.25 0.47  RJ  181 40  5.89 56  5  3  36  59.16 0.98  RJ  182 40  5.89 30  12  5  53  134.42 2.33  RJ  183 60  4.80 91  1  1  6  30.25 0.46  RJ  184 60  4.80 67  3  3  26  59.16 0.96  RJ  185 60  4.80 35  12  7  46  176.77 2.71  RJ  186 60  5.37 81  2  2  15  30.25 0.47  RJ  187 60  5.37 60  7  3  30  59.16 0.96  RJ  188 60  5.37 0  18  8  74  118.95 1.97  RJ  189 60  5.07 71  2  2  25  30.25 0.41  RJ  190 60  5.07 62  3  3  31  59.16 0.78  RJ  191 60  5.07 19  9  7  66  152.33 2.44  RJ  192 80  4.94 42  4  3  51  30.25 0.47  RJ  193 80  4.94 22  14  9  55  59.16 0.94  RJ  129  No T, ºC M, % Shrinkage* Elastic Released Plastic F, N  Stress, MPa Structural  194 80  4.94 4  15  11  70  70.63 1.13  RJ  195 80  4.69 36  11  12  41  59.16 0.95  RJ  196 80  4.55 82  6  2  10  59.16 0.93  RJ  197 80  4.55 28  13  9  50  169.71 2.69  RJ  198 80  4.72 88  3  4  6  30.25 0.47  RJ  199 80  4.72 47  6  5  43  59.16 0.93  RJ  200 80 4.72 12 13 8 68 131.16 2.06 RJ * All the values for Shrinkage, Elastic, Released and Plastic are percentages from free shrinkage. II  Table B.7. Tangential recovered shrinkage values S R . No  T, ºC  M, %  S RII , %  F, N  Stress, MPa  1  40  17.24  4.07  0.00  0.00  TM  2  40  17.24  3.56  30.25  0.59  TM  3  40  17.24  3.11  59.16  1.16  TM  4  40  17.24  2.52  96.41  1.87  TM  5  40  17.63  4.02  0.00  0.00  TM  6  40  17.63  2.87  30.25  0.60  TM  7  40  17.63  2.70  59.16  1.18  TM  8  40  17.63  2.89  77.94  1.49  TM  9  40  17.26  3.41  0.00  0.00  TM  10  40  17.26  2.58  59.16  1.19  TM  11  40  17.26  2.42  76.31  1.53  TM  12  40  17.24  4.31  0.00  0.00  TM  13  40  17.24  3.43  30.25  0.60  TM  14  40  17.24  2.76  59.16  1.19  TM  15  40  17.72  3.62  0.00  0.00  TJ  16  40  17.72  3.66  30.25  0.59  TJ  17  40  17.72  2.64  87.17  1.71  TJ  18  40  17.68  4.41  0.00  0.00  TJ  19  40  17.68  4.19  30.25  0.57  TJ  20  40  17.68  3.09  59.16  1.15  TJ  21  40  17.68  3.03  66.00  1.26  TJ  22  40  17.87  3.84  0.00  0.00  TJ  23  40  17.87  3.19  30.25  0.56  TJ  24  40  17.87  2.97  59.16  1.15  TJ  25  40  17.72  4.39  0.00  0.00  TJ  26  40  17.72  3.78  30.25  0.57  TJ  27  40  17.72  3.39  59.16  1.08  TJ  28  40  17.66  4.69  0.00  0.00  TJ  29  40  17.66  3.80  30.25  0.55  TJ  30  40  17.66  2.52  59.16  1.08  TJ  31  40  11.77  6.57  0.00  0.00  TM  32  40  11.77  4.82  30.25  0.59  TM  33  40  11.77  4.00  59.16  1.08  TM  34  40  11.77  3.33  123.55  2.43  TM  35  40  11.85  6.54  0.00  0.00  TM  130  Structural  No  T, ºC  M, %  S RII , %  F, N  Stress, MPa  Structural  36  40  11.85  5.75  30.25  0.61  TM  37  40  11.85  4.51  59.16  1.18  TM  38  40  11.85  3.72  111.07  2.16  TM  39  40  11.92  6.77  0.00  0.00  TM  40  40  11.92  5.75  30.25  0.62  TM  41  40  11.92  4.15  59.16  1.21  TM  42  40  11.92  2.76  156.13  3.11  TM  43  40  11.58  6.04  0.00  0.00  TM  44  40  11.58  5.81  30.25  0.60  TM  45  40  11.58  3.96  59.16  1.19  TM  46  40  12.11  5.06  0.00  0.00  TJ  47  40  12.11  5.04  30.25  0.59  TJ  48  40  12.11  4.72  59.16  1.14  TJ  49  40  12.11  4.45  109.44  2.10  TJ  50  40  12.07  5.77  0.00  0.00  TJ  51  40  12.07  4.80  30.25  0.58  TJ  52  40  12.07  3.92  59.16  1.14  TJ  53  40  12.07  3.25  110.81  2.17  TJ  54  40  11.89  4.80  0.00  0.00  TJ  55  40  11.89  4.63  30.25  0.56  TJ  56  40  11.89  4.02  59.16  1.11  TJ  57  40  12.32  5.81  0.00  0.00  TJ  58  40  12.32  5.79  30.25  0.56  TJ  59  40  12.32  5.08  59.16  1.10  TJ  60  40  5.73  7.44  0.00  0.00  TM  61  40  5.73  7.42  30.25  0.60  TM  62  40  5.73  6.02  59.16  1.13  TM  63  40  5.76  6.46  0.00  0.00  TM  64  40  5.76  5.85  30.25  0.61  TM  65  40  5.76  4.72  59.16  1.18  TM  66  40  5.63  6.99  0.00  0.00  TM  67  40  5.63  4.98  59.16  1.19  TM  68  40  5.99  8.41  0.00  0.00  TM  69  40  5.99  5.75  30.25  0.60  TM  70  40  5.99  5.02  59.16  1.22  TM  71  40  6.07  6.93  0.00  0.00  TJ  72  40  6.07  6.54  30.25  0.59  TJ  73  40  6.07  5.94  59.16  1.14  TJ  74  40  6.07  3.78  161.56  3.20  TJ  75  40  5.89  6.73  0.00  0.00  TJ  76  40  5.89  6.16  30.25  0.60  TJ  77  40  5.89  5.28  59.16  1.20  TJ  78  40  5.84  6.61  0.00  0.00  TJ  79  40  5.84  5.67  30.25  0.56  TJ  80  40  6.03  6.50  0.00  0.00  TJ  81  40  6.03  6.24  30.25  0.55  TJ  82  60  17.15  3.56  0.00  0.00  TM  131  No  T, ºC  M, %  S RII , %  F, N  Stress, MPa  Structural  83  60  17.15  3.03  30.25  0.58  TM  84  60  17.15  2.28  59.16  1.13  TM  85  60  17.15  2.81  54.59  1.07  TM  86  60  17.18  3.64  0.00  0.00  TM  87  60  17.18  3.03  30.25  0.59  TM  88  60  17.18  2.62  59.16  1.17  TM  89  60  17.18  2.50  69.25  1.36  TM  90  60  17.03  3.98  0.00  0.00  TM  91  60  17.03  3.15  30.25  0.59  TM  92  60  17.03  2.52  59.16  1.18  TM  93  60  17.95  3.86  0.00  0.00  TJ  94  60  17.95  2.93  30.25  0.60  TJ  95  60  17.95  2.15  59.16  1.14  TJ  96  60  17.95  1.54  50.25  1.01  TJ  97  60  17.58  3.07  0.00  0.00  TJ  98  60  17.58  2.72  30.25  0.59  TJ  99  60  17.58  1.79  59.16  1.15  TJ  100  60  17.58  1.91  43.19  0.83  TJ  101  60  16.73  4.35  0.00  0.00  TJ  102  60  16.73  3.43  30.25  0.56  TJ  103  60  16.73  2.93  59.16  1.14  TJ  104  60  18.14  3.64  0.00  0.00  TJ  105  60  18.14  2.87  30.25  0.56  TJ  106  60  18.14  2.05  59.16  1.12  TJ  107  60  17.99  4.35  0.00  0.00  TJ  108  60  17.99  2.83  30.25  0.56  TJ  109  60  17.99  2.34  59.16  1.13  TJ  110  60  10.94  5.59  0.00  0.00  TM  111  60  10.94  4.61  30.25  0.59  TM  112  60  10.94  3.05  59.16  1.19  TM  113  60  10.94  2.07  111.61  2.19  TM  114  60  11.36  5.57  0.00  0.00  TM  115  60  11.36  3.70  30.25  0.59  TM  116  60  11.36  2.80  59.16  1.16  TM  117  60  11.36  1.50  126.81  2.47  TM  118  60  11.35  6.08  0.00  0.00  TM  119  60  11.35  4.94  30.25  0.60  TM  120  60  11.35  3.76  59.16  1.15  TM  121  60  11.35  1.75  146.90  2.91  TM  122  60  10.52  6.18  0.00  0.00  TM  123  60  10.52  5.31  30.25  0.60  TM  124  60  10.52  4.21  59.16  1.18  TM  125  60  11.07  5.47  0.00  0.00  TJ  126  60  11.07  4.88  30.25  0.59  TJ  127  60  11.07  3.72  59.16  1.18  TJ  128  60  11.07  3.43  105.09  2.08  TJ  129  60  10.93  5.45  0.00  0.00  TJ  132  No  T, ºC  M, %  S RII , %  F, N  Stress, MPa  Structural  130  60  10.93  4.11  30.25  0.54  TJ  131  60  10.93  3.76  59.16  1.03  TJ  132  60  10.93  3.39  86.63  1.52  TJ  133  60  10.34  6.24  0.00  0.00  TJ  134  60  10.34  4.33  30.25  0.56  TJ  135  60  10.34  3.90  59.16  1.08  TJ  136  60  10.98  6  0.00  0.00  TJ  137  60  10.98  5  30.25  0.57  TJ  138  60  5.24  7.52  0.00  0.00  TM  139  60  5.24  6.16  30.25  0.60  TM  140  60  5.24  5.91  59.16  1.17  TM  141  60  5.28  7.24  0.00  0.00  TM  142  60  5.28  6.02  30.25  0.59  TM  143  60  5.28  3.94  59.16  1.15  TM  144  60  5.06  6.38  0.00  0.00  TM  145  60  5.06  5.06  30.25  0.61  TM  146  60  5.06  4.74  59.16  1.20  TM  147  60  4.82  6.42  0.00  0.00  TM  148  60  4.82  6.26  30.25  0.64  TM  149  60  5.32  6.18  0.00  0.00  TJ  150  60  5.32  5.08  30.25  0.58  TJ  151  60  5.32  3.62  59.16  1.16  TJ  152  60  5.32  1.87  131.70  2.60  TJ  153  60  5.29  5.94  0.00  0.00  TJ  154  60  5.29  5.69  30.25  0.62  TJ  155  60  5.29  5.39  59.16  1.20  TJ  156  60  5.29  3.66  115.95  2.35  TJ  157  60  5.30  6.85  0.00  0.00  TJ  158  60  5.30  4.53  30.25  0.60  TJ  159  60  5.30  3.84  59.16  1.20  TJ  160  60  5.30  2.46  103.55  2.15  TJ  161  60  5.18  7.60  0.00  0.00  TJ  162  60  5.18  6.28  30.25  0.55  TJ  163  60  5.18  5.63  59.16  1.08  TJ  164  60  5.17  6.30  0.00  0.00  TJ  165  60  5.17  6.08  30.25  0.57  TJ  166  60  5.17  5.08  59.16  1.08  TJ  167  80  15.64  4.31  0.00  0.00  TM  168  80  15.64  3.62  30.25  0.59  TM  169  80  15.64  2.28  59.16  1.16  TM  170  80  15.64  2.76  51.88  0.99  TM  171  80  15.74  4.29  0.00  0.00  TM  172  80  15.74  4.04  30.25  0.60  TM  173  80  15.74  3.01  59.16  1.18  TM  174  80  15.74  3.90  44.82  0.88  TM  175  80  15.58  5.49  0.00  0.00  TM  176  80  15.58  2.68  30.25  0.58  TM  133  No  T, ºC  M, %  S RII , %  F, N  Stress, MPa  Structural  177  80  15.58  2.34  59.16  1.15  TM  178  80  14.66  5.43  0.00  0.00  TM  179  80  14.66  3.72  30.25  0.60  TM  180  80  14.66  1.93  59.16  1.17  TM  181  80  15.69  4.65  0.00  0.00  TJ  182  80  15.69  3.64  59.16  1.14  TJ  183  80  15.69  3.88  33.26  0.65  TJ  184  80  14.73  4.45  0.00  0.00  TJ  185  80  14.73  2.54  30.25  0.59  TJ  186  80  14.73  2.01  59.16  1.16  TJ  187  80  14.73  2.64  31.53  0.62  TJ  188  80  15.72  4.94  0.00  0.00  TJ  189  80  15.72  2.38  30.25  0.56  TJ  190  80  15.72  1.79  59.16  1.10  TJ  191  80  15.72  4.61  0.00  0.00  TJ  192  80  15.72  2.52  30.25  0.57  TJ  193  80  15.72  1.65  59.16  1.13  TJ  194  80  17.66  4.69  0.00  0.00  TJ  195  80  17.66  1.75  30.25  0.57  TJ  196  80  17.66  0.26  59.16  1.16  TJ  197  80  10.27  5.93  0.00  0.00  TM  198  80  10.27  4.55  30.25  0.59  TM  199  80  10.27  2.83  59.16  1.16  TM  200  80  10.18  4.47  0.00  0.00  TM  201  80  10.18  4.29  30.25  0.58  TM  202  80  10.18  3.03  59.16  1.16  TM  203  80  11.27  5.12  0.00  0.00  TM  204  80  11.27  4.29  30.25  0.59  TM  205  80  11.27  3.33  59.16  1.18  TM  206  80  11.27  2.60  102.38  1.99  TM  207  80  9.54  6.59  0.00  0.00  TM  208  80  9.54  5.24  30.25  0.60  TM  209  80  9.54  3.66  59.16  1.18  TM  210  80  10.48  6.71  0.00  0.00  TJ  211  80  10.48  4.90  59.16  1.15  TJ  212  80  10.48  4.53  81.29  1.59  TJ  213  80  10.63  6.04  0.00  0.00  TJ  214  80  10.63  3.76  59.16  1.18  TJ  215  80  10.63  3.48  63.12  1.22  TJ  216  80  10.95  4.80  0.00  0.00  TJ  217  80  10.95  2.93  30.25  0.59  TJ  218  80  10.95  2.44  59.16  1.14  TJ  219  80  10.95  2.58  58.69  1.14  TJ  220  80  9.71  6.18  0.00  0.00  TJ  221  80  9.71  5.28  30.25  0.56  TJ  222  80  9.71  3.13  59.16  1.08  TJ  223  80  10.81  6.02  0.00  0.00  TJ  134  No  T, ºC  M, %  S RII , %  F, N  Stress, MPa  Structural  224  80  10.81  4.82  30.25  0.56  TJ  225  80  10.81  3.01  59.16  1.16  TJ  226  80  4.71  6.77  0.00  0.00  TM  227  80  4.71  6.00  30.25  0.59  TM  228  80  4.71  3.94  59.16  1.18  TM  229  80  4.59  5.67  0.00  0.00  TM  230  80  4.59  5.47  30.25  0.61  TM  231  80  4.59  4.43  59.16  1.16  TM  232  80  4.05  6.18  0.00  0.00  TM  233  80  4.05  5.96  30.25  0.60  TM  234  80  4.05  5.55  59.16  1.17  TM  235  80  4.77  7.24  0.00  0.00  TJ  236  80  4.77  5.02  30.25  0.59  TJ  237  80  4.77  4.19  59.16  1.17  TJ  238  80  5.14  6.95  0.00  0.00  TJ  239  80  5.14  6.54  30.25  0.59  TJ  240  80  5.14  4.29  59.16  1.15  TJ  241  80  5.14  3.09  109.92  2.22  TJ  242  80  4.62  7.58  0.00  0.00  TJ  243  80  4.62  7.22  30.25  0.55  TJ  244  80  4.62  4.82  59.16  1.08  TJ  245  80  4.59  6.67  0.00  0.00  TJ  246  80  4.59  5.35  30.25  0.59  TJ  247  80  4.59  4.94  59.16  1.09  TJ II  Table B.8. Radial recovered shrinkage values S R . No  T, ºC  M, %  S RII , %  F, N  Stress, MPa  Structural  1  40  17.37  2.38  0.00  0.00  RM  2  40  17.37  1.85  30.25  0.60  RM  3  40  17.37  1.50  59.16  1.14  RM  4  40  17.37  1.34  68.96  1.35  RM  5  40  17.60  2.11  0.00  0.00  RM  6  40  17.60  1.67  30.25  0.58  RM  7  40  17.60  1.36  59.16  1.13  RM  8  40  17.60  1.36  76.31  1.52  RM  9  40  17.60  2.28  0.00  0.00  RM  10  40  17.60  1.71  30.25  0.60  RM  11  40  17.60  1.46  59.16  1.15  RM  12  40  17.60  1.20  68.17  1.32  RM  13  40  17.29  2.17  0.00  0.00  RM  14  40  17.29  1.69  30.25  0.58  RM  15  40  17.29  1.44  59.16  1.15  RM  16  40  17.29  1.44  56.77  1.09  RM  17  40  18.02  1.95  0.00  0.00  RM  18  40  18.02  2.01  30.25  0.58  RM  19  40  18.02  1.65  59.16  1.13  RM  135  No  T, ºC  M, %  S RII , %  F, N  Stress, MPa  20  60  17.15  1.97  0.00  0.00  RM  21  60  17.15  1.20  30.25  0.59  RM  22  60  17.15  1.06  59.16  1.20  RM  23  60  17.63  1.93  0.00  0.00  RM  24  60  17.63  1.38  30.25  0.58  RM  25  60  17.63  1.06  59.16  1.17  RM  26  60  17.63  1.16  52.96  1.03  RM  27  60  17.48  1.79  0.00  0.00  RM  28  60  17.48  1.02  30.25  0.58  RM  29  60  17.48  0.91  59.16  1.13  RM  30  60  17.48  1.18  45.91  0.91  RM  31  60  17.60  1.59  0.00  0.00  RM  32  60  17.60  1.44  30.25  0.61  RM  33  60  17.60  1.22  59.16  1.17  RM  34  60  17.61  1.75  0.00  0.00  RM  35  60  17.61  1.40  30.25  0.59  RM  36  60  17.61  0.67  59.16  1.16  RM  37  80  15.76  2.19  0.00  0.00  RM  38  80  15.76  0.35  30.25  0.61  RM  39  80  15.76  0.63  59.16  1.17  RM  40  80  15.76  0.63  27.98  0.53  RM  41  80  15.56  2.20  0.00  0.00  RM  42  80  15.56  1.06  30.25  0.61  RM  43  80  15.56  0.71  59.16  1.20  RM  44  80  15.56  1.24  20.39  0.41  RM  45  80  16.08  2.13  0.00  0.00  RM  46  80  16.08  0.77  30.25  0.58  RM  47  80  16.08  0.55  59.16  1.13  RM  48  80  16.08  0.65  22.56  0.43  RM  49  80  15.63  2.32  0.00  0.00  RM  50  80  15.63  1.46  30.25  0.59  RM  51  80  15.63  0.73  59.16  1.15  RM  52  80  15.63  0.91  32.88  0.64  RM  53  80  15.54  2.19  0.00  0.00  RM  54  80  15.54  0.61  59.16  1.24  RM  55  80  15.54  1.08  35.59  0.73  RM  56  80  15.86  2.03  0.00  0.00  RM  57  80  15.86  0.98  30.25  0.59  RM  58  80  15.86  0.65  59.16  1.17  RM  59  40  11.79  3.74  0.00  0.00  RM  60  40  11.79  2.38  30.25  0.60  RM  61  40  11.79  1.85  59.16  1.13  RM  62  40  11.79  1.57  90.43  1.77  RM  63  40  12.03  3.52  0.00  0.00  RM  64  40  12.03  3.05  30.25  0.59  RM  65  40  12.03  2.20  59.16  1.15  RM  66  40  12.03  1.28  120.04  2.36  RM  136  Structural  No  T, ºC  M, %  S RII , %  F, N  Stress, MPa  67  40  11.92  3.58  0.00  0.00  RM  68  40  11.92  3.15  30.25  0.58  RM  69  40  11.92  1.93  59.16  1.20  RM  70  40  11.92  1.69  111.61  2.20  RM  71  40  11.89  3.33  0.00  0.00  RM  72  40  11.89  2.89  30.25  0.63  RM  73  40  11.89  2.42  59.16  1.17  RM  74  40  11.89  1.24  118.67  2.35  RM  75  40  12.04  3.07  0.00  0.00  RM  76  40  12.04  2.50  30.25  0.59  RM  77  40  12.04  2.26  59.16  1.14  RM  78  60  10.60  3.50  0.00  0.00  RM  79  60  10.60  2.52  30.25  0.59  RM  80  60  10.60  1.20  59.16  1.16  RM  81  60  10.60  0.81  79.03  1.54  RM  82  60  10.74  2.97  0.00  0.00  RM  83  60  10.74  2.44  30.25  0.62  RM  84  60  10.74  1.85  59.16  1.20  RM  85  60  10.74  1.40  102.92  2.09  RM  86  60  11.01  3.11  0.00  0.00  RM  87  60  11.01  2.20  30.25  0.61  RM  88  60  11.01  1.50  59.16  1.27  RM  89  60  11.01  1.20  89.34  1.80  RM  90  60  10.74  3.96  0.00  0.00  RM  91  60  10.74  2.50  30.25  0.62  RM  92  60  10.74  1.38  59.16  1.18  RM  93  60  10.74  1.52  83.92  1.75  RM  94  60  11.02  2.99  0.00  0.00  RM  95  60  11.02  2.64  30.25  0.58  RM  96  60  11.02  2.05  59.16  1.12  RM  97  80  10.58  3.09  0.00  0.00  RM  98  80  10.58  1.52  30.25  0.62  RM  99  80  10.58  1.06  59.16  1.15  RM  100  80  10.58  1.26  58.93  1.17  RM  101  80  10.26  4.03  0.00  0.00  RM  102  80  10.26  1.38  30.25  0.66  RM  103  80  10.26  1.28  59.16  1.34  RM  104  80  10.26  1.34  47.00  1.00  RM  105  80  10.51  3.09  0.00  0.00  RM  106  80  10.51  1.50  30.25  0.63  RM  107  80  10.51  1.10  59.16  1.25  RM  108  80  10.51  1.04  52.42  1.10  RM  109  80  10.57  3.17  0.00  0.00  RM  110  80  10.57  1.75  30.25  0.59  RM  111  80  10.57  0.85  65.45  1.26  RM  112  80  11.33  3.05  0.00  0.00  RM  113  80  11.33  1.56  30.25  0.60  RM  137  Structural  No  T, ºC  M, %  S RII , %  F, N  Stress, MPa  Structural  114  80  11.33  0.93  59.16  1.18  RM  115  40  5.80  5.37  0.00  0.00  RM  116  40  5.80  4.04  30.25  0.60  RM  117  40  5.80  2.34  59.16  1.15  RM  118  40  5.80  1.16  96.94  1.99  RM  119  40  5.73  3.94  0.00  0.00  RM  120  40  5.73  3.90  30.25  0.59  RM  121  40  5.73  3.01  59.16  1.18  RM  122  40  5.73  1.44  114.32  2.29  RM  123  40  6.03  3.92  0.00  0.00  RM  124  40  6.03  3.90  30.25  0.62  RM  125  40  6.03  3.01  59.16  1.21  RM  126  40  5.82  4.27  0.00  0.00  RM  127  40  5.82  3.74  30.25  0.62  RM  128  40  5.82  3.48  59.16  1.21  RM  129  40  5.40  4.35  0.00  0.00  RM  130  40  5.40  4.17  30.25  0.59  RM  131  40  5.40  3.27  59.16  1.14  RM  132  60  5.02  4.37  0.00  0.00  RM  133  60  5.02  3.25  30.25  0.63  RM  134  60  5.02  1.42  59.16  1.20  RM  135  60  5.02  0.93  81.74  1.73  RM  136  60  5.06  4.47  0.00  0.00  RM  137  60  5.06  3.27  30.25  0.60  RM  138  60  5.06  2.62  59.16  1.21  RM  139  60  5.06  1.10  94.23  1.98  RM  140  60  5.28  4.02  0.00  0.00  RM  141  60  5.28  3.90  30.25  0.62  RM  142  60  5.28  3.15  59.16  1.21  RM  143  60  5.30  4.69  0.00  0.00  RM  144  60  5.30  3.70  30.25  0.60  RM  145  60  5.30  2.72  59.16  1.18  RM  146  60  5.23  3.37  0.00  0.00  RM  147  60  5.23  2.91  30.25  0.61  RM  148  60  5.23  2.34  59.16  1.18  RM  149  80  4.66  4.41  0.00  0.00  RM  150  80  4.66  3.07  30.25  0.62  RM  151  80  4.66  1.91  59.16  1.24  RM  152  80  4.66  1.16  107.06  2.19  RM  153  80  4.59  4.45  0.00  0.00  RM  154  80  4.59  2.54  30.25  0.64  RM  155  80  4.59  1.59  59.16  1.27  RM  156  80  4.59  0.93  88.26  1.91  RM  157  80  4.61  4.92  0.00  0.00  RM  158  80  4.61  3.31  30.25  0.61  RM  159  80  4.61  2.95  59.16  1.21  RM  160  80  4.61  1.20  94.78  2.06  RM  138  No  T, ºC  M, %  S RII , %  F, N  Stress, MPa  161  80  4.61  4.33  0.00  0.00  RM  162  80  4.61  3.33  30.25  0.59  RM  163  80  4.61  2.46  59.16  1.23  RM  164  80  4.80  4.41  0.00  0.00  RM  165  80  4.80  3.78  30.25  0.61  RM  166  80  4.80  2.64  59.16  1.21  RM  167  40  16.98  2.28  0.00  0.00  RJ  168  40  16.98  1.81  30.25  0.58  RJ  169  40  16.98  1.46  59.16  1.14  RJ  170  40  16.98  1.67  57.85  1.09  RJ  171  40  18.05  1.73  0.00  0.00  RJ  172  40  18.05  1.42  59.16  1.16  RJ  173  40  18.05  1.59  34.79  0.69  RJ  174  40  17.61  1.93  0.00  0.00  RJ  175  40  17.61  1.50  30.25  0.59  RJ  176  40  17.61  1.20  59.16  1.16  RJ  177  40  17.61  1.44  36.68  0.71  RJ  178  40  17.61  1.85  0.00  0.00  RJ  179  40  17.61  1.57  30.25  0.62  RJ  180  40  17.61  1.28  59.16  1.16  RJ  181  40  17.61  1.00  80.12  1.55  RJ  182  60  17.59  1.61  0.00  0.00  RJ  183  60  17.59  1.28  30.25  0.59  RJ  184  60  17.59  1.16  59.16  1.16  RJ  185  60  17.59  1.28  44.28  0.85  RJ  186  60  17.43  1.59  0.00  0.00  RJ  187  60  17.43  1.30  30.25  0.60  RJ  188  60  17.43  1.12  59.16  1.13  RJ  189  60  17.43  1.18  26.90  0.52  RJ  190  60  17.50  1.52  0.00  0.00  RJ  191  60  17.50  1.46  30.25  0.59  RJ  192  60  17.50  1.30  59.16  1.22  RJ  193  60  17.50  1.48  36.13  0.72  RJ  194  80  15.81  1.97  0.00  0.00  RJ  195  80  15.81  1.42  30.25  0.58  RJ  196  80  15.81  1.22  59.16  1.15  RJ  197  80  15.81  1.40  35.05  0.68  RJ  198  80  15.66  1.99  0.00  0.00  RJ  199  80  15.66  1.06  30.25  0.61  RJ  200  80  15.66  0.81  59.16  1.17  RJ  201  80  15.66  0.89  29.62  0.59  RJ  202  80  15.86  1.69  0.00  0.00  RJ  203  80  15.86  1.04  30.25  0.60  RJ  204  80  15.86  0.73  59.16  1.20  RJ  205  80  15.86  0.98  32.33  0.63  RJ  206  40  11.62  2.87  0.00  0.00  RJ  207  40  11.62  2.70  30.25  0.59  RJ  139  Structural  No  T, ºC  M, %  S RII , %  F, N  Stress, MPa  Structural  208  40  11.62  2.40  59.16  1.16  RJ  209  40  11.62  2.01  160.48  3.14  RJ  210  40  11.54  2.80  0.00  0.00  RJ  211  40  11.54  2.42  30.25  0.60  RJ  212  40  11.54  1.77  59.16  1.26  RJ  213  40  11.54  1.46  81.20  1.61  RJ  214  40  11.70  2.87  0.00  0.00  RJ  215  40  11.70  2.80  30.25  0.60  RJ  216  40  11.70  2.22  59.16  1.20  RJ  217  40  11.70  2.32  106.72  2.09  RJ  218  60  10.71  3.11  0.00  0.00  RJ  219  60  10.71  3.07  30.25  0.59  RJ  220  60  10.71  1.63  59.16  1.17  RJ  221  60  10.71  1.81  133.33  2.60  RJ  222  60  10.81  2.97  0.00  0.00  RJ  223  60  10.81  2.54  30.25  0.60  RJ  224  60  10.81  1.63  64.37  1.29  RJ  225  60  10.92  2.76  0.00  0.00  RJ  226  60  10.92  2.44  30.25  0.60  RJ  227  60  10.92  2.01  59.16  1.23  RJ  228  60  10.92  1.73  93.69  1.92  RJ  229  80  10.81  2.461  0.00  0.00  RJ  230  80  10.81  0.866  26.64  0.53  RJ  231  80  11.27  2.54  0.00  0.00  RJ  232  80  11.27  1.99  30.25  0.63  RJ  233  80  11.27  1.42  59.16  1.26  RJ  234  80  11.27  0.85  51.63  1.06  RJ  235  80  10.43  2.81  0.00  0.00  RJ  236  80  10.43  2.48  30.25  0.60  RJ  237  80  10.43  1.50  59.16  1.18  RJ  238  80  10.43  1.38  96.41  1.91  RJ  239  80  10.55  2.91  0.00  0.00  RJ  240  80  10.55  2.42  30.25  0.61  RJ  241  80  10.55  1.22  74.69  1.50  RJ  242  40  5.70  4.00  0.00  0.00  RJ  243  40  5.70  3.05  59.16  1.27  RJ  244  40  5.70  2.26  190.89  3.58  RJ  245  40  5.91  5.26  0.00  0.00  RJ  246  40  5.91  3.44  30.25  0.64  RJ  247  40  5.91  3.31  59.16  1.21  RJ  248  40  5.89  4.33  0.00  0.00  RJ  249  40  5.89  3.37  30.25  0.61  RJ  250  40  5.89  2.76  59.16  1.27  RJ  251  40  5.89  2.03  134.42  3.02  RJ  252  60  4.80  4.04  0.00  0.00  RJ  253  60  4.80  3.78  30.25  0.60  RJ  254  60  4.80  2.97  59.16  1.24  RJ  140  No  T, ºC  M, %  S RII , %  F, N  Stress, MPa  Structural  255  60  4.80  2.19  176.77  3.52  RJ  256  60  5.37  4.09  0.00  0.00  RJ  257  60  5.37  3.46  30.25  0.61  RJ  258  60  5.37  2.85  59.16  1.24  RJ  259  60  5.37  1.06  118.95  2.56  RJ  260  60  5.07  4.53  0.00  0.00  RJ  261  60  5.07  3.41  30.25  0.54  RJ  262  60  5.07  3.11  59.16  1.02  RJ  263  60  5.07  1.56  152.33  3.18  RJ  264  80  4.94  3.58  0.00  0.00  RJ  265  80  4.94  1.77  30.25  0.61  RJ  266  80  4.94  1.59  59.16  1.23  RJ  267  80  4.94  1.08  70.63  1.47  RJ  268  80  4.69  3.31  0.00  0.00  RJ  269  80  4.69  1.95  59.16  1.23  RJ  270  80  4.55  3.46  0.00  0.00  RJ  271  80  4.55  3.13  59.16  1.21  RJ  272  80  4.55  1.73  169.71  3.50  RJ  273  80  4.72  3.94  0.00  0.00  RJ  274  80  4.72  3.70  30.25  0.61  RJ  275  80  4.72  2.24  59.16  1.20  RJ  276  80  4.72  1.26  131.16  2.68  RJ  141  

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