HORIZONTAL DENSITY DISTRIBUTION OF PARTICLEBOARD: ORIGIN A1]) IMPLICATIONS by WET XU B.Sc., The Central South Forestry University, 1983 M.Sc., The Chinese Academy of Forestry, 1986 A THESIS SUBMIITED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Forestry) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA December, 1993 © Wei Xu, 1993 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. (Signature) Department of The University of British Columbia Vancouver, Canada Date DE-6 (2/88) 3/774 ii ABSTRACT Particleboard products have been manufactured for over a half century. During this time, it has been recognized that a vast number of material and processing variables influence board properties. Little is known about the internal structure of particleboard, and a fundamental principle or theory interrelating structure, processing and properties of particleboard has yet to be developed. Such basic knowledge of particleboard structure is not only necessary to fully understand present particleboard technology, but also important for the future upgrading and development of wood composites. This study was designed to develop some of this knowledge base. The two major objectives of this study were: (1) to investigate the influence of raw material characteristics on horizontal density distribution (HDD), and (2) to determine the effect of particleboard nonuniformity as defined by HDD, on some key board properties. Twenty six particleboard panels made with precisely cut particles were used to study the first objective, while thirty boards involving different particle sizes and distributions, and different wood species combinations and were manufactured to study the second objective. In addressing the first objective, the Equation S = a(1/A)b was found to be appropriate for relating standard deviation of density (S) and specimen size (A), where a and b are constants. At relatively larger specimen sizes, particleboard made with larger particles exhibited greater density variation, while particleboard made with smaller particles showed larger variations at smaller specimen sizes. Two aspects of voids, namely number and size, were identified as factors contributing the relation between particle size and HDD. iii In addition, a layer concept was developed to relate particle thickness, wood density, board density and board thickness to HDD. This concept predicted a decrease of density variation as particle layers increased. In addressing the second objective, modulus of rupture (MOR), modulus of elasticity (MOE), internal bond (TB) and thickness swelling (TS) of particleboard were shown to be greatly controlled by nonuniformity of board structure. All these properties were improved as structure uniformity improved. A nonuniformity effect concept, expressed as P = m(1/S) was proposed in relating board properties (P) to standard deviation (S) of horizontal density, in which, m and n are constants. While TS was influenced most by the high density portions, mechanical properties were dominated by the low density areas. The concept of HDD was also used in this study to investigate the relationship of specimen size effect on TB and TS, for one commercial waferboard. Both average values and standard deviations of TB and TS decreased as specimen size increased. A criterion based on HDD concept was proposed for the future establishment of testing standard in terms of specimen size selection. The relationship between HDD, raw material characteristics and board properties, demonstrated that HDD was a fundamental variable useful for characterizing particleboard structure and technology. The HDD concept has the potential of linking the effects of raw material characteristics and forming techniques to board properties in short-fiber wood composites. iv TABLE OF CONTENTS ABSTRACT ii TABLE OF CONTENTS iv LIST OF TABLES LIST OF FIGURES viii x ABBREVIATIONS USED xvi ACKNOWLEDGEMENT xvii 1. INTRODUCTION 1 2. LITERATURE REVIEW 5 2.1. Pressing strategy 5 2.2. Raw material characteristics 7 2.2.1. Particle geometry 7 2.2.2. Wood density 8 2.3. Resin content 10 2.4. Dimensional Stability 11 2.5. Model Development 12 2.6. Particleboard Standard 13 2.7. Particleboard Structure 15 2.8. Paper Structure 24 2.9 Summary 31 3. RESEARCH DIRECTION 32 4. METHODOLOGY 34 4.1. Materials 34 4.1.1. Roundwood 34 4.1.2. Wood particles 35 4.1.2.1. Specialty particles 35 4.1.2.2. Commercial and laboratory particles 35 V 4.1.3. Adhesive 38 4.1.4. Commercial wood products 38 4.1.4.1. Waferboard 39 4.1.4.2. Parallam 39 4.1.4.3. Medium density fiberboard (MDF) 39 4.1.4.4. Waferboard/OSB 40 4.1.5. Laboratory particleboard 4.2. Density Measurement 40 41 4.2.1. Density measurement methods 41 4.2.1.1. Gravimetric method 41 4.2.1.2. X-ray scanning method 44 4.2.1.3. y-ray method 46 4.2.2. Sampling of density specimens 4.2.2.1. Gravimetric method 46 46 4.2.2.1.1. Laboratory particleboard 46 4.2.2.1.2. Commercial waferboard 48 4.2.2.2. X-ray and y-ray methods 4.3. Determination of Board Properties 31 51 4.3.1. Modulus of rupture and modulus of elasticity 51 4.3.2. Internal bond 52 4.3.3. Thickness swelling 53 5. RESULTS AND DISCUSSION 55 5.1. Aspect of Horizontal Density Distribution 55 5.1.1. Phenomenon of horizontal density variation 5.1.2. Relationship between standard deviation of density and specimen size 62 5.1.3. Estimation of S to A relationship 67 vi 5.2. Influence of Raw Material Characteristics on Horizontal Density Distribution 68 5.2.1. Particle size 68 5.2.1.1. Parameter b 77 5.2.2. Particle thickness, wood density, board thickness and board density 82 5.2.2.1 Layer concept 82 5.2.2.2. Verification of layer concept 83 5.2.2.2.1. Particle thickness 83 5.2.2.2.2. Wood density 86 5.2.2.2.3. Board thickness 89 5.2.2.2.4. Board density 91 5.2.3. Summary 93 5.3. Implication of Horizontal Density Distribution on the Selection of Specimen Size for Some Particleboard Property Evaluations 95 5.3.1. Introduction 95 5.3.2. Internal bond 96 5.3.3. Thickness swelling 112 5.4. Influence of Horizontal Density Distribution on Some Board Properties 119 5.4.1. Introduction 119 5.4.2. Application of adhesive 119 5.4.3. Board formation 122 5.4.4. Modulus of rupture and modulus of elasticity 126 5.4.5. Internal bond 133 5.4.6. Thickness swelling 133 vii 5.4.7. Summary . 137 138 6. SUMMARY AND CONCLUSIONS 140 6.1. Future Developments 7. LITERATURE CITED 142 APPENDICES 149 A. Description of Particles Used for the Study of the Influence of Horizontal Density 149 Distribution on Board Properties B. Description of Obtainment of TB Specimens 156 for Commercial Waferboard C. Description of Obtainment of TS Specimens 157 for Commercial Waferboard D. Derivation of Equation (13) Var(Da)/Var(Db) E. Derivation of Equation (19) Var(Db) = = AilAa [(1+p)Var(D)]/2 F. Derivation of Equation (21) Var(Db)/Var(Da) = (112)21) 158 159 160 0. Significance Test of Parameter b in Equation (23) 161 H. Derivation of Equation (24) Var(Db) 164 = (la/lb)Var(Da) I. Derivation of Equation (38) a = x(S) 165 J. Derivation of Equation (41) ç = iV(S)c 166 viii LIST OF TABLES Table 1. Roundwood information 34 Table 2a. Particles used for studying particle size effect on horizontal density distribution Table 2b. Particles used for verifring layer concept Table 3. Particleboards used to verif5r layer concept Table 4. Particleboards used to study the influence of horizontal density distribution on board properties Table 5. 36 37 42 43 Partitioning procedure for density determination of commercial waferboard 50 Table 6. Density determination of commercial waferboard 60 Table 7. Density determination of laboratory particleboard 69 Table 8. S to 1/A models for laboratory particleboard 70 Table 9. Comparison of density variations in X and Y directions 82 Table 10. Particleboards with different particle thicknesses 84 Table 11. Particleboards with different wood species 87 Table 12. Particleboards with different board thicknesses 89 Table 13. Particleboards with different board densities 93 Table 14. Internal bond results of commercial waferboard at different specimen sizes 97 Table 15. Thickness swelling (%) of commercial waferboard at different specimen sizes and soaking times Table 16. Density measurement for laboratory particleboard 113 123 Table 17. Modulus of rupture and modulus of elasticity of laboratory particleboard Table 18. Internal bond and thickness swelling 129 ix of laboratory particleboard Table G-1. Calculations for normal distribution test .134 162 x LIST OF FIGURES Figure 1. A typical vertical density profile of a three layer particleboard (Data from Plath and Schnitzler, 1970) Figure 2. A schematic of a particle mat (Adapted from Suchsland, 1967) 6 16 Figure 3. A schematic theoretical horizontal density distribution of particleboard. Values in brackets are particle thickness (Adapted from Suchsland, 1959) 18 Figure 4. Particle distribution models in one layer (Kusian, 1968a) (b) Shifted deposition (a) Parallel deposition 19 Figure 5. Relationship between mat density and particle aspect ratio as given by Equation (3) 21 (Data from Kusian, 1968b) Figure 6. Relationship between probability of horizontal density distribution and particle dimension as given by Equation (4) (Adapted from Kusian, 1968a) 22 Figure 7. Relationship between average particle overlapping length and particle dimension as given by Equation (5) (Adapted from Kusian, 1968a) Figure 8. A photograph of a 2.5 g/m2 23 sheet of paper (Kailmes and Corte, 1960) Figure 9. A random network of lines (Kallmes and Corte, 1960) 25 27 Figure lOa. Distributuin characteristic of void size of one paper sheet with NIL = 69 (Adapted from Kailmes and Corte, 1960) Figure lOb. Variance of distribution of mass density of one machine made paper as functions of 29 xi specimen size (Data from Corte, 1970). Figure 11. Drill press set-up for density determination 30 45 Figure 12. A schematic of the procedure for allocating drilling specimen 47 Figure 13. Cutting pattern for preparing test specimens for laboratory particleboard 54 Figure 14. Horizontal density variation of one commercial waferboard 56 Figure 15. Density distribution characteristic of one commercial waferboard at specimen size of 29.16 cm 2 57 Figure 16. Density distribution characteristic of one commercial waferboard at specimen size of 0.31 cm 58 Figure 17. Standard deviation of density vs. specimen size of one commercial waferboard 61 Figure 18. Scatter plot of standard deviation of density vs. 1/’iKof one commercial waferboard 63 Figure 19. Relationship between correlation coefficient of density and Lag for one commercial waferboard/OSB 65 Figure 20. Influence of particle length on standard deviation of density of particleboard at several specimen sizes. Data sets with same particle width are connected and labeled by width (cm) 71 Figure 21. Influence of particle width on standard deviation of density of particleboard at several specimen sizes. Data sets with same particle length are connected and labeled by length (cm) Figure 22. Influence of particle size on standard deviation of density at several specimen sizes. The curve 72 xii is fitted by eye without regression analysis 73 Figure 23. A schematic of particle and void distribution in one layer under hand-forming operation (a) Small particle (b) Large particle 75 Figure 24. Influence of particle size on parameter b. The curve is fitted by eye without regression analysis 79 Figure 25. Relationship between parameter b and density variation . The curve is fitted 2 at specimen size of 0.141 cm by eye without regression analysis 80 Figure 26. Relationship between correlation coefficient of density and Lag for MDF and Parallam 81 Figure 27. Influence of particle thickness on density variation. The lines are model predictions, and points are experimental measurements 85 Figure 28. Influence of wood density on density variation. The lines are model predictions, and points are experimental measurements 88 Figure 29. Influence of board thickness on density variation. The lines are model predictions, and points are experimental measurements 90 Figure 30. Influence of board density on density variation. The lines are model predictions, and points are experimental measurements 92 Figure 31. 2-P and 3-P Weibull distribution fits to internal bond of one commercial waferboard at specimen size of 6.27 cm2 Figure 32. 2-P and 3-P Weibull distribution fits to internal 98 xiii bond of one commercial waferboard at specimen size of 225.79 cm 2 99 Figure 33. Influence of specimen size on 50th percentile and average strength of internal bond of one commercial waferboard 101 Figure 34. Relationship between average strength of internal bond and standard deviation of density of one commercial waferboard 103 Figure 35. Influence of specimen size on standard deviation of internal bond of one commercial waferboard 104 Figure 36. Relationship between standard deviation of internal bond and standard deviation of density of one commercial waferboard 106 Figure 37. Relationship between density and internal bond of one commercial waferboard at specimen size of 6.27 cm 2 107 Figure 38. Relationship between density and internal bond of one commercial waferboard at specimen size of 225.79 cm2 108 Figure 39. Influence of specimen size on coefficient of variation of internal bond of one commercial waferboard. The curve is fitted by eye without regression analysis 109 Figure 40. Influence of specimen size on 5th percentile, 95th percentile and average of internal bond of one commercial waferboard Figure 41. Influence of specimen size on average thickness 110 xiv swelling of one commercial waferboard at different soaking times 114 Figure 42. Influence of specimen size on standard deviation of thickness welling of one commercial waferboard at different soaking times 115 Figure 43. Thickness swelling vs. soaking time of one commercial waferboard at specimen size of 4.26 cm 2 Figure 44. Influence of apparent resin content on internal bond 117 121 Figure 45. Standard deviation of density vs. specimen size for laboratory particleboard 124 Figure 46. Standard deviation of density vs. 1/A for laboratory particleboard Figure 47. Reproducibility of board formation of board P1 125 127 Figure 48. Relationship between modulus of rupture and standard deviation of density of laboratory particleboard. The specimen size used to determine standard deviation of density is different and indicated in each plot 130 Figure 49. Relationship between modulus of elasticity and standard deviation of density of laboratory particleboard. The specimen size used to determine standard deviation of density is different and indicated in each plot 132 Figure 50. Relationship between internal bond and standard deviation of density of laboratory particleboard. The specimen size used to determine standard deviation of density is different and indicated in each plot Figure 51. Relationship between thickness swelling and standard deviation of density of laboratory particleboard. The 135 xv specimen size used to determine standard deviation of 136 density is different and indicated in each plot Figure A-i. Distribution of dimensions of aspen commercial particle p1. n = number of observations, = average, s = standard deviation.. .. 150 Figure A-2. Distribution of dimensions of aspen commercial particle p2. n = number of observations, 5 = average, s = standard deviation. 15i . Figure A-3. Distribution of dimensions of aspen commercial particle p3. n = number of observations, = average, s = standard deviation. 152 . Figure A-4. Distribution of dimensions of aspen laboratory particle p5. n = number of observations, I = average, s = standard deviation. 153 . Figure A-5. Distribution of dimensions of aspen laboratory particle p6. n = number of observations, = average, s = standard deviation. . . 154 Figure A-6. Distribution of dimensions of birch laboratory particle p7. n = number of observations, 5 = average, s = standard deviation.. 155 Figure D-1. Relationship between specimen sizes 158 Figure E-1. Diagram showing Ab = 2Aa 159 Figure G-1. Residual plot based on Equation (23) 161 Figure H-i. Diagram showing the layer concept 164 xvi ABBREVIATIONS USED HDD TB MDD M1)F MOE MOR OSB RBA TS - - - - - - - - - horizontal density distribution internal bond mass density distribution medium density fiberboard modulus of elasticity modulus of rupture oriented strand board relative bonded area thickness swelling xvii ACKNOWLEDGEMENT I would like to thank Dr. Paul Steiner, Department of Wood Science, UBC, for his invaluable direction, supervision and patience throughout this project. I also wish to thank my supervisory committee, Drs. David Barrett, Simon Ellis, Valerie Lemay and Anoush Poursartip, UBC, for their guidance during this thesis study. Thanks also go to Dr. Ricardo Foschi, Department of Civil Engineering, UBC, for his encouragement and suggestions. The assistance of Pansmill Woodenware Ltd., CAE Machinery Ltd. in producing particles, and the permission of both Forintek Canada Corp., forthe use of their particle screening device, and of Canadian Forest Products for the use of a y-ray density measurement device are all readily acknowledged. The help and cooperation of technician staff, Department of Wood Science, UBC, especially Mr. Rob Johnson and Mr. Bob Myronuk are appreciated. I would also like to thank Weyerhaeuser Canada and Asa Johal for their financial support of my Ph.D. studies. Finally, my greatest gratitude goes to my parents and my wife for their continuous support and patience during my educational studies. 1 1. INTRODUCTION The concept for creating particleboard*, a sheet-like product of wood particles bonded with an adhesive, has been known since the beginning of this century. The first plant for particleboard production was erected in Germany in 1941 (Kollmann et al., 1975). Since then, worldwide research and development efforts have resulted in the emergence of several major particleboard-type products and corresponding manufacturing techniques, together with dramatic improvements in board properties. The properties and performance of lamella based wood composites can be predicted from the laminate theory (Agarwal and Broutman, 1980), by knowing the laminae property and laminate lay-up. In contrast, a general theory on short-fibre wood composites is lacking, although some modelling efforts on Oriented Strand Board (OSB), a typical short-fibre wood composite in North America, have been attempted in the past decade (Higgins, 1989; Lau, 1982; Shaler and Blankenhorn, 1989). Consequently, particleboard technology has been limited to the evaluation of board properties as functions of intermediate characteristics, such as production parameters, rather than basic variables (Suchsland, 1959). Since any given process has a vast number of variables which often interact in a complex manner, the task of developing a fundamental knowledge base about particleboard process or properties on the basis of these intermediate characteristics becomes almost impossible (Kunesh, 1961). Therefore, a more basic analytical characteristic needs to be Throughout this thesis, the term “particleboard” is used in the broad sense of the FAO (1957) and interchangeably with the term “short-fibre wood composite”. This covers all dry formed boards made with sawdusts, splinters, flakes or wafers. Commercial products are designated by their specific names. * identified. It may be argued that for commodity type particleboard products, which typically have been developed through trial-and-error methods, a complete and thorough understanding of the effects of manufacturing variables is not necessary. However, in the past, an improved understanding of manufacturing technology has helped the development of new products, new production techniques and new quality control methods. Such developments as OSB and steam-injection pressing technology and the use of vertical density profile measurement as a quality control method are evidences of this trend. Improved understanding of the fundamental principles of wood composites is believed to be a key factor for the design of new generations of products, and the upgrading of existing boards. Recent investigations of short-fibre wood composites have been directed at an improved understanding of particle behaviour during pressing, reducing board density and improving dimensional stability while maintaining or increasing strength properties, and basic mechanical behaviour of particleboard. These studies have recognized several common concepts referred to as “localized distribution of stress” (Humphrey, 1989), “voids”, “void volume”, “particle packing” (Steiner, 1989) and “local contact” (Hansel and Neumuller, 1988; Hansel and Niemz, 1989), which reflect the spatial nonuniformity of the structure of particulate composites. Spatial structure is believed to be one of the most fundamental and important characteristics affecting basic particleboard properties. The spatial structure of particleboard can be defined by the concept of a three-dimensional-density-distribution, which can be separated into a 3 vertical component and a horizontal component. The vertical component, i.e., the vertical density profile, which indicates the density variation through the horizontal layers in the thickness direction, has been extensively studied. The relationships between vertical density profile, pressing strategy and board properties are well documented (Kelly, 1977). The concept of horizontal density distribution (HDD) or variation, proposed by Suchsland (1959), which characterizes the horizontal micro-density nonuniformity in the plane of the board, has never been determined directly (Suchsland and Xu, 1989). The relation of HDD to raw material characteristics and board properties is not well understood. It is this density distribution component which will be the subject of this study. The hypotheses of this thesis were that raw material characteristics have an overall effect on HDD of particleboard, and this distribution influences board properties. These hypotheses were addressed in three phases. The first phase undertook a quantitative determination of HDD in relation to raw material characteristics. In the second phase, the effect of test specimen size on some board properties was studied to establish the importance of the HDD concept for future testing standard development, in terms of specimen size designations for two particleboard property evaluations. In the third phase, boards with different HDD characteristics were made by choosing different particle size ranges, different wood species and combinations of each. Physical and mechanical properties of these boards were compared to determine the significance of HDD of particleboard on physical and mechanical property variations. 4 Contrary to naturally formed products, such as solid lumber, particleboard is a manufactured material involving complicated synthetic processes. Developing this knowledge may provide a useful means to rationalize choices of raw material characteristics and lay-up (formation) methods to improve the performance and efficiency of wood-based composite products, and to develop a criterion for designating specimen sizes for some board property determinations. The attainment of this knowledge may also present a critical step towards establishing a three dmensional density distribution for short-fibre wood composites. The concept of a three dimensional density distribution would allow the structural characteristics of particleboard to be described in an improved fashion, and lead to the possible development of a general theory on short-fibre wood composites similar to the laminate theory for continuous fibre composites. 5 2. LITERATURE REVIEW 2.1. Pressing strategy In the development of particleboard technology, two subjects have received much attention. One of these was the effect of pressing strategy on board properties. This included parameters such as press closing speed (a function of pressure applied), temperature, moisture content and its distribution, and more recently steam-injection pressing. The second subject concerned the influence of raw material characteristics on board properties. Wood density, particle shape and particle geometry, including length, width, thickness, lengthJthickness ratio, length/width ratio and width/thickness ratio, were the main parameters. Studies emphasizing pressing strategy identified the vertical density profile as an important factor affecting many board properties. A typical vertical density profile of particleboard is shown in Figure 1. This density profile is formed during the pressing process when wood particles in different layers of the mat experience different conditions of temperatures and moisture contents, which affect their compressibility and stress relaxation behaviour (Kelly, 1977). The contribution of these parameters to the formation of vertical density profile has been extensively studied and is well understood. In general, increasing pressing temperature, particle moisture content and press closing speed or pressure leads to differences in density between surface and core regions of the panel (Fahrni, 1956; Geimer, 1982; Geimer et a!., 1975; Heebink et a!., 1972; Strickler, 1959; Suchsland, 1962). A close relationship has been identified between vertical density profile and most board properties. Specifically, modulus of rupture (MOR) and modulus 6 1.0 0.9 I I 0.8 0.7 0.6 0.5 0 5 10 15 Thickness (mm) Figure 1. A typical vertical density profile of a three layer particleboard (Data from Plath and Sehnitzler, 1970). 20 7 of elasticity (MOE) are favourably affected by the increase of particleboard surface density (Fahri, 1956; Geimer et al., 1975; Heebink et al., 1972; Plath, 1971b; Plath and Schnitzler, 1974; Strickler, 1959); internal bond (TB) is improved by increasing core density (Neusser, 1978; Plath and Schriitzler, 1974); and layered torsion shear strength is positively related to individual layer density (Shen and Carroll, 1969, 1970). As a result, the singular parameter of vertical density profile has been used extensively to characterize the effects of pressing strategy, which involves multi-parameter effects. For example, vertical density profile measurement has been used, to a certain extent, as a quality control method (Gibbon and Tundak, 1989; Lemaster, 1989). Thickness swelling (TS) is one property which does not seem to be strongly related to vertical density profile. 2.2. Raw material characteristics 2.2.1. Particle geometry The effects of particle geometry on board properties have not been as conclusive as have pressing strategy parameters. The effects of particle length, thickness and lengthJthickness ratio on MOR and MOE appear to be well documented. However, most reports offered only general or conditional statements, such as MOR and MOE improve as particle length or length/thickness ratio increases within certain ranges (Brumbaugh, 1960; Gatchell et al., 1966; Kimoto et al., 1964; Lehmann, 1974; Mottet, 1967; Post, 1958, 1961; Rackwitz, 1963; Stewart and Lehman, 1973; Turner, 1954). While general statements could be extracted from the literature that TB improves as the particle configuration changes from a long, wide flake to planar shavings or to slivers, some exceptions to this finding have been documented 8 (Brumbaugh, 1960; Gatchell et al., 1966; Heebink and Hann, 1959; Rackwitz, 1963; Lehman, 1974; Stewart and Lehman, 1973; Talbott and Maloney, 1957). Most reports were unanimous in stating that better thickness stability is obtained with boards produced from thin particles rather than from thick particles. Much less agreement was found regarding the influence of particle length and width on TS. Many studies utilized particles produced by a variety of production methods. These represented wide variations in particle geometries which were often not documented. Consequently, it is uncertain if published information concerning the particle geometry effect on board properties presents the true picture. Furthermore, no satisfactory explanation for describing how particle geometry may affect board properties is offered, although some qualitative analyses were made regarding the effect of particle length and width on MOR and TB (Kusian, 1968a; 1968b; Rackwitz, 1963;). Strictly speaking, it is difficult to separate and study one geometric parameter from another, since changes in one parameter will affect some other parameters. For example, changes in particle length will alter length/thickness and length/width ratios. Therefore, a more basic parameter(s) or variable(s) is needed to characterize the effect of particle geometry on board properties, similar to the manner in which vertical density profile is used to quantify the influence of pressing strategy on board properties. 2.2.2. Wood density Wood composites have been manufactured from a variety of wood species. Usually, a particular wood composite is assembled from one or two 9 main wood species, or a combination of wood species. The typical example would be Waferboard/OSB production in North America, where aspen (Populus Spp.) is the main raw material of choice. The choice of a specific wood species or species combinations and the establishment of corresponding manufacturing technology were usually accomplished through extensive experimental studies. Wood density was found to be the primary factor influencing board properties and for the selection of manufacturing parameters. At the same product density and manufacturing conditions, particleboard made from higher density wood species was always inferior both in mechanical and dimensional stability properties than particleboard made from lower density wood species (Hse, 1975; Kehr, 1979; Stegmann and Durst, 1964; Stewart and Lehmann, 1973; Vital et al., 1974). Compaction ratio, which is the ratio of board density to wood density, has been proposed as a concept to guide the selection of production parameters (Hse, 1975). It is generally accepted that a minimum range of compaction ratios of 1.3 necessary to achieve reasonable board properties. - 1.5 are Consequently, substantially higher particleboard density results when high density wood species are used, provided that other board manufacturing conditions are the same. It is recognized that the concept of compaction ratio was based on experimental evidence, rather than on real composite structure consideration. Limited studies in the past suggest that disbonding between particle surfaces in tension and bending modes control the failure mechanism in particleboard (Laufenberg, 1984; Rackwitz, 1963; Suchsland, 1968). This may explain why the higher wood strength associated with high wood density does not contribute to board properties as expected. This also suggests that 10 knowledge of particleboard structure is necessary to fully understand how wood density affects board properties, and subsequently the design and manufacture of wood composites. 2.3. Resin content Particleboard adhesive level studies, traditionally expressed as the weight percentage of solid resin relative to the oven-dry weight of wood particles, have been conducted mainly with liquid phenolic or urea formaldehyde systems. Investigators were unanimous in their findings that increasing resin content increased all strength properties and improved dimensional stability of particleboard (Kelly, 1977). But the magnitude of this improvement was property dependent. Higgins (1990) reported that in aspen boards made with randomly oriented short strands, MOR increased according to a diminishing curvilinear relationship with increasing resin content. Only small strength gains were achieved above 7-10 percent resin content. This general trend has also been reported with other wood species at different conditions (Adams, 1981; Kehr, 1967; Kimoto et al., 1964; Lehmann, 1970; Post, 1961; Price, 1974). Internal bond is the most sensitive property responding to resin content changes. The literature showed a continuous increase in TB as resin content increased in the ranges studied (Lehmann, 1970; Kehr, 1967). This suggests that the TB test is the most appropriate for studying bonding in short-fibre wood composites. Thickness swelling was also positively affected by increasing resin content, but the same literature suggested that the improvement was not as significant as that for TB. However, the effect of 11 resin content on TS was greatly influenced by test method, board density and other manufacturing conditions (Xu, 1989). Instead of expressing resin content as a weight percentage of wood, the calculation of resin content based on particle surface area may be more appropriate in studying adhesive level effects. The importance of particle thickness on adhesive requirements relative to particle surface area was considered by Post (1961) and Gunn (1963). However, constant resin contents based on wood weight have been historically used as a basis for different studies. Thus, studies relating wood density and particle geometry, especially particle thickness effects to particleboard properties are ambiguous, since actual quantities of resin on a particle surface area basis are inconsistent. While limited information has been reported on adhesive level effects for powder adhesive, other adhesive characteristics, like flow properties and wood anatomy interactions were reviewed and studied by Ellis (1989). 2.4. Dimensional stability Thickness swelling in particleboard is usually taken as a primary measure of dimensional stability, although linear expansion properties are also considered in some cases. Thickness swelling generally originates from two sources. One is from the hygroscopic swelling of wood itself which is a reversible process. The other is from the release of compressive stress incorporated into the particleboard during the pressing operation, which is an irreversible process and the major component of TS. Several important studies on the rheological behaviour of wood in compression perpendicular to the grain were undertaken to better understand TS phenomenon (Kunesh, 1961; Kollmann, 1962; Young, 1957; Wang, 1985, 1987a, 1987b). Some 12 possible strategies for improving dimensional stability and at the same time decreasing the density of particleboard were proposed. These included maintaining a high moisture content during the pressing operation (Kunesh, 1961), and increasing the compressibility of particle surfaces by chemical treatment (Wang, 1989). However, very limited experimental progress has been reported on these aspects. A complicating factor is that the aggregate of particles in a mat respond to the applied force in a nonuniform manner, due to the heterogeneous structure of the particle mat. Knowledge obtained from studying solid wood cannot be applied directly to the particleboard pressing operation. Therefore, understanding particleboard structure may be a prerequisite to improve TS behaviour. 2.5. Model development Because of the continual reduction in quality of the available timber resources, short-fibre wood composites will become a more important structural material in the future. The successful modelling of their elastic and strength properties will be a requirement for acceptance in engineering applications. Some modelling efforts have been made for OSB (Higgins, 1989; Lau, 1982; Shaler and Blankenhorn, 1989). These studies have utilized elasticity theory, the rule of mixtures (Agarwal and Broutman, 1980), the Halpin-Chai Equation (Halpin and Chai, 1967), a modified rule of mixture developed for non-wood fibre-polymeric composites, and the Hankinson formula (Bodig and Jayne, 1982), involving a simplified expression for offaxis strength estimation of wood. With all these theories, certain assumptions, such as a perfect alignment of particles, maximum bonding between particles and a continuous glueline were made. As some of these 13 assumptions are far from realistic for OSB, discrepancies were found between model predictions and experimental results. Particleboard made with randomly distributed particles is probably more difficult to model than OSB, since its structure is even more difficult to define. Just as knowledge of laminate lay-up is an essential element of laminate theory, knowledge of particleboard structure is believed to be the prerequisite for the successful modelling of its material properties. 2.6. Particleboard standard Historically, wood-based panel products were manufactured according to descriptive product standards, such as PS 1-74 for commercial and industrial plywood (U.S. Department of Commerce, 1974), ANSI A208.1 for mat formed wood particleboard (American National Standards Institute, 1979) in the United States, CSA-0121-M78 for plywood (Canadian Standard Association, 1978), and CAN3-0188.2-M78 for waferboard and OSB (Canadian Standard Association, 1978) in Canada. These standards are manufacturing prescriptions in which the raw material and method of assembly into large sheets are set down for minimum product requirements. They prescribed how the products should be manufactured without being directly concerned about their service applications (O’Halloran, 1980). As a consequence, change or modification of manufacturing process, development of new products or use of new raw materials were hampered by these rigid standards. Acceptance by major building codes of products deviating from these product standards was extremely difficult. By 1980, a new approach emerged for wood composites, with the development of performance standard, such as Performance Standards and 14 Policies for Structural-Use Panels by the American Plywood Association (1980) and Construction Sheathing by Canadian Standards Association (1988). In contrast to a product standard, a performance standard defines requirements of specific end use application of the product. The objective was to assure that for a particular end use the product would satisfSr the requirement of the application for which it was intended (O’Halloran, 1980). Since product manufacturing procedures were flexible (within a product category), products could be accepted by building codes as long as it satisfied the specific performance standard for the application. Therefore, performance standards allow for innovations. It should be emphasized that the development of performance standards was not the result of improvements in the fundamental understanding of particleboard technology. Beginning in the mid 1980’s, a reliability-based limit states design philosophy based on engineering computations for timber structure emerged in Canada (Canadian Standard Association, 1984). A U.S. version is now being considered. Currently, short-fibre wood composites are used together with other products in timber structures. Although this mixture is accepted by building codes through performance standards, a reliability level is not calculated either for wood composites or the whole system. This deficiency will be recognized more as reliability-based design becomes more prevalent. It is believed that successful modelling of strength characteristics, and establishment of design values are needed for reliability calculations of wood composites or structures involving wood composites. Since fundamental knowledge of wood composites is limited, design properties for engineering calculations have not been established or recognized, even though some 15 efforts have been made to achieve this goal (McNatt, 1973; O’Halloran, 1988). Further knowledge of structure and other fundamental aspects of wood composites would help this effort. 2.7. Particleboard structure The concept of HDD in particleboard, was first proposed by Suchsland (1959) to analyze particleboard process. A schematic presentation of a particle mat, which consists of wood particles and voids interspersed is shown in Figure 2. If very small vertical sections reaching from one surface of the board to the other were isolated and their densities measured, one would find that the densities vary to a smaller or larger extent about the average overall board density (Suchsland and Xu, 1989). A model, based on a stack of veneers each containing equal number of randomly distributed holes, was developed to characterize this density variation of particleboard (Suchsland, 1959). From this model structure, the distribution of the sums of the veneer thicknesses over any small area element followed a binomial distribution defined as 0(m) = (1) where 0(m) = fraction of total area over which the number of solid veneer elements is equal to m; n = total number of veneer layers; p = 1 A A = relative air volume of each veneer layer. - = relative wood volume of each veneer layer; __ ____ ___ 16 k\\\ F R 1 I\\\N RV \\\ \\1 k\’ F I\1 I\\\I \\\ k\I ‘I k\ \\N I\ k\\i l\\\I k\\ k\ I k\\I i\\ \“i \\\\ I \\1 \\\\ \I 1\\\N k\ \iJ\\\1 kI ISi__h\i I\\I k\ i\\V1 1\\\\I h\\I \c\\H\\\ F1 [\\I [\\\I l\ \\[ k-\I k\\ t\\I I\\\I k’\ \\\\I \\\J I\\\\1 T \\1 1\ k1 t\\\1 \ \ \[ kN I\\\ I I\\1 I\I k\ f\\\I I\Ik\\I I\\J I\\ \\\\1 I’\\ \\\1 t\\\ l\\jl\\\1 I\ I\1 ‘\\I I’\I I\M k\\\I I i\\i I\I \\ t\\ ET R\\ii\\\L j\ \‘1 l \ \\4 t\\’\I I\\I [\\\\ \ I \ I \\\\I\\ F\’\I j\ ‘I \1 I\’L \\\I1\\ \I_I\_\ l\\iI\\ 1\\! I 1\ \S t\ \1 - L\_.\_\\_I I\\\ILILd L\\\R\i l I \\H\TI I \ \ Figure 2. A schematic of a particle mat (Adapted from Such sland, 1967). 17 The resulting theoretical density distribution derived from this binomial distribution would be like one of the curves shown in Figure 3. The possible effect of particle dimension on density distribution is also shown in Figure 3, which indicated a more uniform structure as particle thickness decreases, and particle shape changes from long slender to square ones. The significance of relative area of compressed solid wood instead of the average board density for developing bending strength was also realized (Suchsland, 1959). Another model, consisting of narrow veneer strips arranged in mutually perpendicular layers so that veneer strip overlap area becomes the element of a matrix representing the variation of the amount of wood material, was developed 30 years later (Suchsland and Xu, 1989). Direct measurements of TB and TS on these matrix elements were used to study the effects of nonuniformity of particleboard structure and other processing variables (Suchsland and Xu, 1989; 1991). Although these approaches were mainly efforts to simulate the structure of particleboard using veneers or veneer strips, it appears that at this time Suchsland was the principal researcher attempting to identify this relationship. In investigating the influence of particle size on the structural and strength properties of particle materials, another researcher also realized the nonuniformity of particleboard structure (Kusian, 1968a; 1968b). Unlike the “brick” structure model in Figure 2, localized deposition of arbitrarily oriented particles within circular areas was taken as a geometric model (Figure 4). As this model was based on plane projections, both particle length and width could be analyzed. First, the number of particles deposited in one layer was calculated based on model (a) and a more compact model (b) in 18 C.? I 0.0 0.4 0.8 1.2 1.6 Density (g/cm3) Figure 3. A schematic theoretical horizontal density distribution of particleboard. Values in brackets are particle thickness (Adapted from Suchsland, 1959) 2.0 19 a b Figure 4. Particle distribution models in one layer (Kusian, 1968a). (b) Shifted deposition (a) Parallel deposition 20 Figure 4. Then, the overlapping and crossing of particles in between layers were considered. Kusian (1968a) was able to relate void volume of particle mat, mat density, probability of horizontal density variation and average particle overlapping length to particle size. For model (a), Kusian (1968a) showed that the relationship between mat density and particle size could be expressed as [mI Dmat2Dwii 2 +lj (m2 — (2) \m 2 +1 I in which, Dmat and D are the densities of the particle mat and wood particles, m = 1/b is the aspect ratio between particle length 1 and width b. The probability (f) of horizontal density variation was given by m+1 1 f=k (3) 1 where k = Wmat/(DwdFmat), W and Fmat are the weight and surface area of particle mat respectively and d is the particle thickness. For model (b), the average particle overlapping length L was expressed as L = 2b -- iJm2 It 3 +1 + 12 2 in m 4 +1+1 m m2+1_1 4 + m in Jm + + .Jm2+1_m) These analyses predicted a particleboard structure with less horizontal density variation and longer particle overlapping length when particle length and width increased, and a particle mat with less void volume as aspect ratio increased. Figures 5, 6 and 7 are graphical presentations of Equations (2), (3) and (4) respectively. Although only the mat density expression was compared 21 0.6 0.5 0.4 I 0.3 0.2 0.1 0.0 0 7 14 28 21 Aspect Ratio m = 1/b Figure 5. Relationship between mat density and particle aspect ratio as given by Equation (3) (Data from Kusian, 1968b). 35 22 1.0 0.8 C) C) 0.6 Cu C) 0.4 Cu 0 0.2 0.0 0 8 16 Aspect Ratio m 24 = 32 1/b Figure 6. Relationship between probability of horizontal density distribution and particle dimension as given by Equation (4) (Adapted from Kusian, 1968a). 23 20 16 I 12 8 4 0 0 8 16 24 Aspect Ratio m = lJb Figure 7. Relationship between average particle overlapping length and particle dimension as given by Equation (5) (Adapted from Kusian, 1968a). 32 24 with experimental data (Figure 5), Kusian’s (1968a) mathematical analyses was helpful in understanding the significance of particle size (length and width) in terms of particleboard inner structure. 2.8. Paper structure 2 sheet of paper, Figure 8 is a reproduction of a photograph of a 2.5 g/m roughly showing the arrangement of wood fibres in actual paper (Kailmes and Corte, 1960). Similar to particleboard products, the strength of paper comes from the interactive forces between fibres, although it is recognized that no adhesive is added during paper making. Two requirements are necessary for such forces to operate. First of all, fibres must be brought into close contact. Secondly, sites for adhesion must be present on the surfaces of these fibres (Page, 1969). The pressing operation in particleboard is designed to achieve similar effects. An estimation of relative bonded area (RBA) or the relative contact area of fibres, achieved by measuring the light scattering coefficient of paper, was developed by Parsons (1942). This technique is presently used in paper physics studies. The influence of fibre coarseness and the extent of beating on RBA, and the contribution of RBA to the mechanical properties of paper have been studied extensively (Ingmanson and Thode, 1959; Jones, 1972; Page, 1969; Parson, 1942; Rathff 1949; Seth, 1990). Generally, beating increases RBA, coarser fibres decrease RBA. While tensile and burst strength are positively related to RBA, tear strength seems negatively related to RBA. Page’s (1969) theory predicts a linear relationship between tensile strength and RBA of paper. Another similarity between particleboard and paper products is that both products exhibit different sized voids and local variation of the areal 25 Figure 8. A photograph of a 2.5 gIm 2 sheet of paper (Kailmes and Corte, 1960). 26 mass density in the direction of the plane. The term distribution of the mass density (DMD) was coined to describe the latter for paper (Corte, 1969). These phenomenon arise from the fibrous network which makes up paper structure. Figure 9 shows a random fibre network of the same number and average length of lines as in Figure 8, in which the coordinates of the line centres were determined by random number pairs and the angle was uniformly distributed (Kailmes and Corte, 1960). Some similarities between Figure 8 and Figure 9 are apparent. The application of geometric probability to study this random paper network structure was initiated in 1953 (Le Cachenx, 1953), according to Corte (1982). For this random network, the probability of finding r fibre centres in a square was given by the Poisson Equation (Kailmes and Corte, 1960; Corte and Kalimes, 1961) p(r) e-mmr/r! = (5) where, m is the average number of fibre centres in a square. The frequency of void having a size between v and v+dv was given by (Kailmes and Corte, 1960) N[ f(v) = T Pie dv (6a) 2L in which, N is the average number of fibres intersecting a scanning line with length of L (cm). The variance of DM1) Var(d) was expressed as (Corte, 1969) Var(d) = 2 lwDk/a (6b) in which, d is the variable areal mass density, 1 is the fibre length, w is the 2 is the specimen weight per unit length of the fibre, D is the average of d, a size and k is a factor related to the size of fibre and specimen. I —3 28 Figure lOa shows the results of the actual measurement of void size distribution for one paper sheet with NIL = 69 fibres/cm, and the theoretical calculations by Equation (6a). A good agreement between theoretical consideration and experimental measurement was apparent. This good match indicates the randomness of fibre depositions during formation for this very low basis weight paper sheet (NIL = 69), which may not the case for real commercial paper sheet. For real paper products, the permeability study involving gas flow and mercury injection methods have to be used to estimate the void size distributions (Corte, 1965). The development of the f3-ray absorption technique in the 1960’s made the actual measurement of DMD possible. A comprehensive series of measurements comparing 24 different machine made papers was published in 1970 (Corte, 1970). Significant differences of DMD were found among these papers. The measured variance of DMD for one paper sample is plotted in Figure lOb, together with the theoretical variance of DMD calculated by Equation (6b). It is noted that the actual variance of DMD was significantly larger than the theoretical one based on the random network model. This provided a strong support for the long time claim in paper physics study that a random structure would yield the most uniform paper, and it should be the aim of the paper maker if reducing the variance of DMD is the objective. Improved understanding of structure-property relationship in paper physics study has recognized DMD as the most important and appropriate concept to quantify paper structure. However, no systematic research on the effects of raw material and processing variables on DMD have been reported, probably because of the relatively uniform distribution of fibre geometries in paper making. Nevertheless, a few scattered examples examined by Corte 29 60 50 —‘ 40 C.) C) I 30 20 10 0 0 10 20 30 40 50 60 ) 2 Void Size (10 cm Figure lOa. Distribution characteristic of void size of one paper sheet with NIL = 69 (Adapted from Kailmes and Corte, 1960). 70 80 30 10.0 7.5 I 5.0 2.5 0.0 0 30 60 Specimen Size 90 (2) Figure lOb. Variance of distribution of mass density of one machine made paper as functions of specimen size (Data from Corte, 1970). 120 31 (1982) and later studies (Seth, 1990; Sosznski and Seth, 1985) did indicate that many properties and the response of paper in different environments are related to DMD. According to Seth (1993), paper properties are always adversely affected by increasing the variance of DMD. 2.9. Summary While structural nonuniformity in particleboard and paper materials was probably recognized at approximately the same time, the concept of quantifying structure or controlling its formation has yet to be established for particleboard. In fact, a specimen size effect of the variance of HDD is not clearly defined yet for particleboard. As a result, our basic understanding of other aspects of particleboard has been severely hampered, as indicated in the literature review. It is believed that a detailed investigation on HDD may better understand the influence of raw material and forming method on particleboard structure, and through it, on board properties. It should be mentioned that several recent studies have also recognized the spatial structure of particleboard (probably related to HDD) and its significance to board properties (Hansel and Neumuller, 1988; Hansel and Niemz, 1989; Humphrey, 1989; Steiner, 1989). The fact that nonuniformity in particleboard structure has regained increasing attention from different research groups indicates the need for a more systematic study of this parameter. The main task of this thesis study was to examine the effect of raw material characteristics on panel nonuniformity (HDD) and the effect this nonuniformity has on selected particleboard properties. 32 3. RESEARCH DIRECTION Ultimately, horizontal density variation of particleboard and other physical and mechanical properties associated with the plane of the board could be treated as random processes or random fields. This treatment requires the measurement of point board properties, because the density variation concerned in this study is caused by voids, and the differences among boards could probably be detected only when the specimen size for determining this density variation is very small. However, if such techniques could be developed, within board variation of other point properties could be predicted just by knowing the horizontal density process, and the cross correlation functions of these random processes. Furthermore, the properties determined at large specimen size, which is used to discriminate different products, could also be obtained, provided that the relationship between point and large specimen size properties were known. The random field theory has been recently applied to model within board variations of MOE and compressive strength properties of Glulam (Wang and Foschi, 1992; Xiong, 1991). This thesis did not intend to quantify the within board point variations of particleboard properties (although it is also very important). Rather, the main objective of this thesis was to use the concept of HDD to study particleboard technology, by comparing physical and mechanical property differences among particleboards, which were themselves manufactured with different board formations. This endeavor was probably similar, to a certain extent, with the comprehensive in-grade testing program started in the late 197Os, with the objective to quantify the differences of various mechanical properties of different grades and sizes of lumber (Madsen, 1992). Therefore, 33 random field theory may not be necessary. Instead, an approach implied and later used by Suchsland (1959, 1991) was adopted for this study. As Figure 3 implies, given the same average board density, the fractional area that potential bonding may develop and the extent of micro nonuniformity of board structure could be characterized by the standard deviation of density. By studying this standard deviation parameter, determined at different specimen sizes, the contribution of raw material characteristics to board structural nonuniformity could be determined. The study of the relationship between this parameter and board properties would identify the significance of structural nonuniformity on physical and mechanical properties of particleboard. In the process of studying the structure of paper, image representation (Yang and Thorpe, 1977), spectrum presentation (Norman and Wahren, 1973), and direct visual examination of beta radiographs and density histogram method (Corte, 1971) have been used to characterize the structural nonuniformity. Corte (1982) concluded that “the characterization of the nonuniformity of paper by the variance of its DMD permits a numerical formulation to explore the effect of material and process variables on the uniformity of paper and through it, on its performance”. 34 4. METHODOLOGY 4.1. Material 4.1.1. Roundwood Two wood species, trembling aspen (Populus tremuloides Michx.) and white birch (Betula papyrifera Marsh.) were used to manufacture wood particles for this study. Trembling aspen trees were cut from the University of British Columbia (UBC) Research Forest at Williams Lake, B.C. White birch logs were obtained from the province of Alberta, while detailed information was not available. General species information is summarized in Table 1. Table 1. Roundwood information* Species Aspen White Birch Location Williams Lake, B.C. Alberta Harvest Time April, 1991 April, 1991 Diameter (cm) 34-44 14-18 100 100 0.469 0.578 0.029 0.041 n ) 3 Density (g/cm s * n = number of observations; = average; s = standard deviation. The density was determined based on approximately 1.5 cm x 1.5 cm x 10 cm wood specimens at an average moisture content of 6.8%. The actual volume was determined by the water displacement method (Heinrichs, 1954). 35 4.1.2. Wood particles 4.1.2.1. Specialty particles Precisely cut particles were used to study how raw material characteristics affect HDD (measured by the standard deviation of density) of particleboard. Green trembling aspen and white birch logs were debarked by hand and cut into about 40 cm long discs. These discs were then rotary peeled into veneers of predetermined thicknesses at Pansmill Woodenware Ltd. in Vancouver, B.C. The green veneers were cut into particles of predetermined sizes using a table saw. These particles were then slowly dried in a laboratory oven at temperatures of 40-80 OC to maintain the flatness of particles. Final particle dimensions at equilibrium moisture content of 6.8% were measured. Table 2a lists the result of this measurement for particles used for the study of particle size effect on HDD. Dimensions of particles used for the verification of layer concept are provided in Table 2b. From these tables, the difference of actual thicknesses of particle groups Al-Di, El and E2, Fl and F2, and Gl and G2 respectively could be considered negligible. Also for the purpose of analyses, the target length and width dimensions, which differed little from actual dimensions, were used for calculations. 4.1.2.2. Commercial and laboratory particles Commercial and laboratory particles were used to make particleboards with different HDD characteristics. Physical and mechanical properties of these boards were evaluated and related to the board HDD. The choice of * - 40 40 40 40 .640 .636 .637 .636 .024 .022 .025 .027 n i s - s 2.0 30 2.00 0.49 2.0 30 1.95 0.49 2.0 30 2.00 0.48 2.0 30 2.00 0.44 10.0 30 9.95 0.40 Target n s 8.0 30 8.05 0.41 6.0 30 5.95 0.42 4.0 30 4.00 0.43 A4 Target n A3 A2 Al 4.0 30 4.00 0.49 6.0 30 5.95 0.43 B2 4.0 30 4.00 0.46 8.0 30 8.00 0.40 B3 4.0 30 4.05 0.48 10.0 30 10.05 0.44 B4 - 40 40 40 40 .640 .635 .641 .637 .026 .025 .024 .025 4.0 30 3.95 0.51 4.0 30 4.00 0.42 Bi All the particles were prepared from aspen logs; n number of observation; I average; s standard deviation. Thickness (mm) Width (cm) Length (cm) Particle Code 6.0 30 5.95 0.49 8.0 30 8.00 0.42 C2 6.0 30 6.00 0.48 10.0 30 9.95 0.42 C3 40 40 40 .639 .640 .637 .025 .028 .023 6.0 30 5.95 0.46 6.0 30 6.00 0.40 Cl Table 2a. Particles used for studying particle size effect on horizontal density distribution* 40 .640 .025 8.0 30 7.95 0.50 8.0 30 8.00 0.41 Dl (A) 37 Table 2b. Particles used for verifying layer concept* Particle Code El E2 Fl F2 Gi G2 Species A A A A B B 10.0 30 9.90 0.43 6.0 30 6.00 0.43 10.0 30 9.95 0.41 6.0 30 6.00 0.40 10.0 30 10.05 0.41 6.0 30 6.00 0.42 2.0 30 1.96 0.47 6.0 30 5.95 0.45 2.0 30 2.00 0.49 6.0 30 6.00 0.50 2.0 30 1.95 0.44 6.0 30 5.95 0.47 40 1.061 .030 40 1.060 .031 40 1.942 .038 40 1.943 .039 40 .696 .028 40 .699 .024 Target Length (cm) n s Target Width (cm) n s n Thickness (mm) * s A Aspen; B Birch; n number of observation; i average; s standard deviation. - - - - - 38 commercial and laboratory particles for this purpose was based on the knowledge gained from HDD evaluations with specialty particles in the first part of this study. Three types of commercial wafers/strands from waferboard/OSB mills were obtained through the courtesy of Alberta Research Council in Edmonton, Alberta. Figures A-i, A-2, and A-3 in Appendix A show the distribution of particle length, width and thickness for commercial particles p1, p2 and p3. It can be seen from these figures that large variations exist in their dimensions. Laboratory particles were cut on a laboratory-type-waferizer located at CAE Machinery Ltd. in Vancouver, B.C. The two species and several different waferizer settings were chosen to produce a variety of particles. Figures A-4, A-5 and A-6 in Appendix A show the distribution of laboratory particles. Variations in dimensions were expected, but they were less than for commercial particles, especially as thickness is concerned. 4.1.3. Adhesive Phenol-formaldehyde powder resin W3154 was used throughout this study. It was provided by Borden Co. Ltd of Canada. This resin has been used both for face and core applications in commercial waferboardlOSB manufacture. 4.1.4. Commercial wood products Waferboard was used for studies involving general HDD of particleboard and specimen size effect. Parallam, M1F and waferboard/OSB were used to test the X-ray density scanning machine. These products provided a wide 39 range of wood composite materials, in terms of the size of constituting wood elements. They were used in the sense that no attempt was made to say anything about their whole productions. 4.1.4.1. Waferboard Commercial waferboard panels were provided by Weldwood of Canada Ltd. Average board density was 0.67 g/cm , and board thickness was 11 mm. 3 The wood element sizes used to manufacture this waferboard were believed similar to that shown in Figure A-2, as both the waferboard and the particles were from the same mill. 4.1.4.2. Parallam Parallam samples were obtained from MacMillan Bloedel Ltd., B.C. It is made by aligning approximately 2.5 m long Douglas-fir strands in one direction, and forming a board which is continuously pressed in a microwave heating environment. The nominal cross section of the strands was 16 mm x 3 mm, and the product used was measured to be 0.68 g/cm 3 in density and 9.5 mm in thickness. 4.1.4.3. Medium density fibreboard (MDF) MDF was obtained from a local lumber supplier. Although the precise dimension of fibres was unknown, it is believed that the wood elements are in the form of fibre bundles. Fibre bundles are generally 1-10 mm in length, and 0.03-0.3 mm in diameter. MDF used in this study was determined to be 0.80 3 in density and 9.7 mm in thickness. g/cm 40 4.1.4.4. WaferboardlOSB One waferboardlOSB product was also obtained from a local lumber supplier. The particle strands are believed to be 10-75 mm long, 5-50 mm wide and 0.25-0.75 mm thick. It was measured to be 0.68 g/cm 3 in density and 11 mm in thickness. 4.1.5. Laboratory Particleboard Basic procedures for manufacturing particleboard in the laboratory were as follows. First, a predetermined amount of wood particles and adhesive were mixed in a laboratory blender for 10 minutes. A resin content of 2 %, based on oven-dry weight of particles, was used to produce boards for studying the influence of raw material characteristics on HDD. The adhesive blended particles were then randomly hand-formed in a 71 cm x 71 cm wooden box into a particleboard mat. During the forming process, mat height at the four corners and the middle of each side of the forming box was measured several times. This method was used to achieve a uniformly thick mat. The mat was then compressed and consolidated into a panel under heat and pressure in the hot-press. In this study, a pressing temperature of 180 OC and a pressing time of 10 minutes were adopted. This relatively long pressing time was used to insure complete adhesive cure. A press closing time of approximately 1 minute was also used. Two groups of boards were manufactured. The first group was designed to study the influence of raw material characteristics on HDD. In this group, one board was made with each type of specialty particles (Table 2a) to study the effect of particle size. These boards had a target density of 0.67 g/cm 3 and 41 thickness of 11 mm. In addition, boards were made to study other parameters of raw material characteristics, and these boards are summarized in Table 3. The second group of boards were manufactured mainly using laboratory and commercial particles to determine the influence of HDD on selected particleboard properties. Table 4 describes the composition of these panels. After manufacture, all particleboards were stored for equilibration in an environmental room, with temperature controlled at 20±2 OC, and relative humidity at 50±2 % for at least 4 weeks before testing. 4.2. Density Measurement 4.2.1. Density measurement methods 4.2.1.1. Gravimetric method A gravimetric method was the principal technique used to study HDD. Depending on the size of the specimen, either a sawing technique or a drilling technique was used. For specimen sizes above 25 cm , a sawing technique 2 was used with specimen cross-sectional area measured by a digital caliper with an accuracy of ±0.01 mm and weight determined on an electronic digital balance of ±0.00 1 g accuracy. The thickness of the specimen was taken to be constant and equal to the target thickness of the board. The density was then calculated as Density = Weight / (Area x Thickness). When specimen size was less than 25 cm , a drilling technique was 2 used. The cross-sectional area was taken to be the size of drill bit, and the weight was taken to be the weight loss of the specimen from before to after 42 Table 3. Particleboards used to verify layer concept* Board Particles Density ) 3 (glcm El El 0.67 11 E2 E2 0.67 11 Fl Fl 0.67 11 F2 F2 0.67 11 Gi Gi 0.67 11 G2 G2 0.67 11 Ki 112E1-i-112F1 0.67 11 K2 1J2E2-i-l/2F2 0.67 11 Ri A4 0.86 11 R2 Cl 0.89 11 Si A4 0.67 6 S2 Cl 0.67 20 Wi A4 0.67 6 W2 Cl 0.67 20 * Thickness (mm) One board was made for each condition; birch furnish was used for boards Gi and G2, other boards used aspen furnish. 43 Table 4. Particleboards used to study the influence of horizontal density distribution on board properties* Board Particles P1 1 p A P2 2 p A P3 p3 A P4 * Species 1/4p1÷114p3+1/4D1÷1/4p6 A P5 p5 A P6 p6 A P7 7 p B P8 213p2÷l/3p7 A+B P9 112p2÷112p7 A+B PlO 113p2+2/3p7 A+B A Aspen; B Birch. Three boards were made for each board condition, with a target board density of 3 and a board thickness of 11 mm. 0.75 g/cm - - 44 drilling. The density was then calculated as Density = Weight / (Area x Thickness). Figure 11 shows the set-up for the drill press. 4.2.1.2. X-ray scanning method An X-ray technique, developed by VisionSmart in Edmonton, Alberta to measure density profile for lumber products, was also used to determine panel density in a non-destructive manner. Although this instrumentation was still under development, it provided a density profile at a resolution of 1 mm x 3.4 mm size. Density at larger specimen sizes could be calculated based on these density readings according to n DA= d/n i=1 (7) where, DA is the density of specimen size A, d is the individual density at specimen size of 1 mm x 3.4 mm, n is the number of adjacent 1 mm x 3.4 mm specimens that are included in size A. Limited access to this technology during this thesis study enabled us to perform an analysis on the relationship between densities at certain distance apart within a panel. The calculation of coefficient of correlation was as follows, p = Cov(X,Y) I fS(X)S(Y)} (8) where, p is the coefficient of correlation between variables X and Y, Cov(X,Y) stands for the covariance between variables X and Y, while S(X) and S(Y) are standard deviations of X and Y. 45 I .;cj Figure 11. Drill press set-up for density determination. 46 4.2.1.3. y-ray method The y-ray measurement of density was performed on the Woodmat production line of Canadian Forest Products Ltd., New Westminster, B.C. This non-destructive technique measures the density of a circular specimen of 35 mm in diameter, and was used to characterize density variations at this size for studying the influence of HDD on board properties. 4.2.2. Sampling of density specimens 4.2.2.1. Gravimetric method 4.2.2.1.1. Laboratory particleboard After being trimmed, the laboratory-made particleboards were approximately 700 mm x 700 mm. As the particle mat spread outwards approximately 10 mm during pressing, final pressed particleboards were larger in size than that of the forming box. Therefore, about 15 mm was trimmed off from around the edges. Panels manufactured to study the influence of raw material characteristics on HDD each were cut into 36 specimens of approximately 110 mm x 110 mm. Those panels made to study the effect of HDD on selected board properties each were sectioned into 25 specimens of approximately 110 nun x 110 mm, with the remaining portions of these panels used for bending specimens (Figure 13, board 3). Density variation at this specimen size was determined. For assessing density variations at smaller specimen sizes, holes were drilled into the 110 mm x 110 mm sections. A simple random sampling procedure was used for selecting these holes. First, the maximum number of drilled holes arranged in squares as shown in Figure 12, for a specific 47 1 2 3 4 5 6 7 8 9 10 13 14 Random number 12 15 = 16 11 Figure 12. A schematic of the procedure for allocating drilling specimen. 48 diameter, that the section could accommodate was determined (some other arrangements of the circles may end up with different maximum numbers of circles). Then, each potential hole was given a different but consecutive numerical value. Figure 12 shows this procedure schematically for a hole size of 5.07 cm . A random number then was chosen. The hole selected by this 2 random number was drilled and its density was measured as a random observation (Figure 12). After the density measurement for one hole size was completed from each 110 mm x 110 mm section, the next smaller sized measurement was chosen by a similar procedures as exhibited in Figure 12. One measurement ), while two 2 was taken from each drilled section for larger hole sizes (> 5 cm or more holes were drilled when the specimen size (hole) was smaller. When this thesis was proposed, a systematic sampling method of density specimens was also considered. This method would allow the calculation of autocorrelation function of density process, which could be used to simulate density process. Since the main hypothesis of this thesis was that particleboard technology could be better understood by studying the magnitude of HDD, a simple random sampling method was adopted. No theory is available to estimate the statistics based on the systematic sampling method, and the variance calculated by using the formula developed for the simple random sampling method is considered biased for a systematic sampling method (Cohran, 1977) 4.2.2.1.2. Commercial waferboard Sixteen commercial waferboard panels of size of 1220 mm x 606 mm were obtained. The manufacturer indicated that these panels came from two 49 adjacent press loads and were cut into this size on the production line. As waferboard is formed and pressed in a continuous process, these panels could be viewed as coming from one big panel. Since it was not the objective from this limited sample to present the whole picture of density and other property variations for waferboard production, these panels were treated as a population themselves in this study, just like the treament for laboratory particleboards. The standard deviation of density at this specimen size of 1220 mm x 606 mm was determined by using 11 of these panels. Afterwards, five of these panels were randomly selected and partitioned in half to give 10 approximately 536 mm x 536 mm sections, and the standard deviation of density was determined at this specimen size. This partitioning process, as shown in Table 5, continued until a specimen size of approximately 117 mm x 116 nim was reached. At this stage, twenty-nine of these specimens were randomly selected (the rest were used later for TB test) and partitioned into 58 smaller specimens measuring 116 mm x 54 mm, and density variation was obtained at this specimen size. These specimens were also subsequently partitioned into 54 mm x 54 mm sections, and the standard deviation of density again was estimated (These 54 mm x 54 mm specimens were reused later for TB test). Fifty waferboard sections of 117 mm x 116 mm were randomly selected from the fifth partitioning stage and used as the basis for density . The drilling technique 2 determinations at specimen sizes less than 25 cm was used and the sampling methodology used for the laboratory particleboard was applied. 50 Table 5. Partitioning procedure for density determination of commercial waferboard Partitioning Stage Approximate Specimen Size Number of Observation 0 l22Ommx6O6mm 5 1 536mmx536mm 10 2 535mmx251mm 20 3 252mmx251mm 40 4 252mmxll7mm 78 5 ll7mmxll6mm 153 51 In one case, a sawing technique was used to partition a 570 mm x 570 mm section of waferboard to specimen sizes of approximately 20 mm x 20 mm for density profile presentation (Figure 14). 4.2.2.2. X-ray and y-ray methods With the X-ray scanning method, the whole board was scanned and the density readings at each point were provided in a spreadsheet format. All these density readings were used for correlation analysis in this study. Consequently, no sampling was involved. With the y-ray method, only one measurement (38 mm in diameter) in the middle of each approximately 110 mm x 110 mm sized specimen was made. This simple choice of measurement was due to the difficulty of moving around the specimens on the production line. 4.3. Determination of Board Properties 4.3.1. Modulus of rupture and modulus of elasticity Modulus of rupture and modulus of elasticity were determined according to CAN3-0437.1-M85 (Canadian Standards Association, 1985). Specifically, the standard requires that the span/thickness ratio of the specimen equals 24 and time to failure should be about 5 minutes. The calculations of MOR and MOE, determined on the same specimen, were as follows: where MOR = 3LPmax/(2bt2) (9) /(4bt [L ) ]p/y MOE = 3 (10) 52 Pmax = ultimate failure load (N); L = span between centres of supports (mm); b = width of the test specimen (mm); t = average thickness of the test specimen(mm); p = increment in load on the straight line portion of the load/deflection curves (N); y = increment in deflection at midspan corresponding to a p increment on load (mm). Three replicates were produced at each board condition to study the influence of H]JD on board properties. Two bending specimens were cut from the edge of each replicate to give a total of six bending specimens (Figure 13). 4.3.2. Internal bond Internal bond was determined following CAN3-0437.1-M85 (Canadian Standard Association, 1985), except that a range of specimen sizes were used. A hot melt adhesive was used to bond the particleboard specimens to aluminum blocks. This test required that the aluminum block not be smaller in size than the particleboard specimen, and test results are valid only when failure does not occur in the glueline. Internal bond (MPa) was calculated according to IBPmax/A where, specimen. (11) ) the area of 2 (N) represents the maximum failure load and A (mm 53 4.3.3. Thickness swelling The method of submerging squared specimens horizontally to a 25 mm depth in 20 OC water as specified in CAN3-0437.1-M85 (Canadian Standard Association, 1985) was followed. When specimen size was larger than 50 mm x 50 mm, specimen thickness was calculated as the average of thicknesses measured to an accuracy of ±0.05 mm at midway points along each side, 25 mm from the edge of the specimen. With specimen size less than 50 mm x 50 mm, thickness was measured only at the centre point of the specimen. Thickness swelling was then calculated to the nearest 1% in accordance with the following formula: TS(t) = [T(t) -T(0)]100/T(0) (12) where TS(t) = T(t) = T(0) = TS after t hours soak (%); average thickness after t hours soak (mm); average thickness before soaking (mm). The cutting pattern used to obtain TB and TS specimens for laboratory particleboard is shown in Figure 13. For commercial waferboard, samples for TB and TS tests were randomly chosen from the set of boards left from the density determinations. This sampling procedures are shown in Appendix B and Appendix C respectively. 54 board 1 lB TS MOR + MOE board2 TS lB MOR + MOE board 3 HDD MOR + MOE Figure 13. Cutting pattern for preparing test specimens for laboratory particleboard. 55 5. RESULTS AND DISCUSSIONS 5.1. Aspect of Horizontal Density Distribution 5.1.1. Phenomenon of horizontal density variation The density map for a commercial waferboard sample of 57 cm x 57 cm size is presented in Figure 14. Individual densities were measured at a specimen size of approximately 20 mm x 20 mm. Gaps of 3 mm, equivalent to a saw blade thickness, existed between adjacent specimens. This figure demonstrates the phenomenon of HDD in particleboard showing the general nonuniformity in structure. Figures 15 and 16 show two density distribution histograms for the 2 and 0.31 commercial waferboard determined at specimen sizes of 29.16 cm 2 respectively. A normal distribution curve was fitted to these histograms, cm together with a calculated Pearson CM-squared statistic indicating the goodness-of-fit. As statistics 2 x ), 2 (x a parameter were less than the corresponding critical values of X (k.r.1 at significance level of 0.05, where k 2 and r are respectively the number of groups used to arrange data and the number of statistics estimated for the hypothesized distribution, k-r-1 is the degree of freedom, it was concluded that the waferboard density approximated a normal distribution. This was expected since individual density measured at any specimen size could always be taken as the average of several smaller sized densities. The central limit theorem supports this normal approximation (Fisher, 1950). Figure 14 suggests that the density variation could be viewed as a. random field. For a random field, the variation of measurements decreases as 56 0.13 I p 0.6 Figure 14. Horizontal density variation of one commercial waferboard. 57 0.20 0.15 0 C 0.10 0.05 0.48 0.56 0.64 0.72 0.80 ) 3 Density (g/cm Figure 15. Density distribution characteristic of one commercial waferboard at specimen size of 29.16 cm . 2 58 0.25 0.20 0 0.15 0 0.10 0.05 0.30 0.65 1.00 ) 3 Density (g/cm Figure 16. Density distribution characteristic of one commercial . 2 waferboard at specimen size of 0.31 cm 59 the measuring area (window) increases (Vanmarcke, 1980). The results of density measurements for the same commercial waferboard at different specimen sizes are given in Table 6. The relationship between the standard deviation of density and specimen size is shown in Figure 17, which agrees with the random field theory with the result that standard devaition of density decreases as specimen size increases. It was believed that three factors were associated with this density variation: variation in particle densities, nonuniformity of the forming process and the existence of voids (Suchsland and Xu, 1989). It can be observed from Figure 17 that the sensitivity of density variation with . 2 specimen size decreased dramatically as specimen size exceeded 25-50 cm This was referred to as the less sensitive range in this thesis. The significant smaller variation in this specimen size range is believed to be the reflection of uniformity of the forming process. The influence of voids and the variation in wood density is likely minimized in these relatively large specimen sizes. When specimen size was less than 25 cm , all of the three factors were 2 probably interactive. The effect due to the variation of particle densities is believed to decrease as board thickness increases, because the number of particle layers increases and the variation of average density of these layers decreases. Furthermore, it is believed that the contribution of variation of particle densities to horizontal density variation is less profound compared to that of voids. If the forming process is quite uniform, the density variation determined at relatively small specimen sizes could be considered to be caused mainly by voids. It is this density variation caused by voids that was the main focus of this thesis. 60 Table 6. Density determination of commercial waferboard ) 3 Density (g/cm Specimen size Standard Deviation ) 2 (cm Sample Size Mean 0.31 69 0.676 0.093 0.71 65 0.699 0.087 1.27 65 0.683 0.074 5.07 55 0.680 0.064 29.16 116 0.656 0.045 62.64 58 0.659 0.039 135.72 153 0.677 0.039 294.84 78 0.677 0.036 632.52 40 0.679 0.032 1342.85 20 0.679 0.028 2872.96 10 0.672 0.022 7393.20 11 0.698 0.021 61 0.10 I I I -I I 0.08 I 0.06 0.00 I I 0 100 200 300 I 400 Specimen Size (cm ) 2 Figure 17. Standard deviation of density vs. specimen size of one commercial waferboard. 7400 62 5.1.2. Relationship between standard deviation of density and specimen size Let Aa and Ab represent respective specimen sizes (areas) in density sets A and B, Da and Db the density variables, and Var(Da) and Var(Db) the variances of densities associated with density sets A and B. If the densities of individual points are independent, then the following relationship (Appendix D) exists according to basic statistics (Fisher, 1950), (13) Var(Da)/Var(Db) = A IAa 1 Taking the square root on both sides of Equation (13), we have S(Da)/S(Db) = (14) where S stands for the standard deviation. Rearranging Equation (14) and letting the equality equal a constant c, we also have S(Da)’JA = S(Db)”dX = c (15) which could be generalized as S = c(1/’IA) (16) When A = 1, c = S, the standard deviation of density at a unit specimen size. Equation (16) indicates a linear relationship between S and ii’1A The scatter plot of S to 1/qA for the commercial waferboard (Figure 18), however, deviated clearly from a straight line. One possible explanation for this non linear trend is that the density of samples of various sizes are correlated. For the purpose of curve fitting, a curvilinear relationship of S to ii.IA was chosen as follows: S = c(1/J)bi or (17) 63 0.10 I I . . 0.08 0.06 0.04 - . - - 0.02 0.00 0.0 I I I 0.4 0.8 1.2 1.6 vx Figure 18. Scatter plot of standard deviation of density vs. lb/A of one commercial waferboard. 2.0 64 S where, b 1 = = c(1/A)b (18) 2b, and both b and b , and c are parameters to be determined by 1 regression. The form of Equation (18) and the possible meaning and range for parameter b can be explained by considering statistical concepts. If a particleboard production is under statistical control (quality control), the density of particleboard at every point should vary within a certain limit around its mean (average board density). Therefore, this density variation could be considered as a stationary process (Bendat and Piersol, 1980). For a stationary process, the measurement within the process must be positively correlated (Bendat and Piersol, 1980). In other words, the coefficient of correlation (p) is larger than or equal to zero. Figure 19 shows the relationship between the correlation coefficient of densities measured on approximately 3.0 mm x 3.4 mm specimens and the Lag distance, performed on a commercial waferboardlOSB panel of 18 cm x 18 cm (X-ray data). Although it was unknown how well this X-ray instrument was calibrated, a clear positive correlation existed among densities. Let us consider two specimen sizes, Aa and Ab again, but specially Ab 2Aa. Since densities were positively correlated, we have (Appendix E) Var(Db) = = [2Var(Da) + 2pVar(D)]/4 [(1+p)Var(Da)]/2 (19) or, Var(Db)/Var(Da) = (l-t-p)/2 (20) By using Equation (18), we also have (Appendix F) Var(Db)/Var(Da) = (V2)2b (21) = 65 1.0 S 0.8 I D 0 0.6 D 0 C.) 0 D 0.4 I D S D 0 D 0 D 0.2 . c. V Q... .cs U C U I C I C 0.0 0 20 40 60 Lag (mm) Figure 19. Relationship between correlation coefficient of density and Lag for one commercial waferboardJOSB. 80 66 Comparing Equations (20) and (21), the following relationship was obtained, b = (22) [ln{(l+p)/2}/ln(l/2)]/2 Therefore, parameter b was related to p, coefficient of correlation of adjacent specimens. Numerically, when p 1 (22), or b = = 0, b = 1/2 according to Equation 1. This corresponds to Equation (16), for which no correlation exists between density measurements. When p = 1, b = 0, variance is not a function of specimen size. This corresponds to the situation where boards are perfectly homogeneous, i.e., density is constant and therefore densities at adjacent points are completely correlated. Naturally, density is constant and specimen size independent. Thus, parameter b possessed a physical meaning that indicates the level of correlation among density points. As b increases to 1/2, strength of correlation decreases. It is interesting to note that parameter b could not exceed 0.5. If b> 0.5, p < 0 according to Equation (22), which violates the property of stationary process. As nonstationary process can usually be converted to stationary process for analyses (Bendat and Piersol, 1980), the case of b > 0.5 can be safely excluded from the real world. Furthermore, b could not be negative. If b < 0, p > 1 according to Equation (22), which does not agree with the definition of correlation coefficient. In fact, if b < 0, Equation (18) predicts an increase of standard deviation as specimen size increases, which is difficult to imagine. It should be mentioned that exactly the same expression as that of Equation (17) was used to relate variance of crop yield per unit area to plot size (Smith, 1938), and this relationship has been widely accepted and 67 applied to predict agricultural crop yields (Kuehi and Kittock, 1969; Nelson, 1981). Recent comparison between geostatistics and Smith’s (1938) expression indicated the appropriateness of the latter, and a range between 0 and 1 was also recognized for parameter b 1 (Zhang et al, 1990). It was also worth mentioning that this model transformed the variable in such a fashion that the relationship between standard deviation of density and specimen size could be better visualized, especially when the specimen size was relatively small. This was evident from the comparison of Figure 17 with Figure 18. 5.1.3. Estimation of S to 1/A relationship Taking natural logarithm of Equation (18) on both sides, we have (23) lnS=lnc+bln(IJA) Through the least square technique, b and c are obtained. For the commercial waferboard, the values 0.1503 and 0.0795 were found. Statistical analyses (Appendix G) indicates that parameter b was significantly different from 0.5 and 0, which were the boundaries for this parameter. Taking these estimates back to Equation (18), it gave S = 0.0795(IJA)0.1503 (24) The coefficient of determination (R2) between the model prediction and experimental data was calculated as n n 2 R = 1 (s-) / - i=1 in which, observation. is the mean, ) (s 1 = (25) 0.98 i=1 is the model estimate and Si 15 the actual 68 5.2. Influence of Raw Material Characteristics on Horizontal Density Distribution 5.2.1. Particle size Density variation results for laboratory boards made with specialty particles are given in Table 7. The fitted equations relating S and specimen size for different boards are listed in Table 8. It is noted in Table 8 that R2 increased as b (the slope in the logarithmically transformed expression as Equation (23)) increased. This is consistent with the properties of regression analysis (Fisher, 1950). Figures 20 and 21 show the relationships between standard deviation of density (S) with particle length and width, respectively, measured at several different specimen sizes. Since these trends as specimen size changes were similar for particle length and width, their product, which , was calculated and plotted against S. 2 is the particle size (area) in unit of cm This is presented in Figure 22. It should be emphasized here that the specimen size used to determine the density nonuniformity is different in each small plot in this figure, but the same set of boards was used throughout. For example, the same particleboard (Al) made with particles of 2 (the first data point from left in each plot) was used for the size of 8 cm measurement of standard deviation of density at all six specimen sizes. It can be seen from Figure 22 that particleboard made with larger particles is less uniform than particleboard made with smaller particles when , as indicated by increased S 2 measured at specimen size larger than 1.267 cm as particle size increased. While particleboard made with smaller particles is observed to be less uniform at smaller specimen sizes, as demonstrated by increased S as particle size decreased. It should also be mentioned here that * 126 131 110 125 .672 .698 .687 .654 .166 .160 .152 .147 121 132 133 120 .676 .654 .680 .664 .184 .179 .169 .167 ii 0.141 72 71 70 69 .696 .693 .686 .666 .102 .113 .103 .112 Code of partideboard is the same as for particles used for the board manufacture; n = number of observations; i = average; s = standard deviation. 1 s s 108 108 102 119 .685 .671 .700 .700 .126 .119 .119 .118 105 124 108 105 .680 .703 .688 .658 .126 .123 .120 .118 n 1 0.317 70 70 71 72 .645 .679 .679 .663 .090 .100 .110 .108 n 1 s 1.267 36 36 35 36 .647 .668 .650 .682 .094 .105 .097 .102 36 36 35 36 .701 .696 .700 .700 .073 .080 .086 .087 36 36 36 35 .666 .689 .671 .692 .070 .078 .086 .096 B4 n 1 s B3 5.067 B2 36 36 35 36 .671 .688 .686 .674 .036 .040 .045 .055 B1 36 35 36 36 .681 .707 .708 .699 .043 .064 .075 .076 A4 n 1 s A3 11.401 A2 36 36 36 36 .653 .677 .674 .673 .020 .025 .030 .034 Al n 1 s Particleboard Density (g/cm ) 3 C2 C3 122 120 120 .677 .681 .666 .149 .134 .129 108 104 108 .685 .669 .669 .107 .101 .103 69 70 72 .681 .665 .657 .098 .095 .100 36 36 36 .651 .662 .658 .085 .085 .098 36 36 36 .701 .704 .700 .078 .074 .090 36 36 36 .670 .658 .670 .042 .040 .049 Cl 7. Density determination of laboratory particleboard* 115.102 2 cm Specimen Size Table 120 .681 .130 103 .689 .107 69 .680 .103 36 .675 .108 36 .666 .095 36 .663 .050 Dl 70 Table 8. S to VA models for laboratory particleboard* c Model b R2 Al 0.097 0.319 0.98 A2 0.105 0.268 0.95 A3 0.113 0.215 0.93 A4 0.111 0.202 0.89 Bi 0.110 0.208 0.94 B2 0.114 0.182 0.90 B3 0.111 0.160 0.92 B4 0.113 0.132 0.93 Cl 0.103 0.166 0.92 C2 0.969 0.157 0.91 C3 0.103 0.120 0.82 Dl 0.107 0.117 0.76 Particleboard * R2 = coefficient of determination. 71 0.10 0.06 •I Size = 115.102 ISize 4 2I 8 ..- 11.401 cm2 ‘8 6 . 6 0.04 4 - oc, 2 ec 2 E 0.08 E CC.) .> . . 0.06 0.02 . . - CI) U2 0.00 4 2 6 0.04 I I 8 10 2 12 4 0.12 012 I 10 12 ISize= + I I jSize=5.067cm2j 1.267cm .— ‘8 . 4 C G 0 8 Length (cm) Length (cm) ., 6 0.11 4 6 2 0.10 c—’ . 0 c 2 6 Q . G 0.08 . L .e -t . 0.09 CI) CI) 0.06 I 4 2 6 I I 8 10 0.08 2 12 4 I I 8 10 12 Length (cm) Length (cm) 0.13 6 0.20 I C 0.18 0.12 . 0 C—’ oc, C,—’ ec. i 1 . 0 :E CC.) . NN @) .t 4 0.14 010 -t .t Isize= 0.141 cm2I [Size=0.317cm’ 0.09 0.12 - 2 4 6 8 Length (cm) 10 12 2 4 6 8 10 12 Length (cm) Figure 20. Influence of particle length on standard deviation of density of particleboard at several specimen sizes. Data sets with same particle width are connected and labeled by width (cm). 72 0.10 0.06 O.04 0.08 o ec ec 10 S. 6 4 . 0A 6 0.06 Size = I 115.102 2{ 0.00 0 - 2 4 6 8 lSize= 11.401cm2I 4 0.04 10 0 2 Width (cm) 4 6 8 10 Width (cm) 0.12 0.12 I . 8 0.11 0.10 10 - 8 0.06 I Ec0.10 . 6 0.09 4 [Size = .4 2 Size= 1.267cm 5.067 2I Ci) 0.06 0.08 2 0 4 Width 6 8 10 0 I I 2 4 (cm) I 6 8 10 Width (cm) 0.13 020 4 6 0 0 fize=0.317cm2I 8 0.12 [Size = 4 6 0.18 10 0.14 1 cm2I 8 10 11 no. 0.16 0.10 0J4 I I 0.09 0 2 4 Width 6 (cm) 8 10 0.12 0 I I I 2 4 8 8 Width (cm) Figure 21. Influence of particle width on standard deviation of density of particleboard at several specimen sizes. Data sets with same particle length are connected and labeled by length (cm). 10 73 0.06 0.10 - 0 a . C) 0 0 0.04 C 0.08 0 oc oc, 00 ‘-S ISize = 115.102 cmj 0.oo 20 0 40 60 80 C F 0.06 tfze = 11.40 1 2 cm 0.04 0 40 20 60 80 Particle Size (m ) 2 Particle Size (cm ) 2 0.12 0.12 I — 0 0 a O.11 C C 0 0 o 0 /KN\\. 0 ‘—S C •0d0 C C) 0 S.-’ 0 10.08 0.09 jjze = 5.067 cm1 ISize = 0.06 20 0 40 0 0.06 80 60 0 Particle Size (cm ) 2 I I 20 40 1.267 cm21 60 80 Particle Size (cm ) 2 0.13 020 ISize 0 = 0.317 ISize = 0.141 cm2l 2) 0 C C) 0.18 0 0 CI 0 c0.11 C Q0.16 C 0 . .0 C 0.10 0.14 C -S U) CI) 0.09 - 0 20 40 60 Particle Size (cm ) 2 80 0.12 0 20 40 80 Particle Size (cm ) 2 Figure 22. Influence of particle size on standard deviation of density of particleboard at several specimen sizes. The curve is fitted by eye without regression analysis. 60 74 the scale of S is different in each small plot of this figure (because density nonuniformity is specimen size dependent). One possible explanation, as dicussed in the following, may provide insight for this trend of S to specimen size. During the hand-forming process, particles were deposited randomly throughout the horizontal plane in a more or less layer by layer fashion. Voids can exist between any adjacent particles in any layer. As particle size increased, the number of these voids was observed to decrease in a unit area within one layer (the number of particles also decreased), while the size of voids increased. Figure 23 schematically shows these two aspects of voids in one layer as affected by particle size under hand-forming operations. This similar phenomenon was also observed in packing wooden rods, fibre glass and sphere shaped particles (Milewski, 1987). These two tendencies of voids are then reflected in Figure 22. When specimen size was relatively large in comparison to the largest void size, an individual density specimen may contain several voids (or several particles) when the particleboard was made with relatively small particles, due to the relative small size of these voids (Figure 23). Under these conditions, voids tended to be distributed more evenly among the density specimens. Less density variations resulted for particleboards made with smaller particles than for particleboards made with larger particles. , as in (a), 2 This was observed when specimen size was larger than 1.267 cm (b) and (c) of Figure 22. When the specimen size for the determination of S was small in comparison to the smallest size of voids, void size may not be that important, compared to the number of voids, in determining the extent of density variations among different boards. As there were less numbers of voids 75 (a) Particle Void (b) Particle Void Figure 23. A schematic of particle and void distribution in one layer under hand-forming operation. (a) Small particle (b) Large particle 76 within particleboards made with larger particles, and since a density specimen consists of several particle layers, large particles may tend to cover these voids more effectively in adjacent layers during the formation process leading to less density variation. For example, it is more unlikely for a small hole to penetrate from one surface of particleboard to the other for particleboard made with larger particles. This happened when specimen size 2 and is shown in (e) and (f) of Figure 22. Kusian’s was smaller than 1.267 cm (1968) model analyses also predicted a decrease of probability of HDD as particle size increased, which seems in accordance with the experimental observations of this study, although Kusian failed to bring specimen size into his discussion. It is understood that this explanation was only based on visual observation, a more rigorous experiment involving permeability test or model analysis (as in paper physics studies) might provide further insight. Furthermore, these void characteristics, and the dependence of the relationship between S and particle dimension on specimen size was based on a simple hand-forming method. It is expected that different forming methods or even the same method but conducted by different persons will generate different results. Consequently, specific values observed in this study are not to be taken as absolute. However, it is believed that the two aspects of voids (number of voids and size of voids) occur with present industrial forming methods or other forming methods, and that the trend observed in this study would be applicable. If a forming technique could be devised in such a way that the void size is independent of particle size, density variation would decrease further for boards made with larger particles at relatively small specimen sizes. This suggests that forming method is as important as choice 77 of particle size in decreasing horizontal density variation, and effort should be directed at this in the future. As these two aspects of voids exist and interact in this study, density variations have to be measured at a range of specimen sizes, in order to understand the mechanism and influence of particle size on density variation and subsequent board properties. Besides particle size effect, particle shapes are also believed influencing HDD of particleboard. For example, Suchsland’s (1959) experiment suggested that square particles might produce more uniform structures than rectangular ones. Two particles (with the same particle size) which could provide this comparison in this experiment were A3 (rectangular: 2 cm x 8 cm) and Bi (square: 4 cm x 4 cm). However, Suchsland’s indication could not be substantiated from this limited data (Table 7). A more comprehensive experiment is needed to investigate this aspect, not only comparing square shaped with rectangular shaped particles, but also with other shaped particles, like circular or triangular ones. 5.2.1.1. Parameter b The parameter b was used in Equation (18) to model the dependence of density variation to specimen size. It was also recognized as an indicator of the strength of correlations among density measurements. Furthermore, the influence of parameter b on density variation could probably be observed more clearly at relatively small specimen sizes, becaise the inverse of specimen size (1/A) and therefore the differences of standard deviations of density due to different b values increase as specimen size decreases. Thus, it was more appropriate to discuss the relationship between parameter b and 78 structural nonuniformity by confining the discussion to smaller specimen . 2 sizes, say 0.14 1 or 0.3 17 cm The influence of particle size on b is shown in Figure 24. It is seen that b decreased as particle size increased, indicating that correlation improves. This may also relate to void characteristics. When specimen size was small, the number of voids within a specimen decreased as particle size increased. When density measurements were closer to each other, stronger correlation resulted. Figure 25 shows the correspondence between b and standard . 2 deviation of density at specimen size of 0.141 cm Figures 26 and 19 show the relationship between coefficient of correlation (p) of density and separation distance (Lag), for Parallam, MDF and waferboard/OSB respectively. These three products exhibited different p to Lag relationships. A more striking feature of this diagram was the directional difference of these products, which testifies to the capability of this analysis technique. The difference between the machine direction (Y direction) and cross machine direction (X direction) came from the intentional alignment of strands for Parallam and waferboardlOSB products, and the tendency of self-alignment of fibre bundles for MDF in the machine direction during formation. As alignment occurs in the machine direction, the number of voids decreases and correlation strengthens in this direction. However, as these three products were produced with different wood species, and board thickness and density were different, a direct comparison of density variation in relation to coefficient of correlation among these products was not possible. But such a comparison was possible for each product in two directions. This comparison is provided in Table 9, which was 79 0.5 I 0.4 .D I I - O.3\ ‘p E 0.2IJ D D 0.1 - 0.0 0 I I 25 50 Particle Size 75 (cm2) Figure 24. Influence of particle size on parameter b. The curve is fitted by eye without regression analysis. 100 80 0.20 I EJ — 018 / 0.16 0.14 / I Ci) / D / 0.12 - 0.10 I 0.0 0.1 0.2 0.3 0.4 Parameter b Figure 25. Relationship between parameter b and standard deviation . The curve 2 of density at specimen size of 0.141 cm is fitted by eye without regression analysis. 81 1.0 0.8 C G) 0.6 C Q 4 C 0 C) . 0.4 C) C 0.2 0.0 0 20 40 60 80 Lag (mm) Figure 26. Relationship between correlation coefficient of density and Lag for MDF and Parallam. 100 82 calculated by using the X-ray density readings. Results support the relationship that variance of HDD negatively relates to correlations. Table 9. Comparison of density variations in X and Y directions ) 3 Standard Deviation of Density (g/cm Parallam MDF WaferboardlOSB X 0.063 0.151 0.104 Y 0.033 0.135 0.063 Product Direction For this thesis, which used randomly hand-formed particleboard made in the laboratory to establish the concept of HDD, the direction dependence of properties should not be significant. 5.2.2. Particle thickness, wood density, board thickness and board density 5.2.2.1. Layer concept Particleboards could be viewed as a non-continuous layered structure. An idealized lay-up could be like that shown in Figure 2. An actual board structure will be less regular and more complex, but it should still have the features of a discontinuous lay-up. In this structure, particles are deposited randomly in each layer due to the nature of the forming operation. As a density specimen is usually composed of several of these layers, the variance of horizontal density variation would be expected to decrease as the number of particle layers increases. 83 This concept can be represented statistically. Let la be the number of layers of particles in particleboard A, ‘b the number of layers within particleboard B, and the ratio of particle layers of board B and A is 11/la. Further, suppose other board conditions are the same, and that Db stands for the density variable of a specimen of a certain size for particleboard B, Da the density variable of the same specimen size for board A. Then (Appendix H), Var(Db) = (la/lb)Var(Da) (26) S(Db) (27) or, ‘117LS(Da) Both Equations (26) and (27) show clearly that variance of HDD decreases as number of particle layers increases. 5.2.2.2. Verification of Layer Concept This layer concept was used to study the influence of particle thickness, wood species, board thickness and board density on HDD in this section. 5.2.2.2.1. Particle thickness Let t 2 be the thicknesses of particles used for boards A and B, 1 and t then the ratio of average particle layers within boards B and A is the ratio of particle thicknesses 1 /t if other board characteristics are the same. Then, 2 t , according to Equation (27), the following was obtained, S(Db) = JS(Da) (28) Experimental boards prepared for the verification of Equation (2)8 are indicated in Table 10. For boards where combinations of particles were used, an arithmetic average of thickness based on weight proportions was used. 84 The S to 1/A models developed earlier for boards A4 and Cl were used to estimate density variations of particleboards with different particle thicknesses. Table 10. Particleboards with different particle thicknesses Particleboard Particles used A4 A4 El El Fl Fl Kl 50% particle El + Cl Cl E2 E2 F2 F2 K2 50% particle E2 + 50% particle Fl 50% particle F2 Figure 27 shows the comparison between model predictions and experimental measurements. For particleboards made of particle length and width of 60 mm (Cl, E2, F2) and boards El and Ki, the specified model agreed well with experimental results. But for board Fl made of particle thickness of 1.942 mm (length of 100 mm and width of 20 mm), a consistent lower measured density variation than model predictions was seemingly evident. This may be due to the greater efforts which were dedicated in forming this particle mat, as it is usually more difficult to obtain a uniform mat structure with slender and thicker particles (particle Fl). Therefore, less 85 (a) 0.36 -T 0.30 ujoard’ K -0.24 —— —— ————— —— 0.18 a* C t 1 boa ..... /_‘ 0.12 0.06 0.00 — 0.0 1.2 2.4 3.6 4.8 6.0 7.2 4.8 6.0 7.2 VA (cm) 2 0.30 I 0.24 0.18 0.12 0.06 0.00 0.0 1.2 2.4 3.6 VA (cm) 2 Figure 27. Influence of particle thickness on density variation. The lines are model predictions, and points are experimental measurements. 86 forming variation may result and contributed to the overall lower density variations. Suchsland’s (1959) analysis indicated that board uniformity improved as particle thickness decreased (Figure 3), which agrees with this layer concept. But a specimen size effect was not recognized in that study. It should be mentioned here that the difference of board structure (defined by standard deviation of density) corresponding to the use of different particle thicknesses was more observable in the small specimen size range than in the large specimen size range (Figure 27). This suggests that relatively small specimen size should be used in order to really understand how board structure is affected by raw material characteristics, and how structure relates to board properties. It is known that all particleboard properties are negatively influenced by an increase of particle thickness. The increase of board nonuniformity as particle thickness increases may provide the structural explanation for this observation. Consequently, alternative methods to reduce nonuniformity may need to be considered when using thicker particles. 5.2.2.2.2. Wood density 1 are the densities of wood particles used for boards B Suppose d 2 and d and A. If other board conditions are the same, the ratio of layers of particles of boards B and A is the ratio of wood densities. Then, the following based on Equation (27) was derived, S(Db) = diS(Da) /‘Jd 2 (29) 87 Actual board conditions used to verify this concept are listed in Table 11. As the thickness of birch particles was different from aspen particles, an adjustment factor based on Equation (28) was applied to Equation (29) to estimate density variations. A good agreement was obtained between the experimental observations and the model (Figure 28). Table 11. Particleboards with different wood species Particleboard Particles used A4 A4 Gi Gi Cl Cl G2 G2 In reality, this experiment involved a combination of wood species and particle thickness effects. The good agreement between experimental data and model predictions demonstrates that the layer concept applies to individual raw material characteristic, as well as to their combinations. The increase of structural nonuniformity may explain why particleboards made with high density wood species are inferior in properties compared to particleboards made with low density wood species. This may also explain why combining low and high density wood species is a recommended practice in the particleboard industry. 88 (a) 0.20 0.15 0.10 0.05 0.00 0.0 1.2 2.4 3.6 4.8 6.0 7.2 4.8 6.0 7.2 hA (cm) 2 (b) 0.18 I 0.12 0.06 0.00 0.0 1.2 2.4 3.6 hA (cm) 2 Figure 28. Influence of wood density on density variation. The lines are model predictions, and points are experimental measurements. 89 5.2.2.2.3. Board thickness Suppose tb and ta are the thicknesses of boards B and A respectively. Then, the following based on Equation (27) was obtained, (30) S(Db) = 7 b5Wa) Table 12 presents board conditions while Figure 29 shows the verification. A good agreement was evident between this hypothesized model and the experimental data. Table 12. Particleboards with different board thicknesses Board thickness (nun) Particleboard Particles used A4 A4 11 Si A4 6 Wi A4 20 ci ci ii S2 Ci 6 W2 Ci 20 In furniture grade particleboard, it is noticed that thinner particles are used to produce thinner particleboard for furniture applications. The influence of board thickness on board nonuniformity may also provide an explanation for this practice. 90 (a) 0.24 0.16 0 0 0.08 0.000.0 1.2 2.4 3.6 4.8 6.0 7.2 4.8 6.0 7.2 VA (cm) 2 (b) 0.21 I -4 0.14 C C 0.07 0.00 0.0 1.2 2.4 3.6 hA (cm) 2 Figure 29. Influence of board thickness on density variation. The lines are model predictions, and points are experimental measurements. 91 5.2.2.2.4. Board density Let db and da be the densities of boards B and A. For the purpose of analysis, board B could be viewed as being made from A in two steps. First, increase the thickness of board A from t to (dilda)t at the density of da, and designate this board C. Secondly, compress board C from thickness (dj,/da)t to t while maintaining the same board weight. For the first step, the following equation was valid based on Equation (30), (31) Var(D) = (da/db)Var(Da) For the second step, Var(Db) = Var(w/(at)) = Var(a(db/da)tDd(at)) = (dijda) Var(Dc) 2 (32) in which, w and a are respectively the weight variable and area of density specimen. Combining Equations (31) and (32), the following was derived, Var(Db) = (dijda)Var(Da) (33) S(Db) = ‘IdiJdaS(Da) (34) or, Experimental conditions are given in Table 13, while verification is shown in Figure 30. A good agreement was also obtained between the theoretical model and experimental data. 92 (a) (b) 0.21 I I 0.14 0.07 0.00 0.0 1.2 2.4 3.6 4.8 6.0 7.2 4.8 6.0 7.2 1/A (cm) 2 0.20 0.15 0.10 0.05 0.00 0.0 1.2 2.4 3.6 VA (cm) 2 Figure 30. Influence of board density on density variation. The lines are model predictions, and points are experimental measurements. 93 Table 13. Particleboards with different board densities Particleboard Particles used Board density A4 A4 0.67 Ri A4 0.86 Cl Cl 0.67 R2 Cl 0.89 ) 3 (glcm 5.2.3. Summary In this section, both a commercial waferboard and laboratory panels manufactured with specific particle geometries were studied to establish the influence of raw material characteristics on HDD. By examining different sized specimens within a panel, it was found that the relationship between standard deviation of density and particle size was specimen size dependent, with standard deviation of density increasing as specimen size decreased. Since particles from the same wood species were of similar density, and the laboratory boards were formed in a consistent manner, this variation was attributed to void quantity and size. In general, the number of voids per unit volume of particleboard, decreased as particle size increased, while the size of voids increased. These two aspects of voids determine, in part, the effect of particle size on HDD. By further development of model equations and data analysis, it was demonstrated that a layer concept was suitable for relating particle thickness, wood density, board thickness and board density to HDD. 94 In the next two sections, this structural characteristic of HDD will be examined in more detail. In particular, the influence of specimen size and its inherent variation in density on the evaluation of particleboard properties, and the effect on some board properties brought about by altering HDD will be investigated. 95 5.8. Implication of Horizontal Density Distribution to the Selection of Specimen Size For Some Particleboard Property Evaluations 5.3.1. Introduction The determination of appropriate specimen size for studying material properties has been a concern for researchers. The greatest change in specimen size designation probably occurred in the late 1970’s, when an ingrade testing philosophy, based on actual structural lumber sizes, replaced the traditional small clear wood specimen method in North America (Madsen, 1992). This transition was the result of the improved understanding of structural behaviour of lumber. For particleboard, different countries use different specimen sizes for property determinations. For example, specimen sizes of 25 mm x 25 mm and 50 mm x 50 mm respectively are used for TS and TB evaluations in Europe (Heimeshoff, 1991), while sizes of 150 mm x 150 mm and 50 mm x 50 mm are used in North America (American Society for Testing and Materials, 1960; Canadian Standard Association, 1985). Tn both standards, specimen sizes for TB and TS evaluations are different, even though these two properties are both measuring performance of particleboard in the same direction perpendicular to board surface. This designation of specimen size makes the preparation of specimens inconvenient. Present testing methods in North America to evaluate particleboard properties are still more or less based on the small specimens of ASTM standard D 1037 (American Society for Testing and Materials, 1960), which was originally intended for fibre-based panels. The deficiencies in this standard was reported in an investigation which examined some new products and new test methods based on different specimen sizes (McNatt, 96 1984). Up to now, a criterion for designating such specimen sizes is yet to be developed. In this section, the concept of HDD was used to study how some particleboard properties are affected by specimen size changes, with the objective of examining the potential of HDD as one possible criterion for specimen size selections for TB and TS evaluations. 5.3.2. Internal bond The strength of a material follows a Weibull distribution (Weibull, 1939), if the failure of the material is governed by the weakest link. Many materials exhibit this phenomenon. Since 1960, this strength theory has been applied to characterize strength properties of wood. Limited tests conducted on wood composites showed that MOR values from larger test specimen sizes were lower than those for smaller test specimen sizes (McNatt, 1984; Post, 1983; Szabo, 1980), indicating that the Weibull strength model might also apply to wood composites. Internal bond values for the commercial waferboard panel tested at several different specimen sizes are given in Table 14. The two parameter (2P) and three parameter (3-P) Weibull distribution fits to the TB data at 2 and 225.79 cm 2 are shown in Figures 31 and 32 specimen sizes of 6.27 cm respectively. Visual examination indicates that both models match well with the experimental data. Generally, the 3-P model fits data better, but the 2-P model is simpler to use. In this study, the 2-P Weibull was used. One result of the Weibull distribution is size effect. That is, strength decreases as volume increases. This has been observed for wood in tension parallel to grain (Madsen and Buchanan, 1986), in bending (Bohannan, 1966), in shear (Foschi and Barrett, 1976) and in tension perpendicular to 97 Table 14. Internal bond results of commercial waferboard at different specimen sizes* Internal Bond (MPa) s Size 2 cm n 2.45 120 0.411 0.112 0.273 6.27 100 0.407 0.098 0.241 17.85 100 0.364 0.078 0.214 23.25 85 0.365 0.076 0.208 29.28 75 0.332 0.062 0.187 56.25 75 0.321 0.048 0.150 101.23 70 0.310 0.044 0.142 225.79 62 0.307 0.041 0.134 398.78 29 0.31 0.033 0.106 * n number of observations; v coefficient of variation. - - - v average; s standard deviation; - 98 1.0 0.8 c 0.6 0 C) 0.4 0.2 0.0 0.0 0.2 0.4 0.6 0.8 Stress (MPa) Figure 31. 2-P and 3-P Weibull distribution fits to internal bond of one commercial waferboard at specimen . 2 size of 6.27 cm 99 1.0 2-P Weibull 0.8 Y = 1 - exp((XlO.33)8.41) 3-P Weibull 0.6 Y = 1 exp(.[(X-O.07Y0.2516s1) 0 0 - C) .. 0.4 C.) 0.2 0.0 0.00 0.15 0.30 0.45 Stress (MPa) Figure 32. 2-P and 3-P Weibull distribution fits to internal bond of one commercia’ waferboard at specimen size of 225.79 cm . 2 100 grain (Barrett, 1974). The expression of this size effect according to Weibulls (1939) 2-P distribution was (35) a=Ikm/V1k where, a and V are the strength and volume of material, k and m are the shape and scale parameters of 2-P Weibull distribution model which can be determined experimentally, and ‘k = re-dz was used by Weibull (1939) in the statistical manipulations. As the thickness of specimens used for the determination of 113 was constant and equal to the thickness of the commercial particleboard, Equation (35) was changed to a = Ikmt/A’ (36) for 113 of particleboard, where A is the specimen size (area) and t is the thickness. Equation (36) could also be rewritten into a general form such as a here, d = 1/k, a = a(1/A)d = IkmJtl]k. Both a and d could be determined by regression (37) analyses of experimental data. Figure 33 shows the 50th percentile of TB strength at several specimen sizes, together with a fit of Equation (37) to the experimental data. The 50th percentile of TB decreased with size in the fashion that Equation (37) prescribed for the range being studied. However, the mean, rather than the 50th percentile of TB is used exclusively in the particleboard industry for the purpose of product evaluation and quality control. It was assumed that Equation (37) would also be a good approximation of the relationship between average TB and specimen size, which is also shown in Figure 33. 101 0.45 I I • ‘ 040 50th percentile R2=0.89 Y = 0.44 14(IJX)° 649 Mean value R2=0.89 Y = O.4366(IJX)0.06 \x C 0.35 - •••. x . — 0.30 .x .......x - 0.25 I I 0 100 200 300 400 ) 2 Specimen Size (cm and average Figure 33. Influence of specimen size on 50th percentilewaferboard. strength of internal bond of one commercial 102 The similarities between Equations (37) and (18), and Figures 33 and 17 were obvious. By combining Equation (37) with Equation (18), a general expression relating average strength and horizontal density variation was obtained (Appendix I), a (38) = in which, ct and f are constants to be determined experimentally. The experimental results, together with a fit of Equation (38) are shown in Figure 34. Another result of the Weibull distribution for defining strength is that the variation of strength is specimen size dependent, i.e., variation decreases as specimen size increases. For the 2-P Weibull distribution, Weibull (1939) showed that the standard deviation of strength ç was ç where, k/2 = 1 = l Vilc ) 2 m(IIk / (39) z. re d 2 For lB property of the commercial waferboard studied, a general form based on Equation (39) can also be derived as ç = e(1/A) here, f = Ilk and e = (40) k are to be determined experimentally. The tIJk I m(Iw / 2 J 1 ) relationship between standard deviation of TB and specimen size is shown in Figure 35, together with the fit of Equation (40). A general relationship between the standard deviation of 113 and standard deviation of density similar to Equation (38), was obtained as (Appendix J) (41) 103 0.45 I I I I . 0.40 . 0 0.35 . R2=0.89 Y = 1.321(X)° 0.30 0.25 0.03 I I I L 0.04 0.05 0.06 0.07 0.08 ) 3 Standard Deviation of Density (glcm Figure 34. Relationship between average internal bond and standard deviation of density of one commercial waferboard. 104 0.12 0.10 0.08 0.06 0.04 0.02 0 100 200 300 Specimen Size (2) Figure 35. Influence of specimen size on standard deviation of internal bond of one commercial waferboard. 400 105 here, N’ and are also constants to be determined experimentally. Figure 36 shows the experiment results and the fit of Equation (41). Thus, variation in mechanical property (TB) decreased as variation of physical property (density) decreased. However, some discrepancies were evident as Equations (37) and (40), ) did not 2 and the Weibull fits for the two specimen sizes (6.27 and 225.79 cm yield the same value for the shape parameter k, which violated a property of Weibull theory. The large difference of k was due to the dependence of TB on density itself. It is widely accepted that TB increases as density increases. This relationship between TB and density for the commercial waferboard at 2 respectively, are shown in 2 and 225.79 cm two specimen sizes, 6.27 cm Figures 37 and 38. As density variation decreased with increasing specimen size, this density dependence characteristic of TB would decrease the variation of lB as specimen size increased. However, the average strength of TB was not affected in this manner. Therefore, larger shape parameters resulted for Equation (37), and for the 2-P Weibull fit at specimen size of . 2 225.79 cm Two consequences of this discrepancy are shown in Figures 39 and 40. Figure 39 shows that coefficient of variation of TB decreases as specimen size increases, rather than a constant value as one property of the 2-P Weibull distribution. In Figure 40, the relationship between average strength, the estimated 5th percentile (estimated by both 2-P and 3-P models), 95th percentile (estimated by 2-P model) of TB and specimen size is presented. Tt could be expected from this figure that below certain percentiles, strength would increase with specimen size within the specimen size range studied. This seems to contradict the Weibull strength theory, but it is the direct 106 0.12 0.10 0.08 0.06 0.04 0.02 0.03 0.04 0.05 0.06 0.07 ) 3 Standard Deviation of Density (gfcm Figure 36. Relationship between standard deviation of internal bond and standard deviation of density of one commercial waferboard. 0.08 107 0.7 I I 0.6 . a a II 0.5 • a • a a . I I I I I a S 0.4 a I :‘ a • I. I S a I. a a. • • a.• • C S ‘ . :; a a I I I I. • S a a R2 = 0.30 Y = -0.20 0.89 X + 0.1 I I 0.0 0.5 0.6 0.7 0.8 0.9 ) 3 Density (g/cm Figure 37. Relationship between density and internal bond of one . 2 commercial waferboard at specimen size of 6.27 cm 108 0.5 I I 0.4 I • . 0.3 I I I I .. • I I • • - .1 I II R C — Ce 0.2 = 0.58 Y = -0.28 ÷ 0.86 X 0.1 0.0 - — 0.5 0.6 0.7 0.8 0.9 Density (g/cm3) Figure 38. Relationship between density and internal bond of one . 2 commercial waferboard at specimen size of 225.79 cm 109 0.3 I I . g 0.2 . o E 0 Q 0.1 - 0.0 I 0 100 200 300 Specimen Size (cm ) 2 Figure 39. Influence of specimen size on coefficient of variation of internal bond of one commercial waferboard. The curve is fitted by eye without regression analysis. 400 110 0.6 p 0 0.5 A 3-P Weibull estimates • 2-P Weibull estimates 0 C 0.4 0 -. o ê-•1 Mean value . . 0.3 A 5th percentile A 0.2 0 100 200 Specimen Size 300 400 (2) Figure 40. Influence of specimen size on 5th percentile, 95th percentile and average of internal bond of one commercial waferboard. 111 result of the density dependence of TB. It was observed in our experiments, that a noticeable number of specimens simply fell apart due to their low . This was not 2 densities, when specimen size was smaller than 6.27 cm observed at larger specimen sizes. This problem of falling apart also existed in the study conducted by Suchsland and Xu (1991), when a small sized matrix element was used as the testing specimen. These observations suggest that specimen size should be large enough to avoid direct testing of defects (low density points), if the influence of defects is to be studied. Tn fact, this concept is similar to that applied in the study of lumber where test specimens are chosen to be significantly larger than major strength reducing defects, such as knots and localized slope of grain. Equations (38) and (41) described positive relationships between average strength, standard deviation of TB with standard deviation of density. According to these relationships, selection of specimen size in the less sensitive range of the S to A curve (Figure 17) would give average strength and standard deviation of TB which change less with specimen size. The selection of specimen size in this range will also avoid direct testing of defects, or low density points, as the variation of density above this specimen size is believed mainly to be controlled by nonuniformity in mat forming. Until now, the mean and standard deviation of particleboard properties are used almost exclusively for the purpose of product evaluation, comparison and quality control. All these observations demonstrate that the S to A curve should be used for the selection of appropriate specimen size for these purposes. The relationships observed in this study should be used as a criterion for the future selection of specimen sizes in relation to testing standards. 112 5.3.3. Thickness swelling The average TS of commercial waferboard, together with the standard deviation of TS, at several different specimen sizes and soaking times are presented in Table 15 and shown in Figures 41 and 42. Several important observations were made and summarized as follows. First, under the standard cold water soaking conditions, average TS decreased as specimen size increased for all the soaking times except at the one week soaking condition. A plateau was reached once specimen size . Thickness swelling was a continuous process involving 2 exceeded 25-50 cm the release of compressive deformation incorporated into particleboard during the pressing operation. Water up-take is a prerequisite for this release. Obviously, smaller specimens more readily absorb water, therefore, rapidly swell in thickness. But this did not account for TS results when . A model concept developed by 2 specimen size was larger than 25-50 cm Suchsland (1973) provided insight on this phenomenon. According to Suchsland, high and low density areas in a TS specimen respond differently to swelling by moisture, and their opposing nature leads to different behaviours of particleboard at different testing conditions. Since density variations in the commercial waferboard at specimen sizes larger than 25-50 2 were believed to be governed by forming uniformity, these sized cm specimens were considered not to be appreciably different as far as their interior structural characteristics were concerned. Therefore, a similar TS should result according to this model concept. With specimen size less than , density variations were considered to be a reflection of the 2 25-50 cm structural nonuniformity of particleboard (Figure 17), and according to 113 Table 15. Thickness swelling (%) of commercial waferboard at different specimen sizes and soaking times* Thickness Swelling (%) Specimen size (cm2) Hours 2 6 12 24 48 168 n 48 13 4.9 48 30 5.9 48 38 6.2 48 43 6.8 48 45 7.3 48 46 7.7 48 6 2.4 48 21 5.8 48 33 6.0 48 38 6.8 48 41 7.3 48 43 7.5 44 4 2.0 44 14 5.3 44 26 5.8 44 33 6.7 44 38 6.8 44 41 7.0 46 3 1.5 46 9 3.3 46 19 5.3 46 30 6.2 46 38 5.7 46 43 6.5 32 3 0.8 32 5 1.1 32 9 2.2 32 18 4.7 32 33 6.2 32 44 6.2 18 3 0.9 18 5 1.0 18 8 2.1 18 13 2.4 18 25 3.4 18 46 4.3 18 3 0.6 18 6 0.8 18 9 1.0 18 14 1.5 18 24 2.2 18 42 4.5 23 3 0.6 23 8 1.0 23 9 1.6 23 17 2.0 23 28 2.7 23 41 3.7 4.26 s n 8.39 s n 12.85 s n 17.49 s n 25.12 s n 56.25 s n 100.38 s n 224.50 s * n = number of observations; i = average; s = standard deviation. 114 50 I I I I 168 hrs. 40 - ‘ “ 30 Cl) ri) C) 20 - \ 10 6h — — — — — 2hrs. 0 0 50 I I I 100 150 200 250 Specimen Size (cm ) 2 Figure 41. Influence of specimen size on average thickness swelling of one commercial waferboard at different soaking times. 115 8 6 \ A \ 4 \ • • 8h.s. 6 •Z \\\ . \ - 2 _±It__. N. “N 6hrs._ • 0 0 50 100 150 200 250 Specimen Size (cm ) 2 Figure 42. Influence of specimen size on standard deviation of thickness swelling of one commercial waferboard at different soaking times. 116 Suchsland’s model concept, individual TS specimens swelled more freely as specimen size decreased. Secondly, as found with horizontal density variation, the standard deviation of TS decreased as specimen size increased, and this decrease was , which was in the 2 not obvious when specimen size was larger than 25-50 cm less sensitive range of the density variation versus specimen size plot (Figure 17). This can be readily explained by the application of Suchsland’s (1973) , density variations 2 concept. When specimen size was larger than 25-50 cm were small and less sensitive to specimen size changes, therefore, small and fairly constant variations of TS resulted. When specimen size was less than , density variation increased as specimen size decreased, and 2 25-50 cm because individual specimens swelled more freely at this specimen size range, large variation of TS resulted. Thirdly, one week of soaking probably released all the TS in particleboard as determined by this cold water soaking method, since the average TS values for all the specimen sizes were fairly consistent. This can be clearly seen from the plot of TS versus soaking time for specimen size of , shown in Figure 43. Since TS did not change significantly from 48 2 4.26 cm hours to one week of soaking, and since TS of all the specimen sizes were consistent at one week of soaking condition, it was concluded that further soaking after one week would not increase the TS significantly for the specimen size studied. Similar to the TB test, the average and standard deviation of TS are used almost exclusively for the purpose of quality control and product comparison. The selection of specimen size from the less sensitive range of 117 50 40 I 30 20 10 0 0 30 60 90 120 150 Soaking Time (hrs.) Figure 43. Thickness swelling vs. soaking time of one commercial . 2 waferboard at specimen size of 4.26 cm 180 118 the horizontal density variation versus specimen size plot (Figure 17) will yield stable and consistent results with less variation, according to the observations made above. These qualitative findings could also be used as one criterion for the future development of TS testing method for particleboard, with regard to specimen size selection. For example, the change of specimen size from 25 mm x 25 mm to 50 mm x 50 mm for furniture grade particleboard in Europe as a result of CEN-standardization resulted in the reduction of variation of this property (Heimeshoff, 1991). Finally, one week soaking should be applied to determine the TS property, especially for the purpose of product evaluation and development, as it was the most reliable and true index of dimensional stability. 119 5.4. Influence of Horizontal Density Distribution on Some Board Properties 5.4.1. Introduction In section 4.2, a detailed investigation on particleboard structure identified some principles regarding the influence of raw material characteristics on HDD. In section 4.3, HDD was found to be a potential concept or criterion in selecting specimen size for some board property evaluations. In this section, particleboards with different HDD characteristics were made using particles more representative of commercial sized distributions. The intention was to establish the relationship between HDD and some common board properties. If this objective was met, the concept of HDD could be used to better understand present and future particleboard technology. 5.4.2. Application of adhesive As discussed earlier, particleboard properties were improved by increasing resin content, with TB being the most sensitive property. The deficiency of using a fixed percentage of resin content based on wood weight, as practiced traditionally in particleboard studies, is well recognized. Since changes in HDD were achieved by using different particle geometries, wood species or combination of both in this study, this resin deficiency needs to be removed in order to accurately study the influence of horizontal density variation on particleboard properties. With the application of powder adhesives, it was believed that only certain quantities of resin were being picked up by wood particles. Two to 120 three percent based on wood weight was believed to be normal for current commercial wafers/strands (Steiner, 1992). Therefore, provided a surplus of resin is applied in the blending operation, maximum and uniform resin pick up could be consistently achieved throughout all the different particles based on particle surface area. Thus, any possible variation of particleboard properties due to resin application is minimized. To test this proposition, an experiment was carried out to blend several different resin contents with commercial particles p1, using TB as the property for evaluation. The same procedures of making laboratory 3 and a particleboard were followed, and a board density of 0.72 g/cm thickness of 11 mm were targeted. The TB mean, together with the calculated 95% confidence interval based on an assumption of normal distribution are presented for several resin content levels in Figure 44. It was concluded that TB was not benefited by increasing apparent resin content above 6%, an indication that a maximum resin pick-up was achieved. It should be mentioned that 6% was not necessarily the actual amount of resin picked by the particles, nor should it be taken as the level to apply to any experimental conditions. This was the resin level at which an obvious amount of extra resin was observed in this experiment to be left in the blender, after the rest was picked up by the particles and the blender surface. The presence of this extra resin is an indication that maximum pick-up of resin has been reached. This indicator was used to manufacture subsequent particleboards for studying the influence of HDD on particleboard properties. Obviously, the actual resin content will depend on moisture content, surface area and surface conditions of particles, size and surface conditions of the blender and other factors. 121 0.60 I I I I 0.45 1 p. -d 0 . - 0.15 1- 0.00 - 0 3 9 12 15 Apparent Resin Content (%) Figure 44. Influence of apparent resin content on internal bond. 122 5.4.3. Board formation Particleboards used to study the influence of HDD on board properties were manufactured in the laboratory. The composition of these boards is presented in Table 4, and the respective distributions of particle sizes are shown in Appendix A. Table 16 presents the density variations for these boards measured at several different specimen sizes. As these particleboards were made using different distributions of particle length, width and thickness, and sometimes a combination of different species, a thorough interpretation of the structural differences of these boards in terms of individual raw material characteristic was difficult. However, the examination of two extreme board cases (P5 and P7) demonstrates that the observations made in section 4.2 were valid. Board P5 was made by using the largest particle size (an average of 119 mm x 88 mm) with smallest particle thickness (an average of 0.52 mm). Accordingly, a much lower standard deviation of density was observed at small specimen sizes. Board P7 was manufactured with the thickest birch particles (an average of 0.93 mm), therefore, much higher density variations were observed. The relationship between the standard deviation of density with both specimen size and the inverse of specimen size are shown respectively in Figures 45 and 46 for these particleboards. In order to present the data more clearly, the boards were divided into two portions for presentations in the figures. Most importantly, this data showed that these boards differed considerably in standard deviation of density at relatively small specimen sizes. This provided the material base for studying the influence of HDD on board properties. 123 Table 16. Density measurement for laboratory particleboard* ) 3 Density (glcm Specimen Size ) 2 (cm Board P1 n s P4 P5 P6 P8 P7 P9 P10 s 25 25 25 25 25 25 25 25 25 25 .747 .744 .752 .753 .758 .759 .755 .746 .747 .751 .034 .026 .039 .046 .050 .040 .041 .032 .035 .045 n 1 s 25 25 25 25 25 25 25 25 25 25 .731 .751 .754 .737 .760 .743 .767 .740 .742 .752 .048 .031 .060 .052 .051 .065 .076 .042 .060 .046 n 25 25 25 25 25 25 25 25 25 25 .746 .745 .757 .758 .764 .755 .736 .752 .761 .748 .057 .045 .071 .055 .086 .082 .091 .078 .088 .066 n 134.560 11.401 s s 25 25 25 25 25 25 25 25 25 25 .752 .749 .757 .730 .744 .764 .724 .752 .743 .743 .104 .089 .084 .09 .069 .06 .075 .081 .088 .09 1.267 n 1 s 50 50 50 50 50 50 50 50 50 50 .748 .752 .757 .764. 760 .769 .776 .740 .738 .744 .096 .100 .100 .092 .105 .132 .124 .110 .122 .132 0.317 n 1 s 75 75 75 75 75 75 75 75 75 75 .768 .752 .745 .773 .744 .777 .766 .767 .766 .764 .129 .116 .125 .113 .110 .148 .163 .131 .140 .150 0.126 n 1 s 100 100 100 100 100 100 100 100 100 100 .765 .765 .761 .722 .776 .724 .731 .728 .732 .765 .142 .138 .135 .124 .117 .168 .181 .144 .159 .171 n 5.067 * P3 12 12 12 12 12 12 12 12 12 12 .749 .758 .748 .748 .754 .756 .758 .754 .740 .752 .026 .018 .031 .032 .038 .037 .038 .025 .027 .032 278.48 55.080 P2 . — . n = number of observations; x = average; s = standard deviation. The 2 was measured by y-ray method. density at specimen size of 5.067 cm 124 0.20 I 0.15 0.10 . 0.05 0.00 0 70 140 210 280 210 280 Specimen Size (cm ) 2 0.20 0.15 0 0.10 G) aS 0.05 I 0.00 0 70 140 ) 2 Specimen Size (cm Figure 45. Standard deviation of density vs. specimen size for laboratory particleboard. 125 0.20 0.15 0.10 j 0.05 3 Ci) 0.0w 4 0 1/A 6 8 6 8 (cm-2) 0.20 I 0.15 0.10 0.05 0.00 0 2 4 hA (cm-2) Figure 46. Standard deviation of density vs. 1/A for laboratory particleboard 126 From Figure 45, it is striking to notice that the standard deviation of density is less size sensitive when specimen size is larger than approximately 2 for all particleboards, which also coincides with the less sensitive 50 cm range for the commercial waferboard (Figure 17). This observation suggests that the less sensitive range may not be influenced much by wood species and particle sizes, within the particle size range being used and the forming menthods being utilized. By using the observations in section 4.3, it was decided to select a specimen size of 100 mm x 100 mm, rather than 50 mm x 50 mm, as specified in published standard (Canadian Standard Association, 1985), for lB and TS tests. A specimen width of 100 mm, rather than 75 mm, was also chosen for bending tests. As three replicates were made for each board condition, and only one board was used to determine HDD characteristics, board reproducibility needs to be examined. Figure 47 shows this examination for board P1. It was assumed that the reproducibility was acceptable for this study. 5.4.4. Modulus of rupture and modulus of elasticity The essence of Weibull theory of strength is that the worst defect or weakest link controls the strength of a material. By applying this theory to different sizes of the same material, a size effect is recognized. Strength decreases as specimen size increases, simply because more defects are expected in a bigger volume. Therefore, volume could be viewed as an index of defect in the size effect formula of Equation (35). Now, let us consider similar materials having different strength properties measured at the same specimen size. If the defects inside a material could be quantified, the 127 0.16 I 0.12 - 0.08x C) CI) X boardi “ board2 D 0.04 - 0.00 0 I I 2 4 1/A Figure 47. Reproducibility 6 (cm-2) of board formation of board P1. 8 128 underlying principle in size effect formula should be applicable to develop a concept to explain the strength differences among materials. Specifically, for particleboards with different HDD characteristics, if this density variability is the major strength reducing defect, then density variability could be taken as the quantifying defect, and used to relate to strength properties of particleboard. A concept of nonuniformity effect, similar to that of size effect formula was proposed here to account for the difference of strength properties by standard deviation of density, that was: P = m(1/S) (42) where, P and S are the property and standard deviation of density of particleboard respectively, and m and n are constants. Modulus of rupture and modulus of elasticity results for laboratory boards are presented in Table 17. The relationship between MOR and standard deviation of density is shown in Figure 48, together with a fit of Equation (42). It should be recognized that the specimen size used to determine the standard deviation of density is different in each small plot, but MOR of particleboards were determined at a fixed specimen size and the same MOR values were used throughout the figure to examine the influence of density nonuniformity. For example, P5 has a value of 46.8 MPa (the highest data point in each plot) for MOR, but the standard deviation of density changes when specimen size used to determine this variation changes. As Figures 45 and 46 suggested, particleboard structure differences were detected more clearly and consistently when specimen size was smaller, 129 Table 17. Modulus of rupture and modulus of elasticity of laboratory particleboard MOR (MPa) Board Average P1 P2 P3 P4 P5 26.9 25.1 31.6 25.5 29.4 33.1 25.5 24.2 26.2 27.8 29.1 25.3 32.1 35.1 34.2 36.3 41.9 37.6 38.5 32.1 28.2 34.7 40.5 37.9 42.1 26.5 17.8 48.5 14.5 15.4 43.7 12.3 12.0 44.9 27.5 12.4 49.3 17.5 14.4 52.3 20.5 20.5 28.6 26.3 36.2 35.3 46.8 P6 P7 P8 P9 P10 19.1 24.6 17.2 25.0 20.8 20.8 27.4 18.9 30.2 16.9 19.1 18.0 29.6 27.8 25.2 23.8 23.2 16.3 19.8 15.4 21.2 25.8 20.3 MOE (MPa) Board Average P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 4000 3800 4700 3600 4300 4600 3100 2900 3300 3700 3500 3800 4300 5000 5100 5100 5300 5400 4600 4000 4000 4200 5100 5000 6000 6100 5700 5700 6300 6600 3900 3000 3400 3600 3400 3600 1900 1600 1800 1600 1300 2200 3100 3800 3300 3800 3600 3500 3100 3100 3900 3700 3800 3000 1600 2000 2000 2400 2500 1700 4200 3400 5000 4500 6100 3500 1700 3500 3400 2000 130 60 60 JSize= 1.267cm2j 2 [ize=5.067 cm a 0 40 40 a I 0 0 0 0 0 0 0 MOR = 5.124(1,)o.663 R2 = 0.09 0— 0.04 0.06 MOR = 0.537(IiS)’7 R2 = 0.49 0.08 0.10 0 0.08 0.12 0.10 60 60 = 0.14 Standard Deviation of Density ) 3 (g/cm Standard Deviation of Density ) 3 (g/cm [Size 0.12 1 Size= 0.126cm 1 2 0.3 17 cmj 0 40 40 0 I 0 — 20 0 0 20 0 MOR = 0.273(L) ° 224 R2 = 0.77 0— 0.10 0.12 0.14 MOR = 6 .’ 2 0.414CL) ° R2 = 0.84 0.16 Standard Deviation of Density ) 3 (g/cm 0.18 0— 0.10 0.12 0.14 0.16 0.18 Standard Deviation of Density ) 3 (glcm Figure 48. Relationship between modulus of rupture and standard deviation of density of laboratory particleboard. The specimen size used to determine standard deviation of density is different and indicated in each plot. 020 131 therefore, only the four smallest specimen sizes (used to measure density nonuniformity) were used in the presentations in Figure 48. As expected, MOR decreased as standard deviation of density or density nonuniformity increased. It is believed that the low density portions controlled the bending failure of particleboard, as poor or no bonding occurred in these portions. As density nonuniformity increased, these lower density portions increased, and a lower MOR resulted. Moreover, the fit of Equation (42) improved as specimen size used to detect the density nonuniformity decreased (R2 increased as specimen size decreased). This suggests that a certain size resolution is needed, if a procedure is going to be developed to detect structural nonuniformity. Particleboards used to study the relationship between HDD and MOR in this thesis were manufactured with different particle length, width, thickness distributions, different wood species (aspen and birch) and combinations thereof. A direct analyses of MOR in terms of these raw material characteristics, which was the traditional approach, is not feasible. The rationalization of MOR in terms of standard deviation of density (R2 are 0.77 2 respectively) 2 and 0.126 cm and 0.84 when specimen size are 0.317 cm demonstrates that density nonuniformity or HDD is a true structural feature of particleboard. The close relationship between HDD and raw material characteristics indicates that a singular parameter of HDD is sufficient to study the effects of the latter on MOR, just as vertical density profile is used to characterize pressing strategy parameters. A similar analysis for MOE is shown in Figure 49. Although MOE is not a strength property, Equation (42) was still used to relate MOE to standard 132 8000 8000 [Size = 5.067 I Size 2l = 1.267 cm2l 0 6000- 6000 0 0 0 000 0 4000 0 0 2000 0 - 2000 0 0 MOE = 339.65(1IS)°-937 =0.13 2 R 00.04 0.06 0.08 - 0 MOE • 448()1.987 2 = 0.43 R 0.10 0— 0.08 0.12 Standard Deviation of Density ) 3 (g/cm 0.10 0.12 014 Standard Deviation of Density ) 3 (g/cm 8000 8000 I Size = 0.3 17 cm2 Size = 0.126 cm2] 0 60O0 6000 a 0 0 11000 a 4000 0 0 0 0 — •2000 2000 0 0 .582 2 MOE = 18.75(t) R2 = 0.70 0 0.10 MOE = 29.22(1j)2 497 R2 = 0.78 0— I 0.12 0.14 0.16 Standard Deviation of Density ) 3 (g/cm 0.18 0.10 0.12 0.14 0.16 0.18 Standard Deviation of Density ) 3 (glcm Figure 49. Relationship between modulus of elasticity and standard deviation of density of laboratory particleboard. The specimen size used to determine standard deviation of density is different and indicated in each plot. 0.20 133 deviation of density. Again, a significant relationship (R2 = 0.78 at a specimen size of 0.126 cm ) existed between MOE and density nonuniformity, and the 2 fit of Equation (42) improved (R2 increased) as specimen size used to determine density variation decreased. The close relationship between HDD and this elastic property further demonstrates that HDD is a parameter to characterize particleboard structure, and is capable of describing the effects of raw material characteristics, which involve multi-parameters. 5.4.5. Internal bond Internal bond values are provided in Table 18. Figure 50 shows the influence of standard deviation of density on TB, together with a fit of Equation (42). A significant relationship (R 2 0.77 at a specimen size of ) between micro-density nonuniformity and TB was obtained. Apart 2 0.126 cm from the explanation given in 4.4.3, there may be another reason that 113 decreased as nonuniformity increased. That is, at the same board density, relative bonded area (section 2.1.8) decreased as density variation increased. It is believed that TB is positively related to RBA. The same particleboards used to study the effect of HDD on MOR and MOE were used in the study of TB. The reason why raw material characteristics affect IB, which was not understood well in the past, was readily explained by HDD, a structural phenomenon of particleboard. 5.4.6. Thickness swelling Thickness swelling results of these particleboards based on one week cold water soaking are also presented in Table 18. The influence of horizontal density variation on TS is shown in Figure 51. Although TS is not a strength 134 Table 18. Internal bond and thickness swelling of laboratory particleboard* Internal Bond (MPa) Board P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 n 25 25 25 25 25 25 25 25 25 25 .430 .400 .410 .501 .631 .261 .289 .440 .441 .329 .044 .042 .044 .046 .042 .047 .048 .051 .038 .043 s Thickness Swelling (%) Board P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 n 25 25 25 25 25 25 25 25 25 25 5 44 42 42 31 25 55 63 52 58 54 s 5.1 3.2 4.4 4.8 4.1 5.0 5.3 4.6 4.5 5.1 * n = number of observations; = average; s = standard deviation. 135 0.8 0.6 ISize= 1.267cm21 [= 5.067 2] 0 0 0.6 C 0 0 0 0.4 C) 0 B 0.4 C) 0 02 02 - lB = 0.0214(IJS)1.S288 R2=0.47 lB = O.1513(1IS)° R2=O.05 0.0 0.04 0.0 0.08 — — 0.10 0.08 0.06 0.12 0.8 - [Size 0.14 0.12 Standard Deviation of Density ) 3 (g/cm Standard Deviation of Density ) 3 (glcm 0.8 0.10 I I — = 0.317 2] I Size = 0.126 cm2 0 0 0.6 0 — .0 0.4 - 0 0 0 0 0 00 0.4 C) C) 0 1-4 02 02 - lB = =0.77 2 R lB = 0.0138(IJS)1.6610 = 0.70 2 R 0.0 0.10 0.0 0.10 — — 0.12 0.14 0.16 Standard Deviation of Density ) 3 (g/cm 0.18 0.12 Standard 0.14 0.16 0.18 Deviation of Density ) 3 (g/cm Figure 50. Relationship between interna:1 bond and standard deviation of density of laboratory particleboard. The specimen size used to determine standard deviation of density is different and indicated in each plot. 020 136 80 80 I Size = 5.067 21 lSize= L267cx1 a e 60 60 0 b 0 B 0 . — . C) C4O u Ci) 40 - U) ,.C) a 0 . 20 20 TS = 146(1iS)°47 R = 0.05 2 0— 0.04 0.06 0.08 0.10 T5 1244(1)’6’ R2 = 0.48 0— 0.08 0.12 Standard Deviation of Density ) 3 (g/cm 0.12 0.10 0.14 Standard Deviation of Density ) 3 (glcm 80 80 ISize=0.i26cm2I FSize=0.317Cn1!j r 0 0 60 0 0 0 0 C 0 Ci) 40 U) U) C) 0 20 20 TS = 2496(1/s)1.98 R2 = 0.79 0— 0.10 TS = 1713(j.)1.89 R2= 0.86 I 0.12 0.14 0.16 Standard Deviation of Density ) 3 (g/cin 0.18 0— 0.10 0.12 0.14 0.16 0.18 Standard Deviation of Density ) 3 (g/cm Figure 51. Relationship between thickness swelling and standard deviation of density of laboratory particleboard. The specimen size used to determine standard deviation of density is different and indicated in each plot. 020 137 property, Equation (42) was still adopted to relate TS to standard deviation of density. A good fit was obvious between this physical property and structural 2 and 0.317 property (R2 are 0.86 and 0.79 when specimen sizes were 0.126 cm 2 respectively), which also demonstrates that HDD is an important cm structural phenomenon. This can be readily rationalized by using Suchsland’s (1973) model concept. Suchsland reasoned that at higher moisture content, higher density portions dominated TS. As density nonuniformity increased, higher density portions increased. Therefore, higher TS resulted according to Suchsland’s concept, and Equation (42), if used for TS property, agrees with this concept. 5.4.7. Summary While TS was controlled by the higher density portions of a panel, strength properties (MOR and TB) and MOE were believed to be controlled by the lower density portions. In either case, standard deviation of density was a good index to distinguish among particleboards. This was probably why Equation (42) provided a good fit between micro-density variation and different properties. Although this equation may not necessarily best fit the data points in terms of goodness-of-fit, the simplicity of this equation helps to better understand the significance of the horizontal density phenomenon. After all, Equation (42) was proposed on the basis of the concept of Weibull (1939) theory of strength. The associations between HDD, raw material characteristics and some board properties, demonstrates that HDD is a singular structural parameter capable of describing the effects of raw material characteristics and possibly forming technology. 138 6. SUMMARY AND CONCLUSIONS The concept of HDD was first proposed by Suchsland in 1959 to analyze particleboard technology. A gravimetric method involving a drilling technique was shown to be capable of detecting the micro-density variation in particleboard, as well as distinguishing particleboards in this regard. It was found that this variation decreased as specimen size, used in determining this density nonuniformity, increased. If standard deviation of density was used as the index of nonuniformity, the expression S = a(IJA)b was shown to be appropriate to relate density variation (S) to specimen size (A). Parameter b related to correlations of density points, and a range between 0 and 0.5 was determined for this parameter. It was found that b decreased as particle size increased. Raw material characteristics influenced HDD. Generally, with larger specimen sizes, particleboards made with larger particles exhibited greater density variations. With smaller specimen sizes, particleboards made with smaller particles showed larger density variations. The size and number of voids were identified as responsible for these results for mats provided under hand-forming operations. The recognition of these two aspects of voids suggests that forming method plays a significant role in determining the magnitude of HDD. Any method which reduces the size of voids in between particles would improve board uniformity. A layer concept was developed and used to study the effects of particle thickness, board thickness, board density and wood species on HDD of particleboard. This concept was based on the observation that an increase in particle layers reduces density variations. 139 Particleboard properties were shown to be greatly influenced by horizontal density nonuniformity. While TS was considered to be controlled by high density portions of the boards, MOR, MOE and TB were believed to be controlled by low density portions. A concept of nonuniformity effect expressed as P = m(1/S), similar to the size effect formula, was proposed and was shown to be feasible in relating conventional particleboard properties (P) to standard deviation of horizontal density (S). The concept of HDD was also shown to be a potential criterion for the future development of particleboard testing standards in relation to specimen size selections. Both the average values and standard deviations of TB and TS decreased as specimen size increased. The selection of specimen size for TB and TS tests from the less sensitive range in the density variation vs. specimen size curve, was capable of producing consistent and stable test results. In the thickness swelling tests, one week of cold water soaking probably released most of the thickness expansion. One week soaking is recommended for evaluation and comparison of dimensional stability of particleboard. The relationships between HDD, raw material characteristics and board properties, demonstrate that HDD is a fundamental variable for studying particleboard structure and technology. HDD can be used to describe raw material characteristics effects, just as vertical density profile is used for studying pressing strategy parameters. This study showed that: - - raw material characteristics affect HDD, conventional board properties are controlled by HDD, 140 - the concept of HDD should be a criterion for the selection of test specimen size, 6.1. Future Developments The gravimetric method using the drilling technique was capable of detecting micro-density nonuniformity, but it is destructive and time consuming. A non-destructive method with good resolution, probably based on VisionSmart X-ray technology, is required for future development of the concepts presented in this thesis. The availability of that technique will make it possible for both physical structure and board properties to be determined on the same board. The finding that the number and size of voids influence the horizontal micro-density nonuniformity, suggests that a future priority should be given to research and development of an improved forming technology, in which size of voids could be minimized and board uniformity improved. Ultimately, particleboard could be viewed as a three dimensional nonuniform structure. With the establishment of the concept of horizontal density distribution, a concept of a three dimensional density distribution could be developed by combining the knowledge of vertical density profile. This concept could lead to the development of a general theory on short-fibre wood composites, similar to the laminate theory for continuous fibre composites. This thesis did not examine how well particle bonding was achieved. 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Trend: the activities of the pulp and paper research institute of Canada. 15:7-12. - Parsons, S. 1942. Optical characteristics of paper as a function of fibre classification. Paper Trade J. 115:314-322. Plath, L. 197 lb. A contribution on particleboard mechanics. Holz als Roh-und Werkstoff. 29(10):377-382, Plath, L.; E. Schnitzler. 1974. The density profile, a criterion for evaluating particleboard. Holz als Roh-und Werkstoff. 32(1l):443-449. Post, P. W. 1958. The effect of particle geometry and resin content on bending strength of oak particleboard. For. Prod. J. 8(l0):317-322. Post, P. W. 1961. Relationship of flake size and resin content to mechanical and dimensional properties of flakeboard. For. Prod. J. l1(l):34-37. Post, P. W. 1983. Effect of test piece size on panel bending properties. International Council for Building Research Studies and Docurñentation Working Commission W18-timber Structure. Rackwitz, 0. 1963. Influence of chip dimensions on some properties of wood particleboard. Holz als Roh-und Werkstoff. 21(6):200-209. Ratliff, F. 1949. The possible correlation between hemicelluloses and the physical properties of bleached kraft pulps. Tappi. 32(8):357-368. Seth, R. S. 1990. Fibre quality factors in papermaking 1. The importance of fibre length and width. Mat. Res. Soc. Symp. Proc. 197:125-141. - Seth, R. S. 1990. Fibre quality factors in papermaking 2. The importance of fibre coarseness. Mat. Res. Soc. Symp. Proc. 197:143-161. - 147 Seth, R. S. 1993. Personal communication. Shaler, S. M.; P. R. Blankenhorn. 1990. Composite model prediction of elastic moduli for flakeboard. Wood and Fibre Sci. 22(3):246-261. Shen, K. C.; M. N. Carroll. 1969. A new method for evaluation of internal strength of particleboard. For. Prod. J. 19(8):17-22. Shen, K. C.; M. N. Carroll. 1970. Measurement of layer strength distribution in particleboard. For. Prod. J. 20(6):53-55. Smith, H. F. 1938. An empirical law describing heterogeneity in the yields of agricultural crops. J. Agr. Sci. 28:1-23. Soszynski, R. M. and R. S. Seth. 1985. Improving the strength of linerboard. 1985 international Packaging Conference Proceedings, Beijing, China. 590-604. Stegmann, G.; J. Durst. 1964. Particleboard from beech wood. Holz-Zertralbe. 90(153):3 13-318. Steiner, P. R. 1989. Personal communication. Steiner, P. R. 1992. Personal communication. Stewart, H. A.; W. F. Lehmann. 1973. High-quality particleboard from cross grain, knife-planed hardwood flakes. For. Prod. J. 24(9):104-106. Strickler, M. D. 1959. Effect of press cycle and moisture content on properties of Douglas-fir flakeboard. For. Prod. J. 9(7):203-205. Suchsland, 0. 1959. An analyses of the particleboard process. Agr. Exp. Sta., Mich. State Univ. 42(2):350-372. Q. Bull., Mich. Suchsland, 0. 1962. The density distribution in flakeboards. Agr. Exp. Sta., Mich. State Univ. 45(11):104-121. Q. Bull., Mich. Suchsland, 0. 1967. Behaviour of a particleboard mat during the pressing cycle. For. Prod. J. 17(2):51-57. Suchsland, 0. 1968. Particleboard Lumberman. 139-144. from southern pine. Southern Suchsland, 0. 1973. Hygroscopic thickness swelling and related properties of selected commercial particleboards. For. Prod. J. 23(7):26-30. Suchsland, 0.; H. Xu. 1989. A simulation of the horizontal density distribution in a flakeboard. For. Prod. J. 39(5):29-33. Suchsland, 0.; H. Xu. 1991. Model analyses of flakeboard variables. For. Prod. J. 41(11/12):55-60. 148 Szabo, T. 1980. Flexual properties of waferboard. Technical Report 505ER, Forintek Canada Corp. Talbott, J. W.; T. M. Maloney. 1957. Effect of several production variables on the modulus of rupture and internal bond strength of boards made of green Douglas-fir planer shavings. For. Prod. J. 7(10):395-398. Turner, H. D. 1954. Effect of particle size and shape on strength and dimensional stability of resin bonded wood-particle panels. For. Prod. J. 4(5):210-222. U.S. Department of Commerce, National Bureau of Standards. 1974. Voluntary product standard for construction and industrial plywood, PS 1-74. Vanmarcke, E. H. 1984. Random fields: analysis and synthesis. The MIT press, Cambridge, Massachusetts. Wang, P. 1985. Determination of rheological parameters of wood in compression perpendicular to grain. Scientia Silvae Sinicae. 21(4):404413. Wang, P. 1987a. The rheological behaviour of poplar wood in compression perpendicular to grain. I. Viscoelasticity. Scientia Silvae Sinicae. 23(2): 182-190. Wang, P. 1987b. The rheological behaviour of poplar wood in compression perpendicular to grain. II. Plasticity. Scientia Silvae Sinicae. 23(3):357363. Wang, P. 1989. The rheological behaviour of poplar chips in compression perpendicular to grain. Scientia Silvae Sinicae. 25(6):522-528. Wang Y. T.; R. 0. Foschi. 1992. Random field stiffness properties and reliability of laminated wood beams. Structural Safety. 11:191-202. Weibull, W. 1939. A statistical theory of the strength of materials. Swedish Royal Inst. Eng. Res. Proc., Stockholm, Xiong, P. 1991. Modelling strength and stiffness of Glulam. M.Sc. thesis. The University of British Columbia. Xu, W. 1989. Thickness swelling of particleboard. Unpublished directed study. The University of British Columbia. Young, C.; J. Thorpe. 1977. Density distribution vs. wet strain in paper sheets. Tappi. 60(12):141-145. Youngs, R. L. 1957. The perpendicular-to-grain mechanical properties of Red Oak as related to temperature, moisture content, and time. U.S. For. Service Report FPL No. 2079. Zhang, R.; A. W. Warrick; D. E. Myers. 1990. Variance as a function of sample support size. Mathematical Geology. 22(1):107-121. 149 APPENDIX A Description of Particles Used for the Study of the Influence of Horizontal Density Distribution on Board Properties 150 n = = 71.6mm s=15.7mm 0.5 0.40.30.2- 0 100 0.1- •1 20 50 80 140 110 Particle Length (mm) n = 100 1=17.6mm s = 10.3 mm 0.3 g 0.21 0.1-1 0 40 20 I I 60 80 Particle Width (mm) n = 100 1=0.69mm 8=0.23mm 0 0.2.1 a o.i-I 0 0.0 0.4 0.8 1.2 — 1.6 Particle Thickness (mm) Figure A-i. Distribution of dimensions of aspen commercial particle p1. n = number of observations, 1= average, s = standard deviation. 151 n=71 = 46.2 mm s = 6.5 mm 0.4 •. 0.31 a 0.2-I 0.11 20 50 ,80 Particle Length (mm) o n=71 1= 19.5 mm 0.4. 0.3 0.1. 0 30 60 Particle Width (mm) .2 e 0.3 0.2 n=71 Y= 0.56 mm s=0.2lmm 1 0.1 0.0 0.8 1.6 Particle Thickness (mm) Figure A-2. Distribution of dimensions of aspen commercial particle p2. standard deviation. = number of observations, I = average, s 152 = 100 1=82.8mm s=23.8 mm g 0.4 C 0 s.. 0.1 — I I I 20 50 80 •1 140 110 Particle Length (mm) n = 100 1=13.2mm 0.4 8=7.9 mm Particle Width (mm) n = 100 1=0.66mm s = 0.19 mm0.0 0.0 OA 0 1.2 — 1.6 Particle Thickness (mm) Figure A-3. Distribution of dimensions of aspen commercial particle p3. n = number of observations, = average, s = standard deviation. 153 Ti 0 .. 0 0 s-I =75 x= 118.8 mm s = 6.1mm 0.4 0.3 0.2 0.1 90 120 150 Particle Length (mm) n 0.4 = 75 = 87.6 mm s8.0 mm to.2 0.1 5-4 60 74 88 100 120 Particle Width (mm) n =75 0.4 0.3 0.2 i= 0.52 mm s=0.lOmm 0 0.2 0.6 1.0 Particle Thickness (mm) Figur€ A-4. Distribution of dimensions of aspen laboratory particle p5. n = number of observations, = average, s = standard deviation. 154 n=136 g p 0.7 0.6 62.1 mm - - s=9.9mm s... 040.30.20.1• I 20 —F50 -i 140. 110 80 Particle Length (mm) n = 133 33.7 mm s=15.2mm -i---r-—i—-_—i 80 60 Particle Width (mm) 120 n= 0.50.4 =0.96mm _s=mm 0.00 0.32 0.64 0.96 1.28 1.60 Particle Thickness (mm) Figure A-5. Distribution of dimensions of aspen laboratory particle v6. n = number of observations, = average, s = standard deviation. 155 n= 110 =58.8mm 8=9.0mm 0.5 0.4 0 0 0 0.1 30 70 50 90 110 Particle Length (mm) n= 110 Y3L4mm 13.8 mm 8 0.2 I 0 0 rm-rrrH 20 II’’ I 40 80 60 Particle Width (mm) I 0.4 0.3 0.2 0.1 n = 110 1=0.93mm s=0.llmm 1.3 1.6 Particle Thickness (mm) Figure A-6. Distribution of dimensions of birch laboratory particle p7. n = number of observations, = average, s = standard deviation. 156 APPENDIX B Description of Obtainment of TB Specimens for Commercial Waferboard 1. Nine commercial waferboard panels of size of 1220 mm x 606 mm were cut into 18 smaller panels of size of 608 mm x 606 mm. Three of these smaller panels were randomly selected to make approximately 200 mm x 200 mm sized TB specimens; 2. lB specimens at a target size of 150 mm x 150 mm were prepared from 4 panels of 608 mm x 606 mm, which were also randomly selected; 3. Approximately 100 mm x 100 mm sized lB specimens were prepared from 117 mm x 116 mm sized density specimens; 4. One panel of 608 mm x 606 mm was randomly chosen and used to make specimens at a target size of 75 mm x 75 mm; 5. Density measurement specimens of approximately 54 mm x 54 mm were also used for TB test at this size; 6. lB specimens at a target size of 48 mm x 48 mm were cut from one randomly selected panel of size of 608 mm x 606 mm; 7. One panel of size of 608 mm x 606 mm was randomly chosen for preparing specimens of approximately 42 mm x 42 mm for 113 evaluations; 8. Approximately 25 mm x 25 mm TB specimens were prepared from forty unused density specimens of size of 54 mm x 54 mm; 9. One panel of size of 608 mm x 606 mm was randomly chosen for TB specimens at a target size of 15 mm x 15 mm. 157 APPENDIX C Description of Obtainment of TS Specimens for commercial Waferboard 1. Two panels of size of 608 mm x 606 mm were randomly chosen from rest of these sized panels to make TS specimens at a target size of 150 mm x 150 mm; 2. One panel of 608 mm x 606 mm was used for TS test at a specimen size of approximately 100 mm x 100 mm; 3. TS specimens at a target size of 75 mm x 75 mm were prepared from one randomly selected panel of 608 mm x 606 mm; 4. One panel of 608 mm x 606 mm was used to make TS specimens of sizes of approximately 50 mm x 50 mm and 42 mm x 42 mm respectively; 5. TS specimens at target sizes of 36 mm x 36 mm, 29 mm x 29 mm and 21 mm x 21 mm respectively were prepared from one panel of 608 mm x 606 mm. 158 APPENDIX D Derivation of Equation (13) Var(Da)Nar(Db) = A JAa 1 Let Aa and Ab be the sizes of density sets A and B, Da and Db the density variables, and Var(Da) and Var(Db) the variances of density associated with density sets A and B. Further, suppose Ab be multiples of Aa, i.e., Ab = m.Aa (see the following diagram). Aa Aa Ab Aa Aa Ab = 4Aa (m=4) Figure D-1. Relationship between specimen sizes. According to basic statistics, we have, m db = urn dai i=1 (D-1) m urn Var(Dai) Var(Db) = 2 i=1 (D-2) where, db and d are the individual observations of variables Db and Da. Assume Var(Dai) = ... = Var(D) = Var(Da), Equation (D-2) became Var(Db) = jIm Var(Da) (D-3) Var(Da)/Var(Db) = rn (D-4) or As m = Ab/Aa, Equation (D-4) was generalized as Var(Da)/Var(Db) = Ab/Aa (D-5) 159 APPENDIX E Derivation of Equation (19) Var(Db) = [(1+p)Var(DaYI/2 Given the same notations as in Appendix B, and let Ab = 2Aa (see the following diagram). Aa Aa Ab Ab2Aa Figure E-1. Diagram showing Ab = 2Aa We have, db = (dai + (C-i) )/2 2 da Var(Db) = [Var(Dai) + ) 2 Var(Da + 2COV(Dai, Da )]14 2 (C-2) where, COV(Dai, Da2) is the covariance between the adjacent specimens. As Cov(D , Da 81 ), where p is the correlation 2 ) = p’JVar(Dai)Var(Da 2 coefficient between adjacent densities Dai and Da , Equation (C-2) then 2 became Var(Db) = [Var(Dai) + ) 2 Var(Da + )Var(D)J 81 2p’JVar(D (C-3) Assume Var(Dai) = Var(D) = Var(Da), Equation (C-3) was changed to Var(Db) = [2Var(Da) + 2pVar(D)1/4 = [(1+p)Var(Da)]/2 (C-4) 160 APPENDIX F Derivation of Equation (21) Var(Db) = Var(Da) = (1/2)2 Given the same notations as in Appendix D, and according to Equation (18), we have (1/Ab) c b Var(Db) = 2 (F-i) b 2 Var(Da) = C2(i/Aa) (F-2) Dividing Equation (F-i) by Equation (F-2), the following relationship was obtained, Var(Db)/Var(Da) = (Aa/Ab) 21 (F-3) As Ab = 2Aa, Equation (F-3) was changed to Var(Db)/Var(Da) = (i/2)2b (F-4) 161 APPENDIX G Significance Test of Parameter b in Equation (23) Null hypotheses H :b 0 = 0.5, b :b 1 Alternative hypotheses H = 0. 0.5, b 0. In order to test these hypotheses based on Equation (23), several assumptions about this model need to be satisfied. Two of these were that variances of dependent variable ln(S) are homogeneous at different values of independent variable ln(1/A), and in(S) was taken from a normal distribution. These two assumptions were first checked. 1. Homogeneous variance. The following diagram is the residual plot based on Equation (23). The ) was the difference 1 residual at each value of independent variable ln(11A ). As these 1 between the experimental data ln(S) and the model estimate in(S residuals could be assumed reasonably uniform based on this plot, a homogeneous variance was assumed for the model based on this relatively small sample (Conover, 1980). 0.2 I I 01 0 0 0 0 0 0.0 0 -0.1 -02 —10 0 0 —7 0 —4 0 0 —1 ln(1/A) Figure G-1. Residual plot based on Equation (23). 2 162 2. Normal distribution. The lilliefors test for normality was used (Conover, 1980). First, the raw data was normalized as z, = 1 is the individual data (in(S )), 1 1 )/s, x (x - is the arithmetic mean, and s the standard deviation of raw data. Second, the empirical cumulative probability function F(z) based on the normalized data ), and the cumulative probability function Ø(z) of standard normal 1 (z 1 between F(z distribution were calculated. The difference T ) and Ø(z) was 1 calculated and the maximum difference was taken as the test statistic. The following table shows this procedure. Table G-1. Calculations for normal distribution test 1 T ln(S) z F(z) -3.863 -1.472 0.083 0.071 0.013 -3.817 -1.376 0.167 0.085 0.082 -3.576 -0.879 0.250 0.189 0.061 -3.442 -0.604 0.333 0.272 0.061 -3.324 -0.362 0.417 0.359 0.057 -3.244 -0.197 0.500 0.422 0.079 -3.244 -0.197 0.583 0.422 0.162 -3.101 0.097 0.667 0.748 -0.081 -2.749 0.823 0.750 0.794 -0.044 -2.604 1.121 0.833 0.869 -0.036 -2.442 1.455 0.917 0.927 -0.010 -2.375 1.592 1.000 0.945 0.050 163 The maximum difference was 0.162. As it was less than the critical value of 0.242 (obtained from Conover, 1980) at significance level of 0.05, it was concluded that ln(S) follows a normal distribution. Now, back to the original hypotheses tests. The regression analyses of Equation (23) yielded a value of 0.1503 for b, and 0.0049 for standard : b 0 deviation of b. For the first null hypothesis H (0.1503 0.5)/0.0049 - a = = = 0.5, the test statistic t -71.37, was less than the critical value ) = 2 ta(fl = -1.812 at 0.05 (n is the number of observations used for the model, n-2 is the degree of freedom). The first null hypothesis was rejected, i.e., b For the second null hypothesis H : b 0 0.1503/0.0049 = = 0.5. 0, the test statistic t 30.67, was larger than the critical value of 1.8 12 at a The second null hypothesis was also rejected, i.e., b 0. = = 0.05. 164 APPENDIX H Derivation of Equation (26) Var(Db) = (laIlb)Var(Da) Given the same notations as in section 4.2.2.1., and further let multiples Of la, i.e., b 1 b 1 be = mla (see the following diagram). la board A board B mia Figure H-i. Diagram showing the layer concept. The expected value of Db is just an expectation of the average of several Da’S, m E(Db) = E(1/m D) i=i (H-i) m ) 8 tim Var(D Var(Db) = 2 i=i (H-2) and here, E stands for the expectation. Suppose Var(Dai) = ... = Var(Dam) = Var(Da), Equation (H-2) became Var(Db) = Var(Dj/m (H-3) As m = ‘IJ’a’ Equation (H-3) was generalized as Var(Db) = (la/lb)Var(Da) (H-4) 165 APPENDIX I Derivation of Equation (38) a = a(S)P From Equation (18), S = (I-i) c(1/A) we have 1/A Substituting = (1-2) (S/c) Equation (1-2) into Equation (37), the following relationship was obtained, where, = a = a(SIc) dlb, x = ac”. = a(S) (1-3) 166 APPENDIX J Derivation of Equation (41) ç = From Equation (18) S = (J-1) c(1IA) we have 1/A = (S/c)11b (J-2) Substituting Equation (J-2) into Equation (40), the following equation was obtained, where, = ç = e(S/c) N’ = ec”. = NJ(S) (J-3)
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Horizontal density distribution of particleboard: origin and implications Xu, Wei 1994
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Title | Horizontal density distribution of particleboard: origin and implications |
Creator |
Xu, Wei |
Date Issued | 1994 |
Description | Particleboard products have been manufactured for over a half century. During this time, it has been recognized that a vast number of material and processing variables influence board properties. Little is known about the internal structure of particleboard, and a fundamental principle or theory interrelating structure, processing and properties of particleboard has yet to be developed. Such basic knowledge of particleboard structure is not only necessary to fully understand present particleboard technology, but also important for the future upgrading and development of wood composites. This study was designed to develop some of this knowledge base. The two major objectives of this study were: (1) to investigate the influence of raw material characteristics on horizontal density distribution (HDD), and (2) to determine the effect of particleboard nonuniformity as defined by HDD, on some key board properties. Twenty six particleboard panels made with precisely cut particles were used to study the first objective, while thirty boards involving different particle sizes and distributions, and different wood species and combinations were manufactured to study the second objective. In addressing the first objective, the Equation S = a(1/A)b was found to be appropriate for relating standard deviation of density (S) and specimen size (A), where a and b are constants. At relatively larger specimen sizes, particleboard made with larger particles exhibited greater density variation, while particleboard made with smaller particles showed larger variations at smaller specimen sizes. Two aspects of voids, namely number and size, were identified as factors contributing the relation between particle size and HDD. In addition, a layer concept was developed to relate particle thickness, wood density, board density and board thickness to HDD. This concept predicted a decrease of density variation as particle layers increased. In addressing the second objective, modulus of rupture (MOR), modulus of elasticity (MOE), internal bond (TB) and thickness swelling (TS) of particleboard were shown to be greatly controlled by nonuniformity of board structure. All these properties were improved as structure uniformity improved. A nonuniformity effect concept, expressed as P = m(1/S) was proposed in relating board properties (P) to standard deviation (S) of horizontal density, in which, m and n are constants. While TS was influenced most by the high density portions, mechanical properties were dominated by the low density areas. The concept of HDD was also used in this study to investigate the relationship of specimen size effect on TB and TS, for one commercial waferboard. Both average values and standard deviations of TB and TS decreased as specimen size increased. A criterion based on HDD concept was proposed for the future establishment of testing standard in terms of specimen size selection. The relationship between HDD, raw material characteristics and board properties, demonstrated that HDD was a fundamental variable useful for characterizing particleboard structure and technology. The HDD concept has the potential of linking the effects of raw material characteristics and forming techniques to board properties in short-fiber wood composites. |
Extent | 2783642 bytes |
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Thesis/Dissertation |
Type |
Text |
File Format | application/pdf |
Language | eng |
Date Available | 2009-04-08 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0088293 |
URI | http://hdl.handle.net/2429/6911 |
Degree |
Doctor of Philosophy - PhD |
Program |
Forestry |
Affiliation |
Forestry, Faculty of |
Degree Grantor | University of British Columbia |
Graduation Date | 1994-05 |
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UBCV |
Scholarly Level | Graduate |
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