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The strength of bonded wood strand composites Higgins, Edward Donald 1990

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THE STRENGTH OF BONDED WOOD STRAND COMPOSITES By Edward Donald H i g g i n s B . S c , The U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1966 M.S., S t a t e U n i v e r s i t y o f New York 1970 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES F o r e s t r y Department o f H a r v e s t i n g and Wood S c i e n c e 'We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA August 1990. (c)Edward Ebnald Higgins , 1990 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. The University of British Columbia Vancouver, Canada DE-6 (2/88) ABSTRACT A method for modelling the strength of bonded wood strands which are oriented p r i n c i p a l l y in one d i r e c t i o n i s proposed. The hypothesis tested was that strand grain orientation data, f i t t e d to a von Mises probability d i s t r i b u t i o n , could be used i n an analysis for estimating the potential t e n s i l e strength of an i d e a l l y bonded composite. The strand strength, resolved at any loading angle with respect to the p r i n c i p a l composite strand orientation axis, was multiplied by the d i s t r i b u t i o n p r o b a b i l i t y at that angle. When integrated over a l l angles, t h i s product yielded the mathematical expectation of strength for the composite. The model predicted composite strength at o f f -orientation axis angles and represented the material in two dimensions i n an orthotropic fashion. A feature of t h i s research i s the use of a parametrically quantified strand orientation l e v e l in an algorithm developed to estimate composite strength. A p r a c t i c a l number of strand angle readings ( 1 0 0 ) were taken to characterize each composite. These angle readings defined orientation i n terms of a parameter which described composites ranging from random to highly oriented. The model input also required microtensile strength means from samples of strands tested in the longitudinal and r a d i a l or tangential d i r e c t i o n s . Comparisons between the model and a c t u a l s p e c i f i c s t rengths were made at fiv e equally spaced-composite p r i n c i p a l axis load angles from 0 to 9 0 degrees. Both t e n s i l e and f l e x u r a l t e s t s were performed to evaluate the model. The evaluations were designated i n terms of resin content, d i s t r i b u t i o n , and droplet i i size. These variables were studied using colorimetry and computerized image analysis. Composite density p r o f i l e s through the specimens' thickness were obtained from direct reading x-ray densitometry. Composites made of juvenile trembling aspen, red alder, red cedar, mature lodgepole pine and yellow b i r c h were studied. Assumptions concerning wood shear strength and strand length/thickness r a t i o were discussed i n the interpretation of an overlapping strand stress-transfer model. This led to the d e f i n i t i o n of f a i l u r e c r i t e r i a based on stress transfer. A t r i a l of orientation modelling i n e l a s t i c i t y estimation was made and a random function model of composite e l a s t i c i t y based on laminated plate theory i s outlined i n a supplementary proposal for further research. The s i m p l i f i e d algorithm for the strength of aligned.wood strand composites provides design targets for reconstituted high strength strand lumber and panel products of the future. i i i TABLE OF CONTENTS Page ABSTRACT . , . i i TABLE OF CONTENTS , i v LIST OF TABLES v i LIST OF FIGURES v i i ACKNOWLEDGEMENT i x 1. INTRODUCTION . 1 1.1 O b j e c t i v e s . . . . . . . . . . • . 2 2. REVIEW OF THE LITERATURE 4 2.1 O r i e n t a t i o n . . ' 4 2.2 M a c r o s c o p i c S t r e n g t h T h e o r i e s f o r Wood 6 2.3 M i c r o - M e c h a n i c a l S t r e n g t h T h e o r i e s 8 2.4 Composite D e n s i t y 8 2.5 A d h e s i v e L e v e l , D i s t r i b u t i o n and D r o p l e t D i s p e r s i o n 9 2.6 S p e c i e s 11 2.7 Other P r o c e s s V a r i a b l e s . . 13 3. METHODS AND MATERIALS . . . . . . . . . . 14 3.1 D i r e c t i o n a l Data P r o c e s s i n g 14 3.2 The von M i s e s D i s t r i b u t i o n 16 3.3 L i m i t s and A c c u r a c y o f O r i e n t a t i o n E s t i m a t e s . . . 18 3.4 Roundwood 21 3.5 S t r a n d W a f e r i z i n g and D r y i n g 22 3.6 S t r a n d P r o p e r t i e s . . . 23 3.7 A d h e s i v e s B l e n d i n g 26 3.8 Forming O r i e n t e d S t r a n d B o a r d 29 3.9 Hot P r e s s i n g . . . . . . . . . . 32 3.10 M o d e l l i n g Methods 33 3.10.1 Model Development 33 3.10.2 Weighted Average C r i t e r i o n . . 36 3.10.3 Model Assumptions and S t r e s s T r a n s f e r . . 38 3.10.4 D e n s i t y G r a d i e n t E f f e c t and Measurement . 45 3.10.5 Model S t r u c t u r e and Programming 51 3.11 E x p e r i m e n t a l D e s i g n . 53 3.11.1 Composite S t r e n g t h Comparisons 53 3.11.2 R e p e a t a b i l i t y o f O r i e n t a t i o n Parameter . 54 3.11.3 S p e c i e s Comparisons o f S t r e n g t h . . . . . 55 3.12 Test P r o c e d u r e s 55 3.12.1 S t r a n d T e s t i n g , S t r e n g t h 55 3.12.2 Composite T e n s i l e S t r e n g t h 57 3.12.3 Composite F l e x u r a l S t r e n g t h 58 i v 4. RESULTS 60 4.1 Strand Orientation 60 4.1.1 Concentration Parameter, k 60 4.1.2 Goodness of F i t 62 4.2 Process Variables . . . . . . . . . . 65 4.2.1 Strand Tensile Strength 65 4.2.2 Resin D i s t r i b u t i o n : Spectrophotometry . 67 4.2.3 Resin Dispersion: Image Analysis . . . . 72 4.2.4 Composite Density Gradient 7 6 4.3 Results, Sp e c i f i c Tensile Strength . . . . . . . . 81 4.3.1 Tensile Strength, Oriented Composites . . 81 4.3.2 Tensile Strength, Random Orientation . . 88 ' 4.4 Results, Flexural Strength 92 4.4.1 Introduction 92 4.4.2 Flexural Strength, P a r a l l e l to Orientation . . . . . 93 4.4.3 Flexural Strength, Perpendicular to Orientation 108 4.4.4 Flexural Strength, Random Orientation . . 109 5. DISCUSSION 116 5.1 Strength P a r a l l e l to Orientation 116 5.2 Strength, Perpendicular to Orientation . . . . . . 121 5.3 Powdered Vs. Liquid Adhesive . . .125 5.4 Flexural E l a s t i c i t y . 126 6. CONCLUSION . . . 133 7. SUMMARY 135 REFERENCES CITED . . . . . . 137 Appendix i 145 Appendix i i ..... . . 146 Appendix i i i . 148 Appendix i v . . . . . . . . . 149 v L I S T O F T A B L E S Page Table 1. Roundwood 2 1 Table 2 . W a f e r i z e r 2 2 Table 3 . S t r a n d d e s c r i p t i o n : 20°C and 5 0 p e r c e n t R.H. . . . 2 3 Table 4. R e s i n b l e n d i n g 2 8 Table 5 . Compaction r a t i o s 3 3 Table 6. O r i e n t a t i o n l e v e l s 6 1 Table 7. Zero span, s t r a n d s p e c i f i c t e n s i l e s t r e n g t h s . . . 6 5 Table 8. D e n s i t y r a t i o s , s u r f a c e t o mean . 7 9 Table 9. Composite/wood s p e c i f i c s t r e n g t h comparison . . . . 8 2 Table 1 0 . T e n s i l e s t r e n g t h s , t e s t e d p a r a l l e l t o t h e o r i e n t a t i o n d i r e c t i o n 8 4 Table 1 1 . P a r a l l e l s p e c i f i c t e n s i l e s t r e n g t h 8 5 Table 1 2 . P a r a l l e l s p e c i f i c t e n s i l e s t r e n g t h : s p e c i e s . . . 8 5 Table 1 3 . T e n s i l e s t r e n g t h s , t e s t e d p e r p e n d i c u l a r t o t h e o r i e n t a t i o n d i r e c t i o n . 8 7 Table 1 4 . P e r p e n d i c u l a r s p e c i f i c t e n s i l e s t r e n g t h 8 8 Table 1 5 . Random o r i e n t a t i o n , s p e c i f i c t e n s i l e s t r e n g t h a n a l y s i s o f v a r i a n c e 8 8 Table 1 6 . Random o r i e n t a t i o n , s p e c i f i c t e n s i l e s t r e n g t h . . 9 0 Table 1 7 . Comparative t e n s i l e s t r e n g t h o f random composites f o r b o t h r e s i n l e v e l s combined 9 1 Table 1 8 . P a r a l l e l s p e c i f i c f l e x u r a l s t r e n g t h . 1 0 4 Table 1 9 . P a r a l l e l s p e c i f i c f l e x u r a l s t r e n g t h : s p e c i e s . . . 1 0 5 Table 2 0 . Random o r i e n t a t i o n , s p e c i f i c f l e x u r a l s t r e n g t h , a n a l y s i s o f v a r i a n c e 1 0 9 Table 2 1 . Comparative f l e x u r a l s t r e n g t h o f random o r i e n t a t i o n s 1 1 0 Table 2 2 . M.O.E. i n f l e x u r e . . 1 2 9 Table 2 3 . Input e l a s t i c c o n s t a n t s 1 2 9 v i L I S T O F F I G U R E S Page Figure 1. Angle measurement, 14 Figure 2 . Components of the o r i e n t a t i o n vector 15 Figure 3. The von Mises pdf f o r some s e l e c t e d values of o r i e n t a t i o n parameter, k 17 Figure 4. Regression of the o r i e n t a t i o n concentration parameter 19 Figure 5. D i s t r i b u t i o n s of aspen strand dimensions. . . . 24 Figure 6. Orienter 30 Figure 7. Stress t r a n s f e r 40 Figure 8. Strand s t r e s s 42 Figure 9. Densitometry specimen 50 Figure 10. O r i e n t a t i o n model output 52 Figure 11. Curve f i t t i n g - aspen i n d u s t r i a l o r i e n t e d core . 63 Figure 12. Curve f i t t i n g -random aspen, hand f e l t e d . . . 64 Figure 13. Resin d i s t r i b u t i o n - aspen blending 68 Figure 14. Resin d i s t r i b u t i o n - cedar blending 69 Figure 15. Resin d i s p e r s i o n - t r a c e r strands with aspen. . 75 Figure 16. Resin d i s p e r s i o n - powder r e s i n 76 Figure 17. T y p i c a l density gradient p r o f i l e s . 80 Figure 18. S p e c i f i c MOR, o r i e n t e d a l d e r , low r e s i n l e v e l . 94 Figure 19. S p e c i f i c MOR, o r i e n t e d a l d e r , high r e s i n l e v e l . 95 Figure 20. S p e c i f i c MOR, o r i e n t e d cedar 96 Figure 21. S p e c i f i c MOR, o r i e n t e d pine, low r e s i n l e v e l . . 97 Figure 22. S p e c i f i c MOR, o r i e n t e d pine, high r e s i n - l e v e l . -98 Figure 23. S p e c i f i c MOR, o r i e n t e d aspen, low r e s i n l e v e l . 99 Figure 24. S p e c i f i c MOR, o r i e n t e d aspen, high r e s i n l e v e l . 100 Figure 25. S p e c i f i c MOR, o r i e n t e d aspen, powder r e s i n . . . 101 v i i Figure 26. Specific MOR, i n d u s t r i a l core 102 Figure 27. Specific MOR, oriented b i r c h 103 Figure 28. Theory comparison with surface adjusted inputs . 107 Figure 29. Sp e c i f i c MOR, randomly oriented b i r c h . . . . . I l l Figure 30. Sp e c i f i c MOR, randomly oriented alder 112 Figure 31. Sp e c i f i c MOR, randomly oriented cedar 113 Figure 32. Specific MOR, randomly oriented pine. . . . . . 114 Figure 33. Sp e c i f i c MOR, randomly oriented aspen. . . . . . . 115 Figure 34. Tensile strength versus re s i n spread l e v e l . . . 118 v i i i ACKNOWLEDGEMENT The w r i t e r would l i k e t o acknowledge t h e h e l p f u l and i n n o v a t i v e s u g g e s t i o n s o f f e r e d by t h e numerous c o n t r i b u t o r s t o t h i s r e s e a r c h . P h y s i c a l o f f e r i n g s o f m a t e r i a l s and equipment as w e l l as e x p e r t i s e were made by t h e f o l l o w i n g o r g a n i z a t i o n s and i n d i v i d u a l s . S p e c i a l thanks are extended t o my f a m i l y and t o my t h e s i s committee. ORGANIZATIONS Canadian F o r e s t S e r v i c e Weldwood of Canada A l b e r t a Research C o u n c i l M c M i l l a n B l o e d e l R esearch Borden Chemical L t d . R e i c h h o l d L t d . F o r i n t e k Canada C.A.E. Machinery L t d . Paperboard Corp. Econotech S e r v i c e s L t d . UBC Research F o r e s t UBC M e t a l l u r g y Dept. P u l p and Paper Res. I n s t , o f Canada Simon F r a s e r Univ. S t a t i s t i c s Dept. COMMITTEE MEMBERS L. Paszner P. S t e i n e r D. B a r r e t t R. F o s c h i D. T a i t J . Nadeau E. Teghtsoonian INDIVIDUALS J . Arden G. S t o u t M. S t o u t B. S t r o u d P. Crammond C. M i e r a u W. A i n s l e y B. S c o t t L. J o s z a N. Sargent K. B a r t c z a k E.W. H i g g i n s and f a m i l y L.A. F r y G. Eaton J . Cook D. Nguyen G. Bohnenkamp L. Bach D. Seabrook R. Knudson H. E h r e n f e l l e r R. Kerekes M. Stephens i x 1 1. INTRODUCTION Oriented strand board i s one of the fastest growing segments of the forest products industry. Approximately f i f t y North American m i l l s now produce waferboard or oriented board and i t i s projected that by 1993 oriented strand board w i l l reach over 50 percent of t o t a l s t r u ctural panel consumption. In Canada, t h i s means that 63 m i l l i o n square meters per year, 9.5 mm basis, w i l l be produced ( 1 8 ) . An improvement i n composite strength p a r a l l e l to the major panel axis i s obtained i f the strands are aligned with t h e i r longitudinal grain d i r e c t i o n p a r a l l e l to the panel axis. Alignment i s normally done in three multiple layers of strands, with the center layer cross-plied. The term, oriented strand board (OSB) i s used to describe a composite made of oriented grain elements, which have length-to-width r a t i o s greater than 3. A l l new m i l l s have the capability to orient the inner and outer layers of strands. Fundamental understanding i s needed about the orientation effect on the strength of the single u n i d i r e c t i o n a l layers forming t y p i c a l three-layer OSB. This i s also c r i t i c a l to the development of reconstituted strand lumber. A t h e o r e t i c a l model which predicts the ef f e c t of strand alignment changes on strength would be a valuable research and engineering t o o l . The creation and evaluation of such a model was the aim of t h i s research. Engineering process consultants and standards committees have had few theor e t i c a l targets for the design of OSB layers or high strength reconstituted strand lumber. This model i s intended to provide an awareness of an idealized, t h e o r e t i c a l maximum strength of these products. Then product designers can set s t r e n g t h t a r g e t s , compare t e s t r e s u l t s , and a l t e r v a r i a b l e s more knowledgeably. I t i s a l s o i n t e n d e d t o e v a l u a t e the p o t e n t i a l c a p a b i l i t y o f t h e s e p r o d u c t s where h i g h s t r e n g t h i s r e q u i r e d or where t h e y are p l a c e d as n a t u r a l wood s u b s t i t u t e s . In wood composite m o d e l l i n g , t h e v a r i a b i l i t y o f wood has h i s t o r i c a l l y f a v o u r e d s i m p l e models t h a t i n p u t o n l y t h e major f a c t o r s i n f l u e n c i n g a r e s u l t . F o r example, i n plywood f l e x u r a l s t r e n g t h e s t i m a t i o n , t h e c r o s s band veneers a r e o f t e n a s s i g n e d zero modulus i n t r a n s f o r m e d moment o f i n e r t i a e l a s t i c a n a l y s e s , l e a v i n g o n l y the c o n t r i b u t i o n s of p a r a l l e l - g r a i n laminae t o be c o n s i d e r e d . 1.1 O b j e c t i v e s While r e c o g n i z i n g t h e v a r i a b i l i t y o f wood, t h e o b j e c t i v e i s to prepare a s t r e n g t h a l g o r i t h m f o r d e s c r i b i n g s i n g l e d i r e c t i o n wood s t r a n d c o m p o s i t e s . The model i s based on an assessment o f the degree o f o r i e n t a t i o n o f t h e s t r a n d s and t h e i r s t r e n g t h s i n two p l a n a r d i r e c t i o n s . The h y p o t h e s i s i s t h a t such a model i s ac c u r a t e i n a s s e s s i n g t h e s t r e n g t h o f e x i s t i n g and pr o p o s e d s t r a n d composite p r o d u c t s . The t e s t o f t h i s h y p o t h e s i s i s made w i t h a v a r i e t y o f s p e c i e s , a d h e s i v e l e v e l s , and o r i e n t a t i o n l e v e l s i n the t e s t c o m p o s i t e s . The o b j e c t i v e r e q u i r e s : C r e a t i o n of a network a n a l y s i s method o f m o d e l l i n g o r i e n t e d s t r a n d composite t e n s i l e and f l e x u r a l s t r e n g t h , d e t e r m i n a t i o n o f t h e c o n d i t i o n s o f s t r e s s t r a n s f e r between s t r a n d s , under which t h e model i s v a l i d . T h i s i n c l u d e s r e s i n l e v e l and s t r a n d d i m e n s i o n s , 3 q u a l i f i c a t i o n of a n other i m p o r t a n t s t r e n g t h d e t e r m i n a n t , adhesive d e p o s i t i o n , t r i a l a p p l i c a t i o n o f network a n a l y s i s t o modulus of e l a s t i c i t y . The o b j e c t i v e s were t o f u r t h e r a s c e r t a i n : the a b i l i t y o f the model t o p r e d i c t t h e s u r f a c e s p e c i f i c MOR at any angle of composite l o a d i n g w i t h r e s p e c t t o t h e p r i n c i p a l a x i s o f o r i e n t a t i o n , the e f f e c t of r e s i n l e v e l and s p e c i e s on f l e x u r a l s t r e n g t h , comparison of t h e s p e c i f i c t e n s i l e s t r e n g t h o f t h e composites t o t h e s p e c i f i c t e n s i l e s t r e n g t h o f t h e s t r a n d s themselves. In s h o r t , t h e r e s e a r c h f o c u s e s on m o d e l l i n g u n i d i r e c t i o n a l wood composites t h a t are s i m i l a r t o contemporary OSB l a y e r s o r r e c o n s t i t u t e d s t r a n d lumber. The r e s u l t i s an a n a l y t i c a l t o o l f o r g u i d i n g f o r e t h o u g h t i n t h e s e t t i n g o f p r o d u c t s t r e n g t h e x p e c t a t i o n s . I t p r o v i d e s fundamental knowledge on t h e m a n i p u l a t i o n o f o r i e n t a t i o n , s t r a n d c o n f i g u r a t i o n , and r e s i n l e v e l i n a c h i e v i n g o p t i m a l s t r e n g t h t o w e i g ht r a t i o . 4 2. REVIEW OF THE LITERATURE 2.1 Orientation There are s e v e r a l e x p e r i m e n t a l s t u d i e s i n the l i t e r a t u r e concerned w i t h the e f f e c t o f s t r a n d o r i e n t a t i o n on s t r e n g t h . F o r example, P o s t (71), G a t c h e l l e t a l . (23) and Geimer (24, 25, 26) d e a l w i t h s t r a n d o r i e n t a t i o n e f f e c t s on b o a r d s t r e n g t h . One o f the d i f f i c u l t i e s i n u s i n g and comparing t h e s e s t u d i e s i s t h e non-u n i f o r m i t y and d i f f e r i n g i n t e r a c t i o n s o f v a r i a b l e s o t h e r t h a n o r i e n t a t i o n . Only a few of t h e s e s t u d i e s have used a p r o b a b i l i t y d i s t r i b u t i o n f u n c t i o n (pdf) t o d e s c r i b e t h e o r i e n t a t i o n . The m e r i t of t h e pdf i s t h a t i t can be e x p l o i t e d t o g i v e a mathematical e x p e c t a t i o n of s t r e n g t h . To do t h i s , t h e pdf i s used as a f a c t o r which i s i n t e g r a t e d w i t h an e x p r e s s i o n f o r t h e o f f - a x i s s t r e n g t h of s o l i d wood. U n t i l t h e p r e s e n t t i m e , t h i s approach has been t a k e n o n l y w i t h t h e randomly o r i e n t e d b o a r d where the pdf i s u n i f o r m (72). The i n v e s t i g a t i o n s of H a r r i s and Johnson (33) p r o v i d e background f o r t h e p r e s e n t r e s e a r c h . They suggest a p r o b a b i l i t y d i s t r i b u t i o n h a v i n g a c o n c e n t r a t i o n parameter, k, which d e s c r i b e s the d i s p e r s i o n o f s t r a n d g r a i n a n g l e s about t h e most p r o b a b l e o r i e n t a t i o n a n g l e . H a r r i s and Johnson's work r e f e r s t o b i o m e t r i c a p p l i c a t i o n s of c i r c u l a r p d f s . d e s c r i b e d by B a t s c h e l e t (11), and Mardia (58). The work of H a r r i s (34) emphasized the methodology of o r i e n t a t i o n measurement. He t h e n m o d e l l e d th e t e n s i l e e l a s t i c i t y o f a s t r a n d composite by c o n s i d e r i n g v a r i o u s l y o r i e n t e d s t r a n d u n i t s i n the form o f s e q u e n t i a l s t r i p s o f segments. 5 Less d e t a i l e d methods o f d e s c r i b i n g o r i e n t a t i o n have been used. Geimer (25) d e f i n e d t h e p e r c e n t o f w a f e r s h a v i n g a n g l e s f a l l i n g w i t h i n ± 20 degrees o f t h e most p r o b a b l e d i r e c t i o n o f alignment, and l a t e r d e v i s e d a w e i g h t e d average o f a n g l e s from an o r i e n t a t i o n h i s t o g r a m . The a b s o l u t e mean a n g l e , <)), was c a l c u l a t e d by Geimer (26) as the average o f t h e measured a n g l e s (-90° < § < +90°), w i t h o u t r e g a r d t o s i g n . The p e r c e n t alignment was then d e f i n e d as: I 45° - A I pe r c e n t a l i g n m e n t = — 1 4 5 ° — t 1 ] Lau (48) f i t t e d a normal d i s t r i b u t i o n based on t h e above a b s o l u t e mean angle and i t s s t a n d a r d d e v i a t i o n . N u m e r i c a l i n t e g r a t i o n w i t h an e l a s t i c i t y f a c t o r l e d t o a r e g r e s s i o n r e l a t i o n s h i p between d e n s i t y and modulus o f e l a s t i c i t y . Paper p h y s i c s o f f e r s network a n a l y s e s based on s c a n n i n g sheets at a n g u l a r i n t e r v a l s over z e r o t o 360 degrees w i t h r e s p e c t t o t h e machine d i r e c t i o n . The number o f f i b e r s c r o s s i n g t h e sc a n l i n e s are counted. C o r t e and K a l l m e s (15) showed t h e scan d a t a t o d e f i n e a F o u r i e r s e r i e s which t h e y r e l a t e d t o a pdf. T h i s f i b e r c r o s s i n g method was not s u i t e d t o OSB where t h e s t r a n d w i d t h r e q u i r e s e x c e s s i v e l y l a r g e sample boards t o a c h i e v e t h e necessary d a t a c o l l e c t i o n . E x p e r i m e n t a l d e t e r m i n a t i o n of f i b e r o r i e n t a t i o n i n paper by v a r i o u s methods ranges from use o f c o l o r e d f i b e r s , D a n i e l s o n e t a l . (16) t o s u b m i l l i m e t e r l a s e r , by Boulay et a l . (13) . Change i n d i e l e c t r i c p r o p e r t i e s w i t h g r a i n o r i e n t a t i o n have been e x p l o i t e d i n lumber g r a d i n g s e n s o r s by 6 Samson ( 75 ) . The a t t e n u a t i o n of microwaves has been s t u d i e d by M u s i a l (61) t o determine the degree o f s t r a n d o r i e n t a t i o n . M u s i a l ' s i n s t r u m e n t a l methods were used t o c h a r a c t e r i z e a n o t h e r p a r a m e t r i c pdf d e s c r i b i n g s t r a n d o r i e n t a t i o n . Reviews of t h e F o u r i e r s e r i e s d i s t r i b u t i o n , t h e von M i s e s d i s t r i b u t i o n , and t h e i r i n t e r r e l a t i o n , as used t o d e s c r i b e o r i e n t a t i o n i n paper s h e e t s , were p u b l i s h e d by P e r k i n s and Mark et a l . ( 6 8 ) . Advanced i n s t r u m e n t a l methods o f q u a n t i f y i n g f i b e r o r i e n t a t i o n i n paper were p r e s e n t e d i n a c r i t i c a l e v a l u a t i o n by Niskanen and Sadowski (62) . A re v i e w o f methods used i n h i g h performance ( g l a s s , carbon) f i b e r c o m p o s i t e s was i n c l u d e d i n a study o f c o n t i n u o u s f i b e r r e i n f o r c e m e n t ( 9 8 ) . The e x i s t i n g s t r e n g t h t h e o r i e s based on network a n a l y s i s , b o t h i n paper and g l a s s f i l a m e n t composites u s u a l l y a s s i g n z e r o t r a n s v e r s e s t r e n g t h t o t h e f i b e r s . I n wood s t r a n d c o m p o s i t e s , t h e p r e s e n t t h e s i s o f f e r s r e s e a r c h . i n which t h e t r a n s v e r s e s t r e n g t h o f t h e wood s t r a n d i s i n c l u d e d . 2.2 M a c r o s c o p i c S t r e n g t h T h e o r i e s f o r Wood Ma c r o s c o p i c s t r e n g t h t h e o r i e s f o r wood a r e im p o r t a n t because s o l i d wood s t r a n d s a re elements o f t h e model and t h e i r s p e c i f i c s t r e n g t h s a re model i n p u t s . Wood s t r e n g t h models were d i s c u s s e d by P e r k i n s (69 ) , K a m i n s k i e t a l . ( 41 ) , B o d i g and Jayne ( 1 2 ) , and E a s t e r l i n g e t a l . ( 1 9 ) : A d i s t o r t i o n a l energy t h e o r y was o f f e r e d by N o r r i s (65) f o r combined s t r e s s ( o f f g r a i n a x i s ) p r e d i c t i o n o f wood s t r e n g t h . A s i m i l a r , more g e n e r a l e x p r e s s i o n f o r g l a s s f i b e r composites, was devel o p e d by T s a i - H i l l ( 9 1 ) . The Ha n k i n s o n 7 wood s t r e n g t h f o r m u l a and t h e more g e n e r a l Osgood f o r m u l a were compared by Kim (46). Hankinson's f o r m u l a p r o v i d e s a s i n g l e e x p r e s s i o n f o r s t r e n g t h t h a t a p p r o x i m a t e s o t h e r more r e f i n e d a n a l y s e s , f o r example the maximum s t r e s s s t r e n g t h t h e o r y , (12) . I t was chosen because i t deve l o p s o f f - a x i s s t r e n g t h e s t i m a t e s o f s t r a n d s t r e n g t h from two b a s i c i n p u t s , and has proven s a t i s f a c t o r y i n p r e v i o u s s t r a n d c o m p o s i t e s t u d i e s (72). The Hankinson f o r m u l a was deve l o p e d e x p e r i m e n t a l l y i n 1921 and i s a p r a c t i c a l d e s c r i p t i o n o f t h e s t r e n g t h o f wood as a f u n c t i o n o f g r a i n a n g l e . I t can be used t o d e s c r i b e not o n l y s t r e n g t h b u t a l s o p r o p o r t i o n a l l i m i t s t r e s s e s i n b o t h t e n s i o n and c o m p r e s s i o n . An e f f e c t o f l a m i n a t i o n of p l a n a r components can be t o d i s p e r s e f l a w s i n t h e l a m i n a t e , r e s u l t i n g i n a narrower d i s t r i b u t i o n of specimen s t r e n g t h s , and an i n c r e a s e i n average s t r e n g t h . T h i s e f f e c t was demonstrated i n a s t a t i s t i c a l t h e o r y of l a m i n a t e d g l a s s s h e e t s , by Scop e t a l . ( 78). Occurrence o f a c r i t i c a l f l a w i s r e l a t e d t o specimen s i z e and i s known t o a f f e c t s t r e n g t h t e s t s as shown by B a r r e t t (10) and P r i c e (72). I n r e c o g n i t i o n o f t h e s e e f f e c t s , any s t r a n d s o f d i f f e r i n g s p e c i e s which are compared s h o u l d be o f t h e same no m i n a l s i z e d i s t r i b u t i o n . R e l a t i v e bonded area as a s t r e n g t h f a c t o r was s t u d i e d by Suchsland (88), a l s o by Lyon (55) i n a t h r e e - p a r t comprehensive model w r i t t e n f o r mainframe computers. Lyon's s t r e n g t h model employs a s i m u l a t e d o r i e n t a t i o n d i s t r i b u t i o n and does a s t r a n d -b y - s t r a n d a n a l y s i s and s e a r c h f o r l o c a l l a y e r f a i l u r e i n t h e f l e x u r a l s t r e n g t h e s t i m a t i o n . 8 Laminated p l a t e t h e o r y (LPT) was used i n e l a s t i c a n a l y s i s o f plywood by R a u t a k o r p i (74) and has m e r i t as an element of a proposed Monte C a r l o s i m u l a t i o n o f e l a s t i c i t y . T h i s i s d i s c u s s e d i n S e c t i o n 5.4. 2.3 M i c r o - M e c h a n i c a l S t r e n g t h T h e o r i e s An a p p r o x i m a t e l y 25 year span o f l i t e r a t u r e e x i s t s on f r a c t u r e - m e c h a n i c a l t h e o r i e s o f wood s t r e n g t h . Some examples a r e pre s e n t e d by P o r t e r (68), S c h n i e w i n d e t a l . (76), Nadeau e t a l . (62) and P e l l i c a n e e t a l . (67). A c o l l e c t i o n was c o m p i l e d by F o r i n t e k (1) . F r a c t u r e i n p h e n o l i c g l u e l i n e s was s t u d i e d by Ebewele et a l . ( 2 0 ) . I n t e r n a l bond was i n v e s t i g a t e d by L e i e t a l . (54) s u c c e s s f u l l y u s i n g f r a c t u r e mechanics. A c h o i c e was made, based on t h i s l i t e r a t u r e , not t o use a c r a c k growth t h e o r y as an element o f t h e o r i e n t a t i o n model f o r s t r e n g t h . The r e a s o n i s t h a t f r a c t u r e toughness d a t a , e s p e c i a l l y a t v a r y i n g g r a i n o r i e n t a t i o n l o a d a n g l e s a re l a c k i n g i n t h e b r o a d v a r i e t y o f sp e c i e s under s t u d y . 2.4 Composite D e n s i t y Turner (92) and K l a u d i t z (47) c o n c l u d e d t h a t f l e x u r a l s t r e n g t h was s t r o n g l y i n f l u e n c e d by t h e mean d e n s i t y o f t h e board. They d i d not c o n t r o l the surface d e n s i f i c a t i o n . The - f l e x u r a l s t r e n g t h , - w i t h i n t h e mean d e n s i t y range o f 0.5 t o 3 0.7 g/cm , formed a l i n e a r r e l a t i o n w i t h d e n s i t y . No s p e c i f i c a t i o n was g i v e n f o r t h e d e n s i t y g r a d i e n t . F l e x u r a l modulus of r u p t u r e (MOR) i s dependent on t h e t h r o u g h - t h i c k n e s s 9 den s i t y gradient and su r f a c e d e n s i t y produced by p r e s s i n g and c o n s o l i d a t i o n of stra n d s . Such g r a d i e n t s have been measured using x-rays, by S t e i n e r et a l . (83, 84), and W i n i s t o r f e r et a l . (96), and modelled by Harless et a l . (32). Josza et a l . (40) developed x-ray densitometry methods u s e f u l f o r small wood specimens. The f a c t o r s a f f e c t i n g the g r a d i e n t i n t h r e e - l a y e r panel boards were re p o r t e d by Geimer et a l . (27). Composite surfaces are not n e c e s s a r i l y d e n s i f i e d t o the same extent with a l l species under equal p r e s s i n g c o n d i t i o n s . Moisture, temperature and p r e s s i n g r a t e are major f a c t o r s a f f e c t i n g the gradient. I f u n c o n t r o l l e d , these can confound the d e n s i t y gradient with the sp e c i e s or other independent v a r i a b l e s when MOR i s the dependent v a r i a b l e . A l s o , d u r i n g the process of s t r a n d f u r n i s h layup, i t i s p o s s i b l e t h a t f i n e s and adhesive f a l l through to the c a u l p l a t e s i d e of the pre s s charge. T h i s can r e s u l t i n one s u r f a c e being denser or s t r o n g e r than the other (83, 84). The g r a d i e n t can be p a r t l y e l i m i n a t e d by slow p r e s s c l o s u r e , and p a r t i a l s u r f a c e removal by p l a n i n g . The e f f e c t of gradient on the i n t e r p r e t a t i o n of the f l e x u r e formula i s c r i t i c a l i n the use of bending t e s t s to estimate s u r f a c e s t r e s s . 2.5 A d h e s i v e L e v e l , D i s t r i b u t i o n and D r o p l e t D i s p e r s i o n The p h e n o l i c adhesive r e s i n s used i n t h i s r e s e a r c h , b o t h l i q u i d and powder, are p r e s e n t l y o f f e r e d t o the OSB i n d u s t r y . A review of l i t e r a t u r e which d e s c r i b e s chemical and p h y s i c a l features of r e s i n s and t h e i r b e h a v i o r w i t h wood i n c l u d e s , Hse (37), Wilson (94), Go l l o b (30), Stephans et a l . (85) and Go (28, 29) . The i n f l u e n c e of r e s i n l e v e l on t e n s i l e s t r e n g t h of random 10 waferboard was d e s c r i b e d by L a u f e n b e r g (50). In aspen b o a r d s made w i t h randomly o r i e n t e d s h o r t s t r a n d s , t h e MOR r o s e i n a d i m i n i s h i n g c u r v i l i n e a r r e l a t i o n t o r e s i n l e v e l . These b o a r d s ac h i e v e d o n l y s m a l l s t r e n g t h g a i n s a f t e r 7 t o 12 p e r c e n t r e s i n s o l i d s a d d i t i o n . T h i s t r e n d was a l s o o b s e r v e d by P r i c e (72) w i t h sweetgum OSB and by Adams (4) w i t h aspen, balsam f i r , and n o r t h e r n w h i t e cedar u n i d i r e c t i o n a l OSB l a m i n a t e d as power l i n e crossarms. In 1961 P o s t (71) found v e r y modest f l e x u r a l MOR e l e v a t i o n caused by r e s i n i n c r e a s e , when u s i n g randomly o r i e n t e d s t r a n d s of l e n g t h / t h i c k n e s s r a t i o s o f 10 t o 40. The l i t e r a t u r e s u g g e s t s two r e s i n l e v e l s at which t h e o r i e n t a t i o n model s h o u l d be e v a l u a t e d . The f i r s t i s t h e approximate l e v e l a t which i n d u s t r y c u r r e n t l y a p p l i e s i t ' s adhesive. T h i s i s i n t h e range of 2 t o 3 p e r c e n t s o l i d s by weight (29). The second i s near t h e upper l i m i t o f i n d u s t r i a l a p p l i c a t i o n (4-8 p e r c e n t ) , where t h e e f f e c t s o f h i g h e r wood f a i l u r e r e s u l t i n h i g h e r s t r e n g t h i n t h e p a r a l l e l t o g r a i n d i r e c t i o n . A c c o r d i n g t o L a u f e n b e r g (50), t h i s r e s i n l e v e l can y i e l d n e a r l y zero d i s b o n d i n g o f s t r a n d s when used w i t h l e n g t h / t h i c k n e s s r a t i o s o f 100 or more. The c r i t i c a l i mportance o f wafer t h i c k n e s s on a d h e s i v e r e q u i r e m e n t i n terms o f s u r f a c e spread of r e s i n was s t u d i e d by P o s t (.71) and Gunn (31) . The r e s i n l e v e l i n t e r a c t s with the other s t r e n g t h f a c t o r s t o the e x t e n t t h a t many s t u d i e s a re v e r y l i m i t e d i n scope. The most p e r t i n e n t a re mentioned above, but many o t h e r s a re r e v i e w e d by K e l l y (44). The r e s i n d i s t r i b u t i o n i s a c r i t i c a l f a c t o r i n s t r e n g t h d e t e r m i n a t i o n . The b e s t r e v i e w o f t h i s s u b j e c t i s g i v e n by Maloney et a l . (57). The d e f i n i t i v e r e s e a r c h on t h e e f f e c t s o f a p p l i c a t i o n of l i q u i d r e s i n was done by Meinecke and K l a u d i t z i n 1962 (60). The d i s p e r s i o n o f d r o p l e t s ( s p e c i f i c a l l y t h e d r o p l e t s i z e d i s t r i b u t i o n ) on a s t r a n d s u r f a c e and t h e d i s t r i b u t i o n o f r e s i n among s t r a n d s were s t u d i e d as s e p a r a t e e f f e c t s i n Meinecke's and K l a u d i t z ' s work. They c o n c l u d e d t h a t s t r a n d t o s t r a n d d i s t r i b u t i o n o f t h e r e s i n i s o f t e n more i m p o r t a n t t h a n t h e d r o p l e t d i s p e r s i o n . The f r e q u e n t a s s o c i a t i o n o f b e t t e r d i s t r i b u t i o n w i t h b e t t e r d r o p l e t d i s p e r s i o n has sometimes caused the two f a c t o r s t o be c o n f u s e d by d e s i g n e r s o f r e s i n b l e n d e r s . Kasper and Chow (42) r e c o g n i z e d t h e i m p o r t a n c e o f r e s i n d i s t r i b u t i o n and d e v i s e d a s i m p l e c r i t e r i o n f o r d e f i n i n g good d i s t r i b u t i o n . They showed t h a t t h e median/mean r a t i o from t h e frequency h i s t o g r a m of r e s i n p i c k u p on a sample of w a f e r s s h o u l d be u n i t y . T h e i r x - r a y f l u o r e s c e n c e d e t e c t i o n o f bromine t a g g e d r e s i n was used f o r s i m u l t a n e o u s r e s i n a s s a y s of b o t h , combined, s i d e s of t h e wafer. In c o n t r a s t t o t h i s , t h e t h e o r e t i c a l p o t e n t i a l o f r e s o l v i n g i n d i v i d u a l s i d e s i s a l s o u s e f u l . The r e s i n s t a t u s of b o t h s i d e s can be used i n c a l c u l a t i n g t h e p r o b a b i l i t y o f a d i m i n i s h e d r e s i n i n t e r f a c e zone i n a model s t a c k o f s t r a n d s . 2.6 Species The m a n u f a c t u r e r's c h o i c e o f s p e c i e s i s m a i n l y governed by economic f a c t o r s such as a v a i l a b i l i t y , s i z e , c o n c e n t r a t i o n o f t r e e s , and t r a n s p o r t a t i o n c o s t s (36), (38), (77) . Canadian hardwoods have been examined e x t e n s i v e l y from a g e n e r a l u t i l i z a t i o n v i e w p o i n t i n symposia, by M c i n t o s h and C a r r o l l ( 5 9 ) . 12 Populus t r e m u l o i d e s , the main Canadian wood f o r OSB, i s w e l l documented w i t h r e g a r d t o r e s o u r c e f o r e s t r y and wood t e c h n o l o g y . A review o f aspen u t i l i z a t i o n i s o f f e r e d by P r o n i n and Vaughan (73). M i x t u r e s o f w h i t e b i r c h , balsam f i r , r e d a l d e r , balsam p o p l a r , b l a c k spruce and aspen were e v a l u a t e d i n w a f e r b o a r d by Al e x o p o u l o s and S h i e l d s ( 6 ) . Adams (4) p r o v i d e s some r e f e r e n c e data f o r comparison i n a s t u d y o f OSB made from n o r t h e r n w h i t e cedar, balsam f i r , and aspen. Lodgepole p i n e made a s e r v i c a b l e OSB a c c o r d i n g t o d a t a p r e s e n t e d by Maloney (56). Low r e s i n l e v e l when a p p l i e d t o s o f t e r , low d e n s i t y s p e c i e s , made s t r o n g e r b o a r d t h a n h i g h d e n s i t y s p e c i e s a t e q u i v a l e n t f i n a l board d e n s i t i e s a c c o r d i n g t o Stegmann and D u r s t (82), and Al e x o p o u l o s and S h i e l d s (6) . T h i s i s because t h e s o f t e r woods c o n s o l i d a t e b e t t e r . Such s t r a n d s e a s i l y a r t i c u l a t e i n t h e f o r m a t i o n o f more i d e a l bond i n t e r f a c e s . The v a r i a t i o n o f d e n s i t y i n mature woods o f n o r t h e r n s p e c i e s was r e p o r t e d by S i n g h (80) . J u v e n i l e woods w i l l have i n c r e a s e d i m p o r t a n c e i n s t r a n d composites i n t h e f u t u r e . I n j u v e n i l e aspen, t h e age, d e n s i t y , g e n e t i c and growth f a c t o r s were i n v e s t i g a t e d by Dawson e t a l . (17) and E i n s p h a r e t . a l (21). J u v e n i l e b l a c k a l d e r was f o u n d by Chow (14) t o make s u p e r i o r OSB. I n h i g h r e s i n c o m p o s i t e s , where bonding i s maximized, t h e i n t r i n s i c weakness o f j u v e n i l e wood c o u l d a f f e c t composite s t r e n g t h . These s t u d i e s p r o v i d e background f o r a wide c h o i c e o f woods t o t e s t t h e a p p l i c a b i l i t y of the s t r e n g t h model. 2.7 Other P r o c e s s V a r i a b l e s There are numerous o t h e r v a r i a b l e s t h a t a f f e c t OSB s t r e n g t h . For example, m o i s t u r e c o n t e n t , compaction r a t i o , and s t r a n d c u t t i n g a n g l e must be c o n s i d e r e d . These and o t h e r v a r i a b l e s were h e l d c o n s t a n t , c a r e f u l l y s p e c i f i e d , o r randomized i n t h e p r e s e n t r e s e a r c h . The U.S. F o r e s t P r o d u c t s L a b o r a t o r y r e v i e w e d a v a r i e t y o f s t r e n g t h d e t e r m i n a n t s i n a r e p o r t by K e l l y (44) , c o n t a i n i n g 163 r e f e r e n c e s . A s i m i l a r r e v i e w was p r o v i d e d by t h e U.S.D.A. i n 1981 (2). The m u l t i t u d e of f a c t o r s and t h e i r i n t e r a c t i o n s emphasize t h e need t o o r g a n i z e t h e fundamental ones i n models, f o r e x p r e s s i o n o f t h e i r e f f e c t on c o m p o s i t e p r o p e r t i e s . 3 . METHODS AND MATERIALS 3 .1 D i r e c t i o n a l Data Processing The method of quantifying orientation by using the von Mises probability d i s t r i b u t i o n function was developed for OSB by Harris (34). This measures strand orientation d i r e c t l y on the board surface as shown in Figure 1. The angles that strands make with the axis d i r e c t i o n form a data set f a l l i n g between 0 and 180 degrees, (alternatively -90 to 90 degrees). Data i n the 0 to 180 degree i n t e r v a l i s c a l l e d a x i a l data. axis \ ll U 1 i '— jJlvl \ — - ^ ^ 2 0 ° /'' <l\73° ^ J ^ ~ ~ ^ \ 170° ////</ ml AXIAL DATA EXAMPLES Figure 1 . Angle measurement, 0 The angles themselves cannot be meaningfully averaged arithmetically but the set of associated complex points can be averaged. The set of points can be considered vectors with coordinates on the unit c i r c l e given by F i g . 2 . Harris and Johnson. (33) stated,., "the entire set of data can be characterized by an orientation vector, r, whose angular position r e l a t i v e to a preselected reference i s given by a most probable angle, m, and whose length i s related to the central y 15 F i g u r e 2 . Components o f t h e o r i e n t a t i o n v e c t o r . tendency o f t h e s e t . " F o r l a r g e v a l u e s o f n, t h i s i s e x p r e s s e d m a t h e m a t i c a l l y as: n mean x, mean y, x = y = n n Z cos 9t = cosG i=l n Z s i n 8i = sin0 i=l 2 . . 2 v 1/2 o r i e n t a t i o n v e c t o r , ( l e n g t h ) r = (x + y ) a x i s d i r e c t i o n , (most p r o b a b l e angle) m = t a n " 1 sin0 cos9 [ 2 ] [3] [4] [5] A n g u l a r d a t a f o r t h e s e e q u a t i o n s were c o l l e c t e d as f o l l o w s . A c l e a r p l a s t i c g r i d was p r e p a r e d by making h o r i z o n t a l s l o t s on a X-Y c o o r d i n a t e p l a n e o f p l e x i g l a s . T h i s was o v e r l a i d on t h e s u r f a c e o f t h e t e s t specimens w i t h t h e s l o t s p a r a l l e l t o t h e specimen r e f e r e n c e edge. Random p o i n t s chosen as X-Y p a i r s d e f i n e d a n g l e measuring l o c a t i o n s on t h e g r i d . These were pen-marked through the slo t s , by means of dots and reference l i n e s p a r a l l e l to the s l o t s . Grain angles of marked strands were then measured using a hand protractor through a large viewing lens. The actual f i b e r directions, not strand edges, were measured as data. Angles were taken from each side of the five r e p l i c a t e t e s t boards forming a treatment. The a x i a l angle measurements thus c o l l e c t e d were then doubled to form an ordinary, angle set (0 to 360 degrees). This formed data usable i n Equations [2], [3] and [4] for c a l c u l a t i o n (in radians) of the orientation vector length, r. Usually, the re s u l t i n g orientation angle, m, was calculated to be less than one degree. This means the orientation was centered p a r a l l e l to the reference edge and walls of the orientation box. The orientation vector length, r, calculated using Equation [4], was between 0 and 0.85 i n a l l test boards. This value indicates the degree of ori e n t a t i o n . A value of r=0 i s random and r=l i s perfectly aligned. 3.2 The von M i s e s D i s t r i b u t i o n The von Mises pr o b a b i l i t y d i s t r i b u t i o n function (pdf) i s given by: g(0,m,k) 1 kcos2 (8-m) [6] This pdf i s applicable over the required f i n i t e i n t e r v a l of n radians, has equal, recurring end points, and i s a x i a l l y symmetric about m. The parameters m and 1/k c o r r e s p o n d t o t h e mean and v a r i a n c e i n t h e o r d i n a r y l i n e a r normal d i s t r i b u t i o n . g(0,m,k) = g r a i n a n g l e pdf, a two parameter p r o b a b i l i t y d i s t r i b u t i o n f u n c t i o n m an g l e between t h e bo a r d a x i s d i r e c t i o n , s e t a t z e r o degrees, and any chosen r e f e r e n c e (e.g. a x i s a n g l e o f l o a d i n g on b i a s c u t t e s t composites) t h e o r i e n t a t i o n parameter o f s t r a n d ( g r a i n ) a n g u l a r s p r e a d ; t h i s i s a measure o f a n g u l a r c o n c e n t r a t i o n 0 I 0 ( k ) t h e i n d i v i d u a l s t r a n d g r a i n a n g l e , w i t h r e s p e c t t o t h e b o a r d a x i s , F i g . 1. m o d i f i e d B e s s e l f u n c t i o n o f o r d e r z e r o g i v e n by t h e p o l y n o m i a l a p p r o x i m a t i o n f o r m u l a o f Abramowitz and Stegan ( 3 ) , page 378. z o p o z u. o STRAND ORIENTATION ANGLE. DEGREES F i g u r e 3 . The von Mi s e s pdf f o r some s e l e c t e d v a l u e s o f o r i e n t a t i o n parameter, k. 18 The o r i e n t a t i o n parameter i s c a l c u l a t e d u s i n g r , ( E q u a t i o n [ 4 ] ) . The r a t i o o f t h e B e s s e l f u n c t i o n s I„ and I 1 # r e l a t e s t h e o r i e n t a t i o n parameter, k, t o the o r i e n t a t i o n v e c t o r , r , as shown i n E q u a t i o n [7] . r = A(k) = Y 1-^ a n d ' i n v e r s e l y , k = A - 1 (r) [7] B a t s c h e l e t (11) d i s c u s s e d t h e m e r i t s o f k as a maximum l i k e l i h o o d e s t i m a t e . An e s t i m a t e o f k i s determined when r i s known, from the t a b u l a t i o n s o f M a r d i a (58), i n h i s appendix 2.2, or T a b l e B, found i n B a t s c h e l e t (11). A p o l y n o m i a l r e g r e s s i o n o f M a r d i a ' s t a b l e i s p r e s e n t e d i n F i g . 4 and e x p r e s s e d a l g e b r a i c a l l y i n Eq u a t i o n [8] . k = 1.721 + 5.215r 2 - 3 1 . 9 6 r 3 + 9 3 . 0 6 r 4 - 1 2 0 . 9 r 5 + 6 1 . 1 4 r 6 [8] A f u r t h e r a p p r o x i m a t i o n o f k i s g i v e n by M a r d i a (58) k = [ 2 ( l - r ) - ( 1 - r ) 2 - ( 1 - r ) 3 ] " 1 [9], Equ a t i o n [9] y i e l d s t h r e e f i g u r e a c c u r a c y f o r r g r e a t e r 1 t h a n 0.8. 3.3 L i m i t s and A c c u r a c y o f O r i e n t a t i o n E s t i m a t e s A r e s u l t of the H a r r i s ( 3 4 ) t h e s i s on str a n d o r i e n t a t i o n was the c o n c l u s i o n t h a t k v a l u e s i n t h e range o f p r a c t i c a l o r i e n t a b i l i t y , by hand o r machine, c o u l d be s p e c i f i e d by u s i n g a s m a l l , sample s i z e o f 100 s t r a n d angle measurements. To p u t t h i s i n p e r s p e c t i v e , an i n d u s t r i a l OSB was l a t e r found t o have a * k P A R A M E T E R , P O L Y N O M I A L R E G R E S S I O N DATA: K.V. MARDIA.1972 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0.7 0 . 8 MEAN ORIENTATION VECTOR r F i g u r e 4 R e g r e s s i o n of t h e o r i e n t a t i o n c o n c e n t r a t i o n parameter VO 20 value of k = l . l , and the most o r i e n t e d l a b board reached only k=9.0. Another important c o n t r i b u t i o n of H a r r i s was v a l i d a t i o n of the accuracy of h i s method of e s t i m a t i n g m and k. He d i d t h i s by use of s p e c i a l l y made boards having c a l i b r a t e d k v a l u e s , r e s u l t i n g from i n d i v i d u a l l y l a i d down s t r a n d s . He found good agreement between c a l i b r a t e d and e s t i m a t e d values of k. S t a t i s t i c a l t t e s t s were made at the 0.05 l e v e l of s i g n i f i c a n c e . Confidence l i m i t s f o r k values g r e a t e r than k=5.0 can be obtained from an expression given by B a t s c h e l e t (11). x 2 x 2 ^ — < k < ^ — [10] 2n (1-r) 2n (1-r) where = lower c r i t i c a l Chi-square value upper c r i t i c a l c h i - s q u a r e value n = number of t r i a l s r = o r i e n t a t i o n v e c t o r l e n g t h The upper and lower c r i t i c a l c h i - s q u a r e values f o r n-1 degrees of freedom are found i n the cumulative d i s t r i b u t i o n of the C.R.C. Handbook of P r o b a b i l i t y and S t a t i s t i c s , p u b l i s h e d by. the Chemical Rubber Company Press, 1966 e d i t i o n . The p r o b a b i l i t y 2 2 columns headed by 5 percent and 95 percent give the. X L and values, r e s p e c t i v e l y . G r a p h i c a l p l o t s p u b l i s h e d by Mardia (58), g i v e 90% and 98% confidence l i m i t s f o r a f u l l e r range of k v a l u e s and were chosen f o r use because of t h e i r convenience. The confidence i n t e r v a l s can be made s m a l l e r by i n c r e a s i n g the sample s i z e at the researcher's d i s c r e t i o n . 3.4 Roundwood The f i v e Western Canadian woods s t u d i e d i n t h i s r e s e a r c h a l l had good economic reasons f o r OSB c a n d i d a c y , and had w i d e l y v a r y i n g wood d e n s i t i e s . The s p e c i e s were: Tr e m b l i n g Aspen (Populus t r e m u l o i d e s ) Red A l d e r (Alnus rubra) Western Red Cedar (Thuja p l i c a t a ) Lodgepole P i n e (Pinus c o n t o r t a ) Y e l l o w B i r c h ( B e t u l a a l l e g h a n i e n s i s ) The aspen, a l d e r , and cedar were m a i n l y j u v e n i l e , c u t from t r e e s a p p r o x i m a t e l y 2 0 y e a r s o l d . Red a l d e r and r e d cedar were c u t a t t h e Malcom Knapp U n i v e r s i t y o f B.C. r e s e a r c h f o r e s t , Haney B.C. Aspen and l o d g e p o l e p i n e were c u t i n t h e H o p e - P r i n c e t o n r e g i o n o f s o u t h e r n B.C. W i t h t h e e x c e p t i o n o f p i n e , a l l were c u t from m o i s t , open, f e r t i l e s i t e s . D e b a r k i n g was by hand. The i n d u s t r i a l c o r e aspen p a n e l was from mature aspen c u t i n t h e S l a v e Lake, A l b e r t a a r e a . The mature y e l l o w b i r c h was' from Quebec, and was r e c e i v e d as t h i n veneer, ( 0 . 8 4 mm). Table 1. Roundwood Sp e c i e s Age, y e a r s Diameter cm Average p e r c e n t M.C R. A l d e r t r e e 1 1 8 1 4 . 5 1 1 4 2 2 4 1 6 . 0 T. Aspen t r e e 1 1 5 1 3 . 1 1 6 4 2 2 1 2 0 . 0 R. Cedar t r e e 1 34 1 6 . 1 1 0 0 2 2 1 1 6 . 5 L. P i n e t r e e 1 68 1 7 . 0 5 1 2 7 6 1 8 . 5 22 3 . 5 S t r a n d W a f e r i z i n g and D r y i n g A 30 i n c h l a b o r a t o r y d i s c w a f e r i z e r was used t h r o u g h t h e co u r t e s y of C.A.E. Machinery L t d . , Vancouver. The roundwood was w a f e r i z e d i n t h e green c o n d i t i o n s h o r t l y a f t e r c u t t i n g . M o i s t u r e c o n t e n t s r e p o r t e d i n Table 1 were t a k e n from samples d i r e c t l y a f t e r w a f e r i z i n g . The w a f e r i z e r k n i f e s e t t i n g s were unchanged f o r a l l s p e c i e s except aspen where t h e h i g h e r m o i s t u r e c o n t e n t made the wood so f l e x i b l e t h a t i t d i d n ' t f r a c t u r e on the c o u n t e r k n i f e t o the d e s i r e d w i d t h . T h i s was improved by i n c r e a s i n g t h e cou n t e r k n i f e angle from 60 t o 70 degree s . The low d e n s i t y c e d a r f r a c t u r e d i n t o a g r e a t e r number of u n d e r - w i d t h s t r a n d s . T h i s was the only s p e c i e s t h a t r e q u i r e d s c r e e n c l a s s i f i c a t i o n i n o r d e r t o m a i n t a i n t h e same s t a n d a r d o f s t r a n d dimensions i n a l l t h e s p e c i e s . The m e c h a n i c a l set-up o f the w a f e r i z e r . i s shown i n T a b l e 2. Whole 15 cm l o n g b o l t s were f e d t a n g e n t i a l l y so t h a t a u n i f o r m d i s t r i b u t i o n of r i n g a n g l e s was produced i n t h e s t r a n d s . T a b l e 2 . W a f e r i z e r r e a c t o r k n i f e counter k n i f e k n i f e speed Species angle p r o j e c t i o n angle p o s i t i o n angle . R.P,M. L . p i n e R. a l d e r 3 2 d e g . . 6 3 5 mm 6 0 d e g . . 7 6 2 mm 3 0 d e g . 1 3 0 0 R . c e d a r T . a s p e n 3 2 d e g . . 6 3 5 mm 7 0 d e g . . 7 6 2 mm 3 0 d e g . 1 3 0 0 S t r a n d d r y i n g was done th r o u g h t h e c o o p e r a t i o n o f M a c M i l l a n B l o e d e l Research L a b o r a t o r y where a one meter d i a m e t e r by t h r e e meter l o n g . r o t a r y l a b d r i e r was used. R o t a t i o n was a t 14 RPM and r e t e n t i o n t ime was 7 t o 9 minutes a t a t e m p e r a t u r e o f 160°C. The r e s i d e n t wet charge c a r r i e d i n t h e d r i e r was 2 t o 3 kg. Two t o t h r e e passes o f the f u r n i s h t h r o u g h t h e d r y e r were r e q u i r e d t o b r i n g the m o i s t u r e content t o 3.7 t o 4.9 p e r c e n t . Losses as f i n e s were about 10 p e r c e n t . 3 . 6 S t r a n d P r o p e r t i e s Dimensions were o b t a i n e d under ambient c o n d i t i o n s of 20°C and 50 p e r c e n t R.H. on random samples o f about 140 s t r a n d s from each s p e c i e s . The d i s t r i b u t i o n s o f t h e s e d i m e n s i o n s are shown i n F i g . 5, f o r aspen. The e x c e p t i o n was mature b i r c h , which was c u t from veneer u s i n g a " s t r a n d e r " , f a s h i o n e d by Durand-Raute L t d . The s t r a n d e r i s s i m i l a r t o a drum c l i p p e r . These were saw-cut t o l e n g t h and produced a h i g h l y u n i f o r m s t r a n d d i s t r i b u t i o n . T able 3 . S t r a n d d e s c r i p t i o n : 20°C and 50 p e r c e n t R.H. Ave. Length mm Std. Dev. R.Alder T.Aspen R.Cedar L.Pine Y.Birch 57.8 13.6 59.0 13.1 59.5 13.2 58.9 13.0 113.5 1.5 Ave. Width mm Std. Dev. 6.7 4.6 10.3 7.1 8.2 6.1 7.9 5.8 12.7 0.5 Ave. Thickness, mm Std. Dev. 0.59 0.06 0.62 0.09 0.65 0.10 0.62 0.11 0.84 0.03 Length/Thickness, mm 98 95 96 95 135 Ave. Density, g/cmJ Std. Dev. 0.34 0.35 0.31 0.39 0.62 0.04 0.02 0.05 0.04 0.04 2 4 mean 5.9 cm median 6.0 cm s t d . d e v . 1.3 cm e'.N i.ee I'M 3:ee 4.80 S.N 6.88 IM 8.88 9.88 Aspen Strand Length CM mean 10.3 mm median 8.0 mm s t d . d e v . 7.1 mm 4.9 8,8 12,8 16,8 20,8 24.8 28.8 32.8 36.8 48.8 Aspen Strand Width m mean 0.62 mm median 0.60 ram s t d . dev 0.09 mm 8.28 8.38 8.48 0.59 8.(8 8.78 8.88 8.98 1.88 1.18 1.28 Aspen Strand Thickness MM F i g u r e 5. D i s t r i b u t i o n s o f aspen s t r a n d d i m e n s i o n s . Random samples o f 15-20 s t r a n d s were s e l e c t e d from each s p e c i e s f o r d e n s i t y d e t e r m i n a t i o n a t 50 p e r c e n t R.H. and 20°C. The r e s u l t s are r e p o r t e d i n Table 3 . The s t r a n d s e l e c t i o n was randomized over e arlywood and latewood, h e a r t - a n d sapwood, r i n g a n g l e, and v e r t i c a l p o s i t i o n i n g i n t h e two t r e e s o f each s p e c i e s . When the d e n s i t i e s o f Table 3 were a d j u s t e d t o an oven-dry b a s i s , the r e s u l t i n g averages were lower, but w i t h i n one or two s t a n d a r d d e v i a t i o n s of thos e e x p e c t e d by Jessome (39) o f t h e s e woods i n l a r g e r b u l k . The low d e n s i t y e x c e p t i o n was j u v e n i l e aspen, c u t from a h i g h growth s i t e . D e n s i t y f o r c u l t i v a t e d aspen as low as 3 0.299 g/cm (oven d r y b a s i s ) was r e p o r t e d by E i h s p a h r e t a l . (21) . S p e c i f i c t e n s i l e s t r e n g t h i n each p r i n c i p a l d i r e c t i o n o f t h e s t r a n d s was i m p o r t a n t i n t h i s r e s e a r c h because t h e y were i n p u t v a r i a b l e s t o t h e s t r e n g t h model. Specimen s i z e i s an i m p o r t a n t c o n s i d e r a t i o n i n measuring s t r a n d s t r e n g t h . The t e n s i l e s t r e n g t h t y p i c a l l y d e c r e a s e s as the t h i c k n e s s o r gage l e n g t h i n c r e a s e s . For example, Law e t a l . (52) , (51) , u s i n g z e r o span gage l e n g t h , r e p o r t e d h i g h e r s p e c i f i c s t r e n g t h s i n softwoods t h a n W i l s o n (95) u s i n g extended m i c r o t e n s i l e specimens. Wellwood (93) r e p o r t e d s p e c i f i c s t r e n g t h s o f necked m i c r o - t e n s i l e specimens as b e i n g 23 t o 27 p e r c e n t h i g h e r than a c h i e v e d w i t h s t a n d a r d l a r g e s i z e softwood t e n s i l e specimens. Acknowledging t h e s i z e e f f e c t s on s t r e n g t h , t h e zero span specimens were chosen e x p l i c i t l y as p a r t of the model h y p o t h e s i s as d e s c r i b e d i n s e c t i o n s 3 . 1 0 . 1 and 3 . 1 0 . 3 . 26 A Th w i n g - A l b e r t QC-II e l e c t r o n i c t e n s i l e t e s t e r was used a t the campus f a c i l i t i e s of the P u l p and Paper Res. I n s t , o f Canada. T h i s 100 k g - f o r c e machine, was equipped w i t h pneumatic g r i p s and l o a d break d e t e c t o r and was s e t i n a t e s t room a t 22°C and 50 perc e n t R.H.. The microspecimens were d i e - c u t from s t r a n d s . The d i e was a l i g n e d w i t h the s t r a n d g r a i n t o produce r e c t a n g u l a r specimens of 4.2 mm w i d t h . The t h i c k e r b i r c h microspecimens were necked because the g r i p p i n g l e n g t h o f t h e jaws was i n a d e q u a t e t o prevent s l i p p a g e . I n t h i s case t h e neck narrowed t o 1.5 mm i n wi d t h . The necked d i e was t h e same as used by Wellwood (93) w i t h the g r i p t a b s extended t o t a k e advantage o f t h e f u l l jaw l e n g t h . The necked gage l e n g t h was 12.7 mm on t h e b i r c h specimens. A m i c r o s c o p i c i n s p e c t i o n of a l l p a r a l l e l g r a i n specimens i n s u r e d t h a t g r a i n a n g l e was zero o r v e r y s m a l l w i t h r e s p e c t t o t h e p a r a l l e l s i d e s of t h e t e s t zone. P e r p e n d i c u l a r g r a i n t e s t specimens were d i e c u t t o nominal 15 mm wide by 30 mm l o n g dimensions f o r z e r o span t e s t i n g . The specimens a r e i l l u s t r a t e d i n Appendix i v . A l l t e s t s were a t a s t r a i n r a t e o f 4mm/min. P r i o r c o n d i t i o n i n g took p l a c e o v e r n i g h t i n t h e t e s t room a t 22°C and 50 p e r c e n t R.H. A p p r o x i m a t e l y 12 zer o span t e s t s i n p a r a l l e l and 35 i n t h e p e r p e n d i c u l a r g r a i n d i r e c t i o n were i n c l u d e d i n t h e dat a a f t e r c u l l i n g m i s a l i g n e d specimens. F u r t h e r d e t a i l s a r e p r o v i d e d i n s e c t i o n 3 . 1 2 . 1 . Resu l t s are presented i n Table 7. 3.7 Ad h e s i v e s B l e n d i n g A l i q u i d p h e n o l i c r e s i n of 45 p e r c e n t t o t a l s o l i d s , d e s i g n a t e d as W31-54B, was p r o v i d e d by Borden Canada L t d . A c c e s s t o the Can-Car l i q u i d b l e n d e r at Borden L t d . was a l s o p r o v i d e d . 27 No wax was a p p l i e d , because the boards were not t o be t e s t e d f o r d i m e n s i o n a l s t a b i l i t y . The powder r e s i n , BD-019 from R e i c h h o l d L t d . was a p p l i e d i n a s i m i l a r Can-Car b l e n d e r a t F o r i n t e k Corp., Vancouver. Both Can-Car b l e n d e r s were r o t a t i n g drums, 152.4 cm i n diameter by 76.2 cm i n l e n g t h . A s i n g l e i n c l i n e d s p i n n i n g d i s k a t o m i z e r of 25 cm di a m e t e r and r o t a t i o n o f 3600 RPM was used f o r l i q u i d a p p l i c a t i o n . The l i q u i d b l e n d e r r o t a t e d a t 34. RPM and. the powder b l e n d e r at 12 RPM. The powder r e s i n was hand f e d t o the powder b l e n d e r . The b l e n d i n g t ime f o r t h e powder a p p l i c a t i o n was based on i n d u s t r i a l e x p e r i e n c e and i s n o t e d i n Ta b l e 4. The l i q u i d r e s i n a p p l i c a t i o n was based on t h e r a t i o n a l e t h a t o n l y s u r f a c e s t r a n d s h e l d on t h e b l e n d e r w a l l a t t h e l o a d s u r f a c e were exposed t o s p r a y i n g . The sp r a y which o c c u r r e d d u r i n g t h e random f a l l t o th e r e t u r n p o i n t , was n e g l e c t e d . The r e s u l t o f t h i s dynamic a n a l y s i s of s t r a n d movement was a c o n s e r v a t i v e e s t i m a t e o f the time r e q u i r e d t o p r o p e r l y b l e n d a g i v e n amount o f r e s i n onto t h e s t r a n d s . The b l e n d i n g was p l a n n e d so t h a t t h e p r o b a b i l i t y o f any s t r a n d not r e c e i v i n g a d h e s i v e s p r a y e x p o sure on at e x a c t l y one s i d e was l e s s t h a n 0.05. The c e n t r i f u g a l b l e n d i n g t i m e was extended d i r e c t l y as t h e amount o f l i q u i d r e s i n a p p l i e d i n c r e a s e d . The r a t e o f l i q u i d d e l i v e r y t o t h e b l e n d e r ' s a t o m i z e r was a c o n s t a n t 80 g/min. The c a l c u l a t e d l i q u i d r e s i n spreads were based on f i x e d s t r a n d t h i c k n e s s e s t a k e n as t h e sample means. The"spreads were l a t e r c o n f i r m e d by c o l o r i m e t r i c a n a l y s i s . A t t h e h i g h e r r e s i n l e v e l , r e s i n s u r f a c e t a c k i n e s s was b e g i n n i n g t o a f f e c t t h e 28 T a b l e 4. R e s i n b l e n d i n g . Calculated Total r e s i n l i q u i d spread s o l i d s on O.D. charge Blend time mg/cmJ, O.D. O.D. wood Species Size, minutes wood basis percent R. Alder 11. I 8. ,0 0. 57 2.59 T. Aspen 11. 0 7. .5 0. 57 2.44 R. Cedar 11. 0 8. ,0 0. 57 2.64 L. Pine 11. 0 6. , 9 0. 57 2.26 R. Alder 11. I 16. .0 1. 14 5.18 T. Aspen 11. 0 14 . 9 1. ,14 4 .90 R. Cedar 11. 0 16, . 1 1 _ , 14 5.27 L. Pine 11. 0 13 , .8 1. , 14 4 .50 Y. Birch 7 . 5 6, .0 1. ,76 2.87 T. Aspen 4 . 8 20, .0 - 2.00 (powder) dynamics of blending. This may favour the use of less tacky l i q u i d adhesive in high resin content composites. The colorimetric analysis was made by determination.of the amount of resin deposited on the surfaces of v i n y l tracer strands that were spray blended with the normal wood furnish. The tracers had weight length and width equal to the corresponding averages of the wood strands. They were prepared with removable, pressure sensitive tape on one side, so both sides could be analyzed. One half percent Rhodamine B dye, predissolved i n methanol was dissolved i n the Borden W31-54B phenolic r e s i n . After spray blending, the p l a s t i c and tapes were separated and each washed into 25 mL aliquots of 15 percent NaOH water solution. Colorimetry was on a Pye-Unicam SP6-350 Visible Spectrophotometer at 555 nm, using a 5.0 cm c e l l length. Five standard solutions and a background blank were used for creation of the ca l i b r a t i o n curve. The lowest standard solution was 4.0 ppm. The resulting 95 percent confidence l i m i t s on the l i n e a r regression estimates of resi n pickup were i n the order of 2 ± 0.2 mg/cm . These confidence l i m i t s were c a l c u l a t e d a c c o r d i n g to Nalimov (63). The mode of o p e r a t i o n of the b l e n d e r was such that there was very l i t t l e tendency f o r a s t r a n d to p i c k up the same amount of r e s i n on both s i d e s . The l i n e a r independence of the pickup on a l t e r n a t e s t r a n d s i d e s was i n d i c a t e d by a low 2 c o e f f i c i e n t of determination (r =0.04 to 0.20) f o r each b l e n d e r batch. This independence co u l d not be known by methods of r e s i n d e t e c t i o n t h a t ash, d i g e s t , or e l u t e the whole s t r a n d f o r a n a l y s i s of sodium or other r e s i n t r a c e r i o n s . Such methods were developed by Bacon et a l . (7). 3.8 Forming O r i e n t e d S t r a n d Board An o s c i l l a t i n g forming box, 43 cm long, 33 cm wide and 16 cm deep was the b a s i s of the o r i e n t a t i o n d e v i c e . A one c y c l e per second v i b r a t o r y a c t i o n of 2 cm amplitude was a p p l i e d i n the 33 cm d i r e c t i o n . The forming box moved back and f o r t h over the c a u l p l a t e as p i c t u r e d i n F i g . 6. The t h i n alignment vanes s l o p e d 60 degrees to the v e r t i c a l and reached the f u l l h e i g h t o f the f u r n i s h mat. A f t e r a 5 minute forming c y c l e , the vanes were removed and the top c a u l i n s e r t e d i n t o the forming'box b e f o r e p r e p r e s s i n g . The a i r c y l i n d e r o s c i l l a t o r was c o n t r o l l e d by.means of input a i r pressure, exhaust metering, and the r e s e t e l e c t r o n i c timer. Microswitches c o n t r o l l e d the s t r o k e l e n g t h . The a b i l i t y of t h i s o r i e n t e r to a l i g n t o a chosen l e v e l was not as good as the more r e f i n e d l a b equipment of Geimer (26) which used v e r t i c a l v i b r a t i o n s i m i l a r to some i n d u s t r i a l 1. a i r c y l i n d e r 2. p i l o t v a l v e 3. e l e c t r o n i c a u t o r e s e t t i m e r 4. f o r m i n g box and vanes 5. m i c r o s w i t c h 6. c a u l 7. r e g u l a t e d a i r s u p p l y F i g u r e 6. O r i e n t e r 31 equipment. An example of an i n d u s t r i a l o r i e n t e r i s d e s c r i b e d i n U.S. Patent 3,896,536 by K e l l e r e t a l . ( 4 3 ) . P r i c e (72) used a s t a t i o n a r y box c o n t a i n i n g vanes as a g r a v i t y powered o r i e n t e r . B e t t e r c o n t r o l o f o r i e n t a t i o n i n t h e l a b o r a t o r y was r e p o r t e d by H a r r i s (34) , u s i n g an e l e c t r i c f i e l d of i n t e n s i t y up t o 6.7 K v / i n c h . The e l e c t r i c f i e l d method was developed by T a l b o t e t a l . (90) but has f o u n d v e r y l i m i t e d use i n i n d u s t r y because of i t s low e f f i c i e n c y on s t r a n d s o f 75 mm l e n g t h and g r e a t e r . A fundamental reason f o r t h i s i s t h a t t h e a l i g n i n g torque i n c r e a s e s as t h e cube of t h e s t r a n d l e n g t h but the s t r a n d r o t a t i o n a l i n e r t i a i n c r e a s e s as t h e f o u r t h power o f l e n g t h . A l s o , the optimum m o i s t u r e c o n t e n t f o r e l e c t r i c a l i g n m e n t i s h i g h e r than t h a t a p p r o p r i a t e f o r a d h e s i v e s . The s t r a n d f a l l d i s t a n c e i n t h e e l e c t r i c o r i e n t e r makes i t v e r y l a r g e i n p h y s i c a l s i z e , e s p e c i a l l y f o r l a r g e r s t r a n d s . In t h e p r e s e n t r e s e a r c h , b i r c h s t r a n d s , 113.5 mm x 12.7 mm x 0.84 mm were o r i e n t e d t o a maximum k l e v e l o f 9.0. By comparison, v a r i o u s lower l e v e l s o f o r i e n t a t i o n up t o k=2.59 were ac h i e v e d e l e c t r i c a l l y by H a r r i s (34) on l e s s dense, 38.1 mm x 9.4 mm x 0.38 mm Douglas f i r s t r a n d s . In summary, t h e v i b r a t i n g s t r a n d o r i e n t e r performed w e l l i n p r o v i d i n g a h i g h l e v e l o f o r i e n t a t i o n , b u t l a c k e d t h e c o n t r o l o f an e l e c t r i c o r i e n t e r . The apparatus i n F i g . 6 a l s o caused s t r a n d s t o be l a i d down at an a n g l e , ( s h i n g l e d ) . T h i s promoted lay-up r a c k i n g d u r i n g p r e s s c o n s o l i d a t i o n . P r e - p r e s s i n g h e l p e d t o c o n t r o l t h i s . 32 3.9 Hot P r e s s i n g A p p r o x i m a t e l y 135 e x p e r i m e n t a l p a n e l s were p r e s s e d t o a t h i c k n e s s of 7 .9 mm u s i n g s t o p s . The same no m i n a l weight o f f u r n i s h was used f o r each t e s t p a n e l . M i n o r a d j u s t m e n t s i n weight p r o v i d e d a s m a l l range o f d e n s i t i e s w i t h i n each s e t o f f i v e r e p l i c a t e s . M i n o r mat weight a d j u s t m e n t s a l s o p r o v i d e d m o i s t u r e c o n t e n t c o r r e c t i o n . F i v e r e p l i c a t e s were made f o r each s p e c i e s - r e s i n - o r i e n t a t i o n t r e a t m e n t . A l l p r e s s i n g was done i n a randomized sequence t o conform w i t h t h e c o m p l e t e l y randomized e x p e r i m e n t a l d e s i g n . C o n s o l i d a t i o n p r e s s u r e v a r i e d w i t h s p e c i e s and o r i e n t a t i o n . Peak p r e s s u r e v a r i e d from 2 . 0 t o 3.4 MPa on t h e mat. A slow c l o s i n g time o f 1.0 t o 1.5 minutes t o t h e s t o p s was m a i n t a i n e d manually f o r a l l b o a r d s . Other p r e s s c o n d i t i o n s were: t o t a l mat m o i s t u r e ( i n c l u d i n g r e s i n c o n t r i b u t i o n ) . 7-11 p e r c e n t p l a t e n temperature 206°C c l o s e d p r e s s time 5 min time f o r board c e n t e r t o r e a c h 100°C > • 0 . 5 min A l o n g p r e s s time was used t o i n s u r e complete c u r e o f t h e p h e n o l i c r e s i n and m i n i m i z e blows. The t a r g e t d e n s i t y was c a l c u l a t e d t o be i n t h e range o f i n d u s t r i a l b oards c u r r e n t l y made 3 3 from aspen. T h i s was from 0 .59 g/cm t o 0 .69 g/cm . B i r c h was the e x c e p t i o n , where t h e specimens r e a c h e d d e n s i t i e s o f 0 . 82 t o 3 0.97 g/cm . These d e n s i t i e s d e f i n e d t h e compaction r a t i o s w h i c h were c a l c u l a t e d as t h e e q u i l i b r a t e d b o a r d d e n s i t i e s a t 50 p e r c e n t R . H . and 20°C, d i v i d e d by t h e wood s t r a n d d e n s i t i e s a t t h e same c o n d i t i o n . Mid-range e s t i m a t e s o f t h e s e r a t i o s a r e p r e s e n t e d i n Table 5 . 33 T a b l e 5. Compaction r a t i o s R. a l d e r 1.'83 T. aspen 1.77 R. cedar 2.10 L. p i n e 1.64 Y. b i r c h 1.38 i n d u s t r i a l c o r e 1.37 1 1 1 1 1 1 These r a t i o s are i n d i c a t i v e o f how much t h e o r i g i n a l wood volume y i e l d e d i n terms of p r e s s e d b oard volume, and t o g e t h e r w i t h t h e r e s i n c o n t e n t , are i m p o r t a n t f a c t o r s a f f e c t i n g t h e economics o f board making. 3.10 M o d e l l i n g Methods 3.10.1 Model Development The major f a c t o r s o f l o n g i t u d i n a l and t r a n s v e r s e s t r a n d s p e c i f i c t e n s i l e s t r e n g t h s , t o g e t h e r w i t h t h e o r i e n t a t i o n l e v e l , d r i v e the model as i n p u t s . From t h e s e , t h e model can be u s e d t o p r e d i c t the e x p e c t e d t e n s i l e s t r e n g t h o f t h e c o m p o s i t e , a t any angle w i t h r e s p e c t t o t h e p r i n c i p a l a x i s o f s t r a n d o r i e n t a t i o n . In t h i s model, th e s t r a n d s a r e s i m p l i f i e d as b e i n g t r a n s v e r s e l y i s o t r o p i c i n s t r e n g t h . D e n s i t y i s d i m i n i s h e d as a t e n s i l e s t r e n g t h f a c t o r by t h e c h o i c e of s p e c i f i c s t r e n g t h s as i n p u t s and o u t p u t s o f t h e model. A c c o r d i n g l y , i n comparisons of t h e t e s t r e s u l t s , i t i s r e q u i r e d t h a t the t e n s i l e s t r e n g t h o f t h e c o m p o s i t e s be d i v i d e d by t h e composite d e n s i t i e s . In t h e e s t i m a t i o n o f f l e x u r a l s t r e n g t h , a d e n s i t y g r a d i e n t t h r o u g h t h e t h i c k n e s s i s a d j u s t e d f o r a t t h e s u r f a c e because th e MOR i s d e f i n e d a t t h e s u r f a c e . The s t r a n d ' s t e n s i l e s t r e n g t h i s known t o v a r y by a f a c t o r of 15 t o 30 depending on the g r a i n a n g l e . The l o n g i t u d i n a l v e r s u s c r o s s - g r a i n ( a x i a l ) a n i s o t r o p y o f wood d e c r e a s e s as t h e d e n s i t y i n c r e a s e s , a c c o r d i n g t o E a s t e r l i n g e t a l . (19). I t was observed by B o d i g and Jayne (12) t h a t t h e a n i s o t r o p y o f wood i s unsurpassed even by g l a s s - e p o x y u n i d i r e c t i o n a l l a y - u p s . wood EjE7 . . g l a s s - e p o x y E L/E T 24 :1 4 :1 T h i s extreme a n i s o t r o p y suggested t h e p r o p o s i t i o n t h a t t h e s p e c i f i c s t r e n g t h o f a w e l l bonded wood s t r a n d composite c o u l d be modelled t o a f i r s t a p p r o x i m a t i o n , b ased o n l y on t h e s t r a n d o r i e n t a t i o n and s t r a n d p r i n c i p a l s t r e n g t h s . The zero-s p a n s t r a n d s t r e n g t h s were c o n s i d e r e d as model i n p u t s because t h e s t r a n d s have t e n s i l e l o a d a p p l i e d c o n t i n u o u s l y o v e r t h e i r l e n g t h , e x c e p t f o r end shear, i n b o t h the zero span t e s t and i n t h e i d e a l l y bonded board. T h i s i s d i s c u s s e d f u r t h e r i n s e c t i o n 3.12.1. The m a t h e m a t i c a l e x p e c t a t i o n o f s t r e n g t h f o r a c o l l e c t i o n o f n s t r a n d s , each h a v i n g o r i e n t a t i o n a n g l e 9, r e l a t i v e t o t h e (mean) p r i n c i p a l a x i s d i r e c t i o n , was h y p o t h e s i z e d t o be: SJQ) = I i = l p r o b a b i l i t y of a strand g r a i n being at angle 9t to the reference a x i s s t r e n g t h of the strand when loaded at angle 8T t o the reference a x i s [11] The von Mises p r o b a b i l i t y d i s t r i b u t i o n was chosen as t h e f i r s t f a c t o r i n E q u a t i o n [11] f o r r e a s o n s d i s c u s s e d i n S e c t i o n s 3.1 t o 3.3. The Hankinson f o r m u l a was used t o e x p r e s s t h e second f a c t o r , s t r a n d s t r e n g t h , taken a t any p l a n e a n g l e t o t h e p r i n c i p a l a x i s . T h i s c h o i c e i s s u p p o r t e d by P r i c e ' s (72) s t u d y o f wood s t r a n d s t r e n g t h as used i n c o m p o s i t e s . The more r e f i n e d t h e o r i e s r e l a t i n g s t r e n g t h t o g r a i n a n g l e t h a t were d i s c u s s e d i n the l i t e r a t u r e r e v i e w o f f e r o n l y m a r g i n a l improvement i n accuracy. Other r e l a t i o n s h i p s which a c c u r a t e l y r e s o l v e s t r e n g t h as a f u n c t i o n of g r a i n angle a re a d a p t a b l e , but t h e Hankinson formu l a was judged most p r a c t i c a l because i t r e q u i r e s o n l y two i n p u t s t r e n g t h s . The m a t h e m a t i c a l e x p e c t a t i o n o f composite s t r e n g t h was t h e r e f o r e t a k e n as: 71/2 Sm(6) = ( g(m,k,9) «s (9) d9 [12] '-7C/2 g(m, k,9) = von Mises p df m = angle between the p r i n c i p a l o r i e n t a t i o n a x i s and t h e a x i s of l o a d , k = o r i e n t a t i o n parameter, 9 = i n d i v i d u a l s t r a n d g r a i n a n g l e w i t h r e s p e c t t o t h e . specimen's p r i n c i p a l o r i e n t a t i o n a x i s , s (9) = Hankinson e x p r e s s i o n f o r t h e s p e c i f i c s t r e n g t h o f a s t r a n d l o a d e d a t an g l e 9 w i t h r e s p e c t t o i t s g r a i n . The board o r i e n t a t i o n a x i s was d e f i n e d as t h e most p r o b a b l e a n g l e o f s t r a n d o r i e n t a t i o n w i t h r e s p e c t t o t h e b o a r d r e f e r e n c e edge. The o r i e n t a t i o n a x i s and the specimen r e f e r e n c e edge were adjusted t o be p a r a l l e l i n a l l cases (zero degrees) . R e w r i t i n g E q u a t i o n [12] w i t h s u b s t i t u t i o n , y i e l d s t h e w o r k i n g E q u a t i o n [13], where: L = mean s p e c i f i c t e n s i l e s t r e n g t h o f s t r a n d s t e s t e d p a r a l l e l t o g r a i n (zero-span) T = mean s p e c i f i c t e n s i l e s t r e n g t h o f s t r a n d s t e s t e d p e r p e n d i c u l a r t o g r a i n (zero span) K/2 o , f l , ( 1 kcos2 (0-m) L 1 rcl 0(k) 1 + ( (L/T) -1) s i n 6 The c o n s i d e r a t i o n o f E q u a t i o n [13] as an u n b i a s e d e s t i m a t o r o f u l t i m a t e f i b e r s t r e s s i n bending as w e l l as t e n s i l e s t r e n g t h i s d i s c u s s e d i n s e c t i o n 3.10.5. 3.10.2 Weighted Average C r i t e r i o n The model s i m u l a t e s t h e two d i m e n s i o n a l o r t h o t r o p i c b o a r d s t r e n g t h as t h e s t r a n d s t r e n g t h , r e s o l v e d i n t h e composite a x i s d i r e c t i o n , and weighted by the s t r a n d a n g u l a r d i r e c t i o n a l d i s t r i b u t i o n f u n c t i o n . The b o a r d f a i l u r e c r i t e r i o n i s d e f i n e d by the f a i l u r e o f a c h a r a c t e r i s t i c t h r o u g h - t h i c k n e s s s e t o f s t r a n d s taken at a random p o i n t on t h e specimen's s u r f a c e . Innumerable c h a r a c t e r i s t i c s t a c k e d s t r a n d s e t s such as t h i s are i n t e r l o c k e d i n the model composite s t r u c t u r e . They a r e assumed p e r f e c t l y bonded so t h a t the s t r a i n i n a l l s t r a n d s i n t h e s e t o c c u r s e q u a l l y . When the a p p l i e d s t r e s s i n t h e composite reaches t h e c a l c u l a t e d f a i l u r e s t r e s s o f t h e c h a r a c t e r i s t i c a l l y o r i e n t e d model s e t t h e n th e composite i s assumed t o f a i l . The p h y s i c a l model of the m u l t i p l e l a y e r e d s t r a n d s e t f i t s w e l l t o t h e b a s i c d e f i n i t i o n o f t h e m a t h e m a t i c a l e x p e c t a t i o n o f s t r e n g t h based on t h e o r i e n t a t i o n d i s t r i b u t i o n . The m a t h e m a t i c a l e x p e c t a t i o n o f a board's s t r e n g t h i s d e f i n e d as t h e a r i t h m e t i c mean of the estimates made from a l l possible strand samples; i t i s the sum of the estimates af t e r weighting each by i t s ' probability. Equation [11] approximates t h i s expectation. As a further approximation, the input to the model Equation [13] uses arithmetically averaged values of strand p r i n c i p a l strengths, L and T. These are far enough apart i n value that t h e i r d i s t r i b u t i o n s do not overlap and they s h a l l be considered as fixed variables (appendix i i i ) . A further step i n r e f i n i n g t h i s model would be treatment of the L and T strengths as random variables with the model generating a random function (stochastic) prediction of strength. The predicted variance associated with the single stacked strand set i s given by: Equation [14] refers to a single v e r t i c a l stacked strand modelling unit, assumed to be the same at a l l planar locations i n the composite. The actual composite consists of a multitude of such units, having unknown size, shape and number. This set of units has additional components of strength variance, which are driven by such factors as l o c a l o r i e n t a t i o n and density v a r i a t i o n in the plane. This l i m i t s the u t i l i t y of Equation [14]. In a t r i a l calculation, the variance of [14] was much larger than that estimated on the basis of 5 t e n s i l e specimens (ASTM D1037) cut from d i f f e r i n g locations in the board plane. JC/2 [14] -71/2 38 3.10.3 Model Assumptions and S t r e s s T r a n s f e r The model makes assumptions about s e v e r a l c o - d e t e r m i n a n t s o f • s t r e n g t h and n e g l e c t s o t h e r s . F o r example, such f a c t o r s as l a m i n a t i o n m i c r o - d e f e c t s and d u r a t i o n o f l o a d a r e s p e c i a l t o p i c s and s h o u l d be s t u d i e d s e p a r a t e l y . Checks, k n o t s , and g r a i n i m p e r f e c t i o n s are d i s p e r s e d when wood i s w a f e r i z e d and rebonded i n a composite. The composite s t r e n g t h e n i n g e f f e c t o f t h i s d i s p e r s i o n o f f l a w s i s acknowledged i n t h e p r e s e n t model i n w h i c h the i n p u t s t r a n d s t r e n g t h s were t e s t e d on s m a l l specimens t h a t were c l e a r o f k n o t s and checks. These s t r e n g t h s are g e n e r a l l y accepted as b e i n g h i g h e r than l a r g e specimens c o n t a i n i n g such f l a w s . T h i s f u r t h e r s u p p o r t s the c h o i c e o f z e r o span t e s t i n g o f the s t r a n d s . The e x c e s s i v e c o m p l e x i t y o f d e t a i l e d bond s t r e s s a n a l y s i s l e d t o the b r i c k - l a y model of F i g . 7. The s t r a n d s a r e a r r a n g e d i n h a l f - o v e r l a p p i n g a r r a y w i t h t h e g r a i n a n g l e s r e p r e s e n t e d by . the von Mises p r o b a b i l i t y d i s t r i b u t i o n . T h i s r e p r e s e n t a t i o n i s assumed t o model t h e mean r e s u l t s o f a l a r g e number o f s t r e s s t r a n s f e r p o i n t s i n . a composite. The s t r a n d s t h e m s e l v e s a r e c o n s i d e r e d t r a n s v e r s e l y i s o t r o p i c . A n n u a l r i n g a n g l e e f f e c t s on s t r e n g t h were n e g l e c t e d because r i n g a n g l e s are u n i f o r m l y d i s t r i b u t e d i n t h e f u r n i s h and t e n s i l e s t r e n g t h d i f f e r e n c e s from the r a d i a l t o t a n g e n t i a l d i r e c t i o n s a r e s m a l l . A l l s t r e s s e s engendered by P o i s s o n e f f e c t i n t e r a c t i o n s between s t r a n d s and t h e f a i l u r e c r i t e r i a e f f e c t s o f them a r e n e g l e c t e d . The t h e o r y f o l l o w s t h e concept of a c o n t i n u o u s s t r a n d network which has been e s t a b l i s h e d i n g l a s s f i l a m e n t composite des i g n and a l s o paper p h y s i c s . I n t h e i d e a l i z e d network t h e o r y enough bonding and s t r a n d l e n g t h a r e assumed t o p e r m i t maximum s t r e s s development a l o n g the f u l l l e n g t h o f t h e s t r a n d . T h i s i s e q u i v a l e n t t o assuming the s t r a n d s a r e c o n t i n u o u s t h r o u g h t h e composite m a t e r i a l . The l o a d e d s t r a n d s a r e a c t u a l l y d i s c o n t i n u o u s i n some cases and c o n t i n u o u s i n o t h e r s , depending on r e s i n l e v e l and s t r a n d shape. Barnes i n p a t e n t s (8, 9 ) , s p e c i f i e d a minimum l e n g t h t o t h i c k n e s s r a t i o o f 53 and d i s c u s s e d u n i d i r e c t i o n a l c o m p o s i t e s h a v i n g a s l e n d e r n e s s r a t i o of 280 which had MOR a p p r o a c h i n g t h a t o f t h e o r i g i n a l wood. D e n s i t y g r a d i e n t s were not p r e s e n t e d i n Barnes' comparisons, and t h e p a t e n t s a l s o do not r i g o r o u s l y q u a n t i f y o r i e n t a t i o n . The e x p e r i m e n t a l s t r a n d s f o r t h i s : t h e s i s were cut at s l e n d e r n e s s r a t i o s near 100, e x c e p t f o r b i r c h where i t was at 135. L i m i t a t i o n s on m a t e r i a l h a n d l i n g do not p e r m i t p r o d u c t i o n o f o r i e n t e d p a n e l b o a r d s h a v i n g h i g h e r l e n g t h s l e n d e r n e s s r a t i o s t h a n about 160 i n most 1989 OSB m i l l s . The . p r a c t i c a l l i m i t a t i o n s o f p r o c e s s i n g l o n g s t r a n d s are f o r m i d a b l e . Simpson (79) d i s c u s s e d s t r a n d l e n g t h / t h i c k n e s s r a t i o ( s l e n d e r n e s s r a t i o ) i n a p e r f e c t l y p a r a l l e l o r i e n t a t i o n model. He i n d i c a t e d t h a t r a t i o s o f 55 t o 200 would l e a d t o c o m p o s i t e t e n s i l e s t r e n g t h t h a t was 90 t o 95 p e r c e n t o f t h e s t r a n d s t r e n g t h , depending on s p e c i e s . T h i s was based on t h e l i m i t i n g f a c t o r i n s t r e s s t r a n s f e r b e i n g t h e shear s t r e n g t h o f the. wood, not t h e adhesive bond. 40 1 ; — J l I f " 1 f >- z w = w i d t h o f s t r a n d b = t h i c k n e s s o f s t r a n d p = s t r a n d t e n s i l e s t r e s s s = s h e a r s t r e n g t h o f t h e a d h e s i v e bond o r s t r a n d , w h i c h e v e r i s l o w e s t free body F i g u r e 7. S t r e s s t r a n s f e r 41 An expression for the t e n s i l e stress i n strands within a composite i s made with reference to Equation [15]. Only face adhesion i s considered i n the analysis because of the f l a t , t h i n strand shape. The sides and ends of the strands are assumed free of loads. Considering the equilibrium of the free-body diagram in F i g . 7, 2sw dz = [15] The t e n s i l e stresses, p, are hypothetically assumed to be as represented in Fig . 8. It follows from t h i s assumption that the strand shear stresses are represented as i n the second diagram of Fig. 8. Thus, the interface shear stress i s assumed constant along the portion h at the end of the strand length. Either the shear y i e l d strength of the wood or the adhesive bond can define the ide a l i z e d shear stress i n t h i s s i m p l i f i e d analysis. It i s also possible that the material which i s assumed subject to.shear flow i s more accurately considered as a resin-treated wood subzone, having properties d i f f e r e n t from either wood or adhesive. An e l a s t i c model analysis of double lap joi n t stresses can also provide t h e o r e t i c a l estimates of the shear, s, and i t ' s * d i s t r i b u t i o n over the length . (eg. Stresses i n Adhesive Joints, H. Perry, Product Engineering, July 7, 1958). Further experimental research i s needed to tes t the use of the shear flow hypothesis and to estimate h. Equation [15] i s derived with reference to the c r i t i c a l f i b r e length estimate made for discontinuous f i b r e s i n polymer matrices (5). 42 portion of the strand length having constant shear stress with l i m i t s 0 <> h <, 1/2 Shear Stress, s b ,dp\ 2 W h = max. defined by adhesive or wood. - 2 F i g u r e 8. Strand stress. The cancelling of opposing symmetric normal forces occurs i n the model's double lap j o i n t configuration. This s i m p l i f i e s the shear stress loading of p e r f e c t l y oriented and lapped strands. But void gaps, multiple overlaps, and v a r i a t i o n i n strand e l a s t i c modulus with grain angle confound the true state of shear stress in the p r a c t i c a l strand composite. More research on t h i s i s needed. A c r i t i c a l constant shear length, hc, i s derived from Equation [15]. The peak t e n s i l e force applied to the strand i s reached at dz = h c and t h i s substitution i s made i n Equation [15]. The peak t e n s i l e stress i s equal to the ultimate t e n s i l e stress, t, of the strand at the c r i t i c a l constant shear length h c. Therefore, strand t e n s i l e strength, t, i s substituted for the strand stress dp i n Equation [15] to complete the derivation of [16]. For example, a c r i t i c a l constant shear length h c for strand t e n s i l e f a i l u r e can be estimated using the substitution of wood shear strength for the hypothesized constant value of s. Depending on bonding, s does not necessarily reach t h i s wood shear strength l e v e l . Using Jessome (39) for an estimate of aspen p a r a l l e l shear strength (6.8 MPa), the c r i t i c a l length, h c i s about 2.5 mm with the strand thickness, b, set at 0.6 mm. (Table 3) The d e f i n i t i o n of h c allows shear, s, and strand thickness and length necessary for 2 types of f a i l u r e to be designated. Both of these, t e n s i l e and shear f a i l u r e , occur together when h=hc. as i n the example. constant shear length h £ hc, then the strand f a i l s i n tension, constant shear length h < hc, then the interface f a i l s i n shear. According....to the. assumption of constant shear, the c r i t i c a l -constant shear length i s at h=l/2 (midlength). Substituting: bt 2s [16] If: 1 > bt/s 1 <bt/s t e n s i l e f a i l u r e , shear f a i l u r e , [17] [18] 4 4 The s t r a n d l e n g t h l c = b t / s i s termed t h e c r i t i c a l s t r e s s t r a n s f e r l e n g t h of s t r a n d . Thus, when u s i n g s h o r t s t r a n d s o r p a r t i c l e s w i t h 1<1C, s t r e n g t h g a i n s a r e p o s s i b l e t h r o u g h i n c r e a s e d a d h e s i v e shear bonding o n l y up u n t i l s r eaches t h e wood's s h e a r s t r e n g t h . Composite s t r e n g t h i n c r e a s e s w i t h s u n t i l enough s t r e s s t r a n s f e r i s p r o v i d e d t o cause t e n s i l e o r s h e a r f a i l u r e (or both) i n t h e wood. The analogous r a t i o n a l e a p p l i e s t o t h e s t r a n d s t h a t a r e s t r e s s e d p e r p e n d i c u l a r t o t h e g r a i n ( S e c t i o n 5.2). The p e r p e n d i c u l a r t e n s i l e s t r e n g t h and r o l l i n g s h e ar s t r e n g t h a r e t h e n used i n E q u a t i o n [16] f o r h c. I f t h e s t r a n d b o n d i n g l e n g t h 1 were a b u n d a n t l y g r e a t e r t h a n t h e l c , t h e n t h e s t r e n g t h d e v e l o p e d i n t h e composite would be near t h a t o f t h e s t r a n d s . T h i s d e f i n e s t h e p e r f e c t l y bonded s i t u a t i o n , where c o n t i n u o u s s t r a n d s a r e s i m u l a t e d . I n g l a s s f i b e r - e p o x y c o mposites t h i s t y p i c a l l y r e q u i r e s f i b e r l e n g t h , 1 > 50 l c . A " s t r e n g t h f a c t o r " f o r g l a s s f i b e r c o m p o s i t e s d i s c u s s e d by Agarwal e t a l . (5) p r o v i d e s an e s t i m a t e o f c o m p o s i t e s t r e n g t h i n c r e a s e as t h e f i b r e l e n g t h , 1, becomes much l o n g e r t h a n l c . A c c o r d i n g t o Simpson (79) t h e model composite o f F i g . 7, s h o u l d have p a r a l l e l s t r e n g t h near t h a t o f t h e s t r a n d o r p e r f e c t l y o r i e n t e d s t r a n d network when t h e e x p r e s s i o n [ ( 1 / b ) + 1 ] / [ ( 1 / b ) + ( t / s ) ] has a v a l u e c l o s e t o 1. The v a r i a b l e 1 i n Simpson's expression i s the strand length. In the present a n a l y s i s , as. t h e f r a c t i o n 1-(h/1) approaches 1, the., .full...length. .. o f the s t r a n d i s exposed t o t e n s i l e f a i l u r e s t r e s s . The e x p r e s s i o n l - ( h / l ) i s i n t e r p r e t e d as t h e s t r a n d ' s l e n g t h average r e l a t i v e t e n s i l e s t r e s s ( s t r e n g t h f a c t o r ) . Thus, f o r t h e i d e a l i z e d composite s t r e n g t h t o be a c h i e v e d , t h e c r i t e r i a o f 1 >> l c and 1 » h are r e q u i r e d . I t has been assumed (5) t h a t t h i s c o n d i t i o n of maximum s t r a n d (length) t e n s i l e l o a d i n g corresponds t o maximum composite s t r e n g t h . In summary, the t a r g e t of e f f i c i e n t composite formation i s represented by the continuous s t r a n d network model s t r e n g t h , (Equation [13]). T h i s p r o v i d e s an i d e a l i z a t i o n of the maximum a t t a i n a b l e s p e c i f i c t e n s i l e s t r e n g t h when bonding i s s u f f i c i e n t t o cause t e n s i l e f a i l u r e over most of the s t r a n d l e n g t h . 3.10.4 Density Gradient E f f e c t and Measurement The d e n s i t y g r a d i e n t e f f e c t i s taken advantage of i n i n d u s t r i a l p r a c t i c e . Current OSB panels are produced with denser s u r f a c e l a y e r s than core. T h i s i s done with the purpose of maximizing the bending s t r e n g t h while m a i n t a i n i n g a core s t r e n g t h s u f f i c i e n t t o s u r v i v e the n e u t r a l a x i s shear s t r e s s and a l s o pass the standard i n t e r n a l bond t e s t . The presence o f a throug h - t h i c k n e s s d e n s i t y g r a d i e n t was observed i n both experimental and i n d u s t r i a l boards. C o n s i d e r a t i o n of the g r a d i e n t e f f e c t on t e n s i l e s t r e n g t h was s i m p l i f i e d by assuming both s t r a n d and composite s t r e n g t h s as l i n e a r l y p r o p o r t i o n a l t o d e n s i t y , and choosing s p e c i f i c s t r e n g t h as the dependent v a r i a b l e . T h i s g e n e r a l l i n e a r i t y changes only i n extreme d e n s i f i c a t i o n i n the t r a n s v e r s e g r a i n d i r e c t i o n , where (compressive) s t r e n g t h v a r i e s as the cube of d e n s i t y (19). The s p e c i f i c t e n s i l e s t r e n g t h was t h e r e f o r e approximated by d i v i d i n g the u l t i m a t e s t r e n g t h of the t e s t specimen by i t s specimen average d e n s i t y based on oven-dry weight and c o n d i t i o n e d volume at 7 t o 8 percent moisture content. T h i s made the model, t e s t panel, and n a t i v e wood strands, reasonably v a l i d t o compare i n te n s i o n , d e s p i t e the d e n s i t y inhomogeneity ( g r a d i e n t ) , and l i n e a r i t y approximation. Density g r a d i e n t s a f f e c t f l e x u r a l s t r e n g t h i n a complex f a s h i o n . F l e x u r a l t e s t s were concluded a c c o r d i n g t o CAN3-0437-M85 and MOR was c a l c u l a t e d u s i n g the elementary f l e x u r e formula: where: MOR = u l t i m a t e (rupture) f i b e r s t r e s s at the s u r f a c e M = maximum bending moment I =• c r o s s s e c t i o n moment of i n e r t i a c = h a l f t h i c k n e s s of the symetric specimen The formula assumes each l a y e r i n a homogeneous t e s t beam makes an e l a s t i c c o n t r i b u t i o n t o the i n t e r n a l r e s i s t i v e moment p r o p o r t i o n a l t o the l a y e r ' s d i s t a n c e from the n e u t r a l a x i s . T h i s i s based on a l l l a y e r s having the same e l a s t i c modulus and the assumption of pure, g e o m e t r i c a l l y d e f i n e d bending s t r a i n . Because the d e n s i t y g r a d i e n t c o n t r a d i c t s the homogeneity assumption, the bending t e s t r e s u l t s vary, depending on the gr a d i e n t . The g r e a t e r e l a s t i c modulus and s t r e n g t h of the surf a c e l a y e r s i s due to the h i g h e r s u r f a c e d e n s i t y . In a s t r i c t l y r i g o r o u s sense, t h i s means t h a t the comparisons of s p e c i f i c MOR of v a r i o u s d i f f e r e n t composites are v a l i d o n l y when the d e n s i t y g r a d i e n t s are the same. The assumption i s made t h a t u l t i m a t e f l e x u r a l f a i l u r e i s governed by f i r s t f i b e r f a i l u r e at the t e n s i l e s u r f a c e . The modulus of e l a s t i c i t y , E, and the bending ( f i b e r ) s t r e s s , c-Ee, i n c r e a s e p a r a b o l i c a l l y toward the t e s t beam s u r f a c e . Assuming pure bending s t r a i n , the stress at the t e n s i l e surface i s actually greater than the flexure formula, Equation [19] predicts on the basis of a constant or fix e d average value of E. The di v i s i o n of t h i s conservative surface stress by the increased surface density y i e l d s a conservative approximation of the sp e c i f i c f i b e r stress at the beam surface. Therefore the MOR test results used as data i n F i g . 18 to 27 are thought to be low boundary l i m i t s of ultimate f i b e r stress, i n tension, at the bottom surface of the test beam. This conclusion also accommodates any deviation from pure bending, such as f i b e r crushing, on the compression side. An alternative transformed section approach to MOR of boards having density gradient requires c a l c u l a t i o n of the f l e x u r a l e l a s t i c modulus followed by application of a strength c r i t e r i o n based on the maximum f i b e r s t r a i n at the surface. The MOR i s estimated as: a = (calculated f l e x u r a l modulus) x (surface f a i l u r e strain) In a t r i a l c a l c u l a t i o n the above method yielded high MOR values. This was i n the presence of the transformed moment of i n e r t i a analysis producing reasonably accurate estimates of f l e x u r a l modulus as shown i n Table [22]. The transformed section analysis was performed i n section 5.4 using the Appendix i i program fo r f l e x u r a l e l a s t i c i t y which i s applicable to any parabolic- density gradient i n the strand laminate. The accuracy i s similar to that of Geimer (27) who also used a transformed section approach. The details are discussed i n Section 5.4. In the above formula, the 48 apparent f l e x u r a l e l a s t i c i t y results from Appendix i i are multiplied by the f a i l u r e s t r a i n of the composite. The surface f a i l u r e s t r a i n was assumed to be si m i l a r to the tertsile f a i l u r e s t r a i n of the composites i n the p a r a l l e l to grain d i r e c t i o n i n the t e n s i l e tests (Table 10). Strains at f a i l u r e of 3 to 7 percent were observed. The r e s u l t i n g estimates of MOR were at least 5 to 10 times larger than those observed i n Figure 27 and Table 10, because of t h i s excessive s t r a i n at f a i l u r e . The 3 to 7 percent composite f a i l u r e s t r a i n i s above that expected of normal dry mature wood (about 1 percent). Bond creep and strand interlocking may be contributors to t h i s high s t r a i n . For these reasons, the previously described method of estimating s p e c i f i c MOR was used. This provided the advantage of being able to estimate a minimum MOR with knowledge only of the surface density while using a standard test procedure. The MOR test results, divided by t h e i r respective surface densities, provided the low bound experimental s p e c i f i c MOR data displayed in Fig. 18 to F i g . 27 and F i g . 29 to F i g . 33 (averages of nominal: 5 r e p l i c a t e s ) . The method of measuring the density p r o f i l e was dir e c t reading x-ray densitometry. The equipment was developed,by Forintek Canada Corp. for scanning tree increment cores. Therefore, small cross s e c t i o n specimens were requ i r e d . The speed and accuracy of x-ray and higher frequency gamma, radiation (Winistorfer (96), Laufenberg (49)) have made the gravimetric methods (86) obsolete. The Forintek procedure passed a 0.25 by 1.00 mm collimated x-ray beam having power of 2 mA by 15 to 20 kV through the specimens according to F i g . 9. Cold-set urea formaldehyde r e s i n was used to prebond the specimens before sawing to the t e s t shape. The repeated glue l i n e between samples had a lower mass at t e n u a t i o n c o e f f i c i e n t and higher d e n s i t y than the adjacent strands. This separation was u s e f u l f o r i d e n t i f y i n g the samples to w i t h i n one strand t h i c k n e s s . The x-ray d e t e c t o r r e s o l u t i o n was 1 0 0 microns. Scanning was at a i r - d r y ambient conditions and the r e s u l t i n g d e n s i t i e s were adjusted to the same ( 5 0 percent R.H., 2 2 ° C ) c o n d i t i o n s as the mechanical t e s t specimens. The Lambert equation used f o r r e l a t i n g r a d i a t i o n a t t e n u a t i o n to density i s expressed as: In P = [ 2 0 ] •<-*-> t where: 3 P = specimen p o i n t d e n s i t y , g/cm I 0= unattenuated r a d i a t i o n i n t e n s i t y , counts I = attenuated r a d i a t i o n i n t e n s i t y , counts t = specimen t h i c k n e s s , cm (a/p) = l i n e a r a t t e n u a t i o n per u n i t density, (mass 2 a t t e n u a t i o n c o e f f i c i e n t , cm /g) Mass attenuation c o e f f i c i e n t s can be determined experimentally, .or c a l c u l a t e d from c o n s t i t u e n t elemental a n a l y s i s . The mass attenuation c o e f f i c i e n t s of adhesive r e s i n s and moisture.are s l i g h t l y higher than f o r wood. Therefore, a small e r r o r i s caused by n e g l e c t i n g the r e s i n and moisture attenuation i n the Figure 9. D e n s i t o m e t r y specimen. 51 composite, but t h i s u n d e r e s t i m a t i o n o f d e n s i t y was found n e g l i g i b l e i n Laufenberg's (49) stu d y u s i n g gamma r a y s . O l s o n e t a l . (66) showed t h a t m a s s - a t t e n u a t i o n c o e f f i c i e n t s can v a r y w i t h s p e c i e s and ash c o n t e n t when u s i n g gamma r a y s of l e s s t h a n 40 KeV. (Mid-range gamma r a y s have 10 tim e s t h e energy o f x - r a y s . ) F o r i n t e k ' s x-ray m a s s - a t t e n u a t i o n c o e f f i c i e n t was common t o t h e D e l r i n a c e t a l p l a s t i c s t e p wedge used f o r c a l i b r a t i o n , ; a n d t o bot h hardwoods and softwoods (40). E x t r a c t i v e s are s a i d t o decrease the x-ray mass a t t e n u a t i o n c o e f f i c i e n t s s l i g h t l y , and may cause o v e r e s t i m a t i n g t h e m a t e r i a l d e n s i t y when not removed. 3.10.5 Model S t r u c t u r e and Programming The model was based on E q u a t i o n [13] . The program i n t e g r a t i o n between o and % f o r t h e von M i s e s pdf was per f o r m e d u s i n g Simpson's R u l e f o r n u m e r i c a l i n t e g r a t i o n , w i t h 50 i t e r a t i o n s . The an g l e o f l o a d i n g , m, was incremented i n s t e p s o f 4.5 degrees w i t h i n a computer program d e v i s e d t o c a l c u l a t e E q u a t i o n [13] . In t h i s way, a p i c t u r e o f s t r e n g t h was d e v e l o p e d f o r a composite made from wood s t r a n d s o f s p e c i f i c l o n g i t u d i n a l t e n s i l e s t r e n g t h , L, s p e c i f i c t r a n s v e r s e t e n s i l e s t r e n g t h T, and ha v i n g c o n c e n t r a t i o n parameter k, f o r o r i e n t a t i o n . The GWBASIC program f o r c a l c u l a t i n g E q u a t i o n [13] i s p r e s e n t e d i n Appendix i and produces r e s u l t s e x e m p l i f i e d by F i g . 10, when p l o t t e d . The program f a l t e r s at o r i e n t a t i o n s g r e a t e r than k=80 where kcos2(0-m) the r a t i o e / I Q ( k ) became e x c e s s i v e l y l a r g e . At t h i s l e v e l the o r i e n t a t i o n d i s t r i b u t i o n ( F i g . 3) tends t o a s p i k e c o n f i g u r a t i o n and f o r p r a c t i c a l purposes t h e model r e p r e s e n t s 52 Figure 10. O r i e n t a t i o n model o u t p u t . 53 natural wood. F i g . 10 places the k value p d f s i n a vi s u a l display of ranking. As the l e v e l of orientation i s reduced, the composite strength i s also reduced. At the k=12 l e v e l of orientation, for example, the computer model predicts a composite s p e c i f i c t e n s i l e strength p a r a l l e l to the orientation axis of about 80 percent of the p a r a l l e l grain wood strand strength tested at zero-span. The t h e o r e t i c a l t e n s i l e strength for random boards i s given by Equation [21], as expressed by Price (72). 1/2 S* = (LT) x / z [21] Equation [21] presents the value of the in t e g r a l (Equation [13]), with k=0. The pr o b a b i l i t y d i s t r i b u t i o n function becomes uniform with value 1/7C i n the random case. At k=0, i n random orientation, the model predicts a composite s p e c i f i c tensile, strength of about 25 percent of the wood strand's s p e c i f i c t e n s i l e strength p a r a l l e l to grain. It i s obvious that much strength i s lo s t when l i t t l e or no orientation i s present. This deficiency has t r a d i t i o n a l l y been recovered by the panel industry by using surface d e n s i f i c a t i o n to increase MOR. 3.11 Experimental Design 3.11.1 Composite S t r e n g t h Comparisons In comparing the strength results to those predicted by the model, i t was chosen to evaluate the independent variables of resin l e v e l (2), species (5), and the orientation parameter, k, over i t s range between 0 and about 9. This approach 54 comprehensively t e s t e d the accuracy of the p r e d i c t i v e s t r e n g t h algorithm i n a wide range of wood s t r a n d composites. When one f a c t o r was manipulated, the others were h e l d as constant as p o s s i b l e so t h a t the e f f e c t c o u l d be observed i n a r i g o r o u s l y s e l e c t i v e f a s h i o n . The completely randomized experimental design r e q u i r e d t h a t v a r i a b l e s such as board p r e s s i n g order and specimen c u t t i n g and t e s t i n g sequence, i n p a t t e r n and time, be randomized to minimize and d i f f u s e any s y s t e m a t i c e f f e c t on the dependent s t r e n g t h v a r i a b l e under study. The s t r e n g t h data were presented i n both t a b u l a r and g r a p h i c a l form with standard d e v i a t i o n s . Where s t r e n g t h d i f f e r e n c e s r e q u i r e d s t a t i s t i c a l s c r u t i n y , the n u l l h y p o t h e s i s that the model p r e d i c t i o n was not a member of the p o p u l a t i o n s e t represented by the t e s t sample was t e s t e d . The student 1 11" s t a t i s t i c was used f o r t h i s hypothesis t e s t . The t e s t s were normally made at the p=0.05 l e v e l of p r o b a b i l i t y of f a l s e l y r e j e c t i n g the n u l l h y p o t h e s i s . Species and r e s i n l e v e l e f f e c t s • on s t r e n g t h were examined i n (2-way) f a c t o r i a l a n a l y s i s of variance i n random o r i e n t a t i o n boards. 3.11.2 R e p e a t a b i l i t y o f O r i e n t a t i o n Parameter The 95 percent confidence l i m i t s were c a l c u l a t e d f o r e v a l u a t i n g the r e p e a t a b i l i t y of the d e t e r m i n a t i o n of the ' o r i e n t a t i o n parameter, k. The methodology i s based on the c h i -square d i s t r i b u t i o n and was developed f o r t h i s purpose by B a t s c h e l e t (11). R e s u l t s are d i s c u s s e d i n S e c t i o n 4.1.1. 55 A f u r t h e r v e r i f i c a t i o n and assessment o f the goodness o f f i t of the o r i e n t a t i o n d a t a t o the von Mises d i s t r i b u t i o n was made. The n u l l h y p o t h e s i s t h a t the a n g u l a r d a t a d i d not c o n t r a d i c t t h e e s t i m a t i o n o f parameter k, and t h a t d a t a f i t t i n g d i s c r e p a n c i e s c o u l d v a l i d l y be e x p l a i n e d by chance f l u c t u a t i o n was t e s t e d . The c h i - s q u a r e s t a t i s t i c was a g a i n used f o r t h i s h y p o t h e s i s t e s t a t the p=0.05 p r o b a b i l i t y o f f a l s e r e j e c t i o n . G r a p h i c and s t a t i s t i c a l r e s u l t s are p r e s e n t e d i n S e c t i o n 4.1.2. 3.11.3 S p e c i e s Comparisons o f S t r e n g t h The comprehensive d i r e c t comparison o f s p e c i e s e f f e c t s on s t r e n g t h i n a f a c t o r i a l experiment was r e s e r v e d f o r t h e randomly o r i e n t e d case where o r i e n t a t i o n d i f f e r e n c e s between v a r i o u s s p e c i e s and r e s i n l e v e l s were n e g l i g i b l e . I n t h e s e d i r e c t comparisons, f u r t h e r r e s o l u t i o n o f s p e c i e s d i f f e r e n c e s was p o s s i b l e i n a d d i t i o n t o comparing p e r c e n t a g e s o f the model s t r e n g t h s t h a t were a c h i e v e d i n each s p e c i e s . The f a c t o r s were s p e c i e s (4) and r e s i n l e v e l ( 2 ) . The a n a l y s i s o f v a r i a n c e was: r e p e a t e d w i t h b o t h s p e c i f i c t e n s i l e s t r e n g t h and f l e x u r a l s t r e n g t h as independent v a r i a b l e s . The e x p e r i m e n t a l d e s i g n was c o m p l e t e l y randomized. Where s i g n i f i c a n c e was i d e n t i f i e d , Duncan's M u l t i p l e Range Test was used f o r g r o u p i n g f a c t o r s i n t o f u r t h e r s i g n i f i c a n t sub-ranges. 3.12 Test P r o c e d u r e s 3.12.1 S t r a n d T e s t i n g , S t r e n g t h The s t r a n d s i n a p e r f e c t l y a r t i c u l a t e d , bonded, and o r i e n t e d composite are l o a d e d i n t e n s i o n a l o n g t h e i r l e n g t h c o n t i n u o u s l y 56 except f o r s m a l l , randomly spaced d i s c o n t i n u i t i e s . The z e r o span t e s t approximates t h i s l o a d c o n d i t i o n more c l o s e l y than e x t e n d e d gage l e n g t h t e s t i n g . In a d d i t i o n , t h e h i g h e s t c o r r e l a t i o n c o e f f i c i e n t s between d e n s i t y and s t r e n g t h have been found when u s i n g t h i s method i n m i c r o t e n s i l e t e s t i n g (52). T h i s i s important because such l i n e a r i t y i s assumed i n t h e p r e s e n t s t u d y . For these r e a s o n s , t h e f o l l o w i n g z e r o span p r o c e d u r e was adopted. The p a r a l l e l specimens were p r e p a r e d u s i n g t h e same c u t t i n g d i e s as used i n Wellwood's (93) and W i l s o n ' s (95) r e s e a r c h . The specimen shape was n o m i n a l l y 0.42 X 6.0 cm; t h i s was used f o r . aspen, p i n e , cedar and a l d e r . The e x c e p t i o n was b i r c h , because of g r i p p u l l - o u t on t h e t h i c k e r s t r a n d s which were used.. The> b i r c h shapes were changed t o the necked-down c o n f i g u r a t i o n a l s o s p e c i f i e d i n Wellwood's (93) work. These specimens were 9.0 X 0.42 cm w i t h t h e c r i t i c a l necked zone h a v i n g a gage l e n g t h o f 1.27 cm and neck w i d t h o f 0.15 cm. P a r a l l e l g r a i n specimens a r e p i c t u r e d i n Appendix i v . The p e r p e n d i c u l a r t o g r a i n specimens were cut from randomly s e l e c t e d s t r a n d s , t o w i d t h o f 1.5 cm by up t o 3.0 cm.in l e n g t h a c r o s s the g r a i n . Both f l a t c u t and q u a r t e r c u t specimens were i n c l u d e d i n t h e random s e l e c t i o n . A l l p o s i t i o n s i n t h e t r e e were r e p r e s e n t e d by t h e random s e l e c t i o n o f t e s t s t r a n d s . A l l specimen preparation and testing was as 20°C and 50 p e r c e n t R;H. w i t h c o r r e s p o n d i n g e q u i l i b r i u m m o i s t u r e c o n t e n t o f the wood a t 7 t o 9 p e r c e n t . The T h w i n g - A l b e r t QCII e l e c t r o n i c t e n s i l e t e s t e r p r o v i d e d by t h e P u l p and Paper Research I n s t i t u t e of Canada was equipped w i t h pneumatic g r i p s which were a b l e t o appl y 4 MPa p r e s s u r e on the specimens. T h i s i s near the 57 p e r p e n d i c u l a r compressive y i e l d s t r e n g t h of the woods t h a t were t e s t e d and i s a l s o c l o s e t o the pressures used i n p r e s s i n g OSB i n d u s t r i a l l y . The t e n s i l e s t r e n g t h was c a l c u l a t e d as the' l o a d at f a i l u r e d i v i d e d by the uncompressed s t r a n d cross s e c t i o n a l a r e a . The s p e c i f i c s t r e n g t h of a st r a n d was ob t a i n e d by d i v i d i n g t h i s s t r e n g t h by the specimen's d e n s i t y . Weights were at oven-dry and volumes were at 7 to 9 percent EMC i n the d e n s i t y c a l c u l a t i o n . The dimensions of the s t r a n d blanks were measured by micrometer f o r d e n s i t y determination. Alignment i n the g r i p s was c r i t i c a l , and specimens t h a t were mi s a l i g n e d by more than 0.5 degrees from p a r a . l l e l t o the t e s t f o r c e a x i s were d i s c a r d e d . The speed of t e s t i n g (0.45 cm/min) was the same as s p e c i f i e d i n the ASTM D1037-86 procedure which was l a t e r used f o r t e s t i n g the composites i n t e n s i o n . Twelve p a r a l l e l and 35 p e r p e n d i c u l a r specimens were i n c l u d e d i n the data f o r each s p e c i e s . 3.12.2 Composite T e n s i l e S t r e n g t h The t e s t procedure f o l l o w e d ASTM D1037-86 u s i n g necked specimens as diagrammed i n Appendix i v . The r e c t a n g u l a r dimensions of the specimen were 5.1 cm X 25.5 cm wit h a necked gage le n g t h of 5.1 cm. The t e s t average moisture content was 7 to 8 percent as a r e s u l t of p r e c o n d i t i o n i n g at 20°C and 50 percent R.H. -for 6 weeks. Specimens of t h i s shape were used t o t e s t the zero degree d i r e c t i o n , p a r a l l e l t o the a x i s and a l s o the p e r p e n d i c u l a r d i r e c t i o n . The t e s t specimens were cut from 5 pressed r e p l i c a t e panels, as shown i n the Appendix i v . A c l e a r p l a s t i c marking template was p l a c e d on e i t h e r the face or back of 58 the panels randomly and a l s o randomly with res p e c t t o the top and bottom p a r a l l e l r e f e r e n c e edges. The purpose of t h i s was to randomize any systematic o r i e n t a t i o n or d e n s i t y g r a d i e n t a r t i f a c t s . The same procedure was a p p l i e d to the randomly o r i e n t e d boards. One t e n s i l e specimen f o r p a r a l l e l and one f o r p e r p e n d i c u l a r t e s t i n g was cut from each r e p l i c a t e . The r a t e of extension was 0.45 cm/min on the T i n i u s Olsen u n i v e r s a l t e s t i n g machine used at the UBC F o r e s t r y Dept. Con d i t i o n s i n the t e s t room were 20°C and 50 percent R.H. Noting the e f f e c t of specimen s i z e i n b r i t t l e f a i l u r e o f wood p e r p e n d i c u l a r t o g r a i n (10) adds importance to the compromise of u s i n g a s t a n d a r d i z e d ASTM D1037 composite specimen • s i z e . This t e s t s i z e i n c l u d e d bonding e f f e c t s , as opposed t o a zero span t e s t which would have made bond e f f e c t s s m a l l e r . The s i z e e f f e c t s must be t o l e r a t e d f o r the purpose of t e s t i n g an a c t u a l bonded composite. S i z e e f f e c t s are complicated by the st r a n d wood having a d i f f e r e n t c rack m i c r o s t r u c t u r e than the bonded composite. 3.12.3 Composite F l e x u r a l S t r e n g t h The f l e x u r a l t e s t method was Canadian Standards Assoc (CSA) CAN-0437-M85 which c l o s e l y r e f e r e n c e s ASTM standard D1037 on f l e x u r a l strength (MOR). The specimens were rectangular with the width m o d i f i e d from the 7.5 cm s p e c i f i c a t i o n t o 5.0 cm t o accommodate the 5 specimens per board c u t t i n g p a t t e r n shown i n Appendix i v . The l e n g t h was 18.0 cm, a l l o w i n g the requirement that the span be at l e a s t 24 times the t h i c k n e s s (0.55 cm). Five r e p l i c a t e panels were cut u s i n g the angled template i n a 59 randomized f a s h i o n t o mi n i m i z e any w i t h i n - p a n e l i n h o m o g e n e i t y . C o n d i t i o n i n g o f t h e p a n e l s was t h e same as f o r t h e t e n s i l e t e s t s . The s t a t i c b ending t e s t s were performed by t h e A l b e r t a R e s e a r c h C o u n c i l under t h e above s t a n d a r d s and specimen p r e p a r a t i o n u s i n g t h e f u r t h e r s p e c i f i c a t i o n o f : span c r o s s h e a d speed c o n d i t i o n i n g 13.2 cm 0.264 cm/min 20°C, 50%, R.H. - 6 weeks 4. RESULTS 4 .1 S t r a n d O r i e n t a t i o n 4.1.1 C o n c e n t r a t i o n Parameter, k The primary objective of Harris (34) was the establishment of an accurate, v e r i f i e d , sampling technique to estimate k. A feature.of t h i s was the l i m i t a t i o n to a p r a c t i c a l number of 100 strand angle measurements for each k parameter estimate. Using th i s guide for the present thesis, the following levels of orientation were obtained from composites formed i n the laboratory and from an i n d u s t r i a l board core. A description of the lab formation process i s found i n section 3.8. The concentration parameters were calculated using Equations [2], • • • • [3], [4] and [8]. The intent was to assign and measure, not assiduously control, orientation. The Table 6 confidence l i m i t s were based on the plots by Mardia (58). Inspection of t h i s data showed the tendency of i d e n t i c a l furnish samples having equal formation treatments, to orient to higher k parameters when the l i q u i d resin l e v e l was low or when powder resin was used. This e f f e c t was attributed to the higher, tackiness that the high l i q u i d resin levels produced, r e l a t i v e to the low l i q u i d l e v e l and powder resin. This serendipitous : finding led to the speculation that less tacky resins such as crude 4 , 4 diphenyl methane diisoc y a n a t e (MDI), may allow b e t t e r orientation i n some mechanical orienters. The revelation of t h i s tackiness e f f e c t demonstrated the s e n s i t i v i t y of the k measurement very well. Table 6. Orientation levels Liquid Resin Level 0.57 g/cm2 90 percent C L . Oriented k, concentration Strands parameter r upper lower T. Aspen 3.2 0.828 4.0 2.6 R. Al d e r 4.9 0.892 5.5 3.7 R. Cedar 2.8 0.795 3.4 2.3 L. Pine 3.4 0.840 4.2 2.7 Liquid Resin Level 1.14 g/cm2 90 percent C L . Oriented k, concentration Strands parameter r_ upper lower T. Aspen 2.3 0.735 2.7 1.8 R. Al d e r 3.5 0.842 4.4 2.8 R. Cedar 2.1 0.704 2.5 1.7 L. Pine 3.4 0.840 4.2 2.7 Liquid Resin Level 1.76 g/cm2 Oriented Strands R. Cedar Y. B i r c h k, concentration parameter 1.9 9.0 0.689 0.942 90 percent C L . upper lower 2.3 10.2 1.6 7.1 Oriented Strands T. Aspen (lab) T. Aspen ( i n d u s t r i a l ) Powdered Resin Level 2.0% k, concentration parameter 2.4 1.1 0.754 0.471 90 percent C L . upper lower 2.8 1.3 1.9 0.8 (Data Combined) Liquid Resin Levels at both 0.57 and 1.14 g/cm1 90 percent C L . Random k, concentration Strands parameter r upper lower T. Aspen 0.01 0.004 0.0 0.0 R. Alder 0.02 0.009 0.0 0.0 R. Cedar 0.26 0.131 0.5 0.0 L. Pine 0.01 0.008 0.0 0.0 Y. B i r c h 0.15 0.073 0.2 0.0 6 2 4.1.2 Goodness of F i t The choice of the von Mises d i s t r i b u t i o n was taken under the assumption that the d i s t r i b u t i o n of s t r a n d g r a i n o r i e n t a t i o n would f o l l o w t h i s form of continuous p r o b a b i l i t y d i s t r i b u t i o n . The goodness of f i t t e s t was to see i f the o b s e r v a t i o n s c o n t r a d i c t e d the d i s t r i b u t i o n and whether the d i s c r e p a n c i e s c o u l d be e x p l a i n e d by e i t h e r chance f l u c t u a t i o n or the wrong c h o i c e of d i s t r i b u t i o n . The Chi-square t e s t s t a t i s t i c was as used. T h i s i s the same expres s i o n used f o r o r d i n a r y n o n c i r c u l a r d i s t r i b u t i o n s . X 2 = S [ 2 2 ] i = l S i e i = the frequency of o b s e r v a t i o n expected on the b a s i s of the von Mises pdf = the observed frequency of s t r a n d angles i n a c e l l . The a x i a l s t r a n d angle data was s o r t e d i n t o p = 12 c e l l s o f 15 degree increments, t h i s gave the observed frequency • d i s t r i b u t i o n of the 100 measured strands i n each treatment. The expected frequency, e 1 ( of a c e l l was computed by i n t e g r a t i o n o f the von Mises pdf between the c e l l l i m i t s . The r e s u l t i n g f r a c t i o n of the t o t a l sample s i z e (100) gave the expected frequency. The n u l l hypothesis was t h a t the observed sample be c o n s i s t e n t with the expected p o p u l a t i o n curve. T h i s was t e s t e d at the alpha l e v e l of p = 0.05 p r o b a b i l i t y of f a l s e r e j e c t i o n . A frequency polygon Of the data from a sample of i n d u s t r i a l OSB core l a y e r i s shown i n F i g . 11. The hypothesis t e s t showed t h a t 63 >-0 z D 0 UJ a. 40 35 30 H 25 20 H 15 H Aspen, Oriented Industrial Core ORIENTATION CONCENTRATION k= l . l accept Hfl: good f i t .05 d - f - = 8 0 .46 < 1 1 . 1 i f X 2 < X 2 -82.5 -67.5 -52.5 -37.5 -22.5 -7.5 7.5 22.5 37.5 52.5 67.5 82.5 STRAND ORIENTATION, DEGRES • OBSERVED FREQUENCY + EXPECTED FREQUENCY F i g u r e 11. Curve f i t t i n g - aspen i n d u s t r i a l o r i e n t e d c o r e 64 > 0 z Ul 0 0 Ul fl-it 40 35-30 25 20-15-10-Randorn Aspen, ' Hand Felted ORIENTATION CONCENTRATION k=. 01 accept H0: good f i t i f X 2 < X 2 J 5 d.f. = 8 2.93 < 11.1 \ i . i / i I \ I i -82.5 -67.5 -52.5 -37.5 -22.5 -7.5 7.5 22.5 37.5 52.5 67.5 82.5 STRAND ORIENTATION, DEGRES D OBSERVED FREQUENCY + EXPECTED FREQUENCY F i g u r e 1 2 . Curve f i t t i n g - random aspen, hand f e l t e d 6 5 the von Mises pdf f i t the observed data s a t i s f a c t o r i l y . The n u l l hypothesis of a good f i t was not rejected at the p=0.05 l e v e l of error. The same applies to the random arrangement of the hand fel t e d laboratory board orientation represented i n F i g . 12. A summary of the results of the orientation k determination i s provided in Table 6 . 4.2 P r o c e s s V a r i a b l e s 4.2.1 S t r a n d T e n s i l e S t r e n g t h The p a r a l l e l to grain s p e c i f i c t e n s i l e strengths most closely resemble the s p e c i f i c MOR values calculated from the Wood Handbook (U.S.D.A., Madison) for each species at the 12 percent moisture condition. The Wood Handbook p a r a l l e l MOR means were not s i g n i f i c a n t l y d i f f e r e n t from the strand t e n s i l e results presented i n Table 7. The hypothesis of equality i n t h i s comparison was accepted at the p = 0.01 p r o b a b i l i t y l e v e l of error. The perpendicular to grain strength comparison to the larger Wood Handbook t e n s i l e specimens indicates a possible specimen size e f f e c t on strength. T a b l e 7. Zero span, strand s p e c i f i c t e n s i l e strengths, MPa. R.Alder T.Aspen R.Cedar L.Pine Y.Birch P a r a l l e l Grain, L Ave. S p e c i f i c Strength, MPa 146.8 152.2 148.7 166.9 173.9 Std. Dev. 48.5 13.2 71.0 41.7 63.9 Perpendicular Grain, T Ave. Specific Strength, MPa 8.74 10.95 10.80 8.52 9.23 Std. Dev. • -• 3.07 4.48 4.50 3.37 2.03 Wood Handbook, p a r a l l e l grain 164.8 152.4 160.9 158.6 184.6 MOR divided by density, 12% MC Wood Handbook, perpendicular 7.1 4.7 4.6 4.9 10.2 grain t e n s i l e strength, divided by density, 12% MC 6 6 S i n g l e f a c t o r ( s p e c i e s ) a n a l y s e s of v a r i a n c e i n c o m p l e t e l y randomized d e s i g n were performed on t h e s p e c i f i c s t r e n g t h d a t a summarized i n Table 7. Sample s i z e f o r t h e p a r a l l e l g r a i n a n a l y s i s of v a r i a n c e was 12, and a minimum o f 35 specimens o f each s p e c i e s were a n a l y z e d i n the p e r p e n d i c u l a r t o g r a i n d i r e c t i o n . The n u l l h y p o t h e s i s t h a t t h e r e i s no d i f f e r e n c e between s p e c i e s s p e c i f i c t e n s i l e s t r e n g t h , p a r a l l e l t o g r a i n , was acce p t e d at the p=0.05 p r o b a b i l i t y o f f a l s e r e j e c t i o n . T h i s was expected because o f the u n i f o r m e f f e c t s o f c e l l w a l l m a t e r i a l a n t i c i p a t e d by the U.S.D.A. Wood Handbook (p.88). A c u m u l a t i v e p r o b a b i l i t y d i s t r i b u t i o n f u n c t i o n p l o t of t h e p a r a l l e l s p e c i f i c s t r e n g t h o f the s t r a n d s i s p r e s e n t e d i n Appendix i i i . Depending on specimen s i z e , t h e p a r a l l e l t e n s i l e s t r e n g t h o f wood i s - , u s u a l l y l a r g e r t h a n the c o r r e s p o n d i n g b e n d i n g s t r e n g t h and MOR's are o f t e n t a k e n as c o n s e r v a t i v e e s t i m a t e s o f t e n s i l e s t r e n g t h . I t i s thought t h a t t h e use o f j u v e n i l e woods, or an a r t i f a c t o f the l o a d i n g c o n d i t i o n s , such as c r u s h i n g i n t h e t e s t jaws, produced t h e unexpected lower t e n s i l e s t r e n g t h s and congruence w i t h the Wood Handbook bending s t r e n g t h s f o r t h e s e s p e c i e s . In t e s t i n g p e r p e n d i c u l a r wood s t r e n g t h , t h e l a r g e r z e r o span r e s u l t s ( r e l a t i v e t o Wood Handbook v a l u e s ) a r e a s c r i b e d t o specimen s i z e e f f e c t s . B i r c h was t h e o n l y e x c e p t i o n not showing t h i s trend which i s c h a r a c t e r i s t i c of b r i t t l e f a i l u r e . P e r p e n d i c u l a r t o t h e g r a i n , the s p e c i e s f a c t o r was s i g n i f i c a n t at the p=0.05 l e v e l i n t h e a n a l y s i s o f v a r i a n c e . A Duncan's m u l t i p l e range t e s t grouped t h e s p e c i e s as f o l l o w s a t a m u l t i p l e range s i g n i f i c a n c e l e v e l o f 0.01. pine < aspen alder < aspen A t y p i c a l cumulative d i s t r i b u t i o n for the perpendicular s p e c i f i c t e n s i l e strength of cedar at zero span i s plotted as an example in Appendix i i i . In summary, i t should be noted that the strand specimen shape and loading conditions were chosen as part of the model hypothesis. They were contrived to approximate the condition of the strands in the composite, and served t h i s primary purpose. 4.2.2 R e s i n D i s t r i b u t i o n : S p e c t r o p h o t o m e t r y Optimal resin d i s t r i b u t i o n i s the allotment of an equal and controlled amount of adhesive to each strand surface. For quality control or experimentation t h i s should be extended over a l l batches processed. The random nature of blending means that optimal d i s t r i b u t i o n i s characterized by a narrow, symmetrically shaped histogram of resin take-up per strand. The blending process described i n Section 3.7 achieved t h i s in a l l species and with a l l resin l e v e l s blended. The desired symmetry was present i n two t r i a l widths of p l a s t i c tracer strands analyzed. A poor di s t r i b u t i o n histogram i s marked by extreme skew to the l e f t . This was the conclusion of Meinecke and Klauditz (60) and Kasper and Chow (42) who stressed the importance of strand-to-strand resin d i s t r i b u t i o n . Unpublished investigations by the author using a 90 to 120 micron droplet size, indicated that 25 to 30 percent of the strength perpendicular to the board surface (internal bond) was lo s t when random aspen board had as l i t t l e as 10 percent of the 68 s u r f a c e s i n a d e q u a t e l y covered by a d h e s i v e . M i n i m a l r e s i n l e v e l was d e f i n e d as the lowest spread r e q u i r e d t o cause wood s h e a r f a i l u r e . ' The minimum adhesive s o l i d s coverage was e s t i m a t e d t o 2 be i n the o r d e r of 0.1 t o 0.2 mg/cm , f o r r e s i n i n s m a l l d r o p l e t s (10 micron) on i d e a l l y f l a t , d r i e d , and p r e s s e d s t r a n d s . These minimum spreads are e x t r a p o l a t i o n s t a k e n from t h e work o f Suchsland (88), and Meinecke and K l a u d i t z ( 60). R e s i n d i s t r i b u t i o n i n t h e p r e s e n t r e s e a r c h i s t y p i f i e d by F i g . 13 and 14, where v i r t u a l l y a l l s t r a n d s r e c e i v e d r e s i n i n a r e a s o n a b l y s y m m e t r i c a l d i s t r i b u t i o n . RESIN DISTRIBUTION ON ASPEN STRANDS 28 -Nominal Mt»n of Liquid Spread 0.572 n?/cm2 13 >• U z w D o u as b. ie 0 .1 .2 .3 H»an = .500 Standard Deviation = .219 U a r i a n c * S k t u n t s s .847 LOT .9 1 1.1 1.2 1.3 1.4 RESIN SPREAD MG/CM2 F i g u r e 13. R e s i n d i s t r i b u t i o n - aspen b l e n d i n g . F i g u r e 14. Resin d i s t r i b u t i o n - cedar blending Low blending rates usually favor good d i s t r i b u t i o n , but expose large areas of blender wall surface to resin- capture. Antagonistic to t h i s , larger blender loads minimize resin losses to lab blender walls, but r e s t r i c t good strand c i r c u l a t i o n i n the blender. Losses of resin to the i n t e r i o r surfaces of the blender were estimated by resin recovery from test patches of v i n y l sheeting which were taped to the ends and walls of the blender. When these losses were accounted for, the actual spread s o l i d s were only 4.7 to 12.7 percent under the nominal targets. Resin 70 material balance was correct when the t o t a l resin surface and blender i n t e r i o r were accounted for. The histograms, F i g . 13 and 14, were made by determining the amounts of resin deposited on the surfaces of v i n y l tracer strands that were spray blended with the normal wood furnish. The tracers had weight, length, and width equal to the corresponding averages of the wood strands. F i g . 13 and 14 typify results obtained as quality controls on a l l blender runs made in t h i s research. The most important advantage of determination of resin on separate sides of the strands i s that i t allows a p r o b a b a l i s t i c evaluation of bonding. The following derivation makes.'use of this d i s t r i b u t i o n to assess the bonding p o t e n t i a l of any v e r t i c a l set of interface zones below an arbitrary location on the board surface. Considering a bonding zone of any area size between strands to be a bonding "interface c e l l " i t • i s possible to estimate the prob a b i l i t y , of at least one interface i n a. v e r t i c a l stack sequence through the board thickness having no adhesive spray on either c e l l side. This i s defined as a discontinous : bond sequence with p r o b a b i l i t y f. It i s estimated on a randomly, located v e r t i c a l l i n e through the thickness, disregarding voids. It i s given by: 2 M-1 f = 1 - ( l - p z ) " [23] where: p = probability of zero or less than minimal resin spread on one side of a strand (exactly). This i s termed a blank side. M = the number of strands forming the thickness of the board. The expression [23] i s derived as follows: Consider the interface as a binary c e l l of two sides with the r e s t r i c t i o n s : a) probability of a blank on one side i s independent of a blank being on the other side of the strands (or interface) b) there i s a random order of strands with respect to the stack (M) sequence let p = prob then p 2 = prob and (1-p2) = prob of exactly one side of interface blank both sides of the interface blank not both sides of interface blank = prob successively, of bond interface, with one or both sides sprayed In a stack of M strands there are M-1 interface c e l l s . Therefore for M-1 successive bonded interfaces we have: l-d-p 2)"- 1 = prob not M-1 successive bonded interfaces = prob at least one inter-face not bonded Thus, " f " i s defined, as the pr o b a b i l i t y of there being a weak link of variable size, i n the chain of strand bonds holding the board together. The 11 f" defect c r i t e r i o n was experimentally related to internal bond strength in previous research at Borden Chemical Ltd. The result was a rapid loss of in t e r n a l bond up to f=0.10 followed by a diminished rate of loss (slope) as f exceeded 0.10 72 The probability, p, was also derived from the dynamics of the blender, as mentioned in Section 3.7. In summary, a l l blending for t h i s research was done at a bond defect probability, f, of less than 0.03. The manufacture of specimens in t h i s fashion helped assure that bond defects did not confound the tes t of the orientation model. The strand-to-strand resin d i s t r i b u t i o n was probably more uniform than produced by current i n d u s t r i a l l i q u i d resin blenders, but less than optimum. 4.2.3 R e s i n D i s p e r s i o n : Image A n a l y s i s Maloney et a l . (57) emphasized that a near continuous f i l m of resin be present between bonded strands for maximum and e f f i c i e n t strength development. This requires the dispersion of the resin into fine droplets or fragments that can flow into a fi l m before or during board consolidation. Holding a l l other factors constant, droplet size alone, was shown by Meinecke and Klauditz (60) to have a s i g n i f i c a n t range of influence over the internal bond and t e n s i l e strength of spruce strand boards. This range was secondary to that r e s u l t i n g from manipulation of strand-to-strand d i s t r i b u t i o n . The droplet size (dispersion) effect on strength was found to vanish at a diminishing diameter size depending on the r e s i n melt-flow p r o p e r t i e s , species, and pressing conditions. Strand surface roughness and•drying- hi s t o r y also play roles i n glue l i n e q u a l i t y . The primary importance of glueline strength was emphasized by Simpson (79) i n a t e n s i l e strength model for strandboard. In Simpson's model, the shear strength of the wood or the bond, whichever was lowest, l i m i t e d the tensile strength of the composite. This i s common to the present research. The merit of the examination of droplet size lay in placing in perspective i t s possible contribution to any s h o r t f a l l i n s p e c i f i c t e n s i l e strength r e l a t i v e to the expectation of the model. The documentation of the resin droplet histograms was also important for proper characterization of the composites and for control of the experimental comparisons. A further objective was to explore the use of computerized image analysis in resin droplet and fragment size characterization. A Leitz instrument at the Department of Metallurgy, U.B.C. was used. In i n i t i a l t r i a l s , i t was seen that the method was p r a c t i c a l i f f l a t p l a s t i c tracer strands were used rather than wood strands. This was because o p t i c a l microscopy was limited to p i c t u r i n g a f i e l d of 1 cm diameter containing perhaps 100 droplets. This lacked the depth of f i e l d to focus the height of grooves and roughness found on wood strands. Measurements were made of the major diameter of the i r r e g u l a r resin shapes. The volume of spheres and e l l i p s o i d s r elated t o these diameters was shown by Lehman (53) to be proportional t o the t h i r d power of the diameter. The meaning of t h i s i s that i f the droplet diameter were reduced by one half; then the number of droplets dispersed over the same area would be increased by e i g h t times. This explains how smaller droplet size promotes more continuous resin films by reducing the requirement for melt flow. The use of extremely small p a r t i c l e or droplet size i n adhesives has a l i m i t a t i o n due to the surface roughness of the strands. Resin that i s fragmented or sprayed small enough t o 74 e n t e r i n t o f i b e r grooves, p i t s and wide c u t lumen v e s s e l s i s l o s t to the g l u e l i n e , a c c o r d i n g t o Meinecke and K l a u d i t z (60). T h i s i s e s p e c i a l l y t r u e o f powdered r e s i n s where t h e p a r t i c l e s a r e rubbed i n t o grooves d u r i n g b l e n d i n g and f o r m a t i o n . In m i c r o s c o p i c e x a m i n a t i o n of t h e i n d u s t r i a l powder r e s i n / b o t h s p h e r i c a l and i r r e g u l a r b r o k e n - s h e l l shapes were obs e r v e d . The i r r e g u l a r shapes are p r e f e r r e d because t h e y have l e s s t endency t o migrate t o grooves and t o r o l l o f f t h e s t r a n d s onto t h e c a u l s d u r i n g mat f o r m a t i o n . Examples of t h e l i q u i d r e s i n d r o p l e t s i z e s and powder p a r t i c l e s i z e s o b s e r v e d are p r e s e n t e d i n F i g . 15 and 16. The r e s u l t s are t y p i c a l o f b l e n d e r runs on a l l t h e s p e c i e s i n t h i s t h e s i s . The w i d t h o f t h e p l a s t i c t r a c e r s t r a n d s made no o b s e r v a b l e d i f f e r e n c e t o the r e s u l t s . The i n t e r p l a y o f d r o p l e t s i z e and minimum s p r e a d was s t u d i e d i n d e t a i l by Meinecke and K l a u d i t z (60). W h i l e assuming a good s t r a n d t o s t r a n d d i s t r i b u t i o n , t h e y showed t h a t r e d u c t i o n o f d r o p l e t s i z e from 100 microns t o 50 m i c r o n s r e s u l t e d i n an approximate 30 p e r c e n t g a i n i n t e n s i l e s t r e n g t h , p a r a l l e l t o t h e s u r f a c e , i n random f l a k e b o a r d . The a c t u a l optimum d r o p l e t s i z e i s dependent on t h e r e s i n , m o i s t u r e c o n t e n t , t e m p e r a t u r e , s p e c i e s , board d e n s i t y , s t r a n d roughness and c o n s o l i d a t i o n p r e s s u r e . L e h m a n (53) f o u n d b o n d i m p r o v e m e n t b y m e r e l y r e d u c i n g t h e v a r i a n c e o f -the d r o p l e t d i s p e r s i o n , u s i n g a p h e n o l formaldehyde (P.F.) r e s i n h a v i n g an average d r o p l e t d i a m e t e r of 37 t o 39 microns. The b e s t a v a i l a b l e s p i n n i n g d i s k a t o m i z e r s a r e now c l a i m e d t o o p e r a t e i n t h e 40 t o 80 m i c r o n range. However a p p l i c a t i o n r e s u l t s v a r y w i t h b l e n d e r d e s i g n , how f u l l y t h e 7 5 Droplet Size Image Analysis Histogram TRACER STRANDS WITH ASPEN 100 150 200 250 300 350 400 450 500 550 Major Worn.tar. Microns F i g u r e 15. R e s i n d i s p e r s i o n - t r a c e r s t r a n d s w i t h aspen. b l e n d e r i s loaded , and how c l o s e t h e s t r a n d s pass t o t h e d i s k ( s ) . In summary, t h e e x p e r i m e n t a l use o f a r e l a t i v e l y l a r g e average d r o p l e t s i z e (138 micron) opened t h e q u e s t i o n o f a s c r i b i n g s m a l l l o s s e s i n t e n s i l e s t r e n g t h t o t h e r e s u l t i n g p o s s i b l e l a c k o f a c o n t i n u o u s bonding f i l m . The l a r g e r d r o p l e t ranges used i n c u r r e n t i n d u s t r y and i n t h i s t h e s i s were a c o n c e s s i o n t o the l i m i t a t i o n s of c u r r e n t l y a v a i l a b l e equipment. 76 u t o Q. %-o c Part icle Size Image Analysis Histogram 26 24 -22 -20 -18 -16 14 12 -10 -8 6 -4 2 O POWDER RESIN BO 010 MEAN 40.3 STO.DEV. 47.2 n nn n 34 68 102 136 170 204 238 Major Diameter, microns F i g u r e 16. R e s i n d i s p e r s i o n - powder r e s i n , 4.2.4 Composite D e n s i t y G r a d i e n t As d i s c u s s e d i n S e c t i o n 3.10.4 and 2.4, a d e n s i t y g r a d i e n t , i n c r e a s i n g toward th e b oard s u r f a c e s , has a major e f f e c t on f l e x u r a l s p e c i f i c MOR. Because s t r e n g t h comparisons t o t h e model were t o be made, i t was r e q u i r e d t h a t t h e c o n t r o l l i n g s u r f a c e d e n s i t y be known. Numerous f a c t o r s a f f e c t t h e f o r m a t i o n o f a nonuniform d e n s i t y p r o f i l e , such as: o v e r a l l b o ard d e n s i t y and c ompaction r a t i o , s i z e , shape and o r i e n t a t i o n o f s t r a n d s , p r e s s c l o s i n g r a t e , p r e s s u r e - t i m e p r o f i l e , 77 strand moisture content, steam i n j e c t i o n , type of resin, wood species. Some of these variables were investigated by S t r i c k l e r (86), Steiner et a l . (83), and Harless et a l . (32). The following considerations suggested that a thin layer be removed from the board surfaces a f t e r ' c o o l i n g from the.press. 1. Resin precure can leave a densified but weakly bonded, th i n , surface layer. 2. Higher densification of the immediate 2 or 3 strand layers beneath the pressed surface was observed by S t r i c k l e r (86) . These layers were found to be more c r i t i c a l determinants of MOR than the extreme surface d e n s i t i e s . S t r i c k l e r (8 6) suggested the surface looseness was due to unrestricted spring back on short press cycles. Density p r o f i l e s with this character were also reported by Kieser et a l . (45) and are described f a i r l y commonly in the l i t e r a t u r e . For improved use of the MOR formula, i t was decided that removing the surface layers to a depth of a few strands would avoid possible inaccuracies caused by not being able to assume f i r s t f a i l u r e of the strongest strands at the surface. Moreover, removal of caul glaze and si z i n g to thickness by sanding i s common to a large portion of i n d u s t r i a l production. In t h i s experimental work, i t also allowed better inspection of strand angles for orientation measurements. The results of the density scans are t y p i f i e d in Fig . 17. The numerically integrated average density was divided into the peak surface density to give a r a t i o used as a c r i t e r i o n of surface d e n s i f i c a t i o n . This r a t i o varied with species, orientation, and resin l e v e l . The means of 5 scans of each 78 specimen t y p e r e s u l t e d i n the d a t a o f Ta b l e 8. The r e s u l t s were randomized over t e s t l o c a t i o n s on t h e boards and over board r e p l i c a t e s . S canning t h r o u g h t h e r a d i a l , t a n g e n t i a l and l o n g i t u d i n a l d i r e c t i o n o f the s t r a n d s was a l s o randomized. The r a t i o s were s i m i l a r t o thos e r e p o r t e d by La u f e n b e r g ( 49 ) . The d e n s i t y r a t i o s o f Table 8 were used t o a d j u s t t h e g r a v i m e t r i c average d e n s i t i e s t o v a l u e s r e p r e s e n t a t i v e of t h e s u r f a c e s o f t h e specimens. The MOR v a l u e s o b t a i n e d from t e s t s were then r e p o r t e d i n terms of s p e c i f i c MOR, c a l c u l a t e d as t h e maximum f i b e r s t r e s s (MOR) d i v i d e d by t h e d e n s i t y of the specimen's s u r f a c e . Example: MOR t e s t r e s u l t f o r a t y p i c a l - s p e c i m e n , r e d a l d e r , a t r e s i n l e v e l 0.57 mg/cm2, o r i e n t a t i o n k=4 .9 , and t e s t e d i n t h e p a r a l l e l , 0 ° , d i r e c t i o n . 6 3 . 4 5 MPa Mean d e n s i t y o f r e d a l d e r specimen 0 .59 0 .59 g/cm3 R a t i o s u r f a c e density/mean d e n s i t y , f o r r e d a l d e r . . 1.36 S p e c i f i c MOR ( s u r f a c e ) i s t h e r e f o r e : 6 3 . 4 5 / 0 . 5 9 / 1 . 3 6 = 79 .1 MPa Table 8. D e n s i t y r a t i o s , s u r f a c e t o mean Species R. Alder Resin Level mq/cm' 0.57 oriented 1.14 oriented 0.57 random 1.14 random o r i e n t a t i o n l e v e l 4.9 3.5 0 .02 0.02 Surface/mean density r a t i o a i r dry 1.36 1.43 1.48 1.52 T. Aspen 0.57 oriented 3.2 1.14 oriented 2.3 0.57 random 0.01 1.14 random 0.01 1.27 1.37 1.59 1.63 R. Cedar 0.57 oriented 2.8 1.14 oriented 2.1 0.57 random 0.2 6 1.14 random 0.2 6 1.33 1.43 1.38 1.41 L. Pine 0.57 oriented 3.4 1.14 oriented 3.4 0.57 random 0.14 1.14 random 0.14 1.27 1.30 1.35 1.45 Y. Birch I n d u s t r i a l core, aspen Laboratory oriented aspen Laboratory random aspen 1.76 oriented 9.0 1.76 random 0.15 2.0 percent 1.1 powder 2.0 percent 2.4 powder 2.0 percent 0.4 powder 1.10 1.50 1.10 1.10 1.60 Figure 17. T y p i c a l d e n s i t y g r a d i e n t p r o f i l e s . 81 4.3 R e s u l t s , S p e c i f i c T e n s i l e S t r e n g t h 4.3.1 T e n s i l e S t r e n g t h , O r i e n t e d Composites In the panelboard i n d u s t r y , o r i e n t e d , one d i r e c t i o n m u l t i p l e strand l a y e r s have s u b s t a n t i a l l y r e p l a c e d veneer as laminae i n s t r u c t u r a l panels. Through the e f f e c t s of higher s u r f a c e d e n s i t y and higher o v e r a l l d e n s i t y , i t i s p o s s i b l e f o r the non-veneer panels to gain e q u a l i t y with plywood i n f l e x u r a l s t r e n g t h . However, higher board d e n s i t y r e q u i r e s i n c r e a s e d c o s t . A f e a t u r e of the present s p e c i f i c t e n s i l e s t r e n g t h c r i t e r i o n i s t h a t i t views comparisons on the b a s i s of e f f i c i e n c y of wood usage (per u n i t weight). When t h i s c r i t e r i o n i s used, the e f f e c t of enhanced su r f a c e d e n s i t y i s mostly e l i m i n a t e d . The l e v e l of performance that the non-veneer lamina achieves i s put i n t o an comparative p e r s p e c t i v e with veneer i n Table 9. In Table 9, much of the composite s t r e n g t h r e d u c t i o n r e l a t i v e to n a t u r a l wood i s a t t r i b u t a b l e t o imperfect o r i e n t a t i o n of the strands. P r o v i s i o n of adequate bonding and an o r i e n t a t i o n l e v e l of k=12 would y i e l d a p a r a l l e l - a x i s s p e c i f i c s t r e n g t h o f about 80 percent of t h a t of p a r a l l e l - g r a i n n a t u r a l wood. An o r i e n t a t i o n l e v e l o f k=9.0 was e a s i l y a c h ieved with the long, s t r a n d b i r c h f l e x u r a l specimens ( F i g . 27) i n t h i s r e s e a r c h . At k=9.0 the p a r a l l e l - a x i s s p e c i f i c MOR of the composite was 66.6 percent of the p a r a l l e l - g r a i n s p e c i f i c s t r e n g t h of the wood strands. The .continuous s t r a n d model was used f o r c a l c u l a t i o n of these mathematical e x p e c t a t i o n s , (Equation [13]). Comparison of the experimental o r i e n t a t i o n l e v e l s t o those present i n i n d u s t r y (k=l.l) showed t h a t the p o t e n t i a l s o f o r i e n t a t i o n are not f u l l y e x p l o i t e d by OSB makers. T a b l e 9 . Composite/wood s p e c i f i c s t r e n g t h comparison, MPa u n i t s S p e c i e s R e s i n l e v e l ma/cm2 O r i e n t a t i o n P a r a m e t e r k (Source: Table 10) P a r a l l e l S p e c i f i c T e n s i l e S t r e n g t h o f composite (Source: Table 7) P a r a l l e l g r a i n S p e c i f i c T e n s i l e s t r e n g t h o f s t r a n d P e r c e n t composite/ s t r a n d R. A l d e r R. Cedar L. P i n e T. Aspen 0.57 0.57 0.57 0.57 T. Aspen 2% powder ( i n d u s t r i a l c o r e ) R. A l d e r R. Cedar L. P i n e T. Aspen R. Cedar 1.14 1.14 1.14 1.14 1.76 4.9 2.8 3.4 3.2 1.1 3.5 2.1 3.4 2.3 1.9 49.2 36.3 47.5 36.0 21.7 57.5 46.8 52. 8 47.1 54.5 146.8 148.7 166. 9 152.2 152.2 146. 8 148.7 166.9 152.2 148.7 33.5 24 . 4 28.5 23.6 14.2 39.2 31.5 31. 6 30. 9 36.6 oo 83 An i m p o r t a n t f e a t u r e o f t h i s r e s e a r c h was the comparison o f the a c t u a l u l t i m a t e s t r e n g t h s t o t h e p r e d i c t i o n s of t h e model. These comparisons a re p r e s e n t e d i n T a b l e s 10 and 11. The r e s u l t s a l s o p e r m i t s p e c i e s and r e s i n e f f e c t s t o be e v a l u a t e d , but w i t h the r e s t r i c t i o n t h a t t h o s e compared have s i m i l a r (k) v a l u e o f o r i e n t a t i o n . T a b l e s 10 and 11 show t h a t t h e s t r e n g t h s e x p e c t e d of c o n t i n u o u s s t r a n d networks were not t o t a l l y a c h i e v e d i r i any s p e c i e s . These c o n c l u s i o n s were made u s i n g i n d i v i d u a l " t " t e s t s f o r the mean s t r e n g t h s a g a i n s t t h e model p r e d i c t i o n . The t e s t s were at t h e p=0.05 l e v e l o f s i g n i f i c a n c e . The t e s t p e r c e n t a g e s o f t h e t h e o r e t i c a l model s p e c i f i c t e n s i l e s t r e n g t h s , p a r a l l e l t o o r i e n t a t i o n , i n c r e a s e d w i t h r e s i n c o n t e n t , as seen i n Table 11. The c o n t i n u o u s s t r a n d model e x p e c t a t i o n s of Table 11 are based on E q u a t i o n [ 1 3 ] . Two opposing e f f e c t s on the s p e c i f i c t e n s i l e s t r e n g t h a re demonstrated i n Table 10. The o r i e n t a t i o n parameters, 1 k, i n column D are l e s s t h a n o r e q u a l t o t h e c o r r e s p o n d i n g ones i n column C. In the p a r a l l e l t o a x i s d i r e c t i o n , i n c r e a s e d k v a l u e s i m p l y h i g h e r e x p e c t e d t h e o r e t i c a l s t r e n g t h s (see F i g . 10). Thus, we expect a s t r e n g t h d e c r e a s e f o r column D r e l a t i v e t o C, f o r any decreases i n k. But i n comparing D t o C, we note a d o u b l i n g o f r e s i n l e v e l . This overcomes t h e e x p e c t e d s t r e n g t h d e c l i n e and replaces i t with an increase i n a l l species. T a b l e 10. T e n s i l e s t r e n g t h s , t e s t e d p a r a l l e l t o the o r i e n t a t i o n d i r e c t i o n , MPa. S t r e n g t h at 0.57 mg/cm2 r e s i n l e v e l Strength at 1.14 mg/cm2 r e s i n l e v e l S p e c i f i c Strength at 0.57 mg/cm2 r e s i n l e v e l D S p e c i f i c Strength at 1.14 mg/cm2 r e s i n l e v e l E F Th e o r e t i c a l S p e c i f i c Strength based on O r i e n t a t i o n 0.57 mg / cm2 r e s i n l e v e l 1.14 mg/cm2 r e s i n l e v e l Red A l d e r (k=4.9) Mean 32.8 Std. Dev. 5.3 Red Cedar (k=2.8) Mean 21.5 Std. Dev. 4.4 Lodgepole Pine (k=3.4) Mean 30.1 Std. Dev. 2.6 Trembling Aspen (k=3.2) Mean 23.5 Std. Dev. 9.2 (k=3.5) 37.1 6.7 (k=2.1) 32.5 1.6 (k=3.4) 35.3 6.7 (k=2.3) 30.7 2.4 (k=4.9) 49.2 5.4 (k=2.8) 36.3 7.3 (k=3.4) 47.5 2.3 (k=3.2) 36.0 10.3 (k=3.5) 57.5 8.6 (k=2.1) 46.8 0.9 (k=3.4) 52.8 10.6 (k=2.3) 47.1 5.7 (k=4.9) 100.1 (k=2.8) 92.1 (k=3.4) 100.6 (k=3.2) 98.5 (k=3.5) 93.7 (k=2.1) 83.4 (k=3.4) 100.6 (k=2.3) 87.9 Strength S p e c i f i c Strength T h e o r e t i c a l S p e c i f i c Strength Based on O r i e n t a t i o n Trembling Aspen l a b o r a t o r y board 2% powder r e s i n Mean Std. Dev. Trembling Aspen I n d u s t r i a l Core 2% powder r e s i n Mean Std. Dev. Red Cedar 1.76 mg/cm2, r e s i n l e v e l Mean Std. Dev. (k=2.4) 22.7 4.9 (k=l.l) 11.9 1.4 (k=1.9) 33.3 4.8 (k=2.4) 36.8 8.5 (k=l.l) 21.7 2.0 (k=1.9) 54.5 5.0 (k=2.4) 89.2 (k=l.l) 66.6 (k=1.9) 81.1 85 T a b l e 11. P a r a l l e l s p e c i f i c t e n s i l e s t r e n g t h Species Percent of Model Expectation 0.57 mg/cm2' 1.14 mg/cm2 r e s i n l e v e l r e s i n l e v e l R. Alder 48.6 61.4 R. Cedar 39.4 56.1 C. Pine 47.2 52.2 T. Aspen 36.5 53.6 Percent of Model Expectation T. Aspen Lab board, 2 percent powder r e s i n 41.2 T. Aspen I n d u s t r i a l core 2 percent, powder 32.6 R. Cedar 1.76 mg/cm2 l i q u i d phenolic 67.2 An example o f Table 11 r e s u l t s a r e demonstrated f o r r e d a l d e r by d i v i s i o n o f t h e t e s t s p e c i f i c t e n s i l e s t r e n g t h ( r e s i n 0.57 mg/cm2) by t h e model s p e c i f i c s t r e n g t h . The GWBASIC program i n Appendix i ge n e r a t e s t h e s t r e n g t h model e x p e c t a t i o n . r e d a l d e r t e s t s p e c i f i c t e n s i l e s t r e n g t h (k=4.9) ..... 49.2 MPa r e d a l d e r e x p e c t e d s p e c i f i c s t r e n g t h (k=4.9) ...... 100.1 MP a 49 2 T h e r e f o r e , p e r c e n t o f model e x p e c t a t i o n = ^TJTJ^y = 49.1 % Some unplanned d i r e c t comparisons o f s p e c i e s were p o s s i b l e where t h e k parameters were s i m i l a r i n t h e o r i e n t e d c o mposites o f Tabl e 10. Three comparisons a re p r e s e n t e d i n Table 12. Tab l e 12. P a r a l l e l s p e c i f i c t e n s i l e s t r e n g t h : spec ies R e s i n L e v e l S p e c i e s Compared S p e c i f i c T e n s i l e S t r e n g t h 0.57 mg/cm2 Aspen v s . P i n e no s i g . d i f f . 1.14 mg/cm2 Aspen v s . Cedar no s i g . d i f f . 1.14 mg/cm2 A l d e r v s . P i n e no s i g . d i f f . 86 These r e s u l t s were v a l i d at t h e p=0.05 c o n f i d e n c e l e v e l i n one t a i l e d " t " t e s t s , f o r o r d i n a r y t e n s i l e s t r e n g t h as w e l l as s p e c i f i c s t r e n g t h . I t was c o n c l u d e d t h a t s i g n i f i c a n t s p e c i f i c s t r e n g t h d i f f e r e n c e s were not apparent between t h e s e composites of these p a r t i c u l a r s p e c i e s . No d i f f e r e n c e s had been a n t i c i p a t e d i n t he (Table 12) p a i r s because p a r a l l e l s p e c i f i c s t r a n d s t r e n g t h s , r e s i n l e v e l s , and o r i e n t a t i o n l e v e l s , were common w i t h i n each s e t . A f u r t h e r d i s c u s s i o n o f p a r a l l e l t e n s i l e s p e c i e s s t r e n g t h d i f f e r e n c e i s p r e s e n t e d i n S e c t i o n 5.1. The p e r p e n d i c u l a r t o o r i e n t a t i o n s p e c i f i c t e n s i l e s t r e n g t h s are p r e s e n t e d i n Table 13. Two r e i n f o r c i n g e f f e c t s on 1 p e r p e n d i c u l a r t e n s i l e s t r e n g t h a re e v i d e n t i n Table 13. The o r i e n t a t i o n parameters, k, i n column D a r e l e s s t h a n o r e q u a l t o those of column C. Note t h a t i n t h e p e r p e n d i c u l a r t o o r i e n t a t i o n d i r e c t i o n a change t o a lo w e r k l e v e l o f o r i e n t a t i o n l o g i c a l l y n e c e s s i t a t e s an i n c r e a s e i n e x p e c t e d o r t h e o r e t i c a l s t r e n g t h (see F i g . 10). T h e r e f o r e i n F i g . 13 t h e o b s e r v e d i n c r e a s e i n s t r e n g t h from column C t o D, and from E t o F, i s j u s t i f i e d by both a r e s i n i n c r e a s e and by an o r i e n t a t i o n change. The comparison of p e r p e n d i c u l a r s p e c i f i c t e n s i l e s t r e n g t h t o t h e t h e o r e t i c a l e x p e c t a t i o n i s made i n T a b l e 14. T a b l e 13. T e n s i l e s t r e n g t h s , t e s t e d p e r p e n d i c u l a r t o the o r i e n t a t i o n d i r e c t i o n , MPa. Strength at 0. 57 nvg/cm2 r e s i n l e v e l Strength at 1.14 mg/cm2 r e s i n l e v e l S p e c i f i c Strength at 0.57 mg/cm2 resin l e v e l S p e c i f i c Strength at 1.14 mg/cm2 resin l e v e l E F Theoretical S p e c i f i c Strength based on Orientation 0.57 mg/cm2  resin l e v e l 1.14 mg/cm2 resin l e v e l Red Alder Mean Std. Dev. Red Cedar Mean Std. Dev. Lodgepole Pine Mean Std. Dev. Trembling Aspen Mean Std. Dev. (k=4.9) 2.9 0.6 (k=2.8) 2.9 0.6 (k=3.4) 3.2 1.2 (k=3.2) 4.5 0.3 (k=3.5) 4.7 0.6 (k=2.1) 5.9 1.3 (k=3.4) 3.9 1.1 (k=2.3) 4.7 0.5 (k=4.9) 5.0 1.2 (k=2.8) 5.4 1.2 (k=3.4) 5.0 1.9 (k=3.2) 7.4 1.4 (k=3.5) 7.3 0.9 (k=2.1) 9.6 2.0 (k=3.4) 6.6 2.2 (k=2.3) 8.0 1.6 (k=4.9) 9.3 (k=2.8) 12. 8 (k=3.4) 9.8 (k=3.2) 12. 6 (k=3.5) 10.0 (k=2.1) 14.3 <k=3.4) 9.8 (k=2.3) 13.9 Strength S p e c i f i c Strength Theoretical S p e c i f i c Strength Based on Orientation Trembling Aspen laboratory board 2% powder r e s i n Mean Std. Dev. Trembling Aspen I n d u s t r i a l Core 2% powder r e s i n Mean Std. Dev. Red Cedar 1.76 mg/cm2, r e s i n l e v e l Mean Std. Dev. (k=2.4) 4.5 1.3 (k=l.l) 3.7 0.9 (k=1.9) 4.5 0.8 (k=2.4) 7.4 1.6 (k=l.l) 7.3 1.3 (k=1.9) 7.1 1.3 (k=2.4) 13.7 (k=l.l) 21.6 (k=1.9) 14.9 . CO 88 T a b l e 14. P e r p e n d i c u l a r s p e c i f i c t e n s i l e s t r e n g t h Species Percent of Model Expectation 0.57 mg/cm2 1.14 mg/cm2 r e s i n l e v e l r e s i n l e v e l R. Alder 53.7 73.0 R. Cedar 42.2 67.1 L. Pine 51.0 67.3 T. Aspen 58.7 57.6 Percent of Model Expectation R. Aspen lab board, 2 percent powder r e s i n 54.0 T. Aspen i n d u s t r i a l core, 2 percent powder 33.8 R. Cedar 1.76 mg/cm2 l i q u i d phenolic r e s i n 47.6 4.3.2 T e n s i l e S t r e n g t h , Random O r i e n t a t i o n The comprehensive comparison of species strength i n a f a c t o r i a l analysis was reserved for the random case where the orientation parameter was near k=0 i n the various species and resin l e v e l combinations. In these specimens, the orientation parameter, k, was s l i g h t l y above the the o r e t i c a l zero l e v e l because the random mat formation was dropped manually into a rectangular forming box. However, the edges were trimmed, and no sig n i f i c a n t d i r e c t i o n a l strength bias appeared in the randomly oriented t e n s i l e specimens. The data summarized i n Table 16 was Table 15. Random o r i e n t a t i o n , s p e c i f i c t e n s i l e s t r e n g t h a n a l y s i s o f v a r i a n c e Source d. f. S. S. M.S. F F,os_ species 3 411.829 137.276 7.085 3.01 s i g . resin 1 18.015 18.015 0.929 4.26 not s i g . s x r 3 17.979 5.989 0.309 3.01 not s i g . error 24 464.990 19.374 to t a l s 31 912.800 8 9 a n a l y z e d i n a c o m p l e t e l y randomized d e s i g n w i t h f i x e d f a c t o r s and f o u r r e p l i c a t e s . The two main f a c t o r s were s p e c i e s and r e s i n l e v e l . The independent v a r i a b l e was s p e c i f i c t e n s i l e s t r e n g t h . S p e c i e s was a s i g n i f i c a n t f a c t o r , and r e s i n l e v e l and i n t e r a c t i o n were not s i g n i f i c a n t i n t h e i r e f f e c t on s p e c i f i c t e n s i l e s t r e n g t h as shown i n Table 15. On t h e b a s i s o f Duncan's m u l t i p l e range t e s t at a s i g n i f i c a n c e l e v e l p = 0.05, t h e randomly o r i e n t e d p i n e boards were found lower i n s p e c i f i c t e n s i l e s t r e n g t h t h a n the aspen, ce d a r and a l d e r . No o t h e r , d i f f e r e n c e s were s i g n i f i c a n t . L i k e t h e p e r p e n d i c u l a r t o o r i e n t a t i o n case, t h e random case showed no i n c r e a s e i n s t r e n g t h w i t h e s c a l a t i o n o f r e s i n l e v e l s . The v e r y few s t r a n d s i n p a n e l s h a v i n g random o r i e n t a t i o n w i t h g r a i n d i r e c t i o n near p a r a l l e l t o t h e s t r e s s a x i s a r e t h e o n l y ones ca p a b l e o f c a r r y i n g h i g h e r l o a d s than t h e a p p l i e d adhesive w i l l b e a r . In a s h o r t e r s t r a n d random aspen w a f e r b o a r d 2 o f 5 p e r c e n t r e s i n c o n t e n t ( a p p r o x i m a t e l y 1.14 mg/cm ), Laufenberg (50) obser v e d about 4 p e r c e n t u n f a i l e d s t r a n d p u l l -o u t s i n a m i c r o s c o p i c study o f f a i l u r e s u r f a c e s . On t h i s b a s i s i t was thought t h a t s t r e n g t h s a p p r o a c h i n g t h a t o f t h e model p r e d i c t i o n would be a c h i e v e d a t b o t h r e s i n l e v e l s . T h i s i s v e r i f i e d f o r a l d e r i n T a b l e s 16 and 17. The t h e o r e t i c a l v a l u e s a r e based on E q u a t i o n [21] . The t h e o r e t i c a l p r e d i c t i o n s of Tab le 17 p r o v i d e a r e a s o n a b l e f i r s t a p p r o x i m a t i o n o f s t r e n g t h i n 3 out of 5 s p e c i e s . The s t r e n g t h s i n T a b l e 17 were averaged over b o t h l i q u i d r e s i n l e v e l s , because t h e a n a l y s i s o f v a r i a n c e (Table 15) i n d i c a t e d no s t r e n g t h e f f e c t a s c r i b a b l e t o the r e s i n l e v e l . Table 16. Random orientation, s p e c i f i c t e n s i l e strength (Means were taken from 5 specimens cut at 0, 22.5, 45, 67.5 and 90 degrees to the axis) A Strength 0.57 mg/cm2 r e s i n l e v e l MPa B Strength 1.14 mg/cm2 r e s i n MPa Sp e c i f i c Strength 0.57 mg/cm2  resin, MPa D Spec i f i c Strength 1.14 mg/cm2 resin, MPa E F Theoretical Strength based on orientation, MPa R. Alder Mean Std. Dev. 21.62 3.03 21.4 5.6 33.3 5.21 32.7 5.58 35.7 (k=.02) R. Cedar Mean Std. Dev. 16.8 5.11 17 .7 2.3 27.3 5.16 30.2 1.47 40.7 (k=.26) L. Pine Mean Std. Dev. 14.2 3.91 14.1 4.92 22.6 3.91 24.6 4 .23 37. 5 (k=.01) T. Aspen Mean Std. Dev. 16.7 4. 09 17.3 4.65 30.2 3.1 33.1 1.6 40.8 (k=.01) Trembling Aspen, laboratory board 2% Powder r e s i n Mean Std. Dev. Strength 13.9 3.33 Sp e c i f i c Strength 24.2 2.06 Theoretical S p e c i f i c Strength, MPa 40.8 (k=.04) Because s l i g h t alignment was measured i n the random orientations, the tabulated s p e c i f i c strength ranges presented are averages. The t h e o r e t i c a l e f f e c t of the s l i g h t orientation was a range of about ± 5 MPa from the p a r a l l e l to cross o r i e n t a t i o n d i r e c t i o n . o 91 T a b l e 17. Comparative t e n s i l e s t r e n g t h of random c o m p o s i t e s f o r b o t h r e s i n l e v e l s combined.' Species R. Alder R. Cedar L. Pine T. Aspen Composite S p e c i f i c T e n s i l e Strength, MPa 33.0 28. 8 23.6 31.6 Percent of T h e o r e t i c a l S p e c i f i c Strength 92.4 70.7 62.9 77.6 T e n s i l e Strength as a Percent of P a r a l l e l Grain Strand Strength 22.5 19.4 14.1 20.8 T. Aspen (2% powder) (laboratory) 24.2 59.3 15.9 The s p e c i f i c t e n s i l e s t r e n g t h o f l o d g e p o l e p i n e random o r i e n t e d composites was s i g n i f i c a n t l y l ower t h a n t h a t o f t h e o t h e r s p e c i e s . P i n e had t o be p r e s s e d a t lower compaction r a t i o s r e l a t i v e t o t h e o t h e r s i n T a b l e s 16 and 17, t o a c h i e v e t h e same nominal d e n s i t y . T h i s was n e c e s s a r y because o f the h i g h e r d e n s i t y o f t h e p i n e s t r a n d s t h e m s e l v e s . The lower c o m p a c t i o n r a t i o means t h a t t h e c o n s o l i d a t i o n o f t h e s t r a n d s a l l o w s more i n t e r n a l v o i d s , and l e s s i n t e r n a l b onding a r e a . The r e s u l t i s e x c e s s i v e shear s t r e s s l e v e l s w i t h i n the s t r a n d b o n d i n g a r e a s and inadequate s t r e s s t r a n s f e r . T h i s mechanism i s thought t o p a r t l y e x p l a i n t h e f a i l u r e o f t h e l o d g e p o l e p i n e t o r e a c h a h i g h l e v e l of s p e c i f i c t e n s i l e s t r e n g t h r e l a t i v e t o t h e t h e o r e t i c a l model. 92 4.4 R e s u l t s , F l e x u r a l S t r e n g t h 4.4.1 I n t r o d u c t i o n Knowledge of the f l e x u r a l s t r e n g t h of u n i d i r e c t i o n a l l a y e r s i s important i n the design of three l a y e r OSB and the o r i e n t e d s t r a n d lumber products of the f u t u r e . To review, the o b j e c t i v e r e q u i r e d d e t e r m i n a t i o n of: the a b i l i t y of the model to p r e d i c t the s p e c i f i c MOR at any angle of composite l o a d i n g with r e s p e c t t o the p r i n c i p a l a x i s of o r i e n t a t i o n , the e f f e c t of r e s i n l e v e l and species on f l e x u r a l s t r e n g t h , comparison of the u l t i m a t e s p e c i f i c s u r f a c e s t r e s s i n f l e x u r e of the composites to the s p e c i f i c t e n s i l e s t r e n g t h of the strands themselves. The l i m i t a t i o n of the f l e x u r a l t e s t to assess the u l t i m a t e f i b e r s t r e s s of m a t e r i a l s having e l a s t i c inhomogeneity ( d e n s i t y gradient) was d i s c u s s e d i n Secti o n s 3.10.4 and 4.2.4. D e s p i t e the v i o l a t i o n of an assumed constant m a t e r i a l e l a s t i c i t y , the f l e x u r e formula i s commonly used by engineers t o c a l c u l a t e nominal MOR i n wood panel composites. F u r t h e r , i t should be recognized t h a t v a r i a t i o n between compression and t e n s i l e p r o p e r t i e s w i t h i n a specimen can a l t e r the MOR t o be d i f f e r e n t from the f i b e r s t r e s s estimate of Equation [19]. F i g . 18 to 27 show the an i s o t r o p y of the specific MOR in f i v e s p e c i es and at two r e s i n l e v e l s of o r i e n t e d s t r a n d composite. The o r i e n t a t i o n l e v e l s go from lowest, (k=l.l) i n the i n d u s t r i a l core, t o hi g h e s t (k=9.0), i n the yellow b i r c h specimens. The l i m i t bars a s s o c i a t e d with the means r e p r e s e n t the standard d e v i a t i o n bounds of the t e s t data. The continuous 93 s t r a n d t h e o r y s o l i d l i n e s are the c a l c u l a t e d r e s u l t s o f E q u a t i o n [13]. An e f f i c i e n t way t o e v a l u a t e t h e r e s e a r c h h y p o t h e s i s (model accuracy) i n t h e bending p r o p e r t y , i s t o a s s e s s t h e f i t o f data i n Fig.18 t o Fig.33 by v i s u a l i n s p e c t i o n . Tendencies of t h e d a t a t o f a l l m o d e s t l y s h o r t of the t h e o r e t i c a l MOR r e p r e s e n t e d by t h e s o l i d l i n e s i n F i g . 18 t o 27 were i d e n t i f i e d i n most comparisons, p a r t i c u l a r l y a t l o a d a n g l e s a p p r o a c h i n g p a r a l l e l t o t h e o r i e n t a t i o n . The s u r f a c e s p e c i f i c MOR was p r e d i c t e d w e l l by E q u a t i o n [13], a t o f f - a x i s a n g l e s . The model's s p e c i f i c MOR s t r e n g t h p r e d i c t i o n was u s u a l l y w i t h i n one s t a n d a r d d e v i a t i o n o f t h e t e s t d a t a mean. D i s c r e p a n c i e s i n t h e p a r a l l e l d i r e c t i o n are d i s c u s s e d i n s e c t i o n 5.1. The i n p u t s t o t h e model E q u a t i o n [13] were the mean s p e c i f i c t e n s i l e s t r e n g t h s o f t h e s t r a n d s i n t h e two p r i n c i p a l g r a i n d i r e c t i o n s , L and T, (Table 7). A l t h o u g h t h e s e i n p u t s t o t h e s t r e n g t h a l g o r i t h m are random v a r i a b l e s , t h e e f f e c t s on p r e d i c t e d s t r e n g t h o f v a r i a t i o n w i t h i n them are r e l a t i v e l y s m a l l . T h i s i s because t h e y are w i d e l y s e p a r a t e d i n s t r e n g t h and because t h e a l g o r i t h m i s v e r y s e n s i t i v e t o o r i e n t a t i o n ( k ) . 4.4.2 F l e x u r a l S t r e n g t h , P a r a l l e l t o O r i e n t a t i o n The s p e c i f i c MOR v a l u e s p a r a l l e l t o o r i e n t a t i o n are p r e s e n t e d as t h e z e r o degree s t r e n g t h s i n F i g . 18 t h r o u g h 27. I n p a r a l l e l s p e c i f i c MOR, t h e composites ranged from 26.9 t o 66.6 p e r c e n t o f t h e s p e c i f i c t e n s i l e s t r e n g t h o f t h e wood s t r a n d s , p a r a l l e l t o g r a i n . These extremes are f o r t h e aspen i n d u s t r i a l c ore and b i r c h composites r e s p e c t i v e l y . 94 Specific M.O.R.,Oriented Alder RESIN .57 MG/CM2, ORIENTATION k=4.9 0 4.5 9 13.5 18 22.5 27 31.5 36 40.5 45 49.5 54 58.5 63 67.5 72 76.5 81 85.5 90 LOAD ANGLE WfTH RESPECT TO ORIENTATION • AVG.0F 5 REPLICATES THEORY F i g u r e 18. S p e c i f i c MOR, o r i e n t e d a l d e r , low r e s i n l e v e l Specific M.O.R.,Oriented Alder RESIN 1.14 MG/CM2. ORIENTATION k=3.5 i i i i i i i — i — i — i — i — i — i — i — r — r O 4.5 9 13.5 18 22.5 27 31.5 36 40.5 45 49.5 54 58.5 63 67.5 72 76.5 81 85.5 90 LOAD ANGLE WITH RESPECT TO ORIENTATION O AVG.OF 5 REPLICATES THEORY F i g u r e 19. S p e c i f i c MOR, o r i e n t e d a l d e r , h i g h r e s i n l e v e l Speci f ic M.O.R..Oriented Cedar RESIN 0 . 3 7 M C / C M 2 ORIENTATION K s 2 . f l 1 2 0 -> 1 1 0 -1 0 0 -0 4 .3 9 13 .3 18 2 2 . 3 2 7 3 1 . 3 36 4 0 . 3 4 3 4 9 . 3 3 * 3 8 . 3 63 6 7 . 3 7 2 7 6 . 3 81 8 3 . 3 9 0 LOAD A N C L E WITH R E S P E C T TO ORIENTATION Q A V C . O F 3 R E P L I C A T E S T H E O R Y Speci f ic M.O.R..Oriented Cedar RESIN 1 .14 M C / C M 2 O R l C N T A T l O N K » 2 . l 1 2 0 - , 1 10 -1 0 0 -9 0 -0 i — I — I — I — I — I 1 1 — I — I — I — I — I — I — I — I — I 1 — I 1 — 0 4 . 3 9 1 3 . 3 18 2 2 . 1 2 7 3 1 . 3 36 4 0 . S 4 3 4 9 . 3 34 3 8 . 3 63 6 7 . 3 7 2 7 6 . 3 81 8 3 . 3 9 0 L O A O A N C L E WITH R E S P E C T T O ORIENTATION • A V C . O F 3 R E P L I C A T E S T H E O R Y Speci f ic M.O.R..Oriented Cedar RESIN 1.76 M C / C W 2 . ORIENTATION K = 1 . 9 1 2 0 -r • F i g u r e 20. S p e c i f i c MOR, o r i e n t e d c e d a r 97 Specific M.O.R. ,Or iented Pine RESIN .57 MG /CM2, ORIENTATION k=3.4 i i l i i i r~~\ i i i r i i T — i — i — r — r 0 4.5 9 13.5 18 22.5 27 31.5 36 40.5 45 49.5 54 58.5 63 67.5 72 76.5 81 85.5 90 LOAD ANGLE WITH RESPECT TO ORIENTATION AVG.OF 5 REPLICATES THEORY F i g u r e 21. S p e c i f i c MOR, o r i e n t e d p i n e , low r e s i n l e v e l 98 Specific M.O.R.,Oriented Pine RESIN 1.14 MC/CM2. ORIENTATION k=3.4 120 -j 110 -* H — i — i — i — i — ; — i — i — ! — i — i — i — t — i — i — I — I — I — I — I — 0 4.5 9 13.5 18 22.5 27 31.5 36 40.5 45 49.5 54 58.5 63 67.5 72 76.5 81 85.5 90 LOAD ANGLE WfTH RESPECT TO ORIENTATION O AVG.OF 5 REPLICATES — THEORY F i g u r e 22. S p e c i f i c MOR, o r i e n t e d p i n e , h i g h r e s i n l e v e l Specific M.O.R.,Oriented Aspen RESIN .57 MG/CM2, ORIENTATION k=3.2 1 I I I I I I I I I I I I I I 1 1 1 1 1 0 4.5 9 13.5 18 22.5 27 31.5 36 40.5 45 49.5 54 58.5 63 67.5 72 76.5 81 85.5 90 LOAD ANGLE WITH RESPECT TO ORIENTATION • AVG.OF 5 REPLICATES THEORY F i g u r e 23. S p e c i f i c MOR, o r i e n t e d aspen, low r e s i n l e v e l 100 c o a 2 I r-0 z Ul tr. W o L. 0 u Q. Ul pecific M.O.R.,Oriented Aspen RESIN 1.14 MG/CM2. ORIENTATION k=2.3 1—i—I—I—I—I—I—I—i—i—i—i—i—i—i—i—i—i—r 0 4.5 9 13.5 18 22.5 27 31.5 36 40.5 45 49.5 54 58.5 63 67.5 72 76.5 81 85.5 90 LOAD ANGLE WITH RESPECT TO ORIENTATION • AVG.OF 5 REPUCATES THEORY F i g u r e 24. S p e c i f i c MOR, o r i e n t e d aspen, h i g h r e s i n l e v e l Specific M.O.R.,Oriented Aspen 2 PERCENT POWDER , ORIENTATION k=2.4 "i i i i r i i i i i r~ i i i i i i i—r O 4.5 9 13.5 18 22.5 27 31.5 36 40.5 45 49.5 54 58.5 63 67.5 72 76.5 81 85.5 90 LOAD ANGLE WITH RESPECT TO ORIENTATION AVG.OF 5 REPLICATES THEORY F i g u r e 25. S p e c i f i c MOR, o r i e n t e d aspen, powder r e s i n 102 0 o. 2 I h 0 z u a: r-1/1 0 k. u Id a in Specif ic M.O.R.Industrial Core ORIENTATION k=1.1 2.0% POWDER RESIN i i i i r i i i i i i i i i i—r—i—i—r 0 4.5 9 13.5 18 22.5 27 31.5 36 40.5 45 49.5 54 58.5 63 67.5 72 76.5 81 85.5 90 LOAD ANGLE WITH RESPECT TO ORIENTATION • AVG.OF 5 REPUCATES THEORY F i g u r e 26. S p e c i f i c MOR, i n d u s t r i a l c o r e 103 o n 2 I l-O z y X H 1/1 0 C 0 u a Specific M.O.R.,Oriented Birch RESIN 1.76 MG/CM2. ORIENTATION k=9.0 i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — r 0 45 9 13.5 18 22.5 27 31.5 36 40.5 45 49.5 54 58.5 63 67.5 72 76.5 81 85.5 90 LOAD ANGLE WITH RESPECT TO ORIENTATION 0 AVG.OF 3 REPLICATES THEORY F i g u r e 27. S p e c i f i c MOR, o r i e n t e d b i r c h I 104 Table 18 summarizes the t e s t s showing t h a t both r e s i n l e v e l s were s u f f i c i e n t to permit s t r e n g t h development c l o s e t o the model p r e d i c t i o n . The data at the higher rjesin l e v e l f i t b e t t e r t o the i d e a l because of the p e r f e c t adhesion 1, r e q u i r e d of the t h e o r y . Contrary to the e x p e c t a t i o n of some s o l i d woods, the s p e c i f i c MOR was l a r g e r than the s p e c i f i c t e n s i l e s t r e n g t h i n the case of p a r a l l e l o r i e n t a t i o n . The o r i e n t a t i o n parameters must be s i m i l a r f o r d i r e c t species comparisons. R e s u l t s on q u a l i f i e d specimens, a l s o h a v i n g the same r e s i n l e v e l s , are presented i n Table 19. T a b l e 18. P a r a l l e l s p e c i f i c f l e x u r a l s t r e n g t h Species Percent of Model E x p e c t a t i o n 0.57 mg/cm2 1.14 mg/cm2 r e s i n l e v e l r e s i n l e v e l R. Alder 79.0 92.0 R. Cedar 78.5 84.5 L. Pine 80.1 88.6 T. Aspen 80.1 82.1 Percent of Model E x p e c t a t i o n T. Aspen l a b board, 2% powder r e s i n 82.5 T. Aspen i n d u s t r i a l core 2% powder r e s i n 61.6 Y. B i r c h 1.76 mg/cm2 l i q u i d p h e n o l i c r e s i n 88.3 In Table 19, the r e s u l t s were ob t a i n e d by a p p l y i n g the t - t e s t s t a t i s t i c a l s i g n i f i c a n c e c r i t e r i o n at the p=0.05 l e v e l of confidence. Table 19. P a r a l l e l s p e c i f i c f l e x u r a l s t r e n g t h : s p e c i e s R e s i n L e v e l S p e c i e s Compared ' S p e c i f i c MOR 0.57 mg/cm2 Aspen v s . P i n e no s i g . d i f f . 1.14 mg/cm2 Aspen v s . Cedar no s i g . d i f f . 1.14 mg/cm2 A l d e r v s . P i n e no s i g . d i f f . PRACTICAL EXAMPLE In F i g . 18 t h r o u g h 27, t h e t e s t d a t a were a d j u s t e d t o a s p e c i f i c MOR c a l c u l a t e d as f l e x u r a l s t r e n g t h d i v i d e d by t h e s u r f a c e d e n s i t y . The assumption o f s u r f a c e f a i l u r e i s i m p l i c i t i n t h i s d a t a m a n i p u l a t i o n . I f t h e same assumption i s a p p l i e d i n the converse c o m p u t a t i o n t h e n a more p r a c t i c a l r e s u l t i s o b t a i n e d . T h i s i s where t h e s t r a n d wood s t r e n g t h s o b t a i n e d i n t e s t i n g a r e f i r s t a d j u s t e d by t h e s u r f a c e d e n s i t y and t h e n a s s i g n e d as i n p u t t o t h e model E q u a t i o n [ 1 3 ] . The model o u t p u t t h e n becomes t h e e x p e c t e d u l t i m a t e f i b e r s t r e s s MOR o f t h e , composite. The e x p r e s s i o n f o r l i n e a r l y a d j u s t i n g t h e L and T s t r e n g t h s o f t h e s t r a n d s t o t h e e l e v a t e d s u r f a c e d e n s i t y s t r e n g t h i s s i m p l y : a d j u s t e d i n p u t = The composite s u r f a c e d e n s i t y i s o b t a i n e d from m u l t i p l i c a t i o n o f ( s t r a n d d e n s i t y , T a b l e 3) by (compaction r a t i o , Table 5) by ( d e n s i t y r a t i o , T a ble 8 ) . t e n s i l e t e s t s t r e n g t h o f th e s t r a n d c o m p o s i t e s u r f a c e d e n s i t y average s t r a n d d e n s i t y 106 A d e m o n s t r a t i o n o f t h i s i s p r o v i d e d i n F i g . 28 where comparison of t h e p r e d i c t e d and a c t u a l MOR i s p r e s e n t e d . The p r e d i c t e d MOR was c a l c u l a t e d by t h e GWBASIC program i n Appendix i . T h i s example demonstrates t h e c o n t i n u o u s s t r a n d t h e o r y t o be adequate i n p r e d i c t i n g t h e t e s t e d MOR. The d i s c r e p a n c y i n t h e p a r a l l e l d i r e c t i o n i s because o f inad e q u a t e s t r e s s t r a n s f e r , as d i s c u s s e d i n s e c t i o n 5.1. I t i s p o s s i b l e t o e s t i m a t e t h e t e s t MOR o f 3 - l a y e r i n d u s t r i a l boards on t h e b a s i s o f t h e network model. When t e s t e d w i t h the span p a r a l l e l t o f a c e o r i e n t a t i o n d i r e c t i o n , t h e t e s t b o a rd MOR i s a p p r o x i m a t e l y e q u a l t o t h e s u r f a c e a d j u s t e d s t r e n g t h c a l c u l a t e d as i n t h e example f o r F i g . 28. As e l s e w h e r e i n t h i s r e s e a r c h , t h e c r i t e r i o n o f f i r s t f i b e r f a i l u r e a t t h e s u r f a c e must be a c c e p t e d i n t h i s e s t i m a t i o n . When t h e span i s p e r p e n d i c u l a r t o t h e o r i e n t a t i o n o f t h e fa c e s t r a n d s , i n t h e 3 - l a y e r board, t h e n t h e p e r p e n d i c u l a r ( c r o s s p l y ) s u r f a c e l a y e r s a r e i g n o r e d as i n t h e case o f s i m p l e plywood a n a l y s i s . The p a r a l l e l o r i e n t e d , i n n e r c o r e i s assumed t o c a r r y t h e l o a d . T h i s would be v a l i d i n w e l l o r i e n t e d c o m p o s i t e s but not n e c e s s a r i l y i n t h e p o o r l y o r i e n t e d boards o f h i g h s u r f a c e d e n s i t y found i n contemporary i n d u s t r y . The d e n s i t y . c o r r e c t e d MORx p r e d i c t i o n o f E q u a t i o n [13] f o r t h e o u t e r f i b e r s o f t h e inner core i s then m u l t i p l i e d by the f a c t o r ( t V t 2 2 ) t o y i e l d t h e expected M0R2 i n t h e f a c e - p e r p e n d i c u l a r t e s t d i r e c t i o n f o r the f u l l t h i c k n e s s specimen. The v a l u e s o f t x and t 2 a r e t h e symmetric t h i c k n e s s e s o f t h e i n n e r c o r e and t h e f u l l p a n e l t h i c k n e s s , r e s p e c t i v e l y . T h i s r e d u c t i o n f a c t o r f o r t h e s t r e n g t h i s o b t a i n e d by u s i n g t h e e x p r e s s i o n ( 3 P l / 2 b t 2 ) f o r MORx and MOR2, 107 M.O.R.,Oriented Aspen RESIN .57 MG/CM2. ORIENTATION k=3.2 i—i i i i i i i i i i i i i i i i i r 0 4.5 9 13.5 18 22.5 27 31.5 36 40.5 45 49.5 54 58.5 63 67.5 72 76.5 81 85.5 90 LOAD ANGLE WITH RESPECT TO ORIENTATION AVG.OF 5 REPLICATES THEORY Figure 28 Theory comparison w i t h s u r f a c e a d j u s t e d i n p u t s 108 with t 2 x and t 2 2 r e s p e c t i v e l y . MOR2 i s then s o l v e d f o r i n terms of MOR:. P, b, and 1 are the ul t i m a t e load, width, and span of the te s t beam and are common throughout. This permits the theory, when a p p l i e d to the inner (core) l a y e r , to be adjusted to estimate the t e s t r e s u l t MOR2 f o r the f u l l t h i c k n e s s board i n the cross panel d i r e c t i o n . 4.4 . 3 Flexural Strength, Perpendicular to Orientation The perpendicular to o r i e n t a t i o n surface s p e c i f i c MOR's are presented as the 90 degree strengths i n F i g . 18 through 27. Comparison of these to the s p e c i f i c t e n s i l e s t r e n g t h ;of the wood strands (Table 7) shows th a t a l l the composites had s p e c i f i c MORs which were not g r e a t l y d i f f e r e n t from the cross g r a i n s p e c i f i c strength of the wood i t s e l f . The low o r i e n t a t i o n i n d u s t r i a l core was the exception, where low o r i e n t a t i o n b e n e f i t s p e r p e n d i c u l a r strength (see F i g . 10). Comparing the perpendicular s p e c i f i c MOR strengths t o the. Equation [13] model p r e d i c t i o n showed the model estimate t o f i t w i t h i n one standard d e v i a t i o n of the t e s t data mean. This f i t i s be t t e r than the Table 14 comparison of perp e n d i c u l a r s p e c i f i c t e n s i l e r e s u l t s to the model. The perp e n d i c u l a r s p e c i f i c MOR's were s l i g h t l y higher than the perpendicular s p e c i f i c t e n s i l e strengths. Compared to the t e n s i l e case, there was l e s s improvement i n perpendicular s p e c i f i c MOR r e l a t i v e to the model p r e d i c t i o n as the r e s i n l e v e l was doubled. 4.4.4 F l e x u r a l S t r e n g t h , Random O r i e n t a t i o n The s u r f a c e s p e c i f i c MOR's were a n a l y z e d i n a c o m p l e t e l y randomized d e s i g n w i t h f i x e d f a c t o r s and t h r e e r e p l i c a t e s ( H i c k s , 35). The r e s u l t p r e s e n t e d i n Table 20 i s from a n a l y s i s o f v a r i a n c e on t h e s p e c i f i c MOR. The independent v a r i a b l e was t h e t e s t MOR d i v i d e d by th e specimen s u r f a c e d e n s i t y . T a ble 20. Random o r i e n t a t i o n , s p e c i f i c f l e x u r a l s t r e n g t h , a n a l y s i s o f v a r i a n c e Source d.f. S.S. M.S. F F.05 species 3 145.431 48.477 3.381 3.24 s i g . r e s i n 1 30.623 30.623 2.136 4.47 not s i g s x r 3 27.693 9.231 0.644 3.24 not s i g e r r o r 16 229.423 14.339 t o t a l s 23 433.169 As i n t h e t e n s i l e t e s t o f random b o a r d s , s p e c i e s was t h e o n l y s i g n i f i c a n t f a c t o r . Duncan's m u l t i p l e range t e s t grouped . the p i n e as t h e l o w e s t i n s t r e n g t h , aspen, c e d a r , and a l d e r , b e i n g h i g h e r . No o t h e r d i f f e r e n c e s were s i g n i f i c a n t a t t h e o v e r a l l t e s t s i g n i f i c a n c e l e v e l o f p=0.05. The f l e x u r a l d a t a i s p r e s e n t e d i n F i g . 29 t h r o u g h 33 , where each p o i n t r e p r e s e n t s a board r e p l i c a t e . The non-zero k o r i e n t a t i o n parameter caused by the use o f t h e r e c t a n g u l a r f o r m i n g box was i d e n t i f i e d as a p e r c e p t i b l e r i s e i n t h e e x p e c t e d t h e o r e t i c a l s t r e n g t h as t h e l o a d angle r o t a t e s t o t h e p a r a l l e l d i r e c t i o n . The d a t a f o r t h e t h e o r e t i c a l s t r e n g t h i n F i g . 29 t o 33 was pr o d u c e d by t h e computer program found i n t h e Appendix i . The average s t r e n g t h o f t h e p e r f e c t l y random composite can be e s t i m a t e d by E q u a t i o n [ 2 1 ] . In a p r e s e n t a t i o n s i m i l a r t o t h e t e n s i l e case (Table 17) comparisons t o t h e wood s t r a n d and t h e t h e o r e t i c a l s t r e n g t h s a r e 110 made i n T a b l e 21. The r e s u l t s show t h a t t h e t h e o r y p r e d i c t e d t h e s p e c i f i c MOR of t h e random boards w i t h s l i g h t l y b e t t e r a c c u r a c y than i t d i d f o r t h e s p e c i f i c t e n s i l e s t r e n g t h s . The r e l a t i v e s h o r t f a l l i n p i n e s t r e n g t h i s thought t o be caused by i t s lower compaction r a t i o . T h i s can l e a d t o poor bonding as d i s c u s s e d i n s e c t i o n s 4.3.2 and 5.1. The random o r i e n t a t i o n s t r e n g t h s , ranged from 74.5 t o 95.5 p e r c e n t of t h e model e s t i m a t e s . T h i s i s c o n s i d e r e d t o be a good m o d e l l i n g r e s u l t , g i v e n t h e a p p r o x i m a t i o n s n e c e s s a r y on b o t h s i d e s o f t h e comparison. The averages o f specimens c u t a t a l l a n g l e s , and t h e average t h e o r e t i c a l s t r e n g t h c a l c u l a t e d from E q u a t i o n [21] were used i n T a b l e 21. Table 21. Comparative f l e x u r a l s t r e n g t h o f random o r i e n t a t i o n s S p e c i f i c MOR Surface Percent of as a Percent S p e c i f i c T h e o r e t i c a l of P a r a l l e l Grain Species MOR MPa S p e c i f i c MOR Strand Strength R. Alder 34.2 95.5 23.3 R. Cedar 33.9 84.6 22.8 L. Pine 28.1 74.5 16.8 T. Aspen 32.1 78.6 21.1 T. Aspen 33.4 81.8 22.8 2% powder Y. B i r c h 1.76 mg/cm2 r e s i n 37.0 92.4 21.3 I l l 120 110 -100-90 -0 o. 5 80 -r 0 7 0 -z Id -K 60-M 0 5 0 -iZ 0 u 0. 4 0 -in3 0 -2 0 -10-0--Specific M.O.R.,Random Birch OREKTATION k=.15 i i i — i — i — i — i — i — r . 0 4.5 9 13.5 18 22.5 27 31.5 36 40.5 45 49.5 54 58.5 63 67.5 72 76.5 81 85.5 90 LOAD ANGLE WITH RESPECT TO BOARD AXIS • 1.76 mg/cm2 RESIN F i g u r e 29. S p e c i f i c MOR, randomly o r i e n t e d b i r c h Specif ic M.O.R.,Random Alder ORIENTATION k=.02 a "I r — i i i i — i — i — | — | — | — | — | — r 0 4.5 9 13.5 18 22.5 27 31.5 36 40.5 45 49.5 54 58.5 63 67.5 72 76.5 81 85.5 90 LOAD ANGLE WITH RESPECT TO BOARD AXIS .572 mg/cm2 RESIN 0 1,14 mg/cm2 RESIN F i g u r e 30. S p e c i f i c MOR, randomly o r i e n t e d a l d e r 1.13 o a 2 2 Id C •h Ul 0 k. o u 0. M Specific M.O.R. Random Cedar ORIENTATION k=.26 ~i i i i i i i i i i i — i — i — i — i — i — i — n r 0 4.5 9 13.5 18 22.5 27 31.5 36 40.5 45 49.5 54 58.5 63 67.5 72 76.5 81 85.5 90 • .57 rng/cm2 RESIN LOAD ANGLE WITH RESPECT TO BOARD AXIS o 1.14 mg/cm2 RESIN F i g u r e 31. S p e c i f i c MOR, randomly o r i e n t e d c e d a r 114 Specific M . O . R . R a n d o m Pine ORIENTATION k=.01 120 - r 110 -100-90 -0 a. 8 0 -I 0 7 0 -z u It 6 0 -H in 0 50 -u. 0 u a 40 -in 3 0 ^ 2 0 -10-0--• 0 4.5 9 13.5 18 22.5 27 31.5 36 40.5 45 49.5 54 58.5 63 67.5 72 76.5 81 85.5 90 LOAD ANGLE WITH RESPECT TO BOARD AXIS • .57 mg/cm2 RESIN o 1.14 mg/cm2 RESIN F i g u r e 32. S p e c i f i c MOR, randomly o r i e n t e d p i n e . Specific M.O.R. Random Aspen ORIENTATION k=.01 110-100 -9 0 -8 0 -7 0 -60 -5 0 -1 I I I I I — 1 — r — I I I . 0 4.5 9 13.5 18 22.5 27 31.5 36 40.5 45 49.5 54 58.5 63 67.5 72 76.5 81 85.5 90 „ , n LOAD ANGLE WITH RESPECT TO BOARD AXIS .57mg/ar,2 + 2% POWDER o 1.l4mg/cm2 F i g u r e 33. S p e c i f i c MOR, randomly o r i e n t e d a s p e n . 5. DISCUSSION 5.1 S t r e n g t h P a r a l l e l t o O r i e n t a t i o n S p e c i f i c t e n s i l e t e s t i n g was chosen f o r p r i o r i t y d i s c u s s i o n because i t i s l e s s compromised by t h e d e n s i t y g r a d i e n t assumptions than i s MOR t e s t i n g . T e s t i n g o f MOR f o r comparison t o the t h e o r y r e q u i r e s the assumption o f f i r s t f i b e r f a i l u r e a t the s u r f a c e , i n a d d i t i o n t o knowledge of t h e s u r f a c e d e n s i t y . Red a l d e r formed the s t r o n g e s t o f a l l c o m p o s i t e s when compared t o t h e e x p e c t a t i o n o f t h e model. T h i s i s thought t o be due t o a s u p e r i o r wood^adhesive i n t e r a c t i o n i n t h i s s p e c i e s . I t i s s p e c u l a t e d t h a t t h e r e e x i s t a d h e s i o n f a c t o r s such as s u p e r i o r w e t t a b i l i t y , s o l u b i l i t y parameter, o r a c i d / b a s e c o m p a t i b i l i t y t h a t improve bonding i n a l d e r . These may be founded i n t h e p e c u l i a r i t i e s o f a l d e r ' s e x t r a c t i v e c h e m i s t r y . The i n d u s t r i a l c o r e was t e s t e d f o r t h e purpose o f p l a c i n g the r e s u l t s i n p e r s p e c t i v e w i t h t h e c u r r e n t m a n u f a c t u r i n g a r t . Table 11 shows t h e c o r e r e a c h e d o n l y 32.6 p e r c e n t o f i t ' s t h e o r e t i c a l s p e c i f i c t e n s i l e s t r e n g t h (the l o w e s t o f a l l t e s t e d ) . Table 6 shows t h a t t h e i n d u s t r i a l c o r e had a l o w e r e s t i m a t e d compaction r a t i o . T h i s i s a p o s s i b l e cause f o r poor bonding, and 3 i s v e r i f i e d by i t s d e n s i t y b e i n g 0.54 8 g/cm , m o d e r a t e l y l o w e r t h a n the o t h e r e x p e r i m e n t a l b o a r d s . Compaction r a t i o , r a t h e r than r e s i n l e v e l , i s cons idered a f a c t o r i n the case of i n d u s t r i a l c o r e because t h e comparable aspen l a b o r a t o r y c o n t r o l boards r e a c h e d 41.2 p e r c e n t o f t h e t h e o r e t i c a l s p e c i f i c t e n s i l e s t r e n g t h . The l a b boards had t h e same 2 p e r c e n t powder r e s i n 117 l e v e l , but a h i g h e r compaction r a t i o ; t h e o r i g i n a l wood s t r a n d d e n s i t i e s are assumed e q u a l . The i n d u s t r i a l c o r e c o u l d be improved t o a h i g h e r p r e d i c t e d MOR, w i t h o u t f u r t h e r d e n s i f i c a t i o n , by o r i e n t i n g t h e s t r a n d s t o an i n c r e a s e d k. l e v e l . A f u r t h e r o p t i m i z a t i o n , w i t h o u t c o s t l y r e s i n i n c r e a s e , i s p o s s i b l e by measuring t h e debonding s h e a r s t r e n g t h , s, and u s i n g t h i s t o e s t i m a t e c r i t i c a l s t r a n d , l e n g t h l e . ( s e c t i o n 3.10.3). S t r e n g t h improvement would come w i t h s e l e c t i o n o f an i n c r e a s e d s t r a n d l e n g t h , 1, which i s much l o n g e r than- l c . Methods of t e s t i n g t h e bond shear s t r e n g t h o f s t r a n d s which withdraw s t r a n d s embedded i n t h e composite may p r o v e u s e f u l i n t h i s s t u d y . R e s i n e f f e c t s on s p e c i f i c s t r e n g t h s were s t u d i e d d i r e c t l y by p r e p a r i n g a s e r i e s o f cedar c o m p o s i t e s t o have a p p r o x i m a t e l y t h e same o r i e n t a t i o n l e v e l but w i t h a sequence o f i n c r e a s i n g r e s i n l e v e l s . F i g u r e 34 was t h e r e s u l t . Here, t h e c o m b i n a t i o n o f bonding f a c t o r s and s t r a n d geometry produ c e d a t y p i c a l a s y m p t o t i c c u r v e c o n v e r g i n g t o a maximum s t r e n g t h a t a r e s i n s p r e a d o f about 2 1.76 mg/cm i n t h e case o f s p e c i f i c MGR. T h i s convergence r e q u i r e d a h i g h e r r e s i n s p r e a d i n t h e case o f s p e c i f i c t e n s i l e s t r e n g t h . L a u f e n b e r g (50) p r e s e n t e d s i m i l a r r e s u l t s f o r randomly o r i e n t e d aspen but w i t h t h e r e s i n s c a l e i n c r e a s e d f o r t h e h i g h e r bonding l e v e l r e q u i r e d o f s h o r t e r , t h i c k e r s t r a n d s h a v i n g a l e n g t h / t h i c k n e s s r a t i o o f about 37. The c o r r e s p o n d i n g l e n g t h / t h i c k n e s s r a t i o s f o r s t r a n d s i n t h i s t h e s i s ranged from 94 t o 134. 118 Cedar Specif ic Strengths vs.Resin Load Parallel to Orientation 100 -i 90 -0 0.57 1.14 1.76 2.33 2.902 LIQUID RESIN SURFACE SPREAD MG/CM2 • SPECIFIC TENSILE x SPECIFIC MOR F i g u r e 34. T e n s i l e s t r e n g t h v e r s u s r e s i n s p r e a d l e v e l . 119 The p r i m a r y e f f e c t s o f o r i e n t a t i o n and r e s i n l e v e l on s t r e n g t h showed c l e a r l y t h r o u g h th e s u p e r p o s i t i o n o f s e v e r a l o t h e r f a c t o r s . Such u n c o n t r o l l e d f a c t o r s were compaction r a t i o , i n t r i n s i c b onding p r o p e r t i e s o f t h e s p e c i e s , wood s o f t n e s s roughness, and p e r m e a b i l i t y . When t h e r e s i n l e v e l was h i g h , t h e p a r a l l e l s p e c i f i c MOR s t r e n g t h s i n c r e a s e d , and approached t h e t h e o r e t i c a l v a l u e , r e a c h i n g i t i n a l d e r and above 61.6 p e r c e n t o f t h e o r e t i c a l i n t h e o t h e r s p e c i e s . For o p t i m a l s t r e n g t h , t h e a d h e s i v e b o n d i n g must be s u f f i c i e n t f o r t r a n s f e r o f t e n s i l e f a i l u r e s t r e s s t o s t r a n d s h a v i n g p a r a l l e l o r i e n t a t i o n s w i t h i n t h e b o a r d . L a u f e n b e r g (50) a n a l y z e d t h e f a i l u r e o f s t r a n d s i n OSB u s i n g t h e maximum s t r e s s t h e o r y . He i n d i c a t e d t h a t h i g h l y bonded s t r a n d s s t r e s s e d between 2.6 and 17 degrees o f f p a r a l l e l t o t h e g r a i n a x i s , f a i l i n s h e a r , a l o n g t h e p a r a l l e l g r a i n o f t h e s t r a n d . T e n s i l e f a i l u r e i n h i g h l y bonded s t r a n d s dominates a t below 2.6 degrees l o a d a n g l e . T h i s f o r c e d i r e c t i o n i s n e a r l y p a r a l l e l t o g r a i n . I f t h e t h e o r e t i c a l s t r e n g t h i s t o be reached, 1 t h e n bonding s u f f i c i e n t t o a p p l y f a i l u r e s t r e s s t o t h e s t r a n d s a t t h e i r s t r o n g e s t d i r e c t i o n i s r e q u i r e d . I n T able 11 and T a b l e 18 most o f t h e s p e c i f i c s t r e n g t h s are lower t h a n t h e 100 p e r c e n t l e v e l r e p r e s e n t i n g t h e network t h e o r y e s t i m a t e s . The d i f f e r e n c e s are a s c r i b a b l e t o i n a d e q u a t e s t r e s s transfer. This i s confirmed in F i g . 34 where increased r e s i n (adhesion) g r e a t l y improved t h e s t r e n g t h . A t t h e f i x e d s t r a n d dimensions s e l e c t e d f o r t h i s r e s e a r c h , t h e s t r e n g t h d e f i c i t s c o u l d be r e s t o r e d by augmenting t h e v a l u e o f bond shear s t r e n g t h , s, i n E q u a t i o n [16] t h r o u g h a d d i t i o n a l r e s i n s p r e a d . T h i s reduces the v a l u e o f h c , so t h a t h » h c ( s e c t i o n 3.10.3). 120 The composite s t r e n g t h would e x p e c t e d l y i n c r e a s e when t h e s t r a n d l e n g t h i s l a r g e r e l a t i v e t o t h e p a r a l l e l t e n s i l e specimen gage l e n g t h . T h i s gage l e n g t h e f f e c t , t e n d i n g t o s i m u l a t e c o n t i n u o u s s t r a n d s , ( p e r f e c t adhesion) would i n c r e a s e u n t i l t h e ze r o span e q u i v a l e n c e was approached. Thus, a s t r e n g t h advantage ( F i g . 34), may go t o t h e MOR specimen due t o a s m a l l e r peak s t r e s s zone. V a r i a n c e d e c r e a s e s w i t h i n c r e a s e d specimen s i z e ( E q u a t i o n [14]) . P e r t a i n i n g t o t h e Table 11 s p e c i e s b o n d i n g d i f f e r e n c e s r e l a t i v e t o t h e t h e o r y , i t was seen t h a t c e d a r had a lo w e r s p e c i f i c t e n s i l e s t r e n g t h a t t h e 0.57 mg/cm2 r e s i n l e v e l , d e s p i t e h a v i n g a h i g h e r compaction r a t i o t h a n a l d e r . A l l other, f a c t o r s b e i n g e q u a l , i t i s c o n c l u d e d t h a t t h e r e s i n d i d not bond t h e cedar as w e l l as t h e a l d e r . T h i s d i s c o u n t s o t h e r f a c t o r s such as d i f f e r i n g s t r a n d damage d u r i n g c o m paction, and p o s s i b l e b o n d i n g -o r i e n t a t i o n i n t e r a c t i o n . To summarize, i t was ob s e r v e d t h a t t h e p a r a l l e l s t r e n g t h o f an o r i e n t e d s t r a n d composite i s a f u n c t i o n o f how w e l l i t i s o r i e n t e d and how w e l l i t i s bonded. I t i s c l e a r t h a t t h e o r i e n t a t i o n parameter, k, s h o u l d be maximized f o r maximum s t r e n g t h i n t h e c o m p o s i t e . The s t r a n d l e n g t h t o t h i c k n e s s r a t i o s h o u l d be made so t h a t t h e f r a c t i o n l - ( h / l ) i s c l o s e t o 1 ( s e c t i o n 3.10.3). T h i s can remedy t h e c o n d i t i o n o f h<h c where t h e wood o r bond-shear s t r e n g t h , s, i s exceeded and sh e a r f a i l u r e o c c u r s . The bond o r wood shear s t r e n g t h , s, may be exceeded by i n t e r n a l s h e a r s t r e s s because o f t h e e f f e c t s o f any o f t h e f o l l o w i n g f a c t o r s : 121 adhesive l e v e l , type, d i s t r i b u t i o n , dispersion, and cure strand species, drying history, and surface condition compaction r a t i o and pressing s p e c i f i c a t i o n s short, thick strands rather than long, t h i n ones 5.2 S t r e n g t h , P e r p e n d i c u l a r t o O r i e n t a t i o n Perpendicular to orientation, the tested s p e c i f i c t e n s i l e strengths of both the low and high re s i n l e v e l composites were equal or lower i n strength compared to the wood strands themselves. A 3 variable analysis of variance was performed, the 3 variable strengths were of the low and the high re s i n composites and the strands of each species. No s i g n i f i c a n t differences between composites and strands were found i n aspen (p=0.13) or cedar (p=0.22). (reference, Tables 7 and 13). In these comparisons, there are specimen size differences between the strand strengths and the composite strengths that contribute to the strand estimates being r e l a t i v e l y large. The lower wood strengths obtained from larger ASTM sized test specimens are presented i n Table 7. To remain consistent with the model hypothesis, a l l perpendicular wood strengths referred to below were from zero span strand tests, not large block t e s t s . A l l inputs to the model were also zero span strand strengths. At both re s i n levels,..the composite strengths, were expected to be considerably greater than the perpendicular to grain wood strength because of the presence of numerous of f - a x i s strands i n the orientation d i s t r i b u t i o n . Evidently, the small perpendicular strength gains available to the composite because of imperfect 122 o r i e n t a t i o n were l o s t because o f t h e e f f e c t s o f poor s t r e s s t r a n s f e r between t h e o f f - a x i s s t r a n d s , s t r a n d damage, o r specimen s i z e e f f e c t on s t r e n g t h . Now t h e comparisons t o t h e t h e o r e t i c a l models s h a l l be c o n s i d e r e d . The p e r c e n t a g e s o f t h e model s p e c i f i c t e n s i l e s t r e n g t h s p e r p e n d i c u l a r t o t h e o r i e n t a t i o n a x i s (Table 14) were s i g n i f i c a n t l y i n c r e a s e d by i n c r e a s e d r e s i n l e v e l . Aspen was t h e e x c e p t i o n , h a v i n g no s i g n i f i c a n t s t r e n g t h response t o t h e r e s i n i n c r e a s e from 0.57 mg/cm2 t o 1.14 mg/cm2 s p r e a d . A l l comparisons were by " t " s t a t i s t i c s a t t h e p=0.05 s i g n i f i c a n c e l e v e l . I t i s n o t e d from Table 14 d a t a t h a t d o u b l i n g t h e a d h e s i v e s p r e a d i n aspen d i d not i n c r e a s e t h e p e r c e n t a g e o f t h e t h e o r e t i c a l p e r p e n d i c u l a r s p e c i f i c t e n s i l e s t r e n g t h . T h i s , t o g e t h e r w i t h t h e e v i d e n c e t h a t t h e p e r p e n d i c u l a r s p e c i f i c t e n s i l e s t r e n g t h s o f t h e composites were o n l y e q u a l t o t h e wood s t r a n d ' s (Tables 7 and 13) l e a d s t o t h e c o n c l u s i o n t h a t t h e adh e s i o n a t t h e s t r a n d b o n d i n g zones was adequate, but t h a t t h e r o l l i n g s h e a r s t r e n g t h o f t h e s t r a n d s would not su p p o r t t h e shear s t r e s s n e c e s s a r y t o t r a n s f e r t e n s i l e f a i l u r e l o a d t o t h e p e r p e n d i c u l a r s t r a n d s . T h i s means t h a t s t r a n d p u l l o u t can a l s o be a s t r e n g t h f a c t o r i n t h e p e r p e n d i c u l a r d i r e c t i o n . A p r o b a b l e r e a s o n f o r t h i s l i e s i n t h e s t r a n d s ' e f f e c t i v e s o l i d w i d t h b e i n g much n a r r o w e r t h a n t h e a p p a r e n t 8 mm n o m i n a l , m e a s u r e d a s ... u n f l a w e d wood. T h i s i s summarized i n the. u n d e r s t a n d i n g t h a t t h e s t r a n d ' s p e r p e n d i c u l a r t e n s i l e s t r e n g t h does not always govern the composite s t r e n g t h i n t h e p e r p e n d i c u l a r d i r e c t i o n . P a r a l l e l t o - t h e - g r a i n c r a c k s i n t h e s t r a n d s can g r e a t l y reduce t h e e f f e c t i v e w i d t h . The e f f e c t o f t h i s on s t r e n g t h i s 123 seen w i t h a low v a l u e o f shear s t r e s s t r a n s f e r l e n g t h i n E q u a t i o n [18] . The r e s u l t o f h < h c can be sh e a r f a i l u r e a t t h e bond i n t e r f a c e . I n a d d i t i o n t o damage d u r i n g c u t t i n g , i t i s p r o b a b l e t h a t some s t r a n d damage o c c u r s d u r i n g p r e s s i n g because t h e t h i n , dry s t r a n d s a r e q u i t e f r a g i l e and e a s i l y b r e a k p a r a l l e l t o t h e g r a i n . F u r t h e r damage can o c c u r i n d r y i n g , s t o r a g e , and h a n d l i n g o f s t r a n d s , t h i s produces t h e d e t r i m e n t a l narrow s t r a n d f r a c t i o n seen i n F i g . 5. The s t r e n g t h l o s s e x p l a n a t i o n i s p a r t l y based on the s u b s t a n t i a l narrow s t r a n d ( f i n e s ) p o r t i o n i n d i c a t e d i n t h e d i s t r i b u t i o n o f F i g . 5. The s t r a n d t e n s i l e s t r e n g t h governs i n the wide and u n f l a w e d p o r t i o n o f t h e d i s t r i b u t i o n when adequate ad h e s i o n i s p r e s e n t . Damage d u r i n g p r e s s i n g adds t o t h i s w i d t h l o s s . C r a c k i n g i s a l s o promoted by t h e way t h e wood s t r a n d s a r e pr e p a r e d . They a r e p e e l e d from t h e t a n g e n t i a l f a c e o f wood b l o c k s u s i n g t h e same t a n g e n t i a l c u t t i n g p r i n c i p l e as used i n p r e p a r i n g v eneer. T h i s produces l o o s e f a c e checks,, and o f t e n d e s t r o y s t h e c r a c k - f r e e w i d t h o f t h e s t r a n d s . The m e r i t s o f a -way o f p r e p a r i n g s t r a n d s w i t h o u t t h e p a r a l l e l g r a i n c r a c k s a r e worthy o f f u r t h e r r e s e a r c h . A s l i c i n g d e v i c e which p e e l s p a r a l l e l t o g r a i n ( l o n g i t u d i n a l l y ) may p r o v i d e improved r e s u l t s , i f t h e s t r a n d i s produced a t low k n i f e a n g l e , u s i n g no c o u n t e r -knife breaker bar. The objective i s a strand with minimal micro-damage . I n c r e a s i n g t h e p e r p e n d i c u l a r - t o - g r a i n bond s t r e n g t h o f h i g h l y o r i e n t e d composites r e q u i r e s a change t o a h i g h e r s t r a n d w i d t h / t h i c k n e s s r a t i o w i t h t h e shear s t r e n g t h , s, s e t a t t h e r o l l i n g s h ear s t r e n g t h o f t h e s t r a n d s . The i d e a l i z e d s t r e n g t h i s 124 reached when the intact strand width, w >> wc and, with 1-(h/w) approaching 1. The factor wc i s calculated i n the perpendicular d i r e c t i o n according to wc =bt/s . The resulting improvement i n stress transfer would enhance achievement of the strength anticipated by the continuous strand model Equation [13]. Another way of increasing the perpendicular strength of the experimental composites would be to decrease the strand thickness, (factor b), i n Equation [16]. This may reduce the stress transfer requirement of shear to less than the r o l l i n g shear capacity of the strands thus allowing perpendicular t e n s i l e strength to govern. However, increasing the crack-free width i s preferable economically, because the weight percent of the costly resin remains constant while the e f f e c t i v e r e s i n spread i s maintained. Removal of the excessively narrow strand fines seen in the width d i s t r i b u t i o n ' o f F i g . 5 would be a further major . contribution to the perpendicular strength. Weak, low density zones, caused by mat forming a r t i f a c t s such as voids'or by the s e r i a l mischance of poor overlapping and interleaving of strands may be causal factors i n the low perpendicular to orientation strengths. Such zones could be induced by an orienter having mechanical separation vanes (Fig. 6 ) . These can interrupt stress transfer from strand to strand and create intolerable interface stress le v e l s i n a fashion similar to cracked strands. But the comparatively low standard deviation of strengths does not support the presence of these superimposed variables. Such factors are worthy of further 125 research i n a fracture mechanics study of strand composite strength in the perpendicular d i r e c t i o n . 5.3 Powdered Vs. L i q u i d A d h e s i v e Considering the data i n Table 17 i t was observed that the aspen composite having either a high or low l e v e l of l i q u i d r e s i n on randomly oriented aspen strands yielded a higher percentage of the t h e o r e t i c a l model t e n s i l e strength (77.6 percent) than the 2 percent powder resin (59.3 percent). This trend was also apparent i n the perpendicular to orientation t e n s i l e strength as seen i n Table 14. Here, the comparison again favours l i q u i d (58.7 percent) over powder resin a p p l i c a t i o n (54.0 percent). Contrary to t h i s , i n t e n s i l e t e s t i n g aspen p a r a l l e l to orientation, the powdered resin yielded s l i g h t l y higher strengths, 41.2 percent of the t h e o r e t i c a l strength, as compared to 36.5 percent of the t h e o r e t i c a l for the l i q u i d resin (Table 11). Of these 3 comparisons, only the f i r s t showed a s i g n i f i c a n t difference between powder and l i q u i d at the p=0.05 l e v e l of confidence. A comparison of resin types i s more convincing i f i t meets the following condition: To preclude resin type-orientation int e r a c t i o n , the . orientation k levels should be the same i n both composites compared. This condition i s not met for the comparisons i n Table 11 or 14. When species are considered c o l l e c t i v e l y i n the analysis of variance i n Table 15 i t was concluded that the resin l e v e l (adhesion) i s not s i g n i f i c a n t as a determinant of t e n s i l e 126 strength i n random composites at the pertinent resin l e v e l s . The i n s e n s i t i v i t y of strength to resin changes i n random orientation weakens the conclusion that the l i q u i d form of resin i s superior. This i n s e n s i t i v i t y i s also evident i n the MOR results, F i g . 33. However, discounting the extra 0.44 percent of p.f. s o l i d s present, the l i q u i d resin performed better i n the random orientation i n aspen s p e c i f i c t e n s i l e strength. Recent improvements i n i n d u s t r i a l l i q u i d blenders have reduced droplet size to the 30-40 micron range. This i s much smaller than the 138 micron range used i n the present research. Therefore, l i q u i d s having small droplets may prove equal to powders, i f good d i s t r i b u t i o n i s also present. The lower cost l i q u i d resins are usually preferred when shipping costs do not dominate. 5.4 F l e x u r a l E l a s t i c i t y Digressing from the topic of composite strength, a discussion of modelling e l a s t i c i t y , using the orientation d i s t r i b u t i o n function, i s worthwhile. The algorithm previously studied, and which had merit as a strength estimator, was thought to have an analogue i n a f l e x u r a l e l a s t i c i t y model. Geimer (27) explored a simple analysis which predicted 74 to 120 percent of the actual tested s t i f f n e s s of three layer cross ply oriented strand.boards. . He used a transformed moment of. inertia- formula for EI estimation. This method i s also found i n laminated beam and plywood design. EI i s the product of the test beam's engineering f l e x u r a l modulus of e l a s t i c i t y and cross sectional moment of i n e r t i a . The present study of t h i s subject used 127 Geimer's approach t o a m u l t i - l a y e r system u s i n g s t r a n d l a y e r s o f c a l c u l a t e d EI c o n t r i b u t i o n a c c o r d i n g t o t h e i r d e n s i t y - r e l a t e d modulus and d i s t a n c e from t h e n e u t r a l a x i s . F i r s t , t h e t e n s i l e s t i f f n e s s i n t h e b o a r d a x i s d i r e c t i o n was e s t i m a t e d f o r a s i n g l e s t r a n d l a m i n a , o r i e n t e d a t any g r a i n a n g l e , 6, r e l a t i v e t o t h e o r i e n t i o n a x i s . T h i s r e q u i r e d use o f an e l a s t i c t r a n s f o r m a t i o n e q u a t i o n i n t h e l o n g i t u d i n a l - t a n g e n t i a l p l a n e such as p r e s e n t e d by B o d i g and Jayne (12). 4 4 2 2 . 1 = cos 8 + s i n 6 + 1^ - 2v T T^ s i n 0 cos 0 [24] E n E L E T G L T E L where: GLT = shear modulus v L T = P o i s s o n ' s r a t i o E T = t a n g e n t i a l t e n s i l e modulus o f t h e s t r a n d l a y e r E L = l o n g i t u d i n a l t e n s i l e modulus o f t h e s t r a n d l a y e r The wood r i n g a n g l e was n e g l e c t e d and t h e s t r a n d s were t r e a t e d as i f t h e y were t r a n s v e r s e l y i s o t r o p i c (2 d i m e n s i o n a l l y o r t h o t r o p i c w i t h 4 independent e l a s t i c c o n s t a n t s ) . T h i s t r a n s f o r m a t i o n E q u a t i o n [24] r e p l a c e d t h e Hankinson e x p r e s s i o n i n t h e E q u a t i o n [13] i n t e g r a l , n u m e r i c a l l y p r o d u c i n g t h e e x p e c t e d l a m i n a t e e l a s t i c i t y f o r a network of s t r a n d s under l o a d i n g a t any chosen a n g l e , m, r e l a t i v e t o t h e p r i n c i p a l a x i s o f o r i e n t a t i o n . Some e x p l a n a t i o n about how t h e board's v e r t i c a l d e n s i t y g r a d i e n t a f f e c t s t h e f l e x u r a l modulus i s o f f e r e d as f o l l o w s . The s u p e r p o s i t i o n o f r e p e a t e d x - r a y d e n s i t y p r o f i l e s , two elements of which are e x e m p l i f i e d i n F i g . 16, showed a r e p e a t e d p a r a b o l i c d e c r e ase i n d e n s i t y toward t h e b o a r d c e n t e r . T h i s i s c o n f i r m e d by S t e i n e r e t a l . (84). A p a r a b o l i c e q u a t i o n was used t o 128 describe the v e r t i c a l density gradient and produce an e l a s t i c modulus de n s i f i c a t i o n factor for increments i n v e r t i c a l l e v e l through the composite. The parabolic shape parameter (focus) was based on these x-ray density p r o f i l e s . It was assumed that the e l a s t i c moduli of wood, E L and E T are d i r e c t l y proportional to the density. Text book values (Table 23) of e l a s t i c moduli for uncompressed wood (12) were used as the primary e l a s t i c constants. The a v a i l a b i l i t y of such values i n the l i t e r a t u r e makes thi s modelling more v e r s a t i l e than the use of e l a s t i c constants determined by tests on thi n sheets taken from descending positions in the laminate (Geimer, 27). A numerical integration of the modified Equation [13] was computed to estimate the composite s t i f f n e s s , EI. The p a r a l l e l axis theorem (22) was used for determination of each lamina's moment of i n e r t i a . The composite thickness was subdivided into laminae represented by the individual strands. Thus, the overlapping and interwoven network of strands was perceived by the model as a laminate of graded density laminae. The cumulative calculation made for the s t i f f n e s s , EI, assumed that each strand layer was approximately equal i n thickness. This uniform thickness introduces the model concept of the densified surface layers as being caused by the void f i l l i n g deformation and consolidation of strands into . i n t e r s t i c i a l c a v i t i e s during hot pressing. The void-.volume i s . . - . thought to be lower i n the surface zones. F i n a l l y , the summed EI result was divided by the apparent moment of i n e r t i a for the whole thickness to estimate an " e f f e c t i v e " E modulus. 129 Two t r i a l s (Table 22) on high r e s i n composites yielded reasonable estimates of MOE r e l a t i v e to actual t e s t s . These results are comparable to some of Geimer's (27) and Woodson's (97) transformed section estimates. The res u l t s are also s i m i l a r to those of Harris (34) who used a layered, s e r i a l , spring model for s p e c i f i c t e n s i l e modulus i n the d i r e c t i o n of orientation. His experimental results f e l l modestly short of his model prediction. The present computations showed, for example, that the density gradient in alder caused an increase from about 6069 MPa ( p a r a l l e l MOE) to the 13883 MPa resu l t when the parabolic gradient was factored into the uncompressed strand network strength. The estimate was within the range of the MOE test average of 9940 MPa. The e l a s t i c input moduli are taken at 12 percent moisture content, but the t e s t i n g was at 8 percent moisture. Therefore, the differences i n Table 22 are p a r t i a l l y explainable by t h i s inconsistency. T a b l e 22. M.O.E. i n flexure (MPa) Network Test Mean Model MOE Flexural MOE Species K P a r a l l e l Perpendicular P a r a l l e l Perpendicular R. Alder 3.5 13883 966 9940 975 Y. Birch 9.0 14291 885 16933 1066 T a b l e 23. Input e l a s t i c c o nstants (MPa) T e n s i l e T e n s i l e Shear Poisson r a t i o Species Er E T GTT LT R. A l d e r 10427 355.86 452.41 .50 Y. B i r c h 14629 640.69 721.37 .50 C o n s i d e r i n g t h e d a t a o f Tab l e 22, one so u r c e o f m o d e l l i n g d i s c r e p a n c y i n t h e p a r a l l e l d i r e c t i o n i s th o u g h t t o be due t o t h e c o n t r i b u t i o n t o s t i f f n e s s caused by e l a s t i c i n t e r a c t i o n s between the wood s t r a n d s . The p a r a l l e l p l y , ( t r a n s f o r m e d s e c t i o n ) e s t i m a t i o n o f e l a s t i c i t y used f o r plywood c r o s s p l y l a m i n a t e s i s even l e s s t h e o r e t i c a l l y r i g o r o u s f o r use w i t h m u l t i - d i r e c t i o n a l , o r i e n t e d wood s t r a n d l a m i n a t e s . The e l a s t i c i n t e r a c t i o n i s accommodated i n LPT ( l a m i n a t e d p l a t e t h e o r y ) t h r o u g h t h e r e q u i r e d m u l t i p l i c a t i o n o f t h e t e n s o r elements o f t h e p l a t e c o n s t i t u t i v e e q u a t i o n . The i n t e r a c t i o n i s reduced, but not e l i m i n a t e d , because of t h e s t a t i s t i c a l symmetry about t h e midplane o f t h e o r i e n t a t i o n a n g l e s and s t a c k p o s i t i o n s o f s t r a n d l a m i n a e h a v i n g e q u a l t h i c k n e s s and e l a s t i c p r o p e r t i e s . T h i s a l l o w s t h e assumption(s) o f z e r o c o u p l i n g between e x t e n s i o n o r b e n d i n g w i t h t w i s t i n g o f t h e l a m i n a t e . (5) In t h i s c a s e , t h e c o u p l i n g s t i f f n e s s m a t r i x [B^] = 0 . St r a n d i n t e r w e a v i n g , and o v e r l a p p i n g , c o n t r i b u t e t o t h e apparent modulus o f the p r a c t i c a l wood s t r a n d c o m p o s i t e . Some e r r o r i n t h e t h e o r e t i c a l modulus i s i n c u r r e d because o f t h e a p p r o x i m a t i o n t h a t e l a s t i c m o d u l i i n c r e a s e d i r e c t l y p r o p o r t i o n a t e l y t o d e n s i t y . Any damage i n p r e s s i n g i s n e g l e c t e d . The c o n c l u s i o n i s t h a t t h e network a n a l y s i s p r o v i d e s a f i r s t approximation estimate of f l e x u r a l MOE of variable accuracy i n -the p a r a l l e l t o . o r i e n t a t i o n a x i s d i r e c t i o n and one..of-good acc u r a c y i n t h e p e r p e n d i c u l a r d i r e c t i o n . The GWBASIC program i n . 131 Appendix i i c a l c u l a t e s t h e s e e s t i m a t e s a c c o r d i n g t o t h e t r a n s f o r m e d moment of i n e r t i a method and c o u l d be used f o r s t u d y i n g r e c o n s t i t u t e d wood s t r a n d lumber o r OSB c o r e l a y e r MOE as f u n c t i o n s o f o r i e n t a t i o n , wood s p e c i e s , o r d e n s i t y g r a d i e n t . An improved model o f MOE would i n c l u d e t h e e l a s t i c e f f e c t s o f one s t r a n d upon t h e o t h e r . A s u g g e s t e d a l t e r n a t i v e model would f i r s t d e s c r i b e t h e p r o b a b i l i t y d i s t r i b u t i o n f u n c t i o n f o r o r i e n t a t i o n , as does the network model. The proposed e l a s t i c i t y model would t h e n randomly choose a sequence o f sample s t r a n d a n g l e s , w e i g h t e d by t h e p r o b a b i l i t y d i s t r i b u t i o n f o r o r i e n t a t i o n , t o r e p r e s e n t a n g u l a r arrangements t h r o u g h t h e t h i c k n e s s o f a model specimen. D e n s i t y g r a d i e n t e f f e c t s on t h e e l a s t i c p r o p e r t i e s would t h e n be accommodated t h r o u g h p a r a b o l i c , adjustment r e g r e s s i o n s . C l a s s i c a l l a m i n a t e d p l a t e t h e o r y (LPT) would f i n a l l y be a p p l i e d t o t h e composi t e g i v i n g a t o t a l c o n s t i t u t i v e e q u a t i o n which i n c l u d e s t h e e f f e c t s o f e l a s t i c i n t e r a c t i o n s between laminae. As a Monte C a r l o s i m u l a t i o n , t h i s c o u l d be c a l c u l a t e d m u l t i p l e t i m e s t o b u i l d a s t a t i s t i c a l , d e s c r i p t i o n o f t h e e l a s t i c p r o p e r t i e s o f t h e composite.. T h i s s t o c h a s t i c model would produce a random f u n c t i o n t e n s i l e , f l e x u r a l , o r shear modulus o u t p u t f o r each d i s c r e t e value, o f k, the o r i e n t a t i o n parameter. There is substantial practical merit in the ability-., to-f o r e c a s t . - t h e - t e n s i l e .-and b e n d i n g e l a s t i c p r o p e r t i e s - o f a .. . u n i d i r e c t i o n a l m u l t i p l e l a y e r o f s t r a n d s . However, t h e commodity OSB p a n e l b o a r d i s composed o f 3 such c o m p o s i t e s , c o n s i s t i n g o f d e n s i f i e d f a c e and back l a y e r s and a low d e n s i t y c r o s s - b a n d c o r e of g r e a t e r t h i c k n e s s . The MOE c a l c u l a t i o n f o r such a p a n e l i s 132 thought t o be p o s s i b l e t h r o u g h m a n i p u l a t i o n o f t h e pr o p o s e d s t o c h a s t i c - l a m i n a t e d p l a t e t h e o r y (LPT) model i n an expanded form, u s i n g one or more o r i e n t a t i o n p a r a m e t e r s . Such i s l e f t t o the c o n s i d e r a t i o n o f t h o s e c h o o s i n g t o i n t e n s i v e l y s t u d y wood s t r a n d composite e l a s t i c i t y . I f t h e r e s e a r c h e r chooses t o use l e s s r e a d i l y a v a i l a b l e i n p u t s such as t h e 4 independent e n g i n e e r i n g e l a s t i c c o n s t a n t s r e q u i r e d by 2 d i m e n s i o n a l o r t h o t r o p i c LPT, t h e n t h e composite e l a s t i c r esponse d e s c r i b e d above might be m o d e l l e d . The LPT i n p u t d i f f i c u l t y i s l a c k o f i n f o r m a t i o n on how d e n s i t y a f f e c t s the c o n s t a n t s and s p a r s i t y o f i n f o r m a t i o n , on a l l s p e c i e s , f o r th e e l a s t i c c o n s t a n t s t h e m s e l v e s . 6. CONCLUSION 133 This research creates and examines an orientation model for the maximum strength performance of bonded wood strand composites. The ultimate s p e c i f i c t e n s i l e and s p e c i f i c bending strengths of wood composites were determined by tests and compared to a mathematical algorithm which estimates the strength of the composites when the stress transfer between strands i s close to i d e a l . The orientation model shows that the use of, high orientation w i l l permit i n d u s t r i a l evolution of new panel and strand-lumber composites having s p e c i f i c strengths approaching those of wood. The von Mises pr o b a b i l i t y d i s t r i b u t i o n function was found to accurately describe the orientation of i n d u s t r i a l and experimental wood strand composites. It was also concluded that the potentials of composite orientation are not f u l l y exploited i n contemporary i n d u s t r i a l products. A quantitative understanding of the contribution of the strand orientation l e v e l to composite strength was v e r i f i e d by studying of the . relationship between the experimental results and the orientation models, at d i f f e r e n t resin l e v e l s . The orientation model was concluded to be accurate when s u f f i c i e n t resin was used to provide adequate stress transfer.. The experimental levels of phenolic resin required: to produce composites having the orientation model's id e a l p a r a l l e l s p e c i f i c MOR, ranged from 2 to 3 times the 2 percent l e v e l of resin t y p i c a l l y applied i n d u s t r i a l l y . This factor became 5 to 7 times the resin applied i n d u s t r i a l l y when comparing s p e c i f i c t e n s i l e strength to the orientation model. The fashion in which strength i n c r e a s e d w i t h r e s i n i n t h e p a r a l l e l d i r e c t i o n was demonstrated t o be a s y m p t o t i c t o a p o i n t near t h e s t r e n g t h p r e d i c t i o n o f t h e o r i e n t a t i o n model. In a c o r e from a contemporary i n d u s t r i a l c omposite, t h e poor a d h e s i v e bond l i m i t e d t h e s t r e n g t h p a r a l l e l t o t h e a x i s . Bonding was i n c r e a s i n g l y c r i t i c a l t o t h e p a r a l l e l s t r e n g t h as t h e o r i e n t a t i o n l e v e l i n c r e a s e d . At t h e o t h e r extreme, i n randomly o r i e n t e d c o m p o s i t e s , d o u b l i n g t h e i n d u s t r i a l r e s i n l e v e l had no e f f e c t on s p e c i f i c t e n s i l e s t r e n g t h o r MOR. As t h e l o a d a n g l e w i t h r e s p e c t t o o r i e n t a t i o n moved t o t h e p e r p e n d i c u l a r , a s m a l l e r gap between model p r e d i c t i o n and t e s t r e s u l t s appeared i n b o t h f l e x u r e and t e n s i o n . T h i s i s c o n s i s t e n t w i t h t h e c o n c l u s i o n t h a t t h e s t r e s s t r a n s f e r r e q u i r e m e n t s f o r s t r a n d f a i l u r e were more e a s i l y s a t i s f i e d by t h e a d h e s i v e when th e s t r a n d s were l o a d e d near p e r p e n d i c u l a r t o t h e g r a i n a x i s . 135 7. SUMMARY Th i s r e s e a r c h i s m e a n i n g f u l i n g u i d i n g p r o g r e s s t oward h i g h e r s t r e n g t h t o weight r a t i o s i n i n d u s t r i a l wood s t r a n d c omposites. A c h i e v i n g t h e i n t e n t of h i g h s p e c i f i c s t r e n g t h i s dependent on t h e composite b e i n g bonded so t h a t t h e maximum p r i n c i p a l s t r e s s e s a r e t r a n s f e r r e d from one l o a d b e a r i n g element t o another. I d e n t i f i c a t i o n o f composite bond weakness was made p o s s i b l e by use o f t h e o r i e n t a t i o n model f o r an e s t i m a t e o f t h e composite's p o t e n t i a l s t r e n g t h when p e r f e c t l y bonded. S t r e n g t h d e f i c i t s can o n l y be e l i m i n a t e d when t h e i d e a l s t r e n g t h i s known. Fo r example, i n p a r a l l e l s p e c i f i c MOR, t h e h i g h e r o r i e n t e d . e x p e r i m e n t a l b i r c h composite reached 66.6 p e r c e n t o f t h e s p e c i f i c t e n s i l e s t r e n g t h o f t h e p a r a l l e l g r a i n wood i t s e l f and 88.3 p e r c e n t of t h e c o n t i n u o u s s t r a n d o r i e n t a t i o n model p r e d i c t i o n o f u l t i m a t e s t r e s s . The a d h e s i v e l e v e l which i s adequate t o produce t h e s t r e n g t h e q u i v a l e n t o f a c o n t i n u o u s s t r a n d o r i e n t a t i o n model v a r i e s w i t h t h e s p e c i e s , r e s i n t y p e , compaction l e v e l , and s t r a n d shape. I d e a l l y , t h e most c o s t e f f e c t i v e b onding i s a c h i e v e d when u s i n g -s t r a n d s of h i g h l e n g t h t o t h i c k n e s s r a t i o . The r e s e a r c h was br o a d i n terms o f composite d e n s i t y profile, resin level, resin distribution, and resin, dispersion, a l l of which, i n c l u d e d ranges used i n i n d u s t r i a l p r a c t i c e . -C e r t a i n u n i f o r m i t i e s i n t h e s e v a r i a b l e s were a t t a i n e d f o r v a l i d a t i o n o f t h e s t r e n g t h comparisons. The a n a l y s i s p r e s e n t e d i n t h i s r e s e a r c h l e a v e s c h a l l e n g e s t o equipment d e s i g n e r s and f o r e s t p r o d u c t s m a n u f a c t u r e r s t o make 136 more s t r e n g t h e f f i c i e n t and p r o f i t a b l e wood s t r a n d c o m p o s i t e s . 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A l i t e r a t u r e s u r v e y o f populus s p e c i e s w i t h emphasis on P. t r e m u l o i d e s . F o r e s t Prod. Lab. Rpt. No.0180, Madison. 65 pp. 74. R a u t a k o r p i , H. 1971. An a n a l y s i s o f c o n s t r u c t i o n a l plywood. The S t a t e I n s t i t u t e F o r T e c h n i c a l Res., J u l k a i s u F i n l a n d P u b l i c a t i o n . 165 64 pp. 75. Samson, M. 1984. Measuring g e n e r a l s l o p e of g r a i n w i t h t h e s l o p e o f g r a i n i n d i c a t o r . F o r e s t Prod. J . 3 4 ( 7 ) : 27-32. 76. Schniewind, A.P. and T. Ohgama, T. H o k i , T. Yamada. 1982. The e f f e c t of s p e c i f i c g r a v i t y , m o i s t u r e c o n t e n t and temperature on f r a c t u r e toughness of wood. Wood Sc. 15 (2 ) : 101-109. 77. S c h u l e r , A.T. 1982. Resource p o t e n t i a l f o r w a f e r b o a r d p r o d u c t i o n i n Canada. Canadian Waferboard Symp. F o r i n t e k . SP508E: 179-185. 78. Scop, P. and A. Argon, 1967. S t a t i s t i c a l t h e o r y o f l a m i n a t e d composites. J . Composite M a t e r i a l s ( 1 ) : 92-99. 79. Simpson, W. 1977. Model f o r t e n s i l e s t r e n g t h o f o r i e n t e d f l a k e b o a r d . Wood S c i . 1 0 ( 2 ) : 68-71. 80. Singh, T . 1987. Wood d e n s i t y v a r i a t i o n i n t h i r t e e n Canadian t r e e s p e c i e s . Wood and F i b e r Sc. 1 9(4): 3 6 2 - 3 6 9 . 81 . Stamm, A . J . 1964. Wood and C e l l u l o s e S c i e n c e , R o n a l d P r e s s , New York. 549 pp. 82 . Stegmann, G. and J . D u r s t . 1965. P a r t i c l e b o a r d frOm beech wood. H o l z - Z e n t r a b l . 9 0(153): 313-318. 143 83. S t e i n e r , P.R. L.A. Jozsa, M.L. Parker, and S. Chow. 1978. A p p l i c a t i o n of x-ray densitometry to determine d e n s i t y p r o f i l e i n waferboard. Wood; Sc. 11(1): 48-55. 84. S t e i n e r , P.R., S. Chow and D. Nguyen. 1978. Improving m i l l wafer p r o p e r t i e s by x-ray densitometer e v a l u a t i o n methods. F o r e s t Prod. J . 28(12): 33-34. 85. Stephans, R.S. and N. Kutscha. 1987. E f f e c t of r e s i n molecular weight on bonding f l a k e b o a r d . Wood and F i b e r Sc. 19 (4) : 353-361. 86. Stevans R.R. 1978. S l i c i n g apparatus a i d s i n the determination of l a r g e r - d e n s i t y of p a r t i c l e b o a r d . F o r e s t Prod. J . 28(9): 51-55. 87. S t r i c k l e r , M.D. 1959. P r o p e r t i e s of D o u g l a s - f i r f l a k e b o a r d . F o r e s t Prod, J . 9(7): 203-215. 88. Suchsland, 0. 1960. An a n a l y s i s of the p a r t i c l e b o a r d process. Michigan Q u a r t e r l y B u l l e t i n , Dept. of F o r e s t Products, A r t i c l e 42-31, 42(2): 370-371 89. Suchsland, 0. 1959. The s t r e n g t h of glue j o i n t s i n wood obtained with minimum glue spread. Q u a r t e r l y B u l l e t i n , Mech. A g r i c . Expt. Sta., Mich. 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Some p o i n t s of o r g a n i z a t i o n w i t h i n growth zones of c o n i f e r o u s woods. F a c u l t y of F o r e s t r y p u b l i c a t i o n , Univ. of B.C., Vancouver. 15pp. 96. W i n i s t o r f e r , P.M. W.C. Davis, and W. Moscher. 1986. A d i r e c t scanning densitometer t o measure d e n s i t y p r o f i l e s i n wood composite products. F o r e s t Prod. J . 36 (11/12): 82-86. 144 97. Woodson, G.E. 1976. P r o p e r t i e s o f F i b e r b o a r d from Southern Hardwoods. PhD. T h e s i s , C o l o r a d o S t a t e U n i v . 126pp. 98. Y u r g a r t i s , S.W. 1987. Measurement of s m a l l a n g l e f i b e r m i s a l i g n m e n t s i n c o n t i n u o u s f i b e r c o m p o s i t e s . Composites S c i e n c e and Technology 4(30) 279-293. Appendix i STRENGTH 145 LIST 2 PRINT" CONTINUOUS STRAND NETWORK MODEL" 4 R E M Inputs are strand specific L and T strenqths,yielding output as composite specific strength OR strand L and T strengths which have been adjusted to the strength equivalent of the composite surface , 5 R £ M this option yields the fle:<ural M.O.R. estimate. 6 D I M X(200) : O I M RGC200) : DIM XP(200) 7 INPUT"longitudinal str. L";L: INPUT"transverse str. T";T:INPUT"ori entati on par ameter,k";K B PRINT "longitudinal str. L-";L,"transverse str. T»";T,"orientation k-";K :FRIN T" " 9 Q-K/3.75:I-BJOPEN "AL.PRN" FOR OUTPUT AS * 1 10 OPEN "GAL.PRN" F O R OUTPUT AS #2 11 REM I°Bessel function 12 IF K<-3.75,THEN I-1+3.5I562*Q*Q+3.08994*(Q~4)+1.20674*(Q~6>tGOTO 20 15 Q-l/Q :1-0 iFl-0 16 I-<EXP (K)/SQR(K) )*(. 39894+(.01329*Q>+.00225*(Q*Q)-.00158*(Q*Q*Q)) 18 I-I+(EXP (K)/SQR(K>>*(.00916*(Q~4)-.02058*(Q~5)+.02635*<Q'-6)-.01647*(Q~7>) 20 W-l/(3.14139265**1) 22 PRINT"angle deg. von Mises p.d.f." 25 FOR N«=0 TO 20: M-(1.570796327H/20>*N 99 REM Simpsons Rule integration 100 D-0:E-3.14159265HtF«50 120 B-(E-D)/2/F 130 A-0:X-D:G0SUB 500 140 A-Y+AjX-X+B:G0SUB 500 150 A-Y*4+AtX-X+B:G0SUB 500 160 A-Y+A:F-F-1 170 IF FOB GOTO 140 180 C-A*B/3 182 C-W»C 185 IF N-0.THEN GOSUB 600 188 M-M*57.29577931» 190 PRINT C,MiWRITE *1,AL,C,M 198 NEXT N 500 G-(EXP(K*C0S(2*(X-M>>)>tRG-G«W 501 IF N-0.THEN X(Fl)-XiR6(Fl)-RB:Fl-Fl+l 502 Z-SIN(X) 305 H-L/(1+(L/T-1>*Z*Z> 508 Y-G#H 510 RETURN 600 Ml-50 610 FOR NX-0 TO Ml 620 XP(NX>-(X(NX)-1.5707963H)«90/1.5707963H tNG-Ml-NX 630 PRINT XP(NX),RG(NQ):WRITE #2,GAL,XP(NX),RG(NG) 640 NEXT NX 650 Ml-50 660 FOR NX-0 TO Ml 670 XP(NX)-X(NX)»90/1.3707963* 680 PRINT XP(NX),RG(NX>tWRITE #2,GAL,XP(NX),RG(NX) 690 NEXT NX 691 PRINT" " iPRINT" model 1o*d"iPRINT"composite s t r . angle deg." 700 RETURN 701 REM This program f i l e s the p . d . f o u t p u t < a s Ci\DOS\GAL.PRN and s t r e n g t h output as C:\D0S\AL.PRN f o r f i l e import t o LOTUS or other g r a p h i c s . 0 146 Appendix i i ELASTICITY LIST 1 PR I NT"FLEXURAL ELASTICITY OF WOOD STRAND NETWORK:PARAROLIC DENSITY GRADIENT" 2 PR INT"The von Mises p.d.f. concentration paraineter,k, characterizes the orientation" 3 DIM X(200):DIM RG(200):DIM XP(200):DIM C(30):DIM M(30) 4 PRiNT"lnput3 are elastic constants for an uncompressed strand layer,un1ts In MPa.":PRINT "Strands assumed transversely Isotropic in the cross grain dire ctlon" 5 INPUT"paralle1 grain MOE";EPA:INPUT"transverse grain MOE";EPE:INPUT "parallel shear modu1 us";S:INPUT"para 11e1 grain poissons ratio";P 6 PRINT" parallel grain MOE.";EPA,"transverse grain MOE.";EPF," parallel shear modulus";S,"paralle1-transverse poissons ";P 7 INPUT"strand orientation k parameter";K 8 PRINT "strand population orientation pa r a me t e r,k";K 9 Q = K/3 . 75 : 1 = 0 :OPEN "AL.PRN" FOR OUTPUT AS It 1 10 OPEN "GAL.PRN" FOR OUTPUT AS V 2 12 IF K<=3.75,THEN I = 1 +3.51562*Q*Q + 3.08994 *(Q"4)+1 .20674 *(Q"6) :GOTO 20 15 Q=l/Q :1=0 :F1=0 16 I = (EXP (K )/SQR(K ))*(. 39894+ (.01329*0) »• .00225*(Q*Q )-. 00158 * < Q*Q*Q ) ) 18 I=H-(EXP (K)/SQR(K))*( .00916*(Q"4)-.02058*(Q*5)+.02635*(Q"6)-.0164 7*<Q*7)) 20 W=1/( 3.14159265»*I ) 21 PRINT"Composite E ,wlthout correction for the parabolic density gradient is output at 4.5 degree intervals of loading anqle." . 25 FOR N=0 TO 20:M=(1.570796327#/20)*N 100 D=0:E=3.14159265»:F=10 120 B=(E-D)/2/F 130 A=0:X=D:GOSUB 500 140 A=Y+A:X=X+B:GOSUB 500 150 A=Y*4+A:X=X+B:GOSUB 500 160 A=Y+A:F=F-1 170 IF FO0 GOTO 140 180 C=A*B/3 182 C=W*C:C(N)=C 188 M=M*57.2957795111 :M(N)=M 190 PRINT N,C,M 198 NEXT N 200 GOTO 705 500 G=(EXP(K*COS(2*(X-M)))):RG=G*W 501 REM To view pdf,type line 501 if n=0,then print x ,rg 502 Z=(SIN(X))*(SIN(X) ) : ZZ = (COS(X) ) *(COS(X)) 505 H = l/((ZZ*ZZ/EPA)+ (Z*Z/EPE)+ ((l/S)-(2*P/EPA))*Z*ZZ ) 508 Y=G*H 510 RETURN 705 INPUT"centre density,g/cm3";DC 707 lNPUT"uncompressed strand density,g/cm3";DS:INPUT"tota1 composite thickness, mm";TB 710 INPUT"nearest odd number of gradient strands in total thickness";NL 712 PRINT "uncompressed strand density g/cm3";DS,"total composite thickness,mm"; TB 713 PRINT "nearest even number of strands in total thickness";NI.+l :TH=TB/(NL+1 ) 147 714 DIM t.( 100) : DIM DF(100):DIM E1I(30):DIM EFF(3Q):DIM Y(100) 715 PRINT "average t h i c k n e s s of a t r a n d j ,mm" : TH 716 INPUT "shape constant (focus) of p a r a b o l i c d e n s i t y g r a d i e n t " ; C F 717 HEM As CF i n c r e a s e s from j u s t above the value of the c e n t r e d e n s i t y , i t y i e l d s d e c r e a s i n g E and decreasing average d e n s i t y i n the composite. 7113 NL2-NL/2: SU~0 720 FOR L- 0 TO Nl_ 723 Y (L)-((NL2--L)^2)/5B/CF+DC:PRINT"pressed s t r a n d d e n s i t y was"; Y(L> : DF(L)-Y(L> /DS:-SIJ"SU*Y'(L) : WRITE »2,L,Y(L) 732 PRINT " f o r lamina number,"(L,"with packing densi f i c a t i o n f ac tor";DF(L) 735 NEXT L 736 PRINT". " : PRINT"centre density,g/cm3";DC 737 PR INT"surface density,y/cm3";Y(Q> 730 AD^SU/ (NL+1):PR I NT"average density,g/cm3";AD:PRINT" " 739 PRINT-Lo^d Anrjl* Ef f . FI ex . E , MPa 740 FOR N2-U TO 20 745 FOR L.-I3 TO NL 746 REM P a r a l l e l a x i s theorem,with e l a s t i c i t y weighted f a r density(df(1)»c(n2)) 747 EI I "EI I + DF (L) *C (N2) * ( ( ( (NL+l-L) *TH)~3) - ( (NL-L) *TM> ~3> / 12 750 NEXT L 755 EI I(N2)-EI I 760 (TB)-^)/12 765 EFF(N2)-EII'.N2)/IA 770 PRINT M(N2>,EFF(N2):WRITE *1,M(N2),EFF(N2) " 772 EII-0 773 NEXT N2 780 END Appendix i i i 148 S p e c i f i c S t r e n g t h H i s t o g r a m , . A l 1 S p e c i e s of S t r a n d s 60 • 50 40-30 20-10 X ax i s u n i t s i n MPa Z e r o s p a n C.D.F. p a r a l l e l t o g r a i n *XXXXX>] 30 Mean = Standard D e v i a t i o n 180 160.54 Uariance = 2647 51.45 Skeuness = .5314 230 280 330 S p e c i f i c Strength Histogram , Cedar Strands he an = Standard Deviation s 10.795 Uariance = 20.56 4.534 Skeuness = .6362 A p p e n d i x i v 149 birch 0.42 cm A 0.15 era •1 . J t t«- 1.27 era 9.0 cm MICROTEHSILE SPECIMENS 1 aspen cedar alder }-*-pine J _0.42 cm 6.0 cm-2.0 to 3.0 cm 1 COMPOSITE SPECIMENS U< 43 cm ->|i.5 cmj TENSILE ~T SPECIMENS 1 3.8 cm 25.5 cm t-L 5.1 cm FLEXURAL SPECIMENS _ A 5.0 cm h* 18 cm 

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