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Analysis of fillet function in wood-based sandwich construction Kaneko, Tatsuhei 1972

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ANALYSIS OF FILLET FUNCTION IN WOOD-BASED SANDWICH CONSTRUCTION .  by  TATSUHEI KANEKO B.Sc.  ( F o r . ) , Hokkaido U n i v e r s i t y , 1960  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS. FOR THE DEGREE OF MASTER OF FORESTRY i n t h e Department of Forestry 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 required standard  THE UNIVERSITY OF BRITISH COLUMBIA J a n u a r y , 1972  In p r e s e n t i n g t h i s t h e s i s  in p a r t i a l  fulfilment  o f the  requirements  an advanced degree at 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 , the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r I further  reference  I agree t h a t and s t u d y .  agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s  thesis  f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department by h i s r e p r e s e n t a t i v e s . of  It  this thesis for financial  or  i s understood that copying or p u b l i c a t i o n gain s h a l l  written permission.  Department The U n i v e r s i t y o f B r i t i s h Vancouver 8, Canada  for  Columbia  not be a l l o w e d w i t h o u t my  ABSTRACT  When a porous honeycomb c o r e i s g l u e d t o p l a n e f a c i n g s t o make a sandwich c o n s t r u c t i o n , g l u e  fillets  (concave m e n i s c i ) are formed around the c o r e c e l l edges. It  i s known t h a t g l u e  strengthening  fillets  p l a y an i m p o r t a n t r o l e i n  the bond o f the c o n s t r u c t i o n , b u t o n l y  few  s t u d i e s on the r e a l f u n c t i o n o f the f i l l e t have been reported.  T h i s t h e s i s i n v e s t i g a t e s the r e l a t i o n s h i p s  between f i l l e t  s i z e and b o n d i n g s t r e n g t h i n sandwich con-  s t r u c t i o n f o l l o w e d by a s t r e s s a n a l y s i s o f t h e Sandwich p a n e l s w i t h v a r i o u s  fillet  fillets.  s i z e s were  produced by means o f a g l u e a p p l i c a t o r o f o r i g i n a l using a modified  phenol-resorcinol  design  r e s i n g l u e , k r a f t paper  honeycomb c o r e s and Douglas f i r plywood f a c i n g s .  Tensile  s t r e n g t h t e s t s normal t o t h e sandwich specimens o f 1 by i n c h , and  f l e x u r e t e s t s on the sandwich beams o f 3.75  i n c h e s were p e r f o r m e d .  F i l l e t rupture  s i z e s and  by  1 12  actual  f i l l e t d i m e n s i o n s were measured. A h i g h l y s i g n i f i c a n t c o r r e l a t i o n was fillet  s i z e and b o n d i n g s t r e n g t h .  g r e a t e r bonding s t r e n g t h .  Larger  found between  fillets  When a sandwich was  provided  subjected  t e n s i l e l o a d , a v e r t i c a l s h e a r f a i l u r e took p l a c e at c e n t e r of the f i l l e t  concave meniscus r e g a r d l e s s  of  to  the fillet  size.  By assuming the u n i f o r m i t y  of f i l l e t  shape, the  following equation: x was  B  =  B  a t the  y a t B, where m and  in  + d ,  found t o e x p r e s s the r e l a t i o n s h i p between the  shear s t r e s s x  had  my  f r a c t u r e p o i n t B and  d were c o n s t a n t s .  fillet  large  height  fillets  tendency t o form v o i d s o r b u b b l e s w i t h i n them r e s u l t i n g lowering The  strength  Most o f the  values.  appearance of f r a c t u r e i n the g l u e l i n e i n f l e x u r e  t e s t specimens was  s i m i l a r t o t h a t i n the t e n s i l e t e s t .  sandwich specimens w i t h  i n the g l u e l i n e , w h i l e f a i l e d i n core shear.  those with  plywood.  The  smaller  fillets  larger f i l l e t s  This observation  s u p e r i o r i t y of l a r g e r f i l l e t s  was  Too  the  vertical  failed  mostly  also indicated  the  i n b o n d i n g o f honeycomb-to-  cause o f g l u e l i n e f a i l u r e i n the  flexure test  deemed t o r e s u l t from a complex system o f s h e a r , compres-  s i o n and  tensile stresses.  However, a m a t h e m a t i c a l e x p r e s s i o n  d e s c r i b i n g t h a t system o f s t r e s s e s was  not  found.  iv  TABLE OF CONTENTS Page ABSTRACT  i i  TABLE OF CONTENTS  iv  LIST OF TABLES  v i i  LIST OF FIGURES  viii  ACKNOWLEDGEMENTS  ...  X  INTRODUCTION  1  LITERATURE REVIEW  7  MATERIALS AND METHODS Construction  15  o f Glue A p p l i c a t o r  15  Materials  19  P r e p a r a t i o n o f Sandwich P a n e l s  21  T e n s i l e T e s t Specimen and T e s t P r o c e d u r e  . . . .  23  F l e x u r e T e s t Specimen and T e s t P r o c e d u r e  . . . .  26  RESULTS AND ANALYSIS OF DATA  30  T e n s i l e Test 1.  3 0  F i l l e t H e i g h t and F i l l e t Relationship  2.  F i l l e t H e i g h t and T e n s i l e Relationship  3.  F i l l e t Width and T e n s i l e Relationship  4.  Deflection at Fracture Strength R e l a t i o n s h i p  Width 31 Strength Strength  33 35  and T e n s i l e 37  5.  F a c i n g F a i l u r e and T e n s i l e Relationship  Strength  6.  F i l l e t H e i g h t and D e f l e c t i o n a t Fracture Relationship  40 40  V  Page 41  F l e x u r e Test 1.  F i l l e t H e i g h t and F i l l e t Relationship  2.  F i l l e t H e i g h t and Shear S t r e n g t h Relationship  47  F i l l e t Width and Shear S t r e n g t h Relationship  49  D e f l e c t i o n a t F r a c t u r e and Shear Strength Relationship  51  3. 4. 5.  Width  44  F i l l e t H e i g h t and D e f l e c t i o n Relationship  DISCUSSION  51 54  F i l l e t Geometry  54  Tensile Strength  59  Shear S t r e n g t h  65  SUMMARY AND CONCLUSION  68  BIBLIOGRAPHY  VI  TABLES  74  APPENDICES  92  1 - T a b l e s o f A n a l y s i s o f V a r i a n c e and Duncan's New M u l t i p l e Range T e s t f o r F i l l e t Width Means i n T e n s i l e T e s t Specimens 2 - T a b l e s o f A n a l y s i s o f V a r i a n c e and Duncan's New M u l t i p l e Range T e s t f o r T e n s i l e S t r e n g t h Means i n T e n s i l e T e s t Specimens .  94  3 - Basic Equations  95  4 - T a b l e s o f A n a l y s i s o f V a r i a n c e and Duncan's New M u l t i p l e Range T e s t f o r F i l l e t Width Means i n F l e x u r e T e s t Specimens . . . . . . .  97  5 - T a b l e s o f A n a l y s i s o f V a r i a n c e and Duncan's New M u l t i p l e Range T e s t f o r Shear S t r e n g t h Means i n F l e x u r e T e s t Specimens .  98  93  vi Page 6 - T a b l e s o f A n a l y s i s o f V a r i a n c e and Duncan's New M u l t i p l e Range T e s t f o r D e f l e c t i o n Means i n F l e x u r e T e s t Specimens 7 - Sequences o f F i l l e t Width Means 8 - V a l u e s o f k/m Groups  f o r t h e Four F i l l e t  9 - Core Shear S t r e s s under Loading  99 1 0 0  Height 100  Two-Point 101  vii  LIST OF TABLES Table 1.  Page P a r t i a l Results of P r e l i m i n a r y Test for Determination of Loading System  2.  Results of T e n s i l e Test f o r F i l l e t  3.  H e i g h t Group [0.5] Results of T e n s i l e Test f o r F i l l e t H e i g h t Group [1.0]  4. 5. 6. 7. 8.  9. 10. 11. 12. 13. 14. 15.  75  7  6  77  Results of T e n s i l e Test f o r F i l l e t H e i g h t Group [1.5]  78  Results of Tensile Test f o r F i l l e t H e i g h t Group [2.0]  79  Glue Depth and F i l l e t H e i g h t i n T e n s i l e T e s t Specimens  80  F r a c t u r e / F i l l e t - W i d t h Ratio i n Selected T e n s i l e T e s t Specimens  81  A u x i l i a r y Table f o r S t a t i s t i c a l A n a l y s i s of T e n s i l e Test Results (A)  82  A u x i l i a r y Table f o r S t a t i s t i c a l A n a l y s i s of T e n s i l e Test Results - ( B )  84  Results of Flexure Test f o r F i l l e t H e i g h t Group [0.5]  85  Results of Flexure Test f o r F i l l e t H e i g h t Group [1.0]  86  Results of Flexure Test f o r F i l l e t H e i g h t Group [1.5]  87  Results of Flexure Test f o r F i l l e t H e i g h t Group [2.0]  88  Fracture/Fillet-Width Ratio i n S e l e c t e d F l e x u r e T e s t Specimens  89  A u x i l i a r y Table f o r S t a t i s t i c a l A n a l y s i s of Flexure Test R e s u l t s .  90  viii  LIST OF FIGURES Figure  Page  1.  Fillets  . .  2.  Stress Concentration  6  Factors i n  Tension  12  3.  Glue A p p l i c a t o r - Base P l a t e  17  4.  Glue A p p l i c a t o r - F o u r D o c t o r B l a d e s  18  5.  K r a f t Paper Honeycomb  20  6.  D i m e n s i o n a l Nomenclature o f Expanded Honeycomb T e n s i l e T e s t Specimen i n L o a d i n g  22  Fixture  24  8.  Honeycomb C e l l S e c t i o n  26  9.  Apparatus f o r Conducting Flexure o f Sandwich C o n s t r u c t i o n F i l l e t H e i g h t and F i l l e t Width R e l a t i o n s h i p i n T e n s i l e Test Specimens  7.  10. 11. 12. 13. 14. 15.  16. 17.  F i l l e t H e i g h t and T e n s i l e Relationship F i l l e t Width and T e n s i l e Relationship Tensile Strength Relationship  Test 28 34  Strength 36 Strength 38  and D e f l e c t i o n  Selected Load-Deflection i n Flexure Tests  39 Curves 42  F i l l e t H e i g h t and F i l l e t Width Relationship i n Flexure Test Specimens  45  F i l l e t H e i g h t and Shear Relationship  48  F i l l e t Width and Shear Relationship  Strength Strength 50  ix Figure  Page  18.  F i l l e t H e i g h t and D e f l e c t i o n R e l a t i o n s h i p i n F l e x u r e T e s t Specimens  19.  D i m e n s i o n a l Nomenclature on F i l l e t S e c t i o n and Shear S t r e s s D i s t r i b u t i o n  53 ....  58  X  ACKNOWLEDGEMENTS  The  A u t h o r w i s h e s t o thank t h e f o l l o w i n g p e o p l e :  Mr.  L. V a l g , A s s i s t a n t P r o f e s s o r , F a c u l t y o f  F o r e s t r y , the U n i v e r s i t y of B r i t i s h Columbia, f o r h i s s u g g e s t i o n s t h r o u g h o u t t h e e x p e r i m e n t and g r e a t h e l p i n t h e preparation  of the manuscript.  Dr. N.C. F r a n z , P r o f e s s o r o f t h e F a c u l t y o f F o r e s t r y a t the U n i v e r s i t y o f B r i t i s h Columbia, f o r h i s needed a d v i c e  and c r i t i c i s m w h i c h improved t h e q u a l i t y o f  this thesis. Dr.  R.W. Wellwood, P r o f e s s o r o f t h e F a c u l t y o f  Forestry at the U n i v e r s i t y o f B r i t i s h Columbia,for a s s i s t a n c e i n a l l my s t u d i e s o v e r t h e p a s t two y e a r s . Mr.  L. Adamovich, A s s o c i a t e  Professor of the Faculty  of F o r e s t r y a t the U n i v e r s i t y o f B r i t i s h Columbia, f o r reading  and c o r r e c t i n g t h e m a n u s c r i p t from t h e v i e w p o i n t  o f an e n g i n e e r . The  author i s a l s o indebted  understanding, patience  to his wife for her  and encouragement d u r i n g t h e  compilation of this thesis.  INTRODUCTION  A laminated  c o n s t r u c t i o n w h i c h c o n s i s t s o f two f a c i n g s  o r c o v e r s and a c o r e i s g e n e r a l l y r e f e r r e d t o as a sandwich construction.  The s a n d w i c h - p a n e l c o n s t r u c t i o n t h a t i s a  l a m i n a t i o n o f two t h i n f a c i n g s w i t h a t h i c k c o r e and d e s i g n e d to give a high strength-weight sandwich c o n s t r u c t i o n .  ratio i s called a structural  According  t o the Standard of the  A m e r i c a n S o c i e t y f o r T e s t i n g and M a t e r i a l s sandwich c o n s t r u c t i o n i s d e f i n e d a s : comprising  (5),  "A l a m i n a r  a combination of a l t e r n a t i n g  a  structural  construction  dissimilar  simple  o r composite m a t e r i a l s assembled and i n t i m a t e l y f i x e d i n r e l a t i o n t o each o t h e r  so as t o use t h e p r o p e r t i e s o f each  t o a t t a i n s p e c i f i c s t r u c t u r a l advantages f o r t h e whole assembly." The  s t r u c t u r a l design  o f sandwich c o n s t r u c t i o n may  be compared t o an I-beam i n which f l a n g e s c a r r y c o m p r e s s i v e and t e n s i l e l o a d s , w h i l e t h e web c a r r i e s shear l o a d s when the beam i s s u b j e c t e d  t o a b e n d i n g moment  (25, 3 9 ) .  In  s t r u c t u r a l sandwich c o n s t r u c t i o n s t h e f a c i n g s c o r r e s p o n d t o the f l a n g e s o f t h e I-beam, w h i l e t h e c o r e f u n c t i o n s as t h e web. Not purposes.  a l l sandwich p a n e l s a r e used f o r s t r u c t u r a l Some a r e s i m p l y d e s i g n e d t o a c t as t h e r m a l o r  a c o u s t i c a l b a r r i e r s , while others  may be i n t e n d e d f o r  2 weather s h i e l d s o r f i r e w a l l s  (21).  The major  properties  o f a sandwich p a n e l a r e d e t e r m i n e d by the c o m b i n a t i o n o f the f a c i n g and c o r e m a t e r i a l s .  I n o t h e r words, the c h o i c e o f  t h e f a c i n g and c o r e m a t e r i a l s f o r a s a n d w i c h - p a n e l c o n s t r u c t i o n depends upon the purpose o f the p a n e l use. Wood-based sandwich c o n s t r u c t i o n s have found a wide use i n house and b u i l d i n g c o n s t r u c t i o n s t a k i n g  advantage  o f good i n s u l a t i o n c h a r a c t e r i s t i c s , r e l a t i v e l y low c o s t and easy p r o c e s s i n g (22).  Plywood, v e n e e r , h a r d b o a r d  paperboard are s u i t a b l e f o r the f a c i n g s .  Balsawood,  and paper  honeycomb, f i b r e b o a r d and wood e x c e l s i o r b o a r d have been used as t h e c o r e m a t e r i a l s .  V a r i o u s c o m b i n a t i o n s o f wood-  based and non-wood-based m a t e r i a l s , o r c o m b i n a t i o n s o f two d i f f e r e n t wood-based m a t e r i a l s can produce e i t h e r o r n o n - s t r u c t u r a l sandwich  structural  constructions.  I n any s a n d w i c h - p a n e l c o n s t r u c t i o n , the f a c i n g must be a t t a c h e d t o t h e c o r e by means o f b o n d i n g o r o t h e r s u i t a b l e methods.  I f t h e j o i n t between t h e c o r e and t h e f a c i n g s h o u l d  s e p a r a t e , the p a n e l i s u s e l e s s .  A strong joint i s p a r t i c u l a r l y  i m p o r t a n t f o r a s t r u c t u r a l sandwich c o n s t r u c t i o n i n w h i c h t h e j o i n t must s u s t a i n a p p r o x i m a t e l y t h e same s h e a r s t r e s s as t h e c o r e .  W h i l e s o l d e r i n g , b r a z i n g and w e l d i n g are  a p p l i c a b l e t o produce a l l - m e t a l sandwiches  of e x c e p t i o n a l  s t r e n g t h and h e a t r e s i s t a n c e , a d h e s i v e b o n d i n g i s a d a p t a b l e t o almost any c o m b i n a t i o n s o f m a t e r i a l s . development  In f a c t , t h e  o f s t r u c t u r a l sandwich c o n s t r u c t i o n may  be  3 credited after  t o the rapid  Extensive  (1).  The  towards and  Forest  primary  published sandwich  a  geometry  (16/ large  with  26,  fillet,  rather  or glue  i s filling facing with  core  but only  may  The  of core  such  new  that  publications  the  glueline  be  size  use o f a  Under  a  as:  the glue  such  "fillet."  cell  foamed  of open-celled  and  fillet used.  pores  rubbers,  A  body  wall  and t h e a d h e s i v e small  have  glue-  form  the core  implies  The  given  and shape o f a  cell  as b a l s a ,  (11).  t h e most e f f i c i e n t  defined  con-  geometry might  adhesives.  should  context,  as c e l l s  has  on s t r u c t u r a l  attention  of glueline  the corner between  i n this  aircraft  geometry i n a sandwich  of efficient  found  1).  to  Laboratory  a few o f t h e  construction  the type  as w e l l  The  directed  strength.  inventing  fillet,  exclusively  was  construction  30).  of  f o rt h e p a s t two decades  studies  some r e s e a r c h e r s '  i t was  cores,  almost  number o f t e c h n i c a l p a p e r s  than  (Figure  cell,  continuous  28,  the g l u e l i n e  i n a sandwich  resins,  of these  of the importance  circumstances,  The  17,  from the p r a c t i c e s  adhesive  varies  objective  has drawn  recognition  the  Products Laboratory  and t h e b o n d i n g  struction  that  undertaken  the r e l a t i o n s h i p s between  Recently,  line  have been  construction,  have d e a l t  technology  on t h e s t r u c t u r a l p r o p e r t i e s  the a p p l i c a t i o n o f sandwich  missiles  arisen  studies  construction  b y t h e U.S.  i n the adhesive  II.  W o r l d War  sandwich  advancement  of  and  or gridded  foamed  type  4 cores  such  as  The the  fillet  terms  of  fillet paper  honeycomb  main  relationship  size,  and  honeycomb  uniformity fillet  it  has  of  and  several  the  fillet  with  glue  to  but  sample a  In strength,  would  was  Those  were  Sandwich C297-61)"  to  of  the  and  sets  test  "Flexure  as  only  between  room  filleting  of  of  core  and  flow  because  one  filleting  of  kind  Tension  Flat The  former  strength facings  of  which  of  70°F.  were  Test  of  called Flat  Designation:  Constructions  covers  in tension an  study.  bonding  (ASTM  Sandwich  great  adhesive,  adhesive  on  one  effects  this of  methods  Plane  of  i n comparing  temperatures  of  character-  application  scope  effects  in Flatwise  the  measurement  variable of  testing  Method  C393-62)."  the  glue  a  immediate  employed  for determining  bond  upon  comparison  at  Test  kraft  since i t s  facings  difficulties  made w i t h  "Standard  (ASTM D e s i g n a t i o n : procedure  f o r the  phenol-resorcinol resin  Constructions and  material  c o n d i t i o n s , the  the  purpose,  simplifies  i s recognized  commonly  were  core  depends  The  beyond  this  or  applications.  induce  another.  handle  two  the  chosen  surrounding  order  For  was  shape  analyse  geometry,  Plywood  fillet  to  glueline  size  construction  be  construction in  strength. for  will  sandwich  and  panels  to  thesis  shape  modified  easy  this  between  chosen  variations  interest,  for.  cell  adhesives  glue  was  was  practical  istics  namely  bonding  size.  Since  The  objective of  f u n c t i o n i n wood-based  the  of  (8).  the flatwise  assembled  sandwich  5  panel.  The e x p r e s s i o n , " t e n s i o n f l a t w i s e , " means t e n s i o n  normal t o the p l a n e o f t h e sandwich  (8).  The  l a t t e r covers  a procedure f o r determining p r o p e r t i e s of f l a t  sandwich  c o n s t r u c t i o n s s u b j e c t e d t o f l a t w i s e f l e x u r e i n such a manner t h a t the a p p l i e d moments produce c u r v a t u r e o f the p l a n e o f a s h e e t o f the sandwich c o n s t r u c t i o n .  T h i s t e s t may  be  p r i m a r i l y conducted t o d e t e r m i n e f l e x u r a l and s h e a r modulus, and s h e a r s t r e n g t h o f the c o r e , or c o m p r e s s i v e o r t e n s i l e s t r e n g t h of the f a c i n g s . s h e a r s t r e n g t h may  However, the t e s t t o e v a l u a t e c o r e  also evaluate  bonds between c o r e and  f a c i n g s inasmuch as c o r e shear s t r e s s v a l u e s may  be  lower  t h a n a c t u a l c o r e s h e a r s t r e n g t h , thus i n d i c a t i n g t h a t i n i t i a t e d i n the bond  (4).  failure  Fillet  height,  X  =  Fillet  Figure  1.  width, Fillets  t  = Honeycomb thickness  wall  7  LITERATURE REVIEW  Hundreds o f p u b l i c a t i o n s on sandwich c o n s t r u c t i o n have been i s s u e d , m o s t l y by t h e U.S. d u r i n g the p a s t q u a r t e r c e n t u r y 38, 4 2 ) . sandwich  Department o f A g r i c u l t u r e ,  (16, 17, 24, 26, 27, 28,  These p u b l i c a t i o n s cover almost a l l a s p e c t s  on  c o n s t r u c t i o n i n c l u d i n g t h e problems o f a d h e s i v e s ,  c o r e s and t e s t i n g methods as fundamental properties.  s t u d i e s on  mechanical  In t h e s e s e r i e s o f p u b l i c a t i o n s , however, n o t h i n g  has been mentioned about f i l l e t  e f f e c t s i n bonding  m a t e r i a l l i k e a honeycomb core t o a n o t h e r  a porous  material.  I t i s not c l e a r when importance o f f i l l e t was r e c o g n i z e d , but i t seems t h a t t h e problem was originally (10),  30,  i n t h e sandwich  answering  panel i n d u s t r y .  first  brought I n 1957,  up Manning  a q u e s t i o n about a p p l i c a t i o n methods o f  c o n t a c t t y p e a d h e s i v e s , mentioned from h i s e x p e r i e n c e t h a t he would p r e f e r a s p r a y a p p l i c a t i o n t o the r o l l e r c o a t f o r t h e purpose o f b u i l d i n g up a f i l l e t honeycomb c o r e .  A l t h o u g h i t was  not d e s c r i b e d why  a p p l i c a t i o n b u i l t up a b e t t e r f i l l e t what the f i l l e t was  on t h e t o p edge o f t h e a spray  than a r o l l e r c o a t  l i k e , he e x p l a i n e d t h a t f o r m a t i o n o f  and this  f i l l e t had a v e r y i m p o r t a n t f u n c t i o n o r r e q u i s i t e i n a d h e s i v e performance,  because i t i n c r e a s e d t h e a r e a o f c o n t a c t ,  particularly  when a c o n t a c t type g l u e was  used.  8  G a t h e r i n g d a t a on sandwich  c o n s t r u c t i o n , Humke (20)  p r e s e n t e d a s e l e c t i o n guide f o r sandwich  panel m a t e r i a l s , i n  w h i c h he p o i n t e d o u t t h a t e p o x i e s and v i n y l b u t y r a l p h e n o l i c a d h e s i v e s had s e l f - f i l l e t i n g  c h a r a c t e r i s t i c s , while elastomer  m o d i f i e d p h e n o l i c , neoprene-rubber  base,  nitrile-rubber  base and p o l y v i n y l a c e t a t e a d h e s i v e s had no s e l f - f i l l e t i n g properties.  He d e s c r i b e d t h a t s e l f - f i l l e t i n g  e x t r e m e l y i m p o r t a n t i n honeycomb s a n d w i c h ,  o r b e a d i n g was  f o r t h e bead  t h a t c l u n g t o t h e edge o f each c e l l f l o w e d i n t o a f i r m  double  f i l l e t when t h e f a c i n g was p r e s s e d i n p l a c e , r e s u l t i n g i n added bond a r e a and a s t r o n g e r s t r u c t u r e . A f u r t h e r d i s c u s s i o n about t h e i m p o r t a n c e o f f i l l e t ing  was p r e s e n t e d by Houwink and Salmon ( 1 9 ) .  " I n t h e most  common c a s e , we have a t h i n f o i l edge, 0.0 3 mm., angles t o cover p l a t e . 1/200  T h i s c o r e f o i l edge r e p r e s e n t s o n l y  o f t h e t o t a l f a c i n g m a t e r i a l a r e a , y e t must r e s i s t t h e  same shear s t r e s s e s as t h e c o r e . for  at right  The most e f f i c i e n t  t h i s a p p l i c a t i o n form a f i l l e t ,  a concave  adhesives  meniscus,  between t h e f a c e s h e e t and t h e honeycomb c e l l w a l l .  Such  a d h e s i v e s become l i q u i d i n t h e c u r i n g o p e r a t i o n , form t h e fillet  by c a p i l l a r y a c t i o n , and p r o c e e d t o cure t o a s o l i d  state.  Those a d h e s i v e s w h i c h do n o t begome t r u l y f l o w a b l e  d u r i n g c u r i n g , a r e p l a c e d i n a s o l v e n t s o l u t i o n , and r o l l e r c o a t e d , d i p p e d , o r s p r a y e d onto t h e c o r e t o a i d f o r m a t i o n of  fillets."  9  R e c e n t l y , D i e t z (12) suggested t h a t i t was  prefer-  a b l e t o c o a t the i n n e r s i d e of plywood f a c e s w i t h g l u e i n a d d i t i o n t o a p p l y i n g g l u e t o the c o r e f o r b e s t r e s u l t s i n b o n d i n g honeycomb c o r e t o plywood s k i n .  He a l s o  proposed  t h a t i t was w i s e t o c o a t the plywood v e r y l i g h t l y and t o a p p l y most o f the a d h e s i v e t o the core b o t h f o r economic r e a s o n s and i n o r d e r t o save w e i g h t . D i e t z , t h e e f f i c i e n t way  This i s , according to  o f making a good f i l l e t w i t h t h e  minimum amount o f a d h e s i v e . Grimes (15) s t u d i e d t h e e f f e c t o f f i l l e t i n g on t h e core p r o p e r t i e s .  F i r s t , he made a comparison  between  two  d i f f e r e n t a d h e s i v e s on t h e shear s t r e n g t h s o f s m a l l and medium f i l l e t s .  The  small f i l l e t  (0.09 l b s . per  f o o t ) o f m o d i f i e d epoxy a d h e s i v e gave the c o r e  square  less  " e f f e c t i v e s t r e n g t h " and " e f f e c t i v e s t i f f n e s s " t h a n t h e medium e p o x y - p h e n o l i c f i l l e t T h i s t y p e of c o m p a r i s o n ,  (0.135 l b s . per square  as he r e c o g n i z e d , may  foot).  be u n f a i r i n  t h a t i f t h e former a d h e s i v e were i n c r e a s e d i n w e i g h t t o t h a t o f the l a t t e r , i t might p o s s i b l y p r o v i d e as good o r better f i l l e t i n g  and c o r e p r o p e r t i e s .  Comparisons were  a l s o made f o r beam s h e a r , drum p e e l , and f l a t w i s e  tensile  s t r e n g t h s between two d i f f e r e n t a d h e s i v e w e i g h t s u s i n g t h e same a d h e s i v e .  I n e v e r y comparison  the i n c r e a s e of glue  weight r e s u l t e d i n the h i g h e r s t r e n g t h .  C o n d u c t i n g some  o t h e r e x p e r i m e n t s , he c o n f i r m e d t h a t the w e i g h t o f a d h e s i v e w i t h i n each t y p e was  not so i m p o r t a n t as the f i l l e t  size.  10 Grimes c o n c l u d e d t h a t the f i l l e t  s i z e was  the most i m p o r t a n t  p h y s i c a l f a c t o r i n o b t a i n i n g t h e maximum s t r e n g t h o f honeycomb c o r e s and sandwich As f o r t h e f i l l e t  properties  constructions.  s i z e and a c t u a l s t r e s s e s a t t h e  f i l l e t , Grimes assumed t h a t : (a)  stresses occur i n a plane perpendicular  t o the  cell  w a l l a t a p p r o x i m a t e l y i t s edge, (b)  t h a t the width of the f i l l e t  s t r e s s plane i s a  f u n c t i o n o f c e l l s i z e and f i l l e t (c)  size,  t h a t t h e l e n g t h of the f i l l e t p l a n e i s e q u a l t o b, the c e l l w a l l f l a t w i d t h ,  (d)  (e)  t h a t the f i l l e t  s t r e s s plane t o t a l width i s  (LF) l a r g e f i l l e t (MP) medium f i l l e t  r/2 r/3  (SF) small f i l l e t  r / 4 , and  t h a t the f i l l e t  s t r e s s p l a n e a r e a f o r each  flat  then becomes (LF);  A  = b r/2 = r t a n 30° = 0 . 5 7 7 r 2  f  2  (square i n c h ) (MF); (SF);  A A  = b r/3 = 0 . 3 8 4 r = b r/4 = 0 . 2 8 8 r , 2  f  2  where r i s the r a d i u s of the i n s c r i b e d c i r c l e o f a c e l l . According to h i s explanation  t h e f l a t w i s e t e n s i l e l o a d from  t h e c e l l w a l l t o the a d h e s i v e i s passed v i a s h e a r , and l o a d t h e n must be t r a n s m i t t e d t o t h e f a c e t h r o u g h fillet  p l a n e by  tension.  the  this  11 Timoshenko and G o o d i e r  (37) have shown t h e s t r e s s  d i s t r i b u t i o n pattern at the f i l l e t p h o t o e l a s t i c method.  o f a m e t a l p l a t e by t h e  Although the f i l l e t  t h e y showed was  not t h a t o f t h e g l u e l i n e i n sandwich c o n s t r u c t i o n , t h e f o l l o w i n g d i s c u s s i o n provides u s e f u l suggestions for the study o f f i l l e t  s i z e and f u n c t i o n .  These w o r k e r s c o n f i r m e d  t h a t t h e maximum s t r e s s o c c u r r e d a t t h e end o f a p l a t e o f two  d i f f e r e n t widths submitted t o c e n t r a l l y applied  tension.  The  r a t i o o f t h i s maximum s t r e s s t o t h e average s t r e s s i n  the n a r r o w e r p o r t i o n o f t h e p l a t e i s c a l l e d t h e " s t r e s s concentration fillet  factor."  t o the width d o f the p l a t e .  stress concentration given  I t depends on t h e r a d i u s R o f t h e  i n Figure  2.  f a c t o r obtained  Several values of the experimentally  (40) a r e  I t i s seen i n t h e f i g u r e t h a t t h e maximum  s t r e s s i s r a p i d l y i n c r e a s i n g as t h e r a t i o R/d i s d e c r e a s i n g . When R/d = 0.1 t h e maximum s t r e s s i s more t h a n t w i c e t h e average t e n s i l e s t r e s s . I n v e s t i g a t i n g t e n methods o f i n s p e c t i n g bonds between the c o r e s and f a c i n g s o f sandwich p a n e l s o f t h e a i r c r a f t t y p e , Heebink and Mohaupt (16) r e p o r t e d  t h a t none o f t h e  t e s t s i n v e s t i g a t e d p r e s e n t e d p r a c t i c a l and dependable means o f i n s p e c t i n g sandwich p a n e l s f o r q u a l i t y o f j o i n t s .  It  a l s o appeared t h a t any c o m b i n a t i o n o f t h e s e t e s t methods would o f f e r l i t t l e  promise o f improvements.  (1) v i s u a l i n s p e c t i o n ,  (2) s p e c i a l l i g h t i n g ,  (4) s u p e r s o n i c i n s p e c t i o n ,  These a r e : (3) t a p p i n g ,  (5) exposure t o vacuum,  12  u o  4->  1  I 0  I  .1  I  .2  I  I  .3  .4  Ratio Figure 2  1_  .5  R/d  Stress Concentration  Factors i n Tension  From S. Timoshenko and J.N. G o o d i e r , "Theory o f E l a s t i c i t y , " 2nd Ed.  (6) vacuum-cup t e s t ,  (7) i n t e r n a l p r e s s u r e  (8) h e a t i n g complete p a n e l , (10) b u t t o n - t e n s i o n  test.  that carefully controlled  test,  (9) l o c a l h e a t i n g ,  and  Heebink and Mohaupt c o n c l u d e d process s p e c i f i c a t i o n s ,  by s u f f i c i e n t number o f d e s t r u c t i v e t e s t s  and  supplemented  by r i g i d i n s p e c t i o n must be r e l i e d upon t o i n s u r e h i g h - q u a l i t y j o i n t s i n sandwich Eickner evaluate end-grain  substantiated  uniformly  panels.  (13) c a r r i e d out f l a t w i s e  tensile tests  the d u r a b i l i t y of the g l u e j o i n t s i n aluminum b a l s a sandwich c o n s t r u c t i o n .  the t e s t method and t e s t i n g  The  principles  to and of  a p p a r a t u s were l a t e r employed  13 i n t h e ASTM D e s i g n a t i o n C297-52  ( r e v i s e d i n 1961).  For f a b r i c a t i o n o f t h e t e n s i o n and shear o f plywood-faced Laboratory  sandwich p a n e l s , t h e U.S. F o r e s t  (38) recommended t h e use o f room  specimens Products  temperature  s e t t i n g r e s o r c i n o l r e s i n a d h e s i v e s which s h o u l d always be a p p l i e d t o both surfaces o f the glue j o i n t . temperature  Intermediate  s e t t i n g p h e n o l r e s i n a d h e s i v e s were a l s o  recommended i f s h o r t e r p r e s s i n g p e r i o d s were d e s i r a b l e . F u r t h e r d e t a i l s about specimen s i z e and l o a d i n g methods proposed i n t h e r e p o r t were t h e same as those w h i c h were l a t e r t a k e n up i n t h e ASTM s t a n d a r d methods (7, 8 ) . According t o Kuenzi  (27) t h e b e s t l o a d i n g method i n  f l e x u r e t e s t i s t o apply the concentrated load at the q u a r t e r span p o i n t s on a beam s i m p l y s u p p o r t e d  at the supports.  The  r e a s o n g i v e n i s t h a t t h e maximum moment and t h e maximum s h e a r s t r e s s i n d u c e d i n t h e beam l o a d e d a t t h e q u a r t e r - s p a n p o i n t s a r e e q u a l t o t h o s e i n d u c e d i n t h e beam on which t h e load i s uniformly d i s t r i b u t e d . elementary  mechanics.  T h i s i s e a s i l y proved by  The s i n g l e c o n c e n t r a t e d l o a d i n g a t  the mid-span o f t h e beam i s t h e s i m p l e s t way o f a p p l y i n g the l o a d .  But, t h i s  l o a d i n g produces s t r e s s c o n c e n t r a t i o n  a t t h e l o a d i n g p o i n t as much as t w i c e t h e c o r r e s p o n d i n g s t r e s s concentrations at the supports.  Hence, i t may happen  t h a t t h e s i n g l e c o n c e n t r a t e d l o a d i n g method cannot d e t e c t a f a u l t w h i c h i s l o c a t e d near t h e s u p p o r t s ( 2 7 ) . I n o r d e r t o e v a l u a t e t h e shear s t r e n g t h o f t h e c o r e t o - f a c i n g bond, however, t h e abovementioned t w o - p o i n t  loading  i s not appropriate  (19).  I t i s known t h a t t h e c e n t r a l  p o r t i o n between two l o a d i n g p o i n t s i s n o t s u b j e c t e d t o s h e a r stress.  That i s , i f q u a r t e r - s p a n  p o i n t l o a d i n g i s employed,  the g l u e l i n e s h e a r s t r e n g t h o f one h a l f o f t h e span cannot be t e s t e d .  Houwink and Salmon (19) s t a t e d t h a t t h e u s u a l  method o f t e s t i n g t h e sandwich bond s t r e n g t h i n s h e a r i s t o l o a d a s h o r t sandwich beam specimen under t h r e e - p o i n t ( i . e . mid-span l o a d i n g )  loading  and t o c a l c u l a t e t h e s h e a r s t r e n g t h  from t h e f a i l i n g l o a d u s i n g t h e s i m p l e beam t h e o r y .  This  method i s a p p l i c a b l e when t h e c o m p r e s s i v e o r t e n s i l e  strength  of the f a c i n g i s not l e s s than the g l u e l i n e shear I f t h e f a c i n g cannot w i t h s t a n d f a i l s i n f l e x u r e before  t h e a p p l i e d l o a d and i f i t  f a i l u r e takes place i n the g l u e l i n e ,  t h e s t r e n g t h o f t h e c o r e - t o - f a c i n g bond cannot be The  strength.  evaluated.  c o n v e n t i o n a l o v e r l a p s h e a r t e s t used t o e v a l u a t e  s t r u c t u r a l adhesives i s not appropriate  t o measure t h e  s t r e n g t h o f a d h e s i v e t o f i l l e t i n sandwich c o n s t r u c t i o n ( 1 9 ) . In o r d e r t o e v a l u a t e  adhesives f o r bonding core t o f a c i n g s ,  sandwich p a n e l s s h o u l d be p r e p a r e d .  Following t h i s , the  s h e a r s t r e n g t h o f g l u e l i n e s as w e l l as t h e a b i l i t y o f t h e t o t a l s t r u c t u r e t o c a r r y a l o a d i s d e t e r m i n e d i n beam f l e x u r e tests  (34).  A d d i t i o n a l adhesive strength values  from f l a t w i s e t e n s i l e  tests.  are obtained  15  MATERIALS AND  METHODS  Since the o b j e c t i v e of t h i s t h e s i s i s t o i n v e s t i g a t e the r e l a t i o n s h i p between f i l l e t s i z e and b o n d i n g s t r e n g t h , f i l l e t s o f d i f f e r e n t s i z e must be p r e p a r e d .  V a r i a t i o n of  f i l l e t s i z e can e a s i l y be g e n e r a t e d by d i p p i n g t h e edge o f t h e honeycomb i n . u n i f o r m l y s p r e a d g l u e l a y e r s o f v a r i o u s depths.  A f t e r b e i n g d i p p e d i n t h e g l u e , t h e honeycomb i s  p l a c e d on the f a c i n g and l e f t under t h e c o r r e c t p r e s s u r e u n t i l t h e g l u e hardens. and forms a f i l l e t .  In the meantime, the g l u e f l o w s  From t h e p r e l i m i n a r y e x p e r i m e n t s  l e a r n e d t h a t l a t e r a l g l u e f l o w on plywood was t o r y f o r making a good f i l l e t . all  not  i t was  satisfac-  T h e r e f o r e , i n t h e main t e s t  o f t h e i n n e r s i d e s o f t h e plywood f a c i n g s were l i g h t l y  c o a t e d w i t h t h i n n e d g l u e o f t h e same t y p e t o l e t t h e g l u e on the c o r e f l o w onto the plywood.  The  same p r o c e d u r e  f o l l o w e d f o r the o t h e r s i d e o f t h e c o r e and, t h u s , a was  was sandwich  produced.  C o n s t r u c t i o n o f Glue A p p l i c a t o r In  o r d e r t o produce u n i f o r m g l u e l a y e r s o f v a r i o u s  d e p t h s , s e v e r a l methods o f making u n i f o r m l a y e r s o f p a i n t and s i m i l a r m a t e r i a l s were e x p l o r e d (2, 3, 6, 32, 33). TLC  c o a t i n g u n i t f o r chromatography was  also tried.  t h e s e were d e s i g n e d t o meet the r e q u i r e m e n t  A  A l l of  o f making a  u n i f o r m l a y e r o n l y once on a p a r t i c u l a r p l a t e o r a s h e e t . F o r t h e p u r p o s e o f m a k i n g a u n i f o r m g l u e l a y e r on one p l a t e r e p e a t e d l y s o t h a t a s p e c i f i c g l u e h e i g h t c o u l d be t r a n s f e r r e d t o t h e honeycomb c o r e a t e a c h a p p l i c a t i o n , t h e a b o v e mentioned apparatus  was f o u n d  t o be i n c o n v e n i e n t .  Conse-  quently, a simple, y e t e f f i c i e n t glue a p p l i c a t o r o f o r i g i n a l d e s i g n was c o n t r i v e d f o r t h i s  experiment.  This glue a p p l i c a t o r c o n s i s t s o f a s e t o f doctor blades flat on  and a base p l a t e  ( F i g u r e s 3, 4).  The b a s e p l a t e i s a  p l a t e w h i c h i s made o f a l a m i n a t e d p l a s t i c  sheet  glued  a o n e - i n c h - t h i c k plywood sheet w i t h two-stepped s i d e r a i l s  f i x e d on b o t h rails  l o n g i t u d i n a l edges o f t h e p l a t e .  a r e made o f l a m i n a t e d p l a s t i c  o f one s t e p o f t h e r a i l strip  strips.  s t e e l bars  four doctor blades  prepared  There a r e  s o as t o p r o d u c e f o u r  different  Two o f t h e d o c t o r b l a d e s h a v e a  length t h a t can bridge the lower  steps o f the side  The o t h e r t w o b l a d e s  l e n g t h t o b r i d g e t h e upper s t e p s . each l e n g t h i s notched  plastic  The d o c t o r b l a d e s a r e  and have s t r a i g h t edges.  depths o f t h e glue f i l m .  across the plate.  The t h i c k n e s s  i s that o f the laminated  a n d a c t u a l t h i c k n e s s i s 1.4 mm.  ruler-like  The s i d e  a r e extended i n  One o f t h e b l a d e s o f  a t t h e edge on b o t h  c l e a r a n c e between t h e b l a d e  rails  ends so t h a t t h e  edge a n d t h e p l a t e b e d p r o d u c e s  a h a l f t h i c k n e s s o f one s t e p o f t h e r a i l one-and-one-half thickness o f the step  ( F i g u r e 4, A) o r  ( F i g u r e 4, C ) .  Top View  4 50  200  Unit: mm.  ±1.4-  Side View  Figure 3.  Glue Applicator —  Base Plate  Scale: Three-Eighths  Doctor blade  Figure 4.  Glue  Glue Applicator —  Base plate  (A) Glue depth :  [0.5]  (B)  fl.O]  (c)  [1.53  (D)  [2.0]  Four Doctor Blades  19 I n o r d e r t o make a u n i f o r m g l u e l a y e r on t h e p l a t e , the d o c t o r b l a d e i s moved by hand from one end o f t h e p l a t e t o t h e o t h e r s l i d i n g on t h e s i d e r a i l s .  The c l e a r a n c e  between t h e b l a d e edge and t h e p l a t e bed c o n t r o l s t h e g l u e d e p t h , f o r t h e b l a d e edge s c r a p e s o f f t h e e x c e s s g l u e poured on t h e p l a t e and l e v e l s t h e g l u e l a y e r .  The g l u e  depth  produced by a h a l f s t e p c l e a r a n c e was r e f e r r e d t o as [ 0 . 5 ] . S i m i l a r l y , t h e g l u e depths produced by one s t e p , one-ando n e - h a l f s t e p , and two s t e p c l e a r a n c e s were r e f e r r e d t o as [1.0],  [1.5] and [ 2 . 0 ] , r e s p e c t i v e l y .  i n b r a c k e t s a r e t h e names o f g l u e depth  These numbers e n c l o s e d t r e a t m e n t s , and  r e p r e s e n t n e i t h e r a c t u a l g l u e depth n o r r a t i o s .  These symbols  were a l s o used f o r e x p r e s s i n g t h e f i l l e t h e i g h t groups. example, t h e f i l l e t h e i g h t group [1.0] means t h o s e w h i c h were made by t h e g l u e depth  treatment  For  fillets  [1.0].  Materials Facing  . . . .  Douglas f i r plywood; 1/4 i n c h t h i c k , sanded, good one s i d e .  Core  . . . .  K r a f t paper honeycomb; H e x c e l l , HNC 3/8 - 80 (18) E, 1 i n c h t h i c k , 3/8 i n c h c e l l s i z e ( F i g u r e 5 ) .  Adhesive  . . .  Modified phenol-resorcinol  resin  g l u e ; P a c i f i c R e s i n s , Resorsabond 2600. Catalyst  ...  P a c i f i c R e s i n s , P a r a c CR 40.  Figure 5 .  K r a f t Paper Honeycomb  21 Preparation  o f Sandwich  Plywood  was  i n c h e s w i t h the f a c e dimension. wood to  with  been  Prior  into  grain  The  was  f o r more  to bonding  two weeks  before  was  mixture  of phenol-resorcinol resin,  ratio  grams  per square  obtained  For parts  by  weight  the  four  foot  empirically  10  by  was  used.  glue  depth  into  seconds on  was  added  restored.  facing  were  the glue After  the core  a pre-wetted  Following was  6)  and  thinned  ±  face  glue  (the  and water i n  This  was  1 part  each  stacked  carefully  of  catalyst  f o r each glue  the core  of  by  edge  pulled  up  and  plywood.  application  semi-assemblies i n such  was  i n the glue f o r  the necessary  t o the a p p l i c a t o r so that The  of  cores  until  remaining was  6.3  figure  applied with  layer  of  test.  and  were  1%  glued.  coverage  form.  parallel  50  were  ply-  pieces  the sanded  mean  a preliminary  treatments  the p l a t e bed.  glue  they  Twenty-two honeycomb  touched  placed  as t h e  (Figure  14  longer  the g l u i n g of core-to-facing, the mixture  the core  then  The  of phenol-resorcinol resin  three  size  catalyst  i n the thinned  dipping  about  i t with  o f 10:1:5 by w e i g h t ) .  to the  ± 1°F  to the facing,  by b r u s h i n g  o f 4 by  and t h e honeycomb  plywood  the  similar  direction  plywood  the core  pieces  parallel  t h e c o n d i t i o n o f 70  than  wetted  cut into ribbon  sawn  under  rectangular  direction  the transverse  kept  humidity  sawn  Honeycomb  the length.  had  Panels  original  of the core  a manner  that  amount  and  the core  glue  of depth  one was  placed  22  SINGLE  L  CELL  WALL  - RD = L o n g i t u d i n a l r i b b o n  W - RD = T r a n s v e r s e  Figure  ribbon  direction  direction  T  . = Honeycomb  thickness  6.  Dimensional Nomenclature Honeycomb  o f Expanded  23 above  the  facing  for  more  the  pressure,  same  than  depth  treated making Thus,  12  a a  glue  by  Ten from  two  five  1 by  1  made  of  1 by  face  of  the  before  the  i n the  same way  1  inch  ±  initiation loading  i n the  Olsen  universal testing  specimens  inch wise, were  per the  at  minute.  a  The  of  Fillet  was  of  glueplywood  before.  the  core  was  gravity.  group  by  A  cutting  loading  was  bonded as  were  to  in  were than  block each  the  subjected ten  days  procedures. to  was of  meet  the  (Figure to  base  movement  failure  in  measured  apply  tension  and by  the  recommendation  7).  used  strength  was  panels  f o r more  made  rate  height  adhesive  C297-61  facing size  The  as  of  specimens  humidity  maximum  the  pre-wetted  panel.  same  machine  constant  core.  effects  f i r wood  test  Designation  percentage  recorded.  the  testing  fixture  given  the  ASTM  of  a  fillet  one  Douglas  of  the  edges  sandwich  from  The  removing  Procedure  f o r one  using  1%  both  Test  chosen  bonding. 50  on  of  interfering  specimens  1 by  and  The  pressed  and  specimens  1°F  on  randomly  core-to-facing ±  placed  shape  edge  psi.  treated with  then  specimens  inch  were  50  After  was  the  Specimen  made  temperature.  other  fillet  test  room  approximately  the  and  avoiding  Test  at  under  semi-assemblies on  sandwich, uniform  Tensile  70  hours  these  of  pressed  semi-assembly  achieved  to  and  A a  Tinius load  of  0.0  to 2  flat-  fillet  vernier  size calipers  24  Figure 7.  Tensile Test Specimen i n Loading Fixture  f o r t h e f i l l e t h e i g h t and w i d t h a t f o u r random p o i n t s on the f a i l e d s i d e o f each specimen a f t e r s e p a r a t i n g t h e from t h e c o r e .  facing  The measurement o f f i l l e t w i d t h was  made f o r  the t o t a l w i d t h around a s i n g l e c e l l w a l l i n c l u d i n g t h e wall thickness.  F a c i n g f a i l u r e was  cell  e x p r e s s e d by t h e p e r -  centage o f the a r e a exposed where the f a c i n g plywood  was  s t r i p p e d o f f (maximum of o n e - p l y deep) t o t h e whole f a c i n g area. In o r d e r t o o b t a i n the s t r e n g t h o f a d h e s i v e per u n i t f i l l e t  fillet  l e n g t h t h e ASTM D e s i g n a t i o n C297-61 (8) i s  called for.  Strength of Adhesive F i l l e t =  Flatwise Tensile Strength F i l l e t L e n g t h / U n i t Core A r e a  where f i l l e t l e n g t h per u n i t c o r e a r e a can be found by s i d e r a t i o n o f t h e core c e l l geometry.  con-  F o r c o r e s w i t h hexa-  g o n a l o r square c e l l s i t has been found t h a t f i l l e t l e n g t h per u n i t c o r e a r e a e q u a l s f o u r d i v i d e d by the c e l l Proof f o r a hexagonal Let  size.  cell:  t h e l e n g t h o f a s i d e o f hexagon be b  (Figure 8),  then Core C e l l S i z e = v ^ ~ 3 b,  and  Core C e l l A r e a = j /~~3 b . Therefore, . , _ , F i l l e t Length F i l l e t Length per U n i t Core A r e a = —r-^—? ^ Core C e l l A r e a rT  r  6b 3j / / ^3 , b2  4 /  3  ,b  4  Core C e l l S i z e  26  Figure 8  Honeycomb C e l l  Hence, t h i s f i l l e t in  Section  l e n g t h i s t h e l e n g t h o f t h e c o r e c e l l edge  contact with the f a c i n g .  F l e x u r e T e s t Specimen and T e s t P r o c e d u r e The  remaining  twenty sandwich p a n e l s from each  h e i g h t group, e i g h t y p a n e l s f o r f o u r f i l l e t h e i g h t in  fillet  groups  t o t a l , were trimmed i n t o 3.75 by 12 i n c h specimens f o r  flexure  test. Since the o b j e c t i v e o f the f l e x u r e t e s t i n t h i s  study was t o e v a l u a t e  t h e s h e a r s t r e n g t h o f t h e glu,.eline  between core and f a c i n g , i t was deemed d e s i r a b l e t h a t t h e f a i l u r e s h o u l d take p l a c e i n g l u e l i n e s h e a r r a t h e r t h a n i n c o r e b u c k l i n g o r shear, o r f a c i n g t e n s i o n o r c o m p r e s s i o n . p r e l i m i n a r y t e s t was c a r r i e d o u t t o d e t e r m i n e the optimum  A  l o a d i n g system f o r t h e f l e x u r e specimens.  Usual  loading  systems f o r f l e x u r e t e s t o f sandwich p a n e l s a r e mid-span l o a d i n g and t w o - p o i n t l o a d i n g .  In the l a t t e r , the loading  points  are g e n e r a l l y s e t a t a q u a r t e r - s p a n o r o n e - t h i r d - s p a n . M i d span l o a d i n g has an advantage  i n t e s t i n g h o r i z o n t a l shear  s i n c e t h e f u l l span i s s u b j e c t e d t o s h e a r s t r e s s , b u t a f a i l u r e may o c c u r i n t h e f a c i n g , because t h e modulus o f r u p t u r e o f t h e f a c i n g i n b e n d i n g i s maximum a t t h e mid-span (Appendix 3 ) . I n t h e case o f t w o - p o i n t l o a d i n g , t h e modulus o f r u p t u r e o f f a c i n g i n b e n d i n g d e c r e a s e s as t h e i n t e r n a l l e n g t h between t h e two l o a d i n g p o i n t s i n c r e a s e s , b u t t h e a r e a t h a t i s s u b j e c t e d t o h o r i z o n t a l shear s t r e s s decreases s i n c e the p o r t i o n between t h e two l o a d i n g p o i n t s i s n o t under s h e a r stress.  I n t h e p r e l i m i n a r y t e s t s , an e f f o r t was made t o f i n d  t h e minimum i n t e r n a l l e n g t h between t h e two l o a d i n g  points  where no f a i l u r e was e x p e c t e d t o t a k e p l a c e i n t h e f a c i n g s . As a r e s u l t , a q u a r t e r - s p a n was found t o be t h e most s u i t a b l e i n t e r n a l l e n g t h and was employed i n t h i s The  experiment.  specimen was s u p p o r t e d by two round s t e e l b a r s  of 1 i n c h i n d i a m e t e r a t a d i s t a n c e o f 1 i n c h from b o t h ends o f t h e beam.  Load was a p p l i e d by a T i n i u s O l s e n  u n i v e r s a l t e s t i n g machine t h r o u g h two round s t e e l b a r s o f the same s i z e as t h e s u p p o r t i n g b a r s  ( F i g u r e 9 ) . The r a t e  o f movement o f t h e base p l a t e o f t h e t e s t i n g machine was 0.02 i n c h p e r minute.  The d e f l e c t i o n s were measured by a  Apparatus f o r Conducting Flexure Test of Sandwich C o n s t r u c t i o n  d i a l i n d i c a t o r by means o f t h e machine base p l a t e movement. The maximum l o a d , d e f l e c t i o n a t f r a c t u r e and f a i l u r e c h a r a c t e r i s t i c s were r e c o r d e d f o r each specimen (Table 1 ) .  30  RESULTS AND ANALYSIS OF DATA  Tensile  Test Tables  2, 3, 4, and 5 show t h e r e s u l t s o f t e n s i l e  t e s t s f o r t h e f o u r f i l l e t h e i g h t groups [ 0 . 5 ] , [ 1 . 0 ] , [ 1 . 5 ] , and  [ 2 . 0 ] , r e s p e c t i v e l y . The maximum l o a d a p p l i e d t o t h e  specimen d i r e c t l y g i v e s t h e t e n s i l e s t r e n g t h i n p s i . , s i n c e the c r o s s s e c t i o n a l a r e a o f t h e specimen i s 1 square i n c h . The  s t r e n g t h o f adhesive  fillet  can be o b t a i n e d by d i v i d i n g  the t e n s i l e s t r e n g t h by t h e f i l l e t  l e n g t h p e r u n i t core  area. F o r t h e measurement o f t h e f i l l e t h e i g h t and w i d t h , f o u r s i n g l e c e l l w a l l s ( F i g u r e 6 ) and c o r r e s p o n d i n g fillet  four  l i n e s w h i c h were l e f t on t h e s e p a r a t e d plywood were  randomly chosen.  A l l measurements, were made a t t h e c e n t e r  o f s i n g l e c e l l w a l l edges where t h e e f f e c t s o f c o r e geometry due t o t h e s u r f a c e t e n s i o n system were t o be minimum.  cell  considered  T h i s i s because t h e f a c t o r s a f f e c t i n g  fillet  shape and s i z e a t t h e c e n t e r o f s i n g l e c e l l w a l l edges were deemed t o be l e s s v a r i a b l e t h a n those a t a d o u b l e c e l l w a l l o r around t h e c o r n e r o f a n hexagonal c e l l . The  mean v a l u e o f t h e f o u r o b s e r v a t i o n s i n each  specimen was computed and r e c o r d e d Standard  i n Tables  2, 3, 4, and 5.  d e v i a t i o n s and o t h e r b a s i c f i g u r e s needed f o r  31 analysis in  of variance  Tables  8 a n d 9.  established height depth  on  and As  and t h e f i l l e t  throughout  a l l fillet  that  were  walls  due  (Table  (Table traces  Analysis effects  The  to  7). on  values  groups.  constant  the glue  tension  were  These  glue  depth fillet  the  glue  nearly facts  elevations  constant  indicate  on  the  cell  i n the l i q u i d - s o l i d  system  of  fillet  were  Duncan's  made  (Appendix  measurement  was  using  single  vernier  Width  Relationship  Using the data given i n Table  height  treatments  on  fillet  analysis of variance  of significance  Multiple  four  width  mm.  and F i l l e t  width  on  specimen  means  were  Range  means  (Appendix  1-a).  indicates  n o t a l l t h e same. fillet  (N.M.R.) T e s t  8, t h e  width  of the F value  the r e l a t i o n s h i p s between  New  group  The  i n v e s t i g a t e d by  analyze  height  of fracture/fillet  t o 0.05  fillet  the f i l l e t  each  f o r t h e measurement  Variance.  level  from  the f a c i n g of each  Height  of  high  that  specimens  reading  Fillet  were  mean  height  nearly  selected  calipers  1.  height  recorded  6) .  randomly  cell  show,  are  But d i f f e r e n c e s between  to the surface  Five  ratio  the results  analysis  the a p p l i c a t o r and t h e r e s u l t i n g  d i d not agree.  there  correlation  width  was  In  order  means,  carried  out  1-b).  According significant  t o Duncan's  d i f f e r e n c e between  N.M.R. T e s t , fillet  width  there means  was of  no [1.5]  32 group and [2.0] group a t t h e 5% l e v e l .  The  ranking of  f i l l e t w i d t h means was; [0 . 5 ] < [ 1. 0 ] < [1. 5 ] , Correlation  Analysis  [2.0],  (Based on d a t a i n T a b l e 9 ) .  F i l l e t height : X F i l l e t width  SS  x  l  :  X„  = 22.4962,  SS  SP i  X  X  - -siri  = i -  x  = 67.3752,  2  '  o  =  h  Simple r e g r e s s i o n equation  :  b  2  2  8  9  b  x  SP 1 2 X  ~ iH h  = 28.99  X  =  -°-  07  X£ = -0.0 7 + 1.289X^ (SP ) 2 1 2 C o e f f i c i e n t of determination : r = ^ — = 0.5548 l 2 2  X  X  :  X  F =  2 r  ~ 1 - r ( n  2 )  ** i n d i c a t e s  = 47.29**  X  (n = 40)  s i g n i f i c a n c e a t t h e 1% l e v e l .  That i s , t h e  l i n e a r r e l a t i o n s h i p between f i l l e t h e i g h t and f i l l e t was h i g h l y  s i g n i f i c a n t (Figure 10).  width  2.  F i l l e t H e i g h t and T e n s i l e S t r e n g t h  Analysis  of Variance.  Relationship  Using the data given  i n T a b l e 8, t h e  e f f e c t s o f f i l l e t h e i g h t t r e a t m e n t s on t e n s i l e s t r e n g t h means were i n v e s t i g a t e d by a n a l y s i s o f v a r i a n c e The s i g n i f i c a n c e o f F v a l u e  (Appendix 2 - a ) .  i n d i c a t e s that the t e n s i l e  s t r e n g t h means were n o t a l l t h e same.  In order t o analyze  the r e l a t i o n s h i p s between t e n s i l e s t r e n g t h means, Duncan's N.M.R. T e s t was c a r r i e d o u t (Appendix 2-b). According  t o Duncan's N.M.R. T e s t , t h e r e were no  s i g n i f i c a n t d i f f e r e n c e i n t h e t e n s i l e s t r e n g t h means between [0.5]  and [ 1 . 0 ] , and between [2.0] and [1.5] a t t h e 5% l e v e l .  The r a n k i n g o f t e n s i l e s t r e n g t h means was; [ 0 . 5 ] , [1.0] < [ 2 . 0 ] ,  C o r r e l a t i o n Analysis F i l l e t height  (Based on d a t a i n T a b l e 9 ) . :  X  1  Tensile strength  : Y  SS  SS = 7481.6, y  x  = 22.4962, x  [1.5]  SP = 223.54 x y x  SP b  i  =  s s ^ = HT4TT " = 9  937  ' o  Simple r e g r e s s i o n equation  b  = 5  - A b  =  3 8  '  0 4  : Y = 38.04 + 9.94 X  Figure  10.  F i l l e t H e i g h t and F i l l e t Width i n T e n s i l e Test Specimens  Relationship  35  C o e f f i c i e n t of determination  : r  2  (SP X  = g-g x  Coefficient of linear correlation  F =  " 1 - r  r 2 ( n  2 )  = 16.05**  4  )  2  Y  g^— = 0 .2969  l "  Y  : r = 0.545  (n = 40)  ** i n d i c a t e s s i g n i f i c a n c e a t t h e 1% l e v e l .  That i s , t h e  l i n e a r r e l a t i o n s h i p between f i l l e t h e i g h t and t e n s i l e s t r e n g t h was h i g h l y s i g n i f i c a n t ( F i g u r e 1 1 ) .  3.  F i l l e t Width and T e n s i l e S t r e n g t h R e l a t i o n s h i p  C o r r e l a t i o n Analysis F i l l e t width  (Based on d a t a i n T a b l e 9 ) . :  X  2  Tensile strength : Y SS  b  x  x  = 67.375, 2  =  y  x y * = 6.089 , x 2  s s  SS  = 7481.6,  b  Q  SP  = Y - h  ±  *  y  = 410.26  2  ^ = 43.30  S i m p l e r e g r e s s i o n e q u a t i o n : Y = 43.30 + 6.09  C o e f f i c i e n t of determination  : r  2  C o e f f i c i e n t of l i n e a r c o r r e l a t i o n  (SP =  )2  X  2  2 — g g — = 0. 3339 x' y X  Y  :  : r = 0.578  •  T  A  [0.5] [1.0]  -t-  [1.53  a  [2.0]  50  Y « 38.04 + 9.94X,  -L 1  Figure 11.  2  3  F i l l e t Height (mm.) F i l l e t Height and Tensile Strength Relatlonshi  37 r fn - 2) ** F = — — £L = 19.06. 1 - r 2  (n = 40)  [  ** i n d i c a t e s the  s i g n i f i c a n c e a t t h e 1% l e v e l .  l i n e a r r e l a t i o n s h i p between f i l l e t w i d t h and t e n s i l e  s t r e n g t h was h i g h l y  4.  That i s ,  Deflection  Correlation  a t F r a c t u r e and T e n s i l e  Analysis  Deflection Tensile SS  x  s i g n i f i c a n t (Figure 12).  :  Strength  Relationship  (Based on d a t a i n T a b l e 9 ) . X^  strength  = 3.514,  :  SS  3  y  Y = 7481.6,  SP  x y  = 110.69  3  SP x.y b  i  =  S  g  .  =  3 1  -  5 0  '  b  o  =  Y  " 3  "  b  i 3 X  =  3 8  -  5  X  Simple r e g r e s s i o n  e q u a t i o n : Y = 38.5 + 31.5 X^  C o e f f i c i e n t of determination : r  2  (SP  x  = ^  3  3  r (n 2  F =  —^  - 2)  1 - r  7^-  ** i n d i c a t e s the  =  ** 33.16 .  significance  )  2  ss~~  =  x * C o e f f i c i e n t of l i n e a r c o r r e l a t i o n  y  ^.466  y  : r = 0.683  (n = 40) a t t h e 1% l e v e l .  That i s  l i n e a r r e l a t i o n s h i p between d e f l e c t i o n a t f r a c t u r e  and  •  C0.5] [1.0] [1.5] [2.0]  •  ++  50  W  •P hfl d <i>  r • 43.30 + 6.09x  2  CO 0) CO  a)  2 F i l l e t Width (mm.) Figure 12.  3  F i l l e t Width and Tensile Strength Relationship 00  t e n s i l e s t r e n g t h was h i g h l y  5.  Facing Failure  (Based on d a t a i n T a b l e 9 ) .  Facing f a i l u r e : Tensile strength  x  = 1477.1,  X^ :  SS  4  Coefficient  (Figure 13).  and T e n s i l e S t r e n g t h R e l a t i o n s h i p  C o r r e l a t i o n Analysis  SS  significant  Y  Y = 7481.6,  SP  * y  = 504.4  4  of determination : r  2  (SP = ^ 4  F =  n.s.  of l i n e a r c o r r e l a t i o n  2 r  ~ 1 - r ( n  = 0.89'  2 )  2  indicates  n , S  *  (n = 40)  n o n - s i g n i f i c a n c e a t t h e 5% l e v e l .  f a i l u r e and t e n s i l e  Analysis  Deflection  :  between  That  facing  strength.  F i l l e t H e i g h t and D e f l e c t i o n  Correlation  2  : r = 0.152  i s , t h e r e was no s i g n i f i c a n t c o r r e l a t i o n  6.  y  ;  x  Coefficient  )  4 — g ^ — = 0.023 * y X  at Fracture  Relationship  (Based on d a t a i n T a b l e 9 ) . X^  F i l l e t h e i g h t : X.^  41  SS x  3  = 3.5140,  SS  l  X  = 22.4962,  SP 1 3 X  C o e f f i c i e n t of determination : r  = 3.580  X  (SP  2  = — x  Coefficient of l i n e a r correlation  X  1 3 — X  l  )  2  = 0.162 x  3  : r = 0.403  2 F =  r  ~ 1 - r ( n  2 )  * indicates the  = 7.35 *  (n = 40)  s i g n i f i c a n c e a t t h e 5% l e v e l .  That i s ,  l i n e a r r e l a t i o n s h i p between f i l l e t h e i g h t and d e f l e c t i o n  a t f r a c t u r e was s i g n i f i c a n t .  Flexure Test The  r e s u l t s of the flexure t e s t f o r the four  h e i g h t groups, [0.5],  [1.0],  [ 1 . 5 ] , and [2.0] a r e g i v e n i n  T a b l e s 10, 1 1 , 12 and 13, r e s p e c t i v e l y . shear s t r e s s  fillet  The h o r i z o n t a l  i n t h e g l u e l i n e were c a l c u l a t e d by u s i n g t h e  e q u a t i o n g i v e n i n A p p e n d i x 3-a. The  types of f a i l u r e o f t h e specimens a t t h e maximum  l o a d P were n o t a l l a l i k e . in  When t h e f a i l u r e took p l a c e o n l y  the g l u e l i n e , the l o a d - d e f l e c t i o n  release load  of stress  (Figure  c u r v e showed a sudden  i n t h e specimen a f t e r r e a c h i n g t h e maximum  14, [ 0 . 5 ] -  3, [ 1 . 0 ] -  14).  This type o f  f a i l u r e was o b s e r v e d m o s t l y i n t h e s m a l l f i l l e t  groups,  42  Figure 14.  Selected Load-Deflection Curves i n Flexure Tests  CF = Core f a i l u r e GF = Glueline f a i l u r e  CF  0  01  DEFLECTION (INCH)  0.2  [0.5] and [ 1 . 0 ] .  When t h e f a i l u r e was due p a r t l y t o t h e  g l u e l i n e f r a c t u r e and p a r t l y t o t h e c o r e shear o r b u c k l i n g , t h e r e was no c o n s p i c u o u s change o f s t r e s s i n t h e specimen a f t e r a g l u e l i n e f r a c t u r e was o b s e r v e d , and t h e d e f l e c t i o n proceeded u n t i l a r u p t u r e o c c u r r e d i n t h e f a c i n g . a case t h e maximum l o a d was r e c o r d e d a t t h e f i r s t  I n such point  where t h e g l u e l i n e f a i l u r e was o b s e r v e d even i f t h e l o a d increased s l i g h t l y after that point In the  larger f i l l e t specimens  ( F i g u r e 14, [ 1 . 5 ] - 3 ) .  g r o u p s , e s p e c i a l l y i n [2.0] g r o u p , most o f  f a i l e d i n c o r e shear and/or b u c k l i n g .  The  g l u e l i n e s o f t h o s e specimens were c o n s i d e r e d t o have m a i n t a i n e d t h e i r s t r e n g t h up t o t h e maximum c o r e s h e a r s t r e s s , so t h e f i r s t p o i n t from w h i c h t h e l o a d - d e f l e c t i o n c u r v e became p a r a l l e l t o t h e d e f l e c t i o n a x i s was chosen f o r d e t e r m i n a t i o n o f P ( F i g u r e 14, [ 2 . 0 ] - 6 ) . The measurements o f f i l l e t h e i g h t and f i l l e t were same as t h o s e i n t h e t e n s i l e t e s t .  width  The f a i l u r e t y p e s  were c l a s s i f i e d i n t o CF f o r c o r e f a i l u r e , GF f o r g l u e l i n e f a i l u r e , and FF f o r f a c i n g f a i l u r e .  When a l o a d was a p p l i e d  on t h e sandwich beam and i f any w r i n k l e s appeared on t h e honeycomb c o r e w a l l s , i t was c o n s i d e r e d t h a t a f a i l u r e took place i n the core.  I n most c o r e f a i l u r e s s l a n t i n g w r i n k l e s  appeared on t h e c o r e w a l l s around t h e n e u t r a l a x i s o f t h e sandwich beam a t t h e o u t e r s i d e s o f t h e l o a d i n g p o i n t s . some cases c o r e b u c k l i n g , w h i c h appeared as s l i g h t n e a r t h e g l u e l i n e , accompanied t h e c o r e s h e a r  folds  failures.  In  44 The g l u e l i n e f a i l u r e was o b s e r v e d f a c i n g d e l a m i n a t i o n from t h e c o r e .  as a s l i d e o f t h e  Minor p e e l i n g damages  o f t h e s u r f a c e o f f a c i n g s which sometimes accompanied t h e d e l a m i n a t i o n s were r e g a r d e d as a p a r t o f t h e g l u e l i n e failure.  F a c i n g f a i l u r e s were such t h a t e i t h e r t o p o r  bottom f a c i n g was r u p t u r e d by bending  a t o r near t h e c e n t e r  o f two l o a d i n g p o i n t s . F i v e specimens from each f i l l e t h e i g h t group  except  [2.0] were s e l e c t e d f o r t h e measurement o f f r a c t u r e / f i l l e t width r a t i o  (Table 1 4 ) .  From [2.0] group t h e t h r e e  specimens which f a i l e d i n t h e g l u e l i n e s were s e l e c t e d f o r t h e same purpose.  The method o f measurement was as same as  t h a t i n t h e t e n s i l e t e s t specimens.  1.  F i l l e t H e i g h t and F i l l e t Width R e l a t i o n s h i p  Analysis  of Variance.  U s i n g t h e d a t a g i v e n i n T a b l e 15,  the e f f e c t s o f f i l l e t h e i g h t t r e a t m e n t s  on f i l l e t  means were i n v e s t i g a t e d by a n a l y s i s o f v a r i a n c e 4-a).  width (Appendix  The h i g h l e v e l o f s i g n i f i c a n c e o f t h e F v a l u e  i n d i c a t e s t h a t t h e f i l l e t w i d t h means were n o t a l l t h e same.  I n o r d e r t o a n a l y z e t h e r e l a t i o n s h i p s between  w i d t h means, Duncan's N.M.R. T e s t was c a r r i e d o u t  fillet  (Appendix  4-b) . A c c o r d i n g t o Duncan's N.M.R. T e s t , f i l l e t means ranked a s :  width  Figure 15.  F i l l e t Height and F i l l e t Width R e l a t i o n s h i p i n Flexure Test Specimens  [0.5]  < [1.0]  < [1.5]  <  [2.0]  a t t h e 1% l e v e l o f s i g n i f i c a n c e . C o r r e l a t i o n Analysis F i l l e t height :  X  F i l l e t width  X„  SS  SP b  l  :  = 56.782,  l  x  X  ss'  =  SS  x  x  2  = 19.935,  2  =  0 -5246 ,  b  Q  = X  X  =  1 2  " b  2  : X  .  C o e f f i c i e n t of determination  ±  X  = 0 . 9 9 + 0 . 5 2 X^  2  : r  2  Coefficient of l i n e a r correlation  r  ~ 1 - r ( n  0.99  =  ( S P  = g-g X  F =  29.790  X  l  Simple r e g r e s s i o n equation .  SP  X  1  X  15).  (Based on d a t a i n T a b l e  2 )  = 284**  x  x  12  )  2  = 0.784  ;—g-g  l  x  2  : r = 0.886  (n = 80)  ** i n d i c a t e s s i g n i f i c a n c e a t t h e 1% l e v e l .  That i s ,  t h e r e was a h i g h l y s i g n i f i c a n t l i n e a r r e l a t i o n s h i p between f i l l e t h e i g h t and f i l l e t w i d t h .  As t h e f i l l e t  i n c r e a s e d , so d i d t h e f i l l e t w i d t h  (Figure 1 5 ) .  height  2.  F i l l e t H e i g h t and Shear S t r e n g t h R e l a t i o n s h i p  A n a l y s i s of Variance.  U s i n g t h e d a t a g i v e n i n T a b l e 15,  t h e e f f e c t s o f f i l l e t h e i g h t t r e a t m e n t s on s h e a r s t r e n g t h means were i n v e s t i g a t e d by a n a l y s i s o f v a r i a n c e 5-a).  (Appendix  The s i g n i f i c a n c e o f F v a l u e i n d i c a t e s t h a t t h e s h e a r  s t r e n g t h means were n o t a l l t h e same.  In order t o analyze  the r e l a t i o n s h i p s between shear s t r e n g t h means, Duncan's N.M.R. T e s t was c a r r i e d o u t (Appendix 5-b). There was a s i g n i f i c a n t d i f f e r e n c e i n shear s t r e n g t h means between h e i g h t t r e a t m e n t s o f [1.0] and [0.5] a t t h e 5% l e v e l a c c o r d i n g t o Duncan's N.M.R. T e s t , b u t i t was n o t h i g h l y s i g n i f i c a n t a t t h e 1% l e v e l . t h e two g r o u p s ,  The d i f f e r e n c e between  [1.0] and [0.5] as one g r o u p , [1.5] and  [2.0] as a n o t h e r , was h i g h l y s i g n i f i c a n t a t t h e 1% l e v e l . C o r r e l a t i o n Analysis  (Based on d a t a i n T a b l e 1 5 ) .  F i l l e t height : X  x  Shear s t r e n g t h : Y  SS  = 56.782,  SS = 1487.96, y  SP = 156.99 x y x  SP b  i  =  ss  = x  2  -  7  6  5  '  b  o  =  Y  -  b  i  x  i  =  4  6  -  9  l  Simple r e g r e s s i o n e q u a t i o n : Y = 46.9 + 2.77 X^ 2 C o e f f i c i e n t o f d e t e r m i n a t i o n : r = 0.2917  Y = 46.9  2  + 2.77X  F i l l e t Height  Figure l 6 .  1  (mm.)  3  F i l l e t Height and Shear Strength Relationship  X  l  Coefficient of linear correlation F = 32.13**  (n = 80)  ** i n d i c a t e s the  s i g n i f i c a n c e a t t h e 1% l e v e l .  That i s ,  l i n e a r r e l a t i o n s h i p between f i l l e t h e i g h t and s h e a r  s t r e n g t h was h i g h l y  3.  : r = 0.540  s i g n i f i c a n t (Figure 16).  F i l l e t Width and Shear S t r e n g t h  C o r r e l a t i o n Analysis  (Based on d a t a i n T a b l e 1 5 ) .  F i l l e t width :  X  2  Shear s t r e n g t h : SS  x  = 19.935, 2  Relationship  Y  SS  y  = 1487.96,  SP  x y  = 92.61  2  SP h  1  =  = 4. 646 , X  b  Q  = Y - b  X  2  Simple r e g r e s s i o n  equation :  Y = 43.0 + 4.65 2  C o e f f i c i e n t of determination :  r  Coefficient of l i n e a r correlation  the  = 43.6  2  F = 15.48**'  (n = 80)  ** i n d i c a t e s  significance  = 0.2895 :  r = 0.538  a t t h e 1% l e v e l .  That i s ,  l i n e a r r e l a t i o n s h i p between f i l l e t w i d t h and shear  s t r e n g t h was h i g h l y  s i g n i f i c a n t (Figure 17).  Y s 43.0  + 4.65X  2  2 F i l l e t Width Figure 17.  F i l l e t Width and Shear S t r e n g t h  (mm.)  3  Relationship  4.  Deflection  a t F r a c t u r e and Shear S t r e n g t h  C o r r e l a t i o n Analysis Deflection  x  (Based on d a t a i n T a b l e 1 5 ) .  at fracture :  Shear s t r e n g t h SS  Relationship  :  = 141.889,  Y SS  3  y  = 1487.96,  SP = 280.378 x y 3  SP x y b  l  =  ss  3  x  =  1  -  9 7 6  '  b  Q  = Y - b  x  X  3  = 45.8  3  Simple r e g r e s s i o n  e q u a t i o n : Y = 45.8 + 1.98 X  Coefficient of determination : r  2  (SP  x  =  : x  Coefficient of linear correlation  the  F = 46.24**  (n = 80)  ** i n d i c a t e s  significance  y  : r = 0.61  That i s ,  significant.  of Variance.  Relationship  U s i n g t h e d a t a g i v e n i n T a b l e 15,  e f f e c t s o f f i l l e t h e i g h t t r e a t m e n t s on d e f l e c t i o n means  a t f r a c t u r e were i n v e s t i g a t e d (Appendix 6-a). the  3*  a t t h e 1% l e v e l .  F i l l e t H e i g h t and D e f l e c t i o n  Analysis the  2  3 — ^ g — = 0. 3723 y  l i n e a r r e l a t i o n s h i p between d e f l e c t i o n a t f r a c t u r e and  s h e a r s t r e n g t h was h i g h l y 5.  )  3  by a n a l y s i s  of variance  The s i g n i f i c a n c e o f F v a l u e i n d i c a t e s  d e f l e c t i o n means a t f r a c t u r e were n o t a l l t h e same.  that In  52 o r d e r t o a n a l y z e t h e r e l a t i o n s h i p s between d e f l e c t i o n means, Duncan's N.M.R. T e s t was c a r r i e d o u t (Appendix 6-b). A c c o r d i n g t o Duncan's N.M.R. T e s t , t h e r e was no significant difference  between t h e d e f l e c t i o n means o f [0.5]  group and [1.0] group a t t h e 1% l e v e l . d e f l e c t i o n means was; C o r r e l a t i o n Analysis  SS  x  :  SP  X3 X  b.1 = ._ bb  1  SS 3 x  = 1. 307,  1  r  X  X  :  = 56.782,  l  [1.0] < [1.5] < [ 2 . 0 ] .  (Based on d a t a i n T a b l e 1 5 ) .  F i l l e t height Deflection  [0.5],  The r a n k i n g o f t h e  l  Simple r e g r e s s i o n  = 141.889,  b_ =(JX- -J b equation  SP 1 3 X  1  :r  Coefficient of linear correlation  ** i n d i c a t e s  = 74.222  X,1 =1 0.6838  : X^ = 0.73 + 1.307 X^ 2  C o e f f i c e i n t of determination  F = 168.68  X  = 0.6 838 : r = 0.827  (n = 80) significance  a t t h e 1% l e v e l .  That i s ,  the l i n e a r r e l a t i o n s h i p between d e f l e c t i o n and f i l l e t was h i g h l y  s i g n i f i c a n t (Figure 18).  height  a  1  2 F i l l e t Height  Figure 18.  a  a  3  X  l  (mm.)  F i l l e t Height and D e f l e c t i o n R e l a t i o n s h i p i n Flexure Test Specimens  w  54  DISCUSSION  Fillet  Geometry For  cant  the  tensile  difference  treatments  of  in fillet [1.5]  however,each of different tensile  from only test  the  in fillet  test two  the  For  flexure  [2.0],  four height width.  of  test  one  fillet  sandwich  treatments  fillet  fillet  height  be  height  height  height specimens,  significantly  fact  that  the  group were  while  the  from  inference based  fillet  width  cut  flexure  g r o u p w e r e made  the  signifi-  test  was  more r e l i a b l e as  and  no  fillet  the  panels,  panels,  specimens w i l l  on  the  Considering one  was  between  o r i g i n a l sandwich  twenty d i f f e r e n t  discussion  and  specimens, there  width  specimens of  specimens  flexure  test  on  f a r as  the general  relationship  i s  concerned. As highly and  was  significant linear  fillet  width  observations if the  the  shown i n t h e  were  parabolic  considered means o f  test  chapter,  correlation  i n "both t y p e s o f  treatment  flexure  previous  t o be  are  was  fillet  a  height  s p e c i m e n when a l l t h e  fillet  specimens  between  there  independent.  height  taken  and  into  However,  fillet  width  consideration,  a  curve X  1  =  -  0.06  X  2  +  °'  5  ( X  2  "  >  fc  , 0.8  < X  2  _<  in  2.9  and X^  can be f i t t e d , where  denote the f i l l e t h e i g h t  and  the f i l l e t w i d t h , r e s p e c t i v e l y , and t denotes the t h i c k n e s s o f the honeycomb paper.  The  boundary c o n d i t i o n s o f X^  o b t a i n e d by e x t e n d i n g the sequence o f e x p e r i m e n t a l X s 1  2  to both l i m i t s The  data of  (Appendix 7 ) .  minimum f i l l e t w i d t h  (X^ = 0.30)  were  (X^  = 0.80)  and  height  g i v e n i n Appendix 7 are e x p l a i n e d i n the f o l l o w i n g  discussion.  When a honeycomb c e l l w a l l edge i s p l a c e d on a  l i q u i d glue surface  (glue depth = 0.00), the g l u e w i l l  p u l l e d up on t h e c e l l w a l l by the s u r f a c e f r e e energy the e q u i l i b r i u m i n l i q u i d - s o l i d system i s r e a c h e d . h e i g h t w i l l be 0.3 the p r e - w e t t e d  mm.  be until  This  When t h i s c e l l w a l l i s p l a c e d  plywood, the g l u e a t t a c h e d around the  on cell  w a l l edge w i l l f l o w sideways by the s u r f a c e t e n s i o n and mechanical The  the  f o r c e o f t h e c e l l w a l l movement toward the f a c i n g .  t o t a l w i d t h o f t h e s e f l o w s on b o t h s i d e s o f the  w a l l w i l l be 0.8  mm.  Then, the f i l l e t w i d t h on one  cell side of  the c e l l w a l l e x c l u d i n g the c e l l w a l l t h i c k n e s s i s 0.3  mm.  I f the c e l l w a l l i s d i p p e d into the g l u e f o r 1.40  mm.  for 1.40  example, the c e l l w a l l becomes w e t t e d + 0.30  be 1.90  mm.  = 1.70  upper l i m i t . or higher.  = 2.90  f i l l e t w i d t h i n t h a t case w i l l  T h i s means t h a t the f i l l e t w i d t h w i l l  be l a r g e r than 4.5  mm. mm.  can  by e x t e n d i n g the sequence t o the  As t h i s p o i n t the f i l l e t h e i g h t w i l l be  become l a r g e r t h a n 2.9 may  The  S i m i l a r l y , the maximum w i d t h o f the f i l l e t  be e s t i m a t e d as X^  mm.  mm.  to a height of  even though the f i l l e t  4.5 not  height  56 Grimes  (16) s u g g e s t e d  that a large f i l l e t  i s defined  as one whose w i d t h i s e q u a l t o r / 2 , where r i s t h e core c e l l s i z e ; s i m i l a r l y t h e w i d t h o f medium f i l l e t the width o f s m a l l f i l l e t  i s r/4.  i s r / 3 , and  Since the radius of  honeycomb c e l l used i n t h i s t h e s i s i s 3/8 i n c h , o r 4.7  mm.,  l a r g e f i l l e t w i d t h becomes r/2 = 2.4 mm.,  width  i s r/3 = 1.6 mm.,  medium f i l l e t  and s m a l l f i l l e t w i d t h i s r/4 = 1.2  mm.  The f i l l e t w i d t h on one s i d e o f t h e c e l l w a l l , i . e . ( X 2  0.25)/2, f o r t h e f o u r f i l l e t h e i g h t groups a r e ;  [0.5]  i  (1. 37 -- 0 .25)/2 = 0.56 (2. 58 -- 0 .25)/2 = 1.17  [1.0] [1.5]  :  (3. 80 -- 0 .2 5)/2 = 1.78  [2.0]  :  (3. 84 -- 0 .25)/2 = 1.80  T h e r e f o r e , a c c o r d i n g t o t h e c l a s s i f i c a t i o n by G r i m e s , t h e f i l l e t s i n [1.5] and [2.0] b e l o n g t o t h e medium f i l l e t while in  [1.0] b e l o n g s t o t h e s m a l l f i l l e t .  The f i l l e t  [0.5] group i s a p p r o x i m a t e l y o n e - h a l f o f t h e s m a l l  group,  width fillet  width. F i l l e t geometry a t a j o i n t o f honeycomb and plywood cannot be determined The shape o f f i l l e t  by t h e f i l l e t h e i g h t and w i d t h o n l y . i s a l s o an i m p o r t a n t f a c t o r .  When a  g l u e - t r e a t e d honeycomb was p l a c e d on a plywood s u r f a c e t h e fillet  s u r f a c e was convex a t f i r s t , b u t i t changed  concave w i t h t h e passage o f t i m e .  into  T h i s may be p a r t l y due  to  t h e change o f s u r f a c e t e n s i o n s between t h e l i q u i d and  s o l i d s t h a t was i n d u c e d by t h e g l u e d i f f u s i o n i n t o t h e honey comb w a l l and plywood.  The s h r i n k a g e o f t h e g l u e body which  took p l a c e as a r e s u l t o f g l u e s o l i d i f i c a t i o n i s p r o b a b l y c o n t r i b u t i n g t o t h e change o f s u r f a c e shape, t o o .  Although  no n u m e r i c a l measurement was made f o r d e t e r m i n i n g t h e c u r v e of  fillet  s u r f a c e s , i t was assumed f o r f u r t h e r  analysis  t h a t e v e r y concave c u r v e was f o r m i n g a p a r t o f a c i r c l e as i l l u s t r a t e d i n F i g u r e 19 - ( A ) . The  t y p e o f a d h e s i v e used i n t h i s e x p e r i m e n t was  a m o d i f i e d p h e n o l i c - r e s o r c i n o l r e s i n as was mentioned e a r l i e T h i s was a c o m m e r c i a l l y b l e n d e d a d h e s i v e and no d e t a i l o f t h e f o r m u l a was o b t a i n a b l e , n e v e r t h e l e s s i t i s assumed t h a t t h e a d h e s i v e c o n s i s t e d o f a r e s o l e b a s e d p h e n o l i c and r e s o r c i n o l formaldehyde solubility water  r e s i n s from i t s p r o p e r t y o f w a t e r  (43, 5 4 ) . I f s o , t h e g l u e s h o u l d c o n t a i n some  f o r a d i s p e r s i n g agent.  A s m a l l amount o f water i s  a l s o r e l e a s e d by t h e c o n d e n s a t i o n p o l y m e r i s a t i o n r e a c t i o n i n b o t h p h e n o l i c and r e s o r c i n o l r e s i n s ( 3 2 ) . Only s c a n t e x p e r i m e n t a l p r o o f e x i s t s f o r t h e r e a s o n of  bubble o r v o i d f o r m a t i o n i n a s o l i d i f i e d g l u e o f any  type  ( 8 ) , b u t w a t e r i s one o f t h e l i k e l y main causes o f v o i d  formation.  Some f i l l e t s  i n t h e specimens o f [2.0] group had  a r e l a t i v e l y l a r g e c a v i t y beneath t h e t h i n g l u e s k i n  which  was f o r m i n g t h e outward s u r f a c e o f t h e f i l l e t .  fact  may e x p l a i n t h e r e a s o n why f i l l e t  This  shear s t r e n g t h o f [2.0]  Figure  19.  Dimensional S e c t i o n and  Nomenclature Shear Stress  on F i l l e t Distribution  59 was  not  larger  t h a n t h a t of  s i z e i n f i l l e t h e i g h t and  [1.5]  i n s p i t e of the  w i d t h , f o r v o i d s and  a s o l i d i f i e d adhesive l a y e r  are  weakening of t o t a l g l u e l i n e  strength  Tensile  the  between the  [1.5]  major f a c t o r s  low  fillet  groups of and  i n t e n s i l e s t r e n g t h was  groups of  [1.5],  [0.5],  [ 2 . 0 ] , t h e r e was  no  t r e a t e d as one  no  and  the  group.  i n f i l l e t w i d t h between [0.5]  significant difference  Between in  Hence, t h e s e  In s p i t e of the  found  high  s i g n i f i c a n t difference  can  difference  [1.0]  [ 2 . 0 ] , as s t a t e d e a r l i e r .  f i l l e t w i d t h or t e n s i l e s t r e n g t h .  was  which cause  (8).  either be  bubbles i n  Strength A significant difference  fillet  larger  two  significant  and  [1.0], there  i n t e n s i l e s t r e n g t h between  them. By a f t e r the fracture  o b s e r v i n g the  fracture  t e n s i l e t e s t , i t was took p l a c e by  honeycomb and  was  found t h a t most of  t e n s i l e f a i l u r e i n the  total glueline p o i n t s h o u l d be  the  j o i n t of  f i l l e t s are  s t r e n g t h the known.  stress  contributing  to  d i s t r i b u t i o n and  F i l l e t shape i s assumed to  s y m m e t r i c a l w i t h r e s p e c t t o the f o r f i l l e t on one  c e l l w a l l , and s i d e o f the  paper  fillet.  a p p r o x i m a t e l y p e r p e n d i c u l a r t o the  In o r d e r t o examine how  c a r r i e d out  specimens  plywood p l u s s h e a r f a i l u r e i n the  shear f r a c t u r e  be  l i n e s i n the  The facing.  the rupture be  analysis  cell  wall.  will  F o r t h e purpose o f m a t h e m a t i c a l  expression, the  f a c i n g s u r f a c e i s t a k e n as X - a x i s and t h e c e l l w a l l i s t a k e n as Y - a x i s fillet  ( F i g u r e 19 - A ) .  I f a t e n s i l e load P per u n i t  l e n g t h i s a p p l i e d t o t h e c e l l w a l l , t h e g l u e l i n e OA  w i l l be s u b j e c t e d t o t h e t e n s i l e  X  °  1  stress:  P  2iqTt  =  ••••  [ 1 ]  A t t h e same t i m e v e r t i c a l shear s t r e s s i s d i s t r i b u t e d i n t h e f i l l e t as shown i n F i g u r e 19 - ( B ) .  The magnitude o f t h e  shear s t r e s s a t p o i n t B, x - d i s t a n c e from 0, i s x,  p  x  B  = £. . _  2  x x  r 21  "* * '  n  I f t h e concave f a c e o f a f i l l e t i s assumed t o be a q u a r t e r p o r t i o n o f a c i r c l e w i t h r a d i u s x^ then t h e f i l l e t h e i g h t y a t B i s e x p r e s s e d by:  y = x  1  - / 2 x x - x^  .... [3]  1  L e t R be t h e r a t i o o f f r a c t u r e w i d t h * X X , w  t o the f i l l e t  width  then  x = (R X  and  f  x  ±  2  - t)/2  [4]  = (X - t)/2  [5]  2  * The d i s t a n c e between t h e shear ( F i g u r e 19 - A ) .  f a i l u r e p o i n t s , B and D  S u b s t i t u t i n g t h e v a l u e s o f R (Table 7) and X^ (Table 8) i n t o  [4] and c a l c u l a t i n g t h e r a t i o , x / x ^ , i t i s  found t h a t x / x ^ becomes c o n s t a n t f o r a l l f i l l e t  height  groups;  i.e.  x=0.3x  Substituting  ....[6]  1  [6] i n t o  y = 0.3 x  [ 3 ] , i t i s determined t h a t  x  y = x  .... [7]  T h i s r e s u l t shows t h a t t h e shear f a i l u r e p o i n t on t h e f i l l e t s u r f a c e was t h e c e n t e r o f t h e concave (the p o i n t C i n F i g u r e 19 - A ) . Substituting  [6] i n t o [ 2 ] ,  = 0.35 P  x J3  S i n c e P i s p r o p o r t i o n a l t o Y, T_, i s p r o p o r t i o n a l t o Y, t o o . Therefore, x  can be e x p r e s s e d a s :  T = kY  [8]  B  where k i s a c o n s t a n t .  I n o r d e r t o examine whether o r n o t  the s h e a r s t r e n g t h o f f i l l e t  i s p r o p o r t i o n a l t o y, the  62  hypothesis  x_, = my, where m i s a c o n s t a n t , w i l l be t e s t e d . o  From [ 8 ] ,  T  = my = kY ,  d  then  y  or  ^ Y  JO  = — Y , m '  1  = c ,  where c i s a c o n s t a n t .  B u t , t h e r e s u l t s o f c a l c u l a t i o n o f — x 100 f o r [ 0 . 5 ] , Y [1.5]  and [ 2 . 0 ]  tively.  were 0 . 3 4 4 ,  0.632,  0 . 7 3 1 and 0 . 7 9 5 ,  [1.0],  respec-  That i s ,  Y then or,  7^  T_,  my  t h e shear s t r e n g t h o f the f i l l e t  a t p o i n t B was n o t p r o -  p o r t i o n a l t o t h e f i l l e t h e i g h t a t B.  Moreover,  ^ Y as e i t h e r f i l l e t w i d t h o r f i l l e t h e i g h t i n c r e a s e d .  increased The  v a l u e ^ x 100 i s a parameter which i n d i c a t e s t h e weakness o f Y fillet  under t h e v e r t i c a l shear Although  stress.  t h e shear s t r e n g t h was n o t d i r e c t l y  t i o n a l t o y, i t d i d n o t i n d i c a t e t h e l a c k o f l i n e a r s h i p between t h e shear s t r e n g t h and y.  proporrelation-  Suppose t h e r e i s a  l i n e a r r e l a t i o n s h i p between them, then  T  b  =  my  +  d  where d i s a c o n s t a n t .  . . . .  Substituting  [9]  into  [8],  [9]  63  k  m  Y  T a k i n g — = 0.22* and s u b s t i t u t i n g t h e v a l u e s o f Y and y f o r m each f i l l e t h e i g h t group, t h e v a l u e s o f k— a r e found t o be nearly constant  (Appendix 8 ) .  This s u b s t a n t i a t e s the  hypothesis [ 9 ] . These r e s u l t s r e v e a l t h a t , when a t e n s i l e l o a d normal t o a sandwich f a c i n g i s g i v e n , a f i l l e t  rupture occurs i n  v e r t i c a l shear a t the center o f the f i l l e t in  concave f a c e and  t e n s i o n a t o r near t h e j o i n t between a d h e s i v e and t h e  f a c i n g , and t h a t t h e s h e a r s t r e n g t h o f t h e f i l l e t  increases  as t h e f i l l e t h e i g h t i n c r e a s e s under t h e r e l a t i o n s h i p :  T = my The  + d,  where 0 < m < 1  and  d > 0  absence o f s i g n i f i c a n t d i f f e r e n c e i n t e n s i l e  s t r e n g t h between [1.5] and [2.0] may be owing t o t h e l a c k o f significant difference i n f i l l e t  s i z e between them.  absence o f s i g n i f i c a n t d i f f e r e n c e i n t e n s i l e  strength  between [0.5] and [1.0] cannot be e x p l a i n e d . * From [1.0] and [ 1 . 5 ] , 0.348 + d/m 54.9  0.531 + d/m 72.6  t  •  d/m = 0.22  The  Although t h e r e was a h i g h l y s i g n i f i c a n t between d e f l e c t i o n fillets  correlation  a t f r a c t u r e and t e n s i l e s t r e n g t h ,  glue  are not c o n s i d e r e d as the main f a c t o r c o n t r i b u t i n g  to the d e f l e c t i o n .  The e l o n g a t i o n  i n the composite  of  plywood and paper honeycomb may be the main f a c t o r . proposed reasons (a)  The  are:  The magnitude o f d e f l e c t i o n was g r e a t e r than the fillet  height.  much as i t s  The f i l l e t  height,  since  i t breaks by shear b e f o r e (b)  It is  cannot e l o n g a t e it  is  so b r i t t l e  so that  i t e l o n g a t e s t h a t much.  supposed t h a t s t r e s s e s i n e i t h e r plywood  o r honeycomb d i d not exceed the p r o p o r t i o n a l limit.  That i s ,  the d e f l e c t i o n  of plywood o r  honeycomb was p r o p o r t i o n a l t o the t e n s i l e Hence the l i n e a r c o r r e l a t i o n between the s t r e n g t h and the d e f l e c t i o n highly  load. tensile  o f the specimen was  significant.  The type of f a c i n g f a i l u r e was such t h a t the plywood edge s p l i t p a r a l l e l to the g r a i n t o the depth o f the i n n e r face ply. for  The average percentages [0.5]  as the lowest and 9.2% f o r  S i n c e these v a l u e s 10%, the  o f f a c i n g f a i l u r e were [1.0]  are c o m p a r a t i v e l y low,  as the i.e.  f a c i n g f a i l u r e i s not c o n s i d e r e d as a  f a c t o r f o r the a n a l y s i s o f f i l l e t  functions.  a l s o supported by the c o r r e l a t i o n a n a l y s i s .  1.2%  highest.  l e s s than significant This fact  is  Shear S t r e n g t h A c c o r d i n g t o t h e d a t a p u b l i s h e d by H e x c e l , I n c . t h e s h e a r s t r e n g t h o f t h e honeycomb used f o r t h i s t h e s i s was 70 p s i . ( p e r p e n d i c u l a r t o r i b b o n d i r e c t i o n ) .  By u s i n g t h e ( 4 ) , the  f o r m u l a f o r d e t e r m i n a t i o n o f c o r e shear s t r e s s maximum l o a d f o r f l e x u r e t e s t i s approximated  .  s  where  i , (h + c ) b P  S = 70 p s i . , h = 1.5 i n c h ,  i n c h and  as f o l l o w s i  c = 1.0 i n c h ,  b = 3.75  = l o a d i n l b s . by mid-span l o a d i n g .  P  x  = S ( h + c ) b = 656.25 ( l b s . ) .  T h i s means t h a t t h e sandwich  p a n e l specimen w i l l  f a i l by c o r e  shear i f t h e f l e x u r e l o a d exceeds 656 l b s . by mid-span l o a d ing.  The v a l u e o f P w i l l  i n c r e a s e t o some e x t e n t  under t h e l o a d i n g method p r a c t i s e d i n t h i s t h e s i s 9).  ( P = 685) 2  (Appendix  As t h e d a t a show (Tables 10, 11, 12, 13) no f l e x u r e l o a d  exceeded 600 l b s , n e v e r t h e l e s s most o f t h e specimens o f l a r g e r f i l l e t groups, i . e . [1.5] and [ 2 . 0 ] , f a i l e d i n c o r e s h e a r b e f o r e g l u e l i n e f a i l u r e took p l a c e . to for  T h i s might be due  the lack of e x t r a c a u t i o n taken during pressure the higher f i l l e t  control  groups.  When paper honeycomb i s w e t t e d by g l u e i t becomes much s o f t e r than i n t h e d r y c o n d i t i o n .  The paper honeycomb  treated  with the  portion  than  fore,  the  buckling groups  control higher  the  higher i f the  50  the  their  those  100  gauge  was  p s i . , hence  i t w o u l d not be a b l e t o  a  or  compressive  In  spite  and less  and  that of  groups  the  shear  core  sufficiently  the  sandwich  show  case  first  into  fillet  fillet.  of  in  the  beyond Even  of  of  though over-  this  by  fillet between  fillet  width  [1.0]  was  significance. I f the  fillet  medium  fillet,  chapter,  horizontal  more s h e a r  found  strength of  interpretation  i s , the  carries  were  s m a l l and  construction i s affected  smaller  sensitive  higher  between  level  in  larger  How-  applied.  i n the  i s unknown.  section  i n the  That  5%  data.  The  group.  panels  subsequently  statistical sandwich  approx-  i t s i n h e r e n t s t r e n g t h when  failures  at the  a l l fillet  p a p e r h o n e y c o m b was  correlations  classified  difficulty  the  for  was  condition.  mean s h e a r  particular are  wet  s t r e n g t h , and  The  [0.5]  discussed i n the  r e m a i n s no  pressure  not  l o a d was  significant  for this  height  of  strength.  than  cause  as  highly  shear  The  soft  There-  to the  glue height  once  and  g r e a t e r chance  the  i n the  pressed  height  l a r g e r wet  groups might have been overpressed  f a i l u r e were i n v i s i b l e ,  fillet  a  curing process.  proportional limits  groups,  a  same p r e s s i n g l o a d i s g i v e n  pressure  below  had  shallower spreads.  groups had  p s i . regardless of  fillet  shear  spread  treated with  fillet  during the  imately ever,  deeper glue  the  stress  of  there  the  shear  strength  fillet than  size.  does  the  The  67 The  appearance of the f a i l u r e i n the g l u e l i n e  s i m i l a r t o t h a t i n the t e n s i l e t e s t .  The  f i l l e t height  [1.5]  groups o f  c a l c u l a t e d as 0.24,  [0.5],  0.27,  0.28  [1.0], and  r a t i o x/x  0.27,  and  was for  1  [2.0]  '.are  respectively.  i t i s assumed t h a t the concave f a c e o f the f i l l e t was quarter is  p o r t i o n o f a c i r c l e w i t h r a d i u s x , t h e n the x  considered  t o have t a k e n p l a c e by b r e a k i n g  the  If the  fracture fillet  v e r t i c a l l y a t the m i d d l e p o i n t s o f the concave f a c e on s i d e s o f the c e l l w a l l and them.  The  f o r m e r was  l a t t e r was  due  both  the g l u e - p l y w o o d j o i n t between t o the shear f o r c e , w h i l e  the  r e g a r d e d as a r e s u l t of the c o m b i n a t i o n o f  c o m p r e s s i o n , t e n s i o n and  the  shear f o r c e s .  More  accurately,  the g l u e - p l y w o o d j o i n t was  also carrying t e n s i l e stress  because of the d e f l e c t i o n  (14).  68  SUMMARY AND  CONCLUSION  When the m o d i f i e d p h e n o l i c - r e s o r c i n o l r e s i n g l u e was used f o r bonding k r a f t paper honeycomb t o plywood a sandwich  construction, f i l l e t s  were formed around the  j o i n t s o f honeycomb and plywood. in  t o make  Fillet  terms o f i t s h e i g h t and w i d t h .  I t was  s i z e was  measured  found t h a t the c o r e s  t r e a t e d w i t h h e a v i e r glue spread produced h i g h e r and wider fillets, was  and the c o r r e l a t i o n between f i l l e t  highly significant.  convex  at f i r s t ,  c a t i o n proceeded. fillet  size.  h e i g h t and width  The s u r f a c e shape o f f i l l e t  but i t changed  was  i n t o concave as g l u e  T h i s phenomenon was  However, some f i l l e t s  solidifi-  true regardless of  i n large f i l l e t  groups,  e s p e c i a l l y i n [2.0] group, had a r e l a t i v e l y l a r g e v o i d underneath a t h i n g l u e s u r f a c e .  I t i s w e l l known t h a t v o i d s i n  a  s o l i d i f i e d adhesive l a y e r are one o f the major  to  decrease  the t o t a l g l u e l i n e s t r e n g t h .  probably apply t o f i l l e t may  as w e l l .  factors  This fact  will  Hence a too l a r g e  fillet  s u f f e r a weakening e f f e c t from v o i d f o r m a t i o n . In  the t e n s i l e t e s t most o f the f r a c t u r e s were  observed a t the glue-plywood j o i n t by the t e n s i l e and a t the middle o f the f i l l e t shear. fillet  T h i s tendency was h e i g h t group.  failure  concave f a c e by the v e r t i c a l  encountered r e g a r d l e s s o f the  69  The a fillet  v e r t i c a l shear s t r e n g t h a t t h e f r a c t u r e l i n e i n  can be e x p r e s s e d a s :  T  where is  f i  =  my + d  ,  i s t h e s h e a r s t r e n g t h a t t h e f r a c t u r e p o i n t B, y  t h e f i l l e t h e i g h t a t B, m and d a r e c o n s t a n t s .  means t h a t t h e v e r t i c a l shear s t r e n g t h o f a f i l l e t  This at the  f r a c t u r e p o i n t B i n c r e a s e s as t h e f i l l e t h e i g h t a t B i n c r e a s e s by t h e r a t i o o f m.  The v a l u e o f m, w h i c h i s  g r e a t e r t h a n z e r o and l e s s than one, can be o b t a i n e d empirically. m.  The v a l u e o f d i s a p p r o x i m a t e l y  e q u a l t o 0.22 x  I f t h e r e e x i s t s a v o i d i n t h e f i l l e t , however, m w i l l  assume a much s m a l l e r v a l u e than t h e c a l c u l a t e d v a l u e based on t h e a n a l y s i s .  I t was a l s o n o t e d t h a t , i n t h e use o f  paper honeycomb as t h e core f o r a s t r u c t u r a l sandwich cons t r u c t i o n , the r i g h t pressure  f o r t h e assembly s h o u l d be  c a r e f u l l y s t u d i e d s i n c e t h e c o r e , when i t i s wet w i t h tends t o f a i l  glue,  i n s h e a r o r c o m p r e s s i v e b u c k l i n g more e a s i l y  t h a n when i t i s d r y . In g e n e r a l , a l a r g e r f i l l e t w i t h s t a n d s B u t , as f a r as t h e a d h e s i v e  too  size increases.  large a f i l l e t  load.  used i n t h i s t h e s i s i s c o n c e r n e d ,  the r a t e o f i n c r e a s e o f f i l l e t fillet  bigger  s t r e n g t h d e c r e a s e s as t h e  I t was p r e v i o u s l y p o i n t e d o u t t h a t  i s a p t t o produce v o i d s w i t h i n i t ,  r e s u l t i n g i n lowering strength values.  Such a  fillet  70 d i m i n i s h e s the c h a r a c t e r i s t i c s t r e n g t h  of i t s s i z e .  There-  f o r e , t o o l a r g e a f i l l e t i s not e f f i c i e n t f o r good b o n d i n g , n o t o n l y f o r e c o n o m i c a l r e a s o n s , b u t a l s o by interference.  technical  71 BIBLIOGRAPHY  1.  A n d e r s o n , L.O. 1964. A r e v i e w o f FPL s t u d i e s on s t r e s s e d - s k i n and s a n d w i c h - p a n e l u n i t s . F o r . P r o d . J . 14 (5) : 192-194.  2.  (Anonymous). 1969. P a i n t t h i c k n e s s . J o u r n a l o f P a i n t Technology. V o l . 41. No. 533. June: 375pp.  3.  ASTM Committee. 1963. A d h e s i o n o f c o a t i n g s o f p a i n t , v a r n i s h , l a c q u e r , and r e l a t e d p r o d u c t s . ASTM D e s i g n a t i o n : D2197-63.  4.  . 1961. F l e x u r e t e s t o f f l a t sandwich c o n s t r u c t i o n s . ASTM D e s i g n a t i o n : C39 3-62. 1961. S t a n d a r d d e f i n i t i o n s o f terms r e l a t i n g t o s t r u c t u r a l sandwich c o n s t r u c t i o n s . ASTM D e s i g n a t i o n : C274-53. 1965. S t a n d a r d methods o f p r o d u c i n g f i l m s of uniform thickness of p a i n t , v a r n i s h , lacquer, and r e l a t e d p r o d u c t s on t e s t p a n e l s . ASTM D e s i g n a t i o n : D823-53. .  1961. Shear t e s t i n f l a t w i s e p l a n e o f f l a t sandwich c o n s t r u c t i o n s o r sandwich c o r e s . ASTM D e s i g n a t i o n : C273-61. 1961. T e n s i o n t e s t o f f l a t sandwich cons t r u c t i o n s i n f l a t w i s e p l a n e . ASTM D e s i g n a t i o n : C297-61. 9.  B i k e r m a n , J . J . 1961. The S c i e n c e o f A d h e s i v e J o i n t s . Academic P r e s s , New Y o r k , pp. 128-133.  10.  B u i l d i n g Research I n s t i t u t e . 1958. A d h e s i v e s and Sealants i n B u i l d i n g . N a t i o n a l Research C o u n c i l , Washington, D.C, 12 3pp.  11.  Cagle, C V . 1968. Honeycomb and sandwich c o n s t r u c t i o n . A d h e s i v e Bonding. M c G r a w - H i l l , New Y o r k , pp. 70-84.  12.  D i e t z , A.G.H. 1969. Composite E n g i n e e r i n g L a m i n a t e s . The M.I.T. P r e s s , Cambridge, M a s s a c h u s e t t s , 70pp.  13.  E i c k n e r , H.W. 1947. D u r a b i l i t y o f g l u e d j o i n t s between aluminum and e n d - g r a i n b a l s a . U.S. F o r . P r o d . L a b . Rep. 1566.  72 14.  Gray, V.R. 1962. The w e t t a b i l i t y o f wood. P r o d . J . 1 2 ( 9 ) : 452-461.  15.  Grimes, G.C. .1966. The adhesive-honeycomb r e l a t i o n s h i p . A p p l i e d Polymer Symposia No. 3. S t r u c t u r a l A d h e s i v e s Bonding. I n t e r s c i e n c e P u b l i s h e r s , New Y o r k , pp. 157-190.  16.  Heebink, B.G., and Mohaupt, A.A. 1947. Investigation o f methods o f i n s p e c t i n g bonds between c o r e s and f a c e s o f sandwich p a n e l s o f the a i r c r a f t t y p e . U.S. F o r . P r o d . Lab. Rep. 1569.  17.  Heebink, B.G. 1950. M o i s t u r e - e x c l u d i n g e f f e c t i v e ness o f edge s e a l s f o r a i r c r a f t sandwich p a n e l s . U.S. F o r . P r o d . Lab. Rep. 1822.  18.  H e x c e l , I n c . 1970. N o n - c o m b u s t i b l e k r a f t paper honeycomb. S p e c i f i c a t i o n Grade D.S. 1007 (1970). H e x c e l , I n c . , Long Beach, C a l i f o r n i a .  19.  Houwink, R., and Salmon, G. 1967. A d h e s i o n and A d h e s i v e s . V o l . 2. E l s e v i e r P u b l i s h i n g Co. , Amsterdam, pp. 361-362, and pp. 533-536.  20.  Humke, R.K. 1958. S e l e c t i o n guide f o r sandwich-panel core m a t e r i a l s . Product Engineering. January 20: 70-75.  21.  For.  . 1958. S e l e c t i o n guide f o r sandwich-panel a d h e s i v e s . P r o d u c t E n g i n e e r i n g . May 26: 56-60.  22.  Hunt, W.D. 1958. The Contemporary C u r t a i n W a l l . F.W. Dodge C o r p o r a t i o n , pp. 309-335.  23.  Japanese Government F o r e s t E x p e r i m e n t S t a t i o n . 1960. Handbook o f Wood I n d u s t r y . Maruzen P u b l i s h i n g Co., Tokyo, pp. 357-420.  24.  Kommers, W.J. 1944. The f l e x u r a l r e s i d i t y o f a r e c t a n g u l a r s t r i p o f sandwich c o n s t r u c t i o n . U.S. F o r . P r o d . Lab. Rep. 1505-A.  25.  K u e n z i , E.W. 1966. A n i s o t r o p i c Sandwich ASTM STP" 40 5 : 14pp.  Constructions.  26.  . 1949 . E f f e c t o f e l e v a t e d t e m p e r a t u r e s on the s t r e n g t h s o f s m a l l specimens o f sandwich cons t r u c t i o n o f t h e a i r c r a f t t y p e . U.S. F o r . P r o d . Lab. Rep. 1804.  27.  . 1951. F l e x u r e o f s t r u c t u r a l sandwich c o n s t r u c t i o n . U.S. F o r . P r o d . Lab. Rep. 1829.  73 28.  L e w i s , W.C. 1 9 4 6 . F a t i g u e of sandwich c o n s t r u c t i o n s for a i r c r a f t . U . S . F o r . P r o d . L a b . Rep. 1559.  29.  Muto, K . , T s u j i i , S . , and Umemura, T . 1959. Kenchiku Kozo R i k i g a k u ( S t r u c t u r a l Mechanics i n A r c h i t e c t u r e ) . Ohm C o . , Tokyo.  30.  Panek, E . , and Heebink, B . G . 1 9 4 8 . R e p a i r o f a i r c r a f t sandwich c o n s t r u c t i o n s . U . S . F o r . P r o d . L a b . Rep. 1584.  31.  Parker, R . S . R . , Adhesives.  32.  P a t t o n , T . C . 1 9 6 4 . P a i n t Flow and Pigment D i s p e r s i o n . I n t e r s c i e n c e P u b l i s h e r s , New Y o r k , pp. 435-415.  33.  P i e r c e , P . E . 1969. Rheology o f c o a t i n g s . Journal of P a i n t Technology. V o l . 41, No. 533, June: 383pp.  34.  Plantema, F . F . 1966. Sandwich C o n s t r u c t i o n . Wiley & Sons, I n c . , New Y o r k , pp. 55-77.  35.  Plywood Manufacturers A s s o c i a t i o n o f B . C . (Undated). Plywood d e s i g n fundamentals. F i r Plywood Reference Manual. Plywood Manufacturers A s s o c i a t i o n o f B . C . , Vancouver.  36.  S c o f i e l d , W . F . , and O ' B r i e n , W.H. 1 9 6 3 . Modern Timber Engineering. Southern Pine A s s o c i a t i o n . New O r l e a n s , p p . 88-94.  37.  Timoshenko, S . , Elasticity. 142.  38.  U . S . F o r e s t Products L a b o r a t o r y . 19 50. Methods f o r c o n d u c t i n g mechanical t e s t s o f sandwich c o n s t r u c t i o n s at normal temperature. U.S. For. Prod. L a b . Rep. 1556 (Revised).  39.  and T a y l o r , P. Pergamon P r e s s ,  1966. Adhesion and O x f o r d , pp. 76-92.  John  and G o o d i e r , J . N . 1951. Theory o f 2nd E d . Kogakusha Co.,Tokyo/ pp. 140-  . 1955. S t r u c t u r a l d e s i g n o f sandwich c o n s t r u c tion. Wood Handbook. A g r i c u l t u r e Handbook No. 72? 291-298.  40.  W e i b e l , E . E . 1 9 3 4 . American S o c i e t y o f M e c h a n i c a l Engineers - T r a n s a c t i o n s . V o l . 56.  41.  Weiss, P . , B e r r y , J . P . , and Bueche, A . M . 1 9 6 2 . Adhesion and C o h e s i o n . E l s e v i e r P u b l i s h i n g C o . , New Y o r k , p p . 18-35.  i 42.  Wood, L . W . 1 9 5 8 . Sandwich panels f o r b u i l d i n g tion. U . S . F o r . P r o d . L a b . Rep. 2121.  construc-  74  TABLES  Table 1.  P a r t i a l Results of Preliminary Test f o r Determination of Loading System  F i l l e t Height flax. Load  Two-Point Loading I  5^7 l b s .  i' = o  Failure  Glueline  Blank Max.  Load  563 l b s .  457 l b s .  Facing tension  Failure  Facing tension  shear  = l A  Mid-Span Loading  [2.0]  380 l b s .  Facing tension  Table 2 .  R e s u l t s of T e n s i l e Test f o r F i l l e t  Sample T e n s i l e DeflecStrength t i o n mm. psi. No.  Fillet  1  2  Height  Height Group [ 0 . 5 ]  mm.  3  4  Mean  Fillet  Width  mm.  1  2  3  4  F.F.  Mean  %  1  39  0.23  1.20  1.40  1.40  1.05  1.26  1.45  1.10  1.15  0.95  1.16  0  2  40  0.25  0.95  1.45  1.50  1.25  1.29  1.30  1.20  1.50  1.40  1.35  0  3  46  0.20  1.10  1.35  1.20  1.10  1.19  1.10  1.25  1.25  1.20  1.20  0  4  51  0.48  0.90  1.55  1.25  1.30  1.25  1.35  1.50  1.30  1.20  1.3^  0  5  46  O.36  1.45  1.45  1.45  1.40  1.44  1.75  1.75  1.60  1.65  1.69  0  6  43  0.63  1.45  1.15  1.00  1.15  1.19  1.40  1.10  1.25  1.30  1.26  0  7  52  0.56  1.45  1.35  1.25  1.10  1.29  1.30  1.25  1.60  1.40  1.39  0  8  52  1.02  1.30  1.50  1.70  1.30  1.45  1.55  1.50  1.70  1.65  1.60  0  9  62  0.51  0.95  1.30  1.20 •1.15  1.15  1.20  1.20  1.20  1.20  1.20  12  10  54  0.38  1.20  1.40  1.35  1.24  1.45  1.50  1.35  1.60  1.48  0  48.5  0.462  1.367  1.2  Mean  1.00  1.275 F.F. = F a c i n g  Failure  Table 3.  Results of T e n s i l e Test f o r F i l l e t  Sample T e n s i l e D e f l e c Strength t i o n mm. No. psi.  Fillet 1  2  Height 3  Height Group [1.0]  mm. 4  Fillet  Mean  1  2  Width 3  mm. 4  F.F.  Mean  %  1  77  0.53  2.00  2.20  2.20  2.00  2.10  4.60  3.20  3.35  2.80  3.^9  8  2  65  1.22  2.00  2.25  2.20  1.95  2.10  1.85  2.35  1.80  2.05  2.01  10  3  50  0.81  1.80  2.15  2.20  2.45  1.90  2.50  2.40  2.55  2.60  2.51  12  4  41  0.33  1.80  1.60  2.00  1.50  1.73  2.20  2.00  2.05  2.05  2.08  24  5  60  0.74  2.20  1.85  1.95  1.95  1.99  2.80  2.40  2.35  2.30  2.46  8  6  61  1.17  1.90  1.75  2.00  2.10  1.94  2.50  2.40  2.10  2.25  2.31  6  7  49  0.56  2.15  2.30  1.90  1.90  2.06  2.90  3.25  2.85  2.80  2.95  12  8  53  0.76  1.85  2.00  1.80  1.80  1.86  2.55  2.25  2.00  2.60  2.35  8  9  55  0.51  1.75  2.50  2.20  2.50  2.24  2.95  2.65  2.90  2.55  2.76  0  10  38  0.33  2.50  2.50  2.20  2.30  2.38  3.05  3.00  2.40  2.85  2.83  4  5^.9  O.696  2.575  9.2  Mean  2.030 F.F. = F a c i n g  Failure  Table 4 .  Sample No.  Results of Tensile Test f o r F i l l e t Height Group [ 1 . 5 ]  Tensile DeflecStrength tion mm. psi.  Fillet 1  2  mm.  Height 3  4  Mean  F i l l e t Width 1  2  3  mm. 4  F.F.  Mean  %  1  66  0.79  2.35  2.55  2.60  2.35  2.46  3.60  3.25  3.70  2.95  3-38  0  2  63  1.15  2.65  2.95  2.90  2.95  2.86  3.80  3.50  3.^5  3.70  3.61  12  3  69  0.99  2.95  2.95  2.60  2.40  2.73  3.25  3.65  4.20  3.40  3.63  14  4  49  0.38  2.50  2.80  2.95  2.55  2.70  3.95  3.30  3.30  3-75  3.58  0  5  72  0.97  3.00  2.95  2.40  2.70  2.76  3.85  3.80  4.50  *K35  4.13  12  6  79  0.99  2.55  2.85  3.10  2.75  2.81  3.75  3.70  4.30  5.00  4.19  8  7  79  1.07  2.50  2.35  2.50  2.45  2.45  4.45  4.45  3.65  4.40  4.24  0  8  93  1.02  2.50  2.35  2.35  2.70  2.48  4.05  3.40  3.20  3.80  3.61  12  9  84  0.99  2.50  2.65  2.70  2.65  2.63  3.55  4.00  ^.35  4.05  3-99  16  10  72  1.02  2.70  2.40  2.60  2.35  2.51  3.60  3.70  3.35  3.70  3.59  0  72.6  0.937  3.795  7.*  Mean  2.639  F.F. = Facing Failure CO  Table 5.  Results of Tensile Test f o r F i l l e t Height Group [2.0]  Sample Tensile DeflecStrength tion psi. mm. No.  Fillet 1  2  Height 3  mm. 4  Mean  F i l l e t Width 1  2  3  mm. 4  F.F.  Mean  %  1  83  1.07  3.15  2.60  2.50  2.90  2.79  4.20  4.00  3.55  4.45  4.05  0  2  75  0.71  3.45  3.20  3.^5  2.95  3.26  3.95  3.65  3.85  3.85  3.83  0  3  70  0.58  3.20  3.20  3.50  3.25  3.29  3.95  4.00  3.80  3.80  3.89  8  4  79  0.86  2.85  3.00  3.20  2.70  2.94  3.90  4.25  3.70  4.20  4.01  0  5  59  0.51  3.40  3.80  3.90  3.20  3.58  3.95  3.80  3.60  3.80  3.79  14  6  69  1.25  3.30  3.15  3.40  3.20  3.26  3.45  3.25  3.05  3.70  3.36  0  7  61  0.51  3.55  3.60  3.15  3.20  3.38  3.10  3.20  4.35  4.60  3.81  4  8  55  0.61  3.50  3.25  3.20  3.45  3.35  4.00  3.85  3.40  4.40  3-91  3  9  58  0.64  3.60  3.35  3.50  3.00  3.36  3.80  4.25  3.65  3.70  3.85  1  10  67  0.64  3.40  3.25  3.35  3.15  3.29  4.25  3.60  4.10  3.60  3.89  6  67.6  0.738  3-839  3.6  Mean  3.250 F.F. = Facing Failure  Table 6.  Glue Depth and F i l l e t Test Specimens  Height i n T e n s i l e  Glue Depth  Fillet  [0.5]  0.7 mm.  1.28  [1.0]  1.4  2.03  O.63  [1.5]  2.1  • 2.64  0.54  [2.0]  2.8  3.25  0.45  Fillet Group  Height  Height  Difference  mm.  0.58 ram.  T a b l e 7.  1  No. X  [0. 5]  w  1 2 3 5 6  40  1 3 6 7 8  130 110 88 113 90  3  145  55 56 60 70  Mean  [1. 0]  Mean  [1- 5]  5 6 10  Mean  [2. 0]  1 2 3 4 8  Mean  Fracture/  X  x /x f  f  140  X  0.231 0.382  137  40 45  0.310 0.322  109 95  0.282 0.300  145  0.341  41  108 80  156 0.354 137 0.273 150 0.375 119 0.325 O.362 O.362 0.321  53 50 50 54  56  0.400  w  f  f  20 20  0.357 0.500  30 35 29  w  X  55 47 76 65 50  0.466  30  X  w  0.374  42  Note: X  2  0.310  17 21 28 25 20  174 52 158 56 165 45 125 47 163 138 138 168  Fillet-Width Ratio  140  133  148  158  140  = Fillet = Width  28  32 21  30 32 32  40 54 64  49 44 42  45 4o  45  55  x /x f  i nSelected  3  w  0.364 0.425 0.369 0.494 0.420  x  w  54 54 54  65  54  0.292 0.416 0.375 0.294 0.338  105 105 93 125 100  0.276  142  0.346 0.466  0.327 0.470 0.300 0.345 O.270 0.285 0.393  x  Tensile Test  x /x  f  f  4  0.444 0.444  24 24  0.306 O.368 0.376 O.360  105 115 89 119 97  45 42 45  0.352 0.330  137  41  0.360  158 125  144  41  0.371  32 35 35  45  28  0.280  50  40  131 136  54  0.420 0.414  49 50  0.297 0.339  53 51  0.321 0.392  165 157 150 165 130  60  49  43  0.286  145  128  129  141  175  145  25 26 30 22  30 36  53 49 50  40  57 50 49 56  w i d t h i n 1/1000 i n c h of fracture i nf i l l e t  f  24  0.426 0.414  23 27 20  w  X  40 56 50 71 47  121  143  X  w  i n  1/1000  inch.  Specimens  x /x f  w  Mean R=Xf/X  0.600  0.430  0.520  0.445  0.446  0.423  0.469  0.422  0.421 0.440  0.432  0.428 0.365 0.393 0.252 0.372  0.314 0.383 0.371  0.300 O.366 0.310 0.328 0.347  0.302 0.336 0.387 0.336 0.388 0.350  0.312 0.442  0.309 0.372 O.318 O.302  0.354 0.280 O.386  0.304  0.328 0.340  0.417  0.344  w  Table 8.  A u x i l i a r y Table f o r S t a t i s t i c a l A n a l y s i s of T e n s i l e T e s t R e s u l t s - (A)  Fillet Height X^  [0.5]  D e f l e c t i o n Facing x F a i l u r e X^  3  13.67  4.62  16.3467  18.9699  2.6708  144  162.5625  186.8689  21.3444  144  0.0904  0.2830  0.5364  s  0.10  0.18  X  1.275  1.367  2  (sx)  2  ss  12  Tensile S t r e n g t h Y.  239.71 235225  129.6  448.5  0.24  3.8  7.1  0.46  1.2  48.5  20.03  25.75  6.96  41.5318  68.0859  412.0900  5^9  5.7H0  1208  31335  663.0625  48.4416  8464  301401  0.3228  1.7796  0.8668  s  0.19  0.44  X  2.030  2.575  ZX^ (SX) SS  2  sx  26.39  zx  69.8577  c  37-95 144.8807  361.6  1194.9  0.31  6.3  11.5  0.696  9.2  5^.9  9  9  726  9.37 9.1979  df  485  92  EX  2  [1.5]  2  12.75  £X zx  [l.o]  Fillet Width X  948  54042  CO  Table 8.  (Continued) x  2  X  3  1440.2025  87.7969  0.2145  0.8604  0.4182  s  0.15  0.31  X  2.639  3-795  X  4  5476  Y  400.4  133^.^  0.22  6.7  12.2  0.937  7.4  72.6 676  5.9990  322  46496  1473.7921  54.4644  1296  456976  0.4590  0.3169  0.5526  s  0.23  0.19  X  3.250  3.839  2  HIT (EX) SS  2  32.50  38.39  106.0840  147.6961  1056.2500  7.38  192.4  798.4  0.25  4.6  9.4  0.74  3-6  67.6  214 2622 1144.9  2436 155844 148352.4  ZX ZX CF  91.94 233.8202 211.3240  115.76 379.6326 312.2574  28.33 23.5787 20.0647  X  0.79 2.30  1.37 2.89  0.31 0.71  2  SS S  22.4962  67.3752  3.51^0  1477.1 6.41  5-35  df  527076  36  sx  Note:  X  696.4321 ss  Total.  l  7^81.6 14.42  60.90  9  9  36  SS = Sum of squares, S = Standard deviation, CF = Correction factor = ( £ X ) / 4 0  CO  Table 9.  Auxiliary Table f o r S t a t i s t i c a l Analysis of Tensile Test Results - (  X^Xg  "^1^3  ^1^  ^2^"  X^Y  X/^Y  [0.5]  17.5674  5-9775  617.38  664.50  230.60  744  [1.0]  52.6600  14.0223  1115.03  1427.11  398.22  4860  [1.5]  100.233^  24.7352  1909.75  2769.IO  695.56  5678  [2.0]  124.6050  23.9656  2180.53  2599.33  5H.60  2255  Total  295.0658  68.7006  5822.69  7460.04  1835.98  13537  GP  2 )  266.07  65.117  SP  3 )  28.99  3.580  Note:  1) Symbols from Table 8 2) Correction factor 3) Sum of products  5599.146  7049.78  1725.29  13032.6  223.5^  410.26  110.69  504.4  Table No.  10.  R e s u l t s o f F l e x u r e Test f o rF i l l e t Fillet  Max. S h e a r DeflecLoad S t r e n g t h t i o n lbs. p s i . nun.  Height  540 475 496 500 443  56.9 50.0 52.2 52.6 46.6  2.54 1.91 2.29 2.87 1.83  1.30 0.60 1.05 0.90 0.60  1.45 0.70 1.00 1.00 0.70  1.40 0.65  6 7 8 9 10  485 455 475 495  51.1 47.9 50.0 52.1 50.7  2.16 2.03  0.85 0.95 0.70 0.70 1.00  0.50  0.80 0.60  0.75 0.80 1.10  0.90  535  56.3 49.1 54.5 51.9 51.8  2.03 1.98 2.11 2.03  0.80 1.00 1.35 0.95 0.90  1.00 0.95 1.15 0.95 0.60  0.95 0.95 1.15  1.91  0.70  0.70  2.80 2.03  0.65 0.80 0.60  0.70 0.85 1.00 0.70 0.85  482  11 12 13  466  15  492  16 17  445 439 490  14  18  19 20  Mean  518 493  500  46.8 46.2 51.6 46.9 52.6  483.5  50-89  446  2.03 I.63  2.46  2.80 1.65  Group  Fillet  [0.5] Width  (mm.)  0.80  0.80  1.25  0.95  O.65  0.75 1.00  1.25 1.00  1.00 1.00 0.80 0.85  2.19  1.70  1.46  1.65 2.00 1.00 1.60 1.70  1.75  1.40  1.55 1.20 1.65  1.25 0.85 0.70  0.93 0.66  1.85 2.00 1.15 1.25 1.60  0.70 0.75 0.80 0.75 1.10  0.71 0.78 0.79 0.75 I.05  1.45 1.30 1.35 1.30 1.45  1.60 1.30 1.60 1.30 1.10  1.45 1.45 1.35 1.65 0.75  1.10 1.00 0.95 1.15 0.95  0.96 0.98 1.15  0.86  1.45 1.10 1.70 1.45 1.25  1.45 1.20 1.70 1.35 1.30  1.25 0.90 1.70 1.20 1.45  0.60 1.10 1.10 0.70 0.85  0.68 0.94 0.94 0.75 0.79  1.10 1.05 1.45 0.95 1.45  1.20 0.85 1.50 1.10 1.35  1.15 1.00 1.50 1.00 1.45  0.80  0.69  1.14  1.08  0.90  Type o f Failure Mean  Mean  1 2 3 4 5  2.80  (mm.)  Height  1.40  1.00 1.70 1.40  1.66 1.74 1.18 1.44 1-59  GF GF GP GF GP  1.60 1.35 1.35 1.60  1.53 1.35 1.43 1.46  GF+CP GF GF+CF GP GP  1.45  1.40  1.45 1.25 1.70  1.64 1.43  GP GF GF+CP GF+CF GP  1.25  1.19 0.95 1.48 1.06 1.41  GP GP GP+CP GP GP  1.55  0.80  1.00  0.90  1.45  1.20 1.40  1.03 1.05  1.31  1.37  N o t e : CP = C o r e f a i l u r e GF = G l u e l i n e f a i l u r e FF = F a c i n g f a i l u r e . CO  Table No.  11.  Max. S h e a r Deflee Load S t r e n g t h t i o n lbs. p s i . mm.  1 2 3 4 5  467 469 470 441 480  49.2 49.4 49.5 46.4  6 7 8 9 10  424 485 453 480 447  44.6  11  50.3  14 15  478 464 402 455 480  16 17  422 460  12 13  18 19 20 Mean  Results of Flexure Test f o rF i l l e t  50.5 51.1  47.7  50.5  47.1  2.16  3-81 2.82 • 1.53 2.04 1.78 2.42 2.80 2.04 2.28  1.50 1.80  1.60 1.90 1.85 1.20  I.65 2.30 1.85 1.40  48.9 42.3 47.9  50.5  44.4 48.4 49.5  2.54 4.82 2.04  1.60 1.10 1.00  425  44.7  3.56  460.6  48.48  3.05  [1.0]  Height  (mm.)  Fillet  Width  (mm.)  Mean  2.00 1.80  56.8  Group  Type o f Fillet  2.04 2.67 1.83 2.80 2.04  470 540  Height  1.50  1.80  1.90  1.35 1.30  Mean  Failure  1.75 1.90 2.10 1.75 1.90 1.80 1.65 1.90 1.85 1.70  1.50 1.95 2.00 1.50 1.85  1.65 1.80 1.85 1.60 1.90  1.60 1.86 1.89 I.69 1.88  1.35 2.35 1.75 1.25 2.00  1.70 1.90 1.80 1.95 1.90  1.85 1.70 1.30 1.70 2.00  1.70 2.10 1.45 1.80 1.90  1.65 2.01 1.58 1.68 1.95  GF GF+CF CF GF GF  1.60 1.60 1.90 1.90 1.45  1.80 1.85  1.60 I.69 1.98 1.90 1-53  I.65 2.15  1.70 2.15 2.15 2.10 2.20  2.15 2.35 2.10 2.05 I.65  1.65 2.25 1.95 2.00 2.15  1.79 2.23 2.15 1.95  GF GF+CF GF GF GF  2.25 1.80 1.45 1.70 1.85  2.25 1.65 1.65 1.90 1.90  2.30 2.00 1.80 2.00 1.80  2.20  1.90  2.15 1.55 1.60 2.70 1.85  2.05 1.80 2.05 2.00 1.95  2.00 1.70 1.45 1.70 2.00  2.09 1.59 I.69 1.88 1.93  GF GF GF GF GF  1.95  1.65 1.30 1.60 1.60 1.35  1.95  1.79 1.30 1.19 I.36 1.34  1.75 1.75 I.85 2.00 2.15  2.00 2.05 1.60 2.05 1.90  2.00 2.15 I.65 2.15 2.00  2.00 2.20 1.65 1.95 2.00  1.94  GF+CF CF+FF GF+CF GF CF  1.40  0.80 1.10 1.25  2.55  N o t e : CF = C o r e f a i l u r e GF = G l u e l i n e f a i l u r e FF » F a c i n g f a i l u r e .  1.80  2.00 1-55  1.40  1.35 1.40 1.45  1.81  1.60 1.85 1.86  1.70  2.40  2.00  1.80  2.15 1.30 I.65 1.80  2.04  2.04  I.69  2.04  2.01  1.90  CO  Table  No.  12.  Max. S h e a r Load Strength lbs. psi.  Results Deflection  mm.  1 2 3 4 5  502 518 517 555 5^5  52.8 54.5 54.4 58.4 57.^  2.92 2.54  6 7 8 9 10  519 54? 472  54.6 57.6 49-7 57.7 56.9  3.04  11 12  500 550  548 541  15  495  52.6 57.9 54.1 52.1  16 17  505 527 510 495 493  53-2 55.5 53.7 52.1 51.9  13  18  19 20 Mean  514  518.2 54.54  3-81 3-81  3.56  3.81 3.81 3.04 3-81  of Flexure Fillet  1  Test Height  f o rFillet  (mm.)  2  3  4  2.40  2.35 1.80 2.35  Group  [1.5]  Fillet  Width  (mm.)  1  2  3  4  Mean  2.35 2.01 2.25 2.26 2.25  2.40  2.20 2.55 2.50 2.45 2.65  2.65 2.30 2.00 2.25 2.25  2.65 2.75 2.25 2.35 2.60  2.48  2.35  2.50 1.80 2.50 2.60 2.35  GF GF GF+CF GF+CF GF+CF  2.30  2.00  2.30  2.50 2.34 2.41  2.30 2.55 2.45 2.60 2.10  2.60 2.15 2.45 2.35 2.15  2.30 2.38 2.45 2.38  2.14  GF+CF CF GF+CF GF+CF GF+CF  2.40  2.35 2.70 2.50 2.15 2.30  2.60 2.40 2.25 2.20 2.25  2.05 2.20 2.60 2.45 2.30  2.20 2.35 2.65 2.55 2.80  2.40  2.41  2.35 2.80 2.30 2.30  2.40  2 30 2.15 2.10  3-91 3-94 3.30  2.35 2.65 2.45 2.30  2.40  2.50 2.35 2.75  2.85 2.45 2.20 2.25  2.85 2.50 2.25 2.50  2.61 2.53 2.31 2.45  2.20 2.10 2 25 2.45  2.25 2.05  3.68  2.60 2.3Q 2.60 2.60 2.85  2.75 2.30 2.30 2.70 2.75  2.55 2.10 2.50 2.45 2.50  2.50 2.35 2.45 2.25 2.65  2.60 2.26  2.20  2.45 2.30 2.35 2.30 1.95  3.81 3.81  3.56 3.30 4.06  Type o f Failure  Mean  2.15 2.00 2.00 1.90 1.90  2.45 2.15 2.15  Height  3.54  2.46  2.50 2.69 2.39  2.40  2.45 2.05 2.45  2.40  2.20  2.40  2.60  2.40  2.20  2.40  2.49 2.39 2.34 2.45  2.10 2.45 2.25  2.20 2.20 2.50  2.40  2.31 2.11 2.33 2.35  GF+CF CF CF CF  2.40  2.35 2.60 2.30 1.95 2.15  2.35 2.58  GF+CF CF CF CF GF  3.00 2.80 2.45 1.85  2.48  2.19 2.10  2.34  N o t e : CF = C o r e f a i l u r e GF = G l u e l i n e f a i l u r e FF = F a c i n g F a i l u r e . CO  Table  13. Results of Flexure Test f o rF i l l e t  No. Max. S h e a r lbs.  psi. 62.6  1 2  595 482  3 4  590 500  5  575  60.5  6  560  7 8  517 508  9 10  526  50.7 62.1  Deflec-  mm. 6.35  3.81  Fillet 1 2.95 2.95 3.00  Height  2 3.05 3.15 3.00  3  2.50  3.U  2.25  3.05 2.85 3.20  3.23 2.66  2.00  3.15  2.35  2.90  3.11  2.64  3.00  3.45 2.50 3.10  2.85  2.90  2.95  2.70  2.45  3.06  2.95 3.65  2.90 3.60  2.80  3.40  3.40  3.33  2.60  3.00  2.79  3.40  3.50  3.90 3.20  3.40 3.20  2.55 3.15  3.05  58.9 54.4  5-85 5.85  3.20  3.80  3.20  53-5  3.81  3.10 2.60  5.08  539  55.4 56.7  3-05 2.25  2.55 2.85 2.40  6.35  3.05  11 12  500  52.6  13  550 536  58.9 57.9 56.4 62.6  5-59 4.32  2.65  560  14  54.2  5.08  3.20  49.5 55-8  5.96 5.04  3.85  505 530  5.40  3.55 3.60  3.75  53.2  2.80  3.20  55.8  5.08  2.95  2.90  2.90  534.2  56.22  5.22  16  515 470  Mean  3.50 3.10 2.80  2.75  595  19 20  3.40  4.57  15  17 18  5.85 4.32  3.45 2.80  530  Note:  3.35 3.70  CF = C o r e f a i l u r e GP = G l u e l i n e f a i l u r e FF = F a c i n g f a i l u r e .  3.45 2.70  (ram.)  Type o f Failure Mean  2.80  3.20  Width  Mean  3.05  3-79 5.85  2.55 3.50  4  G r o u p [2.0]  Fillet  2.65  3.85 2.65  2.90 3.00  (mm.)  2.55 3.30  2.60  52.6  6.35  Height  2.45 2.45 2.50 2.60 2.70  2.80  2.35 2.60  2.05  2.15 2.05 2.85  2.20  2.58 2.49 2.45 2.78 2.58  CF CP CF GP+CF CP  2.90  2.55 2.40 2.80 2.60  2.65  2.60  2.35 2.60  2.36  2.75  2.55 2.70 2.90  2.70 2.75 2.35 2.20 2.20  2.43 2.68  CP CF GP+CP GP+CF CF  2.15 2.65 2.65 2.45 2.60  2.85  2.95  2.15  2.70  2.45  2.80  2.65 2.75  2.35 2.20 2.40 2.40  2.53 2 54 2.58 2.38 2.64  CF CF CP CP CF  3.36  3.00  3-71  2.35  3.43 3.26 2.86  2.35  2.90 3.30 1.60 3-10 3.00  2.98 2.66 2.29 2.93 2.83  CP CF CF+FF CP CP+FP  3.15 2.81  3.56  3.09  3.00  2.60 2.70  2.70 2.75  2.40 2.80  2.85 2.50  2.25  3.20  2.80  2.70  2.30  2.80  2.40 3.10 2.85  2.90 2.75  2.66 2.31  2.58  CO OO  Table  14.  Fracture/Fillet-Width  l  No. x  [0.5]  4 5  0.33 0.37  28  76 70  26 27 24 24 3^  4 11 13 14  [2.0]  25  75  73  70 79  1 2 6 9 10  110 102  4 8 9  200  90  97 121  100 75  X  w  0.37 0.46  1  70  f  2  23 23  65  12  [1.5]  63 50  x /x  f  9 2  [i.o]  w  x  75 49 65 81 65  0.29  19  0.34  75 68 75 80 80  0.39 O.33  0.34 0.43  0.36  40  38 25  0.37 0.28 0.46  ^5 35  70  4o 27  X  w  99 95  f  30  x^/x^  i n Selected  3 X  w  0.40 0.43 0.34 0.43 0.34  57 53 65 65  30 25  0.40  80 70  30  O.38  21 22 35 22  28 40  37 38 43 ^5  0.37 0.37  0.50  69  70 76 75  x  f  24  Flexure  f  w  25  0.42 0.47  25 25  0.39 0.37  20  30 18  25 30 32  0.31  0.38 0.26 O.36  0.40 0.43  0.46 0.45 0.35  30  97 99 100 95 85  ^5 45 35 34  32  O.36 O.38  0.22  195 145  50 50  0.26 0.35  0.29 0.35 0.40  170 128  37  163  62  30  0.23 0.38  150  1/1000  Note: X  w  = Fillet  width i n  X  f  = Width  of fracture  ^5  Test  Specimens  4 x /x  0.37 0.40 0.34 0.40 0.24  125 112 125  O.36  Ratio  0.30  X  w  X  Mean  f  X^/Xw  ?  0.45  65  24 20  75  25  0.37 0.40 0.33  80 73 75 70 85  25 25  55  49  50  100 100 95  116  2<  24  20 27 40  0.49  x77x  w  0.41 0.46 0.33  0.39 0.37  0.39  0.31 0.34 0.27  0.36  0.47  0.46  0.39  0.34 0.34  O.38 O.38  36  O.36  0.39  29  0.31 0.29  0.32  40  120  33 42  139 110 93  48 46 37  0.40  0.35 0.35 0.42 0.40  0.41  O.38 0.32  O.36  0.30 0.35 0.35 0.34  inch  i nfillet  i n  1/1000  inch. CO  Table 15. Auxiliary Table f o r S t a t i s t i c a l Analysis of Flexure Test Results  Fillet Height X £X  [0.5]  sx  2  (sx)  2  Deflection 2  x  3  27.33  48.89  17.1361  38.3119  99.1713  51972.50  746.9289  1926.3321  1035916.84 176.66  327.2481  s  0.20  0.23  0.39  X  0.90  1.37  2.19  50.9  33.92  37.93  51.07  969.7  58.7832  72.6421  142.3241  47202.53  1150.5664  1438.6849  2608.1449  940318.09  11.9169  I86.63  2  (sx) ss  2  1.2549  0.7079  s  0.26  0.19  0.79  X  1.70  1.90  2.55  nx  47.82  46.83  x  2  114.8128  109.9895  70.70 253.1512  df  1017.8  18.09  2.8547  zx  S  Shear Strength Y  0.9655  sx  Ci.53  Fillet Width X  0.7737  ss  [1.0]  x  3.05  3.13  19  19  48.5  1090.8 59604.96  VD O  Table 15.  (Continued)  X  C1.5J  (six)  x  2  3  Y  df  1189844.64  2193.0489  0.4752  0.3371  3.1267  S  0.16  0.13  0.41  X  2.39  2.34  3.54  54.5  HX  61.77  51.68  104.30  1124.3  4998.49  192.4819  134.2492  3815.5329  2670.8224  1.7053  0.7081  s  O.30  0.19  0.88  X  3.09  2.58  5.22  zx  2  (ZX) ss  Total  X  2286.7524  2  SS  [2.0]  l  EX X  2  (rx) SS s  X  2  161.60 383.2140 26114.5600 56.7820 0.86 2.02  163.77 355.1929 26820.6129 19.9351 0.51 2.05  Note: SS = Sura of squares,  558.2140 10878.49 14.7895  269.96 1052.8686 72878.4016 141.889 1.37 3-37  S = Standard deviation  112.73 2.44  19  63481.05 1264050.49 278.53 3.83  19  56.2 4202.6 222261.04 17661846.76 1487.96 4.42 52.5  76  92  APPENDICES  93  APPENDIX 1  Tables of Analysis of Variance and Duncan's New Multiple Range Test f o r F i l l e t Width means i n Tensile Test Specimens  a. Analysis of Variance Source  ss  df  Height Treatment  21.378  64 • 135  3  F  MS  Error  36  3 .240  Total  39  67 • 375  237.53**  0.090  ** indicates s i g n i f i c a n c e a t the 1% l e v e l .  b. Duncan's New Multiple Range Test Tr.  X  2  TV  t Q 5  S3R  > Q 5  ^  D  [2.0]  3-839 3-114  0.2958  +  [1-5]  3-795 3-018  0.2863  +  +  [1.0] 2.575 2.870  0.2762  -  +  [0.5]  2  ^  W  > Q 1  S5R  <Q1  D  l  4.126 0.3919 +  +  4.015 0.3814 +  +  3.851 O.3658 -  +  +  1.367  [0.5] 1.367  [1.0] 2.575  [1.5] 3.795  Means underlined significantly(P = .01).  [2.0] 3.839 by the same l i n e d i d not d i f f e r  APPENDIX  94  2  Tables o f A n a l y s i s of V a r i a n c e and Duncan's New M u l t i p l e R a n g e T e s t f o r T e n s i l e S t r e n g t h Means i n T e n s i l e T e s t S p e c i m e n s  a.  Analysis  of Variance  Source  df  ?  MS  3  3715-4  1238. 5  Error  36  3776.2  104. 9  Total  39  7491.6  Height  Treatment  ** i n d i c a t e s  b.  SS  s i g n i f i c a n c e a t t h e 1%  D u n c a n ' s New M u l t i p l e Tr.  w  .05  S S R  Range  .05  D  l  [1.5] 72.6  3.114  10.09  +  [2.0] 67.6  3.018  9.78  +  [1.0]  2.870  9.30  54.9  11.81**  level.  Test  D  2  D  3  W  .01  SSR  D  > 0 1  4.126  13.36  +  +  4.015  13.00  + +  +  3.851  12.47  -  2  D-j  +  [0.5] 48.5 / EMS  n = 10, [0.53 48.5  =\/- - = 3.239 n  [1.0] [2.0] [ 1 . 5 ] 67.6 72.6  54.9  Means u n d e r l i n e d b y t h e same l i n e significantly  (P = .01).  d i dn o t d i f f e r  -  95  APPENDIX 3  Basic Equations  a. Modulus of Rupture of Pacing i n Bending ( 3 0 ) M y I  b~  M =TT ( i - / )  _ ^(" - o ) " 12 3  T 1  3  j P i - I') »h = b h3 - 3  =  =  (rb  0  3Ph(i -1') 2b(h3 - o ) J  —  where  cr : modulus of rupture i n bending (psi.) b  M  bending moment ( i n . l b . )  I  moment of I n e r t i a ( i n . )  4.  b : width of beam (in.) P : load (lbs.)  -h  •4\  £P  4P  C  JL  APPENDIX 3 (Continued)  b. Horizontal Shear Stress i n Glueline (37)  VQ  Q  lb £?(b/8)(h b(h  where  3  2  - c ) 2  - c ) h 3  12  - ~  8  t>(h  3P(h  2  - o )  4b(h  3  - c )  2  -  c ) 2  2  : horizontal shear stress  3  (psi.)  V : t o t a l shear a t the section  (lbs.)  Q : s t a t i c a l moment of the area above the plane upon which the unit shear i s computed, taken 3  about the neutral axis of the beam ( i n . ).  97 4  APPENDIX  T a b l e s o f A n a l y s i s o f V a r i a n c e a n d Duncan's New M u l t i p l e R a n g e T e s t f o r F i l l e t W i d t h Means i n F l e x u r e T e s t S p e c i m e n s  a.  Analysis  of Variance  Source  SS  MS  3  17.216  5.739  Error  76  2.719  Total  79  19.935  Height  df  Treatment  ** i n d i c a t e s  b.  Tr.  x  2  T V  .05  Range  SSR.05  D  l  D  2  3.066  0.129  +  [1 • 51 2 . 3 4  2.969  0.125  +  +  [1.0]  1.90  2.821  0.118  +  +  [0.5]  1.37  n = 20,  2  v  t h e 1% l e v e l  D  3  +  TV .01  3 S R  .01  D  l  of significance.  2  0.169  +  3.905  0.164  +  +  3-746  0.157  +  +  t o D u n c a n ' s N.M.R. T e s t ,  <[1.0]<[1.5J<[2.0]  D  4.013  n  means r a n k e d a s :  at  level.  S= = 1 / ^ = 0.042  According  [0.5]  a t t h e 1%  Test  2.58  [2.0]  160.3**  0.0358  significance  D u n c a n ' s New M u l t i p l e  F  fillet  width  D  3  +  98  APPENDIX 5  Tables o f A n a l y s i s o f V a r i a n c e and Duncan's New M u l t i p l e R a n g e T e s t f o r S h e a r S t r e n g t h Means i n f l e x u r e T e s t S p e c i m e n s  a.  Analysis  of Variance  Source  MS  F  3  733.42  244.47  Error  76  755-54  9.93  Total  79 1487-96  Height  Treatment  ** i n d i c a t e s  b.  ss  df  significance  D u n c a n ' s New M u l t i p l e Tr.  1  TV  t  Q  SSR  5  Range  > Q $  ^  24.62**  a t t h e 1% l e v e l .  Test D g D3  TV  < Q 1  SSB  > 0 1  D  D  1  [2.0] 56.22 3.066  2.160  +  4.013 2.827 +  [1.5] 54.54 2.969  2.092  + +  3.905  2.751  + +  [0.5] 50.89 2.821  1.987  -  3.746  2.639  -  + +  2  +  [1.0] 48.48 / EMS  n = 20,  S =\j - g - = 0.7045 Y  At  t h e 5% l e v e l  of significance;  At  t h e 1% l e v e l  of significance;  [1.0] [0.5] [1.5] [2.0] 48.5 50.9 54•5 56.2 [ l . o ] [0.5] [1.5] [2.0] 48.5 50.9 54.5 56.2  Means u n d e r l i n e d b y t h e same l i n e significantly.  d i d not  differ  D3  -  99  APPENDIX 6  T a b l e s o f A n a l y s i s o f V a r i a n c e a n d Duncan's New M u l t i p l e R a n g e T e s t f o r D e f l e c t i o n M e a n s i n F l e x u r e Test Specimens  a.  Analysis of Variance Source  df  MS  3  109. 59  Error  76  32. 30  Total  79  141. 89  Height  Treatment  ** i n d i c a t e s  b.  SS  x  3  T V  .o  S S R 5  Range  .05  D  l  D  2 3 D  5.22 3.066  0.448  +  [1.5J  3.54 2.969  0.433  +  +  [1.0]  2.55 2.821  0.412  +  +  [0.5]  2.19 = 20,  [0.5] 2.19  S^  0.425  Test  [2.0]  n  -  T V  .01  3 S R  .01  D  l  2 3  D  D  4.013  0.585  +  3.905  0.570  +  +  3.746  0.546  +  +  =^jp = 0.146  [1.0] [1.5] C2.0] 2.55 3.54 5-22  Means u n d e r l i n e d b y t h e same l i n e significantly  85.95**  36.53  s i g n i f i c a n c e a t t h e 1% l e v e l .  D u n c a n ' s New M u l t i p l e Tr.  F  ( P = .01).  d i d not differ  -  100 APPENDIX 7  Sequences o f F i l l e t  Width Means (Unit  Empirical  Ext. Glue Depth  h  h - t ~2  1st  difference  2nd  difference  1.40  2. 10  2.80  3.50  4.20  0.30  0. 90  1.70  2. 39  3. 09  3.80  4.50  0.80  1. 37  1.90  2. 34  2. 58  2.80  2.90  0.30  0. 60  0.85  1.05  1. 20  1.30  1.35  0.30  0.25  0.05  = Fillet  height  X  2  = Fillet  width  = Honeycomb c e l l =  Ext.  0.70  1  Ext.  0.20  0.05  wall  0.15  0.05  thickness  0.10  0.05  0.05  0.05  (0.2  mm.)  Extrapolated APPENDIX 8  Y a l u e s o f k/m f o r the Four F i l l e t Y  mm.)  0.00  X  t  :  x  1  = (X  2  Height  - t ) / 2 y = 0.3*1  Groups 1  0  0  k  /  [0.5]  48.5  0.557  0.167  0.81  [1.0]  54.9  1.161  0.348  1.03  [1.5]  72.6  1.771  0.531  1.04  [2.0]  67.6  1.793  0.538  1.13  Jc_ _ y +_0.22 m " Y  m  101  APPENDIX 9  Gore Shear Stress under Two-Point Loading When two  loading points are located at a distance  of 3/8-span from each support, core shear stress i s c a l c u l a t e d as follows S =  where  (.4):  (h + c)b  k  core shear s t r e s s (psi.) h = sandwich thickness  = 1.5  inch  c = core thickness = 1 inch b = sandwich width = 0.375 inch P  = flexure load (lbs.) —3 k = 1 - e , and 2  f = f a c i n g thickness = 0.25  inch  E = modulus e l a s t i c i t y of the f a c i n g = 1,800,000 psi.(36) G = e f f e c t i v e core shear modulus = 8,000 p s i .  If  S = 70 p s i •  then  P  2  = 70  (1.5  »  + 1)  x 3.75  x 0.958  = 685 l b s .  

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