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Some mechanical and rheological properties of the netted gem potato Timbers, Gordon Ernest 1964

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SOME MECHANICAL AND RHEOLOGICAL PROPERTIES OF THE NETTED GEM POTATO  by  GORDON ERNEST TIMBERS B.S.A., • U n i v e r s i t y o f B r i t i s h Columbia,  1962  A THESIS SUBMITTED IN PARTIAL FULFILMENT OP THE REQUIREMENTS FOR THE DEGREE OF MASTER OP SCIENCE IN AGRICULTURE  i n . t h e Department of Agricultural  Mechanics  We accept t h i s t h e s i s as conforming t o t h e required  standard  THE UNIVERSITY OF BRITISH COLUMBIA MAY,  196^  In  presenting this thesis i n p a r t i a l fulfilment of  the requirements for an advanced degree at the University Of • B r i t i s h Columbia, I agree that the Library shall make i t available for reference and study.  freely  I further agree that per-  mission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives.  It i s understood that,- copying or publi-  cation of this thesis for financial gain shall not be .allowed without my written permission.  Department of  Agricultural Mechanics  The University o f B r i t i s h Columbia, Vancouver 8, Canada Date"May, 196b  ii  ABSTRACT  In  o r d e r to'be a b l e t o p r e d i c t , t h e b e h a v i o u r  of the potato  under c o n d i t i o n s o f a p p l i e d l o a d ; a d e s c r i p t i o n o f the m e c h a n i c a l  tuber  and  T h e o l o g i c a l p r o p e r t i e s i n terms o f e n g i n e e r i n g parameters i s necessary.-.  • !Phe b e h a v i o u r of.,external, l o a d . •  o f t h e p o t a t o was s t u d i e d under s e v e r a l c o n d i t i o n s  Equipment t o . f a c i l i t a t e t h e a p p l i c a t i o n o f v a r i o u s  t y p e s o f l o a d s t o the m a t e r i a l was purchased  or c o n s t r u c t e d .  Electronic  s e n s i n g and r e c o r d i n g equipment was used t o observe t h e response o f t h e . m a t e r i a l t o . t h e a p p l i e d loads-.  One-half p o t a t o t u b e r s were used.to  study t h e response o f t h e  potato to the a p p l i c a t i o n of a constant s t r e s s .  • Whole t u b e r s were  s u b j e c t e d t o c o n d i t i o n s o f c o n s t a n t s t r a i n t o observe t i o n w i t h i n the potato tuber.  One i n c h , and two i n c h c o r e s as w e l l  as h a l f t u b e r s were used when s t u d y i n g t h e response compression  stress relaxa?  of the potato to  over a range o f s t r a i n ' r a t e s . a n d under f o u r l o a d i n g a r e a s .  Under c o n d i t i o n s of e x t e r n a l l o a d i n g i t was found t h a t - t h e p o t a t o behaves as a v i s c o e l a s t i c m a t e r i a l and t h a t t h e methods f o r t h e a n a l y s i s of l i n e a r v i s c o e l a s t i c behaviour  were a p p l i c a b l e .  When h e l d under a c o n s t a n t s t r e s s t h e p o t a t o was found t o exh i b i t the property of creep.  The creep r a t e was dependent on t h e  a p p l i e d s t r e s s and t h e t o t a l creep d e f o r m a t i o n was dependent on t h e s t r e s s and t h e d u r a t i o n o f l o a d i n g .  The p o t a t o t u b e r s p o s s e s s t h e p r o p e r t y . o f s t r e s s  relaxation*  The  s t r e s s or f o r c e r e l a x a t i o n curve may, b e • r e p r e s e n t e d  e x p o n e n t i a l e q u a t i o n f o r p e r i o d s up•to t e n m i n u t e s .  by a t h r e e term  For periods'longer  t h a n . t e n minutes a f o u r term e x p o n e n t i a l e q u a t i o n would be adequately  d e s c r i b e the f o r c e r e l a x a t i o n c u r v e .  •When s u b j e c t e d . t o compressive l o a d i n g the was  found  required.to  potato tuber  flesh  to become more r i g i d w i t h . i n c r e a s i n g r a t e s o f s t r a i n .  a r e a o f the t e s t p l u n g e r  used t o l o a d t h e sample was  found t o have a  marked i n f l u e n c e - o n the apparent modulus o f e l a s t i c i t y ,  when.this  value-was c a l c u l a t e d from the s l o p e o f t h e s t r e s s - s t r a i n the l o a d i n g under s m a l l d i a m e t e r - p l u n g e r s a reasonable  approximation  The  curve.  While  i s o f a v e r y complex nature,  o f the apparent modulus of e l a s t i c i t y  may  be o b t a i n e d u s i n g the a n a l y s i s f o r a r i g i d d i e a c t i n g . o n a semiinfinite elastic  solid.  The  unsupported p o t a t o f l e s h was  apparent.modulus o f e l a s t i c i t y f o r - t h e found  to be 579  + 76 p s i .  The degree of e l a s t i c i t y of the p o t a t o t u b e r was •relatively  c o n s t a n t up. t o a l o a d o f 70  0.820 j> .0^1. 70  to-120 l b s . , was of  O.69I  e l a s t i c i t y was  The  strain.  _+ . 026.  The  overall  mean v a l u e f o r the degree  .Ojk.  energy r e q u i r e d t o produce f a i l u r e  The  loads  The mean degree o f e l a s t i c i t y f o r l o a d s from-80  O.765 _+  under compression was of  between t h e l o a d s - o f  a much.less marked d e c r e a s e • o c c u r r i n g w i t h  g r e a t e r than 80 l b s .  found  i n the p o t a t o  to i n c r e a s e w i t h a d e c r e a s e  tuber  i n the r a t e  i n c r e a s e i n energy r e q u i r e d a t low r a t e s of  strain  i s a t t r i b u t e d t o the p r o p e r t y o f s t r e s s r e l a x a t i o n e x h i b i t e d . b y potato.  t o be  l b s . w i t h a.mean v a l u e o f  An abrupt, decrease-was observed  and 80'lbs..with  found  the  The p o t a t o was  found, t o absorb a l a r g e p o r t i o n of t h e energy  used i n d e f o r m i n g , t h e t u b e r , as i n d i c a t e d . b y The  a.large  h y s t e r e s i s l o s s on t h e f i r s t l o a d i n g c y c l e was  w i t h an i n c r e a s e i n t h e a p p l i e d f o r c e . t h e r e was  hysteresis-loop.  found t o  F o r t h e subsequent•two c y c l e s  no a p p a r e n t . c h a n g e • i n . t h e l o s s w i t h a n . i n c r e a s e  applied force.  increase  Hysteresis l o s s i n potato-tuber  • be c o n s i d e r a b l y h i g h e r t h a n w i t h w h o l e - t u b e r s .  i n the  cores-was found t o  ACKNOWLEDGEMENT  The author wishes t o express h i s g r a t i t u d e t o P r o f e s s o r L.M. S t a l e y and P r o f e s s o r E.L. Watson f o r t h e i r a s s i s t a n c e and a d v i c e d u r i n g t h i s study.  Thanks  i s extended t o D r . A . J . Renney f o r making a v a i l a b l e the p o t a t o e s used f o r t h i s study.  Acknowledgement  i s made o f t h e a s s i s t a n c e extended b y Dr. D.P.. Ormrod i n regard t o t h e s t r u c t u r e o f the potato i t u d e i s extended t o P r o f e s s o r structive  suggestions  tuber.  Grat-  S.L. L i p s o n f o r h i s ' c o n -  regarding theory  of e l a s t i c i t y .  S p e c i a l note i s made o f t h e s e r v i c e performed by. Mr-. W. Gleave d u r i n g t h e c o n s t r u c t i o n o f t h e t e s t  equip-  ment . Appreciation  i s extended t o the B.C. Coast Vege-  t a b l e M a r k e t i n g Board f o r f i n a n c i a l  support  which  ed i n d e f r a y i n g t h e expenses i n c u r r e d i n t h i s  aid-  study.  v TABLE OP CONTENTS  Page 11  INTRODUCTION  REVIEW OF LITERATURE  1  THE STRUCTURE OF THE POTATO  k  STRUCTURE IN RELATION TO MECHANICAL PROPERTIES  5  I n t e r c e l l u l a r Adhesion  5  C e l l W a l l s and C e l l Contents  5  C e l l Turgor  6  Variability  7  o f t h e P o t a t o Tuber  8  THEORY Stress Relaxation  9  Creep Deformation  9 10  Compression  VISCOELASTIC ANALYSIS  12  The Maxwell Model  13  The V o i g t Model  13  Creep Behaviour  ±h  Relaxation Behaviour  15  16  TESTING EQUIPMENT S t a t i c T e s t Apparatus  16  Compression  18  T e s t Equipment  A.  "Servo-Tec" Compression  B.  B e l l o w s V a l v a i r Hydrocheck  18  Unit Compression  Unit  21  vi  Page  E l e c t r i c a l Measurement and R e c o r d i n g  23  Load C e l l  2k  Beam C a l c u l a t i o n s  2k  O p e r a t i o n o f O s c i l l o s c o p e and an X-Y Recorder  26  TEST PROCEDURES  26  S t a t i c Test T r i a l s  26  Stress Relaxation  27  Hysteresis  28  Compression  T e s t Procedures  Summary o f Compression  Tests  RESULTS  29 31  33  Apparent Modulus o f E l a s t i c i t y  33  Apparent Modulus vs S p e c i f i c G r a v i t y  33  Apparent Modulus v s Rate o f S t r a i n  3I+  Apparent Modulus v s L o a d i n g P l u n g e r Type  35  Relative E l a s t i c i t y  38  Stress Relaxation  kO  Hysteresis  2+3  Creep B e h a v i o u r  kk  F a i l u r e Energy  2+5  Stress-Strain-Rate o f Strain Relationship  k6  DISCUSSION OF RESULTS  i+7  Specific Gravity  2+8  Rate o f S t r a i n  kd  vii  Page  Plunger  Diameter  k°52  Stress Relaxation Failure  i n t h e Potato  53  Tuber  55  Static Failure A R h e o l o g i c a l Model F o r t h e Potato Practical Applications  Tuber  56 57  CONCLUSIONS  60  BIBLIOGRAPHY  6k  6j  APPENDIX A  Compression T e s t Data  APPENDIX B  S t a t i c T e s t Data  87  APPENDIX C  S t r e s s R e l a x a t i o n Data  98  APPENDIX D  H y s t e r e s i s Data  101  viii  LIST OF TABLES  Table I II  Page • Summary of Compression Tests Mean Values For the Apparent Modulus of  31 36  Elasticity Calculated From the Slope of the Stress-strain Curve III IV  Degree of Elasticity Data  39  Stress Relaxation time Constants  h2  ix  LIST OF FIGURES  Figure 1  Diagram o f t h e P o t a t o Tuber  2  T y p i c a l Creep Curve  10  3  S t r e s s - s t r a i n Curve f o r S t r u c t u r a l S t e e l  11  k  H y s t e r e s i s E f f e c t and R e l a t i v e E l a s t i c i t y  12  5  The B a s i c Elements  13  6  E x t e n s i o n Response t o a U n i t F o r c e  15  7  :  Page 6  . 17  . Schematic Diagram o f S t a t i c T e s t U n i t  8  Sample Undergoing S t a t i c T e s t  17  9  "Servo-Tec" Compression U n i t  18  10  "Servo-Tec" D r i v e T r a i n  19  11  Schematic Diagram o f t h e Crosshead Assembly  20  12  B e l l o w s V a l v a i r Compression U n i t  22  13  M o d i f i e d B e l l o w s V a l v a i r Compression U n i t  23  ik  Schematic Diagram o f One Load C e l l Beam  2k  15  Schematic Diagram o f Load C e l l With L.V.D.T. i n P l a c e  25  l6..  Stress Relaxation  28  17  Apparent'Modulus v s S p e c i f i c G r a v i t y f o r 1"  18  A r i t h m e t i c P l o t o f Mean Ea v s P l u n g e r Diameter  37  19  L o g . Mean Ea v s P l u n g e r Diameter  37  20 21  'Ea v s "b" V a l u e s From S/&  Plunger  vs  T e n s i o n F a i l u r e i n Tuber Compressed.Between P a r a l l e l  3^+  . k"J 53  Plates 22  F a i l u r e i n a 1"  23  F a i l u r e Under a 1"  P o t a t o Tuber Core P l u n g e r A c t i n g , on a 2" Core •  5^ 5^  Figure .2.4.  Page P o t a t o Tuber Damage A f t e r Three Weeks Under a  55  S t a t i c Load o f 91'5 p s i . 25  Tuber A f t e r k& Hours Under a S t r e s s o f 91«5  26  Tuber A f t e r k& Hours Under a S t r e s s o f 6 l p s i .  27 28  . Tuber A f t e r kQ Hours Under a S t r e s s o f 3O.5  psi.  psi.  H y p o t h e t i c a l - R h e o l o g i c a l Model t o Represent t h e Potato  55 56 56 57  xi  LIST OF PLATES  To F o l l o w Plate  Page  1  Degree o f E l a s t i c i t y  vs H y s t e r e s i s Loss  39  2  Degree o f E l a s t i c i t y  vs I n i t i a l F o r c e  39  3  Sample X-Y S t r e s s - s t r a i n Record  82  k  Sample S t r e s s - s t r a i n Photographs  82  5  Sample S t r e s s - s t r a i n Photographs  82  6  Extrapolation of Stress Relaxation  7  Sample H y s t e r e s i s Record f o r 1 i n c h Tuber Core  103  8  Sample H y s t e r e s i s Record  103  Equation  98  xii  DEFINITION OF TERMS  Apparent modulus  Apparent modulus o f e l a s t i c i t y f o r a v i s c o e l a s t i c material, c a l c u l a t e d from t h e l o a d i n g segment of the s t r e s s strain  curve.  D e f o r m a t i o n o c c u r r i n g under a  Creep  constant  stress. A loosely f i t t e d hydraulic cylinder.  Dashpot  Ratio of recovered Degree o f  elasticity  total  deformation  to  deformation.  Energy absorbed by t h e m a t e r i a l d u r i n g Hysteresis loss  l o a d i n g and u n l o a d i n g The  Mechanical p r o p e r t i e s  a  cycle.  s t r e n g t h c h a r a c t e r i s t i c s of a  material. P r o p o r t i o n a l i t y constant r e l a t i n g s t r e s s  Modulus o f  elasticity  and  s t r a i n i n an e l a s t i c m a t e r i a l .  Dealing w i t h the o v e r a l l sensation Organeoleptic  of  taste. Stress d i s s i p a t i o n within a stressed  Relaxation  m a t e r i a l h e l d under c o n s t a n t  Rheological properties  Time dependent m e c h a n i c a l p r o p e r t i e s .  Strain  Deformation i n inches per i n c h of material being  Stress  tested.  F o r c e per u n i t a r e a .  strain.  INTRODUCTION  The p h y s i c a l p r o p e r t i e s o f a g r i c u l t u r a l p r o d u c t s must be d e f i n e d i n terms o f e n g i n e e r i n g parameters  "before t r u e d e s i g n c a l c u l a t i o n s  r e g a r d i n g t h e b e h a v i o u r o f t h e p r o d u c t can be i n c o r p o r a t e d i n the design- o f s t o r a g e and h a n d l i n g  facilities.  U n t i l r e c e n t y e a r s work on the m e c h a n i c a l b e h a v i o u r o f a g r i c u l t u r a l crops has been p r i m a r i l y e m p i r i c a l i n n a t u r e .  Considerable  emphasis has been p l a c e d on t e x t u r a l e v a l u a t i o n o f the p r o d u c t s from  an  o r g a n o l e p t i c p o i n t of view, however, such e v a l u a t i o n i s not u s e f u l i n u n d e r s t a n d i n g the fundamental  T h i s study d e a l s cal of  p r o p e r t i e s o f the m a t e r i a l under study.  w i t h  some o f the mechanical  p r o p e r t i e s o f one p r o d u c t , t h e N e t t e d Gem the fundamental  potato.  and  T h e o l o g i -  Some a s p e c t s  n a t u r e o f t h e b e h a v i o u r o f the p o t a t o are s t u d i e d  and a n a l y s i s conducted  i n terms o f e n g i n e e r i n g  The mechanical  parameters.  and r h e o l o g i c a l p r o p e r t i e s o f the p o t a t o  can  be r e g a r d e d as the c h a r a c t e r i s t i c s o f the m a t e r i a l which c o n t r o l or i n f l u e n c e t h e b e h a v i o u r o f t h e p o t a t o under c o n d i t i o n s o f e x t e r n a l l o a d ing.  REVIEW OF LITERATURE  The t e s t i n g o f the p h y s i c a l p r o p e r t i e s o f a g r i c u l t u r a l p r o d u c t s on a f u n d a a e n t a l l e v e l i s a r e l a t i v e l y new  field  Much o f the work s t i l l b e i n g done i s o f a comparative  o f endeavour. nature, which  a l t h o u g h u s e f u l f o r r e l a t i n g v a r i e t i e s o f c r o p s , does not l e n d i t s e l f t o t h e o r e t i c a l a n a l y s i s o f the b e h a v i o u r o f the c r o p .  2 Mohsenin ( l l ,  12)  has developed t e s t i n g , equipment f o r studying  the mechanical p r o p e r t i e s o f a g r i c u l t u r a l crops.  He s t a t e s t h a t t h e  p o t a t o e x h i b i t s a y i e l d p o i n t w e l l below t h e maximum l o a d t h a t t h e p o t ato w i l l w i t h s t a n d b e f o r e by M o h s e n i n . i l l u s t r a t e s  failure.  The f o r c e - d e f o r m a t i o n  t h i s low y i e l d p o i n t .  curve shown  Beyond t h e y i e l d  t h e curve i n c r e a s e s t o a maximum i n a n o n - l i n e a r  fashion.  point  The p r e s -  ence o f a low y i e l d p o i n t i s n o t supported by F i n n e y ( 3 ) who s t a t e s t h a t t h e y i e l d p o i n t c l o s e l y matches t h e f a i l u r e  point.  In h i s D o c t o r a l D i s s e r t a t i o n , F i n n e y ( 3 ) d i s c u s s e s t h e behavi o u r o f t h e p o t a t o under q u a s i - s t a t i c l o a d i n g c o n d i t i o n s . o f whole p o t a t o e s and v a r i o u s  s i z e s o f cores,  s t r a i n from l''/min. t o 40"/min.  The b e h a v i o u r ,  i s s t u d i e d under r a t e s o f  F i v e v a r i e t i e s a r e used t o determine  the i n f l u e n c e o f t h e date o f h a r v e s t  and d u r a t i o n o f s t o r a g e .  F i n n e y notes a d e c r e a s e i n t h e apparent modulus o f e l a s t i c i t y as t h e r a t e o f s t r a i n i s i n c r e a s e d from 20"/min. t o 4©"/min.  The apparent modulus was found t o r e m a i n . f a i r l y constant f o r temperatures between hO°F and 105°F b u t that, a decrease o c c u r r e d  with  temperatures above 105°F.  • When l o a d i n g whole t u b e r s w i t h p l u n g e r s o f d i f f e r e n t s e c t i o n a l areas,  cross-  Finney found t h a t t h e f o r c e and d e f o r m a t i o n r e q u i r e d  t o produce f a i l u r e i n c r e a s e d w i t h i n c r e a s i n g area, w h i l e t h e s t r e s s decreased.  I n t e s t i n g cores  o f d i f f e r e n t diameters under p a r a l l e l p l a t e  l o a d i n g , he found t h a t t h e apparent modulus o f e l a s t i c i t y remained f a i r l y constant  a t 5^-3 + ^3 p s i .  In s t u d i e s on t h e b u l k o r volume modulus o f t h e whole tuber,  3 • F i n n e y found, t h e p o t a t o had a P o i s s o n ' s r a t i d n o f •found t h e b u l k modulus t o ne 11, 300  • F i n n e y e t a l . (4)  + 1680  0.2+92 + 0..0013*  He  psi.  have s t u d i e d t h e i n f l u e n c e o f the time o f  t e s t i n g and V a r i e t y on t h e r e s i s t a n c e o f the p o t a t o t o m e c h a n i c a l damage.  • As w e l l as f i n d i n g . d i f f e r e n c e s between v a r i e t i e s ,  t h e r e s i s t a n c e d e c r e a s e d toward.harvest W o • r e l a t i o n s h i p was  they found  that  and t h e n i n c r e a s e d a f t e r h a r v e s t .  observed between the s p e c i f i c g r a v i t y o f the p o t a t o  a n d . i t s . r e s i s t a n c e t o m e c h a n i c a l damage.  F i n n e y e t a l . (5) have s t u d i e d t h e a p p l i c a t i o n o f t h e t h e o r y o f l i n e a r v i s c o e l a s t i c i t y t o t h e p o t a t o under c o n d i t i o n s o f c o n s t a n t strain.  They found,.it' p o s s i b l e to f i t a f o u r term e x p o n e n t i a l equa-  t i o n t o the s t r e s s r e l a x a t i o n curve o f t h e p o t a t o t u b e r .  In d o i n g so  they made use o f the g e n e r a l i z e d - M a x w e l l model ( l , 15,.  or a s e t o f  f o u r Maxwell models mounted i n p a r a l l e l .  IT)  • As F i n n e y found no i n c r e a s e  i n . r i g i d i t y o f the t u b e r w i t h i n c r e a s e d s t r a i n r a t e s he was t h e p a r a l l e l dashpot  . Lampe (9)  a b l e t o omit  from the g e n e r a l i z e d Maxwell model.  i n Germany has s t u d i e d the i n f l u e n c e o f c l i m a t e ,  weather and v a r i e t y on t h e r e s i s t a n c e o f the p o t a t o t o p e n e t r a t i o n . b y a s m a l l diameter p l u n g e r . ' ingToad  The  equipment used a p p l i e d a c o n s t a n t l y i n c r e a s -  t o t h e t u b e r through a 3 mm'  diameter p l u n g e r .  Lampe s u b j e c t e d  t u b e r s o f f i v e v a r i e t i e s t o t e s t s using, h a r v e s t i n g , equipment and t h e r e s u l t s o f t h i s t e s t t o h i s penetrometer  studies.  related  . He found t h a t t h e  • v a r i e t y w i t h t h e g r e a t e s t r e s i s t a n c e t o p e n e t r a t i o n a l s o showed t h e lowe s t degree  of b r u i s i n g i n the harvester t r i a l s .  Robertson a l s o conducted  (l8)  u s i n g equipment s i m i l a r t o t h a t o f Lampe has  s t u d i e s on t h e r e s i s t a n c e o f t u b e r s t o p e n e t r a t i o n . ..He  observed  a.step-wise  f o r c e - d e f o r m a t i o n curve w i t h v e r y s m a l l i n c r e a s e s  i n f o r c e and then a s m a l l i n c r e a s e - i n . d e f o r m a t i o n . o b t a i n e d was r e l a t i v e l y l i n e a r - . cessive c e l l  The o v e r a l l  The s t e p p e d c u r v e may i n d i c a t e  curve suc-  failure.  THE  STRUCTURE OF THE POTATO  As t h e - s t r u c t u r a l c h a r a c t e r i s t i c s o f t h e p o t a t o t u b e r t o a l a r g e e x t e n t c o n t r o l t h e mechanical  will  and r h e o l o g i c a l p r o p e r t i e s o f  the t u b e r i t i s e s s e n t i a l t o have a b a s i c u n d e r s t a n d i n g  of the c e l l u l a r  structure of the potato.  A c c o r d i n g t o Hayward (7) t h e p o t a t o t u b e r c o n s i s t s o f f i v e primary  zones.  From t h e p e r i f e r y inwards t h e s e zones are;  derm, c o r t e x , v a s c u l a r c y l i n d e r , m e d u l l a r y  the p e r i -  zone and t h e c e n t r a l  pith.  The p e r i d e r m o r s k i n o f t h e p o t a t o v a r i e s i n t h i c k n e s s depending on t h e v a r i e t y , m a t u r i t y and c u l t u r a l p r a c t i c e , b u t may be c o n s i d e r e d as a p r o tective layer six to ten c e l l layers i n thickness.  The p e r i d e r m i s  a l s o c o v e r e d w i t h a t h i n l a y e r o f s u b e r i n , a complex wax m a t e r i a l which i n f l u e n c e s t h e water r e s i s t a n c e o f t h e t u b e r .  Beneath t h e p e r i d e r m i s  found t h e c o r t e x , a band o r l a y e r o f s t o r a g e c e l l s .  The v a s c u l a r c y l -  i n d e r o r r i n g forms a narrow l a y e r o f xylem and phloem bundles l i e s between t h e c o r t e x and t h e m e d u l l a r y extends out t o each o f t h e buds o r eyes.  zone.  The v a s c u l a r t i s s u e  The m e d u l l a r y  p r i s e d o f parenchyma c e l l s which a c t as s t o r a g e t i s s u e . a region of large c e l l s ,  lower  which  zone i s comThe p i t h i s  i n s t a r c h , which r a d i a t e s i n a s t a r -  shaped p a t t e r n from t h e c e n t r e o f t h e t u b e r towards t h e eyes.  5  STRUCTURE IN RELATION TO MECHANICAL PROPERTIES  Matz (10.)  d i s c u s s e s t h r e e f a c t o r s which w i l l i n f l u e n c e the  t e x t u r a l p r o p e r t i e s of c e l l u l a r b i o l o g i c a l m a t e r i a l .  Texture,  as used  by Matz, i s i n e f f e c t an o r g a n o l e p t i c e x p r e s s i o n o f the mechanical p e r t i e s o f the m a t e r i a l , hence t h e s e f a c t o r s w i l l be r e g a r d e d which i n f l u e n c e the mechanical  properties.  r i e s i n f l u e n c i n g t e x t u r e which are;  He o u t l i n e s t h r e e  those  catego-  i n t e r c e l l u l a r f o r c e s b i n d i n g the  i n d i v i d u a l c e l l s togetfeir, mechanical  s t r e n g t h due  c e l l c o n t e n t s , and t h e t u r g i d i t y o f t h e  Intercellular  as  pro-  t o the c e l l w a l l  and  cell.  Adhesion  The i n d i v i d u a l c e l l s o f the p o t a t o f l e s h a r e bound t o g e t h e r by cementing agents found i n t h e i n t e r c e l l u l a r la.  The primary  substances The  spaces  or middle  cementing a g e n t . i s a p e c t i n m a t e r i a l .  lamel-  These^pectin  are h i g h m o l e c u l a r weight polymers o f g a l a c t u r o n i c a c i d .  s t r e n g t h , o f b i n d i n g i s dependent on t h e presence  o f calcium,, which  a c t s w i t h f r e e a c i d groups o f t h e p e c t i c a c i d t o form a f i r m g e l and t h e r e b y - b i n d the c e l l s  C e l l W a l l s and C e l l  together.  Contents  In the p o t a t o , p o l y s a a c h a r i d e s form t h e major components o f the c e l l w a l l .  Pectic  substances,  a l s o p r e s e n t . i n the c e l l w a l l .  c e l l u l o s e and  The  c e l l wall exhibits elastic  t i e s which w i l l i n f l u e n c e the o v e r a l l b e h a v i o u r The p r o t o p l a s m  o f the c e l l  s e v e r a l polymers a r e  of the potato  proper-  tissue.  s h o u l d show p r i m a r i l y v i s c o u s c h a r a c t e r i s -  t i c s as the major component i s water.  Many s t a r c h g r a n u l e s a r e  found  suspended i n t h e p r o t o p l a s m i c f l u i d and w i l l undoubtedly i n f l u e n c e t h e mechanical  behaviour  of the c e l l .  The  i n d i v i d u a l c e l l w i l l a c t as a  6  viscous f l u i d  contained  i n a partially elastic  membrane*  C e l l Turgor The (8)  turgor o f the c e l l s c o n t r o l s the t e x t u r a l c h a r a c t e r i s t i c  of 'crispness'.  ' C r i s p n e s s ' c o u l d b e s t he r e g a r d e d  s i o n o f t h e type o f f a i l u r e t h e m a t e r i a l undergoes. i a l would be expected t o f a i l  In a t u r g i d c e l l motic p r e s s u r e ,  in a brittle  as an  expres-  A . ' c r i s p ' mater-  manner.  t h e c e l l w a l l i s under t e n s i o n due t o - o s -  and thus i s p r e s t r e s s e d t o a c e r t a i n d e g r e e .  This  p r e s t r e s s i n g o f t h e c e l l w a l l would cause more r a p i d c e l l r u p t u r e and lead to a b r i t t l e  fracture.  A l o s s o f water from w i t h i n t h e c e l l r e s u l t s i n t h e c e l l b e coming- ' f l a c c i d ' , which i s i n e f f e c t , , t h e l o s s o f t e n s i o n f o r c e s i n the c e l l w a l l .  A flaccid cell will  undergo g r e a t e r d e f o r m a t i o n  r u p t u r e o f t h e c e l l w a l l due t o i n t e r n a l h y d r a u l i c p r e s s u r e . cid will  tissue will withstand  withstand  g r e a t e r deformation  greater loads before  before  A  flac-  than t u r g i d t i s s u e and  failure. A p i c a l bud (eye) Periderm Cortex Vascular Medullary  ring zone  L a t e r a l bud Pith  Fig.  1  Diagram o f t h e Potato  Tuber (Adapted from T a l b u r t  (19))  7 V a r i a b i l i t y o f t h e P o t a t o Tuber The mechanical  s t r e n g t h o f t h e p o t a t o t u b e r i s found t o v a r y  under t h e i n f l u e n c e o f many f a c t o r s . out by F i n n e y iod  T h i s v a r i a t i o n has been p o i n t e d  ( 3 ) and Lampe ( 9 ) i n s e p a r a t e s t u d i e s .  Work over, a p e r -  o f y e a r s by Lampe i n Germany shows t h a t t h e p r o p e r t i e s o f t h e p o t -  ato w i l l v a r y i n response and f e r t i l i z a t i o n .  t o c l i m a t e , weather, s o i l ,  The p r o p e r t i e s w i l l  cultural practice  a l s o be a f f e c t e d by v a r i e t y  and m a t u r i t y .  F i n n e y p o i n t s out t h a t t h e p r o p e r t i e s o f t h e t u b e r w i l l with the d u r a t i o n o f the storage period.and digging date. t h a t t h e s t r e n g t h d e c r e a s e s toward'harvest period i n storage.  Finney  vary  He found  and then i n c r e a s e s f o r a  (k) a l s o notes t h e d i f f e r e n c e s between  v a r i e t i e s and t h e l o c a t i o n o f growth.  The p h y s i c a l p r o p e r t i e s o f t h e p o t a t o may a l s o be expected to v a r y w i t h c h e m i c a l c o m p o s i t i o n  o f t h e i n d i v i d u a l t u b e r s , however,  l i t t l e work has been done on t h i s  aspect.  As t h i s study was o f a fundamental n a t u r e and was ing, t o observe  attempt-  the: b e h a v i o u r p a t t e r n s o f t h e potato,, an e f f o r t was  made t o c o n t r o l as many v a r i a b l e s as p o s s i b l e .  Consequently  one v a r i e t y , one d i g g i n g d a t e and one l o c a t i o n o f growth were A l l t u b e r s were m a i n t a i n e d  used.  i n t h e same s t o r a g e room,. w i t h t h e temp-  e r a t u r e c o n t r o l l e d between t h e l i m i t s o f 38° i t y was r e l a t i v e l y h i g h .  only  a n c  i  kO°F,  The humid-  P r e v i o u s s t u d i e s on t h i s u n i t would  con-  s e r v a t i v e l y estimate t h e l o s s t o be l e s s than 2% over a s t o r a g e p e r i o d of  t h r e e months.  noticed.  A marked d i f f e r e n c e between h a r v e s t y e a r s was  8 . THEORY  When s u b j e c t e d c h a r a c t e r i s t i c manner.  to applied loads  a l l m a t e r i a l s respond i n a  The response i s dependent on t h e p r o p e r t i e s  o f t h e m a t e r i a l and can be used t o d e s c r i b e  t h e m a t e r i a l under t e s t .  E l a s t i c i t y i s t h e c h a r a c t e r i s t i c o f a m a t e r i a l which  allows  the m a t e r i a l t o r e t u r n t o i t s o r i g i n a l dimensions upon t h e r e l e a s e o f a deforming s t r e s s .  I n an i d e a l e l a s t i c m a t e r i a l t h e s t r a i n i s p r o -  p o r t i o n a l t o t h e a p p l i e d s t r e s s and t h e s e two f a c t o r s a r e r e l a t e d t h r o u g h the''Modulus o f E l a s t i c i t y ' o r Young's Modulus.  This  rela-  t i o n s h i p may be expressed i n t h e form: -  where  E = Young's Modulus = S t r e s s , i n pounds p e r square i n c h £  = S t r a i n , i n inches per i n c h  A viscous material w i l l  show no tendency t o r e t u r n t o i t s o r i -  g i n a l , dimensions o r i n t e r n a l arrangement a f t e r i t has been s t r a i n e d . V i s c o s i t y i s commonly c o n s i d e r e d  i n r e l a t i o n t o f l u i d s and i s r e g a r d e d  as t h e i n t e r n a l r e s i s t a n c e o f t h e m a t e r i a l t o t h e a p p l i c a t i o n o f a shearing  force.  A m a t e r i a l which e x h i b i t s b o t h e l a s t i c and v i s c o u s i s d e f i n e d as b e i n g  properties  'viscoelastic'.  V i s c o s i t y may a r i s e i n a s o l i d due t o a f l o w o f t h e p a r t i c l e s of the material i n respect hardening.  t o each o t h e r without e x h i b i t i n g a s t r a i n  V i s c o s i t y i n a s o l i d i s c h a r a c t e r i s e d b y two f a c t o r s ;  9  creep, and s t r e s s ' r e l a x a t i o n .  Stress  Relaxation S t r e s s r e l a x a t i o n i n a m a t e r i a l i s characterised..by  ual  the grad-  d i s s i p a t i o n o f an a p p l i e d s t r e s s when t h e m a t e r i a l i s h e l d under a  constant  strain.  teristic  o f t h e m a t e r i a l under t e s t and i s used t o d e f i n e t h e r e l a x a t i o n  time c o n s t a n t s  The form o f t h e s t r e s s r e l a x a t i o n c u r v e i s c h a r a c -  of the material.  The r e l a x a t i o n time o f a m a t e r i a l i s  d e f i n e d as t h e - t i m e r e q u i r e d f o r t h e a p p l i e d s t r e s s t o reduce t o l / e o f the i n i t i a l  stress value.  r e l a x a t i o n constants  Many v i s c o e l a s t i c m a t e r i a l s have s e v e r a l  t o take i n t o c o n s i d e r a t i o n t h e shape o f t h e r e l a x -  a t i o n curve.  Creep Deformation Creep i s d e f i n e d as t h e d e f o r m a t i o n o c c u r r i n g i n a m a t e r i a l which i s m a i n t a i n e d under a c o n s t a n t under a constant Upon i n i t i a l tically.  stress.  a p p l i c a t i o n o f t h e s t r e s s t h e m a t e r i a l may deform e l a s -  The i n i t i a l  e l a s t i c deformation i s normally  a t i o n , i s a p e r i o d o f t r a n s i e n t creep..  but  deforms  {ih, 17)»  s t r e s s t h r e e phases must.be c o n s i d e r e d  upon t h e removal o f t h e a p p l i e d s t r e s s .  by  When a m a t e r i a l  a decreasing  rate o f deformation.  reduces t o z e r o • w i t h  time.  Following  recoverable  the e l a s t i c  This period i s characterised This rate i s high  S t a r t i n g simultaneously  initially with the  t r a n s i e n t creep i s t h e t h i r d phase, t h a t o f minimum: r a t e creep or steady s t a t e creep (l7)«  deform-  (lU)  The r a t e o f steady s t a t e c r e e p i s a con-  s t a n t and w i l l c o n t i n u e as l o n g as t h e s t r e s s remains on t h e m a t e r i a l .  Creep d e f o r m a t i o n may l e a d t o t h e f a i l u r e o f t h e m a t e r i a l under r e l a t i v e l y , low s t r e s s i f allowed t o c o n t i n u e f o r extended of t i m e .  periods  ID  Deformation  Time :  Fig*  where  -2-  T y p i c a l Creep  a = elastic  Curve  deformation  b = t r a n s i e n t creep • c- = steady s t a t e c r e e p  Compression To study t h e b e h a v i o u r o f a m a t e r i a l under compression which i n c r e a s e s  at a f i x e d rate, i s a p p l i e d to the m a t e r i a l .  The  strain, change  i n s t r e s s which o c c u r s due t o the s t r a i n i s observed, and a s t r e s s s t r a i n r e l a t i o n s h i p obtained f o r the m a t e r i a l . curve may  This s t r e s s - s t r a i n  be used i n t h e a n a l y s i s o f t h e m e c h a n i c a l b e h a v i o u r o f the  material.  The  s l o p e o f the s t r e s s - s t r a i n curve f o r an e l a s t i c  material  d e f i n e s the modulus o f e l a s t i c i t y up t o t h e p r o p o r t i o n a l l i m i t . a m a t e r i a l which i s not p u r e l y e l a s t i c i t may the secant o r tangent modulus.  T h i s - p o i n t may  o r may  be n e c e s s a r y t o use e i t h e r  I f the s t r a i n i n g of the m a t e r i a l i s  c o n t i n u e d t o f a i l u r e b o t h the s t r e s s and ermined.  For  s t r a i n at f a i l u r e may  be d e t -  not be a t t h e maximum s t r e s s which t h e  11  material  undergoes  Stress  Strain  Pig.  :3:.  S t r e s s - s t r a i n Curve f o r S t r u c t u r a l S t e e l . where  A = proportional  (20)  limit  B - yield C = ultimate  strength  D = failure  I f a v i s c o e l a s t i c m a t e r i a l i s l o a d e d and unloaded w i t h i n t h e p r o p o r t i o n a l , l i m i t t h e m a t e r i a l may not r e t u r n t o t h e i n i t i a l For  such a m a t e r i a l the r e l a t i v e e l a s t i c i t y may be d e f i n e d .  strain.  (6)  v a l u e i s g i v e n as t h e r a t i o o f the r e c o v e r e d s t r a i n t o t h e t o t a l  This strain.  In t h e case where t h e m a t e r i a l does not r e t u r n t o i t s o r i g i n a l dimensions energy i s l o s t .  The l o s s o f energy appears as a h y s t e r e s i s  l o o p i n t h e s t r e s s - s t r a i n diagram.  Strain P i g . .k".' where  Hysteresis  E f f e c t and R e l a t i v e E l a s t i c i t y  A = loading  curve  B = unloading curve C = hysteresis loop a = recovered deformation b = t o t a l deformation  VISCOELASTIC ANALYSIS  In the mathematical a n a l y s i s of the behaviour of v i s c o e l a s t i c m a t e r i a l s , use i s made o f m e c h a n i c a l models.  Most m e c h a n i c a l  models a r e b u i l t up from two b a s i c elements, t h e s p r i n g o r e l a s t i c element and t h e dashpot o r v i s c o u s  element.  More complex m a t e r i a l s  r e q u i r e such a d d i t i o n a l elements as s l i d i n g w e i g h t s t o a d e q u a t e l y r e p r e s e n t t h e i r b e h a v i o u r ( l , 15,  l6).  1-3  S p r i n g Element P i g . 5'  The f o r c e - e x t e n s i o n given  Dashpot The B a s i c  Element  Elements  responses f o r t h e two b a s i c  elements i s  as f o l l o w s .  For the s p r i n g :  F = Ea  (l)  For the dashpot:  P =^Da  (2)  where  P = applied E =. s p r i n g a =  force constant  extension  D = operator,  denoting d i f f e r e n t i a t i o n  with  r e s p e c t t o time = dashpot  The Maxwell  constant  Model  The Maxwell model c o n s i s t s o f a s p r i n g and dashpot element nected i n s e r i e s .  The f o r c e - e x t e n s i o n  con-  response o f t h i s model i s g i v e n  by  equation (3). Da = - DF + E  I F  (3)  The V o i g t Model The V o i g t model c o n s i s t s o f a s p r i n g and dashpot r i g i d l y connected i n p a r a l l e l .  E q u a t i o n (k) g i v e s t h e f o r c e - e x t e n s i o n  response f o r  Ik. t h i s model. F = Ea +^Da  (k)  Creep B e h a v i o u r To study t h e creep b e h a v i o u r o f a model a u n i t f u n c t i o n o f s t r e s s i s a p p l i e d t o the model.  The f o r c e a p p l i e d t o t h e model i s then g i v e n "by:  (5)  F = CH(t) where •  C = constant E&H).  = the unit  function  i.e.  H(t) = 0 f o r t < 0  and  H(t) =  1 for t > 0  For t h e e l a s t i c element: a(t)  = gEfctt)  For the viscous Da(t)  (6)  element:  = £ H(t) as a = 0 a t t = 0  or a = £ t H ( t )  V  (7)  For t h e Maxwell model: Da  =gS(t) E  where  6 ( t ) = DH(t)  or  a ( t ) = C^|  +  +£H(t) ^  iJH(t)  (8)  For t h e V o i g t model: Ea =/>jDa + CH(t)  Using t h e i n t e g r a t i n g f a c t o r exp. ( E / ^ ) t t h i s may be to y i e l d :  integrated  15  a(t) - ^ 1  exp (- l  t  (  H  ( )  (9)  t  a = 0 at t = 0  since  This procedure may be extended to more complex models,  Time Fig. 6v Extension Response to a Unit Force Relaxation Behaviour The relaxation behaviour of a material deals with the rate of stress dissipation within the material when held at, a constant strain. To study this with models requires the application of a unit extension to the model. For the elastic element: F(t) = Ea(t) + KEH(t)  (10)  For the viscous element: F(t) = ^Da(t) + K^6(t)  (11)  16"  For the Maxwell Model: from eqn* ( 3 ) F(t) = KE exp ( - E t) H(t)  K1 J  (12)  For the Voigt Model: from eqn. (k) (13)  F(t) = KEH(t) +K/p8(t)  TESTING EQUIPMENT  To study the behaviour, of the potato under conditions of controlled loading, certain test equipment was required. For static load or constant stress conditions, the load must remain constant and f a c i l i t i e s for accurately measuring the deformation over long periods of time provided. For studying cyclical loading-, and constant strain rates, i t is desirable to have accurately controlled speed over a wide range.  The  equipment must be readily reversible to study the hysteresis effect and should be able to maintain a fixed strain on the material, to study stress relaxation. Testing equipment constructed, and purchased as well as the electronic sensing and recording equipment used, are discussed in the follow• ing section. Static Test Apparatus Two static test units were constructed to study the tuber under conditions of constant stress. the load application area.  The two units were the same except for  17 The l o a d a p p l i c a t i o n i s through hinged, equipped weights  with either  .250"  o r .354"  counterbalanced  c i r c u l a r loading plungers.  levers, Lead  are used d i r e c t l y above t h e sample t o p r o v i d e the l o a d .  Measurement o f the d e f o r m a t i o n  i s o b t a i n e d u s i n g a s u r f a c e mic-  rometer under the f r e e end o f t h e l o a d i n g l e v e r .  Each d e v i c e t e s t s f i v e ing one-half a potato tuber.  samples s i m u l t a n e o u s l y , each sample be\  •Counterbalance -Hinge  -Lead Weights  - Surface Micrometer  -Specimen Fig.  v7--  Fig.  Schematic  8.  Diagram o f S t a t i c T e s t U n i t  Sample Undergoing S t a t i c  Test  18' Compression  A.  T e s t EcjUipment  "Servo-Tec" Compression  Unit  To observe t h e b e h a v i o u r o f t h e p o t a t o under c o n t r o l l e d r a t e s o f l o a d i n g t h e "Servo-Tec" u n i t was c o n s t r u c t e d .  Power t o d r i v e t h e c r o s s h e a d i s o b t a i n e d from a o n e - h a l f H.P., 220 V.D.C. e l e c t r i c motor.  The motor speed i s c o n t r o l l e d by means o f a  " t h y r a t r o n " tube arrangement, tachometer on t h e motor. the  o p e r a t i n g i n c o n j u n c t i o n w i t h an e l e c t r i c  The motor i s r e v e r s i b l e and o p e r a t e s througn  same speed range i n r e v e r s e .  Pig.  9 . "Servo-Tec" Compression  Unit  19  D r i v e Screw  Chain  Coupler  Speed Reducer  Chain  Coupler  Motor  Pig.10  "Servo-Tec" D r i v e T r a i n  Power from t h e motor i s t a k e n t h r o u g h an 800:1 r e d u c t i o n box, t o a  machined d r i v e screw.  double worm gear  T h i s d r i v e screw has a l / 8 "  l e a d o r p i t c h and i s f i t t e d w i t h two r e c i r c u l a t i n g b a l l b e a r i n g s l e e v e s . The r e c i r c u l a t i n g b a l l  s l e e v e s a r e f i t t e d i n t o t h e c r o s s h e a d and s e r v e t o  t r a n s f o r m t h e r o t a t i o n a l motion  of the shaft into l i n e a r t r a v e l of the  crosshead.  The c r o s s h e a d i s c o n s t r u c t e d o f t a n g u l a r box shape.  cold r o l l e d  steel i n a rec-  The r e a r o f t h e c r o s s h e a d i s f i t t e d w i t h a r e c i r -  c u l a t i n g b a l l s l e e v e which t r a v e l s on a 1"  splined shaft.  T h i s assemb-  l y p r e v e n t s ' r o t a t i o n o f t h e c r o s s h e a d and s e r v e s t o remove some o f t h e moments developed d u r i n g t h e compression  cycle.  The motor and gear box a r e mounted i n a framework c o n s t r u c t e d o f 2" x 2" x'.j^-" a n g l e i r o n . the compression  section.  T h i s framework a l s o s e r v e s as a base f o r  20  Head Screw S h a f t  F i g . I I Schematic Diagram o f t h e Crosshead  Assembly  The maximum c o n t i n u o u s t e n s i o n l o a d which may be a p p l i e d t o t h e screw d r i v e i s g i v e n b y t h e manufacturer's  s p e c i f i c a t i o n s as 200 l b s .  The c r o s s h e a d speed was determined u s i n g a d i a l i n d i c a t o r b r a t e d i n .001" and a s t o p watch.  cali-  The speed was d e t e r m i n e d over t h e f u l l  range o f t h e speed c o n t r o l p o t e n t i o m e t e r .  The c r o s s h e a d v e l o c i t y i s  l i n e a r w i t h r e s p e c t t o t h e p o t e n t i o m e t e r s e t t i n g and t h e e q u a t i o n o f speed vs.. p o t . s e t t i n g was found t o be:  y = 0 . 6 l x - Ik where  y ± c r o s s h e a d v e l o c i t y i n .001"/min. . x = potentiometer  setting  .21 The c a l i b r a t i o n curve i s g i v e n on graph Wo.  B.  I.  Bellows V a l v a i r Hydrocheck Compression U n i t To o b t a i n h i g h e r r a t e s of l o a d i n g a pneumatic-driven,  c a l l y c o n t r o l l e d compression  u n i t was  purchased.  bydrauli-  A c c u r a t e speed  control  over a range o f speeds from 1"/min. t o 65"/min. i s p r o v i d e d by t h e hydr a u l i c checking, u n i t a t t a c h e d t o the pneumatic c y l i n d e r . a v a i l a b l e commercially  and i s d e s c r i b e d by Mohsenin  Speed' c a l i b r a t i o n was  This u n i t . i s  (ll).  done u s i n g the " M e t r e s i t e " linear- v a r i a -  b l e - d i f f e r e n t i a l t r a n s d u c e r i n c o n j u n c t i o n w i t h the B r u s h  oscillograph.  • A sample sp;eed c a l c u l a t i o n i s shown below.  Sample C a l c u l a t i o n  Valve s e t t i n g  =3*5  Oscillograph  12  mm.  =  .100"  Chart speed = 25 d i v . / s e c = 125  1.  div.. req'd f o r  2.  time r e q / d f o r  .3.  velocity  1.32  = ^5«5  0.100" 0.100"  mm./sec.  3.3  travel =  travel =  sec./in.  .1  1.32  in,/min.  «3  i i v - — _ 25 d i v . / s e c . 3  x  1  =  0.132  .758"/sec.  sec./.l i n .  GRAPH I  Velocity Calibration - Curve Serve—Tec Compression Unit  60Q_  50d  g  hod-  o  S 200|  100  !  100  200  300  400  500  600  Potentiometer Setting  Pig. .'13."  Modified Bellows Valvair Compression Unit  The results of the speed calibration are shown on graph No. II. The speeds for the up and down movement of the piston are controlled independently and calibration for upward speed would be required for the equipment i f i t was to be used for controlled unloading rates. Electrical Measurement and Recording Several commercial units were purchased to measure and record the stress and strain behaviour of the potato under the various controlled loading conditions. 1) Brush Model RD amplifiers (Two) 2)  Brush Oscillograph, two channel  3)  Tectronix dual beam oscilloscope  k)  Polaroid camera for the oscilloscope  5)  Electro-Instrument, X-Y, X-T recorder  GRAPH I I  V e l o c i t y . C a l i b r a t i o n Curve  '-Bellows-Valvair  Compression Unitfe,..  6)  Brush."Metresite", l i n e a r v a r i a b l e d i f f e r e n t i a l  The • 7) 8) .9)  Load  f o l l o w i n g equipment was a l s o  S t r a i n gauge l o a d  constructed:  cell  D.C. power supply f o r t h e l o a d Bridge balancing  cell  unit f o r the load  cell  Cell T h e - l o a d c e l l was c o n s t r u c t e d  using  f o u r simple c a n t i l e v e r  beams,, each equipped w i t h two T a t n a l l " M e t a l f i l m " f o i l The  eight.gauges from t h e f o u r beams were w i r e d . i n  stone b r i d g e . the w i r i n g  Beam  s t r a i n gauges.  s e r i e s i n a wheat-  Pour beams were used i n p r e f e r e n c e t o t h r e e t o s i m p l i f y  system.  Calculations  P i g . '.Ik'  The lbs.  transducer  Schematic Diagram o f one l o a d c e l l beam  l o a d c e l l was d e s i g n e d t o c a r r y a l o a d o f a p p r o x i m a t e l y  200  C o l d . r o l l e d s t e e l was s e l e c t e d f o r t h e beam m a t e r i a l .  S e l e c t e d Beam x = 1" b = d =  5/l6" = .3125" 1/8" = .125"  E = Young's Modulus (30 x 10 p s i ) P = Load ( i n l b s )  £=  deformation ( i n / i n )  S = stress ( p s i )  £- S " E "  Then  . ,..(6) (P) (1) (30) (10) (.0156) (.3125)  6  P x E;hd  (.0254). ( 1 0 )  "(P) ( 1 0 ) > f i n / l n  For c o l d r o l l e d s t e e l :  S at proportional l i m i t  e-f =T#w Then l o a d a t prop., l i m i t : E b d  Then:  The L.V.D.T.  -  0 0 2 i n / i n  •  2 0 0 0  ^-/m  ( f o r one "beam)  £  =  58.75 l b s .  capacity f o r load c e l l P = (4)  =  60,000 p s i  assuming evenly  (58.75) = 195  load c e l l  The M e t r e s i t e  distributed load  lbs...  i s used i n c o n j u n c t i o n  w i t h the Brush  Metresite  i s mounted i n such a way as t o measure o n l y t h e  deformation that i s occurring  i n t h e specimen under t e s t .  •Plunger L.V.D.T Specimen  X  Fig.  15  Loadcell  Plate  Schematic Diagram o f Load C e l l With L.V.D.T.. i n P l a c e  O p e r a t i o n o f O s c i l l o s c o p e as an X-Y  Recorder  The d u a l "beam o s c i l l o s c o p e i s used as an X-Y r e c o r d e r by  opera-  t i n g t h e v e r t i c a l p l a t e s t o sense l o a d i n t h e l o a d c e l l and u s i n g t h e h o r i z o n t a l p l a t e s to sense•deformation  o f t h e L.V.D.T. .  The p o l o r o i d camera  i s used t o r e c o r d t h e f o r c e d e f o r m a t i o n c u r v e t r a c e d on t h e s c r e e n o f t h e oscilloscope.  TEST PROCEDURES S t a t i c Test T r i a l s A s e r i e s o f s t a t i c t e s t t r i a l s were r u n t o d e t e r m i n e t h e behavi o u r o f t h e p o t a t o under c o n d i t i o n s o f c o n s t a n t s t r e s s .  This series  b r o k e n down i n t o t e n t e s t s w i t h f i v e r e p l i c a t i o n s o f each t e s t .  The  t e s t s : o r t r e a t m e n t s c o n s i s t e d o f f i v e l o a d s and two l o a d i n g a r e a s . l o a d s ranged i n 1.5  pound i n c r e m e n t s from 1.5  two l o a d i n g p l u n g e r s had d i a m e t e r s o f  0.354 i n c h e s (.0982 s q . i n . ) .  pounds t o 7«5  was ten The  pounds.  The  0.250 i n c h e s (:.Qk91 s q . i n . ) and  The f o l l o w i n g t a b l e shows trie s t r e s s  values l b / s q . i n . f o r the ten t e s t s .  Diam.  Area  Load r  1.5  3.0  4.5 91.5  0.250  0.0491  30.5  61.0  0.354  0.0982  15.25  30.5  . 45.75  6.0 122 61.0  7-5 152.5 • 76.25  T h i s arrangement g i v e s a t e n - f o l d range i n t h e s t r e s s v a l u e s a c t i n g on t h e p o t a t o t u b e r s . The-loads were a p p l i e d i n such a manner as t o g i v e a s t e p function of stress.  The l o a d was  a p p l i e d f o r t w e l v e hours and t h e d e f -  o r m a t i o n o c c u r i n g i n t h e t u b e r over t h i s p e r i o d o f t i m e r e c o r d e d .  The  l o a d was then.removed from t h e t u b e r and the r e c o v e r y o v e r t h e f o l l o w i n g twelve, hours o b s e r v e d .  D e f o r m a t i o n r e a d i n g s were t a k e n u s i n g a s u r f a c e micrometer c a l i b r a t e d i n 0.001  inch.divisions.  The r e a d i n g s o b t a i n e d w i t h t h e m i c r o -  meter were double t h e a c t u a l d e f o r m a t i o n due t o , t h e l e v e r arrangment o f the t e s t  apparatus. The d e f o r m a t i o n t a k e n a t a p p r o x i m a t e l y one minute was  as t h e i n s t a n t a n e o u s d e f o r m a t i o n f o r t h e purposes o f t h i s  regarded  study.  The samples used f o r t h i s t e s t , were randomly s e l e c t e d from •tubers r e g a r d e d as b e i n g o f s u i t a b l e q u a l i t y f o r t h e consumer market. E a c h . t e s t sample c o n s i s t e d o f o n e - h a l f a t u b e r c u t a l o n g t h e major a x i s . The c u t s i d e o f t h e t u b e r was imbedded i n wax on t h e t e s t i n g d e v i c e i n o r d e r t o m i n i m i z e water l o s s from t h e t u b e r d u r i n g t h e t e s t p e r i o d . T h i s was n e c e s s a r y i n o r d e r t o a v o i d erroneous  e r r o r s which would r e -  s u l t from s h r i n k a g e o f t h e t u b e r sample.  Stress Relaxation S t r e s s r e l a x a t i o n s t u d i e s were conducted  t o observe t h e d i s -  s i p a t i o n o f s t r e s s i n t h e p o t a t o t u b e r when h e l d under c o n s i d e r a t i o n s o f constant s t r a i n or deformation.  Whole t u b e r samples were l o a d e d t o s e t  l o a d v a l u e s and t h e d e f o r m a t i o n then h e l d c o n s t a n t .  The  Electro-  Instrument- 300T-recorder was used as an X/T r e c o r d e r t o f o l l o w t h e change i n stress i n the potato tuber w i t h time.  S t r e s s r e l a x a t i o n was  f o r a p e r i o d o f t e n minutes i n each sample. were used.  These v a l u e s were: . 20,  30,  35,  r e p l i c a t i o n s were used a t each l o a d v a l u e .  observed  Five i n i t i a l load values ^5  and 60  pounds.  Three  The samples were-loaded a t a r a t e o f  0.59&  i n c h e s per-minute.  Stress  Time  P i g . 16  Stress Relaxation  Hysteresis To determine t h e energy absorbed by t h e p o t a t o t u b e r under c y c l i c a l l o a d i n g c o n d i t i o n s a s e r i e s o f t e s t s were performed on whole t u b e r samples.  The samples were l o a d e d and unloaded t h r o u g h t h r e e  cycles at a rate of  O.596  i n c h e s p e r minute.  The r e s u l t a n t  force-  d e f o r m a t i o n c u r v e s were r e c o r d e d ud'ing t h e E l e c t r o - I n s t r u m e n t • 3 0 0 T X-Y recorder.  In a l l t h i r t y - o n e samples o f whole t u b e r s were used.  l o a d v a l u e s ranged from 20 pounds t o 120  pounds i n 10  The  pound i n c r e m e n t s .  Three r e p l i c a t i o n s were used w i t h t h e e x c e p t i o n o f t h e two h i g h e s t  load  v a l u e s where o n l y two r e p l i c a t i o n s were o b t a i n e d .  The a r e a s under each of the t h r e e l o a d i n g c u r v e s and :  inside  each..of the..hysteresis - l o o p s were measured u s i n g t h e compensating i n c h planimeter.  The l o s s on each.loop was then c a l c u l a t e d as a percentage  o f the energy  expended i n t h e l o a d i n g segment o f t h a t l o o p .  A t r i a l was a l s o conducted l o n g and one i n c h . i n d i a m e t e r .  on a s e t . o f e i g h t e e n c o r e s  one.inch  These c o r e s were l o a d e d t o a v a l u e o f  s i x t y pounds a t f o u r l o a d i n g r a t e s r a n g i n g from.0.126 i n c h e s per. minute to O.596 i n c h e s - p e r minute.  The l o s s f o r each l o o p was a g a i n  calcula-  t e d from the areas as measured by t h e compensating i n c h p l a n i m e t e r .  Compression T e s t  Procedures  In May I963, t h r e e compression  t e s t s were conducted.  Each  t e s t used twelve t u b e r samples w i t h from two t o f o u r core samples each t u b e r .  from  Pour slow speed l o a d i n g r a t e s were used f o r each t e s t ,  u s i n g t h r e e t u b e r samples a t each r a t e o f l o a d i n g . d e t e r m i n a t i o n s were performed  gravity  f o r each o f t h e t u b e r samples u s i n g t h e  " w e i g h t . i n a i r - w e i g h t i n - w a t e r " method. t e s t s were performed  Specific  The i n d i v i d u a l  compression  on c o r e s o f the t u b e r f l e s h which were one i n c h  -long and.one i n c h i n d i a m e t e r .  Following the alphabetical test iden-  t i f i c a t i o n , , these t e s t s were l a b e l l e d A, B and C.  In September-1963, t e s t s were resumed u s i n g t h e 1963 crop, potatoes.  T e s t D was conducted  i n t h e same manner as the p r e c e d i n g  t h r e e t e s t s , u s i n g a g a i n twelve t u b e r s w i t h two c o r e s removed from .for purposes  o f the t e s t .  S p e c i f i c g r a v i t y v a l u e s were  each  again.determined.'  F o r t e s t s E, F and G, which were used as t h r e e r e p l i c a t i o n s o f a r a t e . o f s t r a i n study, t h e ' B e l l o w s - V a l v a i r Hydrocheck' l o a d i n g u n i t and t h e 300T r e c o r d e r were used.  S i x r a t e s o f s t r a i n r a n g i n g from O.308  i n c h e s p e r minute t o twenty i n c h e s p e r minute were used.  Specific  grav-  30 • i t y determinations--were conducted on each o f t h e t u b e r s used f o r t e s t s E and' F.  T e s t H'used f i v e r a t e s o f s t r a i n r a n g i n g from t h i r t y i n c h e s p e r minute t o . - s i x t y - f i v e i n c h e s per-minute.  The d a t a from t h i s t e s t was used  t o determine t h e i n f l u e n c e o f t h e response time o f t h e 300T-recorder on the s t r e s s - s t r a i n c u r v e s . carded from f u r t h e r  The d a t a from t h i s t e s t was subsequently d i s -  analysis.  T e s t I was t h e f i r s t , t e s t i n a s e r i e s conducted t o study t h e i n f l u e n c e o f t h e l o a d i n g p l u n g e r t y p e on t h e s t r e s s - s t r a i n response o f the potato tuber. the rate of s t r a i n . R.  T h i s s e r i e s was a l s o used t o study t h e i n f l u e n c e o f I n a l l t e n t e s t s were conducted,  F o r t h i s s e r i e s f o u r l o a d i n g p l u n g e r s were used.  were-jj-, 3/8,-\ and 1 i n c h : i n d i a m e t e r . These were:  i . e . tests I t c These p l u n g e r s  Three c o r e t y p e s were used.  \ .potato t u b e r c u t t o 1" t h i c k , two i n c h c o r e s , one i n c h  t h i c k and t h e 1" x 1" c o r e t y p e .  T e s t s K, 0, P, Q and R used n i n e  r a t e s o f s t r a i n from O.3O8 i n c h e s p e r minute t o 65 i n c h e s p e r minute. The remainder ..of. the t e s t s i n t h i s s e r i e s used e i g h t r a t e s , t h e O.308 I n c h per•minute r a t e b e i n g o m i t t e d . Valvair'  system f o r compression  These t e s t s used t h e 'Bellows-  and t h e o s c i l l o s c o p e camera f o r t h e  . stres.s.rstrain .recording.  The f o l l o w i n g summary t a b l e g i v e s t h e v a r i o u s t e s t s w i t h t h e c o r e type,, p l u n g e r type, l o a d i n g r a t e s and t h e l o a d i n g and r e c o r d i n g equipment - used.  31 Summary, of Compression Tests Test  Core Type  A  1" x 1"  B  Plunger 1"  Trial  Strain Rate  Loading  Recording  I  0.126"/min.  S.T.**  Sc  II  0.292"/min.  S.T.  Scope  III  0.41+3 "/min.  S.T.  Scope  IV  0.596"/min.  S.T.  Scope  B.V. *  300T  °P* ** e  •• Rep. two of test A.  C  Rep. three of test A.  E  1" x 1"  XX XX  1"  I II  - 1.26"/min.  B.V.  300T  III  3.42"/min.  B.V.  300T  IV  6.9"/min.  B.V.  300T  V  12.5"/min.  B.V.  300T  20"/min  B.V.  300T  VI D  Note: . F  1" x . l "  1"  Note:  I  0.l40"/min.  S.T.  300T  II  0.290"/min.  S.T.  300T  III  0.445"/min.  S.T.  300T  IV  0.596"/ ain.  S.T.  ' 300T  B.V.  300T  i  Core I lateral, Core 2 longitudinal. 1" x . l "  1"  Rep. two of test E . Rep. three of test E.  G H  0.308 /min. w  1" x 1"  1"  Test H used to check response of the 300T recorder.  32' Summary of Compression Tests (continued) Test  Core Type  Trial  Strain Rate  Loading  Recording  in 4  1-8  1.26-65"/min.  B.V.  Scope  Plunger  AAA .  tuber  I  •J  • 1" x . l "  . In 4  1-8  1.26-65"/min.  B.V.  Scope  K  ;\. tuber  3/8"  1-9  O.308-65"/min.  B.V.  Scope  L  2"d. x l "  1-8  1.26-65"/min.  B.V.  Scope  i  II  4  M  . 2"d.- x 1"  3/8"  1-8  1.26-65"/min.  B.V.  Scope  N  , 2"d. x . l "  in 2  1-8  1.26-65"/min.  B.V.  Scope  1 4  1-9  .308-65"/min.  B.V.  Scope.  3/8"  1-9  .308-65"/min.  B.V.  Scope  G  2".d. x 1"  P  ,-2"d. x 1"  .Q  2"d. x 1"  in 2  1-9  .308-65"/min.  B.V.  Scope  R  1" x 1"  1"  1-9  .308-65"/min.  B.V.  Scope  Note:  * ** *** ****  II  B.V. = Bellows Valvair Compression Unit S.T. = Servo-Tec Compression Unit Scope = Tectronix Dual Beam Oscilloscope 300T = Electro-instrument X-Y, X-T Recorder Table I Summary of Compression Tests  ' •  33  i  RESULTS  Apparent Modulus o f E l a s t i c i t y Under the c o n d i t i o n s o f t h e compression t e s t s over a wide range .of s t r a i n r a t e s t h e p o t a t o t u b e r f l e s h appears t o a c t . i n an e l a s t i c manner on l o a d i n g ,  The u n l o a d i n g curve, however, shows a v e r y l a r g e hys-  t e r e s i s l o s s and a r e l a t i v e l y l a r g e permanent.set  or d e f o r m a t i o n .  p o t a t o then a c t s i n a manner t h a t i s n o t . f u l l y e l a s t i c .  The  C a l c u l a t i o n of  t h e Young's modulus f o r such a m a t e r i a l i s t o a l a r g e extent meaningless as a l a r g e p o r t i o n o f t h e energy expended i n deforming t h e t u b e r i s not recoverable..  The p a t t e r n o f t h e l o a d i n g curve was  a l y s i s appeared warranted. modulus was  studied.  such- t h a t f u r t h e r  an-  Consequently a v a l u e c a l l e d t h e apparent  T h i s parameter I s i n e f f e c t a v a l u e o f t h e modulus  o f e l a s t i c i t y a p p l i e d o n l y t o t h e ' l o a d i n g p o r t i o n o f the compression  test.  The apparent modulus i s determined from.the s l o p e o f the l o a d i n g curve and has the. same u n i t s - a s i t h e modulus o f e l a s t i c i t y  (i.e.  p.s.i.  ( Values f o r t h e apparent modulus have been c a l c u l a t e d f o r a l l compression t e s t samples,  and t h e s e v a l u e s s t u d i e d . a s they are i n f l u e n -  ced by t h e r a t e o f s t r a i n , , diameter o f the l o a d i n g p l u n g e r and t h e t y p e of  sample.  Apparent Modulus vs S p e c i f i c  Gravity  The i n f l u e n c e o f the s p e c i f i c g r a v i t y o f t h e p o t a t o t u b e r on t h e apparent modulus was  studied.  I n i t i a l l y i t was  f e l t t h a t the spec-  i f i c g r a v i t y o f t h e t u b e r would g r e a t l y a f f e c t the b e h a v i o u r o f the t u b e r . This,, however, was  not t h e c a s e .  S p e c i f i c g r a v i t y was  i n f l u e n c e on t h e apparent modulus f o r t h e p o t a t o .  found t o have no  4600  4-  +  500 -  Ea  +  t  +•  400 T 1,05  L  1.06  1.07  .1.08  1.09  1.10  S p e c i f i c ^Gravity Fig.  17'".::  J  Apparent Modulus vs S p e c i f i c G r a v i t y F o r  1"  I 1.11  Plunger  Apparent Modulus vs Rate o f S t r a i n The apparent modulus was used as a parameter t o study t h e e f f ect of the rate of s t r a i n .  A n a l y s i s ' f o r t h i s e f f e c t was done on a s t a t -  i s t i c a l b a s i s u s i n g e i g h t r a t e s o f s t r a i n c o v e r i n g t h e range from. i n / i n / m i n . t o 65.2  in/in/min.  1.26  Ten t e s t s w i t h two r e p l i c a t i o n s a t • e a c h  speed were used as b l o c k s f o r a n a l y s i s o f t h e d a t a as a randomized comp l e t e b l o c k experiment.  Duncan's New'Multiple Range T e s t was used f o r  the comparison o f t h e means a t each.speed. o f t h i s d a t a i s shown i n Appendix  The s t a t i s t i c a l  analysis  E.  The r e s u l t s o f Duncan's t e s t on t h e ranked c e l l t o t a l means is  shown i n t h e f o l l o w i n g t a b l e .  Those means j o i n e d by a s o l i d  line  a r e n o t s t a t i s t i c a l l y s i g n i f i c a n t l y d i f f e r e n t from e a c h . o t h e r . Duncan's T e s t R e s u l t s ^ Test Cell Mean  1  4277.8  3  4681.5  4  4851.6  6  2  4884.7  4978.2  5  49?8;8  7  5283.5  8  5516.8  •  T h i s a n a l y s i s was done a t t h e Vfo s i g n i f i c a n c e l e v e l .  The  35  r e s u l t s show t h a t t h e r e i s a h i g h l y s i g n i f i c a n t i n c r e a s e i n t h e v a l u e o f Test-8,  the apparent modulus w i t h t h e i n c r e a s e i n t h e r a t e o f s t r a i n . at. 6 5 . 2 i n / i n / m i n i s s i g n i f i c a n t l y h i g h e r t h a n t e s t s 1 , S.-api ^» 6 and 7 a r e s i g n i f i c a n t l y h i g h e r t h a n  Tests  test:1.  The s l o p e o f t h e l o a d i n g curve i s g r e a t e r a t t h e h i g h e r r a t e s of strain.  The p o t a t o f l e s h behaves i n a more r i g i d manner when l o a d e d  at t h e h i g h e r r a t e s o f s t r a i n .  The s t r e s s r e l a x a t i o n c h a r a c t e r i s t i c o f  t h e p o t a t o f l e s h p l a y s a g r e a t e r r o l e a t t h e lower  s t r a i n r a t e s by a l l o w -  i n g more o f t h e a p p l i e d s t r e s s t o be d i s s i p a t e d as t h e s t r e s s i s b e i n g applied.  This allows a greater deformation  u n i t s t r e s s and c o n s e q u e n t l y lower  of the tuber material per  y i e l d s a s t r e s s - s t r a i n c u r v e which has a  slope.  Apparent Modulus vs Loading  Plunger  Type  The p o t a t o t u b e r f l e s h was t e s t e d i n compression plunger types.  using four  The one i n c h p l u n g e r was used i n c o n j u n c t i o n w i t h a  one i n c h c o r e o f t h e t u b e r m a t e r i a l , , however, w i t h t h e smaller, diameter p l u n g e r s i t was n o t p o s s i b l e t o use a c o r e sample t h e same s i z e as t h e plunger.  The apparent  modulus was.used as a c r i t e r i o n f o r s t u d y i n g  the e f f e c t o f the plunger  size.  Wide v a r i a t i o n between t h e v a l u e s f o r Ea were observed f o r the d i f f e r e n t p l u n g e r  sizes.  Wo  s t a t i s t i c a l a n a l y s i s was f e l t  nec-  e s s a r y t o study t h e s i g n i f i c a n c e o f t h e s e d i f f e r e n c e s due t o - t h e l a r g e magnitude o f t h e d i f f e r e n c e s .  Mean v a l u e s f o r Ea f o r each p l u n g e r  s i z e were c a l c u l a t e d a c r o s s t h e f u l l range o f t h e r a t e o f s t r a i n .  Mean v a l u e s f o r t h e apparent modulus o f e l a s t i c i t y i n the f o l l o w i n g t a b l e .  a r e shown  i  Test I J  • L. 0  Core  No. of Samples *  Mean Ea  . in  \ . tuber  . 16  :3260 psi  in  1"  28  3300  1"  16  • 3071  2"  18  3521  78  3296 psi  Plunger 14.  •u 111  • k-. 111  Total K  3/8"  2"  18  2217  M  •3/8"  2"  18  2393  P  3/8"  2"  18  2300  54  2303 psi  2"  16  1885  2"  18  1808  34  1846 psi  Total N  in 2  Q  2  111  Total R  1"  1"  18  561  E  1"  1"  20  578  A  1"  1"  32  604  B .  1"  1"  24  634  C  1"  • 1"  22  652  D  1"  1"  20  •465  P  1"  1"  20  528  Total  156  579 psi  Table II Mean Values for the Apparent Modulus of Elasticity Calculated from thesSlo'pe3 of the Stress-Strain Curve r  37 From T a b l e II i t can be seen t h a t t h e v a r i a t i o n i n t h e apparent modulus w i t h t h e f o u r p l u n g e r s i z e s i s over f i v e f o l d , , t h e range i n means b e i n g from  579 + 76  p s i f o r the  using the ^" plunger.  1"  c o r e samples t o  3296  _+ p s i f o r t e s t s  The r e l a t i o n s h i p o f apparent modulus t o p l u n g e r  diameter i s o f a l o g a r i t h m i c form. 4000 -  3000 _ '•'Ea  2000 1000 .  J  i" Pig.  18 ".  L  • 3/8"  1  J  #" P l u n g e r Diameter  l "  A r i t h m e t i c P l o t o f Mean Ea vs P l u n g e r  Fig.  19  Log Mean Ea-vs P l u n g e r  Diameter  Diameter  38 Relative  Elasticity Frey-Wyssling  (7)  d e f i n e s r e l a t i v e e l a s t i c i t y o r degree o f e l -  a s t i c i t y as-the r a t i o o f t h e r e c o v e r e d d e f o r m a t i o n t o t h e t o t a l deformat i o n when t h e m a t e r i a l i s l o a d e d t o a c o n s t a n t s t r e s s .  To.determine  t h i s c h a r a c t e r i s t i c of the potato tuber the f i r s t loops o f the hysteres i s t r i a l s were used as an i n d i c a t i o n o f t h e degree o f e l a s t i c i t y . t h i s d a t a i t i s n o t p o s s i b l e t o use a t r u e s t r e s s v a l u e ,  For  consequently  t h e v a l u e s o f f o r c e a r e used.  I t was found t h a t t h e degree o f e l a s t i c i t y v a r i e d from imum o f  0.640  t o a maximum o f  O.905  w i t h a mean o f  a min-  0.765.  A c r o s s t h e range o f l o a d s from.20 l b s t o 120 l b s t h e degree o f e l a s t i c i t y showed a d e c r e a s e , however, a maximum was reached a t a l o a d o f 60 l b s .  A wide range o f s c a t t e r i s e v i d e n t when t h e d a t a i s p l o t t e d ,  however, a marked drop o c c u r s between t h e l o a d s o f 70 and 80 l b s . from t h e h i g h v a l u e a t t h e 60 l b l o a d t h e degree o f e l a s t i c i t y t o remain r e l a t i v e l y c o n s t a n t a t l o a d s l e s s than 70 l b s . beyond 80 l b s t h e degree o f e l a s t i c i t y  shows a s l i g h t  Apart  appears  For loads  decline.  An apparent d i s c r e p a n c y a r i s e s when-the r e l a t i v e e l a s t i c i t y i s compared w i t h t h e r e s p e c t i v e v a l u e f o r h y s t e r e s i s l o s s .  I t would be  expected t h a t . t h e h y s t e r e s i s l o s s would i n c r e a s e w i t h a decrease i n t h e degree o f e l a s t i c i t y .  While t h i s i s t h e c a s e w i t h h y s t e r e s i s l o s s e s  g r e a t e r than 60 'jo, t h e t h r e e p o i n t s w i t h low l o s s a l s o show a low degree of  elasticity  39  Test No.  1 4 •5 6 7 8 9 10 11 12 •13 14  15. 16 17 18 19 20 21 22 24 25 26 27 • 28 30 31 32  Force  .20113.  30  . 40 50 6o 70 80 „  90 100 110 120  Total Deformation  Recovered Deformation  .080" .115 .120  .065" .090 .100 .110 .090 .115 .095 .115  .135  .115 .135 .120 .150 .170 .150 .170 .190 .210 .205 .225 .205 .250 .260 .275 .250 .260 .280 .280 •255 .285 • 295 • 360 .265  ' Degree of Elasticity  .140  .125 .150 .150  .190  .175 .170 .170 .180 .180 .195 .165 •175 .200 • 195 .180 .200 .195 .230 .190  •813 .782 .833 .815 .782 .852 • 792 .767 .823 .835 .883 • 790 .905 •855 .756 .830 I : ^ : .720 .693 .710 .660 .673 .715 .697 .705 .702 .662  .813  .717  '.679  .640  Mean  Table I I I Degree of Elasticity Data  Force Mean  .765  .810 .809 .808 .859 .814 .708 .667 I  V  .706 .682  Plate 2  Degree o f E l a s t i c i t y v s I n i t i a l  Force  +  + ©  +  + -I0  .8  +  +  + +  + O  + >> -P  +  +  •H  V •r-i -P CQ  cd W  .61  O 0) 0)  bO cu Q  o o H  H o  10  20  30  kO  50  60  Force ( l b s )  70  80  90  100  no  120  si •d t» cn co  oo  ko  Stress Relaxation The a n a l y s i s o f t h e s t r e s s r e l a x a t i o n d a t a was done "by means of a graphical for  a p p r o x i m a t i o n method (l7)«  the r e l a x a t i o n s t u d i e s ,  As whole p o t a t o e s were used  t h e c o n t a c t a r e a i s i n d e t e r m i n a n t and. t h e  c a l c u l a t i o n s a r e done on t h e "basis o f f o r c e • r e l a x a t i o n .  The r e l a x a -  t i o n curve f o r t h e s t r a i n e d t u b e r s cannot "be approximated by a s i n g l e u n i t Maxwell model as t h e s i n g l e term.exponent  w i l l not f i t t h e i n i t i a l  segment o f t h e c u r v e .  The g r a p h i c a l method a l l o w s t h r e e  exponential  terms t o be c a l c u l a t e d ,  each term h a v i n g a d i f f e r e n t r e l a x a t i o n  con-  stant .  The d a t a was f i r s t  p l o t t e d on s e m i - l o g a r i t h m i c p a p e r .  s t r a i g h t l i n e r e l a t i o n s h i p was found a f t e r about 250 seconds. s l o p e and F ( t ) , i n t e r c e p t f o r t h i s ined.  straight line  A The  segment were determ-  The d i f f e r e n c e between t h i s s t r a i g h t l i n e and t h e t r u e c u r v e  were p l o t t e d on s e m i - l o g . paper and t h i s v a l u e was found t o be l i n ear a f t e r about kO seconds. culated  The s l o p e and i n t e r c e p t were a g a i n c a l -  and a second d i f f e r e n c e p l o t performed t o - d e t e r m i n e t h e  t h i r d r e l a x a t i o n constant.  I n g e n e r a l form t h e r e l a x a t i o n e q u a t i o n may be w r i t t e n  F where  (t) = Ae ±  --t Ti  +  -±-  A e 2  as :-  t  + A e % 3  ..'F ( t ) = f o r c e a t any time t t  = time i n seconds  f  = r e l a x a t i o n time c o n s t a n t  A = F ( t ) axis  intercept  The v a l u e s f o r t h e t h r e e A terms are o b t a i n e d from t h e semilog  p l o t s and t h e r e l a x a t i o n time c o n s t a n t s a r e c a l c u l a t e d from t h e  . hi s t r a i g h t l i n e segments o f t h e curves u s i n g t h e e q u a t i o n :-  I n F i - I n F2  * ~  which i s t h e slope o f t h e s t r a i g h t l i n e  Values itial  segment.  f o r t h e t h r e e A and T" c o n s t a n t s a t . e a c h o f t h e f i v e i n -  s t r e s s l e v e l s were c a l c u l a t e d u s i n g t h i s method.  Mean v a l u e s '  f o r t h e t h r e e r e l a x a t i o n time c o n s t a n t s were c a l c u l a t e d and t h e v a l i d i t y of u s i n g t h e mean c o n s t a n t s checked.by c a l c u l a t i n g t h e r e l a x a t i o n u s i n g t h e s e mean v a l u e s and comparing them w i t h t h e o r i g i n a l  T h e . . c a l c u l a t i o n graphs f o r t h e r e l a x a t i o n e q u a t i o n s  curves  curves.  a r e shown  i n Appendix C.  Sample C a l c u l a t i o n s : - f o r T e s t Wo. 1  20 l b s .  I n i t i a l load From Graph  l r: -  ' 2 " ^1 " InFi - InF  ft ' l  =  1  t  From Graph  2r  : -  = 2  17.1  lbs.  600. - 0 I n 17.1-ln 16.8  =  3 Q  >  0 0 0  A2 = . 1.01.lbs..  180 - 0  rf  "2  I n 1.01  =  From Graph  1  A  3  The  _ "  3r  : -  - I n 0.1  A^ = 1.9  20 - 0 I n 1.9 - In.0.035  =  7°  lbs.  ~  5  r e l a x a t i o n time c o n s t a n t s f o r t h e f o u r • h i g h e r • l o a d v a l u e s  were c a l c u l a t e d i n t h e same manner.  The r e s u l t i n g time c o n s t a n t s a r e  42 shown i n t h e f o l l o w i n g t a b l e .  Test  r  #1 2 3 4 • 5 Mean  T a b l e IV  z  30,000 20,000 .20,000 27,900 15,800  78 77.5 92 70.5 104  5.01 7.0 4.1 5.4 7-2  . 22,7^0  84.4  5.74  S t r e s s R e l a x a t i o n Time  Constants  The g e n e r a l e q u a t i o n f o r the f o r c e r e l a x a t i o n i n the Netted Gem p o t a t o h e l d a t c o n s t a n t s t r a i n compressed.between p a r a l l e l p l a t e s would be  :t  t  F(t)  where  = A e x  t  " cT4T4"  . ~ 22,740 +  "5775  + A^e '  A2e  J  [  F ( t ) . = f o r c e a t any time t t /  = time i n seconds  T = r e l a x a t i o n time /  constant  A = F(t) axis intercept  The  e q u a t i o n shown c o n t a i n s t h r e e c o n s t a n t s which can be d e t -  ermined g r a p h i c a l l y , however, a l i n e a r r e l a t i o n s h i p was found t o e x i s t .between t h e v a l u e s f o r A and the i n i t i a l l o a d t o which the t u b e r was subjected.  T h i s r e l a t i o n s h i p i s q u i t e w e l l d e f i n e d f o r A]_ and A3  however, i t i s not as c l e a r f o r A « 2  Three e q u a t i o n s were then  calcu-  l a t e d which would a l l o w an a p p r o x i m a t i o n o f the v a l u e s f o r t h e A cons t a n t s from t h e i n i t i a l l o a d a p p l i e d t o the p o t a t o .  These e q u a t i o n s were determined  t o b e :-  ^3  F  where  A-L  =  0.81  F  (o) +.  1.0  A  2  =  0,0k  F  (o) +  0.3  A  3  =  0.13  F  (o) -  0.8  (o) = i n i t i a l f o r c e o r l o a d  - Hysteresis The p o t a t o shows t h e c h a r a c t e r i s t i c o f a b s o r b i n g a l a r g e p o r t i o n o f the energy  used t o produce d e f o r m a t i o n i n t h e t u b e r .  In studies  l o a d i n g whole p o t a t o t u b e r s ' b e t w e e n . p a r a l l e l p l a t e s a l a r g e h y s t e r e s i s l o o p i s found as w e l l as a r e l a t i v e l y , l a r g e permanent d e f o r m a t i o n .  In  t r a i l s u s i n g t h r e e l o a d i n g and u n l o a d i n g c y c l e s w i t h l o a d s from 20 l b . to  120  l b . the p e r c e n t . l o s s ranged  v a l u e o f 71.8$  -at a l o a d o f 120  d e f o r m a t i o n ranged  from  0.017"  The l o s s v a l u e s f o r the second  from a v a l u e o f 49»3$at.30 l b . t o a  lb. at  20  At t h e same time t h e permanent l b . to a value of  34.1$  from  31.0$  to to  46.3$  The range f o r the second  and t h e range f o r the t h i r d l o o p was  w i t h f o u r r a t e s o f s t r a i n was the f i r s t l o o p was  found  for  a l s o conducted.  found t o range from  76$ to-83«6$  0.045".  F i r s t Loop  Core  \ j 1  1bs.  w i t h a mean o f  62.8$  on  79«7$.  at a load  O.O89" w h i l e t h a t  The comparison between the c o r e s  and the•whole p o t a t o t u b e r s i s summarized b e l o w . f o r  1"  to-be  The h y s t e r e s i s l o s s  The mean d e f o r m a t i o n f o r t h e c o r e s was  the whole p o t a t o e s was  Whole Tuber  cycle  a l o a d o f 60  The mean l o s s f o r t h e f i r s t l o o p u s i n g whole p o t a t o e s was  601bs.  lb.  37.7$.  A s e t o f t r i a l s u s i n g one i n c h c o r e s and  of  120  at  and t h i r d c y c l e s ' d i d not v a r y t o n e a r l y  the extent.found w i t h t h e f i r s t l o o p . was  0.127"  Second Loop  60 l b . l o a d .  T h i r d Loop  Deformation  62.8$  .46.3$  37.7$  . 0.045"  79.7$  . 49.1$  46.3$  O.O89"  kk The l o s s and d e f o r m a t i o n .values a r e c o n s i d e r a b l y h i g h e r than those f o r t h e whole p o t a t o t u b e r s . '  This result i s felt-to-be primarily  due t o t h e f a c t t h a t a c o n s i d e r a b l e amount.of f l u i d i s extruded from c o r e s as they undergo compression.  Creep  the  ;  Behaviour The p o t a t o t u b e r s , when h e l d under, a c o n s t a n t s t r e s s , , showed  a creep d e f o r m a t i o n c u r v e which matched the c h a r a c t e r i s t i c form f o r m a t e r i a l s as. shown by Pao ( l 4 ) .  In g e n e r a l the r a t e o f creep d e f o r m a t i o n was w i t h the i n c r e a s e i n s t r e s s . t h e t u b e r s under s t a t i c  found t o i n c r e a s e  A wide range o f v a r i a t i o n was  observed.for  test.  Upon i n i t i a l l o a d i n g t h e t u b e r s show an i n i t i a l • e l a s t i c ormation, f o l l o w e d by. t r a n s i e n t and  steady s t a t e c r e e p p e r i o d s .  t h e l o a d i s removed, an immediate p a r t i a l r e c o v e r y was covery was  still  observed.  defWhen Re-  t a k i n g p l a c e a t t h e end o f t h e twelve hour u n l o a d i n g  period.  The  s t a t i c t e s t s were conducted  under two  g e r s , and because o f t h e complex s t r e s s d i s t r i b u t i o n l o a d i n g c o n d i t i o n , comparison  s m a l l diameter p l u n under-this-partial  o f the b e h a v i o u r o f the t u b e r s under, t h e  i two t y p e s o f p l u n g e r s on the b a s i s o f a p p l i e d s t r e s s would be m i s l e a d ing. The creep d e f o r m a t i o n and r e c o v e r y c u r v e s f o r the p o t a t o t u b ers  under the two  l o a d i n g areas are shown i n Graphs IV and V  curve shown i s the•mean o f f i v e t e s t s . fifty  The  samples t e s t e d i s shown i n Appendix B.  •  Each  s t a t i c t e s t data f o r the  45 F a i l u r e Energy :  The  energy  r e q u i r e d t o cause f a i l u r e i n the t u b e r sample  a t o t a l o f 48  determined.for  e i g h t r a t e s o f s t r a i n and each t e s t .  t u b e r samples.  was  These samples were from  s i x tests -, with two  samples at each r a t e i n  -  The r e s u l t s were a n a l y z e d s t a t i s t i c a l l y as a randomized  complete b l o c k and u s i n g Duncan's t e s t f o r the comparison o f the r a n ked c e l l t o t a l means f o r r a t e o f s t r a i n and p l u n g e r t y p e .  The  stat-  i s t i c a l a n a l y s i s i s shown.in Appendix E.  Duncan's T e s t R e s u l t s : Ranked C e l l Means F o r P l u n g e r Type a t the l*fo L e v e l Test Means  0  P  q  M  R  L  11.49  12.74  13.64  26.66  27.34  28.34  H i g h l y s i g n i f i c a n t d i f f e r e n c e s e x i s t between the f a i l u r e gy f o r the d i f f e r e n t t y p e s o f p l u n g e r s .  . The v a l u e s f o r t e s t s 0,  enerP  Q are h i g h l y s i g n i f i c a n t l y d i f f e r e n t . f r o m t h o s e f o r t e s t s M, R and Wo  s i g n i f i c a n t , d i f f e r e n c e s e x i s t between t h e means w i t h i n , t h e two  i n g s above. a c t i n g on 2" was  T e s t s 0, ;P and Q were r e s p e c t i v e l y -jj-'V 3/8" diameter,. 1"  p l u n g e r s a c t i n g on 2"  The presence  x 1"  cores.  group-  Test R  T e s t s M & L were -5-" and  x . l " c o r e s t h a t have the skin, o f the t u b e r  3/8"  intact.  o f t h e s k i n . l a y e r i n c r e a s e s t h e energy r e q u i r e d  t o cause f a i l u r e by a t l e a s t double t h a t r e q u i r e d w i t h no present.  L.  and\ijr" p l u n g e r s  t h i c k cores of potato tuber f l e s h .  a I " p l u n g e r a c t i n g on 1"  and  skin  layer  T e s t R i s c o n s i d e r a b l y h i g h e r than would be expected f o r a  \ core, without t h e s k i n l a y e r .  T h i s t e s t i s more t r u l y a pure compres-  s i o n t e s t than t h e o t h e r s as i t was column with.an L/d r a t i o o f 1.  performed  on an unsupported  short  The o t h e r s are i n e f f e c t a measure o f  the r e s i s t a n c e of the m a t e r i a l . t o p e n e t r a t i o n by the p l u n g e r .  46  Energy Required to Produce Failure (Energy in i n . l b . / i n ) Test  •o  P  Q  M  R  L  Mean  5.75  6.37  6.82  13.33  13.67  14.17  The influence of the rate of strain on the failure energy was also studied.  In this case the tests were used as blocks in the analy-  sis.  Duncan's Test for Rate of Strain (rate in in./in./min.) .Rate  Mean  60  65.2  31.2  19.0  45.5  53.6  18.15  18.85  18.95  19«78  20.1  20.12  6.9  20.72  1.26  .23.37  At the 5$ confidence level the slowest rate of strain required significantly higher energy to produce failure than any of the other rates of strain.  At the Vfo level the ;islow rate of strain showed sig-  nificantly higher requirements than only the 60, 65.2 and 31.2 i n . / i n . / min. rates.  At both the 1$ and 5$.levels no significant  differences  existed between any other means than those mentioned above.  A slower  rate than the 1.26 i n . / i n . / m i n . was used but was not included in the analysis duetto insufficient data.  The c e l l mean for a rate of 0.31  i n . / i n . / m i n . taken over tests 0, P, Q and R was found to be 24.40. This is equivalent to a mean failure energy of 12.20 i n . l b . / s q . i n . Stress-Strain-Rate of Strain Relationship A logarithmic relationship was observed between the values of stress at failure/rate of strain and the strain at failure/rate of strain. When the values of  ^/£_  sere plotted against the values of  /A-  47 on l o g - l o g paper a d e f i n i t e l i n e a r r e l a t i o n s h i p i s o b s e r v e d .  A  family  o f p a r a l l e l l i n e s r e s u l t s when t h e d a t a f o r t h e t e s t s w i t h d i f f e r e n t p l u n g e r s a r e p l o t t e d on t h e sane g r a p h . evaluated at l o g € . = pective  1>  When the''b' v a l u e s f o r t h e l i n e s ,  a r e compared w i t h t h e Ea v a l u e s f o r t h e r e s -  tests a.linear arithmetic  r e l a t i o n s h i p i s obtained.  While t h i s r e l a t i o n s h i p i s not e x p l a i n e d . i n t h i s study, i t i s mentioned.in  that i t merits further  0 I  I  investigation.  I  500  :1000  1500  "b* Values from s/<s F i g u r e 20  Eavs  1  1  2000  2500  I  vs  "b" Values PromS/g  €/£ vs  €/e.  DISCUSSION OF RESULTS In A p r i l o f 1964  a copy o f Essex E . F i n n e y ' s D o c t o r a l D i s s e r t a -  t i o n became a v a i l a b l e from U n i v e r s i t y M i c r o f i l m s ,  Ann Arbor,  Many a s p e c t s o f t h e work covered i n t h i s study a r e a l s o F i n n e y and c o n s e q u e n t l y many comparisons  Michigan.  discussed.by  a r e drawn w i t h h i s f i n d i n g s .  . k8 Specific Gravity The  s p e c i f i c g r a v i t y o f t h e t u b e r was  found.to have no i n -  f l u e n c e on the v a l u e o f the apparent modulus o f e l a s t i c i t y . i n g i s i n agreement w i t h the f i n d i n g s o f F i n n e y No  e x p l a n a t i o n . i s extended  r e s u l t , , by the two  (3)  c a l c i u m c o n t e n t o f the t u b e r s .  anticipated  The p r i m a r y p o s s i b l e  reason c o u l d be t h a t the i n f l u e n c e o f t o t a l d r y matter dary t o the i n f l u e n c e o f s p e c i f i c  (2k).  and o f Witz  f o r t h i s d i s c r e p a n c y from the  authors mentioned above.  This f i n d -  c o n t e n t i s secon-  substances, p r i m a r i l y the p e c t i n  and  Another p o s s i b i l i t y i s t h a t of t h e  rel-  a t i v e c o n t e n t o f i n c l u d e d a i r i n t h e t u b e r and t h e m o i s t u r e c o n t e n t o f the t u b e r .  Research  (2)  o f the p o t a t o t u b e r may may  i n d i c a t e s t h a t the i n t e r c e l l u l a r a i r c o n t e n t  range from 0.92$ t o 4.5$.  T h i s a i r content  show a f a r g r e a t e r i n f l u e n c e on the s p e c i f i c g r a v i t y than on  p h y s i c a l behaviour  of the p o t a t o t u b e r and thus t h r o u g h i t s v a r i a t i o n  tend t o e l i m i n a t e t h e i n f l u e n c e of s p e c i f i c g r a v i t y . been made t o determine t e s t s performed  the  No  attempt  has  t h e a i r content o f t h e t u b e r s t e s t e d as t h e  were d e s t r u c t i v e i n n a t u r e .  o f t h e t u b e r a i r c o n t e n t are o f dubious  Methods f o r e s t i m a t i o n  merit.  Rate o f S t r a i n The r a t e o f s t r a i n was  found t o have a h i g h l y s i g n i f i c a n t i n -  f l u e n c e on the apparent modulus o f e l a s t i c i t y f o r t h e p o t a t o . r e s u l t i s not i n agreement w i t h t h e f i n d i n g s o f F i n n e y p o r t s no r a t e o f s t r a i n i n f l u e n c e .  (3,  k)  This who  re-  As t h e p o t a t o f l e s h . b e h a v e s i n a  v i s c o e l a s t i c manner t h i s r a t e o f s t r a i n i n f l u e n c e would be due t o t h e f a c t o r o f s t r e s s r e l a x a t i o n .  anticipated  F o r a more d e t a i l e d study o f  t h e i n f l u e n c e of the s t r a i n r a t e i t would be d e s i r a b l e t o have b o t h p a c t v e l o c i t y t e s t s and v e r y slow speed t e s t s .  im-  F o r slow r a t e t e s t i n g  k  9  i t would "be .desirable to conduct tests which would be longer in duration than the relaxation time constants for the material.  With such slow  speed tests a marked drop in the stress at failure should be observed. This is pointed out particularly by the static tests in which, after sufficient-length of time under.-low stress, the material w i l l undergo failure.  Considering the interior of the potato to be an amorphous  mass of cells, the lower apparent modulus of elasticity at.the slow rate may to some extent be due to cells moving in.respect.to each.other, in opposition to only cellular deformation or rupture which would, occur at the higher rates of strain. While the strain rate had a highly significant effect on the apparent, modulus of elasticity,  the actual.form of the stress-strain  curve was not affected by the rate of strain.  This factor i s not the  expected, as stress relaxation at the slow strain rates would be expected to cause: the stress-strain relationship to become more curved with the decrease in the strain rate.  Stress-strain curves for the various  rates of strain are shown in Appendix A. Plunger Diameter The diameter of the test plunger used was found to have a very strong influence on the apparent modulus of elasticity.  The procedure  of using smaller-diameter plungers on large cores was an extension of the method used by Mohsenin (11, 12) and has proven to be very complex in nature.  The complexity of the stress distribution.under the small  plunger was pointed out by Finney (3) and by Mohsenin (13) in later work.  Analysis of the data obtained by these tests would prove com-  plex to analize from a theoretical or-fundamental approach.  Timoshenko  (20) discusses the Boussinesq solution of point loading on semi-infinite  50 elastic  s o l i d s and  extends t h i s  s o l u t i o n to t h e problem.of l o a d i n g areas  o f an e l a s t i c body, where u n i f o r m d i s t r i b u t i o n o f t h e l o a d i s g i v e n . case o f l o a d i n g a s e m i - i n f i n i t e e l a s t i c c i r c u l a r , d i e or plunger  The  s o l i d w i t h an a b s o l u t e l y r i g i d  i s also discussed.  In t h i s case t h e d e f l e c t i o n  under the d i e i s c o n s t a n t a c r o s s t h e e n t i r e a r e a o f t h e d i e .  The i n -  t e n s i t y o f p r e s s u r e a t any p o i n t under the d i e i s g i v e n by t h e  equation:-  27/a where  P  -  Va  2  -  r ' 2  load l o a d i n t e n s i t y at.any p o i n t  a  = radius of the loading d i e  r  = d i s t a n c e from the c e n t r e o f the d i e to the p o i n t under c o n s i d e r a t i o n  The d i s t r i b u t i o n o f p r e s s u r e i s not u n i f o r m and c e n t r e o f t h e d i e (r.=  For  r  =  0 :-  For  r  =  a  ^ p r e s s u r e can be  i s a minimum a t the  0). P  q(min) =  27fa  2  ( i . e . . a t t h e boundary o f t h e l o a d i n g d i e ) , the seen t o become i n f i n i t e .  q  =  2 raVo-' 7  "  ° °  T h i s e f f e c t w i l l produce v e r y l o c a l f a i l u r e a t t h e boundary o f the l o a d i n g p l u n g e r .  The d i s p l a c e m e n t by the e q u a t i o n  :-  of the l o a d i n g d i e i n t o the s o l i d i s g i v e n  51  2 aE  where  P  =  load  E  =  modulus o f e l a s t i c i t y  a  =  radius o f the d i e  v  =  Poisson's  €.  =  ratio  displacement  A n a l y s i s o f t h e d a t a o b t a i n e d f o r t h e p o t a t o t u b e r was to determine  checked  i f t h e s m a l l diameter p l u n g e r c o u l d be used f o r t h e d e t e r -  m i n a t i o n o f t h e modulus o f e l a s t i c i t y for. t h e p o t a t o .  To do t h i s t h e  f o l l o w i n g assumptions were made :•l) 2)  t h e p o t a t o a c t s as an e l a s t i c m a t e r i a l Poisson's r a t i o  f o r t h e p o t a t o i s 0.2+92 (from F i n n e y ( 2 ) )  The v a l u e s f o r l o a d and d i s p l a c e m e n t of f a i l u r e o f the tuber.  were taken a t . t h e p o i n t  The mean v a l u e s f o r displacement  were used from two t e s t s o f each o f t h e  3/8"  and l o a d  and \" p l u n g e r s .  Values f o r t h e modulus o f e l a s t i c i t y were o b t a i n e d u s i n g t h e equation.:-  E  =  P (1 - v ) 2  e  The r e s u l t s  in • ' 4  o b t a i n e d a r e shown below.  Test L  0  Mean 3/8"  2a  E 1  E  Test M  E  P Mean  E  438 p s i  42+2  2+2+0  psi  517  .492 504.5 p s i  52 Test N Q  E  535  515 525  Mean  psi  While t h e s e v a l u e s are not i n complete agreement w i t h the v a l u e o b t a i n e d u s i n g t h e 1"  unsupported  column (579  + 76  psi) it.prov-  i d e s a much c l o s e r e s t i m a t e than the p r e v i o u s c a l c u l a t i o n method The v a l u e s f o r t h e 3/8"  used.  and •§•" p l u n g e r s f a l l w i t h i n the l i m i t s o f v a r -  i a t i o n e s t a b l i s h e d f o r t h e unsupported the'-jj-" p l u n g e r f a l l s w e l l o u t s i d e t h e s e  t i s s u e , although the value f o r limits.  Stress Relaxation The  s t r e s s r e l a x a t i o n c a l c u l a t i o n s used f o r t h e p o t a t o  tuber  were done on t h e b a s i s o f f o r c e r e l a x a t i o n r a t h e r than t r u e s t r e s s  rel-  a x a t i o n as whole p o t a t o e s were used and thus the area o f c o n t a c t i s i n determinant.  A group o f 1"  c o r e s was  a l s o used, however, i t i s f e l t  t h a t w o r k w i t h whole p o t a t o e s i s a p p l i c a b l e t o f i e l d 1  c o n d i t i o n s and  t h a t water l o s s from t h e c o r e samples d u r i n g the t e s t p e r i o d would i n :  v a l i d a t e any r e s u l t s o b t a i n e d i n t h i s manner.  In  t h i s study i t has been shown t h a t t h e f o r c e r e l a x a t i o n  of  t h e p o t a t o may  be r e p r e s e n t e d by a t h r e e term  to  a p e r i o d of ten minutes.  Finney  exponential equation  (5). i n l o n g e r term  s t u d i e s has  t h a t the r e l a x a t i o n curve can b e s t be r e p r e s e n t e d by a f o u r term e n t i a l equation.  curve up  found  expon-  The c u r v e o b t a i n e d u s i n g t h e t h r e e term e q u a t i o n dev-  eloped matches t h a t o f F i n n e y v e r y c l o s e l y up t o t h e time of t e n minu t e s , b u t beyond t h i s time t h e f o u r t h term o f h i s e q u a t i o n comes i n t o e f f e c t and the d i f f e r e n c e between the two curves o b t a i n e d u s i n g t h e two  curves becomes o b v i o u s .  The  e q u a t i o n s a r e compared on Graph I I I .  T h i s comparison would i n d i c a t e • t h a t f o r development o f a v a l i d  relaxa-  53 • t i o n e q u a t i o n s t u d i e s o f a more extended n a t u r e must.be  F a i l u r e i n the Potato Mohsenin (12)  conducted.  Tuber notes t h a t i n a p p l e s t h e i n i t i a t i o n o f f a i l u r e  i s accompanied by l o c a l i z e d f a i l u r e o f c e l l s under t h e s k i n , when t h e whole.specimen.is  loaded using a plunger.  F i n n e y (3)  i s i n general  agreement w i t h t h i s f o r p o t a t o e s under some l o a d i n g c o n d i t i o n s . second type o f damage i s mentioned  by F i n n e y .  A  T h i s type i s t h a t o f  b r u i s i n g i n the centre region o f the potato tuber i n the r e g i o n of h i g h shear f o r c e s as p r e d i c t e d by Timosh'enko  (20).  F a i l u r e o f t h e whole t u b e r s compressed between p a r a l l e l p l a t e s was marked by a c i r c u m f e r e n t i a l c r a c k i n g , o f t h e p e r i d e r m a c companied by a sharp drop i n t h e s t r e s s - s t r a i n c u r v e . f a i l u r e i s a l s o noted by F i n n e y (3)»  This type of  F a i l u r e i n t h i s case a r i s e s  from t e n s i o n f o r c e s s e t up i n t h e p e r i f e r a l r e g i o n o f t h e t u b e r due t o t h e geometry o f t h e t u b e r and t h e p a r a l l e l p l a t e  compression  technique.  Loading  Plate  Specimen T e n s i o n Rack  Loading  ! Fig' 2i.  " '  T e n s i o n F a i l u r e i n Tuber Compressed Between P a r a l l e l  F a i l u r e i n t h e 1"  Plate  Plates  c o r e s was o f a c o n i c a l n a t u r e . i n , a l m o s t a l l  cases, i n d i c a t i n g , t h a t f a i l u r e was i n t h e r e g i o n o r p l a n e o f h i g h shear  54 stress.  I n some cases a p a r t i a l c o n i c a l f a i l u r e o c c u r r e d where t h e cone  was not complete. a 1"  A s i m i l a r c o n i c a l f a i l u r e p a t t e r n was observed when  p l u n g e r was p r e s s e d a g a i n s t a 2" c o r e sample.  p a t t e r n was n o t i n f l u e n c e d rates  The c o n i c a l f a i l u r e  by t h e r a t e d f s t r a i n and o c c u r r e d a t a l l  of strain.  Fig.  F i g . .23  2.2  F a i l u r e i n a 1"  . F a i l u r e Under a 1"  P o t a t o Tuber Core  Plunger Acting  on a 2" Core  55 Static  Failure The p o t a t o t u b e r w i l l undergo s t a t i c  ded p e r i o d s o f time under r e l a t i v e l y  f a i l u r e i f l e f t f o r exten-  low s t a t i c l o a d s .  w i t h s t a n d p r e s s u r e s up t o and exceeding  300 p s i under a  f a i l u r e when t e s t e d a t moderate r a t e s o f s t r a i n ,  The p o t a t o w i l l plunger b e f o r e  however, a l o a d o f 60  p s i w i l l cause p e n e t r a t i o n o f t h e s k i n i f a l l o w e d t o remain f o r a p e r i o d of  approximately  one week.  As no s p e c i f i c  t e s t s were r u n t o determine  the time and l o a d s n e c e s s a r y t o produce s t a t i c  f a i l u r e , t h e above v a l u e  i s o n l y an e s t i m a t i o n from a few t e s t s .  Fig.  F i g . 25  24  *! P o t a t o Tuber Dagiage A f t e r Three Weeks Under A S t a t i c Load o f 91.5 p s i  Tuber A f t e r 48 Hours Under a S t r e s s o f 91.5 p s i  Fig. 26 " Tuber After h8 hrs. Under a Stress of 6l psi  Fig. 27:  Tuber After k& hrs. Under a Stress of 30.5 psi  A noticeable depression may be observed under the loading plunger after k& hrs. under a static stress of 91»5 p s i . stress of 30*5 psi no depression is visible after h& hrs.  Under a Long dur-  ation static loads such as are found in bulk storage conditions would certainly lead to considerable deformation of the tubers, and in many cases probably lead to some form of mechanical damage. A Rheological Model For The Potato Tuber The behaviour of the potato under various conditions of loading may lead to the construction of a-hypothetical model to represent the behaviour of the potato.  The conditions which must be  57 met  by the model are  :-  1)  must be  i n f l u e n c e d by the  strain  2)  must creep under constant  stress  3)  must r e l a x under c o n s t a n t . s t r a i n .  The  'Generalized  Maxwell Model' as d e s c r i b e d by B l a n d ( l )  appears t o meet.the c o n d i t i o n s t h a t the  der  set out above, w i t h one  alteration  s p r i n g element which Bland.shows i n p a r a l l e l i n . t h e model  . i n s t e a d be p l a c e d provide  rate  i n s e r i e s i n the model.  closer estimation  a constantly  increasing  E  1^.  rr)  F i g . 28.  of the  This a l t e r a t i o n  should  e l a s t i c b e h a v i o u r o f the p o t a t o  un-  strain.  2  ^4  z  • Hypothetical Rheological the P o t a t o  Model t o Represent  While mathematical a n a l y s i s o f t h i s model.has not.been p e r f o r med  i t i s f e l t from o b s e r v a t i o n  t h a t i t should  prove adequate.  m a t i c a l a n a l y s i s of the model would be n e c e s s a r y b e f o r e be  used t o d e v e l o p e q u a t i o n s f o r the b e h a v i o u r of the  Practical  Mathe-  the model c o u l d potato.  Applications The  data regarding  the m e c h a n i c a l and  rheological properties  58 of t h e p o t a t o tuber-may be used t o determine t h e a l l o w a b l e storage and . h a n d l i n g s t r e s s e s t h a t may be a p p l i e d t o t h e p o t a t o .  Although t h i s has not been.the o b j e c t o f t h i s lified  example w i l l be g i v e n t o  physical data. mum  study one-simp-  illustrate t h e p o s s i b l e a p p l i c a t i o n o f  The example i s t h a t f o r t h e d e t e r m i n a t i o n o f t h e maxi-  s t r e s s i n t h e t u b e r under p r e s s u r e i n a p i l e o f p o t a t o e s .  F o r many t y p e s o f p o t a t o e s t h e shape c o u l d be assumed as b e ing  spherical,  such as f o r t h e Warba o r t h e P o n t i a c .  is,  however, a much more complex shape,, b e i n g c l o s e r t o an e l l i p t i c a l  c y l i n d e r w i t h rounded ends.  The N e t t e d  Gem  The f o l l o w i n g example i s based on t h e a s -  sumption t h a t t u b e r s o f s p h e r i c a l shape a r e b e i n g  used.  A n a l y s i s o f t h e c o n t a c t pressure-and. d e f o r m a t i o n  for-two  s p h e r i c a l b o d i e s i n c o n t a c t .is d i s c u s s e d by Timoshenko (20) as t h e H e r t z problem.  The c o n t a c t a r e a w i l l be c i r c u l a r i n shape and t h e  p r e s s u r e and d e f o r m a t i o n deformation  w i l l vary across the area of contact.  or displacement  (o<) o f t h e c e n t r e s o f t h e two*bodies toward  each o t h e r under p r e s s u r e i s g i v e n by t h e e q u a t i o n :-  where  The  P  load or force  R  radius  v  Poissoris  ratio  k  The r a d i u s (a) o f t h e s u r f a c e o f c o n t a c t i s g i v e n as :-  59  3T  r  P (*i + k ) (R R ) 2  R  l  +  x  R  2  2  F o r t h e a p p l i c a t i o n o f t h e s e formulae to- t h e p o t a t o t h e f o l l o w i n g assumptions a r e made: .l)  t h e t u b e r s a r e s p h e r i c a l and have a diameter o f 2.5  2)  s p e c i f i c g r a v i t y o f t h e t u b e r s i s 1.080  3)  v = O.i+92 (from F i n n e y  4)  E ~  5)  The p o t a t o e s a r e p u r e l y e l a s t i c  (2))  550 p s i  3 Then :-  inches  ©< = ^ P  k l  =k  __, 2  2  (6.8  =  x  10" ) 6  - - 92 550 U  1  2  =  4.38x10-^  The maximum p r e s s u r e on t h e t u b e r i s 3/2 t h e average p r e s s u r e and i s g i v e n b y :-  3P q  °  2TTa  =  2  Then f o r a t e n f o o t column o f s i n g l e , s p h e r i c a l t u b e r s t h e l o a d on t h e bottom t u b e r i s a p p r o x i m a t e l y 15 l b s . and :-  (5.47 x 10~ )' = .269  'it!. 4  q.o  =  h  3P  52tfa 2  =  45 ,. (6.28) (.0724) /  = 100 p s i :  T h i s c a l c u l a t i o n i s v e r y s i m p l i f i e d and t o c o n t i n u e o r extend t h e u s e f u l n e s s o f such c a l c u l a t i o n s f u r t h e r t i c s would be n e c e s s a r y .  study o f a l l i e d  characteris-  A p p l i c a t i o n o f knowledge o f t h e c r e e p proper-  60  t i e s o f the p o t a t o and  study o f t h e 'packing' or arrangement o f the p o t -  a t o e s i n . b u l k p i l e s would be n e c e s s a r y . found as two  The p o t a t o e s would never  be  s i n g l e spheres i n c o n t a c t . i n s t o r a g e and t h e c o n t a c t . o f  the p o t a t o e s and t h e r e s u l t i n g p r e s s u r e d i s t r i b u t i o n would be r e q u i r e d for  f u r t h e r work i n t h i s  area.  CONCLUSIONS  In t h i s t h e Netted Gem  study on the m e c h a n i c a l  and r h e o l o g i c a l p r o p e r t i e s o f  p o t a t o , the b e h a v i o u r o f t h e p o t a t o has been  terms o f e n g i n e e r i n g parameters.  studied.in  The use.of. e n g i n e e r i n g parameters i s  f e l t t o b e more d e f i n i t i v e than a study o f the p o t a t o i n terms o f t e x t u r al evaluation.  The response  of the p o t a t o tuber, t o v a r i o u s t y p e s o f  a p p l i e d l o a d s has been e x p l o r e d .  1.  Under the a p p l i c a t i o n o f a c o n s t a n t s t r e s s t h e p o t a t o t u b e r e x h i b i t s t h e p r o p e r t y o f creep or d e f o r m a t i o n no a d d i t i o n a l l o a d . b e i n g a p p l i e d .  with  The r a t e o f c r e e p i s 1  dependent on t h e s t r e s s a p p l i e d w h i l e t h e t o t a l  creep  d e f o r m a t i o n i s dependent on.both t h e s t r e s s and  the  d u r a t i o n o f the l o a d i n g p e r i o d .  Upon removal o f the  a p p l i e d s t r e s s t h e t u b e r w i l l r e c o v e r most o f the t r a n s i e n t . creep d e f o r m a t i o n p l u s t h e e l a s t i c  2.  deformation.  .When t h e p o t a t o t u b e r i s m a i n t a i n e d under a c o n s t a n t s t r a i n the s t r e s s w i l l be g r a d u a l l y d i s s i p a t e d . not p o s s i b l e t o determine  i f the  From  this  study i t . i s  will  e v e n t u a l l y reduce t o z e r o . " F o r p e r i o d s up t o t e n  minutes i t i s p o s s i b l e t o d e s c r i b e t h e r e l a x a t i o n  stress  curve  .61 u s i n g a t h r e e term e x p o n e n t i a l e q u a t i o n . o f l o n g e r than t e n minutes  For periods  i t would be e s s e n t i a l t o add  a f o u r t h term t o t h e e x p o n e n t i a l e q u a t i o n .  3.  Compression  t e s t i n g o f the p o t a t o t u b e r i n d i c a t e s an i n -  c r e a s e i n . the r a t e of. strain.when the parameter  of the  apparent modulus o f e l a s t i c i t y i s used f o r comparison of the various r a t e s .  4.  A l t h o u g h t h e use o f s m a l l d i a m e t e r p l u n g e r s i s not as a p p l i c a b l e to t h e o r e t i c a l c a l c u l a t i o n o f t h e apparent modulus o f e l a s t i c i t y as a r e the unsupported c o r e s , it  i s p o s s i b l e - t o o b t a i n an e s t i m a t e o f the modulus  u s i n g t h e method o f Timoshenko f o r r i g i d . d i e of a s e m i - i n f i n i t e e l a s t i c  5.  solid.  The apparent modulus o f e l a s t i c i t y f o r the unsupported p o t a t o f l e s h was  6.  loading  found t o be 579  + 76 p s i .  P o t a t o e s were found t o absorb a l a r g e p o r t i o n o f t h e energy r e q u i r e d t o produce d e f o r m a t i o n o f the t u b e r . The h y s t e r e s i s l o s s on t h e f i r s t - l o a d i n g c y c l e  was  found t o be dependent on t h e l o a d a p p l i e d t o the t u b er.  As t h e l o a d was  increased the percentage of the  energy absorbed by the t u b e r a l s o i n c r e a s e d . fact.was not apparent i n the two  subsequent  This loading  cycles.  7.  The.energy t u b e r was rate of  r e q u i r e d t o produce f a i l u r e o f the p o t a t o found t o i n c r e a s e w i t h a d e c r e a s e i n the  strain.  I t was found that the potato "behaves as a v i s c o e l a s t i c m a t e r i a l and that the mathematics of l i n e a r v i s c o e l a s t i c i t y may "be applied to the a n a l y s i s of the response of the potato to applied f o r c e s .  BIBLIOGRAPHY  6k  BIBLIOGRAPHY  1.  Bland, D.R.  I960.  2.  The t h e o r y of l i n e a r v i s c o e l a s t i c i t y .  j  Permagon P r e s s ,  D a v i s , R.M. T i s s u e a i r space i n t h e potato;, i t s e s t i m a t i o n and r e l a t i o n t o d r y matter and s p e c i f i c g r a v i t y . Am.Pot.J. 39'  298-305,  1962.  3.  Finney, E.E. The "behaviour o f the p o t a t o , solanum tuberosum, under q u a s i - s t a t i c l o a d i n g . Ph.D. T h e s i s , M i c h i g a n S t a t e U n i v e r s i t y , Michigan, 1963.  k.  Finney, E.E., C.W. H a l l and N.R. Thompson. I n f l u e n c e o f v a r i e t y and time o f h a r v e s t on the r e s i s t a n c e o f p o t a t o e s t o mechanic a l damage. As submitted t o Am.Pot.J., Sept., 1963.  5.  Finney, E.E., C.W. H a l l and G.E. Mase. Theory o f l i n e a r v i s c o e l a s t i c i t y a p p l i e d t o a b i o l o g i c a l m a t e r i a l - the potato. As submitted to the B i o p h y s i c a l S c i e n c e J . , Sept., 1963.  6.  Frey-Wyssling,  A.  Deformation  and f l o w i n b i o l o g i c a l  I n t e r s c i e n c e P u b l i s h e r , N.Y.,  systems.  1952.  7«  Hayward, H.E. The & Co., 1938.  8.  Kramer, A. D e f i n i t i o n o f t e x t u r e , and i t s measurement i n vegetable products. Food Technology, V o l . l 8 , . No. 3> March,  s t r u c t u r e o f the economic p l a n t s .  MacMillan  196k.  9.  Lampe, K. D i e W i d e r s t a n d s f a h i g k e i t yon K a r t o f f e l k n o l l e n G g Beschadigungen. (The r e s i s t a n c e of p o t a t o t u b e r s t o i n j u r y . ) E u r . P o t a t o J , V o l . 3, No. 1, i960. e  e n  10.  Matz, S.A.  11.  Mohsenin, N. A t e s t i n g machine f o r d e t e r m i n a t i o n o f t h e mechani c a l and r h e o l o g i c a l p r o p e r t i e s o f a g r i c u l t u r a l p r o d u c t s . B u i . 701 Penn.State Univ., C o l l e g e o f A g r i c .  Food t e x t u r e .  A.V.I.,  1962.  12.  . E n g i n e e r i n g approach t o e v a l u a t i n g t e x t u r a l t o r s i n f r u i t s and v e g e t a b l e s . , A.'S.A^.E.Trans, 6 (2),  13.  • P h y s i c a l p r o p e r t i e s o f a g r i c u l t u r a l products, a new c h a l l e n g e f o r a g r i c u l t u r a l e n g i n e e r s . Presented at 1963 Annual Winter Meeting, A.S.A.E., Chicago, 111.  ik.  Pao,  fac1963  Yoh-han and C.W. M a r i n . An a n a l y t i c a l t h e o r y o f creep d e f ormation o f m a t e r i a l s . A.S.M.E. Trans'., ( j . A p p l i e d Mech.)  20:. 245-252, No. 2,. June  1953.  65  15-  R e i n e r , M. I960.  16..  •  Deformation s t r a i n The f l o w o f m a t t e r .  and-flow,  2nd Bd.  Scientific  Lewis & C o . ,  American, Dec.  1959'  17«  R i c h a r d s , C.W. Co., 1961.  18.  R o b e r t s o n , I.R.  19.  T a l b u r t , W.F. and 0.  20.  Timoshenko, S. and G.H. MacCullough. Elements o f s t r e n g t h o f m a t e r i a l s . 2nd Ed. v a n N o s t r a n d Co., 1940.  21.  Timoshenko, S. and N. G o o d i e r . Hill, 1951.  .22.  Witz,R. Measuring.resistance of potatoes t o b r u i s i n g . J o u r n a l , 35: 241-244, 1954.  23.  Zoerb, G.C. and C.W. H a l l . Some m e c h a n i c a l and r h e o l o g i c a l p r o p e r t i e s o f g r a i n . J . . o f Ag.Eng.Res. Vol. 5, No. 1, i960.  Engineering.materials science.  Wadsworth Pub.  P e r s o n a l communication. Smith.  P o t a t o p r o c e s s i n g . A.V.I.,  Theory o f e l a s t i c i t y .  I96I.  McGrawA.S.A.E.  APPENDIX A  1" Plunger  Test A  No  1" Core  F  S  €.  Ea  135 130 133 123  172 165 168 156  .294 .286 .298 .282  584 578 566 553  I.O96  2  135 133  172 168  .296 .309  580 547  1.075  .3  115 120 128  146 153 162  .274 .266 .294  549 573 551  1.072  150 143  191 181  .314 .294  607 616  . 1.080  5  130 128 139 125  165 162 177 159  .269 .299 .289 .294  614 542 616 541  1.086  6  145 148  184 186  .279 .274  652 684  1.088  137 134  174 170  .246 .264  708 646  I.O98  8  135 155 148 150  172 197 188 191  .279 .309 .284 .286  615 ' 638 662 58l  I.O85  9  125 130  159 165,  .274 .290  581 570  I.O78  131 111  167 141  .274 .264  631 534  •1.082  11  145 140 126  184 178 160  .274 .276 .278  673 645 576  1.088  • 12  133 144  169 183  .292 .284  578 650  I.O76  1  4  7  10  0.138  0.290  0.443  0.596  Mean Ea = 604 p s i  Sp.G-r.  68  Test B  r ' Plunger  1" Core Ea  Sp.Gr.  .330 .309  586 608  I.069  190 192  .312 .314  607 611  1.068  132 142  168 181  -.299 .258  562 700  .1.083  151 • 155  192 197  .309 .299  621 659  I.075  5  145 136  185 173  .309 .283  598 611  1.069  6  156 155  198 197  .313 .293  634 672  I.070  145 150  185 191  .258 .299  712 639  1.074  8  146  186  .288  645  9  135 • 145  172 . 185  .258 .309  666 598  I.069  140 138  178 176  .286 .270  623 650  1.080  11  135 163  172 207  .288 .288  596 719  1.080  12'":  155 152  197 193  .304 .298  648  1.082  Wo  €  p  S  1  O.138  152 148  194 188  2  149 151  3  4  7  10  0.290  . 0.443  O.596  Mean Ea = 634 p s i  e  650  I.083  69  Test C o  : i ' Plunger  1" Core  £  Ea  Sp.G-r.  F  S  135 l40  172 178  .288 .280  597 635  .1.080  2  145 139  185 177  .295 .280  626 633  1.081  3  133  169  .262  646  1.080  130 126  165 160  .268 .263  617 609  . I.O74  5  161 163  205 •208  -.304 .302  675 689  1.072  6  142 149  181 190  .292 .276  620 689  1.072  '7  155  197  .302  653  1.080  8  119 118  151 150  .249 .247  606 607  1.073  .9  122 127  155 162  .248 ...242  627 668  1.082  150 145  191 185  .248 .252  770 .733  1.072  • 11  147 140  187 178  .268 .253  698 708  I.O83  12  115 144  146 183  .263 .268  555 683  1.078  No  1  .4  10  € 0.138  0.290  O.596  Mean Ea = 691 p s i  Test D No  1  *  Sp.Gr.  .280 .300 .272 .295  .•508 480 482 465  1.092  109 130 147 139 130 126  .270 .268 .201 .275 .275 .284  404 485  I.O89  506 473 443  .254 .302 .300  497 417 467  , 1.111  F  0.138  112 113 103 108  142 144 131 137  86 102 116 109 102 99 99 99  0.290  4 5  1" Core Ea  £  2 3  1" Plunger s  €  486  I.O89  1.085 . 1.082 1.101  7  . HO  126 126 i4o  8  100 96  127 122  .286 .298  444  1.098  102 96 91 104  130 122 116 132  .252 .274 .280 .274 .300 .295  516  1.092  4l4  I.O98  497  I.O85  6  9 . 10 • 11  O.M+3  -O.596  117 101  149  128  Mean Ea = 465 p s i  409  446  446  434  1" Plunger  Test E Wo 1  •  0*308  . 2  F  S  126 112 116 117  160 143  148  . 149  1" Core Ea  Sp.Gr.  .275 .300 .275 .290  582 477 528 514  1.101  e  1.091  '3  1.26  116 102  148 130  .243 .267  610 487  1.094  . 4  3.^2  .99  126  .235  536  1.101  = 126 .240 127 *220  525 577  99 100  5 6  6.9  7 8 12.5 9 10 n:.  19.0  106 135 97 . 123 . 112 143 109 139  .215 .230 .220 .255  628 , 537 650 1.100 545 644  106 118 109 120  135 150  139 153  .210 .255 .247 .235  127 107 107  162 136 136  .252 .250 .222  Mean Ea = 578 psi  • 1.092  588 563 650  I.O96  1.109  643  545 613  1.079  72  Test F •  Ko  .308  1 2 3  1.26  4 5  3.42  6 7  6.9  8 9 10 11 12  19  1" Core  F  s  114 108  145  138  .275 .285  470 447  116  148  .245  106  135  103 90  Ea  Sp.Gr.  .894 •926,.  528  1.108  480  .795  602 :  1.110  .300  107  .238  450  1.109  131 115  .280 .290  19.4.0 91.0  .222 .230  468  I.O98 .  93 95  118 120  .244 .260  34.6 35.1  .071 .076  484  1.102  121 99  154 126  .272 .255  45.0 36.8  .079 .074  567 495  .1.105  112 99  143 126  .248  .238  20.6 18.3  .0360 .0345  575  I.O85  " 124  158 -139  .262 .282  22.9 20.2  .0380 .0408  604 493  1.100  . 100 97  127  . 124  .200 .247  10.2 :9:.9  .0160 ' .0198  635 500  I.IO98  112 105  143 134  .245 .260  . 11.4 '10.7  .0196 .0208  582 516  1.101  89  113  .220  5.65  .0110  514  1.088  96  122  ,200  6.10  .0100  610  1.092  109  -12.5  1" Plunger  Mean Ea = 528 p s i  s/e  483  . 395 462  530  73  Test I  v^" Plunger  'One-half Tuber  Wo  €  P  S  G  1  .1.26  17.4  355  .095  282  .0713  ' 3950  .13.8  282  .110  224  .0794  2560  lk.7  300  .080  43.5  .0116  3750  15.0  306  .080  44.3  .0116  3820  12.6  257  .120  13.5  .0063  2140  15.6  318  .100  16.7  .0053  3180  15.0  •306  .150  .0048  2040  16.1  328  .115  .0037  . 2850  13.2  269  .070  5.92  .00153  2850  15.6  318  .080  7.00  .OOI76  3980  12.0  •245  .105  4.57  .00186  2340  16.2  • 3300  .080  6.15  ..00149  4120  13.2  269  .095  4.49  .OOI58  2840  10.2  208  .055  3-^7  .00092  3780  15.6  318  .090  4.87  .OOI38....  3530  21.0  428  .125  6.57  .00192  3420  2 3  6.9  4 5  19.0  6 7  31.2  8 9  ;45.5  10 • 11  53.6  12 13  60.0  14  •15 16  65.2  Mean-Ea = 3260 psi  Ea  s/e  9.82 10.5  .74  Test J  No  1  € 1.26  2 3  6.9  . 4 •5  19.0  6 7  . 31.2  •8  9  45.5  •10 !  11  53.6  12 ;  13  60.0  1^ •15 16  65.2  P  Plunger  1" Core  Ea  S  16.2 •'  330  .100  262  .0795  3300  13.8  282  .095  224  .0755  2970  14.4  294  .110  42.6  .0160  2670  16.2  330  .105  47.9  .0150  3140  -12.6  257  .075  13.5  ..00395  3420  10.8  220  .090  '11.6  .00470  2450  14.1  288  .095  9.24  .00304  3040  •12.6  257  .055  8.25  .00175  4680  12.9  264  .090  5.80  .00198  2940  13.2  270  .085  . 5.93  .00186  3180  14.4  294  .088  5.48  .00164  3340  13.2  270  .070  5.03  .00130  3860  11.4  232  .075  3.86  .00125  3100  12.0  244  .075  . 4.07.  .00125  3250  13.2  270  .080  4.13  .00123  3380  11.4  232  .070  3.55  .00107  3320  Mean Ea = 3300 psi  75  Test K  No  t  .308  1 2 3  1.26  .4 5  6.9  6 1  19.0  •8 9  • 31.2  10 11  45.5  •12 13  53.6  14 15  60  16 17 18  '65.2  3/8" Plunger  One-half Tuber  *4  Ea  •876  .5200  1530  .125  857  .4050  266  .125  211  .0990  2130  31.8  288  .175  228  .1350  1640  32,4  294  .135  42.6  .0196  2170  • 31.2  282  .110  40.8  .0159  2560  •31.8  288  .100  15.2  .00526  2880  28.2  264  .130  13.9  .00685  2030  32.4  294  .115  9.42  .00369  2560  • 25.8  234  .110  7.50  .00352  2130  31.2  282  .110  6.20  .00242  2560  24.6  223  .130  4.90  .00268  1720  32.4  294  .190 "  5.48  .00354  1550  27.6  250  .080  4.66  .00149  3130  24.6  223  .105  3.72  .00175  2120  22.8  206  .085  • 3.44  .00142  2430  30.0  272  .110  4.92  .00199  2470  28.8  261  .110  4.72  .00199  2380  P  s  €  27.0  245  .160  .26.4  239  29.4  Mean Ea = 2217 psi  s/e  •1910 *  76  Test L Wo 1  #  F  1.26  2 •3  .6.9  4 5  19  6 7  31.2  8 9  45.5  . 10 11  53.6  12 13 14 15:  65.2  16;  Ea  Ef  E'f  .110  221  .0874  '2530  .81  16.5  194  .0795  2440  .60  12.2  .12*0  •244  .100  13.8  281  .110  40.7  .0160  256O  • 75  15.3  15.0  •305  .090  44.3  .0130  3390  .65  13.1  16.2  330  .095  17.4  .00500  3480  .77  15.6  12.0  244  .155  12.8  .00815  1575  .74  I5.O  12.0  244  .100  7.82  .00320 . 2440  .56  11.3  15.0  305  .110  9-75  .00352  2780  .80  16.2  18.0  366  .125  8.05  .00274  2930  .96  19.5  16.2  330  .105  7.25  .00231  3140  .81  16.5  14.4  294  .115  5.50  .00215  2560  •71  14.4  •305  .070  • 5.70  .00131  4360  .56  11.3  16.2  330  .095  5.50  .00158  3480  • 71  14.4  11.4  232  .075  3.87  .00125  3100  .42  8.5  15.0  •305  .080  4.68  .00123  3820  .51  10.4  15.6  318  .070  . 4.88  .00107  4550  .81  16.5 •  Mean Ea = 3071 psi * **  2" Core  S  13-7 . 279  .15.0  60  Plunger  Mean E'f = 13. 79iiri^l'b^/sq.in. :  Ef = Energy, to failure (in.lb.) E ' f = Energy to failure ( i n . l b . / s q / i n . )  TiT  3/8" Plunger  Test M  No  1  0  € .308  2 3  .1.26  .4 5  6.9  6 7  19.0  8 9  31.2  10  11  45-5  12 •13  . 53.6  14  15  60  16 17  . 65.2  18  Mean  F  S  . 2" Core  e  Ea  Ef  E'f  26.4  239  .150  775  .487  . 1590  1.80  16.3  24.6-  223  .130  724  .422  1710  1.43  12.9  30.6  277  .120  220  • 0953  2300  2.10  19.0  28.2  255  .090  203  .0793  2840  1.2.5  11.3  28.8  . 260  .105,  • 37.7  .0152  2480  1.37 - 12.4  • 28.2  255  .110  37.0  .0159  2320  •1.47  13.3  21.6  192  1120  10.1  .00632  1600  1.20  10.9  31.8  288  .095  15.2  .00500  3030  1.58  14.3  25.8  234  .140  7.5  .00450  I67O  1.65  15.0  •28.8  260  .110  8.33  .00353  2360  1.50  13.6  26.4  239  .118  5.25  .00260  -2020  1.31  11.8  30.0  272  .090  5.98  .00198  3020  1.26  11.4  33.0  298  .130  5.55  .00242  2290  2.00  18.1  22.2  201  .065  3.75  .00121  3100  •0.75  6.8  31.8  288  .110  4.80  .00183  2620  1.95  17.7  28.2  255  .090  4.25  .00150  2840  1.35  12.2  34.2  310  .115  2.99  .00176  2690  1.95  17.7  21.6  195  .075  4.75  .00115  2600  0.75  .6.8  Ea = 2393 psi  Mean E'f. =113.42 in.lb./sq..in.  78  Test N  No  : | " Plunger  F  Ea  s/e  s  36  183  .100  145  .0795  • I83O  36  183  .i4o  145  .1110  1310  33  168  .160  •24.4  .0232  1050  4  33  168  .090  24.4  .0130  I870  5 . 19  38  191  .100  10.0  .00526  1910  6  35  175  .090  9.22  .00474  1950  38  191  .075  6.12  .00240  2550  40  202  .135  6.47  .00432  1500  39  199  .100  4.38  .00220  1990  4i  206  .095  4.53  .00209  2170  42  214  .080  3.99  .00149  2680  .41  206  .115  3.84  .00215  1790  4l  . 206  .100  3.44  .00167  . 2060  4l  206  .110  3.44  .00183  1870  42  214  .140  3.28  .00215  1530  33  168  .080  2.58  .00123  2100  1  1.26  .• 2" Core  2 3  7  6.9  31.2  8 9  45.5  10 11  53.6  12 13  60  14 15 •16  65.2  Mean Ea = 1885  psi  79  Test 0  •  Wo  P  Plunger  . 2" Core  £  S  l  Ea  Ef  E'f  .308  2380  .469  9-5  8.6  1  .308  ll.i  226  .095  735  2  .308  10.2  208  .070  676  .227  2970  .422  3  1.26  10.2  208  .100  165.  .0793  2080  .515  4  1.26  9.0  183  .065  145  .0515  2820  .304  6.2  5  6.9  -10.8  220  .055  32  .0080  4000  .328  6.7  ,6  6.9  9.6  195  .055  29.2  .0080  3550  .352  7.2  . .00263  .3660  .304  6.2  10.5  7  19  9.0  183  .050:  8  19  9.6  195  .050  10.5  .00263  3900  .328  6.7  ,9  • 31  6.7  137 ,• .o4o  4.4  .00128  3420  .188  3-8  10  31  10.5  214  - .050  6.85  .00160  4280  .304  6.2  •ll  45  10.8  220  .070  4.84  .00154  31^0  .352  7.2  12  45  8.7  . 177  .050  3.89  .00110  3540  .234  4.7  . 13  54  8.7  . 177  .055  3.30  .00105  3220  .234  4.7  l4  54  9.0  183  .055  3.42  .00105  3330  .258  5.2  • 15  60  8.3  169  .040  2.82  .00067  4230  .188  3.8  16  60  • 9.0  183  .. .050  ': 3.^05  .00083  3660  .211  4.3 '  '17  65  9,"©  183  .040  . 2.8l  .00061  4570  .188  3.8  18  65  208  .045  3.19  .00069  4630  .10  4.7  .  .  10.2  Mean Ea =?. 3521  psi - c :;  9.63  1  -Mean E ' f = 6.11  in.lb./sq_./in.  8o  Test P  No  1  .30c"  2 •1.26  3 4  6.9  5 6 7  . 19  8 31.2  9 . 10 11  |  45.5  • 12 13  53.6  14 15  60.0  16 !7 18  65.2  3/8" Plunger  2" Core  4  e  £  F  S  19.2  174  .095  565  .308  19.8  179  .090  581  18.6  168  .090  21.0  190  .080  19.2  174  .080  20.2  183  .070  I9...8  179 .  .090  18,6  •168  I9.8-  Ea  Ef  E'f  1830  • 99  9.0  .292  1990  .90  8.1  133  .0715  1870  .83  7-5  151  .0635  2380  ' .84  7.6  25.2  .0116  2180  '.78  7.1  26.6  .0103  2620  .74  6.6  9.42  .00475  1990  .96  8.7  .070  8.95  .OO369  2400  .63  5.7  179  .110  5.74  .00352  1630  .96'  8.7  •19.2  174  .060  • 5.58  .00192  2900  .60  5-^  16.2  147  .080  3.23  .OO176  18 40  .59  5-3  19.8  179  .065  3.95  .00143  2760  .57  5.2  18.0  163  .070  3.04  .00131  2330  .60  5.4  19.2  174  .090  3.24  .00168  1930  .86  7.7  17.4  157  .055  2.62  .00092  2860  .44  3.9  19.8  179  .065  2.98  .00108  2760  .60  5.4  17.4  157  .080  . 2.4l  .00122  I960  .71  6.4  19.2  174  .055  2.67  .00085  3160  •.60  5.4  Mean Ea = 2300 p s i  Mean E'f =6i62in.lb , / s q . i n .  81  Test Q  Wo  e  2 •3  1.26  •4 5  6.9  6 7  19  •8  9  31.2  10 n  45.5  ' 12 13  53.6  l4 15  60  16 ' 17  65 .2  : 18 I  2"  Core  4  Ea  .4700  1210  e  s  F  .308  •1  I " Plunger  34.5  176  34.5  176 \ .140 J570  30.0  153  .110 122  27.0  138  .100 h.09  30.0  153  .085  31.5  160  36.0  .145  '570  Ef  E'f  2.48 12.6  . 1250  2.44  12.4  .0874  1390  I.65  8.4  .0794  1370  1.73  8.8  22.2  .0123  1800  1.13  5.75  .090  23.2  .0130  1780  1.43  7.3 .  183  .080  C9.6  .0042  2290  1.46  7-4  31.0  158  .085  8.3  .00447  i860  1.46  7.4  33-0  168  .060  5.4  .00192  2800  I.09  5-5  •31.5  160  .090  5.1  .00288  1780  1.13  30.0  153  .075  3.36  .00165  2040  I.05  5.3  27.O  138  .075  3.02  .00165  1830  0.94  4.8  36.0  183  .085  3.4l  .00159  2150  I.58  8.0  34.5  176  .095  3.27  .00177  1850  I.65  8.4  31.5  160  .090  - 2.66  .00150  1780  1.31  6.7  34.5  176  .120  2.92  .00200  1460  I.58  8.0  28.5  145  .070  2.22  .00107 , 2080  I.09  5.5  27.0  138  .075  2.11,  .00115  1830  O.94  4.8  Mean Ea  =>  1808  psi  .455  Mean. E ' f ' =  7*38  :  5.8  in.Tb./sq..in.  82  Test R  No  .308  •1 2 •3  1.26  4 5  6.9  6 7  . 19  8 9  31.2  10 11  45.5  12 13  53.6  Ik  •15  60  16 , 17 . 65.2 18  Mean  1" P l u n g e r  • 1"  Core  Ea  Ef  E'f  .844  550  14.1  18.0  484  .910  532  15.2  19.4  .260  103  .206  500  12.7 . 16.2  131  .235  104  .186  568  12.6  16.0  112  143  .230  20.6  .0334  620  12.7  16.2  •98  124  .240 '  18.0  .0348  517  10.5  13.4  93  118  .210  6.2  .0110  562  9.9  12.6  77  97.^ .160  5.1  .0084  608  6.4  8.15  69  89  .150  2.85  .0048  594  5.4;  8.88  90  115  .225  3.68  .0072  512  10.5. 13.4  98  124  .210  2.73  .00462  590  •10.7 . 13.6  99  126  .230  2.77  .OO505  548  12.0  15.3  105  134  .225  . 2.49  .00420  594  12.0  15.3  100  127  .250  2.37  .00466  508  11.3  14.4  83  105  • 175  1.75  .00291  600  10.5  13.4  96  122  .220  2.03  .00366  555  8.4  10.7  108  137  .220  2.10  .00337  623  11.6  14.8  99  ±26  .240  1*93  .00368  525  12.8  16.3 •  F  S  113  143  .260  465  117  . lk9  .280  102  130  103  Ea = 561 p s i  Mean  E'f ^14.23  in.lb./sq..in.  To f o l l o w page 82  Plate 3  Sample X-Y S t r e s s - s t r a i n R e c o r d  To f o l l o w page 82  Deformation (.050  in./major d i v i s i o n )  2" Core Loaded a t 65.2  in./min. w i t h £ i n . Plunger  Deformation (.050  in/major d i v i s i o n )  2" Core Loaded a t 31.2 Plate k  i n . / m i n . w i t h 3/8"  Sample S t r e s s - s t r a i n Photographs  Plunger  To f o l l o w page  Deformation^ (.050  in./major d i v i s i o n )  2" Core Loaded a t 19.0  i n . / m i n . w i t h |" P l u n g e r  ! <  1  1 I B R  ••  111 1  J  ?!  "  1  •• •  J ,,,, i r  J  : Deformation (.050 in./major d i v i s i o n )  1" Core Sample Loaded a t 45.5 Plate 5  i n . / m i n . w i t h 1" P l u n g e r  Sample S t r e s s - s t r a i n Photographs  82  APPENDIX B  87  STATIC TEST  1.5A!  Loaded Time Rep.  1 Min  15  1  30  Hr.  2  3  .0145 .017 .018  4 .018  5  6  9  12  .0185 .0185 .019 .020  1  .011 ..0125  2  .010 .013 .0145 .0155 .0175 .019 .019 •.019 .0195 .0195 .01-95  3  .0085 .011  4  .006 .0105 .0120 .0155 .0165 .018  .018  5  .004 .0075 .008 .OO95 .011 .011  .0115 .0115 .012 .0125 .013  Mean  .014  .012- • 0135 .0165 .017 .018  .0185 .0185 .019 .0195 .0185 .0185 .019 .019  .0079 .0109 .0121 .0137 .0157 .0166 ,0169 .0172 .0174 .0179 .0182  Unloaded Time Rep.  .1 Min  15  13  30  Hr  14  15  18  21  24  1  • 0135 .0135 .0125 .012 .012 .0115 .0105 .0095 .009  2  .0095 • 0075 .006 .006 .006 .006 .006 .006 .0055  3  .0125 .012 .011 .0105 .010 .009 .008 .0075 .007  4  . .011 .0095 .009 .OO85 .008 .0075 .007 .006 .0055 .0075 .0065 .006 .006 .0055 .005  5  .0045 .004 .0035  .0108 .OO98 .0089 .0086 .0083 .0078 .0072 .0066 .0061 The number g i v e s t h e n u m e r i c a l v a l u e o f t h e l o a d The s u b s c r i p t r e f e r s t o t h e l o a d i n g a r e a  A_ = .0491 s q . i n . ]  A  2  = .0982 s q . i n .  applied  88  STATIC TEST 3.0A-L  Loaded Time Rep  .1  1  15  30  .0205 .024  .027  Min  1 .Hr.  •2  3  .0295 .0335 .035  4  .036 . .0375 .038  .0445  .0295 .030  .0305 .031  .032  3  .014  4  .0145 .0255 .0275 .0305 .0325 .0345 .035  5  .020  Mean  .030  .0325 .035  .0193 .0258 .028  .037  .038  .0306 .0336 .035  .0385 .039  .0415 .043  .0275 .0315 .0335 .0355 .0385 .0395 .041 .0195 .0225 .0265 .028  • 12  9  .041  2  .018  6  5  .0355 .036  .0385 .039 .036  .037  .038  • 0395 .0415. .0435  .0366 .0371 .0382 .0394  Unloaded Time Rep.  1 Min.  15  30  13  14  15  IS  Hr.  :2i  :24  .1  .027  .0265  .026  .0255  .0245  .024  .0235  .023  .022  2  .0245  .024  .023  .022  .021  .0205  .020  .019  .018  3  .0195  .018  .0175  .0175  .017  .016  .015  .0135  .0125  4  .0225  .0205  .020  .0195  .0190  .0185  .0175  .0165  .015  5  .0240  .0215  .0205  .0195  .019  .0185  .0175  .0165  .0155  Mean  .0235  .0221  .0214  .0208  .0201  .0195  .0175  .0177  .0166  89  STATIC TEST 4.5A-  Loaded  .1  Time Rep.  .. 1 Min  !5  1  .029  .033  2  .0395 .045  .049  .0515 .056  .038  .041  .045  4  .0155 .033  .036  .0385 .0415 .0435 .044  5  .0115 .0275 .0305 .0315 .037  :3  Mean  .032  30  2;  Hr.  .0375 .041  3  .0465 .049  .052  4. .051  5 .052  .0575 .0595 .060 .055  .037  6  .060  12 .  9  .0525 .055  .058  .0605 .061 .061  .0635  .0445 .045 .047 \ .039 .0395 .042  .0485  .0575 .0585 .059  .038  n  .045  .0232 .0353 .0388 .0415 .0466 .0484 .0500 .0508 .0512 .0531 .0552  Unloaded  1  13  14  15  18  21  24  .035  .035  .0345  .0345  .034  .0335  .033  .034  .0315  .031  .0395  .029  .028  .0265  .025  .034  .034  .034  .0315  .0305  .0295  .0275  .026  .025  4  .0235  .0205  .0195  .019  .0185  .0175  .017  .016  .0155  5  .024  .0225  .0215  .215  .0195  .0195  .0185  .0175  .017  .0312  .0294  .0283  .0276  .0265  .026  .025  .0239  .0231  Time Rep.  Min.  15  30  1  .0375  .036  2  .037  ••3  Mean  Hr.  90  STATIC TEST 6.0A  1  Loaded Time Rep.  1 Min.  15  1  30  2  Hr. I  3  1  .0355 .0435 .0485 .053  2  .0525 .0605 .066  .3  .0435 .0505 .0545 .059  4  .040  .047  5  .047  .0530 • 0575 .0620 .0665 .068  Mean  4  •5  6  •12  9  —  .0645 .067  .068  .0725 .0765  .0695 .0755 .0785 .0805 -.082  .084  .089  .0595 .063  .066  .094  .0695 .0725 .0745 .0755 .0785 .0815  .0505 .0545 .0585 .0605 .061 .070  .062  .0625 .064  .0715 .073  • 0655  .0785 .084  .0437 .0509 .0554 .0596 .0652 .0679 .0697 .0714 .0726 .0765 .0803  Unloaded Time Rep.  1 Min.  15  30  13  Hr.  14  15  18  21  24  1  .047  .046  ,046  .045  .045  .0445  .043  .042  .0405  • 2  .0605  • 0575 .056  .054  .051  .0500  .0475  .0465  .045  .3  .0495  .0435 .0355  ..034  .033  .032  .0305  .030  .029  4  .0305  .0265 .0255  .0245  .0235  .0235  .022  .021  .020  •5  ..0525  .0465 .045  .043  .042  .041  .038  .036  .034  .0401  .0389  .0382  .0362  .0351  .0337  Mean  .0525  .044  ;  .04i6  91  STATIC TEST 7«5  A  x  Loaded Time Rep.  1  .1  30  15  Min  Hr.  .4  .086  .089  .090  <P915 .092  .0930 .0945  .0805 .081  .084  5  .056  • 2:  .0535 .0635 .0675 .0715 .077  .0785 .079  3  .0535 .064  .0865 .0885 .090  4  .045  .052  5  .052  .0605 .067  Mean  .052  .0615 .0663 .072  .0685 .006  .O83  .0605 .0645 .0665 .067  .056  • 073  12  .3  .1  .0675 .0725 .079  6  •2  .078  .079  .090  .0865  .0925 .0945  .0680 .0685 .0705 .0725  .0805 .082  .0777 .0799 .081  9  .0830 .0865 .0900  .0824 .0829 .0853 .0876  Unloaded Time Rep.  1  13  18  21  24  .047  .045  .0435  .042  .0385  .038  .036  .036  .036  .047  .046  .0445  .o4i  .039  .039  .027  .027  .0265  .026  .025  .0245  .024  .0475  .046  .045  .044  .043  .o4o  .039  .038  .0437  .0425 • .0412  .0406  .0397  .0374  .0364  .0358  Min  •15  30  1  .0555  .0495  2  .049  3  Hr.  14  15  .049  .0485  .048  .044  .042  .0385  .051  .049  .0485  '4  .0315  .0285  . -5  .0505 .0475  Mean  92  STATIC TEST 1.5A  g  Loaded Time Rep.  1 Min.  1  30  15  2 "  .0175 .0185 .020  .1+  5  6  .0215 .0215 .022  .023  .023  .0235 .021+  .0185 .019 • .020  .020  .020  .0205 .021  Hr.  3  12  9  1  .015  2  .0115 .0145 .016  3  .0105 .0125 .0135 .011+5 .016  • 0175 .0185 .0185 .019  .020  .021  k  .0025 .0075 .0075 .009  .011  .011  .0115  5  .008  Mean  .017  .0095 .0105 .012  .011  .011  .011  .0125 .0125 .013  .013  .0135 .oik  .010  .015  .0095 .0123 .0132 .011+5 .0157 .0163 .0169 .0171 .0173 .0178 .0185  Unloaded Time Rep.  1 Min  1  5  30  13 Hr.  Ik  15  18  21  21+  1  .0135  .0135  .0135  .0135  .013  .013  .0125  .012  .012  2  .011+  .012  .011  .0105  .OO95  .009  .0085  .0075  .007  3  .0115  .010  .0095  .009  .0095  .0085  .008  .0075  .007  1+  .0055  .0055  .005  .005  .001+5  .001+  .0035  .003  .003  5  .008  .0075  .007  .0065  .0065  .005  .0055  .005  .001+5  Mean  .0105  .0097  .0092  .0089  .0086  .0081  .0076  .007  .OO67  93  STATIC/.TEST •• .3 .OA  Loaded Test Rep.  1  15  Min  30  ' 1 .022  2  Hr.  1  .016  *0195 .020  2  .023  .0285 .0305 .0315 .035  3  .0215 .025  4  .004  .0155 .016  5  .012  .0135 .0145 .016  Mean  .023  5  •3 .024  .0245  .0355 .037  6  .0255 .026 .038  . 12  9 .026  .0385 .040  .0265 ' .041  .0355 .0365  .0365 .0285 .0305 .0325 .0335 .0345 .035 .0185 .0195 .0205 .0205 .021  .0215 .022  .024  .0175 .0175 .0175 .018  .0185 .019  .0205  .0153 .0204 .0215 .0233 .0251 .026  .0267 .0204 .0279 .0285 .0297  Unloaded Test Rep.  1  13  24  Hr.  14  15  18  .016  .015  .015  .015  .014  .0135  .0135  .026  .025  .0245  .0235  .0225  .0215  .021 '  .020  .021  .020  .020  .019  .0185  .0185  .0185  .018  .016  4  .010  .008  .0075  .0065  .0055  .006  .005  .0045  .0045  5  .0095  .0085  .0085  .008  .008  .0075  .007  .007  .0065  Mean  .0172  .0158  .0154  .0146  .0141  .0139  .0132  .0128  .0121  Min.  15  30  1  .0165  .0165  2  .029  3  21 •  9h  STATIC TEST 4.5A  2  Loaded Time Rep.  ' 1  .1  30  .l Hr.  •2  .039  .0445 .047  .049  .052  2  .024  .031  .0345 .0375 .039  .0405 .0405 .044  3  .019  .0235 .025  .028  .0305 .032  .0335 .035  :4  .014  .031  .033  .035  .0375 .5395 .o4o  .0375 .040  .043  .0455 .048  .0267 .034  .0362 .0384 .0411 .0426 .0438 .0446 .0458 .0483 .0506  5 Mean  Min.  15  .033  .3  4  .0535 .055  .049  .050  5 .056  6  12  9  .0565 .0585 .060 ,048  .053  .0355 .037  .038  .0405 .041  .043  .044  .052  .055  .058  .051  Unloaded Time Rep.  1 Min.  15  30  13  • Hr.  14  15  18  21  24  .1  .030  .0275  .0275  .026  .025  .0245  .023  .0215  .0205  2  .0325  .0305  .0295  .027  .024  .024  .023  .0225  .022  •3  .0195  .0175  ,.0165 ..0155  .0145  .014  .0135  .013  .0115  4  .0175  .016  .0155  .014  .013  .0125  .012  .0115  5  .037  .032  .0305 -0295  .0285  .028  .0265  .0255  .0245  .0273  .0247  .0239  .0226  .0212  .0207  .0197  .0189  .018  Mean  .015  95  STATIC TEST  6.OA,  Loaded Time Rep  1"  1  30  Min  15  1  .056  .O63  2  .0325 .038  .040  .042  3  .0445 .051  .054  4  .036  .0415 .044  5  .033  .036  Mean .  Hr.  2  3  .4  5  6  12  9  .0735, .074  .0755 .0755 .078  .0805  .046  .048  .049  .050  .0515 .055  .059  .0565 .061  .064  .0665 .068  .0685 .071  .074  .0655 .0685 .071  .053 . .054  .056  .058  .0385 .0415 .0435 .0445 .0455 .0465 .047  .050  .052  .047  .050  .0515 .052  .0338 .0459 .0434 .0511 .0543 .0563 .0574 .0586 .0593 .0620 .0647  Unloaded Time Rep,  1  13  21  24  .0375  .036  .O36  .029  .0285  .0275  .0275  .0345  ,033  .031  .029  ,0275  .0225  .0215  .0215  .020  .019  ,0185  .0255  .025  ,024  .0235  .023  .022  .021  .0320  .0311  .0299  .0292  .0280  ,0267  ,0261  Min,  15  30  1  .0476  .0435  2  .036  3  Hr.  14  15  .042  .0405  .040  .039  .0325  .0315  .0315  .0295  .045  .039  .0375  .036  4  .028  .025  .0235  5  .0295  .0265  Mean  .0372  .0333  18  96  7-5^  STATIC TEST  Loaded Time:. Rep.  1  1 Min.  30  •15  l Hr.  ,2  3  4  5  .056  .0605. .063  .067  .070  .0715 .0725 .073  .0735 .075  .0765  .037  .0415 .044  .046  .050  .051  .054  .0565  .052  .053  3  .0355 .0425 .0465 .0505 .0545 .0575 .0605 .061  4  .0275 .0315 .034  5  .042  Mean  12  9  0  .0445  .047  .0365 .0395 .0405 .o4i .050  .053  .054  .055  .055  .0615 .063  .065  .0415 .042  .0435 .045  .056  .0595 .0615  .057  .0398 .0441 .0469 .0500 .0532 .0549 .0562 .0569 .0576 .0592 .0609  Unloaded Time!; Rep.  1 Min.  15  30  -13  Hr.  14  15  18  21  24  1  .0425  .037  .0365  .0345  .033  .032  .031  .031  .031  2  .029  .0275  .0265  .026  .025  .025  .0245  .024  .023  :3  .037.  .034  .0325  .031  .0305  .030  .0275  .026  .025  .4 ' •  .0195  .0165  .016  .0155  .014  .015  .0135  .013  .0125  5  .0285  .0245  .0245  .0235  .023  .022  .021  .020  .0195  < Mean  .0313  .0279  .0272  .0261  .0251  .0248  .0235  .0228  .0222  Graph IV  S t a t i c Test  Time (hours)  100  r-  Graph V  Static Test Loading Area A = 0.0.982 sq.in. 2  Symbol  Applied Load  H3  o  • 12 13 Ik 15  2k  o o  <  Time (hours) vo CA  APPENDIX C  STRESS RELAXATION DATA  1  Test. No. . 2  3  .4  .7-9  10-12  Curve No.  Time Sec.  4-6  0 20 l b 19.6 0.5 .1 19.4 2 19.0 4 18.6 10 18.2 30 17.7 60 17.6 90 17.4 120 17.3 150 17.2 180 17.1 210 17.1 240 17.05 270 17.0 300 17.0 330 16.95 360 16.95 390 16.9 420 ' 16.9 450 16.85 480 "' "16.85 510 16.8 540 .. 16.8 . 16.8 570 600 16.8 ;!  1-3  30 l b 35 l b - 29.4 33.8 29.0 33.3 28.3 32.5 31.8 • 27.7 .27.0 31.0 . 26.2 30.1 25.8 29.8 25.6 29.5 25.5 29.35 .25.4 29.3 25.2 29.1 29.O , 25-1 25.0 28.9 25.0 28.85 24.95 28.8 • 24.9 28.7 24.8 28.7 ,- 24.8 • 28.6 • 24.8 28.6 28.6 • 24.75 . 28.5 24.7 24.6 28.5 24.6 28.4 28.4 24.55 28.3 .24.5  • 5 13-15  34 l b 60 l b 44.0 58.5 43.1 57.6 42.4 56.4 41.5 55-0 40.3 53.6 39-1 51.7 38.6 51.0 • 38.2 50.4 . 38.0 50.1 37.9 49.9 37.7 . 49.8 37.6 49.5 : 3.7.5 . 49.4 37.4 49.2 37.3 49.1 37.2 49.0 . 37.1 48.9 37-1 48.8 37.0 " 48.7 37-0 48.6 37-0 48.5 48.5 36.9 48.4 36.9 36.8 48.2 36.8 48.2  To f o l l o w page 9 8  Stress  Relaxation  1*4  r Stress Relaxation Test 1.  Calculation Graph Load 20 l b s .  1.2  .4 fc-  .21-3 O  HD  .1  O H O TJ  P OP fD  M3 00  To f o l l o w page 9 8  Stress  Relaxation C a l c u l a t i o n Graph  0.01 10  15  Time  (sec.)  25  Test #1 t (sec)  0 10 30 6o 120 300 6oo  CHECK FOR VALIDITY FOR USE OF-MEAN T VALUES A = 1.01 .A =  A . » 17.1  2  r  -VT; 0 0 .00132 .00264 .00528 .0132 .0264  e  /rr  '  1 1 .999 • 997 • 995 .987 .974  A]_e .  17.1 17.1 17.08 • 17.05 . 17.01 16.88 16.66 .  A-L = 25-3  Test #2  q  -V-r  e  2  0 .1185 •3555 .7110 . 1.4220 3.555 7.110  •  J  1  1.01 .897 ' .708 .496  1 .888 .701 .491 .241 .038"; .001  0 1.742 .5.226 • 10+  '.243  .038 '.001  1 .1.75 .006 0 Y  A = 1.32  £ y  A3'e  1.9 • 333 .011 .0 Y  A  2  1.9  3  k  n=/ 20.01 18.33 ' 17.799 n  17-546  I7.255 16.918 •16.66  Actual - (lbs)  Dlft.  (lbs)  20 + .01 •18.2 + .13 17.7 + .299 17.6 • *.054 17.3 ' -.047 -.082 17.0 -.14 16.8  = 3-2  .(  0 10 30 60 120 300 - 600  0.0000 0.0000 0.0013 0.0026 0.0053 .0.0132 0.0264  0 1 25.3 • . 1, . 25.3 ; .1185 25.275 ' .3555 .999, 25.224 ..7110 .997 • 1.4220 • 25.174 .995 24.971 3.555 .987. 24.642 .974 7.110  1 .888 .701 .491 .241  .038 .001  1.32 1.172 .925 .648  .318 .050 • .001 •  0 . 1.742 " 5.226 10+ >  1 .175 .006 0  3.2 .560 .019 0 5  f  . 29.82 27.032 • 26.219 25.872 ' 25.492 25.021 24.642  30 . 27 26.2" 25.8 25.5 24.95 24.5  -0.18  +.032 +.019 +.72 -.008  +.071 + .142  .  Test  29 •  #3  A  s e c  =  -i -L .  t (  2  A  )  -t/r,  T [  -.-t/13  e  i e  1±0  00  C.C  — 4.5 Actual D i f f . (lbs.) (lbs.)  A  A e 3  0 10 30 6o 120 300 6oo  0. 0. 0.0013 0.0026 .0.0053 0.0132 0.0264  Test #4 0 10 30 60 120 300 600  1 1 .999 • 997 • 995 • 987 .974  A  0 0 .0013 .0026 .0053 .0132 .0264  l  0 29.2 29.2 .1185 .3555 - 29.171 29.112 • 7110 .29.054 1.4220 28.820 3.555 28.441 . 7.110  = 37.6  1 1 .999 .997 .995 .987 .974  37.6 37.6 37.562 37.487 37.412 37-111 36.622  A 0 .1185 • 3555 .7110 1.4220 3.5550 7.1100  1.22 .1.083 .855 .599 .294 .046 .001  1 .888 .701 .491 .241 .038 .001  2  1 .888 .701 .491 .241 .038 .001  =  0 1. 742 5. 226 1 0+ 1  (  1 .1"'5 .oc)6 c)  f  2.61 2.61 2.318 1.830 1.282 .629 .099 .003  k  'l r88 » .()27 () r  •>  !  A3 = 0 1-742 5-226 10+ (  1 • 175 .006 :0  f  4.5 .788 .027 0  34.92 31.071 30.032 29.711 29.348 28.866 - 28.442  35 31.0 30.1 29.8 29.35 28.8 28.3  -.08 + .071 -.068 -.089 -.002 + .066 + .142  45 40.3 • 39.1 38.6 •38.0 37-3 36.8  -.29 + .406 +.319 +.169 +.041 -.09 -.175  4.5 44.71 40.706 39.419 38.769 38.041 37.210 36.625  T e s t #5  A  t (sec )  0 10 30 60 120 300 600  =  x  e  '" , 0 0 .=.0013 .0026 .0053 .0132 .0264  1 1 .999• 997 .995 .987 .97^  50  A  A l  2  e  50 50 ' 49.950 •49.850 49.75 • 49.35 48.70  =  2.11  '  A e  *•  2  0 .1185 .3555 .7110 1.4220 3.5550 7.1100  •1 .888 .701 .491 .241  .038 .001  2.11 1.874 1.479 I.O36 .509 .080 .002  A3  =  A .^ 3  ©  .1.742 5.226 10+ ;  >  1 .175 .006 0 1  7.9 1.383 .047 ,0  7  7-9  £A e n  _ t /  f*  60.01 53.257 51.476 50.886 50.259 49.43 .48.7  Actual D i f f . (lbs.). (lbs.)  60 53.6 •51.7 . 51.0 50.1 :-49.1 48.2  + .01 -.343 -.224  -.114 + .159 + .33 + .5  o  3  Hi O  S-  1  o *:  >rf  s>  era ro  co  To- follow page 98 35rPoints from Finney  (5)  30K  20 3 cu o rH  O  fa  10  '1  100  •  I 200  I  3OO Time (sec.)  :  L 400  I  500  1  600  1  APPENDIX D  HYSTERESIS TRIAL  - DATA FOR TRIALS ON WHOLE POTATO • TUBERS LOADED BETWEEN PARALLEL FLAT PLATES  102 HYSTERESIS DATA Area Loop Area Loop Area Loop $ i 4 Test Under Loss Under Loss Under Loss Loss Loss Loss No. Load Loop Area Loop Area Loop Area Loop Loop Loop  1  1  2  2  3  201b 1.56 0.76 1.08 .42 1.18 1 .94 -.32 1.08 2 l . i 0.60 .68 .''.20 . .85 0.41 3.  4 5 6  301b  Mean  7 8 9  501b  .017"  3.34 2.0 2.15 1.00 • 2.09 0.75 60.0 46.5- 35.9 3.45 1.85 . 2.40 .00 2.22 O.78 53.6 37.5- 35.0 3.75 1.28 2.68 1.04 2.35 0.85 34.2 38.8 36.2  .037" .025" .035"  4.44 2.2 4.38 2.59 . 4.61 2.73  2.22 0.79 49.3 40.9 35.7  .032"  3.08 1.08 - 2.87 .80 49.5. 35 27.9 3.13 1.30 3-34: 1.06 59.0 41.5 3 i . 8 3.25 1.25 3.0 1.00 59.3 38.5 33.3  .025" .035" .025"  55.-9- 38.3 31.0  .028"  2.4l 0.98  6.69 4.4 • 4.11 1.7 4.13 1.47 65.8 41.3 35.6 7.98 4.67 5.©8 1.85 . 4.72 1.41 58.5 36.5 30.0 6.2 . 4.0 4.28 1..80 3.80 1.40 64.5 42.0 36.9  .045 .040 .040  62.9 39-9 34.2  .042  Mean  6.9 3.54 .13 601b •9*87 6.2 .14 10..-3 6.68 5.90 2.30 15 12.38 7.5 -9.1 4.4 Mean  .16 17 18  701b 12.96 8.13 12.64 8.40 12.90 8.20  3.60 7.08 2.95 7.83 2.90  8,48  Mean  6.05 2.43 62.8 51.3 40.0 5.90 1.93 65.O 39.0 32.7 7-75 3.14 60.5 48.5. 40.5  .050"  62.8 46.3 37.7  .045"  7.53 2.53 62.5 42,5 33.6 6.73 2.50 66.5 42.5 37,2 7.32 2.53 63.5 37-0 34.6  .045" .070" .050"  64.2 40.7 35.1  Mean  19 801b 20 21  .3  1.13. 0,36 51.6. 34.1 31.7  0.90 0.31  Mean  10 11 12  2  .025" .015" .010"  3.51 1.71 kOlb  1  .39 52 38.9 33.0 .33 54.5- 34 30.5 48.3 29.4  • 1.14 •0,59  Mean  3  Set  8.55 6.0 •4.4 1.84 9.34 6.91 • 4.3 1.70 8.66 6.02 4.37 1.79  .045"  .040"  .055  4.38 1.45 .70.2 42.0 33.1 4.10 1.55 74.0 39.-6 37.8 4.10 1.45 69.5 40.7 35.4  .080" .090" .100"  71.2 40.8 35.4  .090"  ,  103  HYSTERESIS DATA ( C o n t d ) 1  . A r e a Loop, A r e a Loop A r e a Loop H ••i Test Under L o s s L o s s Under L o s s L o s s Under L o s s Load Loss •NO. • Loop. •Area Loop A r e a Loop A r e a Loop Loop Loop 2 ,1 3 .3 2 3 22 23  901b  24  9.40 6 . 6 9 • 10.0 7.0 9.56 6.55  4.52 1.80 5.20 2.30 5.07 2.38  .100"  5 . 2 4 2 . 0 8 7 1 . 4 48.8 3 9 . 8 5 . 3 7 1 . 9 0 70.0 4 l . 5 3 5 . 4 5 . 3 0 1 . 9 2 7 0 . 5 40.7 3 6 . 2  .115" .110" ,100"  7 0 . 6 4 3 . 7 37.1  ;.108"  6.90 2.90 6 . 2 4 2 . 1 2 7 0 . 7 42.0 3 4 Sample Cra( ked 0 1L Looj 1 6.40 2 . 1 5 35.8 33.6 6.80 2.43 70.2  .115"  6.15 3.00 25 LOOlb 1 1 . 9 c 8 . 5 0 ; 1 1 . 4 5 8 . 8 0 , 5 . 8 0 2.40 26. 5.32 2.17 27 ".10.77 7 . 6 0  Mean 12.8  9.05  14.23 1 0 . 0  • 4.291.49 71.2 39-8 34.8 .095" .095" 4.46. 1 . 5 4 7 0 . 0 4 4 . 3 3 ^ - 5 4 . 6 7 1 . 8 8 6 8 . 5 46.8 40.2 • . 1 1 0 " 69.9 43.6 36.5  Mean  • 28 LOllb 29 30  Mean 70.5 . 31-. L201b 32  • Mean  15.1 11.24 13.5 9.33  Set  6 . 5 0 2.84 6.70 2.53  38.9 33.8  6 . 3 5 2.40 .74.5 4 3 . 7 3 7 . 8 6 . 2 5 2 . 1 3 69.O 3 7 . 8 3 4 . 1 71.8 40.8 36.0  .110" .113"  .155 .100 ' .127  To f o l l o w page 103  Hysteresis T r i a l Whole Tijiber Sample  I-  1  CD  CD CO >d H  ro a CO c+ CD  ro cn cn W CD O O  >-i ft  h3  o 3Jj>0-  ISO  D e f o r m a t i o n (.661")!  O  3' •d OQ CD  O  CO  

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