UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Fracture toughness design in equine hoof wall Bertram, John E. 1984

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1984_A6_7 B47_7.pdf [ 5.09MB ]
Metadata
JSON: 831-1.0096032.json
JSON-LD: 831-1.0096032-ld.json
RDF/XML (Pretty): 831-1.0096032-rdf.xml
RDF/JSON: 831-1.0096032-rdf.json
Turtle: 831-1.0096032-turtle.txt
N-Triples: 831-1.0096032-rdf-ntriples.txt
Original Record: 831-1.0096032-source.json
Full Text
831-1.0096032-fulltext.txt
Citation
831-1.0096032.ris

Full Text

FRACTURE TOUGHNESS DESIGN IN EQUINE HOOF WALL BY JOHN E. BERTRAM B.Sc, The University o-f B r i t i s h Columbia, 1981 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES (Department of Zoology) We accept t h i s t h e s i s as con-forming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA June, 1984 (2) John E. Bertram 86 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r a n a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may b e g r a n t e d b y t h e h e a d o f my d e p a r t m e n t o r b y h i s o r h e r r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t b e a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f o o u o & V  T h e U n i v e r s i t y o f B r i t i s h C o l u m b i a 1956 Main M a l l V a n c o u v e r , C a n a d a V6T 1Y3 D a t e D E - 6 (3/81) ABSTRACT T h i s study a p p l i e d an e n g i n e e r i n g -fracture nfechanics approach t o the i n v e s t i g a t i o n of the f r a c t u r e r e s i s t a n c e of Equine hoof w a l l . The f r a c t u r e mechanics parameters of s t r e s s i n t e n s i t y f a c t o r (K), s t r a i n energy r e l e a s e r a t e (G) and the J - i n t e g r a l (J) were used t o determine the e f f e c t of notch o r i e n t a t i o n and specimen h y d r a t i o n on f r a c t u r e , u s i n g the compact t e n s i o n t e s t geometry. The J - i n t e g r a l was found t o pr o v i d e the best i n d i c a t i o n of f r a c t u r e behaviour because i t i s not based on s t r i c t l i n e a r e l a s t i c behaviour, as are K and G. Hoof wall has g r e a t e s t f r a c t u r e r e s i s t a n c e f o r c r a c k s running v e r t i c a l l y , p a r a l l e l t o the t u b u l a r s t r u c t u r e s found i n hoof wall k e r a t i n . For f u l l y hydrated m a t e r i a l t e s t e d i n t h i s 5 d i r e c t i o n , the mean c r i t i c a l J va l u e at f a i l u r e was 1.19 x 10 2 J/m . T h i s was n e a r l y t h r e e times l a r g e r than the va l u e determined f o r the weakest o r i e n t a t i o n , i n which the crack ran p a r a l l e l t o the m a t e r i a l between the t u b u l e s . Hydration l e v e l was a l s o found t o pr o f o u n d l y a f f e c t the f r a c t u r e toughness. An inte r m e d i a t e h y d r a t i o n l e v e l (75X RH) gave t h e h i g h e s t mean 5 2 c r i t i c a l J v a l u e s (2.28 x IO J/m ), which represented a two-fold i n c r e a s e over f u l 1 y - h y d r a t e d and dehydrated m a t e r i a l . These r e s u l t s have been r e l a t e d t o the morphology and f u n c t i o n of the hoof i n the l i v i n g animal. i i i . TABLE OF CONTENTS Abstract '. i i Table of Contents i i i List of Tables '.. v List of Figures vi Acknowledgements v i i i Chapter 1: Introduction 1 Chapter 2: Morphology of the Hoof Wall 10 Chapter 3: Fracture Mechanics Analysis 19 Chapter 4: Materials and Methods 26 I. Acquisition and Preparation of Samples 26 II. Testing Procedures.... 28 III. Analysis of Fracture Data 34 IV. Compliance Calibration 35 V. Tensile Modulus and Yield Strength 38 VI. Histology 39 Chapter 5: Results 41 I. Stress-strain Properties: Tensile Tests 41 A. Orientation Effects 44 B. Hydration Effects 46 II. Fracture Investigation 49 A. Fracture at 100% RH 49 1. Compliance Calibration 49 2. Determination of Fracture Parameters 53 a. Pigmentation, Individual and Location 55 b. Sample Orientation 57 B. Effect of Hydration State 65 1. Pigmentation, Individual and Location 69 2. Notch Parallel to Tubule Axis 71 t 3. Notch Normal to Tubule Axis 77 Chapter 6: Discussion 79 I. Behaviour of Fracture Parameters, K, G and J 79 A. The Stress Intensity Factor, K 79 B. Strain Energy Release Rate, G 82 C. The J Integral 85 D. The Application of Engineering Fracture Parameters to Biological Systems 89 II. Functional Design of Hoof Wall 91 A. Molecular Design of Keratin as a Composite Material 91 B. The Role of the Cellular Architecture 102 References 109 V . LIST OF TABLES Table 1. Tensile modulus of hoof wall keratin 45 Table 2. Fracture parameters as a function of location 56 Table 3. Fracture parameters as a function of orientation 61 Table 4. Results of analysis of variance and multiple comparisons 70 Table 5. Fracture parameters as a function of hydration 72 Table 6. The effect of orientation on dehydrated samples 78 Table 7. Tensile modulus of keratinized structures and the effect of hydration level 95 v i . LIST OF FIGURES T Fig. 1: The effect of crosslinking fibres 5 Fig. 2: Sagittal section of the foot of the horse 11 Fig. 3: Cross-section of hoof wall 12 Fig. 4: Scanning electron micrograph of tubular material 15 Fig. 5: Stress trajectories in a flawed object 21 Fig. 6: Stress levels in a flawed object 21 Fig. 7: The effect of stress concentrations at a crack tip 22 Fig. 8: The G i f f i t h criterion of fracture 22 Fig. 9: The location in the hoof of experimental tissue 27 Fig. 10: The Compact Tension test specimen geometry 31 Fig. 11: Specimen loading system 31 Fig. 12: Analysis of Compact Tension test record 36 Fig. 13: Typical stress-strain curves from tensile tests 42 Fig. 14: Representative stress-strain curves from four hydration levels 48 Fig. 15: Compact Tension test record 51 Fig. 16: Compliance calibration curve 52 Fig. 17: The method of calculating J from energy and crack length data 54 Fig. 18: The effect of location within the hoof on the fracture toughness 58 Fig. 19: Diagram of the orientation of Compact Tension specimens 60 Fig. 20: The effect of specimen orientation on the fracture toughness of hoof v a i l 62 v i i . Fig. 21: Photograph of two CT specimens from different orientations 66 Fig. 22: Polarized light micrograph of crack path 67 Fig. 23: Compliance*calibration curves from four hydrations....68. Fig. 24: The effect of hydration level on the fracture toughness of hoof wall 73 Fig. 25: Apparent crack growth at four hydration levels 76 Fig. 26: The stress intensity factor and apparent crack growth during a Compact Tension test 81 Fig. 27: Strain energy release rate and apparent crack growth during a Compact Tension test 83 Fig. 28: J integral in metallic materials 87 Fig. 29: J integral and apparent crack growth during a Compact tension test 88 Fig. 30: Inter-relationship of tissues within the hoof wall....99 v i i i ACKNOWLEDGMENTS There are a great many people who contributed to t h i s study. Too many, i n fact, to thank here. This thesis could not have been completed, however, without the help of three people. I wish to thank my research supervisor, Dr. J.M. Gosline, for his assistance and encouragement i n every phase of t h i s study. Dr. R.J. Gray of the Faculty of Applied Science gave f r e e l y of his time to guide t h i s investigation and the development of my understanding of his f i e l d . And Mr. Edwin DeMont who assisted with his expertise, common sense and friendship throughout the course of t h i s study. To these three I am e s p e c i a l l y indebted. 1 INTRODUCTION The s k e l e t a l components o-f higher p l a n t s and * animals f u n c t i o n through s o p h i s t i c a t e d design t a c t i c s which e x p l o i t the mechanical p r o p e r t i e s of t h e i r s t r u c t u r a l m a t e r i a l s ( J e r o n i m i d i s , 1 9 7 6 ) . The form a s t r u c t u r a l t i s s u e takes w i l l r e s u l t from an i n t e r a c t i o n of the requirements of f u n c t i o n and the a v a i l a b i l i t y of m a t e r i a l s with a p p r o p r i a t e p r o p e r t i e s . The i n v e s t i g a t i o n of the mechanical p r o p e r t i e s of s t r u c t u r a l b i o m a t e r i a l s and the morphological design on which those p r o p e r t i e s i s based can y i e l d important i n f o r m a t i o n about the type and exte n t of t h i s f o r m - f u n c t i o n r e l a t i o n s h i p i n b i o l o g i c a l systems. The a b i l i t y of an organism t o maintain a b i o l o g i c a l l y r e l e v a n t i n t e r n a l environment i s o n l y p o s s i b l e through i s o l a t i o n and p r o t e c t i o n from the e x t e r n a l environment. Rather s p e c i f i c f u n c t i o n s a re r e q u i r e d of the t i s s u e which a c t s as t h i s b a r r i e r . The i n t e r f a c e m a t e r i a l employed by v e r t e b r a t e s , i n one o r g a n i z a t i o n a l form or other, i s the f i b r o u s p r o t e i n composite k e r a t i n , produced s p e c i f i c a l l y by epidermal t i s s u e . The e p i d e r m i s of t e r r e s t r i a l v e r t e b r a t e s has s e v e r a l unique as p e c t s . U n l i k e other body t i s s u e s , e p i t h e l i a have no orga n i z e d e x t r a c e l l u l a r s t r u c t u r e s . T h e r e f o r e , the epidermis c o n t a i n s no blood v e s s e l s and has no d i r e c t blood supply. A l l s t r u c t u r e s formed by the epidermis are c e l l u l a r and g a i n t h e i r f u n c t i o n a l p r o p e r t i e s from t h e i r c e l l u l a r c o n t e n t s , membrane co n n e c t i o n s and the geometric o r g a n i z a t i o n of the c o n s t i t u e n t c e l l s . Epidermal c e l l s s y n t h e s i z e a d i v e r s e group of p r o t e i n s , c a l l e d k e r a t i n , t h a t a re l a i d down w i t h i n the c e l l . K e r a t i n i s a p r o t e i n composite c o n s i s t i n g of two phases, a f i b r e phase composed of long s l e n d e r Oi — h e l i c a l f i b r e s and an amorphous p r o t e i n matrix. Each f i b r e i s composed of n i n e m i c r o f i b r i l s arranged i n a r i n g with two more p o s s i b l y i n the c e n t r e ( F r a s e r et a l . , 1962). The i n d i v i d u a l m i c r o f i b r i l s a re l i k e l y arranged i n a c o i l e d - c o i l r o p e — l i k e s t r u c t u r e of Ot — h e l i c a l p r o t e i n molecules (Fra s e r and Macrae, 1980) with two or p o s s i b l y t h r e e O x - h e l i c e s per m i c r o f i b r i l (Crewther, 1976; McLachlan, 1978). The matrix of t h i s m a t e r i a l i s composed of amorphous p r o t e i n s which a r e c r o s s l i n k e d t o each other and t o the O c — h e l i c a l f i b r e s through d i s u l p h i d e bonding at c y s t e i n r e s i d u e s (Wainwright e t a l , 1976). The c e l l s r e s p o n s i b l e f o r k e r a t i n s y n t h e s i s , termed k e r a t i n o c y t e s , d i e i n the f i n a l s t a g e s of t h e i r d i f f e r e n t i a t i o n when i n t e r — and i n t r a — m o l e c u l a r d i s u l f i d e c r o s s — l i n k s a re e s t a b l i s h e d . The e x t e n s i v e molecular c r o s s — 1 i n k i n g produces a s t a b l e composite m a t e r i a l of long t h i n f i b r e s embedded i n an amorphous matrix. S i n c e the epidermis i s composed s o l e l y of dead c e l l u l a r t i s s u e , t h e r e i s no means of modifying i t s s t r u c t u r e a f t e r i t i s l a i d down. Rather, i t i s renewed through t h e c o n t i n u a l growth of the basal c e l l l a y e r s . In t h i s way n u t r i e n t s r e q u i r e d f o r c e l l growth and development are secured from the u n d e r l y i n g dermal t i s s u e , and o l d e r e x t e r n a l t i s s u e i s r e p l a c e d as i t becomes worn and damaged. Because t h i s type of d e p o s i t i o n p r e c l u d e s r e m o d e l l i n g or r e g e n e r a t i o n of epidermal t i s s u e s w h i l e they are i n use, a l l mechanical requirements must be a n t i c i p a t e d a t the time of t i s s u e d e p o s i t i o n . S p e c i a l i z e d cutaneous appendages adapted f o r s p e c i f i c mechanical f u n c t i o n s have been developed where the o r g a n i z a t i o n and c o n s t i t u e n t p r o t e i n s have been m o d i f i e d t o match t h e i r v e r y s p e c i f i c f u n c t i o n s (Fraser and Macrae, 1980). Examples of these s p e c i a l appendages i n v e r t e b r a t e s i n c l u d e s c a l e s , f e a t h e r s , h a i r , beaks, and claws. One p a r t i c u l a r l y i n t e r e s t i n g cutaneous appendage i s the Equine hoof. The s p e c i a l i z e d mode of locomotion i n the horse ( p e r i s s o d a c t y l , ungulagrade) and the l a r g e s i z e of t h i s animal put extreme mechanical demands on the epidermal s t r u c t u r e which c o v e r s and p r o t e c t s the d i s t a l end of the limb. We would then expect the morphological o r g a n i z a t i o n of the hoof wall t o re p r e s e n t a response t o the s p e c i a l mechanical demands of i t s f u n c t i o n . The horse hoof i s a very complex s t r u c t u r e t h a t l i k e l y r e q u i r e s many mechanical p r o p e r t i e s of i t s t i s s u e s . The hoof wall w i l l r e q u i r e a c e r t a i n degree of compressional s t i f f n e s s i n order t o support the f o o t and r e s i s t deformation. A l a c k of s t i f f n e s s w i l l r e s u l t i n the hoof deforming without s u p p o r t i n g the animal's weight. U l t i m a t e s t r e n g t h , the maximum f o r c e t h a t a m a t e r i a l can withstand b e f o r e breaking, w i l l a l s o be r e q u i r e d at a reas o n a b l e l e v e l i n order f o r the hoof t o bear the weight 4 of the animal without b r e a k i n g . Thus, the hoof m a t e r i a l must e x h i b i t a combination of reasonable s t i f f n e s s and s t r e n g t h . Compressional s t i f f n e s s ( r i g i d i t y ) i n f i b r o u s composite m a t e r i a l s (such as k e r a t i n ) r e s u l t s from the l i n k i n g of the f i b r o u s components together as a s i n g l e bonded u n i t . T h i s l i n k a g e s t o p s the i n d i v i d u a l components from s l i d i n g r e l a t i v e t o each other under the i n f l u e n c e of s t r e s s produced i n bending deformations (Wainwright e t a l , 1976). The long t h i n f i b r e s a r e a b l e t o r e s i s t compressional f o r c e s without b u c k l i n g , the normal response of long t h i n s t r u c t u r e s , because the matrix t i e s the i n d i v i d u a l f i b r e s t o gether i n t o a s i n g l e r i g i d u n i t ( F i g . 1). The s t a b i l i z a t i o n of the f i b r e s i n hoof k e r a t i n i s due t o e x t e n s i v e c r o s s — 1 i n k i n g of the f i b r e and matrix phases (Fra s e r and Macrae, 1980). In a d d i t i o n , r i g i d bonding at c e l l boundaries through s p e c i a l i z e d c e l l j u n c t i o n s s t a b i l i z e s the m a t e r i a l at the c e l l u l a r l e v e l (Leach, 1980). A composite m a t e r i a l of t h i s s o r t w i l l , thus, be both s t i f f and s t r o n g . However, the r i g i d i n t e r c o n n e c t i o n of components c r e a t e s a continuous medium which may a l l o w f l a w s t o pass e a s i l y through the m a t e r i a l from one phase of the composite t o another (Gordon, 1980). G l a s s , f o r example, i s both s t i f f and s t r o n g , but because f l a w s pass e a s i l y through i t , g l a s s i s a poor s t r u c t u r a l m a t e r i a l . F r a c t u r e i n a r i g i d m a t e r i a l o c c u r s as a r e s u l t of f l a w s or c r a c k s w i t h i n the m a t e r i a l t h a t c r e a t e s t r e s s c o n c e n t r a t i o n s (Gordon, 1976). Loads, which would normally be evenly d i s t r i b u t e d w i t h i n the 5 F i g . 1. S t i f f n e s s produced i n a f i b r e reinforced composite by cr o s s l i n k i n g the f i b r e s . In A the f i b r e s are able to move r e l a t i v e to each other allowinq bending and buckling to occur. In B the matrix links the fibres into a single functional unit which will not buckle. material are concentrated at crack t i p s , and can cause l o c a l i z e d -fracture. The binding of the f i b r e s and the s t i f f e n i n g of the matrix allow these stress concentrations to be passed from f i b r e to f i b r e causing catastrophic f a f l u r e , or fracture, of the material. Once adequate l e v e l s of s t i f f n e s s and strength are achieved i n hoof keratin, the most important mechanical consideration becomes the resistance to crack growth. In materials science t h i s resistance to fracture i s termed fracture toughness. It i s produced through the development of stress dispersing and energy absorbing mechanisms within the material. This study was designed to investigate the fracture of hoof wall and determine which aspects of the t i s s u e morphology influence fracture toughness. Previous studies of hoof wall mechanics have concentrated on s t i f f n e s s and strength aspects (Goodspeed et a l , 1970; Dinger et a l , 1973; Butler, 1976; Butler and Hintz, 1977; Leach, 1980). These studies have recognized several variables, i n addition to t i s s u e morphology, which may influence the mechanical properties. These include water content, sample location and pigmentation. In order to investigate the fracture behavior and determine the influence of these variables on the fracture toughness of t h i s material, an engineering approach to the analysis of fracture behaviour has been employed. The application of fracture mechanics i s r e l a t i v e l y new to b i o l o g i c a l research. However, two biomaterials, wood and bone, have received considerable attention. Wood i s used as an engineering material and, l i k e keratin, i s a c e l l u l a r composite. Because wood has such importance as an engineering material, -fracture studies have been many and varied * (Debaise et a l , 1966; Schniewind and Pozniak, 1971; Jeronimidis, 1976). Wood has a complex c e l l u l a r and molecular architecture that produces a variety o-f subtle but e f f e c t i v e crack r e s i s t i n g properties. Such things as the s p i r a l molecular orientation of some c e l l walls and the general c e l l morphology have been implicated i n energy absorption and stress reduction during fracture i n wood. Fracture concepts have also been used to investigate the functional design properties of bone. Again, s p e c i f i c morphological features, such as osteonic organization and s p i r a l f i b r e orientations, have been found to play an important r o l e i n the resistance to crack growth (Piekarski, 1970; Pope and Outwater, 1971; Simkin and Robin, 1974; Bonfield and Datta, 1976; Wright and Hayes, 1977; Alto and Pope, 1979; Wainwright et a l , 1976). Beyond these two materials, however, very l i t t l e i s known regarding fracture resistance design i n bi omateri a l s . One of the problems i n using fracture analysis to study biomaterials i s that fracture mechanics has been developed expressly for engineering applications. The materials used by engineers generally have l i n e a r s t r e s s - s t r a i n properties, but t h i s i s generally not the case with biomaterials. It i s often expedient to use techniques based on li n e a r e l a s t i c properties, even i f the properties are act u a l l y non—linear. This greatly 8 s i m p l i f i e s the analysis, and, within certain l i m i t s , can y i e l d productive information. In addition, some new techniques that account more pr e c i s e l y for nonlinear properties and high s t r a i n conditions are available. * Structural biomaterials present several problems for the analysis of fracture that are not generally dealt with i n engineering investigations. High s t r a i n conditions are frequently encountered, and often function as energy absorbing mechanisms (Gordon, 1980). Animal tissues can be extremely complex and h i e r a r c h i c a l l y organized (Katz, 1980). There are many opportunities for designing systems which do not communicate stresses and energies to a fracture s i t e (Gordon, 1980). Horse hoof i s a good example of t h i s type of str u c t u r a l biomaterial, and as such, i t provides an outstanding opportunity to determine the a p p l i c a b i l i t y of these analysis techniques to t h i s type of tis s u e . The evaluation of the fracture mechanics approach to the analysis of the fracture properties of horse hoof wall was also one of the purposes of t h i s study. The material under study and the analysis techniques employed i n t h i s investigation are not commonly encountered i n bi o l o g i c a l research. Some knowledge of the complex morphology of the t i s s u e i s c r u c i a l to the understanding of the mechanical behaviour of the tis s u e . For t h i s reason, a short chapter i s included reviewing the known morphology of the hoof wall. In addition, a b r i e f explanation of the theory of fracture and of 9 the testing techniques used in -fracture analysis i s provided to prepare the reader for the study which -follows. A more detailed treatment o-f -fracture mechanics can be -found i n Broek, 1978, Elementary Engineering Fracture Mechanics. ' MORPHOLOGY OF THE HOOF WALL T h i s s e c t i o n i s intended as a brie-f review o-f the morphology o-f the epidermal hoo-f wall i n p r e p a r a t i o n -for d i s c u s s i o n s of the mechanical consequences of t h a t morphology t o be presented i n s e c t i o n s t o f o l l o w . The e x t e r i o r of the f o o t of the horse c o n s i s t s of the epidermal hoof c a p s u l e ( F i g . 2 ) . The hoof wall c o v e r s the d o r s a l and l a t e r a l a s p e c t s of the f o o t . I t forms an angle t o the ground when the animal i s sta n d i n g normally of approximately 45 t o 50 degrees f o r the f r o n t f e e t and 50 t o 55 degrees f o r the r e a r f e e t (Evans e t a l , 1977). The wall connects p r o x i m a l l y with the s k i n at a j u n c t i o n termed the coronet. The i n t e r i o r d i s t a l p o r t i o n of the wall connects t o the s o l e e p idermis at a j u n c t i o n r e f e r r e d t o as the white l i n e . T h i s j u n c t i o n c o n s i s t s of the i n t e r d i g i t a t i o n of hoof wall and s o l e epidermal s t r u c t u r e s . I n t e r i o r l y the epidermal wall connects t o the dermis. The co n n e c t i o n i s accomplished by the i n t e r d i g i t a t i o n of many l a m e l l a e which run v e r t i c a l l y on the i n t e r i o r of the epidermal w a l l . These primary l a m e l l a e d i v i d e i n t o a s e r i e s of secondary l a m e l l a e which connect i n t i m a t e l y with the basal membrane of the epidermal wall and complimentary primary and secondary l a m e l l a e of the dermis ( F i g . 3 ) . The epidermal wall i s a v a s c u l a r and c o n t a i n s no nerves (Sisson and Grossman, 1953). I t c o n t a i n s t h r e e s p e c i f i c l a y e r s (Stump, 1967). The stratum externum c o n s t i t u t e s the e x t e r n a l 11 F i g . 2 . S a g i t t a l s e c t i o n o f t h e E q u i n e f o o t t a k e n f r o m a r e a i n d i c a t e d b y d o t t e d l i n e i n A . T h e r e l a t i o n s h i p o f t h e e p i d e r m a l w a l l a n d o t h e r t i s s u e s o f t h e f o o t i s d e p i c t e d . CB - C o r o n a r y b o r d e r , t h e g e r m i n a t i v e r e g i o n SS - S t r a t u m s p i n o s u m , t h e k e r a t i n i z i n g z o n e SM - S t r a t u m m e d i u m , f u l l y k e r a t i n i z e d t i s s u e WL - T h e w h i t e l i n e , t h e d e r m a l / e p i d e r m a l j u n c t i o n S - S o l e e p i d e r m i s P I I a n d P H I a r e t h e s e c o n d a n d t h i r d p h a l a n x o f t h e E q u i n e l i m b . 12 INTERIOR SL EXTERIOR F i g . 3. Cross-section of hoof wall taken from area indicated by dotted l i n e i n Fi g . 2B. D - dermis, BM - basal membrane, SL - Secondary epidermal lamellae PL - primary epidermal lamellae, SI - Stratum internum, SM - Stratum medium, SE - Stratum externum. c o v e r i n g o-f the hoo-f over most o-f i t s s u r f a c e . T h i s i s a v e r y t h i n c o a t i n g of c e l l s produced by the p e r i o p l e a t the proximal margin of the hoof. T h i s c o a t i n g i s c a r r i e d d i s t a l l y with the u n d e r l y i n g stratum medium as i t grows toward the d i s t a l ground c o n t a c t s u r f a c e . As the c e l l s of the p e r i o p l e are sloughed o f f , the stratum externum takes on the form of a g l o s s y v a r n i s h , and i s b e l i e v e d t o a c t as a water b a r r i e r due t o i t s v e r y high l i p i d content (Leach, 1980). I t i s g r a d u a l l y worn away as the hoof grows d i s t a l l y and may not be present at a l l a t the d i s t a l margin of the hoof. The stratum internum i s the l a y e r a djacent t o the i n t e r n a l t i s s u e s of the f o o t . T h i s i s the l a y e r c o n t a i n i n g the primary and secondary epidermal l a m e l l a e . I t forms the s o l i d c o n n e c t i o n between the hard e x t e r n a l wall and the i n t e r n a l t i s s u e s . The stratum internum i s composed of a continuous l a y e r of l i v i n g c e l l s at the basal membrane, which i s the d i v i s i o n between the epidermal and dermal components of the integument. The stratum medium comprises the m a j o r i t y of the hoof wall and i s the l a y e r d e a l t with i n the mechanical i n v e s t i g a t i o n s of t h i s study. The stratum medium i s l o c a t e d between the stratum externum and the stratum internum. The t h i c k n e s s of t h i s l a y e r v a r i e s with l o c a t i o n on the hoof; i t i s t h i c k e s t at the toe and becomes g r a d u a l l y t h i n n e r toward the p o s t e r i o r l a t e r a l margins. The stratum medium, as with the other l a y e r s of the hoof wall and a l l v e r t e b r a t e epidermal t i s s u e , has a completely c e l l u l a r c omposition. The c e l l u l a r nature and manner of growth of t h i s t i s s u e p r o f o u n d l y a f f e c t s the o r g a n i z a t i o n a l form. New 14 wall m a t e r i a l i s produced c o n t i n u o u s l y . T h e r e f o r e , the stratum medium i s continuous with germinative, k e r a t i n i z i n g and mature f u l l y k e r a t i n i z e d t i s s u e . The hoof wall forms on the epidermal basal membrane l o c a t e d at the proximal bordeV of the hoof w a l l . The ge r m i n a t i v e c e l l s develop and r e p l i c a t e i n t h i s p o s i t i o n . As new c e l l s a re formed the o l d e r ones move d i s t a l l y t o become p a r t of the stratum spinosum ( F i g . 2 ) . In t h i s r e g i o n the c e l l s undergo c y t o d i f f e r e n t i a t i o n and the k e r a t i n i z a t i o n p r o c e s s b e g i n s . The f i b r i l l a r p a t t e r n s are e s t a b l i s h e d as the c e l l s c o n t i n u e t o be pushed d i s t a l l y by newer c e l l f o r m a t i o n . The c e l l s a r e i n c o r p o r a t e d as p a r t of the stratum medium of the wall when the f i n a l s t a g e s of k e r a t i n i z a t i o n take p l a c e . At t h i s s tage the c e l l d i e s as a r e s u l t of i n t e r m o l e c u l a r c r o s s - l i n k i n g of the m a j o r i t y of i t s c y t o p l a s m i c c o n s t i t u e n t s . During k e r a t i n i z a t i o n the c e l l s f l a t t e n s l i g h t l y and, i n a hard k e r a t i n such as the hoof w a l l , s p e c i a l i z e d i n t e r — c e l l u l a r j u n c t i o n s a r e formed. These j u n c t i o n s c l o s e l y resemble the 'narrow j u n c t i o n s ' found by Hashimoto (1971a) i n n a i l c e l l s (Matoltsy, 1975; Leach, 1980). The hoof wall c o n t a i n s approximately equal p o r t i o n s of c e l l u l a r m a t e r i a l o r g a n i z e d i n s p i r a l t u b u l e s and i n t e r t u b u l a r m a t e r i a l which connects the t u b u l e s . The t u b u l e s a re p a r a l l e l s t r u c t u r e s t h a t run the l e n g t h of the hoof wall from the proximal growth zone t o the d i s t a l c o n t a c t s u r f a c e . Each t u b u l e c o n t a i n s a c e n t r a l c a v i t y , the medulla, surrounded by h i g h l y o r g a n i z e d c e l l u l a r m a t e r i a l , the cortex ( F i g . 4 ) . The medulla can c o n t a i n some amorphous m a t e r i a l . The t u b u l e s have been 15 F i g . 4 . S c a n n i n g e l e c t r o n m i c r o g r a p h o f h o o f - w a l l k e r a t i n p r e p a r e d b y t e a r i n g a w e t s a m p l e , s h o w i n g t h e o r g a n i z a t i o n o f t h e t u b u l a r m a t e r i a l . C , c o r t e x ; M , m e d u l l a . S c a l e b a r = 4 0 urn. c l a s s i f i e d i n t o t h r e e c a t e g o r i e s based on p o l a r i z e d l i g h t s t u d i e s . N i c k e l (1938) b e l i e v e d these p o l a r i z i n g p a t t e r n s were caused by a system of a l t e r n a t i n g s p i r a l s h e e t s or laminae. Wilkens (1964) d i s a g r e e s with these f i n d i n g s and concludes t h a t no d i s c r e t e laminae e x i s t . The c r y s t a l l i n e f i b r e s w i t h i n the 4 c e l l s do have a high degree of p r e f e r e n t i a l o r i e n t a t i o n and do present an o v e r a l l s p i r a l l i n g p a t t e r n w i t h i n the t u b u l e s but Wilkens a t t r i b u t e d the d i f f e r e n c e i n p o l a r i z a t i o n p a t t e r n of the v a r i o u s t u b u l e 'types' t o d i f f e r e n c e s i n angular o r i e n t a t i o n s of the component c e l l s . Due t o an u n f o r t u n a t e e r r o r i n t h e E n g l i s h t r a n s l a t i o n of the summary g i v e n i n the o r i g i n a l paper, the s i g n i f i c a n c e of t h i s v a l u a b l e work has been l a r g e l y n e g l e c t e d by E n g l i s h speaking i n v e s t i g a t o r s i n t h i s f i e l d . In d e s c r i b i n g the o r g a n i z a t i o n of the t u b u l e s Wilkens used the analogy of a p i n e cone, s a y i n g the c e l l s of the c o r t e x a d j o i n the medulla at an angle j u s t as the i m b r i c a t e d s c a l e s of a p i n e cone a d j o i n the c o r e . The t r a n s l a t e d summary, however, r e p l a c e d the term 'pine cone' with ' p i n c u s h i o n ' and a l l meaning was l o s t . The s l o p e of the c o n n e c t i o n between the cortex c e l l s and the medulla i s d e r i v e d from the s l o p e of the dermal p a p i l l a on which the t u b u l e i s formed. The l a r g e r innermost t u b u l e s are formed on l a r g e r dermal p a p i l l a e . These p a p i l l a e a r e the same l e n g t h as the narrower p a p i l l a e , and thus, have a sharper s l o p e i n the g e r m i n a t i v e r e g i o n . S e c t i o n s of these t u b u l e s cut the component c e l l s at a d i f f e r e n t angle than c e l l s of the narrower t u b u l e s and g i v e a s l i g h t l y d i f f e r e n t p o l a r i z e d l i g h t p a t t e r n . The c e l l 5 of the i n t e r t u b u l a r m a t e r i a l are s i m i l a r i n general shape t o those of the t u b u l e c o r t e x , but t h e i r o r i e n t a t i o n i s q u i t e d i f f e r e n t . These c e l l s a r e produced on the plane of the ba s a l membrane, and they maintain thi's p l a n a r o r i e n t a t i o n throughout the hoof s t r u c t u r e . The angle formed by the s u r f a c e of these c e l l s and the t u b u l e a x i s can vary. T h i s v a r i a t i o n i s suspected t o be r e l a t e d t o the l o c a t i o n of i n t e r — t u b u l a r c e l l f o rmation, but the exact circumstances are not known. The long axes of these c e l l s l i e g e n e r a l l y i n the plane of the basal l a y e r and at r i g h t a ngles t o t u b u l e d i r e c t i o n . In the e x t e r i o r p o r t i o n of the stratum medium the i n t e r t u b u l a r f i b r e o r i e n t a t i o n tends t o be i n a more c i r c u m f e r e n t i a l d i r e c t i o n , w h i l e the inn e r t i s s u e appears t o have a more interwoven o r i e n t a t i o n . These c e l l s a re generated on the basal membrane between the dermal p a p i l l a e and move d i s t a l l y as they are r e p l a c e d at the g e n e r a t i v e s u r f a c e . The hoof wall p r e s e n t s a complex h i e r a r c h y of s t r u c t u r a l l e v e l s . The understanding of the i n t e g r a t i o n of these l e v e l s i n e i t h e r a morphological or f u n c t i o n a l sense demands t h a t the s c a l e of each be a p p r e c i a t e d . The k e r a t i n composite w i t h i n the c e l l s i s composed of p r o t e i n a c i o u s polymers. The f i b r e s of t h i s composite have a diameter of approximately 7.0 nm. (Fraser and Macrae, 1980), and are themselves c o n s t r u c t e d from s m a l l e r m i c r o f i b r i l l a r u n i t s . The c e l l s , t h a t a re f i l l e d with t h i s f i b r e and matrix composite, are pancake shaped and are approximately 40-50 jAm i n diameter and g e n e r a l l y 5 jJLm t h i c k . At the next l e v e l of the h i e r a c h i c a l o r g a n i z a t i o n , the t u b u l e s are 18 seen t o be g e n e r a l l y c i r c u l a r or s l i g h t l y e l i p t i c a l i n c r o s s - s e c t i o n with a diameter o-f approximately 50 - 150 m depending on the l o c a t i o n i n the w a l l . The s m a l l e r and more e l i p t i c a l t u b u l e s are -found toward the e x t e r i o r s u r f a c e o-f the stratum medium, . w h i l e the l a r g e s t t u b u l e s are -found i n the i n t e r i o r . The diameter o-f a given t u b u l e i s maintained over the e n t i r e l e n g t h o-f the hoof w a l l . Adjacent t u b u l e s can have v e r y d i f f e r e n t t u b u l e diameters, however. The i n t e r t u b u l a r m a t e r i a l l i e s between the t u b u l e s , and t h i s determines t h e i r s p a c i n g . The s i z e of the hoof wall v a r i e s with the s i z e of the f o o t and breed of horse. A normal hoof can be expected t o be 8-12 cm from the coronet p r o x i m a l l y t o the d i s t a l c o n t a c t s u r f a c e . The stratum medium i s approximately one cm t h i c k at the toe, narrowing t o a few m i l l i m e t e r s at the p o s t e r i o r q u a r t e r s . 19 FRACTURE MECHANICS ANALYSIS The study o-f the e f f e c t s of f l a w s on the mechanical behaviour of m a t e r i a l s i s termed f r a c t u r e mechanics. The response of a m a t e r i a l t o the p h y s i c a l c i r c u m s t a n c e s c r e a t e d by a f l a w i s a p r o p e r t y of t h a t m a t e r i a l , as are such p r o p e r t i e s as s t i f f n e s s and s t r e n g t h . However, the a n a l y s i s of the mechanical response t o a f l a w i s a complicated i s s u e . T h i s s e c t i o n i s intended as a b r i e f i n t r o d u c t i o n t o the concepts and t h e o r i e s u n d e r l y i n g the study of f r a c t u r e i n s t r u c t u r a l m a t e r i a l s . I t w i l l a l s o i n c l u d e a s y n o p s i s of the a n a l y s i s t e c h n i q u e s employed i n t h i s study and some of the p r a c t i c a l l i m i t a t i o n s i n h e r e n t i n the a p p l i c a t i o n of these t h e o r y based procedures t o the case of ' r e a l ' m a t e r i a l s . The p r o c e s s of crack propagation depends upon two c r i t e r i a : ( i ) the presence of adequate s t r e s s c o n d i t i o n s at the t i p of a crack or flaw, and ( i i ) the a v a i l a b i l i t y of s u f f i c i e n t energy t o d r i v e the crack e x t e n s i o n (Broek, 1978). The p a t t e r n of s t r e s s w i t h i n an o b j e c t under c o n d i t i o n s of l o a d w i l l be p r o f o u n d l y a f f e c t e d by the presence of a f l a w ( G r i f f i t h , 1921). The energy s t a t e of the o b j e c t w i l l a l s o be a f f e c t e d by the i n t e r a c t i o n of s t r a i n energy w i t h i n the body of the o b j e c t r e s u l t i n g from the l o a d and the energy c o s t of crack growth. N e i t h e r of these two c o n d i t i o n s alone i s s u f f i c i e n t t o cause crack growth (Broek, 1978). In order t o understand the p r o c e s s of f r a c t u r e i t i s necessary t o i n v e s t i g a t e the a c t i o n of s t r e s s e s and e n e r g i e s w i t h i n an o b j e c t under l o a d . 20 An e v e n l o a d on a homogeneous o b j e c t w i l l p r o d u c e a u n i f o r m i n t e r n a l s t r e s s p a t t e r n , where s t r e s s i s d e f i n e d a s t h e f o r c e p e r u n i t a r e a o v e r w h i c h t h e f o r c e a c t s . I f a f l a w i s p r e s e n t i n t h e o b j e c t , no s t r e s s w i l l be c a r r i e d b y trie f l a w e d p o r t i o n o f t h e o b j e c t , and t h e s t r e s s t h a t would h a v e p a s s e d t h r o u g h t h e r e g i o n t h e f l a w o c c u p i e s i s f o r c e d t o d i v e r t a r o u n d t h e f l a w ( F i g . 5 ) . T h i s c a u s e s a c o n c e n t r a t i o n o f s t r e s s a t t h e t i p o f t h e f l a w . The m a g n i t u d e o f a b s o l u t e s t r e s s p r e s e n t i n t h i s s i t u a t i o n c a n be much g r e a t e r t h a n i n t h e r e s t o f t h e o b j e c t ( F i g . 6 ) . The h i g h s t r e s s s t a t e c a u s e d by t h e f l a w w i l l p r o d u c e a l o c a l i z e d s t r a i n ( l e n g t h o f d e f o r m a t i o n p e r u n i t l e n g t h ) i n t h e b o n d s c o n n e c t i n g t h e r e m a i n i n g m a t e r i a l a t t h e t i p o f t h e crack ( F i g . 7 ) . I f t h e s t r e s s a t t h e crack t i p r e a c h e s a c r i t i c a l v a l u e i t w i l l b e g i n t o r u p t u r e t h e m o l e c u l a r bonds, and t h e m a t e r i a l w i l l b e g i n t o f r a c t u r e . The s u r f a c e s o f t h e c r a c k c a n n o t carry any s t r e s s . T h e r e f o r e t h e y a c t a s s t r e s s b o u n d a r i e s and d o m i n a t e t h e d i s t r i b u t i o n p a t t e r n o f t h e s t r e s s c o n c e n t r a t i o n a t t h e c r a c k t i p . The c r a c k g e o m e t r y and l o a d i n g mode ca n be u s e d t o d e t e r m i n e t h e s t r e s s p a t t e r n i n a t e s t s i t u a t i o n ( I r w i n , 1958). The l o a d i n g f o r c e s w i l l o n l y a f f e c t t h e i n t e n s i t y o f t h e s t r e s s f i e l d and n o t i n f l u e n c e i t s d i s t r i b u t i o n p a t t e r n . The s t r e s s r e l a t e d f r a c t u r e p r o p e r t i e s o f a m a t e r i a l c a n t h e n be c h a r a c t e r i z e d by an a n a l y s i s o f t h e s t r e s s i n t e n s i t y f i e l d u n d e r t h e c o n d i t i o n s t h a t c a u s e f a i l u r e o f t h e m a t e r i a l . I r w i n (1958) d e t e r m i n e d t h a t a c h a r a c t e r i s t i c t e r m , t h e s t r e s s i n t e n s i t y f a c t o r ( K ) , e x i s t e d f o r t h e s p e c i f i c s p a t i a l d i s t r i b u t i o n o f s t r e s s e s c a u s e d by a f l a w . The s t r e s s 21 F i g . 5. The e f f e c t of a notch or flaw on the path of stress i n a loaded object. • • • • F i g . 6. The magnitude of stress l e v e l s across an object containing flaws or notches (after Currey, 1962). C - l e v e l of stress 22 F i g . 7. S t r e s s at a c rack t i p caus ing mo lecu la r bond s t r a i n and r u p t u r e . F i g . 8 The G r i f f i t h c r i t e r i o n of f r a c t u r e . Energy i s absorbed d u r i n g f r a c t u r e through such processes as bond s t r a i n and breakage. The energy i s d i r e c t l y p r o p o r t i o n a l to the l e n g t h of c r a c k . The s t r a i n energy r e l e a s e d by f r a c t u r e i s a l s o a f u n c t i o n of c rack l e n a t h . C a t a s t r o p h i c f r a c t u r e occurs when the s lope of s t r a i n energy r e l e a s e i s of equa l magnitude t o the s lope of energy absorbed. 23 i n t e n s i t y factor could then be determined f o r the c r i t i c a l circumstances which would cause f a i l u r e of a material. An a l t e r n a t i v e method of viewing fracture depends upon the energy balance that e x i s t s within a material under stress. A load applied to 1 an object w i l l be r e s i s t e d by the s t r a i n i n g of molecular bonds. The extension of the molecular bonds constitutes work (or energy) performed on the system. The inter—molecular work developed in t h i s manner can be stored e l a s t i c a l l y , and i s referred to as s t r a i n energy. As a crack grows, the volume of material which c a r r i e s no load increases, and as a consequence s t r a i n energy w i l l be released from the adjoining material which had r e s i s t e d stress before the crack passed. For geometrical reasons the s t r a i n energy released w i l l be a function of the length of the flaw, while the energy necessary to rupture the connecting bonds at the t i p of the flaw (the fracture process) w i l l be a function of the area of new surface created. These two energy terms w i l l then interact as a function of crack growth (Fig.8), and the flaw w i l l begin to grow catastrophical1y when an incremental growth r e s u l t s i n the release of more stored s t r a i n energy than i s absorbed by the creation of the new crack surface (molecular bond rupturing) ( G r i f f i t h , 1921). The energy related fracture properties can then be characterized by determining the rate of the s t r a i n energy release (dU/ 3a = G) ( G r i f f i t h , 1921). Provided the material under question exhibits l i n e a r e l a s t i c properties, the two parameters, stres s i n t e n s i t y factor 24 (K) and s t r a i n energy r e l e a s e r a t e (G), w i l l d e s c r i b e the r e s i s t a n c e t o c r a c k i n g , or 'toughness', a m a t e r i a l possesses. However, r e a l m a t e r i a l s do not possess i d e a l e l a s t i c p r o p e r t i e s . N o n - e l a s t i c deformation at the t i p of a f l a w can a l t e r the s t r e s s d i s t r i b u t i o n f i e l d and absorb s t r a i n energy. If the extent of p l a s t i c deformation i s small compared t o the s t r e s s f i e l d s i n v o l v e d , the s t r e s s i n t e n s i t y f a c t o r and s t r a i n energy r e l e a s e r a t e can s t i l l adequately d e s c r i b e the c o n d i t i o n s r e s p o n s i b l e f o r f r a c t u r e ; i f not, o t h e r f r a c t u r e parameters must be employed t o a n a l y s e the f r a c t u r e p r o c e s s . The l i m i t of the a p p l i c a b i l i t y of K and G t o a f r a c t u r e a n a l y s i s s i t u a t i o n i s dependent on the s i z e of p l a s t i c deformation at the crack t i p . Because the m a t e r i a l i n the s t r e s s c o n c e n t r a t i o n zone adjacent t o the c r a c k t i p i s c o n s t r a i n e d by l e s s s t r e s s e d m a t e r i a l f a r t h e r from the s t r e s s c o n c e n t r a t i o n , s t r e s s e s are produced a c r o s s the t h i c k n e s s d i r e c t i o n of the t e s t specimen (Pook and Smith, 1979). T h i s s i t u a t i o n i s termed plane s t r a i n . As long as i t i s maintained, the a n a l y s i s t e c h n i q u e s can p r e d i c t the s t r e s s and energy s t a t e s a t the crack t i p , and the e l a s t i c f r a c t u r e c r i t e r i a apply. If p l a s t i c deformation o c c u r s and the extent of the p l a s t i c zone approaches the t h i c k n e s s of the sample, the s t r e s s r e l i e v i n g deformation w i l l reach the specimen boundaries and the t h i c k n e s s s t r e s s e s w i l l be reduced. T h i s w i l l r e s u l t i n a plane s t r e s s s i t u a t i o n a r i s i n g i n the r e g i o n assumed t o be under plane s t r a i n . Under these circumstances the s t r e s s e s at the crack t i p a r e not d e s c r i b e d by l i n e a r e l a s t i c mechanics, 25 and the s t r e s s i n t e n s i t y f a c t o r and s t r a i n energy r e l e a s e r a t e do not apply. The a n a l y s i s of f r a c t u r e under g r e a t e r degrees of p l a s t i c d eformation p r i o r t o f a i l u r e i s an a r e a of much r e c e n t i n v e s t i g a t i o n i n m a t e r i a l s s c i e n c e , and an a l t e r n a t i v e a n a l y s i s parameter, the J i n t e g r a l (Rice, 1968), has been proposed f o r the e v a l u a t i o n of f r a c t u r e under these c o n d i t i o n s . The J i n t e g r a l i s a path independent e v a l u a t i o n of the e l a s t i c - p l a s t i c energy f i e l d a t the flaw t i p and r e p r e s e n t s the p o t e n t i a l energy a v a i l a b l e f o r crack propagation (Landes and Begley, 1972). As such, i t i s a g e n e r a l i z e d r e l a t i o n f o r the energy r e l e a s e due t o crack p r o p a g a t i o n (Broek, 1978). I t a p p l i e s i n s p i t e of a p p r e c i a b l e p l a s t i c deformation at the crack t i p . Due t o the path independent aspect of the e v a l u a t i o n , the most convenient i n t e g r a t i o n contour can be s e l e c t e d , g e n e r a l l y the specimen boundaries. In t h i s way, a l l energy a v a i l a b l e and r e q u i r e d f o r crack growth can be determined. For f u l l y e l a s t i c m a t e r i a l s the v a l u e of J i s e q u i v a l e n t t o the v a l u e of G, s i n c e the p o t e n t i a l ( t o t a l ) energy (J) i s o n l y i n the form of e l a s t i c energy (G). T h i s f r a c t u r e parameter a l s o depends on plane s t r a i n c o n d i t i o n s predominating i n the r e g i o n of the crack t i p . 26 MATERIALS AND METHODS I. Acquisition and Preparation o-f Samples. 4 Whole horse hooves were obtained -from a commercial abbatoir within two days o-f the animal's slaughter. While at the abbatoir the hooves were kept cold but not frozen. T h i r t y apparently normal hooves were taken from 12 horses. The hooves were c l a s s i f i e d by pigmentation at t h i s stage. Three c l a s s i f i c a t i o n s were used: (1) obviously darkly pigmented, (2) obviously unpigmented, and (3) moderately pigmented. These three classes were quite d i s t i n c t . V e r t i c a l s l i c e s of the mid-toe region (Fig.9) of the hoof were cut with an i n d u s t r i a l band saw and the dermis was removed with a s c a l p e l . The cleaned s t r i p s of hoof epidermis were then l a b e l l e d , placed i n double p l a s t i c bags to maintain t h e i r natural moisture content and re f r i g e r a t e d . A hacksaw was used to cut the s t r i p s of hoof wall into approximately 1.2 cm blocks. The blocks were then shaped to appropriate length, Wt , and height, D, dimensions with a f l a t f i l e . Care was taken to ensure the shaping was done accurately and a l l sides of the samples were p a r a l l e l . However, because some of the cutting was done by hand, variati o n s i n absolute dimensions were unavoidable. These variati o n s were accurately measured and accounted f o r i n the analysis. The samples were washed with d i s t i l l e d water throughout the cutting process to ensure that f r i c t i o n a l heat would be kept to a minimum. The cutting and 1.7 cm TOE F i g . 9 . The l o c a t i o n of hoof w a l l m a t e r i a l t e s t e d . The most d i s t a l and p rox ima l p o r t i o n s were removed. The c e n t r e p o r t i o n of the w a l l was cut s a g i t t a l l y p roduc ing s t r i p s o f hoof w a l l of approx imate ly 1.7 cm. w i d t h . These were then cut i n t o f i v e b l o c k s which were l a t e r cut i n t o the Compact Tension t e s t geometry. T - top, UC - upper centre, C - centre, LC - lower centre, B - bottom. 28 shaping procedure allowed the i n d i v i d u a l samples t o be cut a p p r o p r i a t e l y t o the major morphological -feature, t h a t of the t u b u l e a x i s . The outer s u r f a c e of the specimen b l o c k s were f i l e d p a r a l l e l t o the t u b u l e a x i s and p e r p e n d i c u l a r 7 t o a l l other s i d e s . The outer f a c e of the f i n i s h e d sample block was then a f f i x e d t o a small p l e x i g l a s s mount with polymeric adhesive (Buperglue). These were then l a b e l l e d , p l a c e d over d i s t i l l e d water i n a small vacuum chamber and r e f r i g e r a t e d . I t was c o n s i d e r e d c r i t i c a l t o the a n a l y s i s procedure t h a t the l a t e r a l s i d e s of the t e s t specimen be a b s o l u t e l y p a r a l l e l . To ensure t h i s an Isomet v a r i a b l e speed m e t a l u r g i c a l sample saw was used t o cut i n d i v i d u a l t e s t samples from the shaped b l o c k s . The samples were cu t at a slow r a t e w h i l e being c o n t i n u o u s l y washed with d i s t i l l e d water t o e l i m i n a t e h e a t i n g . A f t e r sawing, the t e s t p i e c e s were i n d i v i d u a l l y p l a c e d i n s e a l e d 2 dram v i a l s and l a b e l l e d . These were then r e f r i g e r a t e d . Holes f o r the c l e v i s and load p i n attachment were d r i l l e d with a Maxitmat 7 d r i l l p r e s s u s i n g a 1.8 mm. d r i l l b i t . Notches were cut i n these t e s t specimens u s i n g a s i n g l e edge r a z o r b l a d e h e l d i n a j i g a t t a c h e d t o the d r i l l p r e s s . The t e s t p i e c e was s e t v e r t i c a l l y and clamped i n a v i c e attached t o the m i l l i n g s l i d e c a r r i a g e . The d r i l l p r e s s head was then lowered onto the t e s t p i e c e u s i n g the v e r t i c a l leadscrew. The s i n g l e edge razor blade gave a narrow, sharp notch. I I . T e s t i n g Procedures. 29 The loading system and specimens were attached -firmly inside s p e c i a l l y designed sealed constant environment test chambers that allowed samples to be hydrated and tested while i n a controlled environment. F u l l hydration was produced either by placing the test samples over d i s t i l l e d water i n the test chambers or by covering the samples with d i s t i l l e d water while in the test chamber. Covering the samples with water made no difference to the f i n a l water content of the samples (mean water content was 38.4% by weight for samples hydrated i n the vapor phase; while the mean for samples covered by water was 39.6%), but reduced the hydration time by a factor of two. The dehydrated condition was produced by preparing the test samples wet and then placing them in the environment test chamber over phosphorus pentoxide drying agent (BDH Laboratories). Periods of 2 to 3 weeks i n t h i s s i t u a t i o n produced specimens which had an apparent water content of 5% by weight, as indicated by weight loss a f t e r oven—drying. It i s assumed that a period of t h i s length i n 0% RH would remove a l l water from t h i s material. The loss of weight observed afte r oven—drying probably represents a loss of some v o l a t i l e aspect of the t i s s u e i t s e l f . Intermediate hydration conditions of 53% RH and 75% RH were produced by placing saturated solutions of Mg (NOj )^ »6H^0 and NaCl i n the environment test chambers (Meites, 1963). These r e l a t i v e humidity l e v e l s produced water content values of 11.7% by weight at 53% RH and 18.1% by weight at 75% RH. 30 In metallurgical investigations compact tension (CT) specimens are generally f i t t e d with c l i p — t y p e displacement gauges which measure displacement of the sample d i r e c t l y . In t h i s case the small s i z e of the samples and the environment chamber tes t regime did not allow t h i s procedure. In t h i s study displacement was measured as test machine cross—head displacement. Since the cross—head was securely connected to a c l e v i s and pin arrangement, i t was considered to be an accurate estimate of the load pin displacement. A l l t e s t s were conducted on an Instron te s t i n g machine Model 1122 f i t t e d with a proportionally driven chart recorder. The chart recorder was run at a proportional drive of 20:1 for the 100% and 75% RH samples and 50:1 for the other le s s compliant hydrations. The cross-head rate was a r b i t r a r i l y standardized at 5 mm/min. This rate was chosen simply because i t was slow enough to give dependable responses from the te s t i n g apparatus. Force was recorded with a 500 Kg max. load force transducer. Maximum loads for these samples approached 120 N (12.25 Kg). The test procedures were adapted from the American Society f o r Testing and Materials (ASTM) Standard Test Procedure E—399—81 "PIain—strain Fracture Toughness of M e t a l l i c Materials Employing the Compact Tension Test Geometry". Due to constraints on the amount of material a v a i l a b l e from the horse hoof, the specimen s i z e s used were smaller than those recommended by t h i s procedure. However, the r e l a t i v e dimensions recommended were maintained (Fig.10). The compact tension test allows controlled conditions to be produced i n reasonably small 31 10 mm 10 mm 3 mm - 2.5 mm F i g . 10 The Compact Tension fracture test specimen geometry. W - t o t a l width of sample, W, -width of sample between loading point ana notched edge, W - width of mechanically e f f e c t i v e sample, A. - t o t a l length of notch, A - mechanically e f f e c t i v e notch length, B -specimen width. Upper load rod ( S t a i n l e s s s t e e l , 3.2 mm diam.) Upper aluminum c l e v i s „ Load pin (1.6 mm diam.) - Notched CT sample Lower c l e v i s Base load rod ( S t a i n l e s s s t e e l , 6.35 mm diam.) F i g . |) Specimen loading system used i n Compact Tension fracture t e s t s . Upper load rod was grasped by clamping system of tes t i n g machine. Base load rod ran h o r i z o n t a l l y and was firmly attached to environment te s t chamber. 32 scale specimens. The l i m i t a t i o n s of the application o-f these procedures are discussed l a t e r . The load -fixtures used consisted o-f the c l e v i s and load pin arrangement advised by the prescribed procedures (Fig.1 1 ) . During a test the c l e v i s load rod of the sample was attached to an aluminium adaptor i n order to allow attachment of the pneumatic grip with which the te s t i n g machine was equipped. The c l e v i s load rod was secured with two set screws, and the head of the adaptor was clamped by the pneumatic grips. The compliance of the system was tested by using an unnotched piece of aluminium of si m i l a r s i z e to the test samples i n place of the hoof specimen. The unnotched aluminium sample was expected to be much s t i f f e r than any test specimen; therefore, the compliance i n t h i s test would indicate the compliance of the system during the tes t i n g of the hoof samples. The tes t -6 system deflected a maximum of 1.3x IO m/N. In the experiments run at f u l l hydration the system compliance accounted f o r les s than 4% of the specimen compliance and has been ignored. In experiments at reduced hydrations, where sample s t i f f n e s s increases, the r e l a t i v e system compliance was larger. In the 07. RH samples the system compliance was as much as 25% of the sample compliance. This error i n de f l e c t i o n measurement was consistent and was accounted for i n the ca l c u l a t i o n s for te s t s run at a l l hydration l e v e l s except lOOTC RH. « During the course of a test only a single seal cap was removed from the test chamber to allow access to the load rod. T h i s kept t o a minimum the exchange o-f environmental humidity. The t e s t i n g o-f a l l 12 samples i n a t e s t chamber l a s t e d a maximum o-f two hours. Immediately upon completion of these t e s t s the samples were i n d i v i d u a l l y removed, weighed a c c u r a t e l y ( M e t t l e r H31 balance, 0.0001 g) and measured f o r the dimensions of t h i c k n e s s B, t o t a l width W^  , d i s t a n c e from the edge of the sample t o the c e n t r e of the l o a d p i n h o l e Wj , h e i g h t D, t o t a l o r i g i n a l notch l e n g t h A t as well as f r a c t u r e angle. The dimensional l e n g t h s of B, Wt and D were measured u s i n g a H e l i o s micrometer (.01 mm). The notch l e n g t h , , was measured under a b i n o c u l a r d i s s e c t i n g microscope u s i n g a p a i r of sharpened screw—type p r o t r a c t o r s as f i n e c a l i p e r s . The depth of the l o a d p i n h o l e , W^  , was measured i n the same manner. W^  was measured f o r both s i d e s of the sample, and the mean was taken as the measured v a l u e . The ligament l e n g t h , W, was determined by s u b t r a c t i n g W^  from the t o t a l specimen width Wt . The o r i g i n a l notch l e n g t h A was determined by s u b t r a c t i n g W^  from A t . F r a c t u r e angle and i n t e r t u b u l a r c e l l o r i e n t a t i o n were measured on a Wild b i n o c u l a r d i s s e c t i n g microscope f i t t e d with a r o t a t i n g stage. T h i s allowed a c c u r a t e d e t e r m i n a t i o n of a l l a n g l e s i n v o l v e d . When the crack v a r i e d i n d i r e c t i o n , the o r i g i n a l d i r e c t i o n was taken as the f r a c t u r e angle. H y d r a t i o n of the i n d i v i d u a l samples was taken as the wet weight, measured immediately a f t e r the t e s t , minus the dry weight, measured a f t e r at l e a s t t h r e e days i n an oven at 34 approximately 80* C. The temperature of the d e s i c a t i o n was maintained a t t h i s l e v e l t o ensure the morphology would be l e f t i n t a c t f o r subsequent h i s t o l o g i c a l s t u d i e s . F u r t h e r d r y i n g beyond the t h r e e days produced no change i n weight. I I I . A n a l y s i s of the F r a c t u r e Data. The mechanical t e s t r e c o r d s were d i g i t i z e d by measuring f o r c e at s t a n d a r d i z e d i n t e r v a l s of loa d p i n displacement. -4 I n t e r v a l s of 2 x 10 m. were used f o r the 100% and 75% RH -5 samples w h i l e i n t e r v a l s of 4 x IO m. were used f o r the lower h y d r a t i o n s t a t e s . The s t r e s s i n t e n s i t y f a c t o r (K> was c a l c u l a t e d from the equ a t i o n : K = ( P / B ) f (a/W) , where; (2+a/W)(.87 + 4.6a/W - 13.3a*/ W* +14.7aJ/W* -5.6a*/W*> f (a/W) = --7 (1 - a/W)* In t h e s e e q u a t i o n s P i s the l o a d , B i s the specimen t h i c k n e s s , W i s the specimen width and a i s the apparent crack l e n g t h . The s t r a i n energy r e l e a s e r a t e (G) was c a l c u l a t e d u s i n g the compliance c a l i b r a t i o n method: where C = the compliance c a l i b r a t i o n r e l a t i o n s h i p . G - 16* The specimen width term was squared i n t h i s a n a l y s i s because the compliance c a l i b r a t i o n c urve had been normalized t o the specimen width ( i . e . C = q/P x B) ( from Broek, 1978 ). The d e t e r m i n a t i o n of the 35 J i n t e g r a l r e q u i r e d t h a t the energy put i n t o the specimen d u r i n g a t e s t be measured. T h i s was done by i n t e g r a t i n g the •force d e - f l e c t i o n r e c o r d at the same de - f l e c t i o n i n t e r v a l s as the •force measurements. C u t t i n g s o-f the a p p r o p r i a t e segments -from photocopied t e s t r e c o r d s were a c c u r a t e l y weighed. A standard 4 area was weighed -from each t e s t r e c o r d i n order t o c a l i b r a t e the i n d i v i d u a l r e c o r d weight t o energy r e l a t i o n s h i p . The J i n t e g r a l v a l u e was determined from J = -l/B(<>U/da) (Rice,196B). In order t o d e f i n e a c r i t i c a l f a i l u r e p o i n t f o r the t e s t specimens, the maximum s u s t a i n a b l e load (P^ ) was determined as the l o a d v a l u e of the t e s t r e c o r d given by t h e i n t e r s e c t i o n of a 5% d e v i a t i o n from the i n i t i a l compliance (F i g . 1 2 ) , a c c o r d i n g t o the recommended procedure (ASTM—E399). P^ was used r a t h e r than P_ t o determine the c r i t i c a l l i m i t s of a l l max the f r a c t u r e parameters analysed i n t h i s study. The v a l i d i t y t e s t of P m a x < 1-10, o r i g i n a l l y designed t o v e r i f y the s t r e s s i n t e n s i t y f a c t o r (ASTM—E399), was used t o e l i m i n a t e t e s t r e c o r d s from the data s e t which d i d not apply t o the a n a l y s i s techniques employed i n t h i s study. IV. Compliance C a l i b r a t i o n . Composite m a t e r i a l s pose a f o r m i d a b l e problem f o r the ac c u r a t e d e t e r m i n a t i o n of the a c t u a l crack l e n g t h d u r i n g f r a c t u r e (Gaggar and Broutman, 1975). The use of a h y d r a t i o n chamber t e s t s i t u a t i o n a l s o r e s t r i c t e d a ccess t o the t e s t sample d u r i n g t e s t i n g . For these reasons a compliance method of 36 DISPLACEMENT F i g . 12. A n a l y s i s of Compact Tension t e s t r e c o r d . C c - i n i t i a l compl iance determined from s lope of l i n e a r p o r t i o n of reco rd P - maximum load m P - f a i l u r e p o i n t d e f i n e d as the load acheived ^ a t the i n t e r s e c t i o n of a l i n e w i t h 5% lower s lope than the i n i t i a l l i n e a r p o r t i o n of the r e c o r d . U - the energy absorbed by the specimen over a g i ven d isp lacement q . to q _ . Th i s was e m p i r i c a l l y measured from the t e s t r e c o r d . 37 c r a c k l e n g t h d e t e r m i n a t i o n was e m p l o y e d . T h i s t e c h n i q u e h a s been s u c c e s s f u l l y u s e d i n s t u d i e s o f s y n t h e t i c c o m p o s i t e s (Gaggar and Broutman, 1975) and i n t h e s t u d y o f bone ( W r i g h t and Hayes, 1976). The c o m p l i a n c e t e c h n i q u e u s e s t h e e l a s t i c r e s p o n s e c h a r a c t e r i s t i c s o f t e s t s p e c i m e n s c a l i b r a t e d o v e r a r a n g e o f c r a c k l e n g t h s . The p r o c e d u r e i n v o l v e s t h e d e t e r m i n a t i o n o f t h e e l a s t i c s p r i n g c o n s t a n t ( r e c i p r o c a l o f t h e l o a d d i s p l a c e m e n t c u r v e ) f o r v a r i o u s n o t c h l e n g t h (A) t o s p e c i m e n w i d t h (W) r a t i o s . F o r c o m p a r i s o n s o f d i f f e r e n t m a t e r i a l s and s p e c i m e n g e o m e t r i e s t h e c o m p l i a n c e c a n be n o r m a l i z e d f o r b o t h modulus and s p e c i m e n w i d t h . In t h i s s t u d y c o m p l i a n c e c u r v e s were d e t e r m i n e d f o r e a c h h y d r a t i o n c o n d i t i o n . T h e r e f o r e a l l s a m p l e s u s e d i n t h e c a l i b r a t i o n had s i m i l a r m o d u l i and a n o r m a l i z a t i o n f o r t h i s f a c t o r was u n n e c e s s a r y . The s a m p l e s were n o r m a l i z e d f o r t h e v a r i a t i o n s i n s p e c i m e n w i d t h . The v a l u e s o f t h e w i d t h n o r m a l i z e d e l a s t i c s p r i n g c o n s t a n t were t h e n c a l c u l a t e d a s C(q/P) x B> f o r a s many e x t e n s i o n s a s p o s s i b l e u n t i l a d e c r e a s e i n t h e s l o p e was s e e n o r u n t i l f i v e v a l u e s were o b t a i n e d . T h e s e v a l u e s were t h e n a v e r a g e d t o d e t e r m i n e t h e i n i t i a l c o m p l i a n c e f o r t h e s a m p l e . T h i s was t h e n p l o t t e d a g a i n s t t h e measured i n i t i a l n o t c h l e n g t h t o s p e c i m e n w i d t h r a t i o (A/W) t o y i e l d t h e c o m p l i a n c e c a l i b r a t i o n c u r v e . S i n c e s p e c i m e n c o m p l i a n c e i s a f u n c t i o n o f A/W, t h e i n s t a n t a n e o u s c r a c k l e n g t h ' a ' t o s p e c i m e n w i d t h r a t i o a/W c o u l d t h e n be d e t e r m i n e d f o r any p o i n t i n t h e t e s t f r o m t h e measured c o m p l i a n c e t a k e n f r o m t h e c o n t i n u o u s m e c h a n i c a l t e s t r e c o r d . 38 It i s important to recognize that the a/W value determined i n t h i s manner represents only the apparent crack length to specimen width r a t i o . The compliance due to any p l a s t i c de-formation -field at the crack t i p , as well as any micro-fracture damage zone w i l l be included in the a/W c a l c u l a t i o n . This method also treats a l l cracks as though they were progressing p a r a l l e l to the o r i g i n a l notch. This was not always the case i n t h i s study, however. The fracture analysis techniques used i n t h i s study characterize the i n i t i a t i o n of fracture and cannot be applied to the large scale, continuous crack growth. The crack growth at the c r i t i c a l point of f a i l u r e was found to be small enough i n a l l samples for any deviation to be considered n e g l i g i b l e . V. Tensile Modulus and Y i e l d Strength Measurement. Tensile t e s t s of thin uniform samples were conducted to determine Young's modulus (E) and y i e l d s t ress. Young's modulus was measured i n order to determine the presence and/or the degree of any anisotropy i n t h i s material. The y i e l d stress was determined i n order to estimate the extent of p l a s t i c zone formation i n the compact tension test pieces. Tensile test pieces were cut in the same manner as the CT samples. The use of the Isomet metallurgical sample saw again ensured that the sides of the samples were p a r a l l e l . Test specimens were cut from the mid—toe region and only those samples coming from above the v e r t i c a l centre region (5.5 cm from the corium) were used. Both tapered and untapered samples 3 9 were used, but i t was -found that untapered samples gave r e l i a b l e r e s u l t s while being -far eas ier to cut . There-fore, they were more genera l ly used. Sample dimensions var ied but each sample was accurate ly measured p r io r to t e s t i n g . Samp'les were - 4 - 4 in the order of 6 x 10 m t h i c k , 4 x 10 m wide and 2 .5 x - 3 10 m long. The samples were clamped above and below using - 3 pneumatic sample g r i p s , leav ing 1.2 x 10 m between (or ig ina l length of tes t sample). Due to s p e c i f i c s t r e s s patterns produced by t h i s type of clamping procedure, the displacement produced in t h i s t e s t s cannot accurate ly be determined from cross-head movement alone. The s t r a i n in the test p ieces used in t h i s study was, therefore , measured with a video dimension analyser (VDA). The change in d is tance between two surface marks on the test sample, placed well away from the sample clamps, was used to determine sample displacement, while the force was determined from the 500 Kg fo rce transducer of the Instron tes t ing machine. These were recorded together on an Ester1ine-Angus X-Y p l o t t e r , which gave a continuous record of t o t a l force and di splacement. VI. H is to logy . Selected f rac tu re tes t samples were prepared for scanning e lec t ron microscopy. Af ter dehydration to determine hydration s t a t e , the tes t sample was glued to an EM stub using s i l v e r conducting pa in t . These samples were then coated with a th in layer of go ld , using a Mikros vacuum evaporator (model VE10). 40 These prepared samples were then viewed in a Cambridge Stereoscan 250 scanning e lec t ron microscope. Photographs were taken with a Poloro id 545 camera and Poloro id P/N -Film. Thick sect ion ing (5—IO microns) of wet t i s s u e was accomplished using a s tee l kn i fe on an American Opt ical Co. * 820' microtome. The densi ty and consistency of the hoof material made embedding conveniently unnecessary. L ight micrographs were taken using e i the r a Wild p o l a r i z i n g compound microscope f i t t e d with a Wild camera or a Wild d i s s e c t i n g microscope f i t t e d with an Asahi SP500 camera. A l l l i g h t micrographs were taken using Kodak Technical Pan f i l m . 41 RESULTS T Two types of mechanical t e s t s were conducted in t h i s i n v e s t i g a t i o n . I n i t i a l l y , t e n s i l e extension t e s t s were used to determine the general s t r e s s - s t r a i n proper t ies of hoof wall kerat in and to inves t igate the e f f e c t of specimen o r ien ta t ion and hydration on these p roper t ies . Fol lowing these i n i t i a l s tud ies , an extensive ana l ys i s of f rac tu re proper t ies was c a r r i e d out to evaluate the f rac tu re toughness of hoof wall kerat in and to determine the e f f e c t of pigmentation, o r ien ta t ion and hydration on toughness. This ana l ys i s employed the compact tension test procedure. I. Stress—Strain P roper t ies : Tens i le Tests . The t e n s i l e modulus and the strength of hoof wall kerat in v a r i e s widely with hydrat ion . Therefore, t h i s account w i l l begin with a desc r ip t ion of the proper t ies of the f u l l y hydrated t i s s u e and then compare these to p roper t ies shown for other hydration cond i t ions . Typical s t ress—st ra in curves fo r f u l l y hydrated material are shown in F i g . 1 3 . The i n i t i a l port ion of the s t r e s s - s t r a i n curve has a low s lope due to s lack in the loading system. Once the specimen i s s t ressed d i r e c t l y a l i n e a r s t r e s s - s t r a i n r e l a t i o n s h i p i s seen, which can be used to determine a Young's modulus (E) for the m a t e r i a l . Beyond the i n i t i a l l i n e a r e l a s t i c region the material y i e l d s and the slope 3. T y p i c a l s t r e s s - s t r a i n curves from t e n s i l e t e s t s of f u l l y hydrated hoof w a l l k e r a t i n . • S t r e s s d i r e c t i o n p a r a l l e l to the t u b u l e s • S t r e s s d i r e c t i o n p e r p e n d i c u l a r t o t u b u l e s E - Young's modulus. Samples f a i l e d at the specimen g r i p s . <*f r o - s t r e s s l e v e l achieved at the p o i n t w y 5 % i n t e r s e c t e d by a l i n e w i t h a 5% lower s lope than the i n i t i a l modulus. 43 decreases. The y i e l d po int , de-fined as the point on the s t ress—st ra in curve in tersected by a l i n e having a s lope o-f 5% l e s s than the s lope o-f the i n i t i a l l i n e a r reg ion , occurred in t h i s case at a s t r a i n o-f about 0 .02. In the post—yield region the material was able to go through a great deal o-f s t r a i n (91% o-f t o t a l s t ra in ) with a modest increase in s t r e s s (44% o-f maximum measured s t r e s s ) . The samples genera l ly f a i l e d at the tes t g r i p s , and consequently the t rue , u l t imate strength and e x t e n s i b i l i t y of the material could not be measured for most samples. The y i e l d in the f u l l y hydrated s ta te was considered to ind ica te a change in the behaviour of the mate r ia l . The s t ress—st ra in curve resembles that shown by amorphous polymeric mater ia ls in t h e i r g lass t r a n s i t i o n . Indeed, i t i s bel ieved that the matrix polypept ide chains of hard kerat in composites, such as hoof w a l l , are convoluted but r e l a t i v e l y i n f l e x i b l e (Fraser and Macrae, 1980). It i s l i k e l y that the y i e l d s t r e s s i n d i c a t e s the s t r e s s leve l at which the weaker, secondary bonding fo rces are disrupted within the matrix . The post—yield reg ion , which al lows a great deal of s t r a i n with a small increase in s t r e s s , would i n d i c a t e an extension of the convoluted matrix polymers. The high proport ion of c r y s t a l l i n e f i b r e s and the r e l a t i v e l y high c r o s s l i n k densi ty within the matrix presumably l i m i t s the extension in the post—yield region to about 20-30%. For comparison, u n f i l l e d , l i g h t l y c ross l inked rubbers can be extended as much as 600%. 44 A. Or ientat ion E f f e c t s . Table 1 summarises the information concern ing , t e n s i l e t e s t s performed on t h i s m a t e r i a l . Since the hoof tubules cons t i tu te a consistent morphological feature , they were used to designate the o r ienta t ion of the tes t sample. Samples in which the tubule ax is was or iented p a r a l l e l to the loading d i r e c t i o n were c a l l e d long i tud ina l t e s t s while samples in which the tubule ax is was perpendicular to the loading d i r e c t i o n were termed l a t e r a l t e s t s . The long i tud ina l samples correspond to the v e r t i c a l aspect of the hoof wall and ind ica te the proper t ies in that d i r e c t i o n . The l a t e r a l samples correspond to the l a t e r a l aspect of the wall and ind ica te the proper t ies in the d i r e c t i o n p a r a l l e l to the ground contact su r face . As shown in F i g . 1 3 , the t e n s i l e p roper t ies of t h i s material appear reasonably s i m i l a r in these two o r i e n t a t i o n s . The data in Table 1 show that at the maximum hydration leve l there are no s i g n i f i c a n t d i f fe rences in s t i f f n e s s or y i e l d s t r e s s . Though not s i g n i f i c a n t l y d i f f e r e n t at t h i s hydrat ion l e v e l , the modulus and y i e l d s t r e s s of the l a t e r a l samples d id appear marginal ly greater than the long i tud ina l samples. The modulus of a f i b r e composite w i l l depend upon the r e l a t i v e angle of the ind iv idua l f i b r e s to the appl ied s t r e s s , and on the proport ion of f i b r e s with a component of t h e i r o r ienta t ion al igned with the d i r e c t i o n of the s t r e s s (Wainwright et a l , 1976). Although the obvious p a r a l l e l arrangement of the tubules 45 Table 1. Tensile Modulus of Hoof Wall Keratin. E - Young's Modulus, S.E. - Standard Error, n - sample s i z e , RH - Relative Humidity l e v e l . RH Orientation E (xlO 9 S.E. N/m2) n Y i e l d Stress (xlO 7 N/m2) S.E. n 100% Long. .410 .032 19 .918 .042 19 100% Lat. .485 .035 24 1.18 .036 22 75% Long. 2.63 . 362 5 3.89 1 75% Lat. 2. 30 .222 14 3.14 .470 5 53% Long. 3.36 .629 2 53% Lat. 5. 32 1.07 8 0% Long. 14.6 .071 2 0% Lat. 5.66 1.23 3 Long. - Tubule axis p a r a l l e l to applied stress Lat. - Tubule axis normal to applied stress 46 might suggest that the hoo-f wall i s therefore st rongly re in forced in the long i tud ina l d i r e c t i o n , po la r i zed l i g h t sect ions of the hoof wall show a marked l a t e r a l o r ien ta t ion of the f i b r e s within the in ter tubular component. Because the tubular and in ter tubu lar components are present in roughly equal q u a n t i t i e s , the r e s u l t i n g mix of f i b r e reinforcement y i e l d s a material with near ly equal p roper t ies in both d i r e c t i o n s . In f a c t , Leach (1980) found the compressional modulus in the l a t e r a l d i r e c t i o n to be 1.48 times that of the long i tud ina l o r i e n t a t i o n . Thus, i t appears that the l a t e r a l l y or iented in ter tubu lar material i s an important, and poss ib l y dominant, mechanical feature of hoof wall k e r a t i n , even though the l o n g i t u d i n a l l y or iented tubules provide a dominant s t ruc tu ra l feature . B. Hydration E f f e c t s . As seen in Table 1, the t e n s i l e modulus of hoof wall kerat in i s h igh ly dependent upon the hydration s ta te of the tes t sample. Hoof wall shows more than a twenty f o l d increase in modulus between 10071 and 071 RH in long i tud ina l tens ion . The intermediate hydrations show a progressive increase in modulus as the hydration i s decreased, in both the l a t e r a l and long i tud ina l o r i e n t a t i o n s . No s i g n i f i c a n t d i f f e r e n c e i s found between the moduli of the two o r ien ta t ions except at absolute dehydration. The low modulus determined for the l a t e r a l o r ienta t ion in the f u l l y dehydrated condi t ion may be an 47 a r t i f a c t of the t e s t i n g specimen s i z e . At very low hydrations the material becomes extremely s t i f f and b r i t t l e . Major d i s c o n t i n u i t i e s within the s t ruc ture of the material w i l l act as s t ress concentrat ion s i t e s in a material with these proper t ies (Currey,1962). In the t e n s i l e samples the tubule 4 diameter was approximately 1/3 to 1/2 the specimen width. Thus, the tubules could cause ser ious s t r e s s concentrat ions in the l a t e r a l l y or iented samples, and these s t r e s s concentrat ions might lower the apparent modulus of the m a t e r i a l . A l t e r n a t i v e l y , i t i s poss ib le that hydration a f f e c t s the proper t ies of the in ter tubu lar material d i f f e r e n t l y than the tubular material or that the v a r i a t i o n in o r ien ta t iona l a rch i tec tu re causes the apparent d i f fe rence at the lowest hydrat ion. Leach (1980) has suggested that these o r ien ta t ions of hoof wall kerat in under compression respond d i f f e r e n t l y to dehydration. Unfortunately , there i s not enough evidence provided in t h i s study to make any conclusions on t h i s po int . A comparison of the s t r e s s - s t r a i n behaviour of representat ive l o n g i t u d i n a l l y or iented t e n s i l e samples i s given in F i g . 14. Noting that energy i s equivalent to fo rce times displacement, the area under the s t ress—st ra in curve represents the energy absorbed by the material under the loading process. The long extensions which occur a f te r the y i e l d point allow a great deal of energy to be absorbed by the 10051 RH specimen. In cont rast , the dryer material (051 and 5351 RH) f a i l s at higher s t resses but much lower s t r a i n s , making the t o t a l energy absorbed l e s s . These changes in behaviour presumably r e s u l t 48 F i g . 14. Representative s t r e s s - s t r a i n curves for t e n s i l e samples stressed p a r a l l e l to the tubule axis at four hydration l e v e l s . Arrow-heads indicate samples which f a i l e d at the specimen grips. The X indicates f a i l u r e within the VDA monitoring range, therefore ultimate strength of material. The dotted l i n e indicates the test record from a 75% RH sample which f a i l e d at the specimen grips. 49 •from the increase in the secondary bonding forces that c ross l ink the matrix phase. Increased c r o s s l i n k i n g w i l l al low s t r e s s to be transmitted more d i r e c t l y from one r e i n f o r c i n g f i b r e to the next, and t h i s could cfause the composite to become more b r i t t l e . The lowest hydration condi t ions i n d i c a t e the extreme of t h i s s i t u a t i o n where the material becomes very b r i t t l e and only small amounts of energy can be absorbed before an e x i s t i n g flaw spreads across the specimen. It i s important to note that the 75% RH samples achieved much higher s t resses than the f u l l y hydrated samples, but many were s t i l l able to maintain the s t r e s s fo r long extensions. This resu l ted in the 75% RH samples absorbing the greatest amount of energy. A l l of the samples tested at 75% RH that f a i l e d between the monitoring l i n e s of the video dimension analysing system (VDA) ( ie . gave a t rue strength measure) gave a s t ress—st ra in curve resembling that in F i g . 14. The t e n s i l e proper t ies d isplayed by the hoof wall at 75% RH suggest that under t h i s condi t ion the f a i l u r e res is tance proper t ies of the material might be opt imized. At t h i s hydration leve l the a b i l i t y to r e s i s t s t ress i s combined with the a b i l i t y to absorb energy through p l a s t i c deformation. II. Fracture Invest igat ions : Compact Tension Tests . A. Fracture Tests at 100% Re la t i ve Humidity. 1. Compliance c a l i b r a t i o n . An in tegra l part of the ana l ys i s of f r a c t u r e with compact tension (CT) samples i s the 50 measurement o-f crack length . The crack length profoundly in f luences the s t r e s s i n t e n s i t y fac tor (K), the s t r a i n energy re lease ra te CG) and the J in tegra l (J) . A complex h i e r a r c h i c a l l y organized composite, such as hoof ke ra t in , poses d i f f i c u l t problems for v isua l measurement of crack growth. The crack growth in t h i s type of material w i l l l i k e l y be nei ther coplanar nor co l inear with the o r i g i n a l notch (Gaggar and Broutman, 1975), and a surface view of the crack may not represent the condi t ions respons ib le for the behaviour of the test specimen. Therefore, an i n d i r e c t method of charac te r i z ing the damage due to f rac tu re was necessary in order to analyse the f rac tu re proper t ies of t h i s m a t e r i a l . The compliance c a l i b r a t i o n method was employed, fo l lowing s i m i l a r techniques used in the study of f rac tu re of other composites inc lud ing bone. The compliance values were determined from CT t e s t s , as i l l u s t r a t e d in F i g . 1 5 . Th is f i gu re shows a t y p i c a l tes t record from a 100% RH sample. The inverse of the i n i t i a l s lope , normalized for specimen width, g ives the i n i t i a l compliance for the sample. It i s assumed that no crack growth occurred in t h i s reg ion , an assumption that i s supported by the fac t that the s t ress—st ra in curve i s l i n e a r . Specimens with var ious o r i g i n a l notch lengths were tes ted , and a consistent r e l a t i o n s h i p was found between the precut notch length and i n i t i a l mechanical compliance (F ig .16) . Polynomial regression of t h i s data gave an empir ical equation (R =0.88) which allowed the determination of the crack length d i r e c t l y from the mechanical tes t record . The crack length determined from the mechanical compliance 51 E X T E N S I O N Fig.15. Trace from a Compact Tension t e s t r e c o r d showing method o f determining apparent crack l e n g t h (a/W) from t e s t r e c o r d . 52 Fi g . 16. Compliance c a l i b r a t i o n data used to determine apparent crack length. The regression was i n i t i a l l y determined with, compliance dependent on crack length r a t i o (R =0.88). The apparent crack length r a t i o during a test was determined from the measured mechanical compliance applied to the regression of A/W dependent on Compliance. A Mean value and standard deviation of o r i e n t a t i o n 3 . • Mean value and standard deviation of o r i e n t a t i o n 4. O Mean value and standard deviation of o r i e n t a t i o n 2. 53 (apparent crack length) was c a l c u l a t e d by t a k i n g the s l o p e from the beginning of the t e s t t o any p o i n t on t h e t e s t r e c o r d d u r i n g the t e s t (Fig.15, broken l i n e ) . T h i s s l o p e was then compared t o the compliance c a l i b r a t i o n curve t o determine the apparent c r a c k l e n g t h . The compliance c a l i b r a t i o n curve at t h i s h y d r a t i o n was determined u s i n g 62 samples, a l l with the p r e c u t notch p a r a l l e l t o the t u b u l e a x i s . T h i s c a l i b r a t i o n curve was used f o r the o t h e r t h r e e o r i e n t a t i o n s as w e l l . The i n i t i a l compliance of these samples was found t o f i t the p a r a l l e l notch c a l i b r a t i o n curve (Fig.16, s p e c i f i c a l l y marked samples). C o n s i d e r i n g the s i m i l a r i t y i n t e n s i l e p r o p e r t i e s seen between o r i e n t a t i o n s , the c o n s i s t e n c y i n the compliance r e l a t i o n s h i p at t h i s h y d r a t i o n i s not s u r p r i s i n g . 2. Determination of f r a c t u r e parameters. The c a l c u l a t i o n of the s t r e s s i n t e n s i t y f a c t o r (K) and the s t r a i n energy r e l e a s e r a t e (G) a r e s t r a i g h t f o r w a r d and r e q u i r e simply the dimensions of the sample, i n c l u d i n g crack l e n g t h , and f o r c e / d e f l e c t i o n d ata. Determination of the J i n t e g r a l was s l i g h t l y more com p l i c a t e d . The energy absorbed (U) d u r i n g a t e s t was measured and p l o t t e d a g a i n s t the r a t i o of apparent crack l e n g t h t o specimen l e n g t h (A/W) f o r each sample ( F i g . 1 7 ) . Polynomial r e g r e s s i o n a n a l y s i s (P< 0.02 f o r a l l r e g r e s s i o n s ) gave an e m p i r i c a l equation f o r energy and crack l e n g t h f o r a s p e c i f i e d e x t e n s i o n , and the p a r t i a l d e r i v a t i v e of t h i s e q uation (du/da) , c o u l d be used t o determine the v a l u e of J at 54 u .010n .008-.006-.004-.002- J r .14 i .28 .42 — r -.56 — i . 7 0 a /W F i g . 17. The valuftof J was determined from the p a r t i a l derivative of energy (U) by apparent crack length (a) for each extension (q). The s o l i d l i n e represents the regression of the data. The dotted l i n e i s a v i s u a l representation of J. 55 any point during the t e s t . The -fracture analysis considered f i v e independent variables which were believed to have potential e f f e c t s on the fracture behaviour of hoof wall. They were pigmentation, v e r t i c a l location on the hoof wall, individual animal from which the sample was taken, sample orientation and hydration state. Five dependent variables were derived from the mechanical test data: cross-head d e f l e c t i o n (q), apparent crack growth (Aa), s t r e s s i n t e n s i t y factor (K), s t r a i n energy release rate (G) and the J integral ( J ) . In order to reduce the number of i n t e r a c t i n g independent variables the data were separated into subgroups which shared as many of the independent variables as possible. A oneway analysis of variance was then conducted on the dependent variables for each of the remaining independent variables. Those independent variables which did not have s i g n i f i c a n t e f f e c t s on the fracture properties of t h i s material were sequentially eliminated from the analysis. This procedure also i d e n t i f i e d independent variables which did have a s i g n i f i c a n t e f f e c t and which required special consideration in further analysis. a. Pigmentation, i n d i v i d u a l s and l o c a t i o n . The r e s u l t s of the analysis of variance and multiple comparisons for the samples tested at 100% RH with s i m i l a r notch orientation are given i n Table 2. There were no s i g n i f i c a n t differences found between the properties of the three pigmentation groups at t h i s hydration. In the 100/i RH material the level of pigmentation 56 Table 2. A. Results of analysis of variance and multiple comparisons fo r data subdivided according to pigment, i n d i v i d u a l animal and lo c a t i o n . Location l a b e l l e d as i n F i g . 9, n - sample s i z e , q - c r i t i c a l extension, a - c r i t i c a l crack length, K - c r i t i c a l Stress Intensity Factor, G -c r i t i c a l S t r a i n Energy Release Rate, J - c r i t i c a l J Integral. S i g n i f i c a n c e determined by Tukey's Honestly S i g n i f i c a n t Difference test p<0.05. q A a K G J Pigment Individual Location 5^9 B. Fracture test r e s u l t s subdivided according to lo c a t i o n . Orientation 1, Hydration 100% RH. S.E. - Standard Error. Location n q (S.E.) A a (S.E.) K (S.E.) G (S.E.) J (S.E.) (xl0 _ 3m) (xl0 _ 4m) (xl0 6N/m 3 / 2)(xl0 4N/m) (xl0 4J/m 2) 1 3 1.4 ( .06) 5. 02 ( .91) 1 .58 (.84) 5.83 (.91) 9.83 (2.2) 3 10 1.4 ( .08) 4. 73 ( .36) 1 .74 (.84) 7.42 (.76) 12.03 (1.5) 5 7 1.7 ( .16) 5. 74 ( .41) 1 .86 (1.54) 7.49 (1.04)13.54 (2.5) 7 10 1.4 ( .06) 4. 67 ( .26) 1 .72 (.69) 6.87 (.56) 11.32 (1.1) 9 5 1.1 ( .17) 5. 05 ( .76) 1 .20 (1.4) 2.70 (.56) 5.22 (.76) 9*3&5&7 9*3&5&7 5*9 57 was a s s o c i a t e d with d i f f e r e n t i n d i v i d u a l horses, consequently, no s i g n i f i c a n t d i f f e r e n c e was found between i n d i v i d u a l s i n t h i s p o r t i o n of the study e i t h e r . Having determined t h a t t h e r e are no s i g n i f i c a n t d i f f e r e n c e s due t o pigmentation and i n d i v i d u a l , i t was p o s s i b l e t o a n a l y s e the e n t i r e data s e t ( t e s t s at 100% RH and p a r a l l e l notch o r i e n t a t i o n ) a g a i n s t l o c a t i o n from which the t e s t samples were c u t . As mentioned i n the m a t e r i a l s and methods s e c t i o n , t h e r e were f i v e p o s s i b l e l o c a t i o n s from which the samples c o u l d be c u t . M u l t i p l e comparisons u s i n g Tukey's Honestly S i g n i f i c a n t D i f f e r e n c e t e s t determined t h a t the means of s e v e r a l of the a n a l y t i c parameters used were s i g n i f i c a n t l y d i f f e r e n t f o r the most d i s t a l p o r t i o n of the hoof w a l l (Fig.18 and Table 2). I t i s apparent from t h i s evidence t h a t f r a c t u r e toughness decreases s h a r p l y near the d i s t a l c o n t a c t s u r f a c e . The m a t e r i a l near t h i s s u r f a c e i s both the o l d e s t i n the hoof wall and, consequently, the most used. I t i s p o s s i b l e , t h e r e f o r e , t h a t the decrease i n f r a c t u r e toughness observed i n d i c a t e s the presence of n a t u r a l f l a w s caused by continuous mechanical use of the m a t e r i a l . b. The e f f e c t s of sample o r i e n t a t i o n . S i n c e l o c a t i o n 9 (the d i s t a l samples) was found t o be s i g n i f i c a n t l y d i f f e r e n t i n p r o p e r t i e s from the remaining samples, i t was not i n c l u d e d i n the o r i e n t a t i o n a n a l y s i s . A n a l y s i s of the remaining samples at 100% RH i n d i c a t e d s i g n i f i c a n t d i f f e r e n c e s i n f r a c t u r e c h a r a c t e r i s t i c s r e l a t e d t o o r i e n t a t i o n of the precut notch. The 58 1 1 1 1 —I 1 a 1 3 5 7 9 b VERT. L O C A T I O N F i g . 18. The mean c r i t i c a l values of stress i n t e n s i t y factor, s t r a i n energy release rate and J in t e g r a l plotted against the v e r t i c a l location on the hoof wall the sample was taken from. 1 - Top, 3 - Upper centre, 5 - Centre, 7 - Lower centre, 9 - Bottom, a - Proximal segment discarded, b - d i s t a l segment discarded. • Stress i n t e n s i t y factor, K. • Strain energy release rate, G. O j i n t e g r a l , J. Error bars indicate 95% confidence l i m i t s . 59 r e l a t i o n s h i p between notch d i r e c t i o n and morphological -features of the hoof w a l l f o r the f o u r o r i e n t a t i o n s used i n t h i s study i s g i v e n i n F i g . 19. O r i e n t a t i o n 1 c o n s i s t e d of samples i n which the pre c u t notch was p l a c e d p a r a l l e l t o the t u b u l e a x i s and, t h e r e f o r e , the notch would run i n a v e r t i c a l d i r e c t i o n i n the hoof w a l l . O r i e n t a t i o n 2 c o n s i s t e d of those samples i n which the notch was p l a c e d normal t o the t u b u l e a x i s and, consequently, r o u g h l y p a r a l l e l t o the ground c o n t a c t s u r f a c e of the hoof. As mentioned i n the d e s c r i p t i o n of the morphology of the hoof w a l l , the i n t e r t u b u l a r m a t e r i a l o r i e n t a t i o n can vary r e l a t i v e t o the t u b u l e o r i e n t a t i o n . In determining the i n t e r t u b u l a r m a t e r i a l angle f o r o r i e n t a t i o n s 1 and 2 i n Fig.19, the mean angle of i n t e r t u b u l a r m a t e r i a l f o r those samples was used. A l l of the samples used f o r o r i e n t a t i o n s 3 and 4 were s p e c i f i c a l l y s e l e c t e d so t h a t the i n t e r t u b u l a r m a t e r i a l was e o r i e n t e d at 45 r e l a t i v e t o the t u b u l e s . The CT t e s t specimens of these samples were then shaped i n r e l a t i o n t o the i n t e r t u b u l a r m a t e r i a l o r i e n t a t i o n r a t h e r than the t u b u l e s . For o r i e n t a t i o n 3 the pre c u t notch was p l a c e d normal t o the d i r e c t i o n of the i n t e r t u b u l a r m a t e r i a l and f o r o r i e n t a t i o n 4 i t was p a r a l l e l t o the i n t e r t u b u l a r m a t e r i a l . In t h i s way two s e t s of samples c o u l d be produced, each with the t u b u l e s o r i e n t e d at o 45 t o the notch but having the i n t e r t u b u l a r m a t e r i a l e i t h e r a l i g n e d with or opposed t o the advance of the cra c k d u r i n g the f r a c t u r e t e s t . The mean v a l u e s f o r the s t r e s s i n t e n s i t y f a c t o r K were not s i g n i f i c a n t l y d i f f e r e n t at the 0.05 l e v e l between the fou r 60 N F i g . 1 9 . A d i a g r a m o f t h e r e l a t i o n s h i p b e t w e e n t h e p r e c u t n o t c h a n d t h e t u b u l a r a n d i n t e r t u b u l a r m a t e r i a l f o r f o u r s a m p l e o r i e n t a t i o n s . N o t e t h a t 1 a n d 2 o r 3 a n d 4 c o u l d b e c u t f r o m t h e same s a m p l e b y a l t e r i n g t h e l o c a t i o n o f t h e n o t c h . Tubular material i s designated by s o l i d l i n e s , i ntertubular by dashed l i n e s . 61 Table 3. A. Results of analysis of variance and multiple comparisons for four orientations tested at 100% RH. Orientation labels given i n F i g . 19, n - sample s i z e , S.E. - Standard Error, q - c r i t i c a l extension, a - c r i t i c a l crack length, K - c r i t i c a l Stress Intensity Factor, G - c r i t i c a l S t r a i n Energy Release Rate, J - c r i t i c a l J In t e g r a l . q A a K G J 1*3&2 1*2&4 1*2&4 4V1&3 4*3 B. Fracture test r e s u l t s according to notch o r i e n t a t i o n . Orientation n q (S.E.) A a (S.E.) K (S.E.) G (S.E.) J (S.E.) (xl0 _ 3m) (xl0 _ 4m) (xl0 6N/M 3 / 2) (xl0 4N/m) (xl0 4J/m 2) 30 1 .46 ( .05) 4. 97 (.20) 1 .74 (.05) 7. 09 (.40) 11.92 (.86) 8 1 .80 ( .15) 6. 6 (.58) 1 .78 (.15) 4. 71 (.66) 8.01 (1.4) 9 1 .77 ( .07) 5. 54 (.51) 1 .73 (.06) 5. 92 (.39) 10.76 (1.1) 6 1 .51 ( .06) 8. 08 (.99) 1 .44 (.03) 3. 79 (.36) 4,57 (.49) 62 F i g . 20. The mean c r i t i c a l va lues of s t r e s s i n t e n s i t y f a c t o r , s t r a i n energy r e l e a s e r a t e and the J i n t e g r a l f o r four o r i e n t a t i o n s of p recut n o t c h . • S t r e s s i n t e n s i t y f a c t o r • S t r a i n energy r e l e a s e r a t e O j i n t e g r a l Lower a x i s - angle between t u b u l e a x i s and notch Upper a x i s - angle between i n t e r t u b u l a r m a t e r i a l and notch E r r o r bars i n d i c a t e 95% conf idence l i m i t s . or ien ta t ions analysed (Table 3 ) . The 95% confidence l i m i t s between o r ien ta t ions 1 and 4 d id not over lap, however (F ig .20) . This might i n d i c a t e that a d i f fe rence did ex i s t but the r igorous s t a t i s t i c a l ana lys i s tes t used in t h i s study d id not f i n d i t due to the small sample s i z e a v a i l a b l e . The mean value for the s t r a i n energy re lease ra te G from or ien ta t ion 1 was found to be s i g n i f i c a n t l y d i f f e r e n t from the values for both o r ien ta t ions 2 and 4 (Table 3 ) . Or ientat ion 3 could not be d is t ingu ished from any of the other o r ien ta t ions at the 0.05 l e v e l . The mean value fo r the J in tegra l at o r ien ta t ion 4 was found to be s i g n i f i c a n t l y d i f f e r e n t from both o r ien ta t ions 1 and 3 (Table 3 ) . For t h i s f rac tu re parameter o r ien ta t ion 2 could not be d is t ingu ished from any of the others . The lowest f rac tu re values for these parameters are c o n s i s t e n t l y associated with o r ien ta t ions in which the in ter tubu lar material i s a l igned with the precut notch (F ig .20) . At the same time, there seems to be no obvious r e l a t i o n s h i p between the o r ien ta t ion of the tubules and the notch d i r e c t i o n . Th is trend i s evident in a general way for a l l the parameters used. The J in tegra l ana l ys i s was able to demonstrate t h i s trend more c l e a r l y . It should be noted that the J in tegra l ana l ys i s technique al lows for some p l a s t i c deformation in the m a t e r i a l , and therefore probably provides the best method for charac te r i z ing the f rac tu re proper t ies of mater ia ls l i k e hoof kerat in at 100% RH. Or ientat ions 3 and 4 had s i m i l a r tubular o r ien ta t ions but opposite in ter tubular d i r e c t i o n s . The s i g n i f i c a n t three—fold d i f fe rence in f rac tu re 64 res is tance proper t ies between these two o r ien ta t ions , as determined by the J in tegra l a n a l y s i s , i nd ica tes that the in ter tubu lar material p lays an important r o l e in in f luenc ing the -fracture o-f hoo-f w a l l . A s i m i l a r comparison o-f tubule o r ienta t ion y i e l d s no s i g n i f i c a n t d i f fe rence in measured p roper t ies . In f a c t , one might a n t i c i p a t e that the f r a c t u r e res is tance would be greater fo r a notch o r ien ta t ion which ran perpendicular to the tubules (or ientat ion 2) because the f i b r e o r ien ta t ion within the tubules would present an obstac le to an advancing crack. Th is i s c l e a r l y not the case. Th is therefore provides add i t iona l evidence that the f rac tu re i s most st rongly inf luenced by the o r ien ta t ion of the in te r tubu lar mater ia l . These f r a c t u r e s tud ies ind ica te that the hoof wall material has one o r ien ta t ion which i s more susceptable to f rac tu re and possesses considerable f rac tu re res i s tance in any other d i r e c t i o n . Since t h i s s i n g l e weaker d i r e c t i o n co inc ides with the o r ien ta t ion found in the in ter tubu lar mate r ia l , i t must be concluded that the in ter tubu lar material p lays a dominant r o l e in determining the f rac tu re of t h i s mater ia l . Photographs of the f r a c t u r e path observed in the samples tested confirm t h i s conc lus ion . Cracks r e s u l t i n g from f rac tu re fol lowed the d i r e c t i o n of the in ter tubu lar o r ien ta t ion regardless of the tubular o r i e n t a t i o n . Th is e f f e c t can be most e a s i l y seen by comparing photographs of the in ter tubu lar normal (or ientat ion 3) and in ter tubu lar p a r a l l e l (or ientat ion 4) o r i e n t a t i o n s . In these two cases the tubular mater ial l i e s at a consistent 45 to the notch plane. However, the crack can be 65 seen to -follow the in ter tubu lar o r ien ta t ion in s p i t e o-f the •fact that the CT test regime i s designed to d r i ve the crack p a r a l l e l to the o r i g i n a l notch plane (F ig .21) . Th is r e s u l t can be ant ic ipated s ince the data shown in F i g . 2 0 ind ica tes that i t i s eas ier in terms o-f e i ther s t r e s s or energy to -fracture along the plane of the in ter tubu lar m a t e r i a l . Micrographs of th in sect ions taken from the CT samples ind icate more c l e a r l y how the crack was d iver ted by the o r ien ta t ion of the in te r tubu lar material (F ig .22) . In s p i t e of the notch being placed within a tubule , i t was d iver ted to the in te r tubu lar m a t e r i a l . It i s a l so poss ib le to see a number of f rac tu re cracks eminating from the s i n g l e precut notch. Th is i l l u s t r a t e s one of the poss ib le mechanisms a v a i l a b l e in the design of t h i s f i b r e composite which increases the toughness of the mate r ia l . More energy i s absorbed through the c reat ion of many surfaces than through the c reat ion of a s i n g l e f rac tu re sur face . B. E f f e c t s of Hydration State . Compliance c a l i b r a t i o n curves were used to determine the apparent crack length of specimens tested at other hydration l e v e l s , in the same manner as the 100% RH data . The compliance c a l i b r a t i o n r e l a t i o n s h i p s of these hydrat ions were found to be best represented by l i n e a r regress ions over the notch lengths used in t h i s study. The four c a l i b r a t i o n curves are shown in F i g . 2 3 . A l l regress ions were found to be s i g n i f i c a n t . 66 F i g . 21. Photographic comparison of the crack path i n samples tested in orientations 3 and 4 . The white s t r i p continuing from the end of the precut notch i s the crack path. Note i n o r i e n t a t i o n 3 that the crack proceeds at r i g h t angles to the axis of the notch. Polarized l i g h t micrograph of a section taken from a Compact Tension sample, showing the crack pattern that developed. The sample was hydrated at 100% RH. N - t i p of precut notch, I - i n t e r t u b u l a r material, T - tubular material, A - crack running along the intertubular-tubular i n t e r f a c e , B - crack diverted to the o r i e n t a t i o n of the intertubular material, a f t e r passing around tubule. Scale bar = 100 uro. .2 C o ( * 1 0 " 8 ) m / N F i g . 23. Compliance c a l i b r a t i o n curves determined f o r four hydration l e v e l s . , 100% RH: A/W = 0.21196119 + 3.4139645 x 10 (C e) - 6.6528977 x 1 0 1 2 ( C o ) 2 + 4.118235 x 1 0 1 8 (C„) 3 (p < 0.001) 75% RH: A/W = 0. 23706 + 7.18884 x 10 (C e) (p< 0.025) 53% RH: A/W = 0. 257563 + 1.20914 x 10 7 (C e) (p<0.025) 0% RH: A/W = 0. 282584 + 1.32607 x 10 7 (C 0) (p<0.010) 69 1. Pigmentation, i n d i v i d u a l and l o c a t i o n . Table 4 summarizes the m u l t i p l e comparisons -for pigmentation, between i n d i v i d u a l s and -for v e r t i c a l l o c a t i o n on the hoo-f w a l l . As with the 100% RH samples, no d i f f e r e n c e was found i n the p r o p e r t i e s a s s o c i a t e d with the t h r e e pigmentation l e v e l s except i n the 53% RH samples. In t h i s case the means f o r c r i t i c a l crack growth (A), s t r e s s i n t e n s i t y (K) and s t r a i n energy r e l e a s e r a t e (G) were found t o be s i g n i f i c a n t l y d i f f e r e n t f o r t h e pigmented and p a r t i a l l y pigmented samples. The means of the J i n t e g r a l f o r both the p a r t i a l and unpigmented samples were found t o be s i g n i f i c a n t l y d i f f e r e n t from t h a t of the pigmented samples. T h i s i s not c o n s i d e r e d a meaningful e v a l u a t i o n , however. The f u l l y pigmented samples of t h i s h y d r a t i o n l e v e l were made up of samples taken from two d i f f e r e n t i n d i v i d u a l s . The a n a l y s i s of v a r i a n c e f o r i n d i v i d u a l s at 53% and 0% RH r e v e a l e d t h a t the i n d i v i d u a l s concerned had s i g n i f i c a n t l y d i f f e r e n t p r o p e r t i e s (Table 4 ) . Not enough data are a v a i l a b l e t o determine i f v a r i a t i o n of p r o p e r t i e s e x i s t between the s e i n d i v i d u a l s , and t h e r e f o r e , the samples were c o n s i d e r e d as a s i n g l e p o p u l a t i o n i n subsequent a n a l y s e s . No s i g n i f i c a n t d i f f e r e n c e s were found f o r any of the f r a c t u r e parameters as a f u n c t i o n of l o c a t i o n i n the hoof at the lower h y d r a t i o n l e v e l s . Having d e a l t with the above v a r i a b l e s , the e f f e c t of h y d r a t i o n s t a t e on the f r a c t u r e of hoof w a l l can be analysed. I t has been determined t h a t notch o r i e n t a t i o n can have a profound e f f e c t on f r a c t u r e p r o p e r t i e s i n t h i s m a t e r i a l . I t i s important, then, t o i s o l a t e o r i e n t a t i o n a l e f f e c t s from 70 Table 4. Results of analysis of variance and multiple comparisons f o r Compact Tension test specimens at the various locations tested. Location denoted by number corresponding to F i g . 9. Orientation 1. q - c r i t i c a l extension, a - c r i t i c a l crack length, K - Stress Intensity Factor, G - St r a i n Energy Release Rate, J - c r i t i c a l J Integral. Individual animals given s p e c i f i c numbers, pigment classes; 1 - pigmented, 2 - unpig., 3 - p a r t i a l . Hydration q A a K G J 100% Pigment Individual Location 5*9 9*3&5&7 9*3&5&7 5*9 75% Pigment Individual Location 53% Pigment Individual 4*2&5 Location — 1*3 1*3 4*2&5 1*3 4*3&5 1*2&3 4*2&3&5 0% Pigment Individual Location 2*3&4 4*2 2*3&4 71 hydration e f f e c t s . This has been accomplished by analysing hydration e f f e c t s within one o r ien ta t iona l group, those having the precut notch or iented p a r a l l e l to the tubules (or ientat ion 1). The e f f e c t of dehydration on tubule normal f r a c t u r e (or ientat ion 2) i s a lso analysed. 2. Notch p a r a l l e l to the tubule a x i s : Or ientat ion 1. Table 5 g ives the data determined for the hydration e f f e c t s analysed in t h i s study fo r samples in o r ien ta t ion 1. The data are a lso p lo t ted in F i g . 2 4 . The s t ress i n t e n s i t y fac to r (K) i s found to increase s i g n i f i c a n t l y with a decrease in humidity from lOOV. to 757. RH. At t h i s point i t reaches a maximum which i s maintained in the lower hydration s t a t e s . Th is ind ica tes that the s t r e s s necessary to i n i t i a t e f rac tu re in the material reaches a maximum at t h i s moderate hydration leve l and i s comparable in a l l of the lower hydration s t a t e s . The s t r a i n energy re lease ra te (G) has i t s maximum at the 100% RH l e v e l , and the s t r a i n energy drops s t e a d i l y to the 53% RH l e v e l . It drops l e s s r a p i d l y to the 0% RH l e v e l . The s t r a i n energy re lease ra te can t h e o r e t i c a l l y be considered in terms of energy necessary to produce new crack sur face . A drop in G ind ica tes l e s s energy i s being absorbed in the crack growth process. The dryer samples were observed to possess a percept ib ly smoother crack surface than the hydrated samples. The high values of G at high hydration l e v e l s are probably re la ted to the complex path the crack i s forced to take during f r a c t u r e . 72 Table 5. A. Results of analysis of variance and multiple comparisons ( l o c a t i o n 9 excluded f o r 100% RH analysis) subdivided according to hydration, n - sample s i z e , S.E. - Standard Error, q - c r i t i c a l extension, a - c r i t i c a l crack length, K - c r i t i c a l Stress Intensity Factor, G - c r i t i c a l S t r a i n Energy Release Rate, J - c r i t i c a l J Integral. A a a l l groups 4*1&2&3 1*2&3&4 2*3&4 1*3 d i f f e r e n t 1*2&3&4 1*2&3&4 2*1&3&4 B. Fracture test r e s u l t s according to hydration l e v e l , Orientation 1. Hydration n q (S.E.) A a (S.E.) K (S.E.) G (S.E.) J (S.E.) (xl0~ 3m) (xl0 _ 4m) (xl0 6n/m 3 / 2)(xl0 4N/m) (xl0 4J/m 2) 100% 30 1.46 ( .05) 4. 97 (.20) 1. 74 (.05) 7.09 ( .34) 11. 93 ( .90) 75% 16 1.11 ( .07) 3. 86 (.38) 3. 82 (.21) 5.02 ( .50) 22. 82 ( .31) 53% 28 .66 ( .05) 3. 08 (.18) 3. 68 (.24) 2.24 ( .27) 5. 63 ( .54) 0% 16 .44 ( .04) 2. 0 (.37) 3. 71 (.26) 1.23 ( .15) 8. 73 ( .97) 73 25 n 15 o x O o r 50 — i — 100 I 75 T " 53 T " 0 30 E o X - 1 0 HY DR ATI ON <% RH) F i g . 24. Mean c r i t i c a l values of stress i n t e n s i t y factor, s t r a i n energy release rate and J i n t e g r a l at four hydration l e v e l s . • Stress i n t e n s i t y factor, K. • Strain energy release rate, G. O J i n t e g r a l , J. Error bars indicate 95% confidence l i m i t s . 74 In a g e n e r a l s e n s e , t h e J i n t e g r a l a p p e a r s t o r e s u l t -from an i n t e r a c t i o n o-f K and G. A t 100% RH, J h a s a m o d e r a t e v a l u e . A t 7 5 % RH, J i n c r e a s e s s h a r p l y , a s d i d K, bec o m i n g j u s t l e s s t h a n t w i c e t h e 1007. RH v a l u e . A t 5 3 % RH, t h e v a l u e o f J f a l l s t o l e s s t h a n t h e 100% RH v a l u e w h i l e t h e v a l u e o f K r e m a i n s c o n s t a n t . T h i s a p p e a r s t o be an e x a g g e r a t e d r e s p o n s e t o t h e d r o p i n s t r a i n e n e r g y r e l e a s e r a t e <G). The J i n t e g r a l i s a p p a r e n t l y u n c h a n g e d between 5 3 % and 0% RH. The J i n t e g r a l i s a measure o f t h e t o t a l e n e r g y a v a i l a b l e f o r c r a c k g r o w t h . T h e r e i s no d i s c r i m i n a t i o n i n t h e J i n t e g r a l a n a l y s i s between t h e mechanism o f crack g r o w t h ( i e . t h e s t r e s s a t t h e c r a c k t i p ) o r t h e p r o c e s s o f c r a c k g r o w t h ( i e . t h e c r e a t i o n o f new crack s u r f a c e s ) . I t i s n o t s u r p r i s i n g , t h e n , t h a t t h e v a l u e o f t h e J i n t e g r a l measured would r e p r e s e n t an i n t e r a c t i o n o f t h e s e two a s p e c t s o f t h e f r a c t u r e o f t h e m a t e r i a l . The v a l u e o f J i s n o t s t r i c t l y an a d d i t i v e c o n s e q u e n c e o f K and G b e c a u s e t h e u n i t s and method o f d e t e r m i n i n g t h e s e p a r a m e t e r s a r e n o t d i r e c t l y c o m p a r a b l e . The d a t a p r e s e n t e d h e r e d o e s , however, i n d i c a t e t h a t J r e p r e s e n t s a q u a l i t a t i v e c o m b i n a t i o n o f t h e o t h e r two f r a c t u r e p a r a m e t e r s . S i n c e t h e t e c h n i q u e s e m p l o y e d i n t h i s s t u d y a l l o w e d t h e c o n t i n u o u s m o n i t o r i n g o f a p p a r e n t c r a c k g r o w t h i n t h e s a m p l e s , i t was p o s s i b l e t o a n a l y s e t h e e f f e c t o f h y d r a t i o n on t h e c r i t i c a l amount o f c r a c k g r o w t h a t f a i l u r e . G r i f f i t h (1920) showed t h a t t h e r e s h o u l d be a c r i t i c a l l e n g t h o f crack g r o w t h a t w h i c h p o i n t t h e e n e r g y a v a i l a b l e t o p r o p a g a t e t h e c r a c k i s e q u a l and becomes g r e a t e r t h a n t h a t n e c e s s a r y t o c a u s e f r a c t u r e 75 (see Fracture Mechanics, sec . 3 ) . A complex material such as hoo-f wall w i l l not -fit G r i f f i t h ' s model p r e c i s e l y , but the data •from t h i s study ind ica te a regular r e l a t i o n s h i p between hydration and extent o-f apparent crack growth at the c r i t i c a l •fracture point (F ig .25) . Th is ind ica tes that at the lowest hydration leve l the c r i t i c a l crack growth i s l e s s than hal f that necessary at the highest hydration l e v e l . In other words, f rac tu re i s s tab le in the higher hydration s ta tes fo r a longer d istance of crack growth. It should be noted, however, that even at the lowest hydration condi t ion t h i s material d i sp lays considerable f rac tu re r e s i s t a n c e , which cont ro l s the spread of a propagating crack. A mere 2 1/2 f o l d decrease in c r i t i c a l crack growth at f rac tu re i n d i c a t e s a conservat ive response of crack growth proper t ies in t h i s material as a consequence of the 15 f o l d increase in s t i f f n e s s which r e s u l t s from dehydrati on. It i s obvious from t e n s i l e t e s t s that hydration s ta te profoundly a f f e c t s the mechanical p roper t ies of t h i s mate r ia l . At extremely low hydrations the material becomes very s t i f f , and appears to become very b r i t t l e . At extremely high hydration s ta tes the material has r e l a t i v e l y low s t i f f n e s s and low y i e l d s t rength , but i s capable of long extensions before f a i l u r e . At intermediate hydration (75% RH) the material i s s t i f f , strong and capable of absorbing large amounts of energy. The d i r e c t evaluat ion of f r a c t u r e toughness using the CT test regime confirms these q u a l i t a t i v e impressions from the t e n s i l e t e s t s , but ind ica te that even while under condi t ions of extreme 76 F i g . 25. Mean apparent crack growth at f a i l u r e for four hydration l e v e l s . Error bars indicate 95% confidence l i m i t s . 77 dehydration t h i s material d isp lays considerable crack res i s tance . 3. Notch normal to tubule a x i s . One a l te rnate o r ien ta t ion was tested at the 07. RH s t a t e , that o-f o r ien ta t ion 2, with the notch or iented normal to the tubular horn. The ana lys i s ind ica tes a s i g n i f i c a n t d i f fe rence to the p a r a l l e l or iented samples at the same hydration as well as a s i g n i f i c a n t d i f fe rence to tubular normal samples at 100% hydration (Table 6) . No data are a v a i l a b l e regarding the locat ion of these samples. The mean value of J fo r o r ienta t ion 2 was found to be 757. of the p a r a l l e l value at 1007. RH, while at 07. RH J was determined to be only 48% of the p a r a l l e l value. This i n d i c a t e s that the process of dehydration has a much greater e f f e c t on the r e l a t i v e f rac tu re proper t ies in the d i r e c t i o n normal to the tubules (#2) than i t does in the d i r e c t i o n p a r a l l e l to the tubules (#1). S imi la r values were found for most of the other f rac tu re parameters. Table 6. Results of comparison of dehydrated samples tested at two ori e n t a t i o n s . S.E. - Standard E r r o r , n - sample number, q - c r i t i c a l extension, a - c r i t i c a l crack growth, K -c r i t i c a l Stress Intensity Factor, G - c r i t i c a l S t r a i n Energy Release Rate, J - c r i t i c a l J Integral, o r i e n t a t i o n as i n F i g . 19. Orientation n q (S.E.) A a (S.E.) K (S.E.) G (S.E.) J (S.E.) (xl0 _ 3m) (xl0" 4m) (xl0 6N/m 3 / 2)(xl0 4N/m) (xl0 4J/m 2) 1 21 2 12 0.44 (.15) 1.64 (.93) 3.76 (.82) 1.27 (.46) 8.45 (3.3) 0.32 (.11) 3.45 (2.4) 2.44 (.75) 0.43 (.18) 4.09 (2.8) 79 DISCUSSION I. Behaviour o-f the Fracture Parameters K, G and J. The design o-f the mechanical analysis techniques employed in t h i s study allowed a continuous monitoring o-f the three main -fracture c r i t e r i a as well as apparent crack growth ( A a). The evaluation of these engineering fracture c r i t e r i a in the context of the unusual properties displayed by the biomaterial being investigated was a major objective of t h i s study. Some representative examples are shown in t h i s section in order to indicate the r e l a t i o n s h i p between the three fracture c r i t e r i a and the apparent crack growth during the course of a fracture characterization t e s t . A. The Stress Intensity Factor, K. The c a l c u l a t i o n of the stress i n t e n s i t y factor, K, i s based on several assumptions which r e s t r i c t the computational analysis to one which i s both expedient and, s t r i c t l y speaking, inapplicable to real materials. T h e o r e t i c a l l y the material being analysed must be i s o t r o p i c and l i n e a r l y e l a s t i c . The test specimen must be s u f f i c i e n t l y thick to produce a s i t u a t i o n of plane s t r a i n at the crack t i p in order to maintain the stress conditions that the analysis assumes, without interference from boundary conditions. In an ideal material no crack growth 80 would occur u n t i l the c r i t i c a l s t r e s s i n t e n s i t y l e v e l was reached. At t h i s p o i n t crack growth would begin and c o n t i n u e as long as the c r i t i c a l s t r e s s i n t e n s i t y was maintained. A p l o t of K vs. A a would then be a s t r a i g h t h o r i z o n t a l l i n e . In non — i d e a l m a t e r i a l s i t i s p o s s i b l e f o r p l a s t i c deformation and/or slow s t a b l e crack growth t o occur. In t h i s case a s l i g h t i n c r e a s e i n crack l e n g t h would be e v i d e n t as the K v a l u e i n c r e a s e d . Although some crack growth would take p l a c e , f r a c t u r e would not become u n s t a b l e u n t i l the s t r e s s i n t e n s i t y l e v e l reached a c r i t i c a l v a l u e . T h i s c r i t i c a l v a l u e need not be i n d i c a t e d by an abrupt change i n the K vs. A a curve but a smooth cu r v e i n d i c a t e s an e x t e n s i v e p l a s t i c deformation and/or crack damage zone. The continuous behaviour of K f o r f o u r samples r e p r e s e n t i n g the h y d r a t i o n c o n d i t i o n s employed i n t h i s study p l o t t e d a g a i n s t apparent crack growth i s shown i n F i g . 26. At the 100% RH l e v e l (Fig.26 A) a smoothly c u r v i n g , c o n t i n u o u s l y i n c r e a s i n g s t r e s s i n t e n s i t y v a l u e i s seen. The c r i t i c a l p o i n t determined from the t e s t r e c o r d 5% s l o p e d e v i a t i o n method i s i n d i c a t e d by the l a r g e s t a r . The smooth r i s e of K as a f u n c t i o n of crack growth shows slow s t a b l e c r a c k i n g i s t a k i n g p l a c e . T h i s behaviour i s i n d i c a t i v e of f r a c t u r e with plane s t r e s s i n the v i c i n i t y of the crack t i p (Pook and Smith,1979). An abrupt change i n K vs. Aa, i n d i c a t i n g an unambiguous v a l u e of K, i s not seen f o r t h i s m a t e r i a l u n t i l h y d r a t i o n l e v e l s of 53% RH or lower (Fig.26 C & D). At these lower h y d r a t i o n l e v e l s u n s t a b l e f r a c t u r e was obvious, and the 81 Stress i n t e n s i t y factor (K) plotted against apparent crack growth (DELTA a) during a te s t for representative samples at four hydration l e v i e s . A - 100% RH, B - 75% RH, C - 53% RH, D - 0% RH. c r i t i c a l f a i l u r e point determined from 5% ^ d e f l e c t i o n of load/displacement record. 82 d e t e r m i n a t i o n o-f the c r i t i c a l K v a l u e was not an a r b i t r a r y matter. At 75% RH t h i s m a t e r i a l was a b l e t o r e s i s t u n s t a b l e f r a c t u r e even at e l e v a t e d s t r e s s i n t e n s i t y l e v e l s . B. S t r a i n Energy Release Rate, G. The s t r a i n energy r e l e a s e r a t e , G, i s , l i k e K , a l i n e a r e l a s t i c f r a c t u r e parameter and, t h e r e f o r e , depends on the same b a s i c assumptions. Again, i n an i d e a l m a t e r i a l no crack growth should occur u n t i l the c r i t i c a l v a l u e of G i s a t t a i n e d , at which p o i n t crack growth would occur as long as the c r i t i c a l G v a l u e were maintained. A p l o t of G vs. A a should, t h e o r e t i c a l -l y , y i e l d a s t r a i g h t h o r i z o n t a l l i n e . If p l a s t i c deformation or damage i s present at the crack t i p some apparent crack growth w i l l be e v i d e n t . The v a l u e of G w i l l c o n t i n u e t o i n c r e a s e u n t i l t he c r i t i c a l l e v e l of G i s reached and u n s t a b l e f r a c t u r e w i l l o c cur. As f o r K , the more abrupt the change i n 6 vs. A a, the more c o n f i d e n c e can be p l a c e d i n i t i n d i c a t i n g a c r i t i c a l f a i l u r e c r i t e r i o n . The continuous behaviour of G f o r the same f o u r samples analysed f o r K are shown i n Fig.27. The 100% RH sample (Fig.27 A) d i s p l a y s a smoothly c u r v i n g , c o n t i n u o u s l y i n c r e a s i n g r e l a t i o n s h i p . T h i s s i t u a t i o n i s again i n d i c a t i v e of f r a c t u r e i n m a t e r i a l s under c o n d i t i o n s of plane s t r e s s i n the v i c i n i t y of the crack t i p (Broek, 1978). The c o n s t a n t l y i n c r e a s i n g v a l u e of G i n d i c a t e s the f o r m a t i o n of a d d i t i o n a l p l a s t i c deformation i n m a t e r i a l at the crack t i p as the crack grows s t a b l y . T h i s 83 Fi g . 27. Strain energy release rate (G) plotted against apparent crack growth (DELTA a) during a test for representative samples at four hydration l e v e l s . A - 100% PH, B - 75% RH, C - 53% RH, D - 0% RH. -A C r i t i c a l f a i l u r e point determined from 5% ^ d e f l e c t i o n of load/displacement record. mechanism accounts -for absorbed in the f rac tu re condi t i ons. Fracture w i l l occur in a material when the value of G i s equal to the energy absorbed by the f rac tu re process. In an ideal m a t e r i a l , f rac tu re energy i s re leased in the formation of new f rac tu re sur face . However, in the presence of p l a s t i c deformation, more energy must be suppl ied to form a new p l a s t i c zone before more f rac tu re can occur. The material then appears to become more tough as the crack extends. Unstable f rac tu re occurs when the energy a v a i l a b l e for crack growth i s greater than that necessary to produce new surfaces and create new p l a s t i c zones as the crack extends. This w i l l occur when the material i s able to achieve high s t r a i n energy l e v e l s r e l a t i v e to the amount of energy absorbed by the p l a s t i c zone. This i s the s i t u a t i o n seen for the 75% RH sample (F ig .27 B) . It was seen in F ig .24 that t h i s material i s capable of a t ta in ing high s t r e s s i n t e n s i t y l e v e l s p r i o r to f a i l u r e . However, the material i s a lso s i g n i f i c a n t l y s t i f f e r at t h i s hydration leve l (Fig.14 and Table 1). This greater s t i f f n e s s means the p l a s t i c zone w i l l be smaller at t h i s hydration l e v e l . As a consequence of these two f a c t o r s , more s t r a i n energy i s stored than i s needed fo r crack growth, and thus, once the c r i t i c a l condi t ion i s achieved unstable f rac tu re w i l l fo l low. The s t r a i n energy re lease ra te i s lower fo r t h i s hydration than at 100% RH because l e s s energy i s absorbed in p l a s t i c deformation in the material near the crack t i p . Th is same unstable f rac tu re 84 the high l e v e l s of s t r a i n energy of t h i s material under high hydration 85 condi t ion i s ind icated -for the lower hydration l e v e l s as well (F ig .27 C & D) . The magnitude o-f G i s progress ive ly lower under these l a t t e r hydration condi t ions because the material i s again sti-f -fer and would have even smaller p l a s t i c de-formation zones than that found in the 75% RH sample. C. The J In tegra l . The J in tegra l ana lys i s technique i s derived from a path independent charac te r i za t ion of the energy l e v e l s around the crack t i p . The path independance al lows the most convenient contour to be chosen for the determination, i e . the specimen boundaries. The path independence of the J i n t e g r a l , however, i s dependent on the deformation theory of p l a s t i c i t y which does not allow for unloading of the material to occur (Broek, 1978). In cases where large sca le p l a s t i c i t y occurs near the crack t i p , slow s tab le f rac tu re w i l l r e s u l t . During slow crack growth unloading of mater ial behind the crack t i p i s i n e v i t a b l e . The J in tegra l does not s t r i c t l y apply to slow s tab le crack growth and should be r e s t r i c t e d only to an a n a l y s i s of crack i n i t i a t i o n . The shape of the J vs . A a curve has been used to ind ica te the process of deformation and crack growth in metals (Kobayashi et a l , 1979; Landes and McCabe, 1979). It has been shown that the J vs . A a curve fo r m e t a l l i c mater ia ls d i sp lays an i n i t i a l l i n e a r region possessing a r e l a t i v e l y steep s lope . Th is corresponds to notch rounding occurr ing at the notch t i p 86 p r i o r to t rue crack growth. Once crack growth i s i n i t i a t e d a new r e l a t i o n s h i p between J and A a i s seen, and the slope decreases. The point at which the abrupt change in slope takes place and t rue crack growth begins i s used as the material f rac tu re c r i t e r i o n (F ig .28) . The J values fo r two specimens tested at 100% RH are shown in F i g . 2 9 A & B. It i s evident that these r e l a t i o n s h i p s are not i d e n t i c a l to the pattern seen in metals. However, d i s c o n t i n u i t i e s are seen which correspond well with the a r b i t r a r i l y chosen 5% dev iat ion va lue. The d i s c o n t i n u i t y in the J vs. A a r e l a t i o n s h i p ind ica tes a change in f rac tu re proper t ies c o n s i s t e n t l y associated with the c r i t i c a l f a i l u r e po int . As mentioned, the meaning of the J in tegra l beyond the crack i n i t i a t i o n point i s not well understood. At 75% RH the J in tegra l curve had the same general shape as the 100% RH curve (Fig.29 C) . However, the curve d id not extend for as long a range, r e f l e c t i n g the lower extensions at which the 75% RH specimens f a i l e d . Again, the c r i t i c a l value determined by the * 5% dev iat ion method corresponded well with the i n f l e c t i o n of the J curve. At the lower hydration condi t ions (53% and 0% RH) (F ig .29 D S< E) the J in tegra l appears to take on a more c l a s s i c form. There are three d i s t i n c t phases to the f r a c t u r e process fo r t h i s type of t e s t : (1) The value of J increases with l i t t l e or no increase in apparent crack growth, (2) a l i n e a r region appearing s i m i l a r to notch b lunt ing occurs with ind i ca t ions of F i g . 28. J i n t e g r a l plotted against crack growth and physical i n t e r p r e t a t i o n for a m e t a l l i c material (after Kobayashi et al., 1979) . 88 F i g . 29. J i n t e g r a l (J) plotted against apparent crack growth (DELTA a) during a test from representative samples at four hydration l e v e l s . A and B - 100% RH, C - 75% PH, D - 53%, E - 0% RH. •C r i t i c a l f a i l u r e point determined from 5% d e f l e c t i o n of load/displacement record. 89 small sca le apparent crack growth, (3) unstable -fracture at J values near those determined from c r i t i c a l point est imat ion . Due to the unstable nature of f a i l u r e at these hydration l e v e l s and the resu l tant lack of cons istent data the true r e l a t i o n s h i p between J and A a, cannot be accurate ly determined. D. The App l i ca t ion of Engineering Fracture Parameters to B i o l o g i c a l Systems. The r e s t r i c t i o n s of l i n e a r e l a s t i c i t y and s t ruc tu ra l isotropy l i k e l y i n v a l i d a t e the absolute quant i ta t i ve values determined for K and G, except poss ib ly at the lower hydration l e v e l s . However, t h i s study i s i n t e r n a l l y cons istent and, as a consequence, the r e l a t i v e values determined represent a consistent charac te r i za t ion of r e l a t i v e f r a c t u r e p roper t ies under the condi t ions o u t l i n e d . The general agreement seen between the several analyses employed combined with the general material p roper t ies and morphological evidence support t h i s asse r t i on. The J in tegra l ana l ys i s technique was o r i g i n a l l y designed in an attempt to extend the a p p l i c a b i l i t y of f rac tu re mechanics ana lys i s beyond the l i near e l a s t i c r e s t r i c t i o n s and allow for ' reasonable ' amounts of p l a s t i c i t y . Although not a widely used technique fo r the ana lys i s of composite mater ia l s , t h i s study ind ica tes that i t i s qu i te u s e f u l . It y i e l d s r e s u l t s consistent with those a n t i c i p a t e d , where enough i s known about the material to a n t i c i p a t e r e s u l t s ( ie . The agreement of the J 90 in tegra l data and the t e n s i l e p r o p e r t i e s ) . However, i t i s l i k e l y that the p l a s t i c p roper t ies of b iomater ia ls in genera l , and c e r t a i n l y the hoof wall at higher hydrat ions, take the a p p l i c a b i l i t y of the J ana l ys i s to i t s very l i m i t s . Taking these l i m i t a t i o n s in to account, the J in tegra l probably provides the best means of charac te r i z ing the f rac tu re proper t ies of a material such as hoof k e r a t i n . Again, the absolute quant i ta t i ve values determined may not be r e l i a b l e in l i g h t of the extensive p l a s t i c deformation t h i s material i s capable of . The r e l a t i v e values are dependable, however, due to the consistency of the comparisons, and as ind icated by the consistency of the r e s u l t s . Absolute charac te r i za t ion of the f rac tu re proper t ies of most mater ia ls i s a tenuous business and much more so fo r b iomater ia ls . The techniques appl ied in the present study have been derived d i r e c t l y from engineering ana lys i s techniques. An attempt has been made to maintain the i n t e g r i t y of the a n a l y t i c a l techniques in every manner except bas ic purpose. The techniques employed were o r i g i n a l l y designed to character i ze the proper t ies of mater ia ls under s p e c i f i c mechanical circumstances, fo r the expressed purpose of q u a n t i t a t i v e l y p red ic t ing t h e i r behaviour once they have been fashioned in to a funct ional s t ruc tu re . In t h i s study, however, the s t ructure has long s ince been fashioned, and i t s f u n c t i o n a l i t y proved in bet ter ways than any a n a l y t i c a l test could determine. The question posed in t h i s study, e s p e c i a l l y cons ider ing how l i t t l e i s known of t h i s s t ruc tu re or the material from which i t i s made, i s not 'how much?', as i t i s in engineering a n a l y s i s , but simply 'how?' . In what manner and under what condi t ions do the independent va r iab les analysed af-fect the growth o-f cracks in t h i s mater ia l? The question o-f absolute magnitude becomes a secondary -feature o-f the a n a l y s i s . In t h i s context the ana l ys i s employed provides a convenient and adequate method to gain ins ight i n to h i the r to unrecognized aspects o-f the - funct ional i ty o-f the hoo-f wall mechanical design. II. Funct ional Design o-f Hoof Wal l . The morphology of the hoof wall i nd ica tes that i t i s a h i e r a r c h i c a l l y organized t i s s u e with important s t r u c t u r e - f u n c t i o n r e l a t i o n s h i p s at several d i f f e r e n t l e v e l s . This d iscuss ion w i l l begin with the design of t h i s t i s s u e at the molecular leve l and work up in sca le descr ib ing the funct ional s i g n i f i c a n c e of each cont r ibut ing l e v e l . The aim i s to ind ica te the subt le mechanical design features that produce the funct iona l p roper t ies of t h i s t i s s u e , i t s e l f an in tegra l component of the foot organ. A. Molecular Design of Kerat in as a Composite M a t e r i a l . Hard k e r a t i n , an extremely important s t ruc tu ra l material in mammals, i s u n i v e r s a l l y produced as a composite containing long th in f i b r e s embedded in a p a r t i a l l y c r o s s l i n k e d , amorphous matrix . Th is i s not simply an inc identa l s i t u a t i o n , e s p e c i a l l y 92 in the hoof w a l l , because t h i s design can be explained in terms of s p e c i f i c funct ional requirements. The funct ion of the hoof wall as a contact and supporting s t ructure requ i res that i t possess a reasonable amount of s t i f f n e s s . Long th in f i b r e s work well in tension but in bending or compression the f i b r e s can s l i d e r e l a t i v e to each other or i n d i v i d u a l l y buckle ( F i g . l ) . Mater ia ls which must funct ion under compression or bending loads requ i re a matrix which can bind and withstand shear fo rces between the f i b r e s . In f i b r e g l a s s the r e s i n funct ions in t h i s r o l e . The mechanical p roper t ies d isplayed by a composite material can be very d i f f e r e n t from those of e i ther of the components (Wainwright et a l . , 1976). These d i f fe rences can be displayed in both the s t ress—st ra in behaviour or the f rac tu re toughness of the m a t e r i a l . Genera l ly , the s t i f f n e s s of the composite w i l l r esu l t from an i n t e r a c t i o n of the proper t ies of the component phases, the r e l a t i v e proport ions of each and the o r ien ta t ion of the f i b r e s r e l a t i v e to the s t r e s s . For a given s i t u a t i o n of f i b r e o r ien ta t ion and composit ion, an a l t e r a t i o n in the s t i f f n e s s of the matrix w i l l be t rans la ted in to changes in the proper t ies of the m a t e r i a l . An extens ib le matrix w i l l al low the f i b r e s to move r e l a t i v e to each other to a c e r t a i n degree and the material w i l l be more ex tens ib le . The opposite i s t rue for a very r i g i d matrix . The f r a c t u r e behaviour of a composite w i l l a l so be af fected by the f i b r e and matrix p roper t ies and by the i r 93 i n t e r a c t i o n . I f the matrix i s e x t e n s i b l e , f r a c t u r e energy can be absorbed through deformations between f i b r e s w h i l e the r i g i d i t y of the m a t e r i a l i s maintained by the s t i f f n e s s of the f i b r e s . T h i s a l l o w s s t r a i n energy t o be d i s p e r s e d t o areas away from the l o c a t i o n of the crack. Crack growth i s i n h i b i t e d because l e s s energy i s a v a i l a b l e at the crack t i p and because the s t r e s s c o n c e n t r a t i o n i s reduced through deformations which d i s t r i b u t e the a p p l i e d l o a d s over l a r g e r a r e a s . In a d d i t i o n , another crack s t o p p i n g mechanism can c o n t r i b u t e t o the f r a c t u r e toughness of a composite even i f the matrix i s q u i t e s t i f f . If the con n e c t i o n between the f i b r e and matrix i s not too s o l i d , the f i b r e s w i l l s e p a r a t e from the matrix d u r i n g f r a c t u r e . In t h i s case the growing crack may spread through the matrix and w i l l be d i v e r t e d when i t reaches the weak i n t e r f a c e at the f i b r e — m a t r i x boundary. The l a r g e number of f i b r e s present i n a composite means the crack w i l l be d i f f u s e d i n t o a great many d i r e c t i o n s absorbing energy and d i s p e r s i n g the s t r e s s at the crack t i p . I t f o l l o w s from the above d i s c u s s i o n t h a t the mechanical behaviour of a composite m a t e r i a l can be determined, t o a l a r g e degree, by the p r o p e r t i e s of the matrix. The composite n a t u r e of hoof w a l l k e r a t i n and the s p e c i f i c c i rcumstances of i t s form a l l o w s e v e r a l of i t s mechanical p r o p e r t i e s t o change as a r e s u l t of the e f f e c t water has on the p r o p e r t i e s of the matrix. The a n a l y s e s conducted i n t h i s study showed t h a t water content a f f e c t s both the t e n s i l e and the f r a c t u r e p r o p e r t i e s of hoof wall k e r a t i n . Other s t u d i e s have i n d i c a t e d a s i m i l a r response 94 to hydration -for the compression o-f t h i s material (Leach, 1980; But le r , 1977). The e-f-fects o-f hydration seen in hoof wall are i d e n t i c a l to those observed in other mammalian hard kerat in mater ia ls (see Table 7 ) . The f i b r e s of kerat in are composed of s tab le o t - h e l i c a l chains which would not be expected to change s i g n i f i c a n t l y under d i f f e r e n t hydration cond i t ions . The matrix, on the other hand, acts as a p a r t i a l l y c ross l inked rubber and has the potent ia l for large a l t e r a t i o n s in p roper t ies dependent on the degree of c r o s s l i n k i n g present. Experiments on wool f i b r e s i n d i c a t e that t h i s i s indeed the case. The dry ing of wool f i b r e s increases the t e n s i l e modulus approximately three t imes, but increases the to rs iona l modulus by a fac tor of 15 (Feugelman, 1959). Since the m i c r o f i b r i l s of wool are s t rongly or iented p a r a l l e l to the ax is of the wool f i b r e , t h i s i n d i c a t e s that dehydration a f f e c t s the proper t ies of the matrix to a fa r greater degree than i t does the f i b r e s (Fraser and Macrae, 1980). Extensive hydrogen bonding between molecules of the matrix i s l i k e l y respons ib le for these changes. Such secondary c r o s s l i n k i n g would decrease the mobi l i t y of the matrix polymers and, in the f u l l y dehydrated s t a t e , the matrix p roper t ies would approach those of the c r y s t a l l i n e f i b r e s . In hoof wall kerat in extensive secondary bonding within the matrix would make the material very s t i f f , a s i t u a t i o n seen for the lower hydration s tate (0% and 53% RH) t e n s i l e t e s t s . Greater or lesser l e v e l s of hydration would a f f e c t the amount of c r o s s l i n k i n g present. The leve l of water content was seen to be inverse ly re la ted to the modulus over the complete range of hydration (Table 1). 95 Table 7. Longitudinal e l a s t i c moduli t^ f keratinized structures and the effect of hydration level (xlO N/m ). (from Fraser & Macrae, 1980) Relative Humidity Material 0% Intermediate 100% Human n a i l 2.6 (70%) 1.8 hair 2.3 (70%) 1.5 stratum corneum 0.19(70%) 0.13 Wool 5.6 2.0 4.5 (60%) 2.5 Horsehair 6.8 5.1 (60%) 2.4 Hoof wall ** 14.6 3.36 (53%) 2.6 (75%) 0.41 (p a r a l l e l to tubules) ** Data from t h i s study. 96 The f r a c t u r e p r o p e r t i e s of hoof wall k e r a t i n were a l s o a f f e c t e d by the water content of the t i s s u e . I t i s e v i d e n t , l o o k i n g at the J I n t e g r a l r e s u l t s , f o r i n s t a n c e (Table 5 and F i g . 2 4 ) , t h a t d e h y d r a t i o n d i d not cause t h i s m a t e r i a l t o become e x c e s s i v e l y b r i t t l e . As mentioned, weak i n t e r f a c e s can p r o v i d e r e s i s t a n c e t o crack growth i n a two phase composite, even when both components are s t i f f . C r o s s l i n k i n g w i t h i n the matrix c o u l d account f o r the s t i f f e n i n g of t h e m a t e r i a l as a whole and produce b r i t t l e - l i k e behaviour, such as the r e d u c t i o n i n crack growth seen at the c r i t i c a l f a i l u r e p o i n t (Fig.25) and the decrease i n s t r a i n energy r e l e a s e (Fig.24) with d e c r e a s i n g water content, without g r e a t l y r e d u c i n g the o v e r a l l f r a c t u r e toughness. At the other end of the h y d r a t i o n range, hoof wall t e s t e d a t 100% RH a l s o p r o v i d e d good crack r e s i s t a n c e . C o n s i d e r i n g the l a r g e s c a l e deformations p o s s i b l e f o r t h i s t i s s u e at t h i s h y d r a t i o n , the a b i l i t y t o absorb energy i n the f r a c t u r e p r o c e s s i s very l i k e l y due t o s t r e s s d i s t r i b u t i n g and energy absorbing p l a s t i c i t y near the crack t i p . At i n t e r m e d i a t e h y d r a t i o n ( i e . 75% RH) a combination of these two f r a c t u r e r e s i s t a n c e mechanisms i s p o s s i b l e . The f i b r e — m a t r i x i n t e r f a c e c o u l d s t i l l f u n c t i o n as a crack stopper, and the e x t e n s i b i l i t y of the matrix (as seen i n the 75% RH t e n s i l e t e s t s ) c o u l d a l l o w energy a b s o r p t i o n through p l a s t i c deformation. Thus, the presence of an i n t e r m e d i a t e degree of secondary c r o s s l i n k i n g might o p t i m i z e the f r a c t u r e r e s i s t a n c e of t h i s m a t e r i a l . T h i s f e a t u r e i s d i s p l a y e d well by the s i g n i f i c a n t i n c r e a s e i n the J i n t e g r a l v a l u e s f o r the 75% RH t e s t s ( F i g . 2 4 ) . The v a r i o u s 97 mechanical responses o-f hoof wall ke ra t in , e i ther as s t ress—st ra in or -fracture behaviour, can thus be re la ted to the e-f-fect of water on the in terna l bonding in the matrix phase and the i n t e r a c t i o n between the matrix and the f i b r e s . L ike other epidermal t i s s u e s , the hoof wall i s the boundary between the dry external environment and the wet, l i v i n g in terna l t i s s u e s . It has been well documented, both in t h i s study and elsewhere (Baden, 1970; Chapman, 1969; Rigby, 1955; Speakman, 1929; Wildnauer et a l , 1971), that hard kerat ins e q u i l i b r a t e with the hydration condi t ions of t h e i r environment. As an i n t e r f a c e between the external and internal cond i t ions , t h i s property produces a hydration gradient within the t i s s u e . This gradient has been measured and, as expected, t i s s u e on the i n t e r i o r i s near sa tu ra t ion , and that at the outer surface i s e q u i l i b r a t e d with the external environment (Leach,1980). The e f f e c t of hydration on the mechanical behaviour of hoof kerat in and the hydration gradient found in v ivo in the hoof wall provide a mechanism through which the mechanical p roper t ies of d i f f e r e n t areas of the hoof wall can be adjusted to the requirements of the hoof organ. Th is i s important consider ing that the mechanical requirements of t h i s t i s s u e are associated with s p e c i f i c l oca t ions in the hoof wall and that the t i s s u e moves continuously as new t i s s u e i s formed. The t i s s u e , therefore , res ides in very d i f f e r e n t l oca t ions during the course of i t s use, and has very d i f f e r e n t funct ions in 98 these d i f f e r e n t l o c a t i o n s . The hoof t i s s u e which comprises the i n t e r i o r connection to the germinative layer (F ig .30 A) cannot allow high s t r e s s l e v e l s to develop or damage w i l l r e s u l t to the s e n s i t i v e l i v i n g c e l l s . The external (F ig .30 B) and d i s t a l (F ig .30 C) por t ions must form a hard capsule in order to deal with abrasion forces from the external environment and protect the foot from in ju ry . Most of the wall th ickness (F ig .30 D) must provide the s t ruc tu ra l i n t e g r i t y to support the animal and r e s i s t f r a c t u r e . At the inner connection layer i t i s important that s t r e s s l e v e l s are kept low because t h i s i s the attachment point between the hoof wall and the l i v i n g germinative c e l l layer . Damage to t h i s c e l l layer could r e s u l t in long term d is rupt ion of the growth of the hoof w a l l . This area of the wall i s maintained at constant ly high hydration l e v e l s in the foot because of i t s c lose proximity to the underlying vascular i zed t i s s u e s (F ig .30 E ) . In t h i s s i t u a t i o n the hoof wall kerat in would behave s i m i l a r l y to the 1007C RH samples tested in t h i s study. Only r e l a t i v e l y low s t r e s s l e v e l s could be achieved before the material began to y i e l d . The e x t e n s i b i l i t y of hoof kerat in and the y i e l d i n g process would allow s t resses to be d i s t r i b u t e d evenly over a large area and kept as low as p o s s i b l e . In loca t ions B and C (Fig.30) the hoof material w i l l be e q u i l i b r a t e d with environmental hydration cond i t ions , which for a t e r r e s t r i a l animal would normally be much d r ie r than the in terna l t i s s u e s . At these pos i t i ons the hoof wall requ i res a hard, abrasion r e s i s t a n t covering to protect against puncture and excessive wear. The r i g i d i t y of 99 F i g . 3 0 . I n t e r - r e l a t i o n s h i p s o f t i s s u e s i n t h e h o o f w a l l . A - s t r a t u m i n t e r n u m B - e x t e r n a l s u r f a c e C - d i s t a l c o n t a c t s u r f a c e D - s t r a t u m m e d i u m D I - d e r m a l / e p i d e r m a l i n t e r d i g i t a t i o n a t 1 ° a n d 2 ° l a m e l l a e L G - l i v i n g g e r m i n a t i v e l a y e r b o t h a t t h e c o r o n a r y b o r d e r a n d a l o n g t h e d e r m a l / e p i d e r m a l i n t e r d i g i t a t i o n E - c o l l a g e n o u s c o n n e c t i o n b e t w e e n e p i d e r m a l w a l l a n d s k e l e t o n . A r e a c o n t a i n i n g v a s c u l a r i z e d t i s s u e . 100 hoof kerat in at hydrations below 53% RH ind ica te i t could possess these proper t ies in these l o c a t i o n s . The major i ty of the hoof wall (F ig .30 D) would be required to provide the s t ruc tu ra l i n t e g r i t y of the w a l l . Considering the s i z e and speed of the horse, a reasonably high degree of s t i f f n e s s i s needed but t h i s must a l so be balanced with the a b i l i t y to r e s i s t f r a c t u r e . These are the proper t ies which appear to be optimized by hoof kerat in at 75% RH (Figs.14 and 24). Leach (1980) found that the major por t ion of the wall midway between the in terna l and external sur faces of the hoof had water contents of between 17-24% water by weight. This i s the same leve l determined for the 75% RH samples tested in t h i s study (18.13% 0.24 s . d . n=23). Thus, hoof wall kerat in must have d i f f e r e n t mechanical p roper t ies at d i f f e r e n t l o c a t i o n s . These t i s s u e s remain as part of the wall fo r approximately a year and grow d i s t a l l y cont inuously . Therefore, mechanical p roper t ies must be adjusted over time as w e l l . Recal l that epidermal t i s s u e s funct ion a f t e r the c e l l s have undergone a programmed death, and thus, the t i s s u e i s unable to p h y s i o l o g i c a l l y adjust i t s components to the varying requirements. The capaci ty fo r preprogramming the material to have d i f f e r e n t mechanical p roper t ies at d i f f e r e n t hydration l e v e l s al lows t h i s one material to f u l f i l l a l l the mechanical r o l e s necessary fo r the optimum funct ion ing of the hoof organ. The modulation of the secondary banding forces within the matrix polymers a l t e r s the mechanical p roper t ies of the e n t i r e t i s s u e and appears to play a major r o l e in the 101 adjustment o-f the t i s s u e p roper t ies . One aspect of t h i s s i t u a t i o n not looked at s p e c i f i c a l l y i n t h i s study i s the capaci ty of the stratum internum to act as a 'shock absorber' fo r the in te rna l germinative laye r . The connection of the hoof wall to the underly ing dermis along the i n s i d e surface (F ig .30 A) i s accomplished through a large number of convolut ions termed primary lamel lae (F ig .3 ) . The primary lamel lae are themselves connected to lamel lae of the dermis through an i n t e r d i g i t a t i o n of much smaller secondary lamel lae or iented perpendicular to the primary lamel lae (F ig .3 ) . Th is system increases the sur face area of the connection and, therefore , reduces the s t resses encountered by the l i v i n g , connecting laye r . The experiments conducted in t h i s study ind icated that the hoof kerat in surrounding t h i s connection region has the a b i l i t y to y i e l d and absorb considerable amounts of energy at low s t r e s s l e v e l s . Th is suggests that the in terna l hoof kerat in i s admirably su i ted to act as a f i n a l ' s a f e t y va lve ' to protect the very important connection between the hoof wall and the remainder of the ske le ta l system. It would be i n t e r e s t i n g to know i f t h i s material could recover i t s o r i g i n a l mechanical c a p a b i l i t i e s once i t was s t ra ined beyond the y i e l d point and, i f so, to what degree and under what cond i t ions t h i s would occur. The experiments performed in t h i s study are of a pre l iminary nature and do not character i ze t h i s material f u l l y . The subt le control of var ious mechanical p roper t ies through 102 s p e c i f i c responses to s p e c i f i c hydration condi t ions has been demonstrated. The determination of the p rec ise molecular mechanism respons ib le fo r t h i s contro l and the l i m i t s to i t are beyond the scope of t h i s study. It would, nevertheless , be i n t e r e s t i n g to know under what cond i t ions , and why, the change in f r a c t u r e proper t ies observed between 100% and 75% RH t e s t s and 75% and 53% RH t e s t s occurred. It i s l i k e l y that very d i f f e r e n t mechanisms are operating to produce the e f f e c t s seen at 100% and 0% RH, and that the proper t ies observed for 75% RH represent a combination of both. B. The Role of the C e l l u l a r Arch i tecture A l l epidermal t i s s u e s are formed on a basal membrane which connects to the underly ing dermal component of the integument. The c e l l s are produced in assoc ia t ion with t h i s membrane and are replaced by newly forming c e l l s as the t i s s u e grows. Th is mode of growth p laces c e r t a i n cons t ra in ts on the c e l l u l a r organizat ion pass ib le within these t i s s u e s . The epidermis of sk in (stratum corneum) i s formed in t h i s manner, r e s u l t i n g in the c e l l s being organized in a plane p a r a l l e l to the basal membrane. Th is arrangement w i l l produce a plane of weakness along which cracks can pass r e l a t i v e l y e a s i l y . Binding the c e l l s f i r m l y together can reduce t h i s e f f e c t , but unless some component i s or iented perpendicular to the crack plane, a crack could spread with l i t t l e obs t ruc t ion . The experiments studying the e f f e c t of the o r ien ta t ion on the f rac tu re 103 proper t ies of the hoof wall showed that the in ter tubu lar material dominated the path of crack growth and that t h i s occurred because, in terms of f rac tu re energy, the cost of crack growth was s i g n i f i c a n t l y l e s s in the d i r e c t i o n of the in ter tubu lar o r ien ta t ion than in a l l other d i r e c t i o n s (Figs. 20 and 21) . The in ter tubu lar material i s formed on a f l a t basal membrane in a manner s i m i l a r to stratum corneum. Consequently, the in ter tubu lar material forms a plane of f rac tu re i n s t a b i l i t y . This organizat ional pattern might al low layers of the wall material to be broken o f f , producing a severe l i m i t a t i o n to the funct iona l c a p a b i l i t i e s of the hoof wa l l . The so lu t ion i s to or ient a s t ruc tu ra l component perpendicular to the plane of weakness, and t h i s component i s provided by the tubular m a t e r i a l . Because kerat inocytes can only be produced p a r a l l e l to the basal membrane, i t i s necessary to modify the arrangement of the basal membrane in order to produce c e l l s or iented perpendicular to the in ter tubu lar m a t e r i a l . Through the simple outpouching of the basal membrane to form the dermal p a p i l l a e , the 'growth plane' for the formation of the tubule c e l l s becomes or iented perpendicular to the in te r tubu lar mate r ia l . C e l l s are produced on the s ides of the p a p i l l a e which have o r ienta t ions perpendicular to the in ter tubu lar mate r ia l , and as a resu l t of the f rac tu re d i s c o n t i n u i t y they present , a material possessing reasonable f r a c t u r e s t a b i l i t y in a l l three d i r e c t i o n s i s c reated . 104 One advantage o-f rein- forcing the planar in ter tubu lar material with tubules i s the lack o-f connection between these tubules . A crack running along the o r ien ta t ion o-f the in ter tubu lar material must pass through many tubules , but a crack running along a tubule must pass through a continuum o-f in te r tubu lar m a t e r i a l . 0-f course, the most important d i r e c t i o n , in terms of maintaining the i n t e g r i t y of the hoof w a l l , remains the v e r t i c a l d i r e c t i o n . The evidence presented in t h i s study shows that the in ter tubu lar material provides an impressive res is tance to f rac tu re in any d i r e c t i o n with a v e r t i c a l component (F ig .20) . The mammals have devloped an amazing d i v e r s i t y of hard kerat in appendages. These take on an extremely wide var ie ty of forms to accomplish an equal ly wide range of funct ions . Among these are hooves, claws, horns of var ious types and even the baleen of whales. An i n t e r e s t i n g feature of a l l these s t ructures i s the presence of tubular s t ruc tu res , produced on dermal p a p i l l a e , embedded in in ter tubu lar m a t e r i a l , (Ryder, 1962; George, 1956). The d iverse funct ions of these appendages suggests that they are not homologous and, therefore , arose independently. Th is supports the asser t ion that t h i s morphological organizat ion requi res only a minor a l t e r a t i o n in the basal membrane and suggests that the s t ruc tu ra l organizat ion has an important funct ional s i g n i f i c a n c e . It i s qu i te p o s s i b l e , consider ing what has been determined here regarding the hoof wa l l , that the tubular organizat ion i s a reinforcement which adds to the f rac tu re toughness and wear 105 proper t ies o-f these d iverse epidermal appendages. The -f inal goal o-f a study such as t h i s i s the in te rp re ta t ion of the data in terms of the funct ion of the animal concerned. As has been seen, design at the molecular and c e l l u l a r l e v e l s can have s i g n i f i c a n t e f f e c t s on the proper t ies of a material such as t h i s . It i s necessary, however, to show how these e f f e c t s apply to the animal when the s t ructure invest igated i s a funct ion ing whole. As yet , the exact morphological r e l a t i o n s h i p between the tubular and in ter tubu lar material throughout the e n t i r e hoof i s not well known. The tubules are always p a r a l l e l to the external surface of the hoof and run cont inuously from the proximal germin i t ive layer to the d i s t a l contact sur face . In genera l , the in ter tubu lar material runs somewhat perpendicular to the tubular a x i s . In l i g h t of the evidence presented, and consider ing t h i s t i s s u e in s t r i c t l y a material sense, i t may seem that the most e f f i c i e n t design would have the tubules and in ter tubu lar material or iented 90 degrees to each other . It was seen, however, that the mean tubular—intertubular angle was approximately 55 to 60 . The samples used in t h i s study were taken from the toe region of the hoof w a l l . It i s i n t e r e s t i n g to note that in a normal horse the hoof wall s t r i k e s the ground at an angle of approx— o e imately 55 fo r the f ront feet and 50 in the rear f e e t . If the in te r tubu lar material were or iented at 90 degrees to the tubules in the toe reg ion , the weakest f rac tu re d i r e c t i o n would be or iented to allow the end of the wall to be broken off (F ig . e o 30). An angle of between 55 and 60 , however, p laces the 106 plane of weakness exact ly leve l with the contact surface of the ground. Evidence has been presented which suggests that the most d i s t a l port ion of the hoof wall can suf fe r from in terna l damage which reduces the f rac tu re res is tance c a p a b i l i t i e s of the t i s s u e (F ig .18 and Table 2 ) . The reduct ion of f rac tu re toughness in a composite as a r e s u l t of use i s genera l l y due to the production of microscopic cracks within the m a t e r i a l . As has been d iscussed , cracks in a material under s t r e s s can lead to larger cracks and f i n a l l y to f r a c t u r e . It i s then advantageous to remove flawed m a t e r i a l . It would appear that the hoof wall i s admirably designed to do t h i s . The congruency found between the weakest f r a c t u r e plane in the hoof wall and the ground contact surface st rongly suggests that the wall i s designed for a degree of c o n t r o l l e d wear while at the same time guarding against f rac tu re in any v e r t i c a l d i r e c t i o n . The hoof kerat in funct ions as part of the hoof w a l l , and in a n o n - l i v i n g s t a t e , fo r approximately one year. For the purpose of e l iminat ing f laws in o ld t i s s u e , cont ro l l ed wear can be advantageous as long as i t does not exceed the ra te at which replacement t i s s u e s can be generated convenient ly . The contro l of the plane of wear would a lso be important in determining the contact of the foot and the ground. The equine leg i s a f i n e l y balanced locomotory s t ructure which depends on deal ing with s p e c i f i c s t r e s s cond i t ions . It i s important to the proper funct ion ing of the rest of the leg that the manner in which the foot s t r i k e s the ground remain cons is tent . 107 This study has shown that i t i s poss ib le to employ some rather abstract or eso te r i c ana lys i s techniques to determine the subt le -functional design s t r a t e g i e s in the hoo-f w a l l . The f ibre—matrix composite design g ives r i g i d i t y and toughness to t h i s material and, through a s p e c i f i c response of the matrix polymers to hydrat ion, al lows these mechanical p roper t ies to be a l te red to the requirements of s p e c i f i c areas of the wa l l . The c e l l u l a r a rch i tec tu re i s dependent on the mode of growth in t h i s t i s s u e . The development of dermal p a p i l l a e with germinative membrane or iented perpendicular to the natural plane of weakness decreases the e f f e c t of the weakest o r ien ta t ion and balances, to some degree, the f rac tu re toughness of the m a t e r i a l . The r e l a t i o n s h i p between the weakest plane of f rac tu re and the ground contact surface al lows cont ro l l ed wear to occur and an appropr iate hoof shape to be maintained. These important b i o l o g i c a l conclusions were determined by analysing the t i s s u e as i f i t were a simple engineering m a t e r i a l . It i s important to remember, however, that , un l ike engineering mater ia ls which are designed as mater ia ls and l a t e r used to b u i l d s t ruc tu res , s t ruc tu ra l b iomater ia ls are designed, produced and used in terms of the s t ruc tu ra l organ they compose. With a material such as hoof w a l l , i t i s very d i f f i c u l t to i s o l a t e the material from the s t ruc tura l p roper t ies . Sect ions removed from the hoof organ to act as test samples cannot represent the t o t a l i n t e r a c t i v e proper t ies of the organ. Considering the complexity of t h i s b i o l o g i c a l 108 s t ruc ture , i t i s very p leas ing to see how much b i o l o g i c a l ins ight can be provided by an abst rac t , engineering a n a l y s i s . 109 REFERENCES A l t o , A. & Pope, M.H. (1979) On the f rac tu re toughness of equine metacarpi , J . Biomech., 12: 415-421. Baden, H.P. (1970) The physical p roper t ies of n a i l , J . Invest. Derm., 55: 115-122. B o n f i e l d , W. & Datta, P.K. (1976) Fracture toughness of compact bone, J . Biomech., 9: 131—134. Broek, D. (1978) Elementary Engineering Fracture Mechanics, S i j t h o f f and Noorhoff Int. Pub. , the Netherlands. Bu t le r , K.D. (1976) The e f f e c t of feed intake and g e l a t i n supplementation on the growth and q u a l i t y of the equine hoof, Ph.D. t h e s i s , Cornel l Un iv . , I thaca, N.Y. But le r , K.D. & Hintz , H.F. (1977) E f f e c t of leve l of feed intake and g e l a t i n supplementation on growth and qua l i t y of hooves of ponies, J . Anim. S c i . , 44: 257-261. Chapman, B.M. (1969) A review of the mechanical p roper t ies of kerat in f i b r e s , J . of the T e x t i l e Ins t i tu te , 60: 181-207. Crewther, W.G. (1976) Primary s t ruc ture and chemical p roper t ies of wool, i n : Proceedings of the 5th International Wool T e x t i l e Research Conf . , Aachen, 1975, K. Z ieg ler (ed . ) , V o l . 1 : l - l O l . 110 Currey, J . D . (1962) St ress concentrat ions in bone, Quart. J . of Microscopical S c . , 103 ( p . l ) : 111-133. DeBaise, G .R . , Por ter , A.W. & Pentoney, R.E. (1966) Morphology and Mechanics of wood f r a c t u r e , Mater ia ls Research and Standards, 6(10): 493-499. Dinger, J . E . , Goodwin, E . E . & L e f f e l , E .C . (1973) Factors a f f e c t i n g hardness of the equine hoof w a l l , S c i e n t i f i c paper No.A2212, Cont. No.5193, Maryland Exp. S t a t i o n , Univ. of Maryland, 20742, U.S.A. Evans, Burton, Hintz & Van Vleck (1977) The Horse, Freeman & Co. Feughelman, M. (1959) A two phase s t ruc ture for kerat in f i b r e s , T e x t i l e Research Journa l , 29: 223-228. F raser , R.D.B. & MaCrae, T . P . (1980) Molecular s t ruc ture and mechanical p roper t ies of kera t ins , i n : Soc iety fo r Experimental Biology Symposium XXXIV, The Mechanical Proper t ies of B i o l o g i c a l Mater ia ls J . F . V . Vincent and J . D . Currey (eds . ) . F raser , R . D . B . , MaCrae, T . P . & Rogers, G .E . (1962) Molecular organizat ion in —kerat in , Nature, Lond. , 193: 1052-1055. Gaggar,S & Broutman, L. (1975) Crack growth res is tance of random f i b r e composites, J . Comp. Mat . , 9: 216—227. George, A .N . (1956) The post—natal development of the I l l horn tubules & -f ibres in the horns of sheep, B r i t i s h Vet Journa l , 112(1): 30-34. Goodspeed, J . , Baker, J . P . , Casada, H.J . & Walker, J . N . E f f e c t s of g e l a t i n on hoof development in horses, J . Anim. S c i . , 31: 201. Gordon, J . E . (1976) The New Science of Strong Mater ia ls or Why You Don't F a l l Through the F loo r , Penguin Books L t d . , Engl and. Gordon, J . E . (1980) Biomechanics: the l a s t stronghold of v i t a l i s m , i n : Society for Experimental Biology Symposium XXXIV, The Mechanical Proper t ies of B i o l o g i c a l Mate r ia l s , J . F . V . Vincent & J .D . Currey (eds . ) . G r i f f i t h , A .A . (1921) The phenomena of rupture and flow in s o l i d s , P h i l . Trans. Roy. S o c , A221: 163-198. Hashimoto, K. (1971) U l t ras t ruc tu re of the human toe n a i l . Ce l l migrat ion, k e r a t i n i z a t i o n and formation of the i n t e r c e l l u l a r cement. Arch. Dermatol. Forsch, 240:1—22. Irwin, G.R. (1958) Fracture , i n : Encyclopedia of Phys ics , S. Flugge, ed. Spr inger , B e r l i n , 6: 551—590. Je ron imid is , G. (1976) The f rac tu re of wood in r e l a t i o n to i t s s t ruc tu re , i n : Wood Structure in B i o l o g i c a l and Technological Research, P. Baas, A . J . Bol ton, and D.M. Cat l ing (eds . ) , Leiden botanical s e r i e s No.3: 253-265, Leiden: the Un ivers i ty Press . 112 Katz, J . L . (1980) The s t rusture and biomechanics of bone, i n : Soc. fo r Experimental Biology Sym. XXXIV, The Mechanical Proper t ies of B i o l o g i c a l Mate r ia l s , J . F . V . Vincent & J .D . Currey (eds . ) . Kobayashi, H. , Nakamura, H . , & Nakazawa, H. (1979) A r e l a t i o n between crack t i p p l a s t i c b lunt ing and the J - i n t e g r a l , i n : Proceedings of the Third Internat ional Conference on Mechanical Behaviour of Mate r ia l s , I . C M . 3 , V o l . 3 : 529-538. Landes, J . D . & Begley, J . A . (1972) The e f f e c t of specimen geometry on J , ASTM STP, 514: 24. Landes, J . D . & MaCabe, D.E. (1979) E f f e c t of specimen s i z e and geometry on d u c t i l e f rac tu re c h a r a c t e r i z a t i o n , i n : Proceedings of the Third Internat ional Conference on Mechanical Behaviour of Mate r ia l s , I. C M . 3, V o l . 3 : 539-547. Leach, D.H. (1980) The s t ructure and functure of equine hoof w a l l , Ph.D. t h e s i s , Dept. of Vet Anatomy, Univ. of Sask . , Saskatoon. Matoltsy , A .G . (1975) Desmosomes, f i laments & keratohyal ine granules: t h e i r r o l e in s t a b a l i z a t i o n & kerat inat ion of the epidermis, J . of Invset igat ive Dermatology, 65: 127-142. McLachlan, A.D. (1978) C o i l e d - c o i l formation and sequence regu lat ions in the h e l i c a l regions of - k e r a t i n , J . of Molecular B io logy , 124: 297-304. 113 Meites Louis (ed. ) , (1963) Handbook of Ana ly t i ca l Chem. McGraw-Hi l l , Toronto. N i c k e l , R. (1938) Uber den bau der hufrohrchen uno seine bedeutung fur den nechanismus des pferdehufes, Dtsch. t i e r a r z t l . Wschr., 46: 449-552. P i e k a r s k i , K. (1970) Fracture of bone, J . of Appl ied Phys ics , 41: 215-233. Pook, L .P . & Smith, R.A. (1979) Theoret ica l background to e l a s t i c f rac tu re mechanics, i n : Fracture Mechanics: Current Status , Future Prospects, Pergamon Press , Oxford. Pope, M.H. & Cutwater ,J . (1971) The f rac tu re c h a r a c t e r i s t i c s of bone substance, J . Biomech., 5 : 457—465. R ice . J .R . (1968) A path independent in tegra l and the approximate ana l ys i s of s t r a i n concentrat ion by notches and cracks , J . Appl . Mech., 35: 379. Rigby, B . J . (1955) Stress—rel axation of wool f i b r e s in water at s t r a i n s of 5-20% extension, Aus t ra l ian J . of Phys . , 8: 176-183. Ryder, M.L. (1962) Structure of Rhinoceros horn. Nature, 193: 1199-1201. Schniewind, A .P . 8c Pozniak, R.A. (1971) On the f rac tu re toughness of Douglas f i r , Engineering Fracture Mechanics, 2: 223-233. Simkin, A. & Robin, G. (1974) Fracture Formation in d i f f e r i n g col lagen f i b r e pattern of compact bone, J . Biomech., 7: 183-188. S isson , S. & Grossman, J . D . (1953) The Anatomy of the Domestic Animals, ' 4th e d . , W.B. Sanders Comp., P h i l . , Pa. Speakman, J . B . (1929) The r i g i d i t y of wool and i t s change with adsorption of water vapour, Transact ions of the Faraday S o c , 25: 92-103. Stump, J . E . (1967) Anatomy of the normal equine foo t , inc lud ing microscopic features of the laminar reg ion , J . Am. Vet. Med. A s s o c . , 151: 1588-1598. Wainwright, S . A . , Br iggs , W.D., Currey, J . D . & Gosl ine , J .M . (1976) Mechanical D is ign in Organisms, Edward Arnord (Pub.) L t d . , London. Wildnauer, R.H. , Botwel l , J.W- & Douglass, A .B . (1971) Stratum corneum biomechanical p roper t ies I. Influence of r e l a t i v e humidity on normal and extracted human stratum corneum, J . Invest. Derm., 56: 72-78. Wilkens, H. (1964) Zur makroskopischen und mickroskopischen morphologie der r inderk laue mit einem verg le ich der arch i tektur von klauen—und hufrohrchen, Z b l . Vet. Med., Ser ies A: 11: 163-234. Wright, T .M. & Hayes, W.C. (1977) Fracture mechanics parameters for compact bone - E f f e c t s of densi ty and specimen th ickness , J Biomech., 10: 410-430. 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0096032/manifest

Comment

Related Items