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Static fatigue of graphite Hodkinson, Pauline H. 1973

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STATIC FATIGUE OF GRAPHITE BY PAULINE H. HODKTNSON B.Sc, U n i v e r s i t y of Sussex, U.K., 1971 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of METALLURGY We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA November, 1973 In p resent ing t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e fo r reference and study. I f u r t h e r agree tha t permiss ion fo r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . It i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l ga in s h a l l not be a l lowed without my w r i t t e n p e r m i s s i o n . Depa rtment The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date \ ° \ \ \ ~ I \ T 1 > - i i -ABSTRACT S u b c r i t i c a l crack growth has been studied i n two d i f f e r e n t grades of a fine-grained i s o t r o p i c graphite and i n p y r o l y t i c graphite. The double t o r s i o n technique was used. Room temperature tes t s revealed a s t r e s s i n t e n s i t y - c r a c k v e l o c i t y behaviour s i m i l a r to the t h i r d stage of crack growth i n soda-lime glass. Thus, i t appears that graphite undergoes s t a t i c fatigue at room temperature only at large f r a c t i o n s (^92%) of the c r i t i c a l s tress i n t e n s i t y . S t r u c t u r a l c h a r a c t e r i s a t i o n studies have enabled the slow crack growth behaviour to be r e l a t e d to m i c r o s t r u c t u r a l features. Transverse rupture tests have shown that f r a c t u r e i n graphite i s i n i t i a t e d at surface flaws, mainly grain pull-outs produced by the p o l i s h i n g process or machining operation employed. Subsidiary cracking or microcracking occurs i n the regions around these flaws on loading p r i o r to f a i l u r e . A mechanism of slow crack growth has been discussed which takes into account the formation of micro-cracks and t h e i r link-up to form a propagating crack. Slow crack growth te s t s were also performed at 500°C on the i s o t r o p i c graphites to reveal the e f f e c t of temperature and e n v i r -onment on crack growth. These tests were complemented by thermo-gravimetric analysis studies. The K T-V diagrams at 500°C s t i l l - i i i -showed stage I I I charac te r i s t i c s but the slopes were about ha l f the values obtained at room temperature, ind ica t ing that thermal and/or environmental assistance of slow crack growth i n graphite occurs at th is temperature. - iv -TABLE OF CONTENTS * Page TITLE PAGE i ABSTRACT i i TABLE OF CONTENTS i v LIST OF TABLES i x LIST OF FIGURES * ACKNOWLEDGEMENT x i v CHAPTER I. INTRODUCTION < 1 1.1 Instantaneous Strength of B r i t t l e Sol ids 2 1.2 Time Dependent Fa i lu re 3 I . 2 . a Stress-Time-to-Failure Curves . . . . . . . . 3 I .2 .b Stress Intensi ty Factor-Crack Ve loc i ty Diagrams 8 I . 2.c S ta t i c Fatigue Models 12 1.3 Previous Studies on the S ta t i c Fatigue of Graphite 1 5 1.4 Objectives of the Present Study 17 CHAPTER I I . EXPERIMENTAL PROCEDURE 19 11.1 Mater ia ls Select ion 19 11.2 St ructura l Characterisat ion 20 I I . 2.a Bulk Density 20 I I .2 .b Helium Pycnometer Density 20 I I . 2 . c Mercury Porosimetry 21 I I . 2 . d Opt ica l Microscopy 22 11.3 E l a s t i c Constants 22 - V -Page 11.4 Oxidation Studies of Isotropic Graphite 24 11.5 Transverse Rupture Tests : 25 I I . 5 . a Unnotched Bars 27 I I . 5 . a . i Fracture Stress S t a t i s t i c a l D i s t r i b u t i o n at Room Temperature... 27 11.5. a . i i High Temperature Tests for Isotropic Graphites 28 I I .5 .b Notched Bars 29 11.5. c Fractography 30 11.6 Slow Crack Growth Tests 30 11.6. a Compliance Ca l ib ra t ion 34 I I . 6.b Stress Intensi ty Factor-Crack Ve loc i ty Diagrams 34 11.6. b . i Observation of the Crack Length and P r o f i l e 36 I I . 6 . b . i i Machine Relaxations 37 I I . 6 . b . i i i Fractography 38 CHAPTER I I I . RESULTS AND CALCULATIONS 39 111.1 St ructura l Characterisat ion 39 I I I . I . a Density and Porosi ty 39 I l l . l . b Pore -S ize-Dis t r ibu t ion 41 I I I . l . c Opt ica l Microscopy 45 111.2 E l a s t i c Constants 45 111.3 Oxidation Studies of Isotropic Graphite 50 111.4 Transverse Rupture Tests 55 I I I . 4 . a Unnotched Bars 55 I I I . 4 . a . i Fracture Stress S t a t i s t i c a l D i s t r i bu t i on at Room Temperature.. 55 - v i -Page I I I . 4 . a . i i High Temperature Tests for Isotropic Graphites' 55 I I I . 4 .b Notched Bars 64 111.4. C Fractography 67 I I I . 5 Slow Crack Growth Tests 74 111.5. a Compliance Ca l ib ra t ion 74 I I I . 5 .b Stress Intensi ty Factor-Crack Ve loc i ty Diagrams 74 III .5.C L i f e Expectancy 96 I I I . 5.d Fractography 100 CHAPTER IV. ANALYSIS OF RESULTS 106 IV. 1 S t ruc tura l Character isat ion 106 IV.2 E l a s t i c Constants 109 IV.3 Oxidation Studies of Isotropic Graphite I l l IV.4 Transverse Rupture Tests 115 IV. 4.a Unnotched Bars 116 IV. 4 . a . i Fracture Stress S t a t i s t i c a l D i s t r i b u t i o n at Room Temperature 116 I V . 4 . a . i i High Temperature Tests for Isotropic Graphites 118 IV.4.b Notched Bars 121 IV.4 .c Fractography 123 I V . 4 . c . i Isotropic Graphite 123 I V . 4 . c . i i P y r o l y t i c Graphite 125 IV.5 Slow Crack Growth Tests 127 IV.5 .a Compliance Ca l ib ra t ion 127 - v i i -Page IV.5.b Stress Intensi ty Factor-Crack Ve loc i ty Diagrams 128 I V . 5 . b . i Isotropic Graphites at Room Temperature 128 I V . 5 . b . i i Isotropic Graphites at 500°C . . . . 130 I V . 5 . b . i i i P y r o l y t i c Graphite at Room Temperature 132 IV.5 .c C r i t i c a l Stress Intensi ty Factors . . . . 134 IV. 5.d Fractography I 3 5 I V . 5 . d . i I sot ropic Graphite 135 IV. 5 . d . i i P y r o l y t i c Graphite 136 CHAPTER V. DISCUSSION I 3 8 V . l Short-Term Strength of Graphite I 3 8 V. l . a Fracture Toughness, C r i t i c a l Stress Intensi ty Factor 141 V ; l . b Flaw Size 145 V.2 Time Dependent Fa i lu re of Graphite 147 V.2 . a Mechanism of Crack Growth 151 V. 2 . a . i Isotropic Graphites at Room Temperature 151 V . 2 . a . i i Isotropic Graphites at 500°C 153 V . 2 . a . i i i P y r o l y t i c Graphite at Room Temperature 156 V.2.b Predict ions of L i f e Expectancy 158 V.2 .c Limita t ions of Slow Crack Growth Tests 159 CHAPTER V I . SUMMARY AND CONCLUSIONS 162 CHAPTER V I I . SUGGESTIONS FOR FUTURE WORK 164 - v i i i -Page APPENDICES 166 BIBLIOGRAPHY 178 - i x -LIST OF TABLES Table Page I Densities and p o r o s i t i e s of graphites at room temperature (based on t h e o r e t i c a l density = 2.25 x 103Kg.m-3 27) 4 0 II Summary of r e s u l t s from mercury porosimetry 46 I I I E l a s t i c constants of graphites at room temperature 49 IV Linear regression analysis of oxidation r e s u l t s for i s o t r o p i c graphites 54 V Transverse rupture test data f o r graphites at room temperature a) Mean frac t u r e stress and standard deviation 60 b) Weibull parameters f o r a u = 0 and best estimated value of o~u 61 VI Transverse rupture t e s t data f o r i s o t r o p i c graphites at various temperatures a) P0X0 AXZ , 62 b) POCO AXF-5Q 63 VII ^ i C ' Y i a n c * c °^ graphites calculated from transverse rupture t e s t s 66 VIII Summary of r e s u l t s from compliance c a l i b r a t i o n s .... 77 IX Summary of r e s u l t s from Kj-V diagrams a) POCO AXZ at room temperature i n a i r 86 b) POCO AXF-5Q at room temperature i n a i r 87 c) POCO AXZ at 500°C i n a i r 88 d) POCO AXF-5Q at 500°C i n a i r 89 e) P y r o l y t i c graphite at room temperature i n a i r ... 90 X Summary of K I c and Y± values f o r graphites i n a i r .. 91 XI Summary of l i n e a r regression analysis equations used for l i f e expectancy c a l c u l a t i o n s « 98 - x -LIST OF FIGURES Figure Page 1 A schematic stress-time-to-failure curve 4 2 Universal Fatigue Curves of 1. Acid-etched soda-lime s i l i c a t e glass 2. E-glass fibers 3. Fused Si02 glass 4. Abraded soda-lime s i l i c a t e glass (after Ritter and Sherbourne7) 6 3 Homologous fatigue stress versus time-to-rupture of Speer RC4 graphite, (after Wilkins 3) 7 4 Schematic stress intensity factor-crack velocity diagram for a material in a stress corrosive environment 9 5 Dependence of crack velocity on stress intensity factor, Kj- in soda-lime-silica glass.. (after Wiederhorn8) 11 6 Double torsion test apparatus and specimen a) Total assembly 32 b) Underside of upper plate 3 3 c) Enlarged view of specimen 3 3 7. Mercury penetration versus pore diameter for isotropic graphites 42 8 Pore-size-distribution curves for a) POCO AXZ "B" 43 b) POCO AXF-5Q "A" 44 9 Optical micrographs of a) POCO AXZ x582 47 b) POCO AXF-5Q x800 47 10 Optical micrographs of pyrolytic graphite a) Basal plane xl33, 4 8 b) Cross-section of basal planes 48* Polarised Light x200 11 Schematic weight loss-time curves for graphites (after Lewis 3 0) 51 12 Oxidation rates of isotropic graphites (calcula-ted on the basis of geometrical and active surface area) 52 - x i -Figure Page 13 T y p i c a l l o a d - d e f l e c t i o n curves f o r transverse rupture t e s t s 56 14 Weibull p l o t s of transverse rupture t e s t s at room temperature f o r graphites, a u = 0 a) POCO AXZ 57 b) POCO AXF-5Q 58 c) P y r o l y t i c graphite 59 15 Modulus of rupture versus temperature f o r i s o t r o p i c graphites (Error bars = 2a) 65 16 SEM photographs of POCO AXZ unnotched bars at 600°C a) Fracture surface xl3.5 68 b) Fracture o r i g i n x300 68 17 SEM photographs of POCO AXZ notched bars at room temperature a) Notch t i p x300 69 b) The same xlOOO 69 18 SEM photographs of POCO AXF-5Q unnotched bars at 700°C a) Oxidation p i t s x30 70 b) Oxidation p i t and grain pull-outs x300 70 19 SEM photographs of unnotched p y r o l y t i c graphite at room temperature,load perpendicular to the c axis a) Overall crack front xl5 71 b) Fracture o r i g i n s x80 71 20 SEM photographs of notched p y r o l y t i c graphite at room temperature,load perpendicular to the c axis a) O v e r a l l f r a c t u r e surface x20 72 b) Notch t i p xlOO 72 21 SEM photographs of notched p y r o l y t i c graphite at room temperature,load p a r a l l e l to the c axis a) Over a l l f r a c t u r e surface x20 73 b) Basal plane layers x300 73 22 Compliance versus load f o r a notched specimen of POCO AXZ 75 - x i i -Figure Page 23 Specimen compliance versus machined notch length of the three graphites 76 24 T y p i c a l load r e l a x a t i o n curves at room tempera-ture f o r a) POCO AXF-5Q 78 b) POCO AXZ , 79 c) P y r o l y t i c graphite 79 25 T y p i c a l load r e l a x a t i o n curve f or POCO AXF-5Q at 500°C 80 26 Kj-V diagram f o r POCO AXZ at room temperature i n a i r 82 27 K-J--V diagram f or POCO AXF-5Q at room tempera-ture i n a i r S3 28 K-r-V diagrams f or POCO AXZ and POCO AXF-5Q at 500°C i n a i r 84 29 K-r-V diagram f o r p y r o l y t i c graphite at room temperature i n a i r 85 30 Comparison of present data f or POCO AXF-5Q at room temperature with Simpson's 3^.. 92 31 a) Schematic diagram of p y r o l y t i c graphite double t o r s i o n specimen showing delamination process 95 b) Photograph of p y r o l y t i c graphite with delaminations xl2 95 32 L i f e expectancy versus applied s t r e s s f o r graphites at room temperature and 500°C i n a i r 99 33 SEM photographs of crack path through i s o t r o p i c graphite, POCO AXZ, room temperature a) Notch t i p x400 ,. 101 b) Subsidiary cracking at crack t i p x400 101 34 SEM photographs of POCO AXZ room temperature fracture surfaces a) xl300 102 b) x3000 102 - x i i i -Figure Page 35 SEM photographs of POCO AXF-5Q fracture surfaces a) Room temperature xll40 ., 103 b) Room temperature x2850 103 c) 500°C x740 104 36 SEM photographs of pyrolytic graphite at room temperature a) Notch t i p x60 105 b) Fracture surface x53 , 105 37 Effect of strain-rate on strength of POCO AXF-5Q at room temperature 140 Al Schematic diagram of a) One torsion bar of the double torsion specimen 168 b) Crack profile for double torsion specimen .. 168 - x i v -ACKNOWLEDGEMENT The author wishes to thank Dr. J.S. Nadeau for his guidance and encouragement with this work. Thanks are also due to Dr. O.J. Whittemore, Jr. and Kunio Aihara of the University of Washington, Seattle who performed the mercury porosimetry experiments. Acknowledgement is made of financial assistance from the Canadian Commonwealth Fellowship Association and Atomic Energy of Canada Ltd. - 1 -CHAPTER I INTRODUCTION The dependence of f r a c t u r e stress of b r i t t l e s o l i d s on the time of loading i s commonly termed s t a t i c f a t igue. This phenomenon 1 2 has been observed i n many glasses , commercial ceramics and c e r t a i n 2 b r i t t l e metals and quite recently has been shown to occur i n 3 graphite. I t has been a t t r i b u t e d to the slow growth of s u b c r i t i c a l flaws under stress, the rate of growth being c o n t r o l l e d by corrosion reactions between agents i n the environment and the material at crack t i p s . The r e s u l t can be a major reduction i n the engineering strength, to about one-third to one-quarter of the instantaneous fracture s t r e s s . B r i t t l e ceramic materials, including graphites, are being used incr e a s i n g l y for load-bearing components i n high temperature envir-onments so that the long-term strength of these materials i s p a r t i c u l a r l y important. Therefore, the cause and c o n t r o l of s t a t i c fatigue i s of great technological as w e l l as s c i e n t i f i c i n t e r e s t . In order to understand delayed f a i l u r e i n graphite, some consideration of the instantaneous strength of b r i t t l e s o l i d s should be made. Time dependent f a i l u r e i s treated afterwards. - 2 -1.1 Instantaneous Strength of B r i t t l e Solids The short-term strength of b r i t t l e s o l i d s , a p r i s generally c o n t r o l l e d by the s t r e s s to propagate small m i c r o s t r u c t u r a l flaws. These may be inherent i n the structure or the r e s u l t of s u p e r f i c i a l damage. According to a modified G r i f f i t h equation the fr a c t u r e strength may be given by _ l r 2 E Y i ^ n s °Fr - Y (-c"^ ) ( 1 ) where Y i s a geometrical f a c t o r , E the Young's modulus, an e f f e c t i v e surface energy for f r a c t u r e i n i t i a t i o n and c a flaw s i z e . In any b r i t t l e s o l i d there w i l l be a d i s t r i b u t i o n of flaw s i z e s and consequently a v a r i a t i o n i n strength. An empirical s t a t i s t i c a l a n a lysis i s a v a i l a b l e and that of most widespread a p p l i c a b i l i t y i s the weakest l i n k model due to Weibull.^ A l t e r n a t i v e l y , equation (1) may be written i n terms of the fra c t u r e mechanics parameter, K j c K I c = Y°-Fv^ ( 2 ) where K-|-c i s the fracture toughness or c r i t i c a l s tress i n t e n s i t y factor f or cracks experiencing.an opening mode of s t r e s s . From equations (1) and (2) i t can be seen that K i s defined by K I c = (2EY 1) I S (3) o r K l c = ^ f l c ^ ( 4 ) - 3 -where i s the c r i t i c a l strain-energy release rate which may be regarded as the d r i v i n g force motivating crack extension. Exact r e l a t i o n s h i p s between the flaw s i z e and the f r a c t u r e toughness, a material property have been developed for many systems. Therefore, the f r a c t u r e strength of an object or component may be calculated with reasonable accuracy, once the f r a c t u r e toughness and e f f e c t i v e flaw s i z e are known. 1.2 Time Dependent F a i l u r e At c e r t a i n stresses l e s s than that required to induce s h o r t -term f a i l u r e s u b c r i t i c a l crack growth can occur and i f the flaw siz e grows to the c r i t i c a l s i z e for that s t r e s s , f a i l u r e w i l l r e s u l t . The l i f e expectancy of the material w i l l , therefore, be the time f o r the flaw to grow to the c r i t i c a l s i z e . I.2.a Stress-Time-to-Failure Curves S t a t i c fatigue data are commonly expressed as stress versus ti m e - t o - f a i l u r e as shown i n Figure 1. The time to rupture increases with decreasing s t r e s s , temperature and environment and appears to approach i n f i n i t y at some s t r e s s , usually a f r a c t i o n of the i n s t a n t -aneous fra c t u r e s t r e s s , c a l l e d the " s t a t i c fatigue l i m i t " . Mould and Southwick were able to reduce data from glass specimens with various treatments to a s i n g l e curve which they c a l l e d the "universal fatigue curve" (U.F.C.). The reduced stress was defined as o/ov,, the f a i l u r e stress divided by the f a i l u r e stress o o o CO <o UJ OC H </> CD Decreasing ^ environment Decreasing temperature i i STATIC FATIGUE LIMIT DURATION OF LOAD (arbitrary scale.) Figure 1 . A schematic s t ress - t ime- to- fa i lure curve - 5 -at l i q u i d nitrogen temperature, and the reduced time as l o g ( t / t n 5), where t i s the f a i l u r e time and t n r>, the f a i l u r e time at h a l f the l i q u i d nitrogen s t r e s s . A U.F.C. fo r various glasses i s shown i n Figure 2.7 3 More recently, Wilkins has p l o t t e d s t a t i c f a t i gue data as homologous stress versus t i m e - t o - f a i l u r e . Normal stress-time-to-f a i l u r e curves exhibit enormous scatte r due to v a r i a t i o n s i n the instantaneous fr a c t u r e s t r e s s . The fatigue properties of a b r i t t l e material with any given flaw d i s t r i b u t i o n can be obtained i f the t i m e - t o - f a i l u r e i s r e l a t e d to both the instantaneous fr a c t u r e stress (which r e f l e c t s the maximum flaw size) and the applied s t r e s s . The homologous stress i s defined as the r a t i o of the applied s t r e s s i n the fatigue t e s t , to the f r a c t u r e stress i n an instantaneous t e s t , CTi CTA a^, i s the applied stress i n normal s t a t i c fatigue tests and the corresponding value of cr^  can be obtained i f an i d e n t i c a l set of specimens i s tested to f a i l u r e by rapid loading. The assumption i s made that the instantaneous strength d i s t r i b u t i o n of the specimens i s the same for both sets and also that the f a i l u r e times for the s t a t i c fatigued samples are i n order of increasing i n i t i a l strength. Figure 3 shows Wilkins' homologous fatigue stress versus time-to-rupture p l o t for an extruded graphite for two d i f f e r e n t values of the applied s t r e s s . The data f i t s the following equation reasonably Figure 2 Universal Fatigue Curves of 1. Acid-etched soda-lime s i l i c a t e glass 2. E-glass f i b e r s 3. Fused SiC^ glass 4. Abraded soda-lime s i l i c a t e glass (a f t e r R i t t e r and Sherbourne 7) 0.95 o 0" A s 3157 psi x <rA - 3069 psi I 0 W 10' 10 10 10 t r , SECONDS io" ier Figure 3 Homologous fatigue stress versus time-to-rupture of Speer RC4 graphite, (after Wilkins^) I - 8 -a R = A + B log t r (6) well where A and B are constants and t r , the time-to-rupture. This d i s t r i b u t i o n i s shown by the s o l i d l i n e s i n Figure 3. I.2.b Stress Intensity Factor-Crack V e l o c i t y Diagrams An a l t e r n a t i v e approach i n i l l u s t r a t i n g s t a t i c fatigue i s the stress i n t e n s i t y factor-crack v e l o c i t y diagram. I t has been g established by a number of i n v e s t i g a t o r s that for a given system (environment, temperature, m a t e r i a l , etc.) there i s a unique r e l a t i o n s h i p between the crack v e l o c i t y , V and the crack t i p stress i n t e n s i t y f a c t o r , K^. A schematic K^-V diagram i s shown i n Figure 4 for a material undergoing environmental stress corrosion. Three regions are apparent; i n stage I the rate of the chemical r e a c t i o n near the crack t i p controls growth; i n stage II the crack v e l o c i t y i s l i m i t e d by the rate of transport of the corrosive species to the crack; i n stage I I I , close to the c r i t i c a l s tress i n t e n s i t y f a c t o r , the crack propagation mechanism i s not well understood. The following equations describe stages I and II Stage I: V = A^K n (7) Stage I I : V - A 2 (8) where n, A^ and A^ are constants. The value of n i s 20-60 for alumina; 15-50 for glass; 30-40 f o r p o r c e l a i n . Therefore large changes i n v e l o c i t y r e s u l t from r e l a t i v e l y small changes i n stress i n t e n s i t y . - 9 -Figure 4 Schematic stress in tens i ty factor-crack ve loc i t y diagram for a mater ia l i n a stress corrosive environment. - 10 -g Kj.-V diagrams were f i r s t obtained by Wiederhorn using the double cant i lever configuration of specimen. Figure 5 i s an example of h i s resu l t s for soda-rl ime-si l ica g lass . Unfortunately, crack growth rate measurements are not ea s i ly made using the DCB technique due to the increasing stress in tens i ty with crack growth. New test methods have been evolved and i n pa r t i cu l a r , the double to rs ion test has proved to be a simple and r e l i a b l e method for studying slow crack growth. The important feature i s that K i s independent of crack length. Thus, unl ike most other tests there i s no tendency for the crack to accelerate under a constant load and produce catastrophic f a i l u r e . The theory of the double to rs ion test i s given i n Appendix 1. Data generated from the double to rs ion technique has been shown to be i n good agreement with previous data obtained from the DCB 2 9 specimen by v i s u a l measurements. ' The equivalence of the s t ress - t ime- to- fa i lure curve and the Kj-V diagram can be seen by ca lcu la t ing the l i f e expectancy. This ca l cu la t ion involves integrat ing the K^-V curve between the l i m i t s (the i n i t i a l stress in tens i ty on a flaw) and K ^ c (the point at which f a i l u r e follows almost immediately). The de ta i l s are given i n Appendix 2 and the resu l t ing equation i s ( n - 2 ) A x Y 2 a A 2 where n and A^ are the constants from equation (7), Y i s a geometric constant and o^, the applied s t ress . - 11 -i 1 1 1 r 4-0 5.0 6.0 7.0 STRESS INTENSITY FACTOR. K,. N/m s / * X I 0 8 Figure 5 Dependence of crack ve loc i t y on stress in tens i ty factor , K-j- i n soda - l ime- s i l i ca glass , (after Wiederhorn 8) - 12 -Thus, a s t r e s s - t i m e - t o - f a i l u r e curve can be p l o t t e d from knowledge of the K^-V diagram. ; A l t e r n a t i v e l y , Wilkins"^ has shown that the slope of the homologous stress versus t i m e - t o - f a i l u r e p l o t may be given by i ° * < W _ i ( 1 0 ) l o g ( t s / t r ) (n-2) where the subscripts s and r r e f e r to two specimens, one having a breaking time of t and the other of t , where t > t and ° s r ' s r correspondingly o > °JJs» n i s the slope of the corresponding Kj-V diagram. Therefore, the equivalence of s t r e s s - t i m e - t o - f a i l u r e curves and Kj-V diagrams i s well proven. I.2.c S t a t i c Fatigue Models Perhaps the most complete theory for s t a t i c fatigue i s the 13 stress corrosion theory of H i l l i g and Charles. They assumed that crack propagation was a thermally a c t i v a t e d process i n which the a c t i v a t i o n energy was stress dependent. Their equation f o r crack v e l o c i t y i s developed from the absolute reaction rate theory. I t indicates that the s t a t i c fatigue l i m i t i s a c h a r a c t e r i s t i c threshold s t r e s s . At stresses greater than t h i s threshold value, flaw sharp-ening occurs, below t h i s threshold, crack blunting. This chemical theory i s i n agreement with most experimental observations on glass and ceramics. - 13 The H i l l i g and Charles theory, however, does not account specifically for environment at crack tips. Other kinetic processes may occur controlling the crack tip environment and the crack propagation rate. For example, control of the crack tip environment by surface chemical reactions may be more important for deep cracks than for shallow cracks or for relatively flaw-free surfaces because of the small volume of solution at the crack tip and the long diffusion distance necessary to equalise bulk and crack tip environ-ment. Similar differences in surface environment have been suggested recently in the case of stress-corrosion cracking of metals.^ 15 An early theory developed by Orowan , attributed static fatigue to a decrease in surface energy caused by the adsorption of species from the environment. The reduction in strength of mica of approxi-mately one-third was compatible with the fact that the fracture energy of mica in vacuum was ten times that in a i r . Assuming that the adsorption process involved chemisorption an equation identical in form to that of H i l l i g and Charles can be obtained. The static fatigue limit would be defined by the minimum stress level compat-ible with the surface energy and the G r i f f i t h condition for failure. However, i t s t i l l remains to relate the reduction in surface or fracture energy to the processes occurring at the crack t i p . In ceramics, the fracture surface energy, Y ^ is generally an order of magnitude larger than.the thermodynamic surface energy, due to other energy terms related to irreversible processes occurring at the crack tip during propagation. These processes - 14 -include p l a s t i c deformation, cleavage step formation, subsidiary cracking, i n t e r n a l stress due to second phase p a r t i c l e s and surface roughness. Thus a reduction i n Y^ could be due to a reduction i n the thermodynamic surface energy but any of the extra energy terms may also be a f f e c t e d . Recently, Stevens and D u t t o n ^ have developed a thermodynamic and k i n e t i c model for the s t a t i c fatigue of b r i t t l e materials based on the behaviour of G r i f f i t h cracks at high temperatures. Two c r i t i c a l flaw sizes were postulated;a c r i t i c a l crack length was proposed for slow propagation by a process such as mass transport away from the crack t i p where the energy supplied to the system i s s u f f i c i e n t to create new surfaces only. For rapid propagation, other energy terms due to i r r e v e r s i b l e processes are involved. For t h i s s i t u a t i o n a larger c r i t i c a l flaw si z e was proposed. The model considered a b r i t t l e material with a s i n g l e flaw. I f the flaw was larger than the c r i t i c a l s i z e f or slow propagation, at the applied s t r e s s , i t grew slowly to the larger c r i t i c a l s i z e and then propagated instantaneously. The growth time from the o r i g i n a l s i z e to the larger c r i t i c a l s i z e i s the fatigue l i f e . The d r i v i n g force for mass transport was calculated i n terms of a chemical p o t e n t i a l gradient and according to the s i g n of t h i s gradient, a crack could e i t h e r propagate or shrink by transport of mass away from or to the crack t i p . An expression for the crack growth rate was obtained by applying mass transport theories and by i n t e g r a t i o n , the time-to-rupture was determined. - 15 -The model appears to f i t the a v a i l a b l e data quite w e l l . 16 • Stevens and Dutton considered three possible mechanisms of crack growth, bulk d i f f u s i o n , surface d i f f u s i o n and vapour phase transport. In order to e s t a b l i s h which mass transport mechanism may be c o n t r o l -l i n g the rupture time for a given system, i t would be necessary to investigate the stress and temperature dependence experimentally. Also for any p a r t i c u l a r system modification of the a n a l y t i c a l equations would be necessary due to the assumptions made i n the a n a l y s i s . The following may have to be accounted f o r : the s t a t i s t i c a l d i s t r i b u t i o n of flaw s i z e s , secondary crack branching and atmos-pheric e f f e c t s which may lower the surface energy cause l o c a l i s e d s t ress-corrosion, a f f e c t the surface d i f f u s i o n c o e f f i c i e n t , the rate of emission by evaporation and the rate of mass transport. 1.3 Previous Studies on the S t a t i c Fatigue of Graphite Time dependent f a i l u r e i n graphite was f i r s t reported by D i e f e n d o r f S t u d y i n g a commercial petroleum coke graphite he measured a consistent 10% decrease i n strength at room temperature -3 -1 when the s t r a i n - r a t e decreased to l e s s than 10 sec . The e f f e c t of environment was also shown by the f a c t that approximately h a l f the strength increase caused by r a i s i n g the temperature to 1000°C could be retained i f the specimen was kept i n a hard vacuum. Admission of a i r reduced the strength to the undegassed value, and other gases had some e f f e c t . D i e f e n d o r f ^ suggested that t h i s was - 16 -a s t ress-corrosion effect s i m i l a r to that observed i n other mater ia ls , such as g lass . ; Although a ce r ta in amount of data on conventional fatigue tes t ing of graphite has been reported, no further studies on t h i s "s t ress-corrosion effect" have been found u n t i l the publ ica t ion of 13 Wilkins data shown i n Figure 3. Wilkins concluded that at room temperature, s t a t i c fatigue of extruded graphite occurs only at a value of the applied stress which i s a very large f rac t ion of the instantaneous strength. Also for a given homologous s t ress , the s t a t i c fatigue l i f e increased with the applied s t ress , deviat ing from the behaviour predicted by the theore t i ca l model of Stevens and Dutton."^ The l a t t e r ' s re la t ionship for low temperatures, which i s pertinent to graphite at room temperature, indicates that the fatigue l i f e should decrease as the applied stress increases at a f ixed homologous s t ress . This would be i n t u i t i v e l y expected 18 from a s ingle flaw model. In a subsequent paper Wilk ins and Jones showed that the resu l t s for RC4 graphite could be explained i f in te rac t ion between the growing fatigue flaw and other flaws occurs. The only other known work on slow crack growth i n graphite has 19 been performed by Simpson who used the double tors ion technique to obtain Kj.-V diagrams both i n a i r and toluene at room temperature. The toluene apparently decreased the tendency of the i so t rop ic graphite to undergo s t a t i c fat igue. In both cases only a s ingle stage Kj.-V curve was produced., Several workers have studied crack propagation i n graphite 20 under increasing load. For example, Knibbs describes the formation - 17 -and growth of cracks i n p o l y c r y s t a l l i n e graphites as observed under 21 22 23 the o p t i c a l microscope. Other workers ' ' • have also studied graphite using both o p t i c a l and ele c t r o n microscopy. F i n a l l y , several studies have been reported on the a p p l i c a t i o n of fracture mechanics concepts to the design of graphite com-24 25 26 25 ponents. ' ' In p a r t i c u l a r , Vitovec and Stachurski obtained values f o r the c r i t i c a l s tress i n t e n s i t y f a c t o r of two graphites both wet and i n the outgassed state using T a t t e r s a l l - T a p p i n bend t e s t s . The fracture toughness of the molded POCO graphite type 5 -3/2 5 AXF-Q1 ranged from 16.8 x 10 N.m ' for the wet to 18.7 x 10 -3/2 N.m for the outgassed condition. This compared with the range 5 -3/2 5 -3/2 11.5 x 10 N.m ' to 18.5 x 10 N.m ' f o r RC4 extruded graphite. Again, t h i s indicates an environmental e f f e c t on the fracture behaviour of graphite. 1.4 Objectives of the Present Study The main aim of the present study i s to obtain some understanding of the s t a t i c fatigue phenomenon i n graphite. The most fundamental piece of frac t u r e infomation f o r b r i t t l e materials i s the stress i n t e n s i t y factor-crack v e l o c i t y curve. The double t o r s i o n technique i s used to generate such data f o r several graphites. An attempt i s made to r e l a t e the observation to micro-s t r u c t u r a l features. High temperature te s t s are also c a r r i e d out to reveal the e f f e c t s of temperature and environment on crack growth. - 18 -Various ancillary studies including structural characterisation, thermogravimetric analysis and transverse rupture tests are performed to complement the slow crack growth results. - 19 -CHAPTER II EXPERIMENTAL PROCEDURE II.1 Materials Selection In order to study the e f f e c t s of structure on slow crack growth two d i f f e r e n t grades of POCOa graphite and a p y r o l y t i c graphite* 3 were selected. POCO graphite i s an i s o t r o p i c f i n e grained material with a maximum p a r t i c l e s i z e of about 25ym. Grades AXZ (~19% porous) and AXF-5Q (~32% porous) were chosen; both are of medium p u r i t y (<660 p.-p.m. p u r i t y ) , the s u f f i x "5Q" i n d i c a t i n g a high temperature g r a p h i t i -27 sation process. Wagner et a l have confirmed that the same s t a r t i n g materials are used f o r a l l POCO graphites and that for t h i s s e r i e s of graphites the primary v a r i a b l e i s the density. In contrast to POCO, p y r o l y t i c graphite was chosen as an example of dense, well-ordered anisotropic graphite. The p a r t i c u l a r specimens used had an ash content of .01% maximum and 10 p.p.m. me t a l l i c impurities. Poco Graphite, Inc., Decatur, Texas. E l e c t r o n i c Space Products Inc., Los Angeles, C a l i f o r n i a . - 20 -II.2 S t r u c t u r a l Characterisation An important part of t h i s work was an i n v e s t i g a t i o n of the porous nature of the graphite. The following type of information can be obtained: 1. The t o t a l porosity 2. The accessible p o r o s i t i e s 3. The d i s t r i b u t i o n s of the pore sizes 4. A d e s c r i p t i o n of the pore shapes For t h i s study the bulk density, helium pycnometer density and pore-s i z e - d i s t r i b u t i o n by mercury porosimetry were measured as w e l l as o p t i c a l microscopy employed. II.2.a Bulk Density The bulk density of each graphite was measured by immersion. Bars of material (~5cm x 1.5cm x .5cm) were smoothed with s i l i c o n carbide powder (down to 1200 mesh), cleaned i n methyl alcohol and dried. Specimens were weighed i n a i r , coated i n p a r a f f i n wax and reweighed and f i n a l l y immersed i n water and weighed. The apparent density could then be determined from the weight i n a i r divided by the diffe r e n c e i n weights i n a i r and water a f t e r allowance for the water displaced by the wax. The density of the wax was c a l c u -lated by pycnometry with methyl alcohol as an immersion l i q u i d . II.2.b Helium Pycnometer Density 3 Helium displacement volumes were measured to ±.03cm using a Micromeritics Helium-Air Pycnometer. Specimens were as large as - 2 1 -possible and smoothed and cleaned as described i n II.2.a. II.2.c Mercury Porosimetry The volume d i s t r i b u t i o n of macropores i n a graphite can be obtained by mercury porosimetry. The minimum pressure, p required to force a non-wetting l i q u i d into a c y l i n d r i c a l tube of radius, r i s given by -2acos6 P = (11) where a = surface tension of the l i q u i d and 9 = contact angle (>90°) between the l i q u i d the the surface of the tube. Therfore, p o r e - s i z e - d i s t r i b u t i o n s can be measured by fo r c i n g a non-wetting l i q u i d into a porous specimen and measuring the penetrating quantity, V as a function of the pressure applied, p. Assuming the pores have a c i r c u l a r cross-section, the pore radius associated with p may be calculated from equation (11). The Department of Ceramic Engineering at the U n i v e r s i t y of Washington, Seattle, have the f a c i l i t i e s f o r undertaking mercury porosimetry measurements and members of that Department performed these t e s t s . Small rectangular blocks of POCO AXZ and AXF-5Q, 3 containing ~0.2cm open pores were prepared as i n II.2.a and sent to Seattle. - 22 -II.2.d O p t i c a l Microscopy For t h i s work the graphite was impregnated with an epoxy r e s i n to reduce the number of pull-outs produced during subsequent p o l i s h i n g . Small chips (~lmm thick) were vacuum impregnated with a sol u -t i o n of Epon 828 r e s i n and curing agent Z. The specimens were suspended above the r e s i n i n a pyrex beaker, the l a t t e r heated to 100°C i n a water bath. The beaker was under water vacuum and a f t e r allowing time to remove the a i r from the specimens, the graphite chips were tipped into the r e s i n . The samples were then poured in t o s i l i c o n e rubber mounts and put i n an oven f o r several hours. The impregnated samples were l a t e r cold-mounted and metallographi-c a l l y ground and polished using s i l i c o n carbide powder; the f i n a l p o l i s h being accomplished with a s l u r r y of 0.05ym alumina i n a 10% 23 aqueous s o l u t i o n of hydrogen peroxide. O p t i c a l photomicrographs i n b r i g h t f i e l d and po l a r i s e d i l l u m -i n a t i o n were prepared to characterise the structure. II.3 E l a s t i c Constants 28 Standard mechanical resonance techniques were used to measure the dynamic Young's modulus of rods of i s o t r o p i c graphite vibrated i n the f l e x u r a l f r e e - f r e e mode. Four specimens of each grade were prepared (20.32cm x 9.40mm x 6.35mm) and the modulus of e l a s t i c i t y , E c alculated from the following equation a f t e r obtaining the f i r s t - 23 mode resonance frequency, F, - C ^ ) * (12) P L where C = constant (429 for the system of units used). h = specimen height L = specimen length and P = specimen density The frequency, F^ was i d e n t i f i e d by f i n d i n g the higher order modes and v e r i f y i n g the r e l a t i o n s h i p s F 2 = 2.76F 1 F. = 5.39F, J 1 1 (13) F, = 8.94F. 4 1 F 5 = 13.34F 1 Values of E were corrected f o r the e f f e c t s of shear displacement 29 and rotatory i n e r t i a as outlined by P i c k e t t . This c o r r e c t i o n amounted to an increase of ~2% i n the value of E calculated from the frequency measurements. S t a t i c measurements of Young's modulus were also performed. Three c y l i n d r i c a l specimens of each POCO grade (38.10mm x 6.35mm diameter) were cut at 90° to each other. The p r e c i s i o n i n the dimensions was ±.05mm f o r the length and ±.03mm f or the diameter. A s t r a i n gauge was used to measure the compression of each cylinder on loading to about one-third the fracture load i n an - 24 -Instron tes t ing machine. The e l a s t i c modulus was calculated from the slope of the s t r e s s - s t r a in curve, an average of these measure-ments being taken i n each case. Attempts were also made to measure the Poisson's r a t i o of i so t rop ic graphite using a scanning L . V . D . T . transducer to obtain the surface p r o f i l e and hence f ind the maximum expansion of a cy l inder halfway along i t s length. Unfortunately, these tests were unsuccessful and the values of Poisson's r a t i o quoted by the manufacturers were used i n subsequent ca l cu la t ions . No measurements of the e l a s t i c constants of p y r o l y t i c graphite were made due to the d i f f i c u l t y of specimen s i z e . The manufacturers data was used as far as poss ib le . I I .4 Oxidation Studies of Isotropic Graphite Quantitative information on the oxidat ion rates of i so t rop ic graphite was obtained by thermogravimetric ana lys i s . The 30 procedure out l ined by Lewis was followed. Small s l i c e s of graphite were cut into d i scs , 6.45mm diameter and 0.64mm thickness. A .23mm radius hole was d r i l l e d a x i a l l y for inse r t ion of a gold suspension wire . The specimens were pol ished, cleaned i n methyl alcohol and dried i n vacuo as i n I I . 2 . a . The i n i t i a l weight of each sample was noted and the external surface area calculated from the dimensions. I t has been reported by several workers that platinum 31 catalyses the oxidation of graphite ; for th i s reason a gold - 25 -suspension wire (0.13mm diameter) was used to support the graphite discs ins ide the heating furnace. Isothermal weight loss experiments were car r ied out at a t o t a l pressure of one atmosphere using a Dupont thermogravimetric analyser swept with 40ml. min ^ of compressed a i r . The gas flow should be su f f i c i en t to remove a l l the product species and i n th i s case 40ml. min ^ was found to be the maximum flow rate that would not disturb the specimen. The oxidat ion of the graphite was suppressed by flushing wi th helium. Once equi l ibr ium at the desired temperature was attained the atmosphere was changed to compressed a i r . Tests were performed between 450°G and 700°C. According to 30 Lewis the oxidat ion rate for graphite i s constant for a considerable period (usually corresponding to ~25% burnoff) after the b r i e f i n i t i a l v a r i a t i o n . For each temperature chosen, a s ingle specimen was oxidised to 25% burnoff. The oxidat ion rate was then calculated from the slope of the weight loss curve divided by the geometrical and act ive surface area (see Chapter I I I and IV) of the specimens assuming that a l l the surface was oxidised at a uniform ra te . I I .5 Transverse Rupture Tests Conventional short-time transverse rupture tests were performed on a l l three graphite i n order to determine 1. The d i s t r i b u t i o n of flaws i n each mater ia l 2. The stresses and temperatures at which to conduct slow - 26 -crack growth experiments 3. The c r i t i c a l stress in tens i ty factor , K ^ c for comparison wi th values obtained from slow crack growth tests 4. Information about the flaw s i z e , c and i t s r e l a t i o n to microst ructural features. Both unnotched and notched bars were tested i n three-point bending. In the former case specimens were machine cut to 46.48mm x 4.06mm x 4.06mm and for the l a t t e r 46.48mm x 3.18mm x 3.18mm. Notches were cut into the second set of samples to a depth not more than halfway through the centre sec t ion; the notch width was 0.31mm. A l l samples were treated to remove too l marks and produce a standard surface by lapping wi th 600 g r i t emery. Specimens were then cleaned i n methyl a lcohol and dr ied . Transverse rupture tests were performed using an Instron machine with each specimen res t ing i n a three-point bend f ix ture made of ceramic. The three knives were sapphire rods with a maximum span of 25.4mm. Samples were loaded at a constant crosshead speed of 4.2 x 10 ^m.sec 1 ( .01" .min - 1 ) to f a i l u r e , the load being applied to the f ix ture by means of a b a l l bearing. The fracture time was between t h i r t y and ninety seconds depending on the material and tes t ing condi t ions . The fracture strength, a of a bar deformed i n three-point bending i s 3Px (14) - 27 -where P = fracture load x = distance between the point of fracture and the nearest outer rod ( x c J l ^ where 8, = span) b = breadth of specimen and d = depth of specimen. a F r i s often referred to as the "modulus of rupture" and repre-sents the maximum longi tud ina l stress on the t ens i l e side of the bar. I I . 5 . a Unnotched Bars I I . 5 . a . i Fracture Stress S t a t i s t i c a l D i s t r i b u t i o n at Room Temperature A s t a t i s t i c a l approach based on the "weakest l i n k " theory of 4 Weibull was used to obtain a funct ional descr ip t ion of the f rac-ture stress d i s t r i b u t i o n for each graphite at room temperature. Thi r ty unnotched bars of each material were tested i n three-point bending i n a i r to obtain the Weibull parameters from the fracture stress d i s t r i b u t i o n . The Weibull d i s t r i b u t i o n function i s based on the assumption that the test specimens are of the same population, so that a l l the p r a c t i c a l data f i t one d i s t r i b u t i o n curve. The p r o b a b i l i t y , S of f a i l u r e of a ceramic test specimen under uniaxial tension i s given by S - 1 - exp [ - V ( ^ ) m ] (15) - 28 -where S <= no. of f a i lu re s /no . of samples + 1 V = volume of specimen under stress a = applied t ens i l e stress a u = zero stress a Q = constant, t y p i c a l of the mater ia l m = Weibull modulus or mater ia l flaw density 32 After manipulation the fol lowing equation can be obtained for the case of three-point loading of a beam £n£n(-j3jr) = (m+1) £ n ( a p r - a u ) - (m+l)£na 0 (16) Thus, (m+1) can be obtained from the slope and £ n a u from the intercept of a p lo t of JUiitnOj^g-) versus SLn(a^-au). Arbi t ra ry values of a u may be chosen and cor re la t ion coe f f i c i en t s , r for a least-squares f i t of the above equation obtained. A value of a u should then exis t where the data give the best f i t to th i s equation, th i s occurs at the maximum value of r i n a plot of r versus a u . For th i s optimum a u , the corresponding values of m and aQ can be calcula ted. In these experiments the Weibull parameters for each graphite for a u = 0 and the optimum a u were determined as out l ined above. I I . 5 . a . i i High Temperature Tests for Isotropic Graphites High temperature transverse rupture tests were car r ied out for the i so t rop ic graphites between 300°C and 700°C. A nichrome - 29 -wound resistance furnace was used and temperatures measured with a chromel-alumel thermocouple placed close to each specimen. Temperatures were attained as r ap id ly as possible followed by a f ive minute soak at the test temperature. A l l samples were i n the furnace for at least ten minutes and no longer than twenty minutes. Ten unnotched bars were tested at each temperature and the mean and standard deviat ion calculated from each set of r e su l t s . I I .5 .b Notched Bars Transverse rupture tests of notched bars enable values of the c r i t i c a l stress in tens i ty factor , to be calcula ted from the plane s t r a i n equation^ o = fracture strength for notched bars Fr 6 c = notch length and v = Poisson's r a t i o In order that plane s t r a i n conditions ex i s t across the major port ion of the crack t i p and that the constraint r e l i e v i n g influence of the free faces are minimised cer ta in geometric conditions have been established for the specimen size" 3 (17) where Y geometric constant = 1.96 - 2.75(% + 13.66Or) d d - 23 .9S(% 3 + 25.22(-j) 4 , for d a - 30 --j- between 4- and 1 a o •7- between -r^ - and -i-d iXi 2 26 Kj.^ i s p a r t i c u l a r l y sens i t ive to notch sharpness and Yahr et a l have recommended <0.15mm for the width of the notch t i p . In th i s work rj- was 1, between ^ and y and notches as sharp as poss ib le , 0.31 mm. Values of K were determined at room temperature and at 500°C for both i so t rop ic graphites. For py ro ly t i c graphite, Kj. was found at room temperature with the load applied both p a r a l l e l and perpendicular to the c ax i s . Ten specimens were tested for each set of conditions and the mean and standard deviat ion ca lcula ted . I I . 5 . c Fractography Fractured specimens were cleaned i n methyl a lcohol and dr ied before examination by scanning electron microscopy. I I .6 Slow Crack Growth Tests Slow crack growth tests were performed both at room tempera-ture and at 500°C to reveal the effects of temperature and environment on the crack growth behaviour and fracture toughness measurements of the three graphites. The theory underlying the double tors ion technique has been described previously . - 31 -The specimens consisted of simple rectangular plates (76.2cm x 25.4mm x 3.2mm) grooved along the i r length with a t h i n diamond saw to leave approximately ha l f the specimen thickness. A notch was then introduced at one end of the groove to a depth of 9.5mm. The f l a t side of each specimen was polished with 600 g r i t emery, the specimens cleaned i n methyl a lcohol and dr ied . A t y p i c a l spec i -men i s shown i n Figure 6 c ) ; the dimension W, t and t n were required accurately and were measured using vernier ca l ipers and a micro-meter screw. Figure 6 a) and b) are diagrams of the loading f i x t u r e . The samples were supported on two p a r a l l e l r o l l e r s and the load applied v i a two hemispheres attached to the f i x t u r e ' s upper p la te . The s ta in less s t ee l test apparatus was designed to f i t into a high temperature compression cage, the l a t t e r being attached to a t ens i l e load c e l l i n an Instron tes t ing machine. Central loading was used, thus the specimen plate received ha l f the Instron load recorded on the chart , the rest being taken up by the back of the f i x t u r e . F r i c t i o n effects were reduced to a minimum by pol i sh ing the back hemispheres and sockets wi th diamond paste. The holder could take high temperature specimens 50.8mm long, however, i t was also used for the 76.2mm long room tempera-ture samples. Only the moment arm, Wm was required with high prec is ion and th i s was measured using a t r a v e l l i n g microscope. Figure 6. Double tors ion test apparatus and specimen a) Total assembly - 33 -Figure 6. Double torsion test apparatus and specimen b) Underside of upper plate c) Enlarged view of specimen - 34 -I I . 6 . a Compliance Ca l ib ra t ion A compliance c a l i b r a t i o n was performed to check the range of crack lengths over which the stress in tens i ty remains constant and the v a l i d i t y of the a n a l y t i c a l equations derived previously . dC Values of the slope, -^g and the intercept , D could also be obtained and used i n the calcula t ions of the stress in tens i ty-crack ve loc i t y curves l a t e r . Previously i t had been ascertained that the compliance of the f ix ture became neg l ig ib l e at loads greater than 15.6N (3.5 lbs) so that specimens were loaded to 17.8N (4 lbs) and the compliance obtained from the slope of the load-defection curve between 15.6N and 17.8N (3.5 lbs and 4 l b s ) . The samples were —8 —1 loaded once at a crosshead speed of 8.5 x 10 m.sec (.0002" . min "^ ) and then three times more quickly at a crosshead speed of 8.5 x 10 ^m.sec 1 (.002". min 1 ) . The compliance was ca lcu-lated from the l a s t run. Notched specimens of each mate r ia l , POCO AXZ, AXF-5Q and pyro ly t ic , graphite (basal planes p a r a l l e l to the largest f l a t surfaces of the specimen) were used, the notch length being successively lengthened af ter each tes t . I I .6 .b Stress Intensi ty Factor-Crack Ve loc i ty Diagrams Stress in tens i ty factor-crack ve loc i t y plots were obtained using the load re laxa t ion technique. A sharp crack was i n i t i a t e d at the end of the notch with a razor blade. The specimen was then loaded i n the Instron machine to accelerate the crack, the - 35 -crosshead stopped and the load relaxation followed on the chart recorder. The crack velocity i s given by equation (A13) from the Appendix V - - lid. <a 1 > £ + jj> ( £ ) y (A13) P where a f refers to the i n t i a l or f i n a l crack length and P f to i , t i , i the i n i t i a l or f i n a l load. The stress intensity factor, for any particular load, P can be computed from equation (A6) Wt t (1-v) n Values of the c r i t i c a l stress intensity factor, K^ .^  were obtained afterwards by loading the specimens rapidly to failure. In general, the following-procedure was carried out: 1) The specimen was loaded incrementally at a crosshead speed —8 —1 —1 of 8.5 x 10 m.sec (.0002".min" ) u n t i l a rapid load drop and relaxation curve were obtained. This indicated the formation of a sharp crack. 2) The load was increased at a crosshead speed of 8.5 x 10 m^. sec 1 (.002". min ^) to accelerate the crack and a second load relaxation curve was produced. 3) When the load had decreased to a sufficiently low value the specimen was removed from the fixture and the f i n a l crack length, a^ measured (see later). 4) The sample was then reloaded to reproduce the load relaxation -4 -1 curve and then fast loaded at a crosshead speed of 2.1 x 10 m.sec - 36 -(0.5".min """) to f a i l u r e , for the determination of K . ^ . Room temperature tests i n a i r were performed on a l l three graphites. In addi t ion high temperature tests at 500°C were car r ied out on the i so t rop ic graphites. The specimens were allowed approximately one and a h a l f hours to equ i l ib ra te at 500°C before t e s t i ng , the same procedure being followed af te r -wards as out l ined above. I I . 6 . b . i Observation of the Crack Length and P r o f i l e Crack length measurements are p a r t i c u l a r l y d i f f i c u l t with opaque materials such as graphite where some means other than v i s u a l observation i s generally needed. Various techniques were attempted. L iqu id dye penetrants and oxidat ion both f a i l e d to show the pos i t ion of the crack front close to i t s f i n a l pos i t i on . The compliance c a l i b r a t i o n was not f e l t to be s u f f i c i e n t l y accurate due to the problems of applying a c a l i b r a -t ion obtained from a simulated rather than a r e a l crack. The most successful method proved to be the use of a dead weight loading apparatus set up wi th a t r a v e l l i n g microscope. Specimens could be t o r s i ona l l y stressed and the crack opening observed v i s u a l l y . Measurements were performed by loading specimens to some load below the value at the end of load re l axa t ion . The stress in tens i ty was, therefore, su f f i c i en t to open the crack but in su f f i c i en t for the crack to move. Secondary cracking was evident close to the crack t i p making the crack length measure-- 37 -merit more d i f f i c u l t but the length was taken as the longest length of the crack i n the crack path d i r e c t i o n . The cracks could only be observed on one side of the specimen, the side that opened on loading. Thus the crack shape could not be ascertained by th is measurement. In view of t h i s , the crack front was assumed to be planar, taking the geometrical factor , <j>, discussed i n Appendix 2 as one. I I . 6 . b . i i Machine Relaxations The main problem encountered with load re laxa t ion tests was the re laxat ion of the machine i t s e l f . This appeared to r e su l t from a) grease on the lead screws, b) f lexure i n the load c e l l , c) f lexure i n the loading t r a i n and specimen f i x t u r e , the l a s t being small compared to a) and b ) . The s t i f f e s t load c e l l su i table for the required load range was the "D" c e l l and t h i s was used for a l l t es t s . An " in teg ra l defeat" switch was i n s t a l l e d on the Instron and also s i x t y pounds of weight was added to the crosshead, which proved jus t suf f ic ien t to prevent i t from " f loa t ing up".when i t was suddenly switched from "downward t r a v e l " to "stop". Most of the remaining background could be removed by loading the specimen to a load below the f i n a l , value and leaving the apparatus for ten minutes. The rest of the background was taken into account i n the ca lcu la t ion by obtaining a background load re laxa t ion curve at a load jus t below P^. Exactly the same fast load procedure was followed for the background as for the true load - 38 -re laxa t ion curve which was obtained afterwards. The resultant background curve was then subtracted from the true load re laxa-t i on curve for a moving crack. At elevated temperatures the extent of load re laxa t ion for the i so t rop ic graphite was found to be greater than at room temperature so that separation of the specimen component of the load re laxat ion and the machine component should have been easier . Unfortunately, at 500°C the background was unpredictable due to small temperature f luctuat ions causing the support rods to expand and contract . Therefore, i t was decided to cycle the temperature at 500°C to ±h°C. The temperature change was monitored on a separate s t r i p chart recorder and the machine load could be seen to change on the Instron chart c y c l i c a l l y wi th the temperature change. After al lowing about one and a ha l f hours for equ i l i b r a t i on a load re laxat ion curve was obtained by fast loading the specimen jus t before the peak of the u p h i l l load cycle was reached. The specimen component of the load re laxat ion was therefore super-imposed on the downhill load cycle of the machine component. To obtain the machine component th i s procedure was repeated at a load below the f i n a l , P^ value as outl ined before. I I . 6 . b . i i i Fractography A se lec t ion of fracture surfaces were examined by scanning electron microscopy. - 39 -CHAPTER I I I RESULTS AND CALCULATIONS I I I . l S t ructura l Character isat ion I I I . I . a Density and Porosi ty The densi t ies and poros i t ies of POCO AXZ, AXF-5Q and py ro ly t i c graphite at room temperature are l i s t e d i n Table I . Each i s o -t rop ic graphite was received i n the form of a s ingle large block, however, the p y r o l y t i c graphite consisted of 3mm th ick p la tes . The larger error i n the bulk density for the l a t t e r was therefore due to sampling differences rather than a r e a l va r i a t i on i n the density of a s ingle specimen. The i so t rop ic graphites had extremely reproducible dens i t ies . For cer ta in carbons helium i s not an idea l displacement 33 f l u i d since i t i s adsorbed at room temperature, th i s adsorption decreasing to zero at 300°C. I t was c l e a r l y impossible to follow the recommended pract ice of making helium density measure-ments with samples at 300°C or higher and as no l i t e r a t u r e could be found report ing such adsorption effects for the graphites investigated here a correc t ion for t h i s was not f e l t necessary. The t o t a l , accessible (open) and inaccessible (closed) poros i t ies were calculated from the equations Table I Densi t ies and porosi t ies of graphites at room temperature o _o 27 (based on theore t ica l density = 2.25 x lO^Kg.m J ) Property POCO AXZ POCO AXF-5Q P y r o l y t i c Graphite Bulk Density „ • _ „ r , 3 -3 1.552 ± .005[4] a 1.854 ± .005[4] 2.19 ± .02L4J xlO Kg.m Helium Pycnometer ± # 0 0 8 [ l ] 2.180 ± .006[l] 2.28 ± .03[l ] Density 3 -3 xlO Kg.m Total Poros i ty % 31.0 17.6 2.7 Closed Poros i ty „ 2.1 3.1 Open Poros i ty 2 Q g 1 4 > 5 2 > 7 % No. of measurements - 41 -Total porosi ty = ( — ^bulkj x 1 Q Q % ( l g ) P Th Closed porosi ty = ( — —) x 100% (19) p Th Open porosi ty = Tota l porosi ty - closed porosi ty (20) where p = theore t ica l graphite density P'bulk = bulk or apparent density p R e = apparent density i n helium pycnometer I l l . l . b Pore-S ize-Dis t r ibu t ion Figure 7 shows the as-received mercury porosimetry curves. For the pore diameter ca lcu la ted , a wetting angle of 130° of _3 mercury on graphite and surface tension of mercury of 485 x 10 N.m 1 were used. The pore - s i ze -d i s t r ibu t ion curves dV/2dr as a function of 2r was then obtained by graphical d i f f e r en t i a t i on and these are shown i n Figure 8 for one sample of each POCO. From the d i s t r i b u t i o n curve the in te rna l surface area, F was ca lcula ted . The t o t a l in t e rna l surface area of a l l pores with r a d i i between r^ and i s given by 2<g)dr (21) 1 For a c y l i n d r i c a l pore p r P I l l I I T i 1 1 i r I . O to 6 0.2I 10 1 O X o CO 0. POCO A X Z POCO AXF-5Q I I I I I 10 8 PORE DIAMETER , X \0" Sm " B " 0. S3 Figure 7 . Mercury penetration versus pore diameter for i so t ropic graphites 1.4 I I I l l i I A 2.41 » i r 12 l.0|-l CU E O 0.8 "O Q6l CM > 0.4 0.2l 04. 0.1 0.2 i t 1 \ 0.4 0.6 1.0 2 k - 6 PORE DIAMETER, X IO - 6 m. Figure 8 a) Po re - s i ze -d i s t r ibu t ion curve for POCO AXZ "B* 6 8 10 0.1 0.2 0.4 0.6 1.0 2 4 6 8 10 PORE DIAMETER, X I0 _ 6 m. Figure 8 b) Pore - s i ze -d i s t r ibu t ion curve for POCO AXF-5Q "A" - 45 -where F , V and r are the surface area, volume and radius of P P P the pore, respec t ive ly . A summary of the resul ts obtained from mercury porosimetry i s given i n Table I I . I I I . l . c Opt ica l Microscopy Opt ica l micrographs of the i so t rop ic graphites and p y r o l y t i c graphite are shown i n Figures 9 and 10. I I I . 2 E l a s t i c Constants Table I I I l i s t s the e l a s t i c constants of the graphites at room temperature. In a p o l y c r y s t a l l i n e body composed of anisotropic c r y s t a l s , a random d i s t r i b u t i o n of these c rys ta l s resu l t s i n i so t rop ic properties on a macroscopic scale . Therefore, values of G, the shear modulus for POCO AXZ and AXF-5Q were calculated from the i so t rop ic e l a s t i c i t y re la t ionship where E = Young's modulus and v = Poisson's r a t i o of an i so t rop ic homogeneous mate r ia l . These resu l t s are also included i n Table I I I . Hence F = (23) Table I I Summary of resul ts from mercury porosimetry Property POCO AXZ POCO AXF-5Q Diameter xlO" 6 m Surface Area 0.79 0.95 xloW1 °'28 °'08 Total Pore Volume ,_-3 3^ -1 0.195 0.21 0.0715 0.0695 xlO m Kg Tota l Surface Area ._3 2TT -1 1.18 0.31 xlO m Kg Most Probably Pore S ize : Maximum Pore Diameter Measured x l0 - 6 m 1 0 1 0 "A" and "B" are two samples of the same nominal mater ia l . - 47 -I—I a ) 10um b) lOum Figure 9 Optical micrographs of a) POCO AXZ x582 b) POCO AXF-5Q x800 - 48 -t 1 a) 100pm , , b) 100pm Figure 10 Optical micrographs of py ro ly t i c graphite a) Basal plane xl33 b) Cross-section of basal planes Polar ised Light x200 Table I I I E l a s t i c constants of graphites at room temperature Property POCO AXZ POCO AXF-5Q P y r o l y t i c Graphite Dynamic Modulus, E GN.m - 2 (x lO 6 ps i ) 7.1 ± 0 . 5 [ 4 ] a (1.03 ± 0.07) 13.4 ± 0.2[4] (1.94 ± 0.03) "a" d i rec t ion 28 - 41 C Sta t i c Modulus, E GN.m - 2 (x lO 6 ps i ) 6.9 ± 0 . l [3 ] (1.01 ± 0.01) 13.1 ± 0 . l [3 ] (1.90 ± 0.01) (4 - 6) Poisson 's Ra t io , v dimensionless Shear Modulus, G GN.m - 2 (x lO 6 ps i ) 0 .25 b 2.7 (0.39) 0.15 b 5.7 (0.83) "a" d i rec t ion - 0 . 1 c "c" d i rec t ion +0.9C No. of measurements Data sheet, POCO Graphite, I nc . , Decatur, Texas Data sheet, E lec t ron ic Space Products Inc . , Los Angeles, C a l i f o r n i a - 50 -III.3 Oxidation Studies of Is o t r o p i c Graphite T y p i c a l weight loss-time curves f o r the oxidation of graphite are shown schematically i n Figure 11, following the notation used 30 by Lewis. For POCO AXZ the i n i t i a l rate of l o s s of weight decreased f a i r l y r a p i d l y to a steady value (Type I ) ; i n comparison, the oxidation rate of POCO AXF-5Q increased i n i t i a l l y (Type I I ) . For both materials the oxidation rate was cal c u l a t e d from the l i n e a r portion of the curve which extended to about 25% burnoff. The accessible surface area was taken as the geometrical and a c t i v e surface area (ASA) where an appropriate value of the ASA was obtained by considering 5% of the i n t e r n a l surface area calculated by mercury porosimetry. The reason for t h i s i s explained i n Chapter IV. By measuring the oxidation rate at various temperatures the a c t i v a t i o n energy f o r the reac t i o n could be obtained from an Arrhenius p l o t . The r e s u l t s are shown i n Figure 12 together with Lewis's data f o r vitreous carbon and p y r o l y t i c graphite. The upper and lower l i m i t s of the data points for POCO AXF-5Q represent 25% and 12%% burnoff, r e s p e c t i v e l y since the oxidation rate f o r t h i s material never attained a true steady-state value at any p a r t i c u l a r temperature. These l i m i t s represent a maximum v a r i a t i o n i n the oxidation rate of ~±13%. A steady-state oxidation rate was achieved i n the case of POCO AXZ and t h i s i s shown as a singl e data point at each temperature. A l l rate measurements for t h i s material were reproducible to within ±5% between 12%% and 25% - 51 -o o co TIME (arbitrary scale.) Figure 11. Schematic weight loss-t ime curves for graphites (after L e w i s 3 0 ) Figure 12„ Oxidation rates of i so t rop ic graphites (calculated on the basis of geometrical and act ive surface area) ; - 53 -burnoff. For c l a r i t y , the error bars have been l e f t out. The o v e r a l l and i n d i v i d u a l rates for the oxidat ion of graphite are usual ly expressed i n the form R = A exp (- | j ) ( P 0 2 ) n (25) where A 8 3 pre-exponential factor E = apparent ac t iva t ion energy pC^ = p a r t i a l pressure of oxygen andn= react ion order. Linear regression analyses for zones I and I I for POCO AXF-5Q and zone I for POCO AXZ were performed and equation (25) used to calculate the apparent ac t iva t ion energies for each zone. The resu l t s are shown i n Table IV. Var ia t ions i n the oxidat ion rate due to the changes i n r e a c t i v i t y from specimen to specimen may be judged from the degree of scatter i n the r e su l t s . After oxidation the specimen discs were remeasured. The only dimensional change appeared to be i n the disc radius , a reduction of .025mm, ind ica t ing preferred oxidat ion from the edges. - 54 -Table IV Linear regression analysis of oxidat ion resu l t s for i so t rop ic graphites Rate equation: R log R A exp - ( P 0 2 ) n -E 1 , fc fc 2"*3R * T* c o n s t a n t y = m.x POCO AXZ POCO AXF-5Q ZONE I No. of data pts . Corre la t ion Coe f f i c i en t , r b m E kJ.mole --'-(kcal .mole - ! ) 7 0.99 11.1 , -1.10x10 12.1 (51) 4 0.99 11.4 -1.09 x 104 12.0 (50) ZONE I I No. of data pts . Corre la t ion Coe f f i c i en t , r b m E kJ.mole --'-(kcal .mole - ! ) 3 0.99 3.4 -4.09 x 10" 4.5 (19) - 55 -I I I . 4 Transverse Rupture Tests Typica l load-def lect ion curves for the transverse rupture tests are given i n Figure 13. In general , type A behaviour was observed but for py ro ly t i c graphite loaded p a r a l l e l to the c axis type B was obtained. I I I . 4 . a Unnotched Bars I I I . 4 . a . i Fracture Stress S t a t i s t i c a l D i s t r i b u t i o n at Room Temperature Figure 14 a)-c) are Weibull p lots of the fracture s tress data at room temperature for the three graphites, a u = 0. The mean fracture s t ress , together with the standard deviations are -4 -6 shown i n Table V; BIO and BIO refer to the stress at which -4 -6 the f a i l u r e p robab i l i ty i s 10 and 10 , respec t ive ly . Values of the Weibull parameters, m and aQ as w e l l as the corresponding coe f f i c i en t , r , are also given i n Table V for both a u = 0 and the best calculated value of a u . I I I . 4 . a . i i High Temperature Tests for Isotropic Graphites Table VI a) and b) l i s t s the mean fracture stress and standard deviat ion of the i so t rop ic graphite tested at various temperatures. The function, mean fracture stress divided by standard deviat ion gives some ind ica t ion of the scatter of the data and as can be seen from Table V i s a parameter s imi l a r to the material flaw density, m for a u = 0. The high temperature - 56 -% INITIATION OF FRACTURE DEFLECTION (arbitrary scale.) DEFLECTION (arbitrary scale.) Figure 13. Typica l load-def lect ion curves for transverse rupture tests PROBABILITY OF FAILURE, % . ro cn o O O O Ln.Ln. (1/ l-S) - £S -Figure 14 b) Weibull p lot of transverse rupture tests at room temperature for POCO AXF-5Q, a u = 0 Ln. <TFr Figure 14 c) Weibul l p lo t of transverse rupture tests at room temperature for py ro ly t i c graphite, a u =0 Table V Transverse rupture test data for graphites at room temperature a) Mean fracture stress and standard deviat ion Mean Fracture Standard M _, . _ „. _ Mean Fracture Stress m . „ n Mater i a l Stress „ Deviation — r - —-z— v ^ r — r - — : m at a = U , „7 -2 , „7 -•) Standard Deviation u xlO'N.m xlO'N.m 1 (psi) (psi) POCO AXZ 5.08 0.60 8.5 8.4 (7,370) (870) POCO AXF-5Q 9.98 0.82 12.2 12.4 (14,477) (1,183) ON o P y r o l y t i c graphite Load perpendicular to"c"axis 16.67 (24,186) 1.99 (2,881) 8.4 8.2 Table V b) Weibull parameters for a = 0 and best estimated value of a r u u Mate r i a l x l0 7 N.m~ 2 (psi) x l0 7 N.m~ 2 (psi) m BIO x l 0 7 N . m - 2 (psi) B I O ' 6 x l0 7 N.m~ 2 (psi) POCO AXZ 0 5.34 (7,752) 0.9755 8.4 2.00 (2,897) 1.22 (1,771) 3.5 (5,077) 1.79 (2,596) 0.9926 1.6 3.55 (5.156) 3.51 (5.091) POCO AXF-5Q 0 10.35 (15,019) 0.99031 12.4 5.20 (7,542) 3.68 (5,344) 2.0 (2,901) 8.35 (12,113) 0.99033 9.6 3.50 (5,080) 2.27 (3,290) P y r o l y t i c graphite 0 kb Load p e r p e n d i c u l a r ( 8 > 7 ° 5 ) 17.55 (25,463) 11.54 (16,736) 0.9906 0.9918 8.2 4.7 6.43 (9,330) 8.30 (12,034) 3.89 (5,647) 7.02 (10,189) to "c " axis Table VI Transverse rupture test data for i so t rop ic graphites at various temperatures a) POCO AXZ Temperature °C (± 1 2°C) Mean Fracture Stress « x l0 7 N.m (psi) Standard Deviation x l 0 7 N . m " 2 (psi) Mean Fracture Stress Standard Deviation No. of Specimens tested 26 5.08 0.60 8.5 30 (7,370) (870) 301 5.43 0.51 10.6 10 (7,875) (746) 401 4.92 0.41 12.0 10 (7,133) (593) 502 4.53 0.41 11.0 10 (6,569) (595) 600 4.40 0.31 14.0 10 (6,388) (457) Table VI b) POCO AXF-5Q Temperature Mean Fracture Standard Deviation Mean Fracture Stress No. of Specimens °C Stress (± < 2°C) x l 0 7 N . m - 2 (psi) (psi) 7 -2 xlO N.m Standard Deviation tested 24 9.98 (14,477) 0.82 (1,183) 12.2 30 300 11.02 (15,985) 0.65 (949) 16.8 10 400 11.11 (16,117) 0.80 (1,154) 14.0 10 500 11.16 (16,187) 0.72 (1,041) 15.6 10 602 10.17 (14,755) 0.69 (996) 14.8 10 701 9.37 (13,596) 0.86 (1,250) 10.9 10 - 64 -resu l t s are p lot ted i n Figure 15, where the error bars represent the standard deviat ion of the r e s u l t s . I I I . 4 .b Notched Bars The c r i t i c a l stress in tens i ty fac tor , K T calculated for J Ic a l l three graphites are shown i n Table V I I . The effect ive surface energy for fracture i n i t i a t i o n , Y^ can be estimated from K J c using the plane s t r a i n equation K I c - £ V (26) 1 0 (1-v ) where E and v can be taken from Table I I I . The flaw s i z e , c, for unnotched bars can now be determined from the modified G r i f f i t h equation °Fr = Y ( — > ( 1 ) where cr = mean fracture stress for unnotched bars Fr Y = geometric constant = 1.945 for the unnotched bars. Values of Y^ and c are also shown i n Table V I I . The beam formula s t r i c t l y applies only to homogeneous, i so t rop ic materials whereas py ro ly t i c graphite i s an iso t rop ic . I t was assumed, however, that the equations could s t i l l be used without appreciable error i f the modulus of e l a s t i c i t y was that for the d i r ec t ion p a r a l l e l to the axis of the beam and the Poisson's r a t i o , the negative of the r a t i o of the s t r a in i n the d i r ec t i on - 65 -12.01-2 0 0 4 0 0 6 0 0 SPECIMEN TEMPERATURE, °C. Figure 15. Modulus of rupture versus temperature for i so t rop ic graphites (Error bars = 2a) Table VI I K , Y^ and c of graphites calculated from transverse rupture tests Mate r i a l Temperature °C (+ <_ 1 °C) xlO Mean Ic 5 M "3/2 N.m Standard Deviation Y i J.m 2 c yms 25 7.65 0.64 38 ± 9 56 ± 20 POCO AXZ 500 7.79 0.63 40 ± 7 73 ± 25 24 15.24 0.51 85 ± 7 60 ± 14 POCO AXF-5Q 500 15.78 0.72 91 ± 10 52 ± 11 P y r o l y t i c graphite Load p a r a l l e l to "c" axis - 67 -p a r a l l e l to the crack root to the s t r a i n i n the d i r e c t i o n p a r a l l e l to the axis of the beam with a s t r e s s applied i n the l a t t e r d i r -24 ection. The appropriate e l a s t i c constants for each o r i e n t a t i o n are -2 6 a Load perpendicular E = 34GN.m (5 x 10 psi) SL to c axis v = -0.1 Load p a r a l l e l E = 34GN.m"2(5 x 1 0 6 p s i ) a a k to c axis v = +0.35 The flaw si z e c a l c u l a t i o n i s independent of the Young's modulus so that values of c may be treated with more confidence than y ^ . No unnotched specimens of p y r o l y t i c graphite were tested with the load p a r a l l e l to the c axis so that an estimate of the flaw s i z e for t h i s o r i e n t a t i o n was not pos s i b l e . The errors shown i n Table VII for y ^ and c were estimated from the standard deviations of °p r» and the dynamic Young's modulus. III.4.C Fractography Scanning electron micrographs of fr a c t u r e o r i g i n s and surfaces of various transverse rupture specimens are shown i n Figures 16-21. Mean value of E a quoted by the manufacturer. b Transverse s t r a i n along planes due to stress perpendicular to planes; value taken from the l i t e r a t u r e ^ . - 68 -Compres-s i v e S u r f a c e I 1 a) lOOOum Fracture Surface Polished Tensile Face outs b) lOOym Figure 16 SEM photographs of POCO AXZ unnotched bars at 600°C a) Fracture surface xl3.5 b) Fracture origin x300 - 69 -Fracture Surface Fracture Surface Machined Surface b) 10pm Figure 17 SEM photographs of POCO AXZ notched bars at room temperature a) Notch t i p x300 b) The same xlOOO Machined Surface - 70 -Fracture Surface Face «pp ... I 1 a) lOOOum Fracture Surface Polished Tensile Face I 1 b) lOOum Figure 18 SEM photographs of POCO AXF-50 unnotched bars at 700°C a) Oxidation pits x30 b) Oxidation pit and grain pull-outs x300. - 71 -F i g u r e 19 SEM photographs of unnotched p y r o l y t i c g r a p h i t e a t room t e m p e r a t u r e , l o a d p e r -p e n d i c u l a r t o the c a x i s . a) O v e r a l l c r a c k f r o n t x l 5 b) F r a c t u r e o r i g i n s x80 - 72 -I 1 a) lOOOum I 1 b) lOOum Figure 20 SEM photographs of notched pyro ly t i c graphite at room temperature, load perpendicular to the c axis a) Overa l l fracture surface x20 b) Notch t i p xlOO I 1 a) lOOOym 1 1 b) lOOum F i g u r e 21 SEM photographs o f n o t c h e d p y r o l y t i c g r a p h i t e at room t e m p e r a t u r e , l o a d p a r a l l e l t o t h e c a x i s . a) O v e r a l l f r a c t u r e s u r f a c e x20 b) B a s a l p l a n e l a y e r s x300 - 7 4 -I I I . 5 Slow Crack Growth Tests I I I . 5 . a Compliance Ca l ib ra t i on Figure 22 shows a plot of the compliance of a notched specimen of POCO AXZ as a function of the load. I t can be seen that the compliance becomes approximately constant at loads greater than 15.6N (3.5 lbs) wi th a standard deviat ion of 2% at higher loads. The specimen compliance versus machined notch length c a l i b r a -t ions for the three graphites are p lot ted i n Figure 23 with a summary of the resul ts i n Table V I I I . The r a t i o of the in tercept , D to the slope, B of the compliance ca l i b r a t i on are also given i n the tab le . The importance of these values on the ca l cu l a t i on of crack v e l o c i t y i s discussed l a t e r . F i n a l l y , the apparent Young's modulus of py ro ly t i c graphite was included for completeness using a value of Poisson's r a t i o of -0.1 i . e . a d i r e c t i o n . I I I .5 .b Stress Intensi ty Factor-Crack Ve loc i ty Diagrams Typica l load re laxat ion curves for the graphites are shown i n Figures 24 and 25. The t o t a l load drop during a re laxat ion was extremely small so that a h ighly sens i t ive load scale was required for accurate measurements. A f u l l scale load of 17.8N (4 lbs) was used i n conjunction with a load suppression sca le . The i n i t i a l -3 stages of the re laxa t ion were followed on the chart at 4.2 x 10 m. sec 1 (10".min "*") and l a t e r at 8.5 x 10 ^m.sec 1 (2".min ^ ) . The t o t a l distance of crack propagation i n the re laxat ion of POCO AXZ B(Figure 24b))was ~1.9 mm measured v i s u a l l y . The length *4 IN c n ro ro I PJ 3 o ro < ro H CO C ca o Pi £u rh O rt 3 o r t O 3* ro a. cn i a ro o fc? ro 3 O o ro o COMPLIANCE, X lO^m.N"1 OJ O O o > ro o 0 0 OJ O 4> o o o Z </> o cn —+ r r o CO r r Q a. rt> to 3 (£> ro r r ex. II II b 00 ol o o ro cn X CD 3 5 5 i 3 O a> p- 3 3 • tt> • 1 o ' j_ ro OJ cn O c r -|a> CD 4>, <X> COMPLIANCE fXI0"^lnch. lbs'1 - S L -- 76 -4 0 -10 © P O C O A X Z + P O C O A X F - 5 Q A P Y R O L Y T I C G R A P H I T E 6 . 0 4.0 O X UJ o < _ J CL 2 O o 2.0 10 2 0 3 0 4 0 5 0 6 0 NOTCH LENGTH ,XI0"V Figure 23. Specimen compliance versus machined notch length of the three graphites Table VI I I Summary of resul ts from compliance ca l ib ra t ions POCO AXZ POCO AXF-5Q P y r o l y t i c graphite Linear regression analysis equation C = 1 = Ba + D P 4 .45xl0~ 5 a + 15.20xl0~ 7 3 . 0 2 x l 0 - 5 a +10.17xl0~ 7 2 . 4 7 x l 0 - 5 a + 1 3 . 4 6 x l 0 - 7 No. of data p ts . Corre la t ion Coef f ic ien t , r 0.99 0.99 0.99 D B x l 0 _ 3 m 34.25 33.68 54.51 A n a l y t i c a l slope B = -= dC_6Wm2(l+v) da' Wt^E x l O " 5 N _ 1 Apparent E from empir ical equation GN.m' -2 ( x l 0 6 p s i ) 8.33 13.40 (1.94) 4.23 18.74 (2.72) "a" d i r ec t ion 20.83 (3.02) Figure 24. Typica l load re laxat ion curves at room temperature for a) POCO AXF-5Q 60 70 80 90 100 110 TIME,sec. Figure 24. Typica l load re laxat ion curves at room temperature for b) POCO AXZ c) P y r o l y t i c graphite - 81 -of crack growth obtained by numerically integrat ing the re laxa t ion curve was ~0.64mm. From the re la t ionsh ip a i P i = a f P f ( 2 7 ) a value of 0.56mm was ca lcula ted . Most of the crack growth occurs i n the i n i t i a l part of the re laxat ion where the reso lu t ion of the v e l o c i t y i s l imi t ed by the recorder chart speed, accounting i n part for the larger value of crack length increase obtained v i s u a l l y . However, neither the correct ion factor , <{> due to the shape of the crack p r o f i l e nor the r a t io were included i n the v e l o c i t y ca l cu la t ion and both factors may have an effect . The K^-V diagrams calculated from the load re laxat ion curves are drawn i n Figures 26-29 and the resu l t s summarised i n Table IX. In the case of py ro ly t i c graphite, a value for Poisson's r a t i o of -0.1 was used i . e . crack propagation was assumed to occur i n the a d i r ec t i on . A summary of the K ^ c and Y^ values for the graphites obtained from the notched bar tests and the double tors ion technique i s 35 given i n Table X. Simpson's data for POCO AXF-5Q i s also included and a graphical comparison of the K -V diagrams for th i s material i s shown i n Figure 30. Although the K -V diagrams generally show considerable scat ter , data for POCO AXF-5Q i s quite reproducible, a l l points 5 -3/2 being wi th in experimental error (~±.05 x 10 N.m ) . However, there appears to be a r ea l v a r i a b i l i t y i n the specimens of POCO K x ,XI0 5N.m- 3 / 2 6.0 6^ 4 6.8 72 7.6 1 1 1 •' ' 578 5.80 5.82 5.84 5.86 5.88 5.90 LOG. Kz Figure 26. K T - V diagram for POCO AXZ at room temperature i n a i r 13.8 14.0 K x , X IO 5 N.m- 3 / 2 14.2 14.4 14.6 A B C D • = A = B o = C A = D = K I C (B) (CandD) 6.140 6.145 6.160 6.150 6.155 LOG. K x Figure 27. K T - V diagram for POCO AXF-5Q at room temperature i n a i r 6.165 - 84 -Figure 28. K^-V diagrams for POCO AXZ and POCO AXF-5Q at 500°C i n a i r - 85 -Kj.X l05N.mr3 / 2 -3 23.4 23.8 24.2 24.6 25.0 Figure 29. K^-V diagram for py ro ly t i c graphite at room temperature i n a i r 6.40 Table IX Summary of results from Kj-V diagrams Linear regression analysis equation: log V = nlogK +A y = m.x + D a) POCO AXZ at room temperature in air Parameter Specimen Mean A T Correlation Coefficient, r 0.88 1.0 0.93 0.99 0.99 0.99 0.94 0.99 0.98 CO -3658 -3698 -4957 -4072 -3935 -3697 -3095 -4191 -2754 -3784 ± 634 n 630 637 855 700 676 632 529 714 469 649 ± 110 K I c xl0 5N.m~ 3 / 2 6.72 7.28 7.78 7.3 + 0.5 J.m -2 35 ± 7 Table IX b) POCO AXF-5Q at room temperature i n a i r Parameter Specimen Mean A B C D Corre la t ion Coefficient , 0.98 0.97 0.96 0.94 r -1451 -1355 -1267 -1320 -1348 + 78 n 235 220 205 214 219 ± 13 co ^4 Ic x l 0 5 N . m " 3 / 2 14.55 14.57 14.57 14.56 ± .01 J . m - 2 78 ± 2 Table IX c) POCO AXZ at 500°C i n a i r T = 503 ± 1°C Parameter Specimen Mean Corre la t ion Coef f i c i en t , 0.86 0.99 0.99 r -277 -370 -459 -368 ± 91 n 47 63 78 63 ± 16 Time i n furnace ~3% ~3% ~3% hrs K x 1 0 5 N # m - 3 / 2 5.96 6.60 6.74 6.4 ± 0.4 T 1 -2 27 ± 5 J.m Table IX d) POCO AXF-5Q at 500°C i n a i r T = 499 ±2.5°C Parameter Specimen Mean A B C D Corre la t ion Coefficient , 0.96 . 0.98 0.96 0.96 r A -896 -742 -697 -821 -789 ± 88 n 146 121 113 " 133 128 ± 14 Time i n 1 furnace ~3% ~3 ~2 ^ ~1% hrs K x S5N.m-3/2 <1 2'7 0> " 1 4 ' 4 7 ( 1 4 ' 2 4 ) Y i J.m' -2 77 ± >2 oo VO Table IX e) P y r o l y t i c graphite at room temperature i n a i r Parameter Specimen Mean D A' Corre la t ion Coeff ic ient , r 0.85 0.95 -3342 -3705 0.94 0.53 0.94 (0.53) (0.94) -1451 -1316 -3243 (-1315) (-3242) A,A* and C 3430 ± 243 B and C 1384 ± 67 V O o n 523 580 227 205 507 (205) (507) A,A' and C 537 ± 38 B and C 216 ± 11 K T Ic x l 0 5 N m " 3 / 2 24.96 25.07 25.02±.06 Y i J . m - 2 90 ± >1 - 91 -Table X . Summary of K_ • and y ± values for graphites i n a i r . Type of Test Notched Bar Double ' Torsion Mate r ia l |, and Temperature Ic i n 5 M -3/2 xlO Nm Y i Jm 2 K I c x l 0 5 N n - 3 / 2 Y i . -2 J.m POCO AXZ Room temperature 7.7±0.6 38±9 7 .3±0.5 35+7 500°C 7.8±0.6 40±7 6.4±0.4 27+5 POCO AXF-5Q Room temperature 15.210.5 85±7 14.5610.1 /c- 35 (Simpson : 14.9) 7812 500°C 15.8+0.7 91110 14.47 77t>2 P y r o l y t i c graphite Room temperature 35+3 179±>25 25.021.06 901>1 (load perpendicular to "c" axis) ("a" d i rec t ion) 4419 244l>100 (load p a r a l l e l to "c" axis) Figure 30. Comparison of present data for POCO AXF-5Q 35 at room temperature wi th Simpson's - 93 -AXZ and p y r o l y t i c graphite. During prel iminary experiments i t was found that when the crack ran prec ise ly down the centre of the guiding groove, lower values of K ^ c were produced and the K^-V diagram was to the l e f t of the p l o t . This was presumably due to the fact that a crack running along the shoulder of the groove experiences a lower stress i n t ens i ty , for the same load, than i f i t were i n the middle of the groove. A larger surface area i s also exposed. Control of the crack path was attained i n the case of POCO AXF-5Q by making the aspect r a t i o , W/t R as large as possible and thereafter spec i -mens were grooved to ha l f the i r o r i g i n a l thickness. However, wi th POCO AXZ the crack s t i l l tended to run along the side of the groove so that data for t h i s mater ia l i s probably on the high s ide; the maximum experimental error due to th i s effect i s estimated to be 5 -3/2 .05 x 10 N.m ' . A great deal of time was spent i n obtaining load re laxa t ion curves for py ro ly t i c graphite. At f i r s t specimens were deeply grooved to about two-thirds the o r i g i n a l thickness i n order to reduce the fracture load for these tes t s . However, a reproducible load re laxat ion curve could not be obtained. A crack would form at a pa r t i cu la r load but i t would stop, and successively higher loads were required before i t would move again. On studying the specimen l a t e r , i t appeared that the crack had not passed through a l l the web but only a few layer packets of basal planes at a time so that on load r e l ax ing , delamination had occurred. - 94 -Presumably, a higher stress in tens i ty would then be required to break through another layer packet and for delamination to occur again. A schematic diagram of t h i s i s shown i n Figure 31 together with a photograph of a specimen. Further experiments were car r ied out using specimens with a th icker web (~2mm) and reproducible load re laxa t ion data was obtained. Another feature of py ro ly t i c graphite was that the crack path was p a r t i c u l a r l y sens i t ive to the specimen alignment. I n i t i a l l y , the crack would move s t ra ight along the centre of the groove, however, on reloading a sample after a load re laxa t ion measurement and estimating the f i n a l crack length, the crack would become crooked and twis t and shear to one side of the specimen. The onset of t h i s was generally marked by a long load re laxa t ion on the Instron chart at a load below that corresponding to the f i n a l P^ value. Therefore, no values of were obtained for specimens A, B or C. was determined using new specimens D and E , after load re lax ing i n the appropriate region and fast loading to f a i l u r e . Study of the crack path afterwards revealed that the cracks were also crooked after fast loading. In a l l cases, the upper l i m i t for the crack v e l o c i t y range was generally determined by the crosshead speed applied to the specimen p r io r to r e l axa t ion ; the lower l i m i t was determined by the machine background. Study of the form of the crack v e l o c i t y equation indicates that as the load required for crack propagation i s ra i sed , the range of crack v e l o c i t i e s that can be obtained -i 1000 pm b . ) F igure 31 a) Schematic diagram of pyro ly t i c graphite double torsion specimen showing process b) Photograph of py ro ly t i c graphite with delaminations x 12 - 96 -sh i f t s to lower values. This was evident from the fact that higher crack v e l o c i t i e s could be obtained for the lowest strength mate r ia l , POCO AXZ. I t was decided not to include the correct ion fac tor , D/B i n the crack ve loc i t y ca l cu la t ion due to the poor correspondence between the apparent and dynamic moduli of the graphites. The crack v e l o c i t y was recalculated to show the effect of t h i s cor-rec t ion for the case of py ro ly t i c graphite, specimen C and th i s i s shown by the dotted dashed l i ne s i n Figure 29. The corresponding equations are given i n brackets i n Table IXe) . The crack v e l o c i t i e s are e f fec t ive ly increased by a factor of f ive resu l t ing i n a change i n the intercept value, A but no change i n the s lope, n of the Kj.-V diagram. This correct ion was neglected i n the subsequent ca lcu la t ion of the l i f e expectancy since the t ime- to^fa i lu re , T i s much more sens i t ive to changes i n n than A. For the i so t rop ic graphites, the apparent correct ion factor was not as large as for ' p y r o l y t i c graphite, being about three compared with f ive for the l a t t e r . I I I . 5 . C L i f e Expectancy The l i f e expectancy for the three graphites was calculated from the equation 2 ( K I i 2 ' n " K l c 2 " n ) x = 1 1 ' 1° (9) (n-2)A Y 2 a 2 A where K^.^ = stress in tens i ty factor at the most serious flaw =Y ° ^ c 0 - 97 -= c r i t i c a l stress in tens i ty factor A = an t i log of the intercept from the Kj-V diagram n = slope of the K^-V diagram y = geometric constant - 1.945 c Q = i n i t i a l flaw s ize a = fracture strength from transverse rupture tests on unnotched bars Inherent i n th i s ca lcu la t ion i s the assumption that the data from macroscopic cracks (K^-V diagrams) Is relevant and can be applied to the propagation of microscopic cracks. Table XI l i s t s the equations used i n the ca lcu la t ions of l i f e expectancy. For POCO AXZ at room temperature a l i nea r regression analysis was performed on the data from each specimen with the value, using a c r i t i c a l crack v e l o c i t y of •sec . In the case of POCO AXF-5Q at room temperature the r e p r o d u c i b i l i t y of the data was such that a l i nea r regression analysis could be made on a l l data points . For the high temperature resu l t s and py ro ly t i c graphite, the equations from Table IX were used. The l i f e expectancy i s r e l a t i v e l y insens i t ive to var ia t ions i n A so that i t was f e l t that no very large error was incurred by taking mean values of A from a l l the specimens of each mater ia l . Solutions to the l i f e expectancy equation are given i n Figure 32 for a l l three graphites. - 98 -Table X I . Summary of l inea r regression analysis equations used for l i f e expectancy ca lcu la t ions . a) POCO AXZ at room temperature i n a i r (Regression analys is of data points for each specimen + K ^ c at 10 "Sn.sec Parameter Specimen B Mean r A n Equation: 0.74 -700 120 log V = 0.81 -456 78 113 log K 7 0.92 -832 141 662 -662±190 113±32 Equation Or ig in of equation b) POCO AXF-5Q at room temperature i n a i r c) POCO AXZ at 500°C i n a i r log V = 2181ogK -1343 log V = 63 logKj-368 Regression analy-s i s of a l l data pts , r = 0.95 Table IXc) d) POCO AXF-5Q at 500°C i n a i r log V = 128 log Kj-789 Table IXd) e) P y r o l y t i c graphite at room temperature log V = 2161ogK^-1384 Table IXe) i n a i r Figure 32. L i f e expectancy versus applied stress for graphites at room temperature and 500°C i n a i r - 100 -I I I . 5 . d Fractography Scanning electron microscope photographs of fracture surfaces of the double to rs ion specimens are shown i n Figures 33-36. - 101 -s? 'ft * * -* $ a) lOOum Subsidiary cracking b) lOOum Figure 33 SEM photographs of crack path through i so t ropic graphite, POCO AXZ, room temperature a) Notch t i p x400 b) Subsidiary cracking at crack t i p x400 (Crack moves r ight to l e f t ) - 102 -I 1 a) 10um , 1 b) 10pm Figure 34 SEM photographs of POCO AXZ room temperature fracture surfaces a) xl300 b) x3000 - 103 -a) 10pm I 1 b) 10pm Figure 35 SEM photographs of POCO AXF-5Q fracture surfaces a) Room temperature xll40 b) Room temperature x2850 - 104 -Figure 35 SEM photograph of POCO AXF-5Q fracture surface c) 500°C x740 - 1 0 5 -Fracture Surface , , b) lOOOum Figure 36 SEM photographs of py ro ly t i c graphite at room temperature a) Notch t i p x60 b) Fracture surface x53 - 106 -CHAPTER IV ANALYSIS OF RESULTS IV.1 S t ruc tura l Characterisat ion The bulk and helium density measurements i n Table I indicate that POCO AXZ i s almost twice as porous as grade AXF-5Q (31.0% compared with 17.6%, r e spec t ive ly ) , however, th i s appears to be due mainly to differences i n open porosi ty since the closed poros i t i es are s imi l a r (2-3%). The correspondence between mercury porosimetry and helium density can be seen by comparing the t o t a l open pore volumes i n Table I I with vot>en = ~ ~ ~ < 2 8) pores p bu lk pHe Hence ^ = Q > 1 9 0 x 1 0 - 3 m 3 t K g - l f o r P 0 C 0 p^Z pores and V Q p e n = 0.081 x 1 0 - 3 m 3 . K g - 1 for POCO AXF-5Q pores Due to i t s small s i z e , less than 3A, the helium atom can be expected to enter much smaller pores than mercury can be forced into under pressure. This i s indicated by the larger value of - 107 -open pores for POCO AXF-5Q obtained using helium compared to the value from mercury porosimetry. For POCO AXZ the volume of open pores established by the two techniques are almost the same and i s believed to be due to var ia t ions i n the samples. The resul ts obtained by mercury porosimetry j u s t i f y the f o l -lowing conclusions about the pore structure of POCO graphite: 1. There i s a very narrow d i s t r i b u t i o n of macropores at pore diameters ~lum with a surface area of between one- f i f th and one-quarter the t o t a l surface area of the pores. 2. There i s also a system of very f ine pores wi th diameters between 0.1 and 0.6ums. 3. The t o t a l surface area of the pores for POCO AXZ and AXF-5Q 3 3 2 -1 are 1.18 x 10 and 0.31 x 10 m .Kg , respect ive ly . The l a t t e r 36 compares w e l l with Dollimore and Freedman's resul t of o 2 i 0.34 x lO-'m . K g ~ x for the Krypton BET spec i f i c surface area of a POCO graphite. For i so t rop ic graphite a l l the mercury penetrates at the 5 -2 same pressure ~8 x 10 N.m (~8 atmospheres). This i s probably due to s l i t -shaped c a p i l l a r i e s , the measured "diameter of penetration" (0.79ym for POCO AXZ and 0.95um for POCO AXF-5Q) i s the minimum diameter of channels that are e s sen t i a l ly continuous throughout the s t ructure . I t should be noted that the difference i n t o t a l open pore volume between samples "A" and "B" of grades AXZ and AXF-5Q are r ea l and represent a va r i a t i on of ~7%% and ~3%, respec t ive ly . - 108 -Both differences appear to a r i se from changes i n the volume of mercury intruded at pore s izes ^0.7ym and must a r i se from var ia t ions i n the volume of closed pores r e l a t i v e to open pores as the t o t a l porosi ty for each grade has been established as uniform. Discussions of the l im i t a t i ons of mercury porosimetry due to the assumptions made i n the der ivat ion of the porosimetry 37 equation have been given by a number of invest igators . Errors ar ise from uncertaint ies i n the knowledge of the contact angle, 6 and the surface tension, a (for an error i n 9 of 1 ° , the f r ac t iona l er ror , A r / r i s ~1.5%; for a errors may be up to 10%); the compres-s i b i l i t y of the mater ia l and of the mercury; penetration h y s t e r i s i s ; the attainment of equi l ibr ium of the mercury. The influence of the pore model on the resul ts can be judged to a cer ta in extent from microscopic examination. The measured po re - s i ze -d i s t r ibu t ion curves are lower bound curves to the extent that i so la ted pores or pores with r e s t r i c t ed entryways occur i n the mate r ia l . The differences i n microstructure of the three graphites are shown i n Figures 9 and 10. The i so t rop ic graphites have pores which are equiaxed and d i s t r ibu ted more or less randomly throughout with no obvious preferred o r ien ta t ion . A ce r ta in number of p u l l -outs (dark regions) are apparent as w e l l as f i l l e r pa r t i c l e s which have sheared along the basal planes ( l i g h t areas). The pores appear to have a d i s t r i b u t i o n of s izes up to ~20ums, the shapes varying from almost c i r c u l a r to s l i t s . In general, the micro-graphs corroborate the density and porosi ty r e su l t s . - 109 -In comparison with i so t rop ic graphite, the primary morphology of a massive piece of p y r o l y t i c graphite i s that of a group of cones of graphite whose axes of symmetry are p a r a l l e l , with the apex toward the substrate or nucleat ion s i t e . The wrinkled nature of the basal planes i s shown i n Figure 10 a) and b) and i s re la ted to the roughness of the substrate and to the sootiness of 34 the manufacturing process . Figure 10b) also indicates the ease of delamination along the (0001) planes p a r a l l e l to the substrate. The delaminations fol low quite c lose ly the micro-structure of the cones with a noticeable curvature near the apex of the gross s tructure. The large grains i n the basal plane appear to be several hundred microns across and th i s cone-type structure i s also seen to occur wi th in the grains on a much f iner scale . 38 Coy has reported the existence of sub-grains ~0.1um i n diameter from electron micrographs. The high density of graphite i s now eas i ly understood; the 2.7% open porosity presumably anisotropic i n nature and resu l t ing from the wrinkles between the layer planes. IV.2 E l a s t i c Constants The errors i n Table I I I were calculated as the standard deviat ions. For the s t a t i c modulus the standard deviat ion indicates $1% v a r i a t i o n i n the moduli for the three orthogonal d i r ec t ions . Experimental errors were ~4% for POCO AXZ and ~6%% fc r POCO AXF-5Q so that these two materials appear to have i so t rop ic e l a s t i c prop-er t ies w e l l wi th in the experimental e r ror . - 110 -Wagner et a l have studied the e l a s t i c constants of a range of POCO graphites as a function of poros i ty . They obtained a l i nea r re la t ionsh ip between the Young's modulus and the t o t a l poros i ty , the e l a s t i c constants varying from 6.2GN.m~2 (0.90 x lO^psi) to 2 6 13.4GN.m~'' (1.94 x 10 psi) for the corresponding porosi ty range of 15-31%. The values of the e l a s t i c moduli i n Table I I I are i n excel lent agreement with the i r f indings . 39 Seldin has shown that for p o l y c r y s t a l l i n e graphites there i s extremely good agreement between the dynamic modulus and the s t a t i c modulus i n the l i m i t of zero s t r a i n . The s t r e s s - s t r a in re la t ionship of a po lyc rys t a l l i ne graphite i s normally characterised by non l inea r i ty , hys t e r i s i s loops formed under c y c l i c s t ress ing and by a res idua l deformation on releasing the applied s t ress . In th i s work the s t r e s s - s t r a in curves for i so t rop ic graphite after a range of pre-stressing were a l l p a r a l l e l but showed a small amount of h y s t e r i s i s , ~.025% for .4% t o t a l s t r a i n . I t was th i s slope from which the s t a t i c modulus was ca lcula ted . Therefore, the difference between the dynamic and s t a t i c modulus i s thought to be due to the decrease i n s t a t i c modulus on prestressing compared with i t s value at zero s t r a i n . For a l l future ca lcula t ions the dynamic Young's modulus i s used. The e l a s t i c modulus for py ro ly t i c graphite i n the a d i r ec t ion i s larger than the e l a s t i c constants of the i so t rop ic graphites. No values for the e l a s t i c constant i n the c d i r ec t ion were given 34 by the manufacturer, however from the l i t e r a t u r e E appears to - I l l -be between 10.7 - 11.0GN.m~z (1.55 - 1.58 x 10 psi) i . e . comparable with the Young's Modulus of POCO graphite. The negative value of Poisson's r a t io i n the a d i r ec t ion for p y r o l y t i c graphite i s a consequence of the high contraction i n the c d i r e c t i o n . IV.3 Oxidation Studies of Isotropic Graphite I t has been established by other workers that the oxidat ion of graphite proceeds by the formation of stable surface oxide and the production of gaseous CO and CO^. At a given temperature the react ion between oxygen and a clean graphite surface has an i n i t i a l t ransient period of surface oxide formation followed by a steady-state react ion of the oxygen with the remaining uncovered part of the react ive surface. This corresponds to type I behaviour as shown i n Figure 11 and has been observed for most graphites. I t i s also observed for POCO AXZ i n the present experiments. Occasionally type I I behaviour i s observed, however as for POCO AXF-5Q and py ro ly t i c graphite. The l a t t e r was reported 30 by Lewis . For both materials there was a marked difference i n the morphology of the specimens after oxidat ion compared with other graphites. The oxidation p i t s formed on the surfaces of POCO AXZ were very smal l , <lum, i r regu la r i n shape but uniformly d i s t r ibu ted over the ent i re surface. In AXF-5Q a smaller number of large c i r c u l a r p i t s , up to 40um, were produced on the surface. In some cases these p i t s coalesced. The oxidat ion of th i s mater ia l was much more sens i t ive to surface treatment. - 1 1 2 -Acharya and Olander explain the behaviour of p y r o l y t i c graphite i n terms of the attainment of an "equi l ibr ium roughness" corresponding to the s t a b i l i s a t i o n of the oxidat ion ra te . I t appears that the same phenomenon occurs for POCO AXF-5Q and i t i s believed to be due to the presence of surface contaminants, the large p i t s would therefore be formed at s i t e s wi th a high l o c a l concentration of impur i t ies . Some support for t h i s i s 30 given by the work of Lewis , who found that py ro ly t i c graphite (type I I behaviour) purged wi th argon at high temperatures exhibited a greater resistance to oxidat ion, the r e a c t i v i t y of vitreous carbon (type I behaviour) however, being only s l i g h t l y reduced. The oxidation rate versus rec iproca l temperature p lo ts i n Figure 12 show a va r i a t i on i n slope ind ica t ing changes i n the r a t e -con t ro l l ing mechanism of the carbon-oxygen react ion . 41 According to Lewis at the lowest temperatures the o v e r a l l rate i s cont ro l led by the surface react ion and the observed ac t iva t ion energy, E and react ion order, n are those per taining to th i s react ion. This region i s termed zone I and values of ac t iva t ion energy for the oxidat ion of carbon and graphite found i n the l i t e r a t u r e generally refer to the chemical surface react ion i n zone I . For POCO AXZ and AXF-5Q these values were 12.1 and 12.0 KJ.mole -"^ (51 and 50 Kcal.mole""*"), respect ively compared with 10.2 K J . m o l e - ! (43Kcal.mole~l) obtained by Lewis 3 ^ for vi treous carbon 41 and py ro ly t i c gr phite. There i s now g neral ag eement th t - 113 -for graphite containing less than 5p.p.m. impurities the overall activation energy i n a dry gas is between 14.3 and 14.8KJ.mole~"*" (60 and 62 Kcal.mole " ) , any value less than this being due to catalytic impurities. Before comparing the oxidation rates of isotropic graphite with those of vitreous carbon and pyrolytic graphite some mention should be made of the active surface area (ASA). The reaction of molecular oxygen with graphite is primarily associated with the perpheral atoms of the basal planes, and the active surface area (ASA) i s the edge plane area. 41 It has been shown that the ASA corresponds to ~5% of the BET area for pure graphites. Thus, 5% of the internal surface area obtained from mercury porosimetry should yield an approximate value 2 - 1 2 - 1 of the ASA. This corresponded to 59m .Kg and 16m .Kg for POCO 2 -1 AXZ and AXF-5Q, respectively compared to 2.6m .Kg for the geometri-cal surface area. Thus, the ASA constitutes a very much larger proportion of the total accessible area. Oxidation rates calcu-lated on the basis of the geometrical and active surface area represent an upper limit as the increase in surface area during oxidation has not been taken into account; increases of up to 50% 42 i n the total specific area after 25% burnoff have been reported. 30 A l l the carbons and graphites studied by Lewis had extremely low porosities so that calculations similar to those described above were not necessary. The oxidation rates for the isotropic graphites in Figure 12 - 114 -are of the same order of magnitude as Lewis 's resul ts for various graphites although measured i n a lower temperature regime. However, the l a t t e r i s consistent with the f ine grain s ize of POCO graphite; materials with smaller grains having more basal plane edge atoms exposed and hence a greater tendency to oxidise at a pa r t i cu la r temperature. 43 Several researchers have shown that there i s no obvious cor re la t ion between porosi ty and oxidat ion rates of graphites and th is i s apparent i n the present experiments. The oxidat ion rates of the two materials d i f f e r at a l l temperatures but th i s difference i s not consistent . In p a r t i c u l a r , the larger oxidat ion rate of POCO AXF-5Q i n zone I compared: with that of AXZ may be explained i n terms of the a c c e s s i b i l i t y of the exposed surface rather than the percentage poros i ty . The "diameter of penetration" i s larger for POCO AXF-5Q than AXZ (0.95ym compared with 0.79um) and also the oxidat ion p i t s were more rounded i n the former case. Both factors w i l l tend to make the geometrical and in t e rna l surfaces of POCO AXF-5Q more accessible to the ox id i s ing atmosphere since the d i f fus ion distance i s smaller. At s u f f i c i e n t l y high temperatures the chemical react ion between carbon and oxygen no longer predominates and in-pore d i f fus ion becomes the r a t e -con t ro l l ing mechanism as the concen-t ra t ion of reactant f a l l s to zero at some point ins ide the specimen. Under these condit ions, termed zone I I , a l l gas molecules entering the pores react . I t has been reported that for zone I I , provided the t o t a l pressure remains constant, the observed 41 ac t iva t ion energy i s E^./2 and the react ion order (nj+l)/2 This behaviour was observed i n the present experiments for 1 1 5 -POCO AXF-5Q, the apparent ac t iva t ion energy for zone I I being 4 . 5 K J . m o l e - 1 (19Kcal .mole - 1 ) compared with 12.0KJ.mole" 1 (50Kcal. mole ~) for zone I . However, the apparent a c t i v a t i o n energy for POCO AXZ appears to increase i n the same temperature region. 30 Lewis has observed a s imi la r behaviour with vi treous carbon and ascribed i t to the presence of impurity centres. S i m i l a r l y , the deviat ion of the oxidat ion rate of POCO AXF-5Q at lower tempera-44 tures from l i n e a r i t y has also been observed for nuclear graphite and was associated with a catalysed react ion . The nature of the Impurities causing enhanced oxidat ion rates for the i so t rop ic graphites are not known. IV.4 Transverse Rupture Tests For a l l three graphites the deformation consisted of an e l a s t i c region, with a non-linear e l a s t i c region jus t p r io r to fracture i n i t i a t i o n . In general, the i n i t i a l crack propagated ca tas t rophica l ly resu l t ing i n a discontinuous drop i n load to zero (type A curve shown i n Figure 13). Type B behaviour was observed only i n the case of py ro ly t i c graphite loaded p a r a l l e l to the c a x i s . The strain-energy release rate was i n su f f i c i en t for catastrophic f a i l u r e and more external work was required to d r i v e the c r a c k . This process occurred several times, the specimens becoming more and more compliant, as the crack length increased before f i n a l rupture. - 116 -I V . 4 .a Unnotched Bars I V . 4 . a . i Fracture Stress S t a t i s t i c a l D i s t r i b u t i o n at Room Temperature The mean fracture stresses at room temperature for a l l three graphites (Table Va)) are s l i g h t l y higher than the values of f l exu ra l strength quoted by the manufacturer. Stevens and Clausen 3 2 obtained 9.0 x 10 7 N.m" 2 (13,050psi) for POCO AXF-1Q 45 7 -2 tested i n four-point bending, Diefendorf quotes 15.9 x 10 N.m (23,000psi) for py ro ly t i c graphite i n three-point bending and Gelbhardt and B e r r y 4 6 obtained 22.8 x 10 7N.m~ 2 (33,000psi) and 7 -2 19.3 x 10 N.m (28,000psi) for surface nucleated py ro ly t i c graphite tested i n three and four-point loading, respec t ive ly . The values i n Table Va) compare w e l l with these r e s u l t s . Generally, the f l exu ra l strength obtained by three-point bending i s larger than for four-point bending since a smaller volume of material i s under stress i n the former case and hence the p robab i l i ty of a large flaw being present i s reduced. The f l exu ra l strength i s usual ly larger than the t ens i l e strength for the same reason. Only for a large bend specimen where the stress gradient i s small w i l l the bending strength equal the t ens i l e strength. The bending strength at tains a maximum when the specimen becomes small compared to the grain s ize or flaw s ize of the mater ia l . In the present experiments the specimen s ize was very much larger than the grain or flaw s i z e , however not so large that the fracture stress calculated may be taken as the value of the t ens i l e strength. - 117 -The mean fracture stresses for the three materials increase i n the order POCO AXZ, AXF-5Q, py ro ly t i c graphite. An increase i n the volume f rac t ion porosi ty i s known to reduce the fracture strength of a ceramic because the volume of s o l i d stressed i s correspondingly reduced. However, the difference i n fracture strength of the i so t rop ic graphites cannot be accounted for so l e ly on the basis of the reduction i n load-bearing area. The pore s i z e , shape and d i s t r i b u t i o n are probably important as w e l l and the fractographic studies should reveal any changes i n fracture mode. The high fracture strength of py ro ly t i c graphite i s consistent with the fracture of a dense, wel l -or iented graphite. Figures 14 a)-c) show the good f i t obtained from the Weibull analysis of the data for a u = 0. The Weibul l parameters are shown i n Tables V a) and b ) . A value of m = 19 (a = 0) was deter-32 mined by Stevens and Clausen from four-point bending tests on POCO AXF-1Q. The present value of m = 12 seems reasonable since more scatter may be expected from three-point bend t e s t i ng . The scatter of strength values for POCO AXZ and py ro ly t i c graphite was much larger (lower m) than for POCO AXF-5Q. In the case of py ro ly t i c graphite th i s can be understood s ince, i n addi t ion to anisotropy, random process var ia t ions from batch to batch can also induce,among other things, i so la ted modules that serve as stress r a i se r s , high grain boundary angles, and delaminations. A l l of these serve to lower test values and to increase the i r scat ter . The parameter mean fracture stress/standard deviat ion as - 1 1 8 -introduced by Stevens and Clausen , i s i n extremely good agree-ment wi th m (a = 0 ) . I t requires much less ca l cu l a t i on than m and was therefore used as an ind ica t ion of the d i s t r i b u t i o n of strengths i n l a t e r experiments. The best estimated values of a u are given i n Table Vb). For POCO AXZ the best a u i s more than ha l f the mean fracture stress ind ica t ing that although the scatter i n fracture stress i s large (small m) the stress corresponding to the largest possible flaw, a u i s large. For POCO AXF-5Q and py ro ly t i c graphite the best o u ' s were both less than ha l f the mean fracture s t ress . However, the value of the cor re la t ion coe f f i c i en t , r indicates that there i s l i t t l e s ignif icance i n zero s t ress , there being very l i t t l e difference between r for o u = 0 and the best estimated value of a u. o"u i s a normalising factor and cannot be related to any physical property of the mate r ia l . The quanti t ies BIO -^1 and B10 - ^ are useful when knowledge of a working stress are required. The chosen values should be on the conservative side i . e . for POCO AXZ and p y r o l y t i c graphite B I O - 6 for the best estimated a and for POCO AXF-5Q BIO" 6 for a, =0. u u I V . 4 . a . i i High Temperature Tests for Isotropic Graphites Figure 15 shows the v a r i a t i o n of the modulus of rupture with temperature for the i so t rop ic graphites. There was l i t t l e v a r i a -t i on i n the standard deviat ion at each temperature ind ica t ing that the d i s t r i b u t i o n of flaws remained f a i r l y constant. The data - 119 -i s i n su f f i c i en t for a complete analysis but ce r ta in trends are apparent: 1. At temperatures above room temperature there i s a s l i g h t increase i n the strength. For POCO AXZ the fracture stress at 300°C i s 7% greater than the room temperature value and for POCO AXF-5Q at 400°C the fracture stress i s 11% above the room temperature s t ress . The error bars i n th i s temperature range overlap so that the difference may not be s i g n i f i c a n t . 2. At higher temperatures there i s a def in i t e decrease i n the fracture stress for both mater ia ls . The 600°C fracture stress for POCO AXZ being 13% below the room temperature value and the 700°C fracture stress for POCO AXF-5Q being 6% less than the room temperature s t ress . 3. V i s i b l e signs of oxidat ion were apparent on the surfaces of the POCO AXF-5Q specimens at 600°C and above. However, for POCO AXZ oxidat ion p i t s were not observed at any temperature. The maximum time for any specimen i n the furnace was twenty minutes and the maximum weight loss was ~6% for a specimen of POCO AXF-5Q at 700°C. An in terpre ta t ion of the strength-tempera-ture data i n terms of the steady-state oxidat ion rates of the two materials would therefore be incorrec t . Rather the i n i t i a l portions of the weight loss-t ime curves should be considered. The effect ive oxidat ion rates of POCO AXZ and AXF-5Q may be expected to be larger (type I behaviour) and smaller (type I I behaviour) than the steady-state oxidat ion rate at any pa r t i cu la r temperature. - 1 2 0 -This may explain the apparent higher temperature required to s i g n i f i c a n t l y reduce the f l e x u r a l strength of POCO AXF-5Q by oxida t ion . Both strength-temperature curves for the i so t rop ic graphites show the same trends so that the same mechanisms appear to be operating for the two mater ia ls . An increase i n strength with temperature has been generally observed for p o l y c r y s t a l l i n e 47 graphites and i s usual ly a t t r ibuted to the closure of the micro-crack structure due to expansion of the c r y s t a l l i t e s at a greater rate than the bulk graphite. The thermogravimetric resu l t s indicate that at temperatures greater than 500°C the oxidat ion rates of the i so t rop ic graphites are s ign i f i can t so that the decrease i n strength i n the higher temperature region can probably be accounted for on the basis of oxida t ion . The appearance of oxidation p i t s on the surface, of POCO AXF-5Q specimens at 600°C and 700°C seems to confirm t h i s . The effect of oxidat ion i s to remove carbon not only from the geometric surface but also from the inner wal ls of each pore so that the structure i s i n t e rna l l y weakened. This was the reason for deciding that slow crack growth tests should be performed at 500°C as w e l l as at room temperature. At the higher temperature s ign i f i can t oxidat ion of i so t rop ic graphite should occur i n longer time tests than those above. - 121 -IV.4.b Notched Bars Table VII indicates that the room temperature values of the c r i t i c a l stress in tens i ty factor , K j c and the fracture energy, Y^ increase i n the order POCO AXZ, AXF-5Q, py ro ly t i c graphite loaded perpendicular to the c axis and p a r a l l e l to the c a x i s . S t r i c t l y speaking, equation (17) for the c r i t i c a l stress in tens i ty factor applies only to a homogeneous l i nea r e l a s t i c medium. In a porous mater ia l the stress in tens i ty i n the s o l i d i s elevated because of the reduction i n load-bearing area. An attempt to account for the effect of uniformly d i s t r ibu ted porosi ty i n the i so t rop ic graphites can be made by d iv id ing the values of K-j- c calculated from equation (17) by (1 - P ) , where P i s the f r ac t iona l porosi ty . Thus, the fracture energy normalised for porosi ty i s Y i y± = —^—j (29) (1-P) Values of Y ^ ' calculated for the i so t rop ic graphites are given i n Appendix 3. As i n the case of the room temperature fracture s t ress , the differences i n fracture energy for the two materials cannot be accounted for so le ly on the basis of the reduction i n the load-bearing area. The work required to make a s ingle su i tab ly oriented crack grow i n graphite generally l i e s between 10 and 20Jm and that _2 48 required to cause continuous fracture of a specimen lOOJm The excess energy i s apparently used up i n the formation of numerous non-propagating cracks, whose existance i s t r ans i to ry . - 122 -The only data that could be found on materials s imi la r to those used i n the present work i s l i s t e d below. 5 -3/2 19 [Double Canti lever Beam K I c = 15.4 x 10 N.m POCO AXF-5Q [Double Torsion K I c = 14.9 x 1 0 5 N . m " 3 / 2 1 9 22 /Double Canti lever Beam y± - 21.8Jm" 2 POCO AXF-1Q, fTat tersal l -Tappin Work- - 69 5Jm~2 2 2 lof -Frac ture Test F ' m The value of K T c for POCO AXF-5Q shown i n Table VII i s i n good 19 agreement with Simpson's resu l t s The high temperature resu l t s for the i so t rop ic graphites show l i t t l e v a r i a t i o n from the room temperature values. No attempt was made to measure the Young's modulus at 500°C, however, an estimate of a 5% increase i n the f l exu ra l modulus between room temperature and 500°C was made from the slopes of the load-def lec t ion curves. This would e f fec t ive ly reduce Y^ by 5% at 1 h 500°C. K T c var ies as ( ^) and so i s r e l a t i v e l y independent of 1-v the va r i a t i on of Poisson 1 s r a t io with temperature. The flaw s i z e , c i s independent of both the Young's modulus and Poisson's r a t i o . The flaw s i z e , c shows l i t t l e change for the two grades of POCO graphite ind ica t ing that the same microst ructura l features may be responsible for the fracture process. In comparison, c for py ro ly t i c graphite loaded perpendicular to the c axis i s approximately twice as la rge . - 123 -IV .4 . c Fractography Fractographic studies revealed that fracture generally or iginated at surface flaws, mainly grain pu l l -ou t s . Pu l l -ou ts are an unavoidable feature when preparing graphite and resu l t from both the po l i sh ing process for unnotched bars and the machining operation i n the case of notched bars. I V . 4 . c . i Isotropic Graphite Figure 16a) i s a t y p i c a l scanning electron micrograph of a fractured specimen of i so t rop ic graphite. Fracture or iginated i n the centre of the t ens i l e edge of the bar. Slow crack growth i s evident from the p a r t i c u l a r l y rugged nature of the surface i n the region around the fracture o r i g i n . The area of rapid crack propagation i s less rugged i n keeping with a macroscopically smooth fracture process occurring at, a speed close to the v e l o c i t y of sound. Figure 16b) shows the fracture o r i g i n i n Figure 16a) at a higher magnificat ion. Typica l grain pul l -outs between 10 and 20ums are also indica ted . From Table VI I the calcula ted flaw s izes for unnotched bars of i so t rop ic graphite were between 50 and 70yms which i s several times larger than the largest surface flaw. Thus, i t appears that fracture occurs by the extension of grain pul l -outs u n t i l a flaw s ize of 50 to 70ums i s attained when catastrophic f a i l u r e occurs. The manufacturers quote a maximum grain s ize of 25ums for i so t rop ic graphite so that the calculated flaw s i ze must - 124 -consist of several grains and pores. In comparison, notched bars of i so t rop ic graphite showed fewer fracture features. The fracture surfaces were perpendicular to the neutral axis as fracture i n i t i a t e d at the notch t i p at the pos i t ion of maximum t ens i l e s t ress . The large number of grain pul l -outs on a machined surface i s w e l l shown i n Figure 17 a) and b ) . The enlarged view of the notch t i p indicates how the grains are torn away by the machining operation. In ca lcu la t ing the c r i t i c a l stress in tens i ty factor using notched specimens, the s ize of the machined flaws should be included with the notch length. However, the l a t t e r was so large that i t was f e l t that l i t t l e error would be incurred by neglecting the length of the machined flaws. The fracture or ig ins of unnotched specimens of POCO AX2 and AXF-5Q at room temperature and 500°C were very s i m i l a r , consistent with the approximately constant values of flaw s ize calculated for the i so t rop ic graphites. Oxidation p i t s were observed only on the polished surfaces of POCO AXF-5Q specimens at 600°C and 700°C. Figure 18a) shows a t y p i c a l t ens i l e face of an unnotched bar of POCO AXF-5Q at 700°C. The oxidation p i t s are very large, rounded and i n some cases have coalesced. Figure 18b) i s an enlarged view of an oxidat ion p i t showing grain pul l -outs at the edges. The rounded nature of the p i t appears to preclude i t s act ing as a stress concentrator and the main effect of such oxidat ion p i t s on the fracture strength of POCO AXF-50 at 600°C and 700°C i s probably a reduction i n the load-bearing area. - 125 -I V . 4 . c . i i P y r o l y t i c Graphite The fracture modes of p y r o l y t i c graphite i n three-point 49 bending have been studied previously by Berry and Gebhardt S.E.M. photographs of specimens used i n the present study are presented merely for comparison with the i so t rop ic graphite and to a id understanding of the fracture mode for the double to r s ion specimen. In contrast to i so t rop ic graphite the fracture features of p y r o l y t i c graphite are en t i r e ly dictated by the anisotropy of the ma te r i a l . P a r a l l e l and perpendicular loading both required fracture of the basal planes. For the perpendicular o r ien ta t ion f a i l u r e was predominantly t ens i l e fracture of the basal planes as shown i n Figure 19. The o v e r a l l crack front i s c l e a r l y shown i n Figure 19a). Fracture occurred by crack growth through basal plane packets i n the a d i r e c t i o n . The growth region i s p a r t i c u l a r l y uneven as the crack moves on different planes being joined by regions of interlaminar cleavage. The delaminated surfaces are v i r t u a l l y indis t inguishable from an as-deposited surface. These different l eve l s eventually connect to conserve the energy involved i n creat ing new area and the region of rapid crack propagation i s r e l a t i v e l y smooth. The gentle undulating path of fast crack growth indicates that long range s t ruc tu ra l inhomogeneities (such as cones or nodules) have some effect on the d i r ec t ion of fracture propagation. - 126 -An enlarged view of the fracture o r ig ins for the perpendi-cular o r ien ta t ion i s given i n Figure 19b). As for the i so t rop ic graphites fracture appear to or ig inate at surface flaws as a resu l t of po l i sh ing , the calcula ted flaw s ize of 118ums being an estimate of the length to which a surface flaw must grow across a given set of layers to i n i t i a t e fracture. The py ro ly t i c graphite surface features include r i v e r patterns, cleavage steps and " t i r e t racks" . The o r i g i n and mechanism of " t i r e track" formation are not known. An example of a notched specimen fractured i n the perpendicu-l a r o r ien ta t ion i s shown i n Figure 20. The height of each layer plane packet i s the width of the notch t i p but i t i s not c lear whether the distance between the packets i s a r e f l e c t i o n of machining flaws at the base of the notch or some s t ruc tura l feature of py ro ly t i c graphite. A l l the features observed previously for unnotched specimens are present but on a f iner scale due to the control led fracture i n i t i a t i o n at the notch t i p . For the p a r a l l e l o r ien ta t ion f a i l u r e usual ly occurred i n a s t ep - l ike fashion, wi th t ens i l e rupture across the specimen i n the c d i r ec t i on forming steps wi th delaminations along the basal planes. A t y p i c a l example wi th complete delamination near the neutral axis i s shown i n Figure 21a). Machining flaws at the notch t i p were presumably responsible for the i n i t i a l delamination. For complete shearing half-way through the specimen an espec ia l ly severe surface defect near the neutral a x i s , the s i t e of maximum - 127 -shear s tress i n bending, would be required. Fa i lu re across the basal planes i s more d i f f i c u l t to under-stand. An enlarged view of a set of basal plane layers i s shown i n Figure 21b). Since delamination occurs, the basal planes must have a r e l a t i v e l y high resistance to crack i n i t i a t i o n . Therefore crack i n i t i a t i o n probably occurs at some points of stress concen-t r a t i o n such as a crack or cone in terface . The random d i s t r i b u t i o n of deposit ion cones i n the structure are believed to account for the general roughness or s l a t e - l i k e appearance of the surface. IV.5 Slow Crack Growth Tests IV .5 . a Compliance Ca l ib ra t ion The s l i g h t increase i n the compliance of the double to r s ion specimen of POCO AXZ p r io r to fracture at 41.IN (9.25 lbs) shown i n Figure 22 has been observed previously for c a l c i a p a r t i a l l y s t a b i l i z e d z i r con ia i n four-point bending"*^ and was a t t r ibuted to the formation of microcracks at the notch t i p . Deviations from e l a s t i c l i n e a r i t y before fracture are usual i n b r i t t l e materials and was commonly observed here both i n the cont ro l led crack growth and transverse rupture tests on graphite. Figure 23 indicates the constancy of the slopes of the compliance curves for the three graphites for crack lengths at least ha l f the specimen length. This confirms the general form of the a n a l y t i c a l expression for the stress in t ens i ty factor , K T - 128 -used i n these experiments. Unfortunately, there appears to be a discrepancy between the empir ical slope of the compliance plot given by the l i nea r regression analysis equation and the a n a l y t i c a l slope as calculated from equation (A8) as seen i n Table V I I I . The difference can also be seen from the apparent Young's modulus (13.40 and 18.74GN.rn - 2 for POCO AXZ and AXF-5Q, respect ively) compared with the dynamic e l a s t i c modulus (7.1 and 13.4GN.m~ , r e spec t ive ly ) . The errors associated with a given compliance measurement are ±.3 x 10~7mN~-'- from the chart and a 2% standard deviat ion due to the v a r i a t i o n of the compliance with load at loads greater than 15.6N (3.5 l b s ) . With a 2% error due to the measurement of the specimen dimensions the o v e r a l l error i n the apparent Young's modulus i s estimated to be ~15% for POCO AXZ, ~27% for POCO AXF-5Q and £29% for py ro ly t i c graphite. Thus, the d i spa r i ty between the apparent Young's modulus and the dynamic modulus for POCO AXZ and AXF-5Q cannot be t o t a l l y accounted for on the basis of experimental e r ror . Precompression of graphite i s known to cause the apparent modulus to decrease so that i f the shakedown procedure was responsible the apparent modulus would be less than the dynamic modulus. However, t h i s i s not the case. At the moment no c lear explanation for the discrepancy i s known. IV.5.b Stress Intensi ty Factor-Crack Ve loc i ty Diagrams I V . 5 . b . i Isotropic Graphites at Room Temperature The resul ts for POCO AXZ at room temperature, as shown i n - 129 -Figure 26 in d i c a t e considerable v a r i a t i o n i n the stress i n t e n s i t y factor required to propagate a crack i n t h i s m a t e r i a l . This v a r i a b i l i t y seems to occur not only from sample to sample but also i n a p a r t i c u l a r specimen. A t y p i c a l load r e l a x a t i o n curve f o r POCO AXZ. i s shown i n Figure 24b) where i t i s apparent that a f t e r the i n i t i a l load r e l a x a t i o n the crack accelerated once more at a lower stress i n t e n s i t y thus producing a second load r e l a x a t i o n . On the Kj-V diagram t h i s appears as a d i s c o n t i n u i t y . For specimen A three load r e l a x a t i o n curves were formed as the crack accelerated a t h i r d time. The steep slopes of the K T-V diagrams resemble the t h i r d stage of crack growth i n soda-lime glass, stage I I I being the region where environmental e f f e c t s are not important. However, the c r i t i c a l s tress i n t e n s i t y f a c t o r s , K I c l i e f a r to the r i g h t of these curves. I t i s doubtful that an environmental e f f e c t occurs at high crack v e l o c i t i e s . Instead, i t i s suggested that a continua-t i o n of the phenomenon observed at intermediate v e l o c i t i e s i s also observed for the high v e l o c i t y range i . e . a serie s of discontinuous K-J--V l i n e s up to the c r i t i c a l stress i n t e n s i t y , KT(,. A Kj-V curve f o r t h i s o v e r a l l discontinuous crack growth process was calculated i n the following manner. The data f o r specimens A, B and D was treated separately and a l i n e a r regression analysis c a r r i e d out including the c r i t i c a l stress i n t e n s i t y factor as a data point. Assuming that the c r i t i c a l v e l o c i t y was the same for both grades of graphite a value of lO""^m.sec-1 was estimated by - 130 -extrapolat ing the K-r-V curve for POCO AXF-5Q at room temperature to i t s K j c value. A mean equation was f i n a l l y obtained by taking the mean value of the slope, n and in tercept , A from the three analyses. The resul tant equation i s given i n Table XI and was used l a t e r i n the ca lcu la t ion of the l i f e expectancy of POCO AXZ at room temperature. In comparison, the load re laxa t ion curve for POCO AXF-5Q usual ly consisted of a s ingle curve as shown i n Figure 24a). The extremely reproducible K^-V diagrams again appear to l i e i n stage I I I . There i s a suggestion of a fatigue l i m i t at crack v e l o c i t i e s —6 —1 of ~10 m.sec . The pos i t ion and general shape of the diagrams are 35 i n good agreement with those of Simpson as shown i n Figure 30. Simpson does not mention correct ing for the machine background which may account for the lower value of slope, n obtained by him for POCO AXF-5Q i n a i r . IV. 5 . b . i i Isotropic Graphites at 500°C The high temperature Kj-V diagrams for the two i so t rop ic graphites are shown i n Figure 28. A l l the POCO AXZ specimens remained i n the furnace for approximately the same time period, three and a ha l f hours so that the va r i a t i on i n the pos i t ion of the Kj-V diagrams i s again a r e f l ec t i on of the v a r i a b i l i t y of the mate r ia l . Although there was considerable background noise present . in the 500°C load re laxat ion curves, each curve appeared to consist of a s ingle - 131 -re laxat ion with no obvious d i scon t inu i t i e s as observed at room temperature. Therefore, the K^-V diagrams have a s ingle continuous stage, with the suggestion of a plateau at v e l o c i t i e s of ~5 x 10~ 7 m.sec - 1 . The c r i t i c a l stress in tens i ty factor , K-r c appears to intersect the curve at v e l o c i t i e s of ~10 "m.sec - 1 fo r specimens B and C. The slope, n = 63 i s considerably less than the room tempera-ture value of 649 or 113 for the o v e r a l l process. This indicates that the high temperature tes t ing has a s ign i f i can t effect an the crack growth behaviour. Specimens A, B, C and D of POCO AXF-5Q were kept i n the furnace at 500°C for 3% hours, 3 hours, 2^3 hours and 1% hours, respect ive ly . Therefore, the var iable stress in tens i ty observed for these samples may be due to ei ther a reduction i n the web thickness by surface oxidat ion or a general decrease i n the mater ia l strength as a resu l t of reduction i n load-bearing area through pore enlargement. No change i n the web thickness was apparent on remeasuring t after t e s t ing . The stress i n t ens i t i e s at a crack ve loc i t y of -4 -1 10 m.sec for specimens A, B and C are 7.9%, 6.2% and 3.6% less than the room temperature value, respec t ive ly . Assuming that a l l three specimens oxidised at the same ra te , the steady-state —2 —2 —1 oxidation rate at 500°C i . e . 0.26 x 10 Kg.m hr , the amount -2 -2 of s o l i d removal i n each case i s 0 .9, 0.8 and 0.6 x 10 Kg.m , respect ive ly . These show a s imi l a r re la t ionship to the percentage reduction i n stress in tens i ty ind ica t ing that the sh i f t i n K-r-V - 132 -curves to lower stress i n t ens i t i e s occurs as a resul t of the reduc-t i o n i n load-bearing area due to oxida t ion . Probably the same effect occurred with POCO AXZ at 500°C, although more obscured by the v a r i a b i l i t y of the mate r ia l . This i s shown to a cer ta in extent by the general sh i f t i n the K -V diagrams to lower stress i n t ens i t i e s at 500°C compared to room temperature. The slope, n - 128 for POCO AXF-5Q at 500°C i s much less than the room temperature value of 218, again ind ica t ing that high temperature tes t ing has a s ign i f i can t effect . The only r e a l i s t i c value of K I c for POCO AXF-5Q was obtained for specimen C. Values for A and D were far too low, probably due to further oxidat ion after obtaining the load re l axa t ion curves. Specimen C, however, was loaded to f a i l u r e immediately after load re laxa t ion . The c r i t i c a l ve loc i t y appears to be , n - l -1 10 m.sec I V . 5 . b . i i i Py ro ly t i c Graphite at Room Temperature Typica l load re laxat ion curves for py ro ly t i c graphite are shown i n Figure 24c) and the resultant K^-V diagrams i n Figure 29. A, A ' and C, C' refer to separate load relaxations obtained on the same specimen. The samples were not unloaded between runs so that the f i n a l crack length, a^ after the f i r s t load re laxat ion was calculated from the f i n a l crack length, a^t measured after the second load re laxat ion using the re la t ionships -133 -(30) and a f a i (31) At least two types of load re laxa t ion curves are apparent. A slope of ~200 was generally obtained when the crack accelerated several times and the steeper slope of ~500 after only one accelerat ion i . e . a s ingle load re laxa t ion . Unlike POCO AXZ the load re laxa-t i on curves for py ro ly t i c graphite were extremely d i f f i c u l t to resolve so that i t was decided not to s p l i t the several components of crack accelera t ion . In general, the steep slopes for the K^-V diagrams suggest stage I I I behaviour as for POCO AXZ and AXF-5Q at room temperature. The pos i t ion of the K T - V diagrams i s f a i r l y reproducible but outside the boundaries of experimental er ror . There appears to be a va r i a t i on i n the mater ia l from sample to sample but ce r t a in ly not as large as for POCO AXZ. For the stress in tens i ty ca lcula t ions for py ro ly t i c graphite i t was assumed that the crack propagates i n the a d i r ec t i on i . e . the leading edge of the crack i s almost orthogonal to the crack front and the appropriate Poisson's r a t i o , -0.1 used. However, i f the crack propagates i n any other d i r ec t ion a larger value of v should be employed and, a l l things being equal, a higher stress in tens i ty obtained since K-r i s proport ional to (1/1-v) 2 . The maximum value of ( 1 / 1 - v ) 2 i s i n the c d i r e c t i o n , 3.3 times larger than for the a d i r ec t i on . In r e a l i t y , the crack probably moves - 134 -i n a d i r ec t ion between the pure a and pure c d i rec t ions and an intermediate value of Poisson's r a t i o and hence (1/1-v) 2 should be used. IV .5 .c C r i t i c a l Stress Intensi ty Factors From Table X i t can be seen that the values of K T from Ic notched bars and the double tors ion specimens are i n excel lent agreement, the double tors ion values being s l i g h t l y lower. This seems consistent with crack propagation from a sharp crack rather than a machined notch. The data for POCO AXF-5Q at room tempera-35 ture i s i n good agreement with that of Simpson The room temperature and 500°C K ^ c values for the i so t rop ic graphites are w i th in experimental error of one another so that the high temperature tests do not appear to have as s ign i f i can t an effect on K I c as on the general crack growth behaviour as shown by the K-r-V diagrams. The double tors ion value of K T c for p y r o l y t i c graphite i s very much less than that obtained from notched bars, ce r t a in ly much lower than might be expected on the basis of crack propagation from a sharp crack rather than a machined notch. Presumably, th i s difference i s due to the value chosen for the Poisson 's r a t i o , as explained previously . The high temperature values of the fracture surface energy, Y ^ were calculated on the basis of the room temperature Young's modulus, as explained for the transverse rupture t es t s , and should - 135 -probably be reduced by 5%. The fracture surface energies for the i so t rop ic graphites normalised for poros i ty , Y ^ 1 are l i s t e d i n Appendix 3 together with the notched bar r e su l t s . IV .5 .d Fractography I V . 5 . d . i Isotropic Graphite Figure 33a) i s a scanning electron micrograph showing the tortuous nature of the fracture path through an i so t rop ic graphite. Some secondary cracks are formed but these do not deflect the main fracture path. Subsidiary cracking at the crack t i p i s shown i n Figure 33b). Examination of the fracture surfaces of the i so t rop ic graphites revealed s l i g h t l y different fracture modes for each grade. Figure 34a) and b) for POCO AXZ at room temperature shows that the fracture i s pa r t ly intergranular and par t ly transgranular, many of the grains having cleavage cha rac te r i s t i c s . In comparison, the fracture mode for POCO AXF-5Q was predominantly transgranular i n nature as can be seen i n Figure 35 a) and b ) ; cleavage has occurred and r i v e r patterns wi th rounded edges are abundant. At 500°C the fracture surfaces of both i so t rop ic graphites seemed less angular with a larger number of cleavage fractures of p a r t i c l e s . Figure 35c) shows th is for POCO AXF-5Q. More cleavage fractures were also observed for both graphites i n the rapid crack propagation region close to the end of the specimen. - 136 -F i n a l l y , the specimens tested at 500°C showed severe oxida t ion , many p i t s being formed on the polished surfaces. These p i t s were larger and more rounded i n the case of POCO AXF-5Q. I V . 5 . d . i i P y r o l y t i c Graphite In comparison to i so t rop ic graphite, the crack path i n py ro ly t i c graphite was very s t ra igh t , only deviat ing s l i g h t l y at cone boundaries. Microcracking i n these regions was apparent. Figure 36a) shows the i n i t i a t i o n of slow crack growth at the notch t i p . Fracture seems to have progressed by the movement of the crack through basal plane layer packets i n the a d i r e c t i o n , as observed previously for transverse rupture specimens loaded i n the perpendicular o r ien ta t ion . The wavy markings on the machined surface indicates faul t regions between sets of as-deposited basal planes and these appear to form natural fracture or ig ins at the notch t i p . Figure 36b) shows the progress of the crack through the layer plane packets further along the fracture surface. River patterns, cleavage steps and t i r e tracks are apparent but i n general the fracture surfaces are much more uneven than those observed i n three-point bending. Basal plane shearing i s extensive and many fragments of mater ial appeared to peel off the edges of the planes. In general, after moving approximately 1cm from the notch t i p , the crack veered to the side of the groove. At th i s point the crack front apparently twisted into the mater ia l and delamination i - 137 -occurred. In fac t , i t was extremely d i f f i c u l t to break the specimens afterwards i n the c d i r ec t ion for studying the fracture surfaces. I t would appear that although the fracture i n i t i a t i o n process had a l l the charac te r i s t i cs of a crack moving along the basal planes i n the a d i r e c t i o n , f i n a l f a i l u r e occurred by delamination. This indicates some change i n the resolved shear stresses act ing at the crack t i p as the crack proceeds since there would otherwise be no reason why the dif ferent l eve l s of basal plane packets should not connect and form a r e l a t i v e l y smooth fracture face as observed for three-point bending specimens loaded i n the perpendicular o r ien ta t ion . - 1 3 8 -CHAPTER V DISCUSSION V.l Short-Term Strength of Graphite A unified approach to the strength of graphite may be developed using equations (1) and (2) . In this general approach the effects of microstructure, temperature and environment on strength are evaluated in terms of their effect on the two major variables, fracture toughness and flaw size. Before discussing these variables some mention should be made of the influence of strain-rate on the fracture strength of graphite. In the transverse rupture tests i t was assumed that the strain-rate or loading-rate was sufficiently fast for no crack growth to occur prior to failure i.e. instantaneous failure at Griffith-type flaws. If crack extension takes place then the calculated fracture strength w i l l be characteristic of a material with flaws larger than those present at the beginning of the test. The effect of strain-rate on strength can be obtained from an integration of the Kj-V curve. An analytical solution to the integration shows that the strength i s given, for large n, by"*~ - 139 -'Fr c ^ co xo l + 2TrEe(n+l) c c V ^ C n - 2) hi Hn+1) . 3/2 l + irEecT ( c I c ~ c T ) VipKiji (32) where e Is the applied s t r a in - ra t e , E i s Young's modulus, the subscript refers to conditions at the onset of crack motion and o rj, refers to conditions at the onset of stage I I ; the other terms have been defined previously . For the present case where only s ingle stage Kj-V curves have been obtained th i s reduces to K Fr c \ o o 1 + 2irEe(n+l)c h 1 W ) V Q K o ( n - 2) (33) Thus, a s t rength-strain-rate curve can be constructed after assuming a value for the i n i t i a l flaw s i z e , c Q . The data for POCO AXF-5Q at room temperature was chosen because of the reprodu-c i b i l i t y of the K - r - V diagrams and the suggestion of a s t a t i c fatigue l i m i t , K q . Assuming an i n i t i a l flaw s ize of 50ums for the unnotched bars and 1.5mm (c/d = h) for the notched bars complete o , h curves were constructed as shown i n Figure 37. r r From the curve for unnotched bars i t can be seen that the fracture strength varies s l i g h t l y with s t ra in- ra te up to a l i m i t i n g value of I ~ l s e c 1 . Appl ica t ion of a s t ra in- ra te less than 10 6 sec 1 would resul t i n fracture strengths ~5% less than the ins tan-taneous value. This compares with D ie f endo r f ' s 1 7 10% decrease i n strength of a petroleum coke graphite at room temperature when -3 -1 the s t ra in- ra te decreased to less than 10 sec . This small - 140 -Figure 37. Effect of s t ra in- ra te on strength of POCO AXF-5Q at room temperature - 141 -s e n s i t i v i t y to s t ra in- ra te i s due to the steep slope of the K-r-V curve. In comparison, the instantaneous fracture strength of alumina, which has a Kj-V curve wi th a slope of 31 for stage I i n a i r , may be reduced by 36% on appl ica t ion of s t ra in-ra tes less „. , n - 1 0 -1 2 than 10 sec In the present transverse rupture tests on unnotched bars -5 -1 a of POCO AXF-5Q a s t ra in- ra te of 4 x 10 sec was used. From Figure 37, th i s implies that the measured fracture strengths were 4.5% less than the instantaneous value due to s u b c r i t i c a l crack growth. The curve for notched bars shows a s imi l a r behaviour to that for unnotched bars. However, for the same s t r a in - ra t e , 4 x 10 sec 1 crack extension does not reduce the fracture stress as much as i n the case for unnotched bars. This i s reasonable since any change i n c would have propor t ional ly a much larger effect on unnotched bars than on notched bars. V . l . a Fracture Toughness, C r i t i c a l Stress Intensi ty Factor From equation (3) i t can be seen that any changes i n fracture toughness may be due to changes i n ei ther the e l a s t i c modulus, E or The s t ra in- ra te i n the region of maximum t ens i l e stress for transverse rupture specimens of square cross-sect ion i s 3P£ 2b3E £MAX = T-T (34) where P = loading rate i = span b = specimen breadth or depth E = Young's modulus - 142 -the effect ive surface energy for fracture i n i t i a t i o n , Y ^ . These w i l l be considered separately. 27 Wagner et a l have accounted for the effects of porosi ty on the e l a s t i c moduli of the POCO series of graphite i n terms of the two types of poros i ty . Any change i n e l a s t i c modulus w i th in th i s series i s due to a v a r i a t i o n i n the i n t e r p a r t i c l e or open poros i ty , which resu l t s from incomplete f i l l i n g of the i n t e r p a r t i c l e packing voids and from shrinkage and gas evolut ion during binder p y r o l y s i s . The f i l l e r - p a r t i c l e or closed porosi ty exis t s mainly as basal plane delaminations and resu l t s from l o c a l stresses introduced by the anisotropic expansion and contract ion of pa r t i c l e s during heat treatment. Due to the lower c r y s t a l l i t e e l a s t i c modulus for shear between basal planes, the f i l l e r - p a r t i c l e porosi ty was i n t e r -preted to be much more ef fec t ive i n reducing the o v e r a l l e l a s t i c moduli of the series to values considerably less than the s ingle —2 6 c r y s t a l constant, C ^ of 55GN.m (8 x 10 p s i ) . The wrinkled nature of the basal planes of p y r o l y t i c graphite due to random stacking would have a s i m i l a r effect i n reducing the e l a s t i c modulus of t h i s mate r ia l . The 5% increase i n the f l e x u r a l e l a s t i c moduli of the i s o -t rop ic graphites between room temperature and 500°C i s consistent 47 with previous workers observations on p o l y c r y s t a l l i n e graphite This increase i s generally a t t r ibuted to the closure of the cracks p a r a l l e l to the basal planes formed during cooling after g r a p h i t i -sa t ion . - 143 -I t has already been shown that the difference i n the ef fec t ive fracture surface energy for crack I n i t i a t i o n , Y^ of the two i s o -t rop ic graphites i s much greater than can be accounted for by arguments regarding reduction i n load-bearing area. Apparently the increased In te rpa r t i c l e porosi ty present i n POCO AXZ must provide preferred low-energy paths for crack propagation, r e su l t ing i n the lower fracture energy compared with POCO AXF-5Q. Examination of fracture surfaces has shown that a greater proportion of transgranular fracture occurred i n the case of POCO AXF-5Q and also when crack propagation was rapid compared wi th slow crack growth. The spher ica l closed pores observed on the fracture surfaces of POCO AXF-5Q would tend to blunt a propagating crack at various points along i t s length reducing the s tress in tens i ty there. Conversely, i n t e r p a r t i c l e pores at gra in boun-daries have sharp angles where the boundary and pore meet and may act as subsidiary crack n u c l e i , requi r ing a lower energy for crack propagation. An intergranular fracture mode may be expected to be easier to maintain i n a mater ia l with a greater proportion of interconnected porosi ty such as POCO AXZ. (This i s shown quant i ta t ive ly i n Appendix 4.) The resultant lower fracture energy would be counteracted i n part , however, by the larger area of the fracture face i n intergranular than i n transgranular f racture. The high temperature values of Y ^ ' shown i n Appendix 3 are wi th in experimental error of the room temperature values so that no obvious effects of temperature and environment are apparent. - 144 -However, fractographic evidence revealed that there was a tendency for an increase i n the proportion of transgranular to intergranular fracture mode at 500°C. The extensive oxidat ion which the double to rs ion specimens experienced i s bel ieved to be responsible. This i s discussed again l a t e r . The larger values of fracture surface energy obtained for py ro ly t i c graphite can be explained i n terms of the very large amount of new surface area produced as a resu l t of the complex fracture process. For the perpendicular or ien ta t ion large sur-face areas were formed due to fracture i n i t i a t i o n on different planes and the resultant interlaminar shear needed to j o i n up these regions to produce a stable moving crack front . For the p a r a l l e l or ienta t ion the large surface area produced was a d i rec t r esu l t of the s t ep - l i ke fracture surface. In addi t ion , propagating cracks might be expected to have encountered more resistance i n specimens with the p a r a l l e l o r ien ta t ion than the perpendicular o r i en ta t ion . In the former case the running cracks would encounter basal plane boundaries more often than i n the l a t t e r case where the propagating cracks generally fol low the regions of faul t between the layer plane packets i . e . cone boundaries. A very large amount of interlaminar shear occurred i n the rapid crack growth region of the double tors ion specimen. Thus, the lower fracture energy obtained for th i s specimen might be explained on the basis of the free surface energy of graphite for - 145 -surfaces p a r a l l e l to the basal planes being very much less than for surfaces perpendicular to the basal planes, 0.15 and 5.4-6.3 -2 47 J.m , respect ively . However, as mentioned previously , the value of the Poisson's r a t i o used i n the analysis i s questionable. In summary, the same trends are observed by the fracture toughness parameter as the ef fec t ive fracture surface energy due to the corresponding re la t ionship for the Young's modulus. V . l . b Flaw s i ze Subsidiary cracking or microcracking at the notch or crack t i p occurred both i n the transverse rupture and double to r s ion tes ts , as evidenced by the change i n compliance p r io r to f a i l u r e and from v i s u a l observation of the graphite samples. I t appears that as the load on a specimen i s gradually i n -creased, the crack t i p stress reaches the c r i t i c a l stress and cracks begin to grow i n the pa r t i c l e s around the t i p . As a resul t of the cracks, the pa r t i c l e s themselves become more compliant causing a r e d i s t r i b u t i o n of stress around the t i p . For the transverse rupture tests on py ro ly t i c graphite loaded p a r a l l e l to the c axis t h i s behaviour would be exaggerated as the s ize of the region of microcracking increased as the crack propagated i n a s t ep - l i ke fashion. Thus, the crack i s extended p r i o r to f a i l u r e and catastrophic crack propagation presumably occurs when the microcracks l ink-up with the main crack. - 146 -In the determinations of fracture energy the flaw s i ze should be that at catastrophic f a i l u r e which i n the case of crack extension by microcracking i s not the same as the i n i t i a l flaw s i z e . The extension i s only of the order of a few gra ins , so i t i s not s ign i f i can t for the notched bars or the double to r s ion specimen. However, i t does imply that the ca lcula ted flaw s ize for unnotched bars i s a measure of the s i ze of a "microcrack zone". The "microcrack zones" for the i so t rop ic graphites at room temperature and 500°C were between 50 and 70ums. (No extensive oxidat ion of the unnotched bars tested at 500°C occurred so that any change i n the flaw s ize as a resu l t of oxidat ion would not be apparent). Thus, i t appears that the extension of surface flaws such as gra in pul l -outs 10-20ums i n s i ze to 50-70ums occurs as a d i rec t resul t of microcracking. In comparison the effect of s t r a in - ra t e , s t a t i c f a t i gue , i n extending the i n i t i a l flaws i s shown l a t e r to be much smaller . For py ro ly t i c graphite the "microcrack zone" i s much larger than for the i so t rop ic graphites due to the nature of the cone structure and the larger "grain s i ze" i n the basal planes. A s imi l a r surface flaw extension model applies as described above. In conclusion, the short-term fracture process i n graphite i s i n i t i a t e d by the extension of surface flaws by microcracking u n t i l the modified G r i f f i t h r e l a t ionsh ip , equation (1), holds and the strain-energy release rate i s su f f i c i en t to create new surface area. Changes i n microstructure, temperature and environ-- 147 -ment appear to influence the short-term strength of graphite only i n so much as they influence the fracture mode which i s indicated to a large extent by changes i n the fracture toughness parameter, K I c . The values of K ^ c are high compared to other p o l y c r y s t a l l i n e ceramics due to the energy involved i n opening up subsidiary cracks and the crack blunt ing due to in te rac t ion of the secondary cracks with the main crack front . The high value of fracture toughness and consequently strength of p y r o l y t i c graphite indicates that the in te rac t ion of crack fronts with weak interfaces i s a good toughening mechanism. V.2 Time Dependent Fa i lu re of Graphite When a graphite specimen supports a t en s i l e stress none of the inherent flaws or cracks are s u f f i c i e n t l y large for catastrophic f a i l u r e to occur. However, these stress concentrating flaws and cracks may grow as predicted by the K-r-V diagram. The room temperature tests have revealed a stress in tens i ty versus crack v e l o c i t y behaviour that resembles the t h i r d stage of crack growth i n soda-lime g lass . Thus, i t appears that l i t t l e s t a t i c fatigue occurs i n graphite at room temperature except at a very high f rac t ion of the c r i t i c a l stress i n t ens i t y . This i s best i l l u s t r a t e d by ca lcu la t ion of the r a t io K T (10 S / K T c , where K-j-(10 6 ) refers to the stress in tens i ty at a crack v e l o c i t y of 10 ^m.sec 1 and K T o the corresponding c r i t i c a l stress i n t ens i t y . - 148 -Values of t h i s r a t i o for the i so t rop ic graphites and p y r o l y t i c graphite are shown i n Appendix 5 and may be considered as an ind ica t ion of the extent of s t a t i c fa t igue. At room temperature K-(10""^)/Kj c ranges from 0.92 to 0.95, the lower value being obtained for the more inhomogeneous POCO AXZ. At 500°C t h i s r a t io i s 0.87 and 0.90 for POCO AXZ and AXF-5Q, respect ively i . e . the effect of temperature and environment on the i so t rop ic graphites i s to reduce K -r ( 1 0 ~ 6 ) / K I c by 5%. I t i s of in teres t to compare the calculated slopes of the K-r-V curves for the three graphites with W i l k i n ' s data for RC4 extruded graphite. The slope log(a„ /a ) / l o g ( t , , / t r ) of Figure 3 corresponds fir HS ° L to ^tn-2) , y i e ld ing n values of ~680 and ~830 i n the case of = 3159 and 3069 p s i , respect ively for the corresponding stress in tens i ty-crack ve loc i t y diagrams. These values are not i n good agreement wi th the present resu l t s of 113, 218 and 216 for POCO AXZ, AXF-5Q and py ro ly t i c graphite, respec t ive ly . W i l k i n ' s resu l t s appear to be more representative of a short region of crack accelerat ion as observed i n the case of POCO AXZ and py ro ly t i c graphite at room temperature. However, data obtained from the double tors ion technique (large preformed cracks) and conventional s t a t i c fatigue tests (inherent microscopic flaws) may not be comparable. An ind ica t ion of the extent of crack growth during s t a t i c fatigue may be obtained by ca l cu la t ion of the homologous s t ress , a H . Consider a mater ia l containing an i n i t i a l flaw of s i z e , c Q . - 149 -On app l ica t ion of an applied s t ress , the i n i t i a l stress in tens i ty on such a flaw i s given by K I i " Y V o * ( 3 5 ) where Y i s a geometrical fac tor . Let the applied stress act ing on the mater ia l increase rap id ly such that no crack growth occurs p r io r to f a i l u r e . The corres-ponding equation for the c r i t i c a l stress in tens i ty i s K l c " YalcCoH <36) where a T i s the instantaneous fracture s t ress . Ic From equations (35) and (36) and the d e f i n i t i o n of homologous s t ress , equation (5) KT" - ~T H ( 3 7 ) Ic Ic A l t e r n a t i v e l y , consider the same i n i t i a l flaw, c Q and l e t i t grow under the constant applied s t ress , cr^. Catastrophic f a i l u r e w i l l occur when the flaw has grown to a c r i t i c a l s i z e , c I c and the c r i t i c a l s tress in tens i ty w i l l be K T = Y o . c T (38) Ic A Ic Equation (35) s t i l l applies for the i n i t i a l stress in t ens i ty act ing on the flaw so that d iv id ing equation (35) by (38) K_. / c • 2 / c \ - 1 5 0 -and wi th equation (37) *Ic " l c V c l c / Therefore, a knowledge of the homologous stress and the i n i t i a l flaw s ize can y i e l d a value for the c r i t i c a l flaw s ize for a flaw growing under a constant applied s t ress . The equation takes the form c- - • c o (41) Thus, the percentage increase i n the i n i t i a l flaw s ize as a resu l t of s t a t i c fatigue can be obtained from (^ ) x 100% = ( 1 " q H } x 100% (42) c H 2 Values for the percentage increase i n c 0 for each graphite were calculated and are a lso shown i n Appendix 5. K - r ^ was taken as the minimum measured stress i n t ens i t y . I t was assumed that for v e l o -c i t i e s less than that corresponding to the minimum measured K-r —6 —1 i . e . approximately 10 m.sec , the flaw extension was n e g l i g i b l e . This seems reasonable since there was a suggestion of a s t a t i c -6 _ i fatigue l i m i t at crack ve loc i t i e s of 10 m.sec i n the case of POCO AXF-5Q at room temperature. From Appendix 5 i t can be seen that the maximum increase i n the i n i t i a l flaw s ize as a resu l t of s u b c r i t i c a l crack growth would be 31% for POCO AXZ tested at 500°C. - 151 -V . 2 . a Mechanism of Crack Growth The steep nature of the K T - V diagrams of the graphites at room temperature suggest that crack growth i s governed mostly by mechanical processes. The form of the curves appear to r e f l ec t microst ructural features i n the materials which cont ro l t h i s mechanical f a i l u r e . For example, the reproducible K-r-V curves obtained for POCO AXF-5Q are consistent with crack growth i n a mater ial having a uniform densi ty, uniform d i s t r i b u t i o n of regular flaws (high Weibull modulus) and which does not have a tendency to deflect the crack path. In comparison, the va r iab le K.J.-V curves for POCO AXZ seem to re f l ec t the more inhomogeneous nature of t h i s mate r ia l , as evidenced by the more var iab le flaw density (lower Weibull modulus) and greater d i f f i c u l t y i n preventing a growing crack from deviat ing from a s t ra ight path. The f a i r l y reproducible resu l t s for p y r o l y t i c graphite are consistent with a r e l a t i v e l y homogeneous microstructure, i n spi te of the low value for the Weibull modulus. The i n i t i a l s t r a igh t -ness of the crack path supports t h i s . V . 2 . a . i Isotropic Graphites at Room Temperature Isotropic graphite i s a f ine grained agglomerate interspersed with pores. Fa i lu re appears to occur by cleavage of f i l l e r pa r t i c l e s and f a i l u r e of basal plane binder coke junct ions , as i s 20 commonly observed for most p o l y c r y s t a l l i n e graphites - 152 -The flaws i n i t i a t i n g fracture i n i so t rop ic graphite are gra in pu l l -ou t s , ~10-20pms i n s ize formed at an applied stress which i s a large f rac t ion of the fracture s t ress . Such microcracks have 22 been observed by Stevens while studying POCO AXF-1Q. He showed that the microcracks often l i e p a r a l l e l , i n groups on the basal plane and that sometimes the d i r ec t ion of propagation i s deflected by a grain boundary. A larger crack could then read i ly form by the l ink-up of several of these smaller cracks. The effect ive s i ze of such a microcrack zone w i l l increase by s t a t i c fatigue under a constant applied stress i f the stress in tens i ty i s high enough; i f K-r>KQ, the s t a t i c fatigue l i m i t . Considering the largest flaw i n a graphite component, the stress in tens i ty at t h i s flaw w i l l increase as the flaw grows according to the generalised equation Kj- - Y aj* (43) In the case of POCO AXF-5Q, having a s ingle continuous K-r-V curve the flaw accelerates u n t i l reaching the c r i t i c a l s i z e , 10% larger than the s ize of the o r i g i n a l microcrack zone, for f i n a l f a i l u r e to occur. The s igni f icance of the discontinuous Kj-V curves i n terms of crack growth i n POCO AXZ i s as fo l lows . A flaw s ta r t s to accelerate at a pa r t i cu l a r stress in tens i ty but i s soon brought to a h a l t , presumably at some'microstructural obstacle". The flaw can only continue to move at a lower v e l o c i t y by circum-- 153 -navigating or breaking through the obstacle, after which the v e l -oc i ty can once more increase. This behaviour appears to occur sev-e ra l times before a c r i t i c a l stress in tens i ty i s at tained corresponding to an 18% increase i n the i n i t i a l flaw s i z e , when the flaw can break through a l l the obstacles and atomic bonds i n i t s path causing catastrophic f a i l u r e . The inhomogeneous nature of POCO AXZ seems to indica te that these microstructural obstacles may be nonuniform regions of intergranular porosi ty or possibly regions where the intergranular pores are less angular and so more l i k e l y to blunt the crack path. Crack propagation would then occur i n regions where the pores act as crack n u c l e i . The s ingle continuous K -r-V curve for POCO AXF-5Q i s consistent with a fracture mode that i s r e l a t i v e l y unimpeded by pores. V . 2 . a . i i Isotropic Graphites at 500°C The K T - V curves for the i so t rop ic graphites at 500°C are s t i l l quite steep ind ica t ing that crack growth i s s t i l l determined mainly by mechanical f a i l u r e . However, the 44% reduction i n the slope at 500°C compared with the room temperature value shows that there i s thermal and environmental assistance at 500°C encouraging s u b c r i t i c a l crack growth to occur at lower stress i n t e n s i t i e s . The effect of oxidat ion at the crack t i p i s to remove mater ia l both from the geometrical surface and from the in t e rna l surfaces of the interconnected pores. For cracks of the same - 154 -dimensions the geometrical surface area exposed w i l l be the same. The steady-state oxidat ion rate of POCO AXF-5Q at 500°C i s approxi-mately four times greater than that of POCO AXZ. Thus, i f a specimen of each material achieve the steady-state oxidat ion rate at 500 °C, more material might be expected to be removed from the geometrical surface area at the crack t i p i n the case of POCO AXF-5Q than i n the case of POCO AXZ. However, the mater ia l removed from the i n t e rna l surface area should be approximately the same for both grades since the act ive surface area of POCO AXZ i s almost four times that of POCO AXF-5Q. Therefore, on t h i s bas i s , the reduction i n load-bearing area as a resu l t of oxidat ion would be expected to be the same for both materials as the ASA consti tutes most of the t o t a l accessible area. No consideration has been made of preferred oxidat ion at exposed s i t e s . A larger edge plane area would be exposed at the crack t i p by an intergranular fracture mode than by a transgranular fracture process. Thus, a knowledge of the quant i ta t ive effects of th i s preferred oxidat ion i s required before i t i s possible to predict wi th confidence the sh i f t s i n the K-r-V curves of POCO AXZ and AXF-5Q to lower stress i n t e ns i f i e s as a r e su l t of the reduction i n load-bearing area. The ove ra l l increase i n the i n t e rna l surface area of the pores as a resul t of oxidat ion i s very smal l . (There i s a 50% increase i n the ASA during oxidat ion but the ASA i s only ~5% of the t o t a l in t e rna l surface.) Therefore, oxidat ion i s not f e l t to have a s ign i f i can t effect on the flaw s ize d i s t r i b u t i o n . - 155 -Rather the effect of oxidat ion on the crack growth mechanism i s f e l t to be more i n terms of the effect of a modif icat ion i n the pore shape due to l o c a l i s e d corrosion at the crack t i p . More rounded pores might be expected to blunt the crack path and i n h i -b i t the intergranular fracture mode. This would be consistent with the increase i n the percentage of transgranular fracture observed for both i so t rop ic graphites at 500°C. The transgranular fracture mode i s less dependent on the presence of intergranular pores which would account for the s ingle continuous K -V curve obtained for POCO AXZ at 500°C. Under these conditions a nonuniform d i s t r i b u t i o n of interconnected pores would have less effect . The p o s s i b i l i t y of stage I I behaviour at v e l o c i t i e s of 5 x 10 7m.sec 1 i n the case of POCO AXZ requires further i n v e s t i -gat ion. Other factors that would a id and retard s u b c r i t i c a l crack growth i n graphite at high temperatures are increased p l a s t i c deformation and the closure of basal plane cracks, respec t ive ly . Graphite deforms read i ly by s l i p along i t s basal planes but such s l i p contributes only two independent systems. Thus,under normal conditions graphite lacks the f ive independent s l i p systems required by von Mises c r i t e r i o n for p l a s t i c deformation capable of producing an a rb i t ra ry s t r a i n ; thus microcracks open up during deformation. I t i s known that the mechanical s t r a i n i n graphite increases with the time for which stress i s applied i f 48 the temperature i s 150°C or higher . However, creep of graphite, - 156 -which i s produced by climb of edge d is loca t ions d i s t r ibu ted near the tips of cracks, only becomes s ign i f i can t above 1000°C. In 52 p a r t i c u l a r , Zukas and Green have measured large creep s t ra ins to fracture i n POCO grade HPD-1 between 2200 and 2500°C, generally exceeding 30%. The effect of creep i n the present experiment i s not f e l t to be s ign i f i can t but there might be a ce r ta in amount of increased d i s loca t i on a c t i v i t y at 500°C. The ind iv idua l effects of temperature and environment i n a s s i s t i ng s u b c r i t i c a l crack growth i n graphite are not resolved at the present time. V . 2 . a . i i i P y r o l y t i c Graphite at Room Temperature The mechanism of crack growth i n p y r o l y t i c graphite i s much more complex than for the i so t rop ic graphites. The fracture i n i t i a t i n g flaws are again surface flaws wi th an associated micro-crack zone. However, the microcracking now appears to occur predominantly at the weak interfaces of the cone boundaries causing delamination and a subsequent r e d i s t r i b u t i o n of s t ress . The r a t i o , Kj-(10 ^)/K-j- c for p y r o l y t i c graphite i s comparable wi th that of POCO AXF-5Q and yet the structure appears to be "semihomogeneous" i n that "microstructural obstacles" are encoun-tered by a moving crack. These obstacles are not as e f fec t ive , however i n slowing down the crack as was the case for POCO AXZ. This i s w e l l shown i n Figure 24c) for the f i n a l accelerat ion i n curve C. The microst ructura l obstacles i n p y r o l y t i c graphite are - 157 -believed to be nodule in ter faces . Since these nodules or cones are present on a microscopic as w e l l as macroscopic scale i t i s f e l t that app l ica t ion of the K T - V curve for p y r o l y t i c graphite to the propagation of microscopic flaws i s re levant . A surface flaw i n a specimen or component of p y r o l y t i c graphite oriented for s u b c r i t i c a l crack growth i n the basal plane d i rec t ion on appl ica t ion of an applied s t r e s s , w i l l s tar t to move i f the stress in tens i ty at the flaw i s greater than K q , the s t a t i c fatigue l i m i t . Such a flaw w i l l continue to grow u n t i l e i ther i t i s brought to a ha l t at a cone interface (corresponding to the K T - V curves with slopes of ~ 5 0 0 ) or u n t i l i t reaches a c r i t i c a l s ize for catastrophic f a i l u r e (corresponding to the K ^ - V curves with slopes of ~ 2 0 0 ) . This c r i t i c a l flaw s ize corresponds to ~ 1 2 % increase. The apparent change i n the fracture mode on catastrophic propagation of a crack i s believed to be due to the wavy nature of the basal planes. Any stress applied to a stack of wavy planes w i l l have resolved components p a r a l l e l and perpendicular to the planes. Thus, crack growth i n the double tors ion specimen of p y r o l y t i c graphite probably occurred by a combination of Mode I opening and Mode I I I shearing. The Mode I I I f a i l u r e would be more apparent at longer distances from the notch t i p where the crack front i s no longer constrained to propagate through the basal planes. - 158 -V.2.b Predic t ions of L i f e Expectancy The l i f e expectancy for the three graphites under an applied t ens i l e stress are shown i n Figure 32. These plots are v a l i d only for specimens having the appropriate Kj-V curves and a flaw s i ze l i k e those i n the transverse rupture tes ts . Also the ca lcula t ions are on the conservative side since the flaw sizes used were too large as a resu l t of s u b c r i t i c a l crack growth i n the transverse rupture tes ts . Fatigue l i m i t s and second stage behaviour have been ignored. I t can be seen that a specimen of POCO AXZ at room g temperature w i l l f a i l i n 10 sees (~3 years) under a t ens i l e stress 70% of the fracture strength. This f a i l u r e time i s reduced to ~30 sees i f the t ens i l e stress i s increased to 80% of the fracture strength or to ~14 sees by increasing the ambient temperature to 500°C. S i m i l a r l y , for POCO AXF-5Q, under a t ens i l e stress 80% of the fracture strength at room temperature f a i l u r e occurs after l O ^ s e c s (~800 years) . At 90% of the fracture strength th i s time i s reduced to ~2secs and at 500°C to ~26secs. The decreased l i f e expectancy of the i so t rop ic graphites at 500°C compared to room temperature i s a d i rec t resul t of the reduction i n slope of the K-r-V curves at t h i s temperature. In the case of py ro ly t i c graphite at room temperature the l i f e expectancy decreases from 10~^ seconds (~800 years) at 60% of the fracture strength to ~10secs under a t ens i l e stress 66% of the fracture strength. - 159 -These values merely indicate the nature of the delayed f a i l u r e In the graphites employed here and can only be extended to other materials i f they f i t p rec i se ly the same boundary condi t ions . V .2 . c Limita t ions of Slow Crack Growth Tests The notched bar and double tors ion technique of measuring fracture toughness of the i so t rop ic graphites were i n good agree-ment wi th one another and also with the values obtained by Simpson. This leads confidence to the double tors ion method and to the stress analysis used to in terpret i t , i n sp i te of the discrepancy between the apparent e l a s t i c modulus computed from the a n a l y t i c a l equation (A8) and the compliance p lo t and the dynamic modulus. A knowledge of the r a t i o D/B and also of the shape of the crack p r o f i l e and hence the correct ion factor , $ would probably produce a s ign i f i can t effect on the value of the crack v e l o c i t y . However, t h i s w i l l be consistent over the ent i re range of stress in tens i ty and does not s i g n i f i c a n t l y affect the app l ica t ion of the K^-V diagrams to ei ther the analysis of slow crack growth mechanisms, or the pred ic t ion of the time dependent f a i l u r e parameters. The main l imi t a t ions of the slow crack growth tests are l i s t e d below. 1. I t has not yet been proven that the v e l o c i t y and hence Kj. are s i m i l a r a l l the way along the crack front of the double tors ion specimen. There i s probably a range of v e l o c i t i e s for a curved crack p r o f i l e and i t i s not known \ - 160 -which v e l o c i t y i s being measured. For any p r a c t i c a l s i t ua t ion i t i s the v e l o c i t y wi th the crack moving i n a d i r ec t i on orthogonal to the crack front that i s required. 9 2. Will iams and Evans analysis of the compliance curve refers to the mid-point of a s t ra ight crack f ront . I t i s not known how a compliance analysis can be applied to a crack with a shape p r o f i l e d i f f e r ing from t h i s ; for example, as shown i n Figure A l b ) . A knowledge of the "effect ive crack length" for a given compliance i s required. The calculated v e l o c i t y w i l l then be for th i s "effect ive crack length" and from knowledge of the shape of the crack p r o f i l e , the v e l o c i t y for a crack t r a v e l l i n g i n the orthogonal d i r ec t i on can be determined. 3. For an anisotropic mater ial such as p y r o l y t i c graphite l inea r e l a s t i c i t y theory i s no longer appl icable and different re la t ionships between the stress in tens i ty factors and the strain-energy release rates are required. 4. I t has not yet been shown whether the data from macro-scopic cracks are relevant to the propagation of micro-scopic cracks. 5. Another major l i m i t a t i o n of the double tors ion technique i s that i t does not allow for s t a t i s t i c a l var ia t ions i n the strength of b r i t t l e mater ia ls . The whole Kj-V diagram i s obtained from only .a few specimens which i s not r e a l l y tenable for materials having a d i s t r i b u t i o n of flaws. A - 161 -merging of the concepts of s t a t i s t i c a l strength var ia t ions and s u b c r i t i c a l crack growth i s required. This could be done, for example by performing a proof tes t which would es tab l i sh the maximum flaw s ize present i n a component at the time of the proof tes t . - 162 -CHAPTER VI SUMMARY AND CONSLUSIONS Slow crack growth studies have shown that l i t t l e s t a t i c fatigue occurs i n graphite at room temperature except at very high fract ions (^ 92%) of the c r i t i c a l stress i n t e n s i t y . The stress in tens i ty versus crack v e l o c i t y diagram resembles the t h i r d stage of crack growth i n soda-lime glass so that s u b c r i t i c a l crack growth i n graphite at room temperature i s determined mostly by mechanical f a i l u r e . The form of these diagrams r e f l ec t micro-s t ruc tu ra l features i n the mater ia l con t ro l l i ng mechanical f a i l u r e . Fracture i n graphite i s i n i t i a t e d at surface flaws, mainly grain pul l -outs produced as a resu l t of po l i sh ing or machining damage. On appl ica t ion of a stress which i s a large f rac t ion of the instantaneous fracture s t ress , microcracks open up i n the regions around such flaws. "Microcrack zones" are commonly observed i n po lyc rys t a l l i ne ceramics not f u l f i l l i n g von Mises c r i t e r i o n for p l a s t i c deformation. Subsequent slow crack growth would occur by the l ink-up of these microcracks when the stress in tens i ty at such flaws i s greater than the stress in tens i ty corresponding to the s t a t i c fatigue l i m i t , as predicted by the K T - V diagram. - 163 -Thermal and/or environmental assistance of s u b c r i t i c a l crack growth i n graphite occurs at 500°C. However, the steep nature of the Kj-V curves indicate that s t a t i c fatigue i s s t i l l determined mainly by mechanical f a i l u r e . - 164 -CHAPTER VII SUGGESTIONS FOR FUTURE WORK 1. Conventional s t a t i c fatigue tests should be performed using i so t rop ic and py ro ly t i c graphite to produce s t ress- t ime-to-f a i l u r e curves and hence values of n , the slope of the corres-ponding K-r-V curves. This should confirm whether the fracture energy requirements for inherent flaws are s imi l a r to those of large preformed cracks and thus i f data from macroscopic cracks can be applied to microscopic crack propagation. 2. Further slow crack growth tests should be performed i n a i r at room temperature and 500°C to obtain stress in tens i ty-crack v e l o c i t y data i n the high and low v e l o c i t y regions. This could be done by adjusting the aspect r a t i o of the specimens, higher v e l o c i t i e s being obtained for small W/ t n and v i ce versa. 3. In order to resolve the i n d i v i d u a l effects of temperature and environment on the slow crack growth behaviour of graphite further double tors ion tests should be performed at 500°C i n a non-oxidising environment such as helium. 4. The high fracture toughness of py ro ly t i c graphite has been shown to be due to crack blunt ing at weak in terfaces . The slow - 165 -crack growth behaviour of a crack propagating between the basal planes of a double tors ion specimen of p y r o l y t i c graphite would therefore be of in te res t . 166 APPENDICES - 167 -APPENDIX 1 Theory of Double Torsion Technique The double to rs ion method for measuring slow crack growth i s based on a technique suggested by Outwater and Jerry 1"'' and further 12 2 9 developed by Kies and Clark and by Evans and Will iams and Evans . Figure Ala) shows a t y p i c a l specimen which can be considered as two tors ion bars, each having a rectangular c ross-sec t ion , loaded to P /2 . For small def lec t ions , y and for bars where the width i s very much larger than the thickness, the t o r s iona l s t r a i n , 0 i s given by e « z „ i S / f t a (AI) » Wt G where P/2 = t o t a l load applied to one bar P/2«Wm = to r s iona l moment G = shear modulus of the material a = crack length i . e . longest port ion of the crack at the lower specimen surface t = bar thickness W/2 = bar width Wm = moment arm - 168 -Figure A l Scematic diagram of a) One tors ion bar of the double to r s ion specimen b) Crack p r o f i l e for double to r s ion specimen - 169 -I f C i s the e l a s t i c compliance, then on rearranging v 3Wm 2a C = * « -~— (A2) P Wt3G I f the crack p r o f i l e Is independent of the crack length, the strain-energy release ra te , fy-may be given by where A = crack area t n = web thickness i n the plane of the crack. For r e l a t i v e l y large crack lengths where the deflect ions are subs tan t ia l ly larger than the deflect ions i n an uncracked specimen, the strain-energy release rate i s obtained by d i f f e ren t i a t ing equation (A2) with respect to a and subs t i tu t ing into equation (A3) 6, = 3 p 2 W m 2 (A4) 2Wt 3 t n G Subst i tut ing i n the fol lowing plane s t r a i n equation for ^ j , the strain-energy release rate for the crack opening mode * - <A5) equation (A4) reduces to K I " Wm < 3 ] >% P ( A 6 ) W t J t n ( l - v ) or K x = A P (A7) 3 A where A = constant = W (—r ) W t J t n ( l - v ) - 170 -Al t e rna te ly , d i f f e ren t i a t ing equation (A2) with respect to a d a Wt3o Wt3E and subs t i tu t ing into equation (A6) K i ' ' K J ^ - T - ^ * <A9> From equations (A6) and (A9) i t can be seen that the stress in tens i ty factor i s a function of the applied load, specimen dimensions and e l a s t i c constants, o n l y - i t i s independent of the crack length. This has been found to be true for up to more than one ha l f of the specimen length from compliance-crack length ca l i b r a t i ons . The v a l i d i t y of the assumptions made for t h i s analysis has 9 been proved by the good agreement obtained by Will iams and Evans between the empir ical and a n a l y t i c a l values of the constant A for glass and 4130 s t e e l . Using the re la t ionship between the specimen compliance and the crack length, the rate of change of compliance can be re la ted to the crack growth ra te , V. Experimentally the rate of change i n compliance can be determined from the rate of change of load at a f ixed displacement. The compliance for the double to rs ion specimen may be given by I" = (Ba + D) (A10) 171 -dC where B = — = slope of the experimental compliance-crack length curve and D = in tercept . D i f fe ren t i a t ion of (A10) wi th respect to time at constant displacement = 0) gives dt T7 / d a \ ,Ba + D^ ,dPx ,.„> V * (dt>y " -(—EF-> tty ( M 1 ) A l s o , at constant displacement P(Ba + D) = P ± ( B a i + D) = P f ( B a f + D) (A12) where the subscripts i and f refer to the i n i t i a l and f i n a l values at the beginning and end of r e laxa t ion . Solving for a The crack v e l o c i t y can therefore be obtained d i r e c t l y from the rate of load re laxa t ion at constant displacement and the i n i t i a l or f i n a l crack length. 2 9 Experiments by Evans and Williams and Evans using the double tors ion specimen have indicated that the crack front i s curved and extends further along the lower face than the upper face as shown i n Figure A l b ) . This shape i s e s sen t i a l ly independent of crack length for a given K^ , but var ies marginally with K^.. General ly, crack propagation i s orthogonal to the crack front so that equation (A13) should include a geometrical modif ica t ion, <j> given by the - 172 -ra t io of the distance moved perpendicular to the crack front and the distance moved p a r a l l e l to the specimen surface Ax L t n * = A"7 = (Aa^ + t n2)% <A14> where t = web thickness of the mater ia l Aa = difference i n crack length on the upper and lower specimen faces. Axi Since the r a t i o , — - i s <1, the crack v e l o c i t i e s should be Ax 2 lower than those given by equation (A13) . For alumina <f> has been found to e f fec t ive ly reduce the crack v e l o c i t y by f i v e . For high strength s t ee l and soda-lime glass the crack p r o f i l e d i f f e r s s l i g h t l y from that shown i n Figure A l ; i t i s more curved and orthogonal to the opening side of the specimen. Therefore, the value of <j> i s one. Thus, for accurate v e l o c i t y data observations of the crack p r o f i l e are necessary. - 173 -APPENDIX 2 An Estimate of Time-to-Failure from Crack Growth Kine t i c s Under constant applied stress o^, of in teres t i n a delayed fracture tes t , the t ime- to - fa i lu re , T i s given by T = | (A15) C i where C^ = i n i t i a l flaw s ize C_ = c r i t i c a l flaw s ize I c V = crack ve loc i t y The time for C >C-C i s n e g l i g i b l e . Since K T f , = Y a ^ C I c dC = J J l . dKT (A16) Y 2 C T 2 A and subs t i tu t ion into equation (A15) gives f K I c T = ^^~k I (A1?)  K I i Reca l l ing equations (7) and (8) V = A^K-j- n (7) and V = A 2 (8) - 174 -and defining as the value separating regions I and I I 2 K I (1-n) Ic Kj-dKj. V (A18) A t h i r d term corresponding to region I I I may be added but t h i s i s generally n e g l i g i b l e . Depending on the environment, the second term i s often n e g l i g i b l e . In a number of ceramics tested under ambient conditions the t ime- to- fa i lure i s cont ro l led so le ly by the behaviour i n region I of the Kj--V diagram and equation (A18) reduces to 2(K. 2-n I i (A19) T (n-2)A Y o A - 175 -APPENDIX 3 Fracture Energies of Isotropic Graphites Normalised for Poros i ty V - Yi/d -P) 2 Type of Test Notched Bar Double Torsion Mater ia l and ^ y ± Y i V -2 -2 -2 -2 Temperature Jm Jm Jm Jm POCO AXZ Room temperature 3 8 + 9 80 ± 19 35 ± 7 73 ± 15 500°C 40 ± 7 8 4 + 1 5 27 ± 5 57 ± 11 POCO AXF-5Q Room temperature 500°C 85 ± 7 91 ± 10 125 ± 10 134 + 15 78 ± 2 115 ± 3 77 ± >2 113 ± 3 - 176 -APPENDIX 4 Mercury porosimetry has shown that the majority of vo id space i n i so t rop ic graphite consists of open pores wi th "diameters of penetration" of 0.79 and 0.95ums cons t i tu t ing 28.9 and 14.5% of the t o t a l volume of POCO AXZ and AXF-5Q, respec t ive ly . I f the pores are considered to be spher ica l and arranged i n a simple cubic array then the distance between nearest neighbour pore centres, x i s given by x = ( ^ f 3 - ) ^ (A20) where a = radius of a spher ical pore P = f r ac t iona l open porosi ty This y i e lds values for x of 0.96 and 1.46ums for POCO AXZ and AXF-5Q, respec t ive ly . Assuming that these open pores can act as crack nuc le i then the distance between nearest neighbour pore centres can be considered as the distance between flaws, so that the range of flaw free path i n each mater ia l i s 0.17 and 0.51ums. - 177 -APPENDIX 5 —6 The r a t i o , K T (10 ) / K T c a n d Percentage Increase In I n i t i a l Flaw  Size of Graphites - T . U - O J T 2) x 100% % Increase m c„ = l a — "° 2 Mater ia l , _ A V K-J.(10 ) a H ~ K i i Increase and — — — — i n c K ' K T c ° Temperature Specimen I c c % POCO AXZ Room temperature D 0.92 0.92 18 500°C B 0.87 0.87 31 POCO AXF-5Q Room temperature Mean 0.95 0.95 10 500°C C 0.90 0.91 21 P y r o l y t i c graphite Room temperature "a" d i r ec t i on Mean 0.95 0.95 12 - 178 -BIBLIOGRAPHY 1. S.M. Wiederhomand L . H , B o l z , J . Am. Ceram. S o c , 53_, 543 (1970). 2. A .G . Evans, J . Mater. S c i . , 1137 (1972). 3. B . J . S . W i l k i n s , J . Am. Ceram. S o c , 54, 593 (1971). 4. W. Weibull, J . App l . Mech., 18, 293 (1951). 5. W.F. Brown J r . and J . E . Srawley, "Plane S t ra in Crack Toughness Testing of High Strength M e t a l l i c Mate r i a l s " , A . S . T . M . S.T.P. No. 410, Ph i lade lph ia , Pa. (1966). 6. R .E . Mould and R.D. Southwick, J . Am. Ceram. Soc. , 42_, 582 (1959). 7. J . E . R i t t e r J r . and C L . Sherbourne, J . Am. Ceram. S o c , 54, 601 (1971). 8. S.M. Wiederhorn i n "Mechanical and Thermal Propert ies of Cera-mics", J . B . Wachtman J r . , E d . , N . B . S . Special Pub l i ca t ion No. 303, Washington (1969), p. 217. 9. D.P. Will iams and A .G , Evans, J . Testing and Evaluat ion, 1., 264 (1973). 10. B . J . S . Wi lk in s , Pr ivate communication. 11. J . 0 . Outwater and D . J . Je r ry , Interim Report, Contract N .O .N.R . -3219 (0NX), Univers i ty of Vermont, Bur l ington, V t . (Aug., 1966). 12. J . A . Kies and A . B . J . C la rk , i n "Fracture-1969", P . L . P ra t t , E d . , Chapman and H a l l , London (1969), p . 483. 13. W.B. H i l l i g and R . J . Charles, i n "High-Strength Mate r i a l s " , V . F . Zackay, E d . , J . Wiley and Sons, Inc . , N .Y . (1965), p. 682. - 179 -14. A . J . Sedriks, J . A . S . Green and D . L . Novak, Met. Trans. , 1, 1815 (1970). 15. E . Orowan, Nature, 153, 341 (1944). 16. v R .N . Stevens and R. Dutton, Mater. S c i . Eng. , J 3 , 220 (1971). 17. 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S o c , 55, 214 (1972). 28. S. Spinner and W.E. Tef f t , A . S . T . M . P r o c , 61, 1221 (1961). 29. G. P i c k e t t , A . S . T . M . P r o c . , 45, 846 (1945). 30. J . C . Lewis, i n "2nd Conf. on Ind. Carbon and Graphite, London, England, 1965", The Soc. of Chem. Ind . , London (1966),p.258. - 180 -31. A . E . B . Presland and J . A . Hedley, J . Nuc l . Mats . , 10, 99 (1963). 32. R. Stevens and T.D. Clausen, A . E . C . L . Report No. 3422 (1969). 33. R . L . Bond, E d . , "Porous Carbon So l i d s " , Academic Press Inc . , London (1967). 34. B.W. Gonser, E d . , "Modern Mate r i a l s " , 7_, Academic Press Inc. (London) L t d . (1970). 35. L . A . Simpson, Unpublished data. 36. J . Dollimore and C M . Freedman, i n "10th B ienn ia l Conf. on Carbon, Bethlehem, P a . , 1971", Am. Carbon Committee, Pennsylvania State Univers i ty , p . 267. 37. J . M . Dickinson and J.W. Shore, Carbon, 6_, 937 (1968). 38. W.J. Coy, J . Am. Ceram. S o c , 45, 223 (1962). 39. E . J . Se ld in , Carbon, 4_, 177 (1966). 40. T.R. Acharya and D.R. Olander, Carbon, 11, 7 (1973). 41. J . B . Lewis, i n "Modern Aspects of Graphite Technology", L . C . F . Blackman, E d . , Academic Press, London (1970), p . 129. 42. F .M. Lang, R. Blanchard, J . C . Fessler and J .R. Donati , Carbon, 6_, 827 (1968). 43. F . K . Earp and M.W. H i l l , i n "Ind. Carbon and Graphite, London, England, 1957", The S o c of Chem. Ind . , London (1958), p. 326. 44. P. Hawtin and J . A . Gibson, Carbon, 4_, 501 (1966). 45. R . J . Diefendorf, i n "Proc. 4th Conf. on Carbon, Buffa lo , 1959", Pergamon Press, N .Y . (1960), p. 483. 46. J . J . Gebhardt and J . M . Berry, A . I . A . A . Journal , 3_, 302 (1965). - 181 -47. H.H.W. Losty, in "Modern Aspects of Graphite Technology", L.C.F. Blackman, Ed., Academic Press, London (1970), p. 201. 48. W.N. Reynolds, "Physical Properties of Graphite", Elsevier Publishing Co. Ltd., London (1968), p. 33. 49. J.M. Berry and J.J. Gebhardt, J. Am. Ceram. Soc, 48, 350 (1965). 50. D.J. Green, P.S. Nicholson and J.D. Embury, McMaster University (Nov., 1972). To be published. 51. A.G. Evans. To be published. 52. E.G. Zukas and W.V. Green, Carbon, 10, 519 (1972). 

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