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Fabrication and mechanical properties of graphite fiber reinforced aluminum alloys 1976

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FABRICATION AND MECHANICAL PROPERTIES OF GRAPHITE FIBER REINFORCED ALUMINUM ALLOYS by KIYOYUKI ESASHI B.E.(1967) and M.E.(1969), TOHOKU UNIVERSITY, JAPAN A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in the Department of Metallurgy We accept th i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA APRIL, 1976 In presenting th i s thes is in par t i a l fu l f i lment of the requirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree ly ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th i s thes is for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t i on of th is thes i s fo r f i nanc i a l gain sha l l not be allowed without my wr i t ten permission. Depa rtment The Univers i ty of B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Date i i ABSTRACT A new method to fabr icate continuous graphite f i b e r reinforced aluminum a l loy composites has been developed and the tens i l e properties of the com- posites have been invest igated. Composites with 601, 201 and 7178 a l loy matrix containing up to 19 volume per cent of Thornel 50 graphite f i be r were studied. These composites showed lower tens i le strength values than the expected values from the " ru le of mixture". A theoret ical model i s discussed in order to understand the tens i l e properties of these composites. In th i s mechanism, graphite f ibers are thought to be broken continuously one a f te r another at maximum loading point of ultimate tens i l e strength during the ten s i l e te s t . A further attempt has been made to improve the ten s i l e strength of these composites, based on the above theoret ical work. i i i TABLE OF CONTENTS Page ABSTRACT i i LIST OF FIGURES v LIST OF TABLES i x ACKNOWLEDGEMENTS * Chapter I INTRODUCTION 1 1-1. General Background 1 1-2. Previous Work on Fabrication Techniques 2 1-3. Previous Work on Strength of Graphite Fiber/Aluminum and/Alloy Composites 12 I- 4. Purpose of Present Work 14 II EXPERIMENTAL PROCEDURE 18 II— 1 - Preparation of Composite Specimens 18 11-2. Tensile Testing 27 I I-3. Microscopic Observations 28 I I- 4. Micro Probe Analysis 29 III EXPERIMENTAL RESULTS 29 111 — 1 - Fiber Volume Fraction 29 I I I- 2. Micro Probe Analysis of the Specimens 29 111-3. Tensi le Stress Strain Curves 29 I I I-4. Ultimate Tensile Strength 36 111-5. Fracture Elongation 40 I I I - 6 . Microscope Observations of Tested Specimens 41 IV DISCUSSION 50 IV- 1. Rule of Mixture 50 I V - l - i . Rule of Mixture for Continuous Fiber Reinforced Materials 50 I V - 1 - i i . Strength of Discontinuous Fiber Reinforced Materials 53 iv Page, IV-2. Propagative Fiber Fai lure Model for Graphite Fiber Reinforced Aluminum Al loy Composites 57 IV-2- i . Ultimate Tensile Strength of Homogeneously Distributed Specimens 57 I V - 2 - i i . Energy C r i t e r i a of Propagative Fiber Fa i lure for Homogeneously Distr ibuted Composites 59 I V - 2 - i i i . Improvement of Tensile Strength in Bundle Structure Composites 76 IV-2-iv. Estimation of Var iables, b and T u t s 80 IV-2-v. Evaluation of Ultimate Tensi le Strength of Composites by Propagative Fiber Fa i lure Model 83 IV-3. Character i s t ics of Powder S l i p Interpenetration Method 89 V SUMMARY AND CONCLUSIONS 91 VI SUGGESTION FOR FUTURE WORK 92 REFERENCES 93 V LIST OF FIGURES Figure Page 1 The Var iat ion of Al^Cg in 5 wt % Graphite Fiber-Aluminum Composite a f te r Annealing for 24 hr at Various Temperatures (from Ref. 29) 9 2 The Var iat ion of Al^C^ in 5 wt % Graphite Fiber-Aluminum Composite a f te r Annealing for Various Times at 600°C (from Ref. 29) 9 3 Strength of Al Coated Graphite Fibers a f te r Heat Treatment for 1 Day at Various Temperatures (from Ref. 40) 10 4 Tensile Strength of the Al-Graphite Fiber Composites Fabricated by the Matrix Fo i l Method (Plotted from numerical data in Ref. 30) 10 5 Tensi le Strength of Graphite Fiber Aluminum Composites Fab- r icated by the Chemical Vapour Deposition Method (from Ref. 2) 13 6 Tensile Strength of Graphite Fiber Aluminum A l loy Composites Fabricated by the I n f i l t r a t i o n Method (Plotted from numerical data in Ref. 24) 13 7 Liquid Phase Hot Pressing Die Configuration to Fabricate Specimens from the Al I n f i l t r a ted Graphite Fiber Composite Wire (from Ref. 25) 16 8 Flow Sheet of the Specimen Fabrication Process 20 9 Scanning Electron Micrographs of the Powders Used, x 1000, (a) Aluminum, (b) Magnesium, (c) Copper, (d) S i l i c o n , (e) Zinc 21 vi Page 10 Schematic Diagram of the Interpenetration Device 23 11 Separating Boat 24 12 Hot Pressing Die Set 24 13 Tensile Specimen Geometries 24 14 Cross Section of a Uniform Composite, 201T6, #29, 12.1% V f , x 114 30 15 Cross Section of a Bundle Structure Composite, 7178T6, #39, 10.0% V f , x 62 30 16 Relation Between the Number of P l ie s for the Interpenetration Process and the Fiber Volume Fraction in Composites 31 17 Stress Stra in Curves of 601T4 A l loy and the Composites 33 18 Stress Stra in Curves of 201T6 Al loy and the Composite 34 19 Stress Stra in Curve of 7178T6 A l loy 35 20 Tensile Strength of 601T4 Composites, and Theoretical Curves 37 21 Tensile Strength of 201T6 Composites, and Theoretical Curves 38 22 Tensile Strength of 7178T6, Uniform and Bundle Structure Composites, and Theoretical Curves 39 23 Fracture Surface of 601T4 Composite, #17, 14.5% V f , x 1000 42 24 Fracture Surface of 201T6 Composite, #29, 12.1% V f , x 1000 43 25 Fiber Fai lure Zone near Specimen Shoulder Polished Surface of a 201T6 Composite Specimen, x 32 43 26 Scanning Electron Micrograph of Fiber Fa i lure Zone Surface Showing Broken Fibers, x 200 43 27 Scanning Electron Micrograph of Zone Surface Showing S l i p Lines, x 1000 43 v i i Page 44 28 Micrograph Indicating Propagation of the Fiber Fa i lure pr io r to Fa i lure of the Specimen, Longitudinal Sect ion, x 32 29 Longitudinal Section around the Zone Showing Matrix Grains, and Broken T i l t e d Fibers, NaOH Solution Etch, x 180 44 30 Longitudinal Sections of Fractured 601T4 Specimens, Showing the Difference in the D i s t r ibut ion of the Fracture Points in (a) Low V f (8.5%), #9, and (b) High V f (14.5%), #17, Composites 45 31 Longitudinal Sections of Fractured 201T6 Specimens, Showing the Difference in the D i s t r ibut ion of the Fracture Points in (a) Low V f (6.4%), #24, and (b) High V f (17%), #29, Composites 46 32 Relation between B f , E c and V f 48 33 Schematic Diagram of Stress Stra in Curves of the Composite, the Fiber, and the Matrix, Obtained According to "Rule of Mixture" 51 34 Tensi le Strength of Copper Reinforced with 5 mm Continuous B r i t t l e Tungsten Wires (from Ref. 41) 51 35 Showing Notation Used in the Kel ly and Tyson's Theory for the Discontinuous Fiber Composites (from Ref. 41) 54 36 Expected Var iat ion of Stress along a Fiber within a P l a s t i c Metal Matrix (from Ref. 41) 54 37 Stress D i s t r ibut ion in the Discontinuous Tungsten Fiber Obtained by Moire Technique. Applied Stress on the Composite i s Low (a) and High (b), (from Ref. 44, 47) 54 v i i i Page 38 Schematic Diagram of Stress Strain Curve of the Matrix and the Fiber 60 39 Half E l l i p t i c Fiber Fai lure Zone in a Composite 60 40 Stress D i s t r ibut ion Change in a Fiber which i s Located in the Fiber Fa i lure Zone 61 41 Fiber Fai lure Zones in a Specimen 63 42 Schematic Curves for Model Development 63 43 Schematic Diagram of Stress Strain Curve at Fa i lure Point 63 44 E la s t i c Loading Curves for Crack Lengths a and a + da 71 45 Schematic Diagram of E la s t i c Energy Released AABC and AADE, when the Crack and the Fiber Fai lure Zone Traverse the Cross Section 73 46 Geometry of the Fiber Fai lure Zone in the Bundle Structure Composite 77 i x LIST OF TABLES Table Page 1 Fabrication Techniques of Metal Composites 3 2 Typical Properties of High Modulus Graphite Fibers Compared with other Reinforcing Materials 11 3 Tensile Properties of Various Aluminum-Alloy-Thornel 75 Composites (from Ref. 25) 15 4 The Nominal Composition of Matrix Al loys 19 5 Properties of Thornel 50 Graphite Fiber 19 6 Numerical Values of Control l ing Factors in Interpene- t ra t i on Process 26 7 Hot Press and Heat Treatment 26 8 Tensi le Test Data of Specimens 32 9 Allowable Limits of the Matrix Composition 36 10 Data for Fiber Fracture Zone Character i st ics 49 11 Observed T u t s Values and Calculation Results of K' 82 12 Calculat ion of Strength of 601T4 Composites 84 13 Calculat ion of Strength of 201T6 Composites 85 14 Calculat ion of Strength of 7178T6 Composites 86 15 Calculat ion of Strength of 7178T6 Bundle Structure Composites 87 X ACKNOWLEDGEMENTS The author g ra te fu l l y acknowledges the helpful discussions with his research d i rec to r , Professor E. Teghtsoonian, and with Dr. J.S. Nadeau. He wishes to thank the members of the facu l ty and fe l low graduate students of the Department of Metallurgy for t he i r continued support and interest in th i s work. Financial assistance was received in the form of an ass i stantship under National Research Council of Canada grant number A-2452, and i s g ra te fu l l y acknowledged. 1 I INTRODUCTION 1-1. General Background Over the past 15 years, much research has been carr ied out in attempts to rea l i ze in pract ice the greater potential of high performance f i be r r e i n - forced composites. The f i be r reinforcement has been considered for the strengthening of weak p l a s t i c mater ia ls, such as res in and some metals. The incorporation of strong f ibers into duct i le metal matrices has been shown to bring remarkable increases in the strengths of these metals by some theor- e t i c a l and experimental work of the early period in the metal matrix composite h istory. An important simple expression for the composite t en s i l e strength and tens i le modulus, so ca l l ed " ru le of mixture", was derived in such work (1) and i t has been quite often used to discuss the ten s i l e properties of various kinds of f i be r composites. In th i s " ru le of mixture", the ten s i l e strength and tens i le modulus of a composite are expressed as the combination or sum- mation of contributed amounts from f ibers and the matrix, to these propert ies. These contributions from each component are taken to be proportional to t he i r volume f ract ion in the composite. This rule was derived assuming the overa l l fracture of f ibers at the same time. The deta i l of th i s expression i s d i s - cussed in a l a t e r sect ion, IV-1. Metal matrix composites are distinguished from the extensively developed resin matrix composites by v i rtue of the i r meta l l i c propert ies. The main advantages of metal matrix as compared with resin matrix are summarized as fol lows: a) The strength of metals i s greater than resins b) Metals have higher tens i le modulus than resins 2 c) Metals possess e l e c t r i c a l c o n d u c t i v i t y and the thermal c o n d u c t i v i t y of metals i s h igher than r e s i n s d) Metals possess g rea te r high temperature s t r e n g t h . 3 Commonly used r e s i n s possess t e n s i l e s t reng th va lues o f 7 - 15 x 10 p . s . i . and t e n s i l e modulus o f 0 . 4—0 .7 x 10 p . s . i . The d e n s i t y o f r e s i n (1.25 gr/cc) i s very low compared w i t h meta l s , so tha t po i n t s a) and b) are not d e f i n i t e advantages o f metals when the composites are used f o r weight c r i t i c a l a p p l i c a t i o n s . Res in mat r i x composites are a v a i l a b l e on l y f o r room temperature use. There fo re , a d e f i n i t e advantage of metal mat r i x composites f o r s t r u c t u r a mate r i a l i s t h e i r h igh temperature c a p a c i t y . 1-2. Prev ious Work on F a b r i c a t i o n Techniques Var ious k inds o f f i b e r composite f a b r i c a t i o n techn iques have been d e v e l - oped so f a r . These f a b r i c a t i o n methods can be c l a s s i f i e d as shown i n Table 1. Most o f these methods, except the u n i d i r e c t i o n a l s o l i d i f i c a t i o n method o f e u t e c t i c a l l o y s , are thought to be combinations o f two proces ses , the f i b e r al ignment process and the c o n s o l i d a t i o n process. In the c o n s o l i d a t i o n process o f these f a b r i c a t i o n methods, hot p re s s ing (H.P.) and l i q u i d phase hot p r e s - s ing (L.P.H.P.) techniques are commonly adopted i n o rder to prevent f i b e r damage. Most of these methods are not used f o r commercial composite p roduct ion because o f the cost or because of c e r t a i n problems i n each method as mentioned i n the f o l l o w i n g pages; however, they are app l i ed to f a b r i c a t e composite specimens shown as examples i n t h i s t a b l e , s u c c e s s f u l l y on ly f o r exper imental purposes. The a p p l i c a t i o n of the plasma spray ing method f o r S iC coated boron f i l ament aluminum mat r i x composites i s a r e p r e s e n t a t i v e example of commercial Table 1. Fabrication Techniques of Metal Composites Applied Examples Method of Fiber Method of Alignment Matrix' Fiber Consolidation Reference Deposition Chemical Vapor Deposition Electro Co- Deposition Electroplating Electroless Plating Plasma Spraying Metal Matrix Unidirectional Sol- idification of Eutectic Alloy Infiltration Al Graphite Fib. Ni.NiCr A l ^ S i C Whisk. Ni Al Al Ni Al 20 3SiC Whisk. Graphite Fib. Boron F i l . Al 20 3SiC Whisk. Ni Graphite Fib. Co Graphite Fib. Al (Alloy) Boron Fil.CSiC Cooted) Ti Boron F i l . Al Cb Zn Ni Co-Cr Ni3Al Ni Al 3Ni Cb2C ZnisTi W (Cr,Co)7C3 Ni3Ta NbC Al(Alloy) Graphite Fib. Ag AI2O3 Whisk. Al(Alloy) AI2O3 Whisk. Ni(Alloy) Al 203 Whisk. Cu W Wire Al Boron F i l . H.P., L.P.H.P. H.P. C P . , H.P., L.P.H.P. H.P. H.P. H.P. H.P. H.P. H.P. H.P. Solidification Solidification of Matrix 2 3,4 3,5 6 7 3,7,8 9,10 10 11,5 5 12,13,14 15,16 17,18 19,16 20,16 21,16 22,16 23,24,25 26,1,3 27,3 7,3 28,1 31 Method of Fiber Alignment Applied Examples Matrix Fiber Solid State Matrix Extrusion of Powder Matrix Alternate Pile up of Metal Foil & Fibers Clad Wire (matrix block with holes for wires) Slurry or Slip of Powder Matrix Al Al Hastelloy Al Al Ti-6A1-4V Ti-6A1-4V Short Graphite Fib. S i . ^ Whisk. W Wire Graphite Fib. Boron Fib. Boron Fi1. Be wire Spinning, Extrusion Ag,Fe,Ni Drawing of Mixture of Al Alloy Metal Powder, Whisker Cu.Mg and Carrier Solution Filtering Slurry and Ni.Cr Settling out of Ni- Al Alloy coated Whiskers and Matrix Powder in Magnetic Field S i 3 N 4 Whisk. Sic whisk. Sic whisk. SiC Whisk. A1 20 3 Whisk. Method of Consolidation Re fe rence 29 Diffusion Bonding 3 7 L.P.H.P. 30 H.P. 7,32 H.P. 7 Mechanical Deformation 33 and Diffusion bonding Burn Off Organic 34,3 Component and 35,3 H.P. or L.P.H.P. 36,3 37,3 5 productions (11). The chemical vapor deposition method seems to be the most expensive process among other methods in th i s tab le. This process usual ly involves the use of halide gas of the matrix metal, so that there i s a l i m i t a t i o n on the var iety of appl icable matrix metal for th i s process. The number of f iber s in a bundle which i s produced in th i s process i s also l im i t ed . In order to obtain a uniform coating f i l m on f i be r surfaces, good penetration of the gas into the bundles i s necessary. The e lectro co-deposit ion, e lectro p lat ing and e lect ro les s p lat ing methods often form small pores in the metal matrix when rather f i ne f iber s l i k e whiskers ofgraphite f ibers are used. Solution i s often trapped in these pores, so that i t i s rather d i f f i c u l t to el iminate these pores by the subsequent consolidation process. The plasma spraying method can be adopted only for large diameter con- tinuous f ibers l i k e boron f ibers (11). Melted metal powder i s sprayed cont in - uously on the f ibers aligned on a th in tape of the same metal. The un id i rect iona l s o l i d i f i c a t i o n method of eutect ic a l loys has been extensively studied because of the high potential to produce high temperature resistance metals for gas turbines etc. (39). Not only the f ibrous eutect i c s , such as ( C r ^o^Cg reinforced (Co, Cr) eutect ic a l l o y , Ni^Ta reinforced Ni^Al a l l oy and NbC reinforced Ni a l l o y , but also the lamel lar eutect i c s , such as NigAl (XJ-Ni^Nb^) eutect ic a l l o y were reported to possess higher strength and more creep resistance than the so-cal led "super a l l o y s " (16). These types of composites have been expected to be suitable for high temperature appl icat ions because of the thermodynamic s t a b i l i t y in the eutect ic systems and the small e f fect of grain boundaries due to the i r large columnar structures. This process has advantages of easy f ab r i ca t i on ; however, the a l loys are l im i ted to 6 the eutect ic a l loys which can form su i table second phase and the volume f ract ion of reinforcements i s l imi ted consequently. The i n f i l t r a t i o n method is used for composites using small diameter f i be r s . The matrix metal must have good wetting property with the f i be r in th i s method. In order to prevent the degradation of f ibers by chemical attack, the proper control of i n f i l - t ra t ion condition i s necessary. Graphite f i be r aluminum a l l o y composites were successful ly fabr icated by th i s method (23)(24)(25). The powder matrix extrusion process tends to damage f i be r s . The matrix f o i l process i s su itable for rather large diameter f iber s which can be ea s i l y handled and al igned. It seems to be d i f f i c u l t to increase the f i be r volume f ract ion of composites and control the f i be r spacing uniformly by th i s method, espec ia l ly in the case of f ine f ibers l i k e graphite f i be r s . Clad wire process can be used only for ordinary metal wire of high d u c t i l i t y . F i na l l y , two methods based on metal powders in an organic solut ion were developed to a l i gn f ine whiskers in a matrix with l i t t l e damage to them. In the f i r s t method, the green composites are fabr icated into a strand shape by some mechanical deformation, such as extrusion. The organic components of the s lurry are burned o f f pr ior to hot pressing. In the second method, green composites are fabr icated into the shape of a mat by s e t t l i n g out and f i l t e r i n g the s lu r ry . P r io r to the s e t t l i n g process, whiskers are coated with magnetic metal in order to permit high alignment of these whiskers by magnetic force during the process. This process seems to have some d i f f i c u l t i e s to obtain uniform d i s t r i bu t i on of f i be r s through the tota l thickness of the mat because of a large dif ference in the s e t t l i n g speed of these two mater ia ls. Boron f iber s have already been successful ly incorporated into metals such 7 as aluminum, magnesium and t i t a n i u m . The a p p l i c a t i o n s o f these composites are l i m i t e d to s p e c i a l f i e l d s because of t h e i r high c o s t . The main p o t e n t i a l advantage f o r g r a p h i t e f i b e r composites i s the much lower f i b e r c o s t . As a matter o f f a c t , l a r g e amounts o f gra p h i t e f i b e r s have been used i n r e s i n matrix composites, such as g o l f c l u b s h a f t s and turbine blades which must have high s t i f f n e s s (Young's modulus) - weight r a t i o . The f u t u r e progress o f g r a p h i t e f i b e r metal matrix composites g r e a t l y depends on the development o f r e l i a b l e and low c o s t f a b r i c a t i o n techniques. I t i s very d i f f i c u l t to f a b r i c a t e metal matrix composites with g r a p h i t e f i b e r s because of the small f i b e r diameter (6-9y) compared with boron f i b e r s (100-125y). The alignment and c o n s o l i d a t i o n processes f o r such f i n e f i b e r composites have to be c a r e f u l l y designed i n order to prevent any mechanical f i b e r damage. The chemical a t t a c k at the f i b e r - m a t r i x i n t e r f a c e may a l s o give severe damage to the f i n e f i b e r s , i f the f a b r i c a t i o n process i n v o l v e s high temperature o p e r a t i o n s . As a matter of f a c t , n i c k e l , c o b a l t and s t e e l d i s s o l v e g r a p h i t e at high temperature and degrade the f i b e r s . Copper i s expec- ted to be a good matrix because of the low carbon s o l u b i l i t y ; however, not many s t u d i e s have been done with copper due to i t s high d e n s i t y r e l a t i v e t o aluminum, and i t s l i m i t e d range of high temperature use comapred with n i c k e l and c o b a l t . In recent y e a r s , aluminum or aluminum a l l o y s have been thought to be the most promising matrix f o r g r a p h i t e f i b e r s because o f the high s t r e n g t h and s t i f f n e s s to d e n s i t y r a t i o . Aluminum i s one of the c a r b i d e forming elements; however, the g r a p h i t e f i b e r aluminum composites are expected to be used s a f e l y at the p r a c t i c a l long time s e r v i c e temperature which i s much lower than the carbide formation temperature (>500°C). 8 Aluminum carbide formation on the surface of PAN Type II* f ibers in pure aluminum composites produced by powder metal lurg ical process was f i r s t observed and measured by G. Blankenburgs (29), using a quant i tat ive X-ray technique. F ig. 1 and 2 show the carbide formation of various temperatures and various times. P.W Jackson (40) also studied PAN Type I * f ibers coated with aluminum by chemical vapour deposit ion. Tests on specimens held at 500°C for one day exhibited no noticeable loss in room temperature strength of the coated f ibe r s . On the other hand, the apparent degradation of the coated f iber s at higher temperature than th i s was recognized as shown in F ig. 3. It was concluded that the f ibe r degradation was caused by the chemcial attack of the f i be r surface by aluminum at such high temperature. Such chemical reaction suggests good wetting between these mater ia ls. The i n f i l t r a t i o n process was f i n a l l y applied to Thornel 50 graphite f i be r 13% s i l i c o n aluminum a l loy composites successful ly by R. Pepper, J . Upp, R. Rossi, and E. Kendall (23) (25). This process has been expected to be a p ract i ca l fabr icat ion process because specimens fabricated by th i s process exh ib i t much higher values than any other fabr icat ion process and sometimes even higher values than the values according to the " ru le of mixture". The real reason for th is remarkable strength increase i s s t i l l unknown. Although many kinds of high modulus graphite f iber s are being produced by manufacturers, only a few have been used for metal matrix composites. They can be c l a s s i f i e d into some categories, of which properties are shown together with other re inforc ing materials in Table 2. (Type II: High strength type; Type I: High modulus type). 5 0 0 550 600 6 5 0 Annealing Temperature °C The Var iat ion of A l i n 5 wt% F i g . l Graphite Fiber - Aluminum Composite a f te r Annealing for 24 hr at Various Temperatures (Determined by Quantitat ive x-ray D i f f rac t ion ) (29). '.5r • *• 1.0 c <u c s to 05 o < 7 Vol % composite annealed at 6 0 0 ° c ~0 5 10 5 0 100 5 0 0 Annea l ing T ime hours Fig.2. The Var iat ion of Al^C^ in 5 wt% Graphite Fiber - Aluminum Composite a f te r Annealing for Various Times at 600°C (29). 10 400 •-• 300t 200 £ 100 200 400 600 800 Processing Temperature C° IOOO Fig.3. Strength of Al Coated Graphite Fibers a f te r Heat Treatment for 1 Day at Various Temperatures (40). 60 40 20 / *7 V • fabricated in air o fabricated in argon 10 20 30 40 Vf % Fig.4. Tensi le Strength of the Al-Graphite Fiber Composites Fabricated by the Matrix Foi l Method. (Plotted from numerical data in Ref.30). 11 T a b 1 e 2. Typical Properties of High Modulus Graphite Fibers Compared with Other Reinforcing Materials. Reinforcement Ultimate Tensile* Tensile* Strength x lO^p.s.i. modulus x 10 p.s.i. Density l b / i n . 3 Diameter u Graphite Fibers Rayon-base Thornel 50 Thornel 75 PAN-base Type I (High modulus type) Type II (High strength type) 275- 320 350- 385 225- 275 325 - 375 44 - 55 7 0 - 80 55 - 6 0 32 - 38 0.06 0.065 6.6 6.0 0.072 7-9.7 0.063 7.6-8.6 Other Reinforcements Boron filament Beryllium wire Tungsten wire Aluminum whisker Silicon carbide whisker 400 - 500 150 - 200 550 - 600 4000 3000 55 - 60 35 - 40 48 - 5 2 62 70 0.092 0.066 0.7 0.14 0.12 100-150 100-250 50-100 1-10 1-10 (* Measured on single fibers). 12 1-3. Previous Work on Strength of Graphite Fiber Aluminum and A l loy Composites A study on graphite f i be r aluminum composites was reported by A. Morris (30). Specimens were fabricated from PAN Type II f iber s and aluminum f o i l s , using a l i q u i d phase hot pressing technique. The ultimate t en s i l e strength va lues ,c r r , as a function of f i be r volume fract ions of these composites are plotted in F ig. 4. The values are highly scattered and considerably lower than the expected values from the " ru le of mixture". P. Jackson et a l - (2) fabricated PAN Type II f i b e r aluminum composite specimens by the chemical vapour deposition process, using T r i - i s obuty l alum- inum. The tens i l e strengths of these composites are shown in F ig. 5, for various fabr icat ion condit ions, as a function of the f i b e r volume f r a c t i on . In spite of considerable e f f o r t to sa t i s f y the requirements of low poros i ty, minimum chemical attack, minimum f i be r breakage and uniform f i b e r d i s t r i b u t i o n , the tens i le strengths of these composites were well below " ru le of mixture" l eve l s . On the other hand, the tens i le modulus of these composites were gener- a l l y close to the expected values. It was suggested that a further mechanism was operating in keeping strength levels down. Pepper eit aj_. (23) (25) fabricated samples by the i n f i l t r a t i o n technique as mentioned e a r l i e r . After mult iple chemical washing, Thomel 50 graphite f i be r bundles were i n f i l t r a t e d i n a batch process with 13% s i l i c o n aluminum 3 a l l oy . The mean ten s i l e strength value of 106 x 10 p . s . i . was obtained with 28% f i be r volume f rac t ion and th i s value was unaffected by 20 thermal cycles between -193°C and 500°C. As mentioned e a r l i e r , t h i s value compares favourably with that expected from a " ru le of mixture" ca l cu l a t i on . In t he i r fol lowing studies, pure A l , Al-7Mg, Al-7Zn and A1 -13Si a l loys were used to fabr icate composites with Thornel 75 graphite f i be r s . The results ao, ._• 60 </)' 7D CO H 40 20 V / o © * * •^x xx> x x° xo A X / • 5 0 0 ° c 5 lons/ in a I hour X 50 o°C5 tons/ in a ihour A 600 o C l /2 tonv " i n 1 l h0ur o 6 0 0 " C VOon/it? I min to 40 50 20 30 V f % Fig.5. Tensi le Strength of Graphite Fiber Aluminum Composites Fabricated by the Chemical Vapour Deposition Method (2). 100 ._• 80 (A CL n O C/J 40 / / / / / / / / . * ° / / • / / / / / •A o • • • • / / • / / / / • / r / A 220 —- • A! 3 o 6061 i 0 10 20 30 vf % 40 Fig.6. Tensi le Strength of Graphite Fiber Aluminum Al loy Composites Fabricated by the I n f i l t r a t i o n Method. (Plotted from numerical data in Ref.24). 14 of th is work are shown in Table 3. The tens i le strength values are again lower than " ru le of mixture" values and scattered very much. Further work on the composites of continuously produced i n f i l t r a t i o n composite strand was done by R. Pepper and R. Penty (24), using Al-13Si (Al3), Al-lOMg (220), and Al-IMg-O.6Si (6061) a l loys with Thornel 50 graphite f i be r s . The tens i le strength values are again lower than the " ru le of mixture" values and s t i l l scattered in very wide region as shown in F ig. 6. These composites fabricated by i n f i l t r a t i o n process usually possess higher ultimate tens i l e strength than the composites by other processes; however, the d i s t r i bu t i on of the f ibers in the matrix of the i n f i l t r a t e d composites i s not uniform. This non-uniformity seems to or ig inate in the hot pressing die con- f igurat ion which involves the use of f i l l e r metal f o i l s among composite wires as shown in F ig. 7 (25). The f i be r d i s t r i bu t i on of these composites must be seen as a bundle structure. 1-4. Purpose of Present Work The i n f i l t r a t i o n technique of aluminum al loys developed by R.T, Pepper et al_. led to remarkable progress in the fabr icat ion of graphite f i be r aluminum composites. The major advantage of th i s process includes low fabr i ca t ion costs, min- imum f i be r damage, and potent ia l l y high strength. The achievement of uniform f i be r d i s t r i bu t i on i s d i f f i c u l t , making theoret ical modeling awkward. The strength values actua l ly achieved are scattered in a very wide range and much lower than the theoret ical values calculated according to the " ru le of mixture". Table 3. Tensile Properties of Various Aluminum-Anoy-Thornel 75 Composites (25) Strength Average „ , . . . . . Average Modulus Volume a Number Low High 3 Matrix Specimen Percent ? of Value Value 2 Composition Condition Fiber MN/m p.s.i. Samples (psi) (psi) (GN/m ) (psi) Commercially- As-infiltrated 32 68 99,000 8 65,000 116,000 178 25.7 pure aluminum Pressed 35 65 95,000 7 85,000 104,000 147 21.3 Aluminum-7 w/o As-infiltrated 32 71 103,000 7 59,000 132,000 166 24.1 zinc Pressed 38 87 126,000 10 102,000 155,000 190 27.5 Aluminum-7 w/o As-infiltrated 31 68 98,000 4 87,000 124,000 195 28.1 magnesium Aluminum-13 As-infiltrated 22 55 80,000 7 73,000 88,000 165 23.8 w/o silicon Fig.7. L iquid Phase Hot Pressing Die Configuration to Fabricate Specimens from the Al I n f i l t r a t ed Graphite Fiber Composite Wire (25). 17 The reason for the difference between experimental results and theor- e t i c a l values has not yet been f u l l y understood. A d i f fe rent mechanism from the " ru le of mixture" might be operating on the tens i l e f racture of these graphite f i be r aluminum composites. The purpose of the present work i s to investigate the mechanical behaviour of the composites and to make a theor- e t i c a l model which can correlate with th i s behaviour. 18 J ! EXPERIMENTAL PROCEDURE 11—1. Preparation of Composite Specimens Three kinds of aluminum al loys were chosen as matrices of the composite. Their nominal compositions are tabulated in Table 4. The composites were fabricated by a unique method which was designed to obtain s t a t i s t i c a l l y or macroscopically homogeneous f i be r d i s t r i bu t i on in the matrix. The s t a t i s t i c a l homogeneity of f i be r d i s t r i bu t i on i s necessary for the present work on f i be r strengthening mechanism. The overal l fabr icat ion process in th i s method i s outl ined in F ig. 8. Blended powders of each a l loy composition were prepared from under 500 mesh powders of aluminum, s i l i c o n , magnesium,and copper shown in F ig. 9. These blended powders were mixed well together with denatured alcohol to make a powder suspended th in s l i p . Thornel 50 graphite yarns were washed in bo i l i ng d i s t i l l e d water for about two hours to dissolve the P.V.A. coating f i lm applied by the manufacturer in order to reinforce the yarns and avoid the i r degradation during handling. After the f ibers were dried and untwisted, they were bundled and the top of the bundles were glued with epoxy res in . The number of f ibers in each bundle was varied from 76,000 to 228,000 depending on the f i be r volume fract ions which were desired in the f i n a l product. The.number of f ibers in one bundle i s l imi ted by geometrical factors related to the diameter of the outer glass tube. Too many f ibers prevent the i r free movement and adequate separation during the subsequent powder penetration. On the other hand, some bundles were prepared from or ig ina l twisted yarns without untwisting them in order to obtain bundle structure f i be r d i s t r ibut ions in the matrices. Table 4. The Nominal Composition of Matrix Al loys A l loy Heat Treatment Mg % Si % Cu % Zn % Al % 601 T4 (Solution Treatment) at. 1.11 at. 0.58 at. 0.11 at. 98.20 wt. 1.00 wt. 0.60 wt. 0.25 wt. 98.15 201 , T6 (Age Hardened) at. 0.46 at. 0.79. at. 1.92 at. 96.84 wt. 0.40 wt. 0.80 wt. 4.40 wt. 94.40 7178 T6 (Age Hardened) at. 3.15' at. 0.80 at. 2.95 at. 93.00 wt. 2.70 wt. 2.00 wt. 6.80 wt. 88.50 Density of Each Element, ^/cc 1 .74 2 .32 8 .96 7.14 2.70 Table 5. Properties of Thornel 50 Graphite Fiber Tensile Strength* p . s . i . 275 — 320 x 10 3 Tensile Modulus* p . s . i . 4 4 — 55 x 10 6 Density 9 / C c 1.66 Elongation at Break % 0.6 Equivalent Diameter y 6.6 No. of Fibers/ply 720 Plies/Yarn 2 (* Measured on Single Fibers) U3 20 THQRNEL50| I A l . Cu. S i ,Mg .POWDERS 76O00~2280OO fibers WAS HED AND DRIED total 3 0 gr — 3 0 0 me sh BLENDED ALCOHOL 400 cc UNTWISTED BUNDLE S L I P I INTER PENETRATION-SEDIMENTATION PROCESS SEPARATION OF EXTRA POWDER 1 : VOLATILIZATION OF ALCOHOL AND SUBSTITUTION WITH CAMPHENE LIQUID P H A S E HOT P R E S S I N G • BURNING OFF OF ORGANIC MATERIALS A T I 5 0 ° C UNDER LOW PRESSURE STEPWISE LOADING UP TO 600 p.s.i. AT HOT PRESSING TEMPERATURE IN H 2 GAS COOLING DOWN TO UNLOADING TEMPERATURE AND PRESSURE RELEASE TO 150 p.s.i. MACHINING JTENSILE TEST PIECE Fig.8. Flow Sheet of the Specimen Fabrication Process  2 2 The f i be r bundles were interpenetrated with the blended powder s l i p s using a device designed spec ia l l y for th i s purpose. This device i s schematically shown in Fig. 10. The outer glass tube (A) i s f i l l e d with the s l i p a f te r a f i be r bundle (B) i s connected to a rod (C) with a spring (D) and inserted into a glass sheath (E) which moves up gradually from the bottom of the bundle to the top with ve r t i ca l v ibrat ion during the operation. A drive and v ibrator assembly at the top of the unit causes ve r t i ca l v ibrat ion of both the connecting rod and the glass sheath. The powder starts to interpenetrate into the bundle and se t t l e among the f ibers opened by these v ibrat ional movements of the rod and the sheath tube. The slow upward movement of the sheath tube makes more complete interpenetration of the powder pa r t i c le s among the f ibers possible. After sedimentation of the powder par t i c le s proceeds, addit ional charge of s l i p i s poured into the glass tube three or four times. Green composites which were produced by th i s operation are pushed out from the outer glass tube. These green composites contain more powder at the boundary of the or ig ina l p l ie s than at the in s ide, because, even i f the p l ie s are untwisted, they s t i l l have a tendency to twist back and keep the o r i g ina l twisted form s l i g h t l y . To remove the extra powder par t i c le s from these areas, the green composites are transferred to a v ibrat ing boat containing a small amount of alcohol (see F ig. 11). The d i s t r i bu t i on of f ibers among the powders becomes more uniform by th i s separation treatment. This process i s repeated a few times, turning the specimens upside down unt i l the amount of flowed out powder becomes very l i t t l e . The green composites are then transferred on to a f l a t plate to be pressed into a rectangular sect ion. Alcohol was half evaporated and Camphene was i n f i l t r a t e d into the green at around 50°C in order to reinforce the g r een com- C A M M E C H A N I S M - S P R I N G - V I B R A T O R - S P R I N G - R O D C O - G L A S S S H E A T H ( E ) C O N E C T I N G S P R I N G ( D ) - O U T E R G L A S S T U B E ( A ) — | G R A P H I T E B U N D L E ( B ) — Flg.10. Schemat ic Diagram o f the I n t e r p e n e t r a t i o n Dev i ce F I L T E R - OVER FLOW A L U M I N U M A L L O Y S U P > suspended zone interpenetrating zone J. settled zone DRAIN 24 , ,-HOLE FOR THERMOCOUPLE GRAPHITE UPPER RAM GRAPHITE SPACER |-Mo COVERED GRAPHITE DIE STEEL STOCK 025 « 0 . 2 2 5 " w X 0 . 0 7 3 " t Fig.13. Tensile Specimen Geometries Fig.12. Hot Pressing Die Set posite; (however, th i s process i s not necessary i f half dried green com- posites are handled very ca re fu l l y in the fol lowing processes because such com- posites have enough strength for handling as long as they are wet). The composites were cut into short lengths to f i t the hot pressing die shown in F ig. 12, and pieces which contained defects were abandoned. A l l of the numerical values of factors in th i s fabr icat ing process are tabulated in Table 6. These pieces of green composites were then hot pressed in fol lowing process. The organic constituent was gradually evaporated under low pressure at around 150°C in the die which was set in a hot pressing chamber. The degree of degassing was checked by a thermal gauge. After th i s degassing treatment, pressure was applied stepwise at the rate of 25 psi/min. at the temperatures shown in Table 7, in hydrogen gas atmosphere unt i l the maximum pressure 600 psi. was obtained. The contents of the die were kept at these temperatures under the pressure of 600 psi for one hour. During th i s period, pa r t i a l melting of the powder occurs forming a l i q u i d phase which eas i l y i n f i l t r a t e s among f i be r s . Unreinforced a l l oy blanks were also fabricated in th i s hot pressing process from blended powders. These blank specimens were used to obtain a basis for f i be r strengthening e f fec t . These hot pressed composite or blank specimens were then machined to the shape of tens i l e test specimens and heat treated to acquire d i f fe rent mechanical properties. The temperature and time for each a l loy are also tabulated in Table 7. Steel stocks were attached to these heat treated specimens with Eastman Kodak 910 in order to protect the specimens from the grips of the ten s i l e test machine, as shown in Fig. 13. 26 Table 6. Numerical Values of Contro l l ing Factors in Interpenetration Process Weight of Blended Powders in S l i p for one charge 30 gr Volume of Alcohol in S l i p for one charge 400 cc Number of PI ies in a Bundle 100 —300 Moving Speed of Sheath About 6 inch/hr Frequency and Amplitude of Bundles Vert ica l Vibrat ion 60 c/s. 0.2 inch Frequency and Amplitude of Sheath 60 c/s. 0.05 inch Diameter of Sheath 9mm x 7 mm Diameter of Outside Glass Tube 14mm x 12 mm Table 7. Hot Press and Heat Treatment 601T4 201T6 7178T6 Hot Pressing Temperature and Time 600°C, 1 hr 550°C, 1 hr 550°C, 1 hr Pressure Releasing Temperature 500°C 450°C 450°C Solution Treatment Temperature and r , n o r o n •„ c n c 0 r on nm°r i c m,-„ j j m e 520 C,30 mm 505 C,30 mm 470 C,15 mm Ageing Temperature and Time 160°C, 18 hr 125°C, 28 hr 27 II-2. Tensile Testing Tensile tests at room temperature were carr ied out with an Instron test ing machine at the cross head speed of 0.02 inch/min, using se l f tightening gr ips. The tens i le strength was determined for these specimens. Due to the very small elongation of the composite specimens (under 1%), i t proved to be very d i f f i c u l t to establ i sh the elongation at f a i l u r e . More accurate stress s t ra in curves and longitudinal e l a s t i c modulus of several typ ica l specimens were obtained using s t ra in gauge on specimen surfaces. 11-3. Microscopic Observations After the fracture surfaces were ground and pol ished, photographs were taken at a magnification of 114 times. The area covered by these pictures i s around 1/7 of the or ig ina l area on the specimen. The volume f ract ion of f ibers in each composite was calculated using the numbers of the f ibers counted in these pictures and a nominal value for f i be r diameter (6.6y). Fracture surfaces and polished longitudinal sections were observed with a scanning electron microscope. The surface of a 201-T6 composite specimen was polished pr ior to tens i le test ing and the deformation mode just before f a i l u r e was observed by opt ica l microscopy. 28 11-4. Micro Probe Analysis The matrix composition of a l l specimens was analysed by means of micro probe analys is. Two counts at each of four points were carr ied out in the sections previously used to count the number of f i be r s . Regions of the matrix which had been l i q u i d during the hot pressing were avoided in order to obtain representative values. The tens i le test data from specimens which showed too much deviation of composition from average values were excluded in order to improve the r e l i a b i l i t y of the data. The big scatter of composition among specimens i s due to the large density difference of each of the elements. This was expected since blended powders were used in the interpenetration process instead of a l l oy powders. The densit ies of these elements are tabulated in Table 4. 29 i III EXPERIMENTAL RESULTS 111-1. Fiber Volume Fraction The volume f ract ion of graphite f ibers in each specimen was ca lcu- lated using pictures as shown in F ig. 14. F ig. 15 shows the bundle structure of the 7178 T6 a l loy composite which was prepared from or ig ina l twisted yarns (1.5 turns/inch). The f i be r volume f ract ion of each specimen is tabulated together with the number of p l i e s which were used to prepare each specimen in Table 8. The average f i be r volume f ract ion is shown plotted against the number of p l ie s per bundle in F ig. 16. 111-2. Micro Probe Analysis of the Specimens The matrix chemical composition of each specimen was analysed by micro probe measurement and calculated using the "Magic" program. Wide scatter ing of analysed composition was found as antic ipated e a r l i e r . In order to avoid uncertainties a r i s ing from var iat ions of matrix com- pos i t ion, l im i t s were established (see Table 9) for allowable compositions. A l l specimens l i s t e d in Table 8 l i e within these established l i m i t s . 111-3. Tensi le Stress Strain Curves Most of the stress s t ra in curves were obtained d i r e c t l y from the Instron recorder. A l imited number of stress s t ra in curves was obtained by measuring the s t ra in with s t ra in gauges attached to the specimen surfaces. Fig.14. Cross Section of a Uniform Composite, 201T6, #29, 12.1% V f , x Fig.15. Cross Section of a Bundle Structure Composite, 7178 T6, #39, 10.0% V~, x 62. 0201 0J5 h o.ioh 0.05L o L ^ ! I ! ! I 1 I 0 100 200 300 Number of Plies in a Bundle Fig.16. Relation between the Number of Pl ies for the Interpenetration Process and the Fiber Volume Fraction in Composites. The dot-dash-line shows the ideal co r re l a t i on . 32 Table 8. Tensile Test Data of Specimens Specimen Number No. Alloy of Plies Ultimate Strain Gauae Fibre Volume Composition,atomic% Tensile Strength Measurement Fraction, V f Mg% SIX Cut Zn% crx103 p.s.i. € - . . , C 5 , E 1 601T4 0 0 0.9 0.59 0.07 33.8 2 601T4 0 0 1.04 0.50 0.09 29.9 3 601T4 0 0 0.78 0.49 0.06 32.1 4 601T4 0 0 0.87 0.51 0.10 32.8 5 601T4 100 4.3 0.89 0.58 0.09 29.0 6 601T4 100 7.8 0.65 0.47 0.09 33.3 7 601T4 150 •6.5 1.00 0.47 0.12 31.4 8 601T4 150 6.7 0.82 0.61 0.11 31.6 9 601T4 200 8.5 0.94 0.58 0.10 33.6 10 601T4 200 7.8 0.79 0.50 0.07 34.0 11 601T4 200 7.8 0.74 0.53 0.10 34.1 12 601T4 200 9.5 0.90 0.59 0.07 35.5 13 601T4 250 7.8 0.62 0.54 0.07 32.2 14 601T4 250 9.3 0.97 0.36 0.15 38.6 15 601T4 250 11.3 0.79 0.60 0.10 39.0 16 601T4 250 12.8 0.53 0.65 0.07 42.4 17 601T4 250 14.5 0.78 0.52 0.07 45.1 18 601T4 250 14.5 0.63 0.47 0.04 46.5 19 601T4 300 9.5 0.76 0.48 0.07 36.8 20 601T4 300 17.0 0.81 0.38 0.06 45.8 21 201T6 0 0 0.45 0.44 1.24 58.5 22 201T6 0 0 0.41 0.40 1.33 62.5 23 201T6 0 0 0.58 0.49 1.22 60.5 24 201T6 130 6.4 0.47 0.69 1.12 64.7 25 201T6 150 8.2 0.63 0.66 1.15 69.5 26 201T6 150 7.4 0.34 0.60 1.39 66.9 27 201T6 250 8.6 0.40 0.37 1.08 66.8 28 201T6 250 10.0 0.45 0.53 1.04 70.1 29 201T6 250 12.1 0.28 0.42 1.38 68.8 30 201T6 250 14.1 0.42 0.36 0.85 66.4 31 201T6 250 17.0 0.50 0.55 1.26 63.2 32 7178T6 0 0 1.06 0.77 2.19 70.4 33 7178T6 0 0 2.79 0.45 2.62 78.2 34 7178T6 0 0 1.49 0.86 3.39 72.0 35 7178T6 0 0 1.06 0.77 3.81 77.5 36 7178T6 250 9.6 2.31 0.39 2.14 68.5 37 7178T6 250 12.8 2.62 0.53 2.22 78.1 38 7178T6 250 13.8 2.38 0.40 2.35 75.7 39 7178T6 250B* 10.0 1.31 0.88 3.53 83.6 40 7178T6 250B* 12.7 1.08 1.00 3.63 83.8 41 7178T6 250B* 16.4 1.47 1.00 3.69 88.6 42 7178T6 250B* 19.0 2.16 0.44 3.74 88.6 6=18xl O^psi { € f a i l = ° - 5 0 % Ec = l3.5xi06psi 0^=49x10 psi cr 6=47xl03psi f€fail = 0.63% \ E C =l53M06psi 066=56x1 0,DSi 006=56x10Jpsi Obe=56x103psi OoiS=56x103psi (*B: Bundle Structure) 6 0 Strain £ % Fig.17..Stress Stra in Curves of 601T4 Al loy and the Composites Fig.18. Stress Strain Curves of 201T6 Alloy and the Composite  36 Table 9. Allowable Limits of the Matrix Composition Al loy Mg, at % S i , at % Cu, at % Zn, at % 601 0.50-1.05 0 .40 -a 60 0.04-0.14 201 0.20-0.60 0.30-0.70 1.00-1.40 7178 2.80-1.00 - 0.35-1.00 2.10-3.90 The measured s t ra in of composite specimens was always small ( 0.06%). The Young's modulus of composite specimens derived from these stress s t ra in curves are shown in Table 8. - These values are in good agreement with the calculated values according to " ru le of mixture". Some of these stress s t ra in curves are shown in F ig. 17, 18, and 19. The stress s t ra in curve of 7178 T6 composite was not obtained because of the shortage of specimens due to the d i f f i c u l t y of cont ro l l i ng a l l oy com- pos i t ion. Il l-4^ Ultimate Tensile Strength The var iat ions in ultimate t en s i l e strength, cr^, of each a l loy com- posites with f i be r volume f r a c t i on , V^, are shown in F ig. 20, 21, and 22. The ultimate ten s i l e strength of unreinforced, blank, specimens, o~m^s> and the strength of the a l loy at the breaking s t ra in of the f i be r s , CT^*, are also plotted in these figures as the points corresponding to zero f i be r volume f r ac t i on . The ultimate ten s i l e strength of non-uniform, bundle structure, 7178 T6 a l loy composites is also shown in F ig . 22 to be compared with uniformly 60 50 40 Q. b 30 x in 3 20 0 Omuts CJ<-' a/w=0 a/w =0.03 a/w =0.05 a/w =0.10 0 10 Fig.20. Tensile Strength of 601T4 Composites, and Theoretical Curves 15  100 90 80 70 60 c x muts Om a/w=0 BUNDLE , o/v»=0.03 a/w= 0.03 • : UNIFORM DISTRIBUTION O : BUNDLE STRUCTURE 10 15 20 Vf (%) Fig.2.2.. Tensile Strength of 7178 T6, Uniform and. Bundle .Structure Composites, and Theoretical Curves 40 d i s t r ibuted composites. The ultimate ten s i l e strength of each composite calculated according to " ru le of mixture" i s also exhibited in these figures as a dot-dash l i n e . In a l l cases, the experimental values are lower than the " ru le of mixture" l e v e l . The discrepancy between the experimental and the " ru le of mixture" values becomes more evident as the f i be r volume f rac t ion increases. This tendency is more prominent in 201T6 composites than 601T4 composites. The tens i l e strength of the bundle structure 7178 T6 composites is higher than the uniform composites as shown in F i g . 22. This re su l t suggests that some other mechanism, which i s d i f fe rent from the " ru le of mixture", i s operating to keep the strength of bundle structure composites higher than the uniform ones. Other curves calculated according to a model which w i l l be discussed l a te r are also shown in these f igures . H I - 5 . Fracture Elongation An attempt was made to obtain the fracture elongation of specimens by measuring the distance between gauge marks on fractured specimen; however, the results were unrel iable because of the d i f f i c u l t y in measuring very small elongations and also because of the frequent f a i l u r e at specimen shoulders outside of the marks. F i na l l y , the measurement'by th i s method was abandoned. Only a few data about the elongation of these composite specimens are ava i lab le from the s t ra in gauge test data as shown in Table 8. 41 111-6. Microscope Observations of Tested Specimens Fractographic observations were made using a scanning electron micro- scope. The p la s t i c deformation of the matrix at the fracture surface is prominent. A small amount of f i be r pul l out was usually observed. Small voids, which are charac te r i s t i c of p l a s t i c f a i l u r e , were observed somewhere on the ridges of the matrix as shown in F ig . 23 and F ig . 24. The f i be r f a i l u r e zone which appeared on the polished 201T6 composite specimen surface was observed using opt ica l and scanning electron microscopy, after straining close to the fracture point. The typ ica l appearance of the zone surface is shown in F ig . 25. Within the zone, f ibers were broken into small fragments as shown in the scanning electron micrograph at low magnif i - cation (x200), F ig. 26. The s l i p l i nes are observed at a higher magnification (x 1000) in the grains between f ibers as shown in F ig . 27. The i n te r i o r structure of th i s specimen was examined by further pol ishing and etching. A f i be r f a i l u r e region around a specimen shoulder is shown as a marked area in F ig . 28. In th i s f i gure , the successive propagation of f i be r f a i l u r e from the r i ght hand side to the l e f t hand side seems to be interrupted at a f i be r free (or low f i be r density) region. Etched grain boundaries, and broken and s l i g h t l y t i l t e d f ibers were also observed as shown in Fig.29. Fractured f ibers can be seen at a considerably longer distonce from the fracture surface in the low composite (Fig. 30a) than in the high composite (F ig. 30b). This same tendency i s also observed in the case of 201T6 composites of d i f fe rent V f values, 6.4% and 17% as shown in F ig. 31 (a) and (b). The broken fragments located closer to the fracture surface have generally shorter lengths than the fragments located at a larger distance Fig.23. Fractured Surface of 601T4 Composite, #17, 14.5% V x 1000. 43 F i g . 2 6 . S c a n n i n g E l e c t r o n M i c r o g r a p h o f F i b e r F a i l u r e Zone S u r f a c e Showing Broken F i b e r s , x 200. F i g . 2 7 . S c a n n i n g E l e c t r o n M i c r o g r a p h o f Zone S u r f a c e Showing S l i p L i n e s , x 1000. Fiber Free Region -Fiber Fa i lure Zone- Fig.28. Micrograph Indicating Propagation of the Fiber Fa i lu re p r io r to Fa i lu re of the Specimen, Longitudinal Sect ion, x 32. Fig.29. Longitudinal Section around the Zone Showing Matrix Grains, and Broken T i l t e d Fibers, NaOH Solution Etch, x 180. -pi 45 (b) Fig.30. Longitudinal Sections of Fractured 601T4 Specimens, Showing the Difference in the D i s t r ibut ion of the Fracture Points in(a)Low V f (8.5%), #9, and(b)High V f (14.5%), #17, Composites, Small C i rc les Showing Fractured Fibers, x 100. 46 Fig.31. Longitudinal Sections of Fractured 201T6 Specimens Showing the Difference in the D i s t r ibut ion of the Fractured Points in a Low V f (6.4%), #24, and(b)High V f (17%), #29, Composites, Small C i r c le s Showing Fractured Fibers, x 100. 47 from the fracture surface, as shown in these p ictures. Scanning electron micrographs at low magnif ication (x50) were used to quantify the f i be r f a i l u r e zone thickness. The quant i tat ive measure- ments were made of the distance, B^, from the fracture surface to the furthest point at which broken f i be r fragments could be observed. The results are given in Table 10. The re l a t i on between B^ and the f i be r volume f r a c t i on , V^, and Young's modulus E c was examined and th i s i s discussed in a l a t e r section IV-2-iv. F i g . 32 shows the var iat ions of values with these factors . 020 \ Ec^Vf-Vfrninf XIO' lb. Fig.32. Relation between E c , and V Table 10. Data for Fiber Fracture Zone Character i st ics Qmuts " ^m* E c x 1 ° P s i E c Al loy ^ u t s + ( S u t s - ^ * V f V f " V fmin < E f V f + E m V ( V V f m i n ) 2 B f i n c h 601T4 0.0446 0.067 0.0224 12.68 25.3 0.17 0.085 0.0404 13.40 8.21 0.06 0.145 0.1004 15.80 1.57 0.02 201T6 0.0385 0.086 0.0475 13.44 5.96 0.09 0.10 0.0615 14.00 3.70 0.05 0.17 0.1315 16.80 0.972 0.02 50 IV DISCUSSION IV-1. Rule of Mixture IV-1- i . Rule of Mixture for Continuous Fiber Reinforced Materials Since Kel ly and Tyson (41) proposed the so ca l led " ru le of mixture" for the strength of composites, i t has been quite often used to evaluate the composite strength. In th i s r u l e , the stress on the composite specimen O" i s expressed as the summation of stresses which both f iber s and the matrix are supporting at the same amount of s t ra in as shown in F ig. 33. This re la t ion can be obtained by assuming the same s t ra in in f ibers and the matrix. V.p : f i be r volume f ract ion Vm : matrix volume f ract ion ( = 1-V f) Dividing eqn. 1 by a s t r a i n , e , which is smaller than the y i e l d s t ra in of the matrix the rule of mixture for Young's modulus of the composite, E i s obtained (1) Where, O" : stress in a composite at a certa in s t ra in cri : stress in f ibers at the same s t ra in cr : stress in matrix at the same s t ra in m E c=cr/ € = , . V F C T / € + V m c r / € (2) E c = V f + Vm E, (3) where, E f = Young's modulus of f ibers E = Young's modulus of the matrix M 4 ) CO 0"c Oh? s —; / / / / i / | FIBER COMPOSITE / I / >^ i MATRIX / /A, A VmO-m c y c f ufs Strain € F1g.33. Schematic Diagram of Stress Strain Curves of the Composite, the Fiber, and the Matrix, obtained according to "Rule of Mixture" 160 £.20 LO 80 Hj 40 3 / o U T S • Y S 02 0.8 0.4 Q6 Fig.34. Tensile Strength of Copper Reinforced with 5 mm Continuous Brittle Tungsten Wires (41). 52 If i t i s assumed that a l l the f iber s f a i l at the same time when they reach the f a i l u r e s t r a i n , the f a i l u r e stress cr can sa t i s f y the " ru le of mixture" condit ion. Consequently, the strength of the composite, cr,, i s given in the fol lowing expression as " ru le of mixture" for the composite strength. cr = V f cr_ + v cr * (4) c f futs m m v ' where, c C p ^ : tens i le strength of f ibers r r * : flow stress of the matrix at the same s t ra in with f i be r m f racture. In the present work, the strength values calculated according to th i s equation have been discussed. When the volume f ract ion of f ibers i s less than V .. , f ibers are c r i t thought to be broken successively, i . e . one a f te r another, before the matrix f a i l s . The maximum strength of such a composite i s expressed in the fol lowing equation, because only the matrix i s thought to support the load at the f a i l u r e point. • °-muts <] " V <5> where, cr ^s : tens i le strength of the matrix The c r i t i c a l f i be r volume f r a c t i on , above which the " ru le of mixture" condition i s s a t i s f i ed ( i f overal l f i be r fracture occurs), i s obtained from Eqn. 4 and 5. V f c r i t = <Vor m * )/(<r f - ° - m - c r m * ) . (6) Furthermore, the f i be r volume f rac t ion has to exceed some value Vmin t 0 strengthen t n e composite. This value i s obtained by subst i tut ing 53 the cr in Eqn. 4 w i t h e r ^ . V . = {cr - cr *)/{cr . -cr *) (7) mm v m m • futs m ' K ' F ig . 34 shows experimental data which were obtained by Kel ly and Tyson to prove " ru le of mixture" for the strength of Cu~W wire composites. I V - 1 - i i . Strength of Discontinuous Fiber Reinforced Materials In the case of discontinuous f i b e r s , the load on a composite i s thought to be transferred to the f ibers through the matrix. The strength of a d i s - continuous f i b e r composite becomes close to the strength of a continuous f i be r composite as the aspect ratio,j2/d , (the r a t i o of f i be r length and diameter) increases. There are three theoret ical works which can be distinguished from each other only by the difference of assumptions about the e l a s t i c i t y or the p l a s t i c i t y of the matrix (42, 43). In th i s sect ion, only Kelly-Tyson's theory (91) i s described which i s based on the assumption of e l a s t i c f ibers and the p l a s t i c matrix, because th i s assumption i s mostly appl icable in the case of metal matrix composites. Now consider the case where the matrix i s allowed to flow p l a s t i c a l l y . When a composite of discontinuous f ibers i s stressed in a d i rect ion along the f i be r ax i s , d i f fe rent ax ia l displacements take place in the matrix and f i be r s , and a large shear stress occurs at the end of the f i be r s . Fig. 35 i s a model of a s ingle discontinuous f i be r in the c y l i nd r i c a l matrix. The load i s transferred from the matrix to the f i be r only by the shear stress at the inter face, r p z , neglecting any stress transfer across the f i be r ends which have small area. The small increment of the load, i 54 Fig.35. Showing Notation Used in the Kelly and Tyson's Theory for the Discontinuous Fiber "Composites (41). Distance F1g.36. Expected Variation of Stress along a Fiber within a Plastic Metal Matrix (41). Fig.37. Stress Distribution in the Discontinuous Tungsten Fiber Obtained by Means of Moire- Technique. Applied Stress on the Composite i s Low (a) and High (b) (44) (47). (x: distance from one end of the fiber, d: diameter) dP, due to the stress transfer at the small interface area 2 7 7 "r Q dz i s given by dP= 2 T r r 0 T r z dz (8) Equation 8 integrates to P = 277-rzr (9) For a p l a s t i c matrix which does not work-harden, r i s constant. If the interface f a i l s , r i s equal to the f r i c t i o n a l force per unit area which the matrix exerts on the f i be r as i t s l ides over the f i be r . For work-hardening matrix, r depends on the st ra in in the composite and i s thought to be iden t i f i ed with the ultimate shear strength of the matrix. Eqn. 9 means that the stress in a f i be r builds up l i n e a r l y from both ends as shown in F ig. 36. The stress in the f i be r at a distance z from the end, Czz , i s expressed by ^ I f r ? (10) subst i tut ing for P from Eqn. 9, 2TZ / *| 1 \ crzz = - p — (11) The s t ra in in the f i be r cannot exceed the s t ra in of the matrix so that cr^ w i l l bui ld up to the value CT f, provided the f i be r i s s u f f i c i en t l y long. If the stress in the f i b e r , cr„, builds up to the fracture stress of the f i be r c j f u t s , the f i be r i s broken. The c r i t i c a l f i be r length, T, for th i s to take place i s given by T = rWT (12) 56 T/2 i s defined as the transfer length. The value of T depends on T . If T i s constant as in the case of a non-work hardening matrix, T i s also constant. If a condition of f i be r length, i , > T , i s s a t i s f i e d , the fracture of the composite occurs when CTp increases to the ultimate tens i l e strength of the f i b e r , c r f u t s - The average tens i l e s t ress , at th i s loading point i s expressed as follows ? f ' \ ' o ' ° " " d z • ° * P - h ) < 1 3 ) An equation which expresses the tens i le strength of the discontinous f i be r composites i s obtained, t reat ing Of as the stress in the f ibers in continuous f i be r composites. From Eqn. 4 and 13, % = G f u t s V f " V 2 £ ) + c r * Vm (14) It i s seen from th i s equation that the strength of a discontinuous f i be r composite becomes closer to the strength of continuous ones i f the f i be r length, 1 , i s much greater than the transfer length, T/2- Miura and Okuno's (44) study on the stress d i s t r i bu t i on of a two- dimensional Al-W wire composite by means of the Moire technique proved the appropriateness of the stress d i s t r i bu t i on in f ibers in th i s model. Their results are shown in F ig. 37. T, T,and are used as important variables l a te r in the fol lowing discussions. The Equation 14 i s used to express the strength of the f ibe r f a i l u r e zone. 57 IV-2. Propagative Fiber Fai lure Model for Graphite Fiber Reinforced Aluminum A l loy Composites IV-2- i . Ultimate Tensile Strength of Homogeneously Distr ibuted Specimens The composite tens i le specimens of 601 T4 (solution t reated), 201 T6 (age hardened) and 7178 T6 (age hardened) a l loys exhibited great d i s - crepancy between experimental strength values and values calculated accor- ding to " ru le of mixture" as shown in F ig. 20, 21, and 22. The experimental U.T.S. values of 601 T4 and 201 T6 a l l oy composites against f i be r volume fract ions appear to be on broad curves in spite of great scatter ing. The scatter of strength values in these experimental resu lts might be due to: a) misorientation of the f ibers with the specimen ax is . The f ibers might not be aligned properly during the in f i l t ra t ion- sed imentat ion process, espec ia l l y in the case of low f i be r volume f ract ion composites. b) non-uniform f i be r d i s t r i bu t i on in the matrix and the contacts of neigh- boring f ibers which may act as defects. c) deviations of matrix chemical composition from average values. The ultimate tens i l e strength of the matrix i s dependent on i t s chemical composition. The great density difference of each a l l o y element might cause great difference of s e t t l i n g speed among the powders of each element in the in f i l t ra t ion- sed imentat ion process. f: d) error in the measurement of f i be r volume f ract ions . The micrographs which cover only one-seventh of the tota l specimen section were used to count the numbers of f i be r s , so that error of a few percent i s unavoidable. 58 No quant itat ive measurements were done to estimate the contr ibutions to the scatter from each one of the above factors . General microscope observation revealed that the breakage of graphite f ibers occurs in a narrow region close to the fracture edge of the spec i - mens; however, the f i b e r s ' f a i l u r e i s in a b r i t t l e manner and the matrix f a i l u r e i s in a duct i le manner as expected from the o r i g ina l deformation character i s t i c s of each mater ia l . This resu l t suggests that most of the p l a s t i c deformation of the matrix takes place in a l imi ted range from the fracture surface, where f ibers are broken. The propagation of a rather highly strained deformation zone was observed in specimens being strained to some extent before the f a i l u r e as shown in F ig. 25. The segments of broken f ibers were also obser- ved in th i s zone as shown in F ig. 26, etc. The s t ra in of the matrix in th i s zone i s higher than the matrix of the other part of the specimen as shown in F ig. 27. From these re su l t s , i t may be said that such a highly strained zone propagates over the section of the specimen, breaking the f i be r successively at the t i p front of the zone, during the tens i l e tes t . Such successive f a i l u r e of f ibers in the matrix has been observed in boron filament r e i n - forced aluminum composites by J . Steele et al_. (45). In the present work, the model proposed i s one in which the ultimate tens i l e strength of the composites corresponds to the accelerated propagation of a f i be r f a i l u r e zone. This f a i l u r e mode of composites i s quite d i f fe rent from the model which A. Kel ly et al_. adopted to establ i sh " ru le of mixture" for large diameter f i be r metal composite l i k e W wire-Cu composites. In the model for " ru le of mixture", a l l the f iber s in the composite are assumed to f a i l at 59 once or at an i d e a l i z e d c o n d i t i o n . The d i sc repancy i n the exper imental s t rength values and " r u l e o f m i x tu re " va lues may be main ly due to the d i f f e r e n c e between the ac tua l propagat ive f a i l u r e mode and the i d e a l i z e d f a i l u r e mode i n " r u l e of m i x tu re " model. The observed propagat ive f a i l u r e mode i s going to be d i scussed i n mathematical expres s ion i n success i ve pages, i n order to g i ve a po s s i b l e exp lana t i on f o r exper imental r e s u l t s . I V - 2 - i i . Energy C r i t e r i a of Propagat ive F i be r F a i l u r e f o r Homogeneously D i s t r i b u t e d Composites. I t i s assumed f o r s i m p l i c i t y t ha t f i b e r s always deform i n an e l a s t i c manner and the mat r i x changes i t s deformation mode from e l a s t i c to p l a s t i c which does not i n c l ude any work hardening e f f e c t when i t i s s t res sed beyond the y i e l d p o i n t , c x ^ , i . e . c r = 0"m* i n F i g . 38. As a s imple i l l u s t r a t i o n , cons ide r a p l a t e specimen o f width w and u n i t t h i c kne s s con ta i n i n g a small h a l f e l l i p t i c a l zone i n which the f i b e r s have f a i l e d i n t o small segments of average t r a n s f e r l e n g t h , T t . The zone length i s expressed as h a l f of the long diameter of an e l l i p s e , a , and the th i cknes s i s a l s o expressed as the short d iameter , 2b, i n F i g . 39. The s t r a i n of the mat r i x out s ide t h i s h a l f e l l i p t i c zone i s expressed as e Q and w i t h i n t h i s zone as the f i b e r f a i l u r e s t r a i n € f u t s > ( € f u t s > € ° ^ " ^ e s t r e s s on f i b e r s ou t s ide of t h i s zone i s expressed as cr •, which i s lower than the maximum s t r e s s on the f i b e r fragments w i t h i n t h i s zone t s - The average s t r e s s on the fragments i s ^Of^- The s t r e s s d i s t r i b u t i o n on broken f i b e r segments i n t h i s zone i s assumed as shown i n F i g . 40. The s t r e s s i s t r a n s f e r r e d from the mat r i x to the segment through a shear s t r e s s , r , a t the i n t e r f a c e o f mat r i x and f i b e r segments. The s t r e s s on the 60 201 'futs r W H Fig.39. Half E l l ipt ic Fiber-Failure Zone in a Composite matrix Strain £ * Fig.38. Schematic Diagram of Stress Strain Curve of the Matrix and the Fiber co CO a> tn To 7\ 7T v—1 / \ / \ \ \ \ i \ / \ / \ / \ / \ T\ TT / \ / Distance Fig.40. Stress D i s t r ibut ion Change in a Fiber which is Located in the Fiber Fa i lure Zone, so l id l i n e : before f a i l u r e , dot-dash-l ine: a f ter f a i l u r e . 62 f i b e r b u i l d s up l i n e a r l y to the value ° f u t s ^ r o m the ends o f the seg- ments. For a p l a s t i c matrix which does not work-harden T i s c o n s t a n t . °futs = T T u t s / r (15) where r : r a d i u s of f i b e r s In other words, f i b e r s are assumed to be broken i n t o small segments which cannot be broken s h o r t e r than t h i s by the f u r t h e r p l a s t i c deformation of the matrix. The average s t r e s s i n a segment i n t h i s zone, c r e g > i s given i n the f o l l o w i n g expression from Eqn. 13. ^ s e g = °futs / 2 (16) Consequently, the s t r e n g t h of t h i s zone,0~ z , i s obtained from Eqn. 14. V \ Vf ûts + Vm V <17> During a t e n s i l e t e s t , such small h a l f e l l i p t i c f i b e r f a i l u r e zones f i r s t s t a r t to grow at some s t r e s s concentrated areas or d e f e c t i v e areas i n a specimen as shown i n F i g . 41, d e v i a t i n g the a c t u a l s t r e s s - s t r a i n curve from a curve expected from " r u l e o f mixture". Some amount of energy, dWz, i s r e q u i r e d to grow a zone from the shape o f a and b to a+da and b+db. During t h i s growth, the load does work,|dL|. A change of e l a s t i c energy, d U , occurs i n the r e g i o n o u t s i d e of the f a i l u r e zone due to the shape change of the zone. The e l a s t i c energy change may be e a s i l y understood i f we c o n s i d e r the f o l l o w i n g s p e c i a l l o a d i n g system shown i n F i g . 42. F i g . 42(a) shows the specimen s t r a i n e d to the s t a t e of e l o n g a t i o n ASL. The area £j" OYAC 63 Fig.41. Fiber Fai lure Zones in a Specimen Fig.43. Schematic Diagram of Stress Stra in Curve at Fa i lure Point 64 c o r r e s p o n d s t o the work which t h e l o a d d i d . I f t h i s specimen i s broken under the c o n d i t i o n o f f i x e d g r i p d i s t a n c e , t h e two s e p a r a t e d p i e c e s s h r i n k e l a s t i c a l l y and r e l e a s e e l a s t i c e n e r g y which c o r r e s p o n d s t o t h e hatched a r e a A A B C shown i n F i g . 4 2 ( b ) . I f we s t r a i n a specimen,^which a f i b e r f a i l u r e zone has t r a v e r s e d t h e c r o s s s e c t i o n , t o g i v e t h e same amount o f e l o n g a t i o n , A d, the l o a d i s i n c r e a s e d f o l l o w i n g t h e s t r e s s - s t r a i n c u r v e OY'ED i n F i g . 4 2 ( c ) . C o n s e q u e n t l y , i f we assume t h a t t he same f i b e r f a i l u r e zone (which t r a v e r s e d t he s e c t i o n ) o f t h i c k n e s s 2b, i s formed i n a specimen between f i x e d g r i p s , t he l o a d i s l o w e r e d from o r i g i n a l , L-j t o the l o a d , L^, which c o r r e s p o n d s t o Eqn. 17. D u r i n g t h i s u n l o a d i n g under the f i x e d g r i p c o n d i t i o n , t he r e g i o n s o u t s i d e o f t h e zone s h r i n k e l a s t i c a l l y r e l e a s i n g e n e r g y which c o r r e s p o n d s t o the a r e a A A E D i n F i g . 4 2 ( c ) . In the c a s e o f h a l f e l l i p t i c f i b e r f a i l u r e zone, some e l a s t i c e n e r g y which i s a c o m p l i c a t e d f u n c t i o n o f the shape o f the zone, a and 2b, i s r e l e a s e d from o u t s i d e o f the zone i n the same way as t h e c a s e o f F i g . 4 2 ( c ) . We l e t dŴ . be t h e t o t a l f r e e e n e r g y change o f a specimen due t o the f o r m a t i o n o f h a l f e l l i p t i c f i b e r f a i l u r e zone. Then dW^ i s g i v e n by dWt. = dl_ + dWz + dU (18) When one o f t h e zones grows up t o a c r i t i c a l s i z e , t h e summation o f the potential energy c h a n g e of the lood.dL, and the e l a s t i c e n e r g y change, dU, can be b i g enough t o s u p p l y the f o r m a t i o n e n e r g y o f the zone, dWz. The e n e r g y b a l a n c e a t t h i s c r i t i c a l p o i n t i s g i v e n by dWt = dL + dW2 + dU = 0 (19) Once t h i s r e l a t i o n i s s a t i s f i e d , t he zone can s t a r t t o grow q u i c k l y w i t h o u t any e x t r a energy s u p p l y from o u t s i d e o f t h e specimen. In o t h e r words, the 65 p r o p a g a t i o n o f the zone i s a c c e l e r a t e d beyond t h i s c r i t i c a l p o i n t which c o r r e s p o n d s t o the s t r o n g e s t s t a t e o f t h e specimen, i . e . u l t i m a t e t e n s i l e s t r e n g t h p o i n t . A f t e r t h i s a c c e l e r a t i o n t a k e s p l a c e , t h e f i b e r s a r e q u i c k l y broken i n t o s m a l l segments i n t h i s zone and a b r u p t l y lower the s u p p o r t i n g l o a d . The f r a c t u r e o f t h e m a t r i x o c c u r s s u c c e s s i v e l y r i g h t a f t e r the t r a v e r s e o f t h e zone. The f u r t h e r p l a s t i c d e f o r m a t i o n l e a d i n g t o t h e f a i l u r e o f the m a t r i x i s t h o u g h t t o t a k e p l a c e a t o n l y l i m i t e d l o c a l r e g i o n s around t h e broken f i b e r ends i n t h e zone. The s t r e s s s t r a i n c u r v e around the f r a c t u r e p o i n t may be shown s c h e m a t i c a l l y as i n F i g . 43, i f we e x a g g e r a t e t h e l o a d d r o p . F o r s i m p l i c i t y , t h e t h i c k n e s s o f t h i s zone, 2b, i s assumed t o remain c o n s t a n t a f t e r the zone s t a r t s t o p r o p a g a t e q u i c k l y . The g r i p d i s t a n c e i s a l s o assumed t o remain c o n s t a n t d u r i n g t h i s q u i c k p r o p a g a t i o n , because the c r o s s head speed o f the t e s t i n g machine i s v e r y low (0.02 i n c h / m i n . ) compared w i t h the p r o p a g a t i n g speed, ( i . e . t h e f i x e d g r i p c o n d i t i o n ) . C o n s e q u e n t l y , t h e l o a d does n o t do any work, so t h a t dL = 0. The t o t a l e nergy change, dWt, has t o d e c r e a s e w i t h the i n c r e a s e o f zone l e n g t h , a , i n o r d e r t o p r o p a g a t e w i t h o u t any e x t r a e n e r g y i n c r e m e n t from o u t s i d e o f the specimen. Then, the c r i t i c a l c o n d i t i o n a t w hich the zone can s t a r t t o p r o p a g a t e s p o n t a n e o u s l y i s s t a t e d as the f o l l o w i n g e x p r e s s i o n ^ _ t d ( U - r W z ) n (20) da " d a _ u T h i s s t a t e m e n t i s o b t a i n e d by f o l l o w i n g the G r i f f i t h (46) t h e o r y f o r an e l l i p t i c c r a c k i n a b r i t t l e m a t e r i a l . I f the l e n g t h o f zone exceeds the c r i t i c a l v a l u e a t which Eqn. 20 i s j u s t s a t i s f i e d , e l a s t i c energy r e l e a s e d i s more than s u f f i c i e n t 66 t o p r o v i d e t h e i n c r e m e n t o f f r e e e n e r g y i n the zone, so t h a t t h e r a t e o f p r o p a g a t i o n i s a c c e l e r a t e d . I t i s n e c e s s a r y t o d e s c r i b e U and Wz i n terms o f t h e e x p e r i m e n t a l p a r a m e t e r s . (A) The f r e e e n e r g y i n c r e m e n t i n t h e f i b e r f a i l u r e zone, W2, F i g . 40, shows t h e s c h e m a t i c s t r e s s d i s t r i b u t i o n i n a f i b e r when i t i s broken i n t h e zone, where T Q i s t h e s t r e s s t r a n s f e r l e n g t h o u t s i d e o f the zone. When f i b e r s a r e broken i n t h e zone, t h e s t r e s s d i s t r i b u t i o n changes from t h e s o l i d l i n e t o t h e d o t t e d l i n e , r e l e a s i n g e x t r a e l a s t i c e nergy t o t h e surroun- d i n g m a t r i x . On t h e o t h e r hand, work i s r e q u i r e d t o break t h e f i b e r s , and s t r a i n t h e m a t r i x i n t h e zone. Wz can be d e r i v e d as the summation o f t h e s e terms. a) The work p e r u n i t t h i c k n e s s , W , n e c e s s a r y t o deform t h e m a t r i x i n t h e zone from eQ, t h e s t r a i n i n t h e m a t r i x o u t s i d e o f t h e zone t o £ f u t s » t h e f i b r e f a i l u r e s t r a i n , i s w = V c r * ( € - € ) wm vm 2 { t u t s o ; TVmqb(Trrr (quts - ° - f 0 > (21) 2 E f b) The work, Wf, n e c e s s a r y t o s t r a i n t h e f i b r e s i n t h e zone from € Q to € f u t s 1 s w _-IflZliSrtslV' <22) f 4Ef c) The r e l e a s e d e l a s t i c e n e r g y from t h e broken f i b r e s , W , i s e x p r e s s e d as the d i f f e r e n c e between t h e e l a s t i c e n e r g y o f t h e f i b r e s b e f o r e t h e i r f a i l u r e and a f t e r t h e i r f a i l u r e . W r = - W b e f + W a f t < 2 3> where, : e l a s t i c e n e r g y which t h e f i b r e s i n t h e zone p o s s e s s b e f o r e breakage. W a f t : e ^ a s t i c energy which t h e fragments o f t h e same f i b r e s i n t h e zone p o s s e s s a f t e r b r eakage. _ V f rr a b + Vf ° T Q ^ 4 E f 2 E f Where, T 0 = r = Then, bef = ~ 4 E f 2 E f c r f u t s W b e f = V f T Q b ^ t s + Vf o T u t ? C 7 f 0 3 ( 2 5 ) Woft - V f ^ ^ - ^ W ( Z ) d z + V f a 2 | cr(z)€(z)dz 2 3 2 3 I 2 T u t s 3 Efr^ + 3 E f r 2 | ^ r l ^ - + — ^ r J ,26) then - w bef+ w aft vi f 0 Tuts ^fo 6 E f °futs 2 E ( (27) d) The i n c r e m e n t o f s u r f a c e f r e e e n e r g y due t o t h e broken f i b e r ends i s n e g l i g i b l y s m a l l and w i l l be i g n o r e d below. The sum o f t h e s e energy terms must be W2 i n Eqn. 21. w z = Wm + Wf + Wr = _ ( V f ° T u t s 1 3 ( H ^ b S ^ l A ^ 0 + 2 f  vf 7 / 0 b °futs Vm7ra bofhorfftsl + 2 E f j ( 2 8 ) (B^) E l a s t i c e nergy U, r e l e a s e d f r o m t h e r e g i o n o f t h e s p e c i m e n . o u t s i d e the e l l i p t i c zone due t o t h e f o r m a t i o n o f t h e zone. I t i s i m p o s s i b l e t o d e r i v e an e x a c t e x p r e s s i o n f o r t h i s term l a c k i n g a m athematical a n a l y s i s o f t h e s t r e s s and s t r a i n i n the n e i g h b o u r h o o d o f t h e zone; however, i t may be p o s s i b l e t o d e r i v e an a p p r o x i m a t e e x p r e s s i o n f o r t h i s term by m o d i f y i n g G r i f f i t h e x p r e s s i o n f o r t h e e l a s t i c r e l e a s e d energy due t o t h e f o r m a t i o n o f a two d i m e n s i o n a l e l l i p t i c a l c r a c k o f l e n g t h 2a, i n an e l a s t i c specimen h e l d between r i g i d l y f i x e d g r i p s under s t r e s s , 0" 69 H i s t h e o r y was l a t e r d i s c u s s e d by Knott etol(48) a n d i t was shown t h a t the assumption o f r i g i d l y f i x e d g r i p s i s n o t e s s e n t i a l t o th e G r i f f i t h energy c r i t e r i o n f o r b r i t t l e f r a c t u r e . The same c r i t e r i o n i s o b t a i n e d i f the c r a c k p r o p a g a t i o n i s assumed t o o c c u r under c o n s t a n t l o a d . In t h e case o f f i x e d g r i p s , the e x t e r n a l f o r c e s cannot do work. The c r i t i c a l l e n g t h o f t h e c r a c k above which i t can p r o p a g a t e s p o n t a n e o u s l y i s then d e t - ermined by th e c o n d i t i o n dWc + d U c = 0 (29) where, dw"c : the f r e e energy r e q u i r e d f o r i n c r e a s i n g t h e l e n g t h o f a c r a c k from 2a t o 2a + da, dUc : t h e e l a s t i c e nergy r e l e a s e d s i m u l t a n e o u s l y i n t h e specimen. T h i s e l a s t i c r e l e a s e d energy i s g i v e n by t h e G r i f f i t h e x p r e s s i o n dUc = . d { ^ V V + b 2)j (30) i n t he c a s e o f p l a n e s t r a i n c o n d i t i o n ( f o r t h i c k specimen) w h e r e , v i s Poisson's r a t i o a n d E is Y o u n g ' s m o d u l u s , a n d b y du c * -d {^ \° 2 + b2>) t31> i n t h e c a s e o f p l a n e s t r e s s ( f o r t h i n s p e c i m e n s ) . In f u r t h e r d i s c u s s i o n s , o n l y Eqn. 30 i s a d o p t e d , because t h e t e n s i l e t e s t p i e c e s i n the p r e s e n t work a r e t h o u g h t t o have r a t h e r l a r g e r t h i c k n e s s (1/3 o f the w i d t h ) . The r e l e a s e d e l a s t i c e nergy under t h e f i x e d g r i p c o n d i t i o n i s shown s c h e m a t i c a l l y as AOAC i n F i g . 44. On t h e o t h e r hand, i f t h e c r a c k p r o p a g a t e s w h i l e t h e l o a d i s kept con- s t a n t , t h e l o a d does work,|dL|, shown as DADBE i n F i g . 44. The e l a s t i c e n e r g y i s i n c r e a s e d by the amount of d U c during this c r a c k p r o p a g a t i o n . T h e total 70 change in potential e n e r g y is a d e c r e a s e of m a g n i t u d e I d L l — dU^.. The du£ i s h a l f o f the dL, as A B D E shown i n F i g . 44, so t h a t h a l f o f t h e e x t e r n a l work i s s t o r e d a s a d d i t i o n a l e l a s t i c e n e r g y o f t h e sp e c i m e n , and t he o t h e r h a l f i s a v a i l a b l e f o r i n c r e a s i n g t h e f r e e e n e r g y o f t h e c r a c k s u r f a c e , d W c « The c r i t i c a l c o n d i t i o n f o r t h i s c a s e i s e x p r e s s e d i n t h e f o l l o w i n g e q u a t i o n . dL + du' + dW =-dU' + dW =0 (32) c c c c Now the r e l a t i o n s h i p between l o a d , L and e l o n g a t i o n , S, i s g i v e n by S = CL (33) where C i s a c o n s t a n t f o r g i v e n c r a c k l e n g t h , c a l l e d t h e c o m p l i a n c e o f t h e system. As the change i n c r a c k l e n g t h , da, tends t o z e r o , we may t r e a t C as i d e n t i c a l f o r c r a c k l e n g t h s 2 o a n d 2 o + do and w r i t e , dS = C dL (34) dU c , dl/, a r e g i v e n by t h e f o l l o w i n g same e x p r e s s i o n s , u s i n g C. dll ~ - A 0 A C = 3 - i S dL = - i CLdL (35) c 2 2 dL - du'=-du'=-A0AB=-LdS + k d S = - k d S = - k L d L (36) C C 2 2 2 For an i n f i n i s t e s i m a l l y s m a l l amount o f c r a c k e x t e n s i o n , t h e d e c r e a s e i n s t o r e d e l a s t i c e n e r g y under t h e f i x e d g r i p s c o n d i t i o n i s i d e n t i c a l t o the d e c r e a s e i n p o t e n t i a l e n e r g y under t h e c o n s t a n t l o a d c o n d i t i o n . Eqn. 29 and 32 show t h a t t h e energy a v a i l a b l e f o r c r a c k p r o p a g a t i o n a t f i x e d g r i p s i s t h e same as a t t h e c o n s t a n t l o a d , so t h a t even i n t h e l a t t e r c a s e , we can use Eqn. 30 to e s t i m a t e t h e energy a v a i l a b l e f o r the p r o p a g a t i o n . 2 2 dL - dU^= -dU^=-dU=-d j 7 7 1 1 " ^ ( a 2 + b 2 ) } (37) ( f o r p l a n e s t r a i n c o n d i t i o n ) A B 0 Elongation S F i g . 4 4 . E l a s t i c L o a d i n g C u r v e s f o r C r a c k Lengths a and a + da. 72 When a comp o s i t e specimen f a i l s by t e n s i o n , ( i . e . c o m p l e t e l y s e p a r - a t e d i n t o two p i e c e s ) , under t h e f i x e d g r i p c o n d i t i o n , e l a s t i c energy which c o r r e s p o n d s t o t h e a r e a A ABC i n F i g . 45 i s r e l e a s e d and t h e en e r g y d OYAB i s s t o r e d i n the specimen. A l t h o u g h , c o m p o s i t e s a r e not p e r f e c t l y e l a s t i c m a t e r i a l , i f we a p p l y t h e G r i f f i t h r e l e a s e d e l a s t i c e nergy e x p r e s - s i o n f o r t h e i r e l a s t i c p r o p e r t y , an e x p r e s s i o n f o r t h e r e l e a s e d e l a s t i c e n ergy ucc d u r i n g t h e p r o p a g a t i o n o f a c r a c k i n a c o m p o s i t e i s g i v e n by _ 7T(1- VZZ) a / ( 0 2 + b 2 , ( 3 8 ) where, y : P o i s s o n s r a t i o o f t h e c o m p o s i t e cr„ : s t r e s s on t h e c o m p o s i t e E c : Young's modulus o f t h e c o m p o s i t e When a f i b e r f a i l u r e zone t r a v e r s e s t h e c r o s s s e c t i o n o f a specimen h e l d between f i x e d g r i p s , t h e m a t r i x does n o t f a i l , but o n l y t he f i b e r s a r e broken i n t o s m a l l f r a g m e n t s o f a v e r a g e t r a n s f e r l e n g t h , T ̂  > i n t h e zone. Then, t h e s t r e s s d rops down from t h e p o i n t A ( < J c r m ) > t o E ( o~^z). The s t r e n g t h o f t h e t r a v e r s e d zone, C7j z , i s g i v e n by CT = VfW + V 0 ~ * = i c r , v r + O - * V (39) t z f : seg m m 2 f u t s f m m v ; D u r i n g t h i s u n l o a d i n g f r o m A to E, t h e r e g i o n o u t s i d e o f t h e zone s h r i n k s e l a s t i c a l l y and r e l e a s e s e l a s t i c e n e r g y which c o r r e s p o n d s t o t h e a r e a A A D E . The amount o f t h i s a r e a A A D E i s e x p r e s s e d i n t h e f o l l o w i n g f o r m u l a i f t h e g r a d i e n t o f Y'E ( i . e . , t h e Young's modulus o f t h e zone) i s assumed t o be K V f + EmV 73 F i g . 4 5 . S c h e m a t i c Diagram o f E l a s t i c Energy R e l e a s e d A ABC and A A D E , when t h e Crack and t h e F i b e r F a i l u r e Zone T r a v e r s e t h e C r o s s S e c t i o n 74 A A D E - ( °crm - Qfz ) E , ( l - V f E f - V m E m ) crc - A A B C crm ( ! T V f O f u t « ) 2 E r A A D /~ " 2 - A A B C (40) ^crml E c - - £ - v f E f ) where, CT : co m p o s i t e s t r e n g t h b e f o r e f i b e r f a i l u r e , c a l c u l a t e d a c c o r - d i n g t o t h e " r u l e o f m i x t u r e " . When the h a l f e l l i p t i c f i b e r f a i l u r e zone has not y e t t r a v e r s e d t h e f u l l c r o s s s e c t i o n , t h e energy which c o r r e s p o n d s t o AAD'E' i s r e l e a s e d . In o r d e r t o m o d i f y t h e G r i f f i t h e x p r e s s i o n f o r t h e e l a s t i c r e l e a s e d energy due t o t h e e l l i p t i c c r a c k , U c c , t o t h e e l a s t i c r e l e a s e d energy due to t h e h a l f e l l i p t i c f i b e r f a i l u r e zone, U, we s i m p l y assume t h a t U / U c c i s p r o p o r t i o n a l t o t h e r a t i o o f t h e t o t a l e l a s t i c energy r e l e a s e d when the c r a c k and zone c o m p l e t e l y t r a v e r s e t h e f u l l c r o s s s e c t i o n ( i . e . U/U c c= AADE/AABC) . U i s g i v e n by, 2 U . i r o - ^ q W + b 2) ( I v ^ ) 2 ( 4 i ) °crm <Ee4VfEf> Because o f t h e h a l f e l l i p t i c shape, U v a l u e s c o r r e s p o n d t o t h e h a l f o f U c c i n t J n e c a s e o f e ^ ^ i p t i c shape c r a c k ( n e g l e c t i n g t h e e f f e c t o f t h e f r e e s u r f a c e o f the h a l f p l a n e ) . S u b s t i t u t i n g 0^rrr]] 2 x . . 2 2 2 7 / 1 1 — 1 / U 8 c 7 c r m < E c - T " V f E f ) 2 ~ i i W - w J + f - ^ I F + V U ( 4 2 ) 8cr E ~ i - V r F ^ L c J 75 From Eqn.20, d ( Wz+U)/do= o, d i f f e r e n t i a t i n g Eqn. 28 and 42 by a, , which i s the s t r e s s i n f i b e r s o u t s i d e o f t h e f a i l u r e zone a t t h e a c c e l e r a t i n g p o i n t , i . e . the U.T.S. p o i n t o f t h e specimen, i s g i v e n by t h e f o l l o w i n g e q u a t i o n . 0-3+ I-*ZJh.ai . + 3T(l-i/?) E f "fats u?l " 30 2 _2oi_ / 3 o 2 4o 3 f b2 2ob2 x 37T(l-v2) E f Q - f u t s cr* 2 _ VT u t sw T u t sw 2 T^w T u t S w 2 / 2 (E c ~l\fE f ) cr c 2 r m * m (2a 3o 2 bLxl f, V m b o *, _ b _ 3 1 Tuts T u t sw Tutsw) \%~ 5tS°"m+ ̂  nj^futs" 377(1-1/2) E f Ofut3svr 2 2 / o 3 • o b2 , , 4 ( E c - ^ V f E f ) 0- c 2 m ^ + — 2 ) + where, ^ V f a f o ( | _ ^ ) + V f ^ ( r a . ) + V m 0 ? ; j (44) °crm = °futsvf + OmVm (45) The s t r e n g t h o f the c o m p o s i t e s can be c a l c u l a t e d from Eqn. 44, u s i n g t h e crfQ v a l u e s o b t a i n e d from Eqn. 43. 76 I V - 2 - i i i . Improvement o f T e n s i l e S t r e n g t h i n Bundle S t r u c t u r e C omposites G r a p h i t e f i b e r r e i n f o r c e d 7178 T6 age hardened a l l o y c o m p o s i t e s which have n o n - u n i f o r m , b u n d l e s t r u c t u r e , f i b e r d i s t r i b u t i o n i n t h e m a t r i x as shown i n F i g . 15 e x h i b i t e d h i g h e r u l t i m a t e t e n s i l e s t r e n g t h t h a n u n i f o r m l y d i s t r i b u t e d c o m p o s i t e s . The r e s u l t was shown i n F i g . 22. The i n c r e a s e o f t h e s t r e n g t h may be a t t r i b u t e d t o the e x i s t e n c e o f t h e f i b e r f r e e r e g i o n s between f i b e r c o n c e n t r a t e d b u n d l e s . These f i b e r f r e e r e g i o n s can work as o b s t a c l e s a g a i n s t t h e p r o p a g a t i o n o f the f i b e r f a i l u r e zone t h r o u g h two p o s s i b l e mechanisms. The t h i c k n e s s o f t h e h a l f e l l i p t i c f i b e r f a i l u r e zone may be e n l a r g e d from 2b t o 2h a t t h i s f i b e r f r e e r e g i o n consuming e x t r a e n e r g y as shown i n F i g . 46. In a d d i t i o n , such f i b e r f r e e zone may a l s o a c t t o i n c r e a s e t h e c u r v a t u r e o f t h e a d v a n c i n g h a l f e l l i p t i c zone, t h u s d e c r e a s i n g t h e s t r e s s c o n c e n t r a t i o n a t the t i p . In the p r e s e n t c a s e , o n l y t h e f i r s t p o i n t w i l l be d i s c u s s e d . L e t the a v e r a g e f i b e r volume f r a c t i o n be t h e a v e r a g e m a t r i x volume f r a c t i o n V m , the f i b e r f r a c t i o n i n a b u n d l e , v f , t h e m a t r i x volume f r a c t i o n i n a b u n d l e , v m , and t h e t o t a l number o f b u n d l e g r o u p s , G, i n t h e c r o s s s e c t i o n o f w i d t h W and u n i t t h i c k n e s s . Then we can o b t a i n t h e f o l l o w i n g e x p r e s s i o n s from t h e g e o m e t r i c r e l a t i o n s shown i n F i g . 46. v f n 2 : = K (46) ;• V f ^ The number o f groups which t h e h a l f e l l i p t i c zone sweeps, G z, i s g i v e n by 77 F i g . 4 7 . S c h e m a t i c S t r e s s S t r a i n Curve f o r a Composite Showing Energy R e l a t i o n - s h i p s i n Eqn. 56. • <x—-4 F i g . 4 6 . Geometry o f t h e F i b e r F a i l u r e Zone i n t h e Bundle S t r u c t u r e Composite D : t h i c k n e s s o f a hexagonal group d : t h i c k n e s s o f a f i b e r c o n c e n t r a t e d a r e a 2b: t h i c k n e s s ; o f t h e zone ( s h o r t d i a m e t e r o f t h e h a l f e l l i p t i c zone) a : advanced d i s t a n c e o f t h e t i p o f the zone •' ( l e n g t h o f t h e h a l f e l l i p t i c zone) 2h: t h i c k n e s s o f t h e zone i n f i b e r f r e e r e g i o n 78 G z = - w - G (48) The a r e a o f a group, A, i s g i v e n by A = ^ D 2 (49) 8 Then D 2 (50) The work per u n i t t h i c k n e s s , W mg, n e c e s s a r y t o deform t h e m a t r i x i n t h e b u n d l e s and f i b e r f r e e z o nes f r o m € t o € £ . i s d e r i v e d i n the o t u t s f o l l o w i n g f o r m s . I t i s t h o u g h t t h a t t h e m a t r i x i n t h e f i b e r f r e e zone can be deformed, on a v e r a g e , up t o t h e f i b e r f a i l u r e s t r a i n , € f u t s > i n t h e d i s t a n c e o f (h - b) from t h e edge o f t h e f i b e r f a i l u r e z o ne. . _ ^ ! C 3 L | J ^ _ v m + 2 ( h - b ) ( l - ^ ) } ,5,) S u b s t i t u t i n g f o r w"m i n Eqn. 28 by t h i s "W , an e x p r e s s i o n f o r the f r e e energy i n c r e m e n t i n t h e f i b e r f a i l u r e zone f o r a bu n d l e s t r u c t u r e composite i s o b t a i n e d . ( T h i s c o r r e s p o n d s t o Wz f o r t h e c a s e o f a u n i f o r m d i s t r i b u t i o n o f f i b e r s ) . Then, t h e f o l l o w i n g e x p r e s s i o n f o r c r f o a t the c r i t i c a l c o n d i t i o n o f zone l e n g t h , o , i s o b t a i n e d . 79 2JL_ b 2 : Ob" T u t s w 2 T u t s w ' T u t s w 2 377tl-z/ 2) E f _ Q f u t s ^ s , 3Q 2 4 a 3 b 5 2 a b j > 4 ( E c - ^ V f E f ) f l T u t S w T u t s w 2 T u t sw T u t s w 2 ) + 2 ( E c -^-v f E f ) c r c r 2 m f m V T u t S T u t s w T u t s w ' / ^ f o 3 TT(\-V2) 4 2 K2 The s t r e n g t h o f b u n d l e s t r u c t u r e c o m p o s i t e s , r r . , can be c a l c u l a t e d from t h e f o l l o w i n g e q u a t i o n , u s i n g t h i s c r f o v a l u e s i n Eqn. 53. *c ~- V fC7 f</1--§-)+ V f - ^ t i ( - £ • ) + V mcr m* (54) 80 I V - 2 - i v . E s t i m a t i o n o f V a r i a b l e s , b and T uts An a t t e m p t was made t o e s t i m a t e t h e a p p r o x i m a t e v a l u e s o f t h e t h e o r e t i c a l v a r i a b l e s , f i b e r f a i l u r e zone t h i c k n e s s , 2b, and s t r e s s t r a n s f e r l e n g t h i n t h e zone, T ^ / 2 , u s i n g s c a n n i n g e l e c t r o n m i c r o s c o p e images o f t h e l o n g i t u d i n a l s e c t i o n . The T u t s v a l u e s a r e i n d e p e n d e n t o f t h e f i b e r volume f r a c t i o n , V^. T u t s d e P e n d s o n l y o n t n e f i b e r - m a t r i x i n t e r f a c i a l s h e a r s t r e n g t h . The T u t s v a l u e can be e s t i m a t e d as a s l i g h t l y l a r g e r v a l u e than the s h o r t e s t l e n g t h o f f ragments n e a r t h e f r a c t u r e s u r f a c e i n t h e h i g h e r V^ c o m p o s i t e s . In the c a s e o f t h e l o w e r V^ c o m p o s i t e s , t h e broken f i b e r segments a r e t i l t e d n e a r t h e f r a c t u r e s u r f a c e o f specimens as shown i n F i g . 3 0 ( a ) . I t i s more d i f f i c u l t t o o b t a i n t h e v a l u e s f r o m t h e m i c r o g r a p h s o f l o w e r V f s p e c i - mens t h a n t h e h i g h e r V^ ones. The h i g h e r V^ c o m p o s i t e s have s t r a i g h t , non- t i l t e d , f i b e r segments. The b v a l u e s cannot be o b t a i n e d d i r e c t l y from t h e m i c r o g r a p h s , b v a l u e can be d e f i n e d as b = n T .̂ (where n: t h e a v e r a g e number o f segments o f a broken f i b e r near t h e f r a c t u r e s u r f a c e ) . The n v a l u e s a r e not c o n s t a n t and depend on V^; however, i t i s a l s o d i f f i c u l t t o e s t i m a t e n v a l u e s i n the m i c r o g r a p h s o f lower V̂ . s p e c i m e n s , a g a i n because o f t h e same r e a s o n . Conse- q u e n t l y , f o r lower V^ specimens, t h e b v a l u e s c o u l d not be o b t a i n e d from t h e m i c r o g r a p h s . A t r e a t m e n t to o b t a i n b v a l u e s f o r a l l V f v a l u e s u s i n g t h e b v a l u e s o f t h e h i g h e r V^ c o m p o s i t e s i s d i s c u s s e d . As mentioned b e f o r e i n s e c t i o n I I I - 6 , the d i s t a n c e B^, between the f r a c t u r e s u r f a c e and t h e f a r t h e s t p o i n t , a t which broken f i b e r segments c o u l d be o b s e r v e d , was measured. The r e l a t i o n between B f and V f and t h e Young's 81 modulus were examined and g i v e n by t h e f o l l o w i n g e x p r e s s i o n E ' f _ , / f m i n where, K: c o n s t a n t 2 B = K £ ? (55) V f n i l- n i s t h e minimum f i b e r volume f r a c t i o n which must be exceeded t o s t r e n g t h e n t h e c o m p o s i t e and e x p r e s s e d i n Eqn. 7. Combining Eqn. 55 and 7, the f o l l o w i n g e x p r e s s i o n i s o b t a i n e d . ( o c - V m°"muts^^ K , 2 Bf = — ( crf - c r m C l t s - o-m) (56) I f we assume cr^* i s c o n s t a n t , t h e r i g h t hand s i d e o f t h i s e q u a t i o n i s c o n s t a n t . T h i s means t h a t t h e e l a s t i c e nergy n e c e s s a r y t o i n c r e a s e t h e s t r e s s i n t h e specimen from V m c r t s t o t h e u l t i m a t e s t r e n g t h o f t h e specimen i s always c o n s t a n t . T h i s e n e r g y i s s c h e m a t i c a l l y shown as t h e hatched a r e a i n F i g . 47. I f we assume t h e t h e o r e t i c a l a v e r a g e b v a l u e v a r i e s d i r e c t l y as B^, we can w r i t e the f o l l o w i n g e x p r e s s i o n b = £' E c (57) 2 ( V W 2 where, K': c o n s t a n t The p r o p o r t i o n a l c o n s t a n t K' i n t h i s e q u a t i o n can be c a l c u l a t e d u s i n g t h e b v a l u e s o b t a i n e d f o r t h e h i g h e r c o m p o s i t e s . Then we can c a l c u l a t e b v a l u e s f o r d i f f e r e n t V f u s i n g t h e K' c o n s t a n t . The r e s u l t o f K' c a l c u l a t i o n i s t a b u l a t e d i n T a b l e 11. T a b l e 11. Observed T u t s V a l u e s and C a l c u l a t i o n R e s u l t s o f K' Specimen V f i n c h n b i n c h K 1 (1 b" 1 i n c h 3 ) 601T4 #17 0.145 7 x 1 0 " 3 2.0 14.0 x l O " 3 8.74 x l O " 1 2 201T6 #31 0.17 2.5 x 1 0 " 3 1.6 4.05 x 1 0 " 3 4.17 x 1 0 " 1 2 7178T6 #38 0.138 2.0 x 1 0 " 3 2.4 4.8 x 1 0 " 3 1.98 x 1 0 " 1 2 83 IV-2-v. E v a l u a t i o n o f U l t i m a t e T e n s i l e S t r e n g t h o f Composites by P r o p a g a t i v e F i b e r F a i l u r e Model The f i b e r f a i l u r e zones s t a r t t o grow a t t h e s t r e s s c o n c e n t r a t e d a r e a s or t h e d e f e c t i v e a r e a s i n t h e specimen. They keep growing l a r g e r g r a d u a l l y u s i n g the energy which i s p r o v i d e d from t h e a p p l i e d l o a d u n t i l one o f them becomes l a r g e enough t o s a t i s f y t h e e n e r g y c r i t e r i o n o b t a i n e d i n f o r m e r s e c t i o n s . Then t h e f i b e r f a i l u r e i s a c c e l e r a t e d and t h e s t r e n g t h o f t h e c o m p o s i t e d e c r e a s e s q u i c k l y . Such a p o i n t must c o r r e s p o n d t o t h e u l t i m a t e s t r e n g t h . o f the specimen. An a t t e m p t was made t o c a l c u l a t e t h e u l t i m a t e t e n s i l e s t r e n g t h o f c o m p o s i t e s f r o m t h e e q u a t i o n s , w i t h t h e e s t i m a t e d v a l u e s o f zone t h i c k n e s s , b, and a v e r a g e t r a n s f e r l e n g t h T u t s i n t h e l a s t s e c t i o n . By f i x i n g t h e r a t i o o f t h e zone l e n g t h , a » and t h e specimen w i d t h , w, a t 0, 0.03, 0.05 and 0.10, t h e s t r e n g t h cr o f 601 T4 and 201 T6 c o m p o s i t e s were c a l c u l a t e d . In t h e c a s e o f 7178 T6 c o m p o s i t e s , t h e ° / w r a t i o s , 0, 0.03 were a d o p t e d f o r t h e c a l c u l a t i o n . T a b l e 1 2 — 1 5 show n u m e r i c a l v a l u e s o f t h e p a r a m e t e r s which were nfecessary f o r t h e c a l c u l a t i o n s and the c a l c u l a t e d r e s u l t s . These r e s u l t s were superimposed on t h e e x p e r i m e n t a l d a t a i n F i g . 20 — 22. The t h e o r e t i c a l c u r v e s r e s u l t i n g from the p r e s e n t model a r e i n v e r y much b e t t e r agreement w i t h t h e e x p e r i m e n t a l r e s u l t s t h a n i s t h e c a s e f o r t h e " r u l e o f m i x t u r e " c u r v e , i n s p i t e o f t h e c o n s i d e r a b l e s c a t t e r o f d a t a . E s p e c i a l l y i n the c a s e o f t h e bundle s t r u c t u r e c o m p o s i t e s o f 7178 T6 a l l o y , t he improve- ment c a n n o t be e x p l a i n e d by t h e " r u l e o f m i x t u r e " i n which t h e volume f r a c t i o n i s t h e o n l y one s t r e n g t h c o n t r o l l i n g p a r a m e t e r . The d i f f e r e n c e among e x p e r i m e n t a l d a t a r e p o r t e d by f o r m e r workers might T a b l e 12. C a l c u l a t i o n o f S t r e n g t h o f 601T4 Composites °/ w Op ksi = 0.17 V f " 0.15 V f = 0.10 V f = 0.06 c rk s i CT f oksi c rks i CJ f oksi c^ksi Cf Q ks i c rks i 0 238.0 0.03 185.3 0.05 150.6 0.10 116.1 55.4 46.3 42.15 35.3 244.5 204.9 183.4 145.0 52.0 45.8 42.6 37.1 261.0 42.3 251.1 41.0 244.6 40.2 230.1 38.4 273.0 33.3 272.5 33.0 272.1 32.4 272.0 32.0 E c x l 0 6 p s i 16.8 16.0 14.0 12.4 W1O3PS1 65.9 60.3 46.2 34.9 / T u t s 0.67 0.90 2.85 (19.69V / w 0.02 0.028 0.089 (0.613*) E f = 50 x 1 0 6 p . s . i . , E m = 10 x 1 0 6 p . s . i . w = 0.225 i n c h c r ^ = 3 0 0 x 1 0 3 p . s . i . c r * = 18 x 1 0 3 p . s . i . c r m u t s = 32 x 1 0 3 p . s . i . T u t s = 7.0 x 1 0 _ 3 i n c h K' = 8.74 x 1 0 " 1 2 i n c h 3 I b _ 1 V f m i n = 0.0446 t ; g a u g e l e n g t h of the s p e c i m e n . T a b l e 13. C a l c u l a t i o n o f S t r e n g t h o f 20TT6 Composites V f = 0.15 V f " 0.125 V f = 0.10 V f " 0.06 °/ c r k s i C T f o k s i c r k s i c r f o k s i c r c k s i c r f o k s i c r k s i 0 262.1 80.1 269.2 75.6 276.0 70.8 285.4 62.2 0.03 188.0 68.8 226.3 70.0 257.1 68.6 281.0 61.8 0.05 151.5 63.5 201.8 66.9 245.6 67.3 279.3 61.5 0.10 82.4 54.2 150.8 60.8 219.4 64.4 281.6 61.2 E c x l 0 ° p s i b / T u t s 16 85.8 1.07 0.012 15 79.5 1.67 0.0186 14 73.2 3.09 0.034 12.5 63.1 22.37 0.249 E f = 50 x 1 0 6 p s i , E m = 10 x 1 0 6 p s i , w = 0.225 i n c h c r = 3 0 0 x 1 0 3 p s i ^ = 4 8 x 1 0 P s j . C 7 m u t s = 60 x 103 p s i , T u t s = 2.5 x 1 0 - 3 ^ K' = 4.17 x 10"'^ i n c h 3 lb-1 V f m i n = 0.0385 00 T a b l e 14. C a l c u l a t i o n o f S t r e n g t h o f 7178 T6 Composites v f - 0.15 V f = 0.125 V ; 0.10 u/ 3 3 xw O- f oxl0°psi c T x l C T p s i . ^ x l O ^ s i 3 c r x l O p s i 3 c r f o x l 0 p s i c r x l 0 3 p s i 0 263.5 87.1 271.6 83.0 278.7 78.3 0.03 174.3 73.6 221.3 76.4 261.6 76.2 E c x l 0 6 p s i 16 15 14 x l 0 3 p s i crm r 92.6 86.5 80.4 b / T u t s 0.94 1.66 3.95 b / 0.0084 0.015 0.035 E f = 5 0 x 1 0 6 p s i E = m l O x l O 6 p s i w = 0.225 i n c h ° f u t s = 300x10 3 psi °"m* = 5 6 x l 0 3 p s i c r m u t s = 74.5x10 3 p s i T u t s = 2 . 0 x l . 0 " 3 i n c h V f • = 0.0581 K' = 1 . 9 8 x l 0 " 1 2 i n c h 3 l b " 1 ca T a b l e 15. C a l c u l a t i o n o f S t r e n g t h o f 7178 T6 Bundle S t r u c t u r e Composites V f = 0.19 V 0.15 V f = 0.10 °/ 7 7 7w < ^ o x l 0 p s i CTxIO p s i C r o X l 0 3 p s i c r x l O 3 p s i c r Q x l 0 3 p s i 3 c r x l O p s i 0 281.6 98.9 0.03 203.6 83.7 289.3 258.2 91.0 284.0 85.8 271.0 78.8 77.1 E c x l 0 6 p s i 17.6 16 14 ^ c r m x l 0 3 p s i 102.4 92.6 80.4 b / T u t s ° - 5 0 0.94 3.95 b / w 0.000225 0.0084 0.0035 E f = 5 0 x l 0 6 p s i E m = 1 0 x 1 0 6 p s i w = 0.225 i n c h C f u t s = 3 0 0 x 1 0 3 p s i c r * = 5 6 x l 0 3 p s i " k i t s = 7 4 . 5 x l 0 3 p s i T u t s = 2 x l 0 " 3 i n c h V f m. n = 0.0581 K' = 1 . 9 8 x l 0 " 1 2 i n c h 3 l b _ 1 ^ = 0.85* h= 1 2 x 1 0 ~ 3 i n c h D CO ( + T h i s v a l u e was e s t i m a t e d from F i g . 15) 8 8 be a l s o u n d e r s t o o d by t h i s t h e o r y . The c o m p o s i t e s f a b r i c a t e d by t h e i n f i l t r a t i o n t e c h n i q u e showed much h i g h e r f i b e r s t r e n g t h e n i n g e f f i c i e n c y t han by the o t h e r f a b r i c a t i o n t e c h n i q u e s , such as t h e c h e m i c a l vapour depos- i t i o n method. The c o m p o s i t e s f a b r i c a t e d by t h e i n f i l t r a t i o n p r o c e s s ore t h o u g h t t o p o s s e s s the b u n d l e s t r u c t u r e d i s t r i b u t i o n i n e v i t a b l y . I t was found t h a t n o t o n l y t h e f a c t o r , V f , used i n t h e " r u l e o f m i x t u r e " b u t a l s o o t h e r new f a c t o r s , such as E c , t h e f i b e r d i s t r i b u t i o n , and the zone t h i c k n e s s , 2b, have an i n f l u e n c e on t h e s t r e n g t h o f c o m p o s i t e s . The d e f o r m a t i o n c h a r a c t e r i s t i c s o f t h e m a t r i x , t h e f i b e r d i a m e t e r , and t h e f i b e r s p a c i n g a r e t h o u g h t t o c o n t r o l t h e zone t h i c k n e s s , 2b. L i s t e d below a r e some problems t h a t s t i l l r e m a i n , c o n c e r n i n g t h e p r e s e n t model. 1) The s h e a r s t r e s s , T , was assumed t o have t h e same v a l u e i n t h e r e g i o n o u t s i d e and i n s i d e o f t h e zone, because t h e work h a r d e n i n g e f f e c t o f t h e m a t r i x was n e g l e c t e d . The a c t u a l s t r e s s s t r a i n c u r v e o f t h e m a t r i x a l l o y does show work h a r d e n i n g . 2) The p r e s e n t e q u a t i o n s were o b t a i n e d , assuming t h e f i b e r f a i l u r e zone has a h a l f e l l i p t i c s hape. T h i s e q u a t i o n c a n n o t be a p p l i e d when t h e h a l f zone t h i c k n e s s i s l a r g e r t h a n t h e l e n g t h ( b > a ) . The c a l c u l a t e d c u r v e s f o r l o w e r v a l u e s a r e i n c o r r e c t . These p a r t s a r e shown i n d o t t e d l i n e s . 3) Some a m b i g u i t y e x i s t s i n t h e method t o o b t a i n a v e r a g e t r a n s f e r l e n g t h , a v e r a g e number o f f r a g m e n t s and t h e zone t h i c k n e s s . 4 ) We c a n n o t o b t a i n t h e s t r e n g t h o f c o m p o s i t e s f r o m t h i s model u n c o n d i t i o n - a l l y as l o n g as t h e e x a c t v a l u e s o f t h e zone l e n g t h , a » a t t h e a c c e l e r a t i n g p o i n t a r e not known. 89 IV-3. C h a r a c t e r i s t i c s o f Powder S l i p I n t e r p r e t a t i o n Method I t has been v e r y d i f f i c u l t t o f a b r i c a t e g r a p h i t e f i b e r r e i n f o r c e d metal c o m p o s i t e s because o f t h e s m a l l f i b e r d i a m e t e r . In t h e p r e s e n t work, a v e r y u n i q u e p r o c e s s was d e v e l o p e d i n o r d e r t o make u n i f o r m l y d i s t r i b u t e d f i b e r c o m p o s i t e s ; however, some problems s t i l l r e m a i n . The f o l l o w i n g c h a r - a c t e r i s t i c s o f t h i s p r o c e s s can be p o i n t e d o u t . 1) Blended powders o f d i f f e r e n t e lements c a u s e t h e s c a t t e r o f m a t r i x com- p o s i t i o n i n t h e g r e e n c o m p o s i t e s , because each element powder has a d i f f e r e n t s e t t l i n g speed i n t h e p r o c e s s . I f a l l o y powders c an be used, t h i s problem w i l l be s o l v e d . 2) E f f e c t i v e i n t e r p e n e t r a t i o n i s dependent on t h e r e l a t i v e s i z e s o f f i b e r s and powder p a r t i c l e s . The more n e a r l y equal t h e s e d i m e n s i o n s a r e , t h e h i g h e r t he volume f r a c t i o n t h a t can be made. 3) T h i s p r o c e s s can be a p p l i e d t o f a b r i c a t e c o m p o s i t e s o f many o t h e r f i b e r - metal systems because t h e w e t t i n g p r o p e r t y o f t h e two components i s n o t n e c e s s a r y f o r t h i s p r o c e s s . 4) T h i s p r o c e s s i s more s u i t a b l e t o produce c o m p o s i t e s o f l a r g e s t r u c t u r a l components than a r e t h e o t h e r p r o c e s s e s such as i n f i l t r a t i o n and c o a t i n g , because t h e s i z e o f a f i b e r b u n d l e which i s p r e p a r e d p r i o r t o t h e o p e r a t i o n o f t h i s p r o c e s s , can be i n c r e a s e d w i t h o u t any p r o b l e m s . In t h e c a s e o f t h e i n f i l t r a t i o n and c o a t i n g p r o c e s s e s , t h e s i z e o f a bun d l e f o r the o p e r a t i o n i s l i m i t e d . The c o m p o s i t e w i r e s have t o be f i r s t f a b r i c a t e d p r i o r t o h o t p r e s s i n g t o f a b r i c a t e t h e c o m p o s i t e s t r u c t u r e . 5) On t h e o t h e r hand, i t i s d i f f i c u l t t o f a b r i c a t e t h e c o m p o s i t e s o f bund l e s t r u c t u r e which c an be e x p e c t e d t o have h i g h e r s t r e n g t h t h a n u n i f o r m l y 90 d i s t r i b u t e d c o m p o s i t e s a c c o r d i n g t o t h e p r e s e n t t h e o r y . The i n f i l t r a t i o n p r o c e s s seems to have a g r e a t e r advantage t h a n t h e p r e s e n t p r o c e s s from t h i s p o i n t o f view. 91 V SUMMARY AND CONCLUSIONS 1) A new f a b r i c a t i o n t e c h n i q u e has been d e v e l o p e d t o f a b r i c a t e g r a p h i t e f i b e r r e i n f o r c e d aluminum a l l o y c o m p o s i t e s o f 5% — 17% f i b e r volume f r a c t i o n s , u s i n g metal powder s l i p and c o n t i n u o u s g r a p h i t e f i b e r s . 2) The s t r e n g t h o f t h e s e c o m p o s i t e s i s l o w e r than t h e " r u l e o f m i x t u r e " v a l u e as o t h e r workers have r e p o r t e d p r e v i o u s l y . 3) A " f i b e r f a i l u r e zone" p r o p a g a t i o n model has been proposed and v e r i f i e d by o b s e r v a t i o n s o f f i b e r f r a c t u r e b e h a v i o u r . 4) An e n e r g y c r i t e r i o n has been f o r m u l a t e d f o r t h e a c c e l e r a t e d p r o p a g a t i o n o f t h e zone i n t h e specimen, and t h e u l t i m a t e t e n s i l e s t r e n g t h o f t h e s e c o m p o s i t e s i s t h o u g h t t o c o r r e s p o n d t o t h i s a c c e l e r a t i n g p o i n t . The e x p e r - i m e n t a l s t r e n g t h d a t a shows b e t t e r c o r r e l a t i o n w i t h t h i s p r o p a g a t i v e f i b e r f a i l u r e model t h a n t h e " r u l e o f m i x t u r e " model. 5) T h i s model s u g g e s t s t h e p o s s i b i l i t y o f i m p r o v i n g t he s t r e n g t h by p r o d u c i n g a b u n d l e s t r u c t u r e f i b e r d i s t r i b u t i o n i n t h e c o m p o s i t e i n s t e a d o f a u n i f o r m f i b e r d i s t r i b u t i o n . 6) T h i s model shows t h a t , i n a d d i t i o n t o f i b e r volume f r a c t i o n , t h e zone t h i c k n e s s i s a l s o a s t r e n g t h c o n t r o l l i n g f a c t o r . The zone t h i c k n e s s seems t o be r e l a t e d i n d i r e c t l y w i t h o t h e r f a c t o r s such as t h e f i b e r d i a m e t e r , f i b e r s p a c i n g , d e f o r m a t i o n p r o p e r t y o f t h e m a t r i x , and t h e m a t r i x - f i b e r bond s t r e n g t h . 92 VI SUGGESTION FOR FUTURE WORK Some l i n e s o f f u t u r e i n v e s t i g a t i o n can be s u g g e s t e d f r o m the d i s - c u s s i o n o f the p r e s e n t work. 1) In o r d e r t o o b t a i n t h e a v e r a g e zone t h i c k n e s s p r o p e r l y , t h e d i s t r i b u t i o n o f s t r a i n i n t h e m a t r i x has t o be measured. 2) A more e x a c t m a t h e m a t i c a l t r e a t m e n t f o r the energy change due t o t h e zone f o r m a t i o n has t o be performed. 3) A method t o o b t a i n t h e e x a c t a v e r a g e l e n g t h s o f f i b e r f r a g m e n t s i n t h e zone has t o be d e v e l o p e d . 4) The zone l e n g t h change d u r i n g t h e t e n s i l e t e s t has t o be measured i n o r d e r t o know t h e f a c t o r s which i n f l u e n c e i t . 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