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Fracture toughness of resin based composites 1982

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FRACTURE TOUGHNESS OF RESIN BASED COMPOSITES by HEMAGUPTHA DHARMARAJ GOONETILLEKE B.Sc.(Eng), The University of Sri Lanka, 1973 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Metallurgical Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1982 © Hemaguptha Dharmaraj Goonetilleke, 1982 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of M e t a l l u r g i c a l Engineering The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 D a t e October 15. 1982, DE-6 (3/81) ABSTRACT A study has been made of several composite systems based on polyester resin matrix, investigating the influence of various parameters on their fracture behaviour. This included the effects of such variables as the specimen geometry, fibr e and f i l l e r volume fractions and the p a r t i c l e size of heavy metal dispersions within the resin i t s e l f or the resin reinforced with glass f i b r e s . Different methods of fabrication have been attempted and tests were carried out on each polyester p a r t i c l e and/or f i b r e dispersion combination in order to examine their fracture resistance. In two phase composite systems, the powder dispersions showed less influence on the resulting fracture toughness than the fibre reinforcement. The toughness of three phase p a r t i c l e f i l l e d f i b r e reinforced composites were also primarily governed by the f i b r e reinforcement. Mechanisms which may have contributed to the fracture behaviour of these composites have been considered. The formation of microcracks due to residual shrinkage stresses and the interactions of the crack front with dispersed p a r t i c l e s may lead to increased fracture toughness in p a r t i c l e f i l l e d composites. The creation of new fracture surfaces which includes f i b r e debonding was found to be mainly responsible for the fracture behaviour of f i b r e reinforced composites. Although i i i these mechanisms have their individual contributions to the fracture toughness of three phase composites, the addition of p a r t i c l e s at high volume fractions may have a detrimental effect on the toughening character of f i b r e reinforcement. i v TABLE OF CONTENTS. Page Abstract i i Table of Contents iv L i s t of Figures v i i L i s t of Tables x Acknowledgement xi Chapter 1 . Introduction 1 1.1 General Background 1 1.2 Previous work 4 1.2.1 P a r t i c l e reinforced composites 5 1.2.2 Fibre reinforced composites 16 1.2.3 Fibre & p a r t i c l e reinforced composites . 30 1.3 Present work 33 1.3.1 Experimental methods 33 1.3.2 Materials used 36 2. Cast Bending Beams 38 2.1 Preparation of composites 39 V 2.2 Fracture toughness testing 43 2.2.1 Specimen preparation 43 2.2.2 Testing & measurements 43 2.2.3 Calculation & discussion of results .... 45 2.2.4 Microscopic observations 60 2.2.5 Compliance method of fracture toughness determination 65 2.3 Determination of Young's modulus 74 3. Injection Moulded Bending Beams 77 3.1 Preparation of composites 78 3.1.1 Description of equipment 78 3.1.2 Specimen preparation 80 3.2 Fracture toughness testing 81 3.2.1 Testing & measurements 82 3.2.2 Calculation & discussion of results .... 83 4 . Cast Compact Tension specimens 86 4.1 Preparation of composites 87 4.2 Fracture toughness testing 88 4.2.1 Specimen preparation 88 4.2.2 Testing & measurements 88 4.2.3 Calculation & discussion of results .... 90 4.2.4 Microscopic observations 98 4.3 Charpy impact testing 98 4.3.1 Specimen preparation 98 4.3.2 Testing & measurements 100 v i 4.3.3 Calculation & discussion of results .... 100 5. Discussion 103 5.1 Fracture toughness of p a r t i c l e f i l l e d polyester 104 5.2 Fracture toughness of f i b r e reinforced polyester 121 5.3 Fracture toughness of p a r t i c l e & fibre reinforced polyester 127 6. Summary and Conclusions 131 References 136 Appendix A 143 Appendix B 149 Appendix C 153 Appendix D. 167 Appendix E 175 Appendix. F 177 V I 1 LIST OF FIGURES Figure Page 1. The mould used for fabrication of cast specimens 40 2. The dimensions of the bending beam fracture toughness test specimens used 42 3. A t y p i c a l load-displacement curve (type I) 46 4. A t y p i c a l load-displacement curve (type II) 47 5. Bending beam fracture toughness of coarse iron and coarse nickel composites 50 6. Bending beam fracture toughness of fin e - n i c k e l and coarse iron plus fine nickel composites 51 7. Bending beam fracture toughness of glass reinforced composites 52 8. bending beam fracture toughness of glass reinforced nickel f i l l e d composites 55 9. Bending beam fracture toughness of glass reinforced iron f i l l e d composites 56 10. Bending beam fracture toughness of glass reinforced iron f i l l e d composites 57 11. Bending beam fracture toughness of glass reinforced iron f i l l e d composites 58 12. Comparison of Kq values of glass reinforced iron v i i i f i l l e d composites 59 13. Micrographs showing the nature of p a r t i c l e d i s t r i b u t i o n in powder composites 61 14. Micrographs showing the nature of fibr e and-particle d i s t r i b u t i o n in fibr e reinforced composites 62 15. Fractured surfaces of powder composites 63 16. Fractured surfaces of f i b r e reinforced composites 64 17. A t y p i c a l experimental compliance plot for a glass reinforced composite 69 18. A t y p i c a l experimental compliance plot for a glass reinforced nickel f i l l e d composite 70 19. Comparison of experimental values of fracture toughness of glass f i b r e composites with the corresponding compliance values 72 20. Comparison of experimental values of fracture toughness of glass reinforced nickel f i l l e d composites with the corresponding compliance values 73 21. A detailed view of the inje c t i o n moulding unit 79 22. Frcture toughness of injection moulded bend beam specimens 85 23. The dimensions of the compact tension specimen used 89 24. Compact tension fracture toughness of coarse iron and coarse nickel composites 92 25. Compact tension fracture toughness of fine nickel composites 93 26. Compact tension fracture toughness of coarse iron plus fine nikel composites 94 ix 27. The effect of curing time on fracture toughness of pure polyester 97 28. The dimensions of the charpy impact test specimens 99 29. The impact energy of iron powder composites 101 30. A plot of the square of the average c r i t i c a l stress intensity factor of coarse iron composites against p a r t i c l e volume fraction 108 31. P r i n c i p a l shrinkage stresses around a r i g i d c y l i n d r i c a l inclusion 110 32. A comparison of the fracture toughness test results of coarse iron and coarse nickel composites obtained for the two specimen geometries 116 33. A comparison of the fracture toughness test results of fine nickel composites obtained for the two specimen geometries 117 34. A comparison of the fracture toughness test results of coarse iron plus fine nickel composites obtained for the two specimen geometries 118 35. A comparison of the experimental values of fracture energy of glass fib r e composites with theoretical models 126 36. Radial and circumferencial stress d i s t r i b u t i o n s in a disc flywheel Vs. r a t i o of inner to outer r a d i i 146 37. Injection moulding unit 178 X LIST OF TABLES Table Page 1. Mechanical properties of some particulate composite systems 7 2. Summary of p a r t i c l e f i l l e d composite fracture 15 3. Fracture toughness test results of some glass reinforced p l a s t i c s 26 4. E l a s t i c moduli of some fi b r e composites 76 5. Models of energy absorption 123 xi ACKNOWLEDGEMENT I wish to express my sincere gratitude to Professor E.Teghtsoonian for his useful advice and guidance throughout the course of thi s study. My thanks are also due to Professor J.S.Nadeau for his helpful advice and encouragement. I would also l i k e to extend a personal note of thanks to Mr. Jim Hogan for his assistance in setting up the injection moulding unit. Thanks are also extended to my fellow graduate students and faculty members in the Department of Metallurgical Engineering. The assistance of the technical staff of thi s department, in pa r t i c u l a r Mr. Roger C Bennett, is greatly apprec iated. I am also grateful to the Department of Metallurgical Engineering, University of B r i t i s h Columbia., for providing f i n a n c i a l support in the form of a research assistantship. 1 I. INTRODUCTION 1.1 GENERAL BACKGROUND;- Fibre reinforced composites have many advantages over the conventional materials. The high strength attainable in fine f i b r e s of some materials provided the necessary technological background for early development of composite materials. Large numbers of these fibres are bonded together in suitable matrix materials to form useful structural materials. In addition to being useful in holding the fibres together the matrix protects them from corrosive environments and a s s i s t s in transfering the stresses from the matrix to the f i b r e . Applications of these fibr e reinforced materials, in p a r t i c u l a r the resin matrix composites, are very common in the pipeline and building industries as well as in a i r , ground and sea transportation i n d u s t r i e s . 1 Rigid particulate f i l l e r s are also often added to matrix materials to increase s t i f f n e s s and abrasion resistance as well as to reduce cost and shrinkage. The mechanical behaviour of the resulting composites have been studied by a number of researchers over the past 10 y e a r s . 2 " 6 This interest is due mainly to the increasing use of these materials in such diverse applications as furniture, high speed cutting/grinding 2 tools, high-temperature structural materials and in deep submergence v e s s e l s . 7 " 8 The concept of strengthening of a matrix by the introduction of p a r t i c l e s of a less compliant phase is of very general application and used extensively in p l a s t i c s to achieve an increase in strength and an increase in e l a s t i c modulus and wear resistance. Interest has been shown recently in the use of three phase composites containing both fibres and p a r t i c l e s together in suitable matrix materials. P a r t i c l e s of a dense material are often added to fib r e reinforced matrices in order to control the weight d i s t r i b u t i o n or increase the density and s t i f f n e s s of the composite. A c l a s s i c a l application of this type of composites is in the multirim super flywheels designed for high s p e c i f i c i n e r t i a l energy storage. 9 As suggested by Rabenhorst 1 0 a multirim composite flywheel capable of storing very large amounts of energy per unit of mass can be constructed by adding increasing amounts of a dense f i l l e r , such as lead powder, to the filament wound inner rings. A brief account of the development of this idea is given in Appendix A. A large fraction of low cost f i l l e r ( 40% by weight ) is sometimes used to reduce the overa l l cost of automotive type sheet moulding compounds which are premixtures of short length fibres and partly cured r e s i n s . 1 1 A widely used f i l l e r material for these compounds is calcium carbonate. A variety of other additives, comprising only a small volume fraction of the 3 composite, help control the chemical reaction, improve the face smoothness and f i r e resistance of many other reinforced polymers which are used for the manufacture of building mater i a l s . 1 The mechanical properties of a composite may bear l i t t l e r e l a t i o n to those of the components, even though the components retain their i n t e g r i t y within the composite. In order to appreciate the potential benefits to be gained from three phase composites, i t is necessary to be aware of the resulting properties which account for their use in load- bearing applications. Despite the published results of an a l y t i c a l and experimental work on several commercial systems, investigating the effects of various components, three phase composites have received much less attention than other composite materials. There is c l e a r l y a need for further study of the influence of f i l l e r s and fibres on the mechanical behaviour of these materials, in particular the resin based composites. The present work is an attempt to develop such a composite containing a dense material, and help c l a r i f y the re l a t i v e influence of f i l l e r and fibres on fracture behaviour of these composites. In the present work, a study has been made of several composite systems based on polyester resin matrix, investigating the influence of various parameters on their fracture behaviour. This included the effects of such variables as the d i s t r i b u t i o n , volume fraction and the p a r t i c l e size of 4 heavy metal dispersions within the resin i t s e l f or the resin reinforced with glass f i b r e s . Various methods of fabrication have been attempted and tests were car r i e d out on each polyester p a r t i c l e and/or fibr e dispersion combination in order to examine their fracture resistance. The fracture toughness, which is considered to be one of the most c h a r a c t e r i s t i c properties that influence the behaviour of these b r i t t l e composite systems in service, was determined. 1.2 PREVIOUS WORK:- It has long been recognized that composite materials possess many a t t r a c t i v e properties which make them very promising in a large number of present-day applications. Lighter but much stronger components for a i r c r a f t , automobiles, buildings, pipe lines and machinery are widely produced nowadays with fibre reinforced composite materials. These materials vary s i g n i f i c a n t l y in terms of their structure and the properties derived through them. With the development of type E glass f i b r e s , the interest in modern resin matrix composites has increased rapidly over the past 40 years and s i g n i f i c a n t progress has been made in this area of composite technology. P l a s t i c s , being low in d e n s i t y , 1 6 appear to be one of the useful matrix materials suitable for lightweight composites. The incorporation of reinforcing materials such as 5 p a r t i c l e s and/or fibres of a di f f e r e n t phase can enhance the resistance of these materials to crack propagation. In the following sections, a review of the work done on these materials is presented with reference to many other b r i t t l e systems of similar kind. Two phase systems containing either p a r t i c l e s or the fibres in a continuous b r i t t l e matrix, and three phase systems in which both the p a r t i c l e s and fibres are incorporated together are discussed separately. 1.2.1 P a r t i c l e Reinforced Composites;- Many publications have appeared during the past few years, on the eff e c t of particulate f i l l e r s on the mechanical properties of b r i t t l e m a t e r i a l s . 2 " 8 The addition of p a r t i c l e s very often enhances the mechanical properties, in p a r t i c u l a r the resistance to crack propagation, strength and modulus. Table I l i s t s t y p i c a l mechanical properties of two matrix materials and their properties after the addition of fine p a r t i c l e s of another m a t e r i a l . 1 7 " 1 9 The extent of the influence depends upon the pa r t i c u l a r composite system being considered and the nature of the dispersion, v i z ; the average p a r t i c l e size, i n t e r p a r t i c l e spacing and the volume f r a c t i o n , which in turn are int e r - related through an equation given by Fullman 2 0 6 d = 2D(1H>) 3* (1.1) where, d = average i n t e r p a r t i c l e spacing D = average p a r t i c l e s i z e <j) = volume f r a c t i o n of p a r t i c l e s Although t h i s r e l a t i o n s h i p holds t r u e f o r any p a r t i c u l a t e system, the e f f e c t s of these v a r i a b l e s on the p r o p e r t i e s mentioned above depend p r i m a r i l y upon the p a r t i c u l a r composite system being c o n s i d e r e d . Systems c o n t a i n i n g r i g i d p a r t i c l e d i s p e r s i o n s i n a g l a s s matrix have been the o b j e c t of s p e c i a l c o n s i d e r a t i o n as model systems to understand the f r a c t u r e behaviour of p a r t i c l e f i l l e d composites. F r a c t u r e e n e r g i e s and c r i t i c a l s t r e s s i n t e n s i t y f a c t o r v a l u e s have been determined e x p e r i m e n t a l l y f o r s e v e r a l model systems u s i n g s t a n d a r d specimen c o n f i g u r a t i o n s . I t has been shown 1 7 t h a t the f r a c t u r e energy, which i s the amount of energy r e q u i r e d a t the moment of crack i n i t i a t i o n to form a u n i t area of f r a c t u r e s u r f a c e , c o u l d be i n c r e a s e d s i g n i f i c a n t l y by the a d d i t i o n of p a r t i c l e s . T h i s i n c r e a s e i s shown to be dependent iipon both the volume f r a c t i o n and the average 7 Table I Mechanical Properties of Some Particulate Composite systems;- Mater i a l Fracture energy J/m2 Strength (MPa) E l a s t i c Modulus (GPa) Ref. No. Glass(Matr ix) 6.28 93.8 80.6 Glass+40 v o l % 3.5 ym A l 2 0 3 p a r t i c l e s 12.80 1 67.5 1 44.0 17,18 Si 3N a(Matrix) 69.20 654.3 306.8 Si 3N„+lO v o l % 5.0 ym SiC «• p a r t i c l e s Si 3N«+40 v o l % 5.0 ym SiC p a r t i c l e s 51 .00 18.60 577.9 390.3 317.8 352.3 1 9 Si 3N«+lO v o l % 32.0 Vm SiC p a r t i c l e s 94.70 390.3 . 317.8 p a r t i c l e size for a g l a s s - A l 2 0 3 system. 1 7 The effect of increasing the volume fraction or the p a r t i c l e size of A l 2 0 3 powder is to increase the fracture energy. For another system containing nickel spheres in a glass m a t r i x , 2 1 " 2 2 a marked increase in fracture energy has been 8 observed as the nickel volume fraction is increased. Fractographic observation of the g l a s s - A l 2 0 3 samples indicated a difference in fracture surface topography for low and high volume fraction composites. At low volume fractions, steps associated with most of the p a r t i c l e s , indicating interaction of the crack front with the p a r t i c l e s , have been observed. These steps become less d i s t i n c t at high volume fr a c t i o n s . A concept of crack front interaction with the second phase dispersion, which is consistent with the fracture behaviour of these systems has been developed by Lange 2 3 and Evans. 2"" 2 5 As the crack front meets an array of p a r t i c l e s present on the crack plane i t bows out between each pair of p a r t i c l e s increasing i t s t o t a l length before being driven through. The f r a c t i o n a l increase in crack front length per unit crack extension was shown to increase with decreasing i n t e r p a r t i c l e spacing, consistent with either an increase in volume fraction or a decrease in p a r t i c l e size (see Equation 1.1). This leads to an increase in fracture toughness, as additional energy is required to increase the length of the crack front. The fracture energy required to form a unit area of fracture surface can be expressed by a relationship of the form; 1 7 Y = Y 0 + F(D) ^ (1.2) 9 where, Y Q = s u r f a c e energy / u n i t area of f r a c t u r e s u r f a c e T = c r i t i c a l l i n e energy / u n i t l e n g t h of the c r a c k f r o n t d = average d i s t a n c e between the p a r t i c l e s The c r a c k f r o n t has a l i n e energy which depends on the a p p l i e d s t r e s s . The c r i t i c a l s t r e s s r e q u i r e d to propagate the crack d e f i n e s the c r i t i c a l v a lue of l i n e energy per u n i t l e n g t h of the crack f r o n t . T h i s value i s c o n s t a n t f o r a given m a t e r i a l , as i t i s g i v e n by the volume i n t e g r a l of the s t r a i n energy a d j a c e n t the crack f r o n t j u s t b e f o r e the atomic bonds are broken. An e s t i m a t e f o r T i n g l a s s f o r example i s g i v e n as 15 to 60 e r g s / c m . 2 3 F(D)[ 0 < F(D) .< 1 ] i s a d i m e n s i o n l e s s f u n c t i o n dependent on the average p a r t i c l e s i z e D, which r e f l e c t s the i n c r e a s i n g e f f e c t i v e n e s s of l a r g e r p a r t i c l e s i n p i n n i n g the c r a c k f r o n t and i n c r e a s i n g the f r a c t u r e r e s i s t a n c e . . I t i s c o n c e i v a b l e that f o r l a r g e r p a r t i c l e s a g r e a t e r amount of bowing should occur before the s t r e s s f i e l d s • i n f r o n t become l a r g e enough to cause the c r a c k f r o n t to break through. Thus, the. magnitude of F(D) i n c r e a s e s w i t h i n c r e a s i n g p a r t i c l e s i z e , c o n t r i b u t i n g more r e s i s t a n c e to c r a c k p r o p a g a t i o n . More i m p o r t a n t l y , the above r e s u l t suggests t h a t the i n t e r p a r t i c l e s p a c i n g i s a more s i g n i f i c a n t parameter than the volume f r a c t i o n i n f r a c t u r e 10 toughness d e t e r m i n a t i o n of a p a r t i c u l a t e composite. S u p p o r t i n g t h i s phenomenon i s the r e s u l t o f a t h r e e d i m e n s i o n a l f i n i t e element a n a l y s i s of s p h e r i c a l p a r t i c l e c o m p o s i t e s , 2 6 t h a t shows the s t r o n g dependence of i n t e r n a l s t r e s s d i s t r i b u t i o n of such m a t e r i a l s on i n t e r p a r t i c l e s p a c i n g . In the o r i g i n a l G r i f f i t h ' s theory of b r i t t l e f r a c t u r e , the s u r f a c e energy y Q i s i d e n t i f i e d as the main energy s i n k term. Thus, an i n c r e a s e i n t o t a l r e l a t i v e f r a c t u r e s u r f a c e area can a l s o be expected to i n c r e a s e the f r a c t u r e toughness. The presence of s u r f a c e steps and s u r f a c e roughness r e s u l t i n g from a p a r t i c l e d i s p e r s i o n i n c r e a s e s the f r a c t u r e s u r f a c e a r e a , and i n t u r n , the v a l u e of Y Q . I t has been shown 1 7 that f o r the g l a s s - A l 2 0 3 system the magnitude of y r e s u l t i n g from t h i s mechanism i s a p p r o x i m a t e l y 1.5 to 2.0 times the f r a c t u r e energy of g l a s s without a second-phase d i s p e r s i o n . Other mechanisms t h a t might be r e s p o n s i b l e f o r the i n c r e a s e d f r a c t u r e toughness of t h i s system have been excluded. These i n c l u d e the energy a b s o r p t i o n by t r a n s p a r t i c l e f r a c t u r e of the d i s p e r s e d phase and the c o n t r i b u t i o n of the f r i c t i o n between p a r t i n g f r a c t u r e s u r f a c e s . S i m i l a r c o n c l u s i o n s have been made in the p r e v i o u s l y mentioned S - g l a s s - N i system. F r a c t o g r a p h i c o b s e r v a t i o n s have i n d i c a t e d a l o c a l r e s i s t a n c e to c r a c k motion that has changed the crack front, c o n f i g u r a t i o n , 11 especially at low volume fractions. It has been s u g g e s t e d 2 1 " 2 2 that this impedance to crack motion was the major contribution to increased fracture toughness while a minor contribution could have resulted from surface roughness and surface step formation. However, as the nickel volume fraction increases a maximum in fracture energy i s reached. It has been proposed that the l o c a l crack front interaction may not be e f f e c t i v e in increasing the fracture toughness once t h i s maximum is exceeded when the p a r t i c l e s become too cl o s e l y spaced within the matrix. To date, published data on polymer composites show similar results and conclusions. Broutman and Sahu 2 7 have reported an increase in fracture energy with increasing volume fraction of glass p a r t i c l e s in glass- sphere f i l l e d polymeric composites, up to a maximum at around 20% volume fraction of p a r t i c l e s . These results are in p a r a l l e l with measurements of work- to-break in uniaxial t e n s i l e tests reported by Lavengood et a l 2 8 and Nicolais et a l , 2 9 " 3 0 though in fracture toughness or notched impact tests a lesser enhancement of toughness by glass p a r t i c l e s is expected. The results of a similar study on an epoxy- alumina trihydrate composite system by Lange & Radford 3 1 are also q u a l i t a t i v e l y consistent with t h i s mechanism of crack interaction. As the volume fraction of the p a r t i c l e dispersion increases, a s i g n i f i c a n t increase in fracture energy has been observed. When fracture energy values are plotted against the average i n t e r p a r t i c l e spacing an 1 2 increase in fracture energy is observed with decreasing p a r t i c l e spacing. Prior to the occurrence of a maximum, the increase in fracture energy is found to be greater, the larger the p a r t i c l e size. The t r a n s i t i o n from a fracture surface containing many cleavage steps to a surface that appeared almost p o l y c r y s t a l l i n e implies the continuous nature of crack propagation that may p r e v a i l at higher volume fractions, when crack pinning become unfeasible energetically. In contrast to these observations, recent work carried out in t h i s department by Godoy 3 2 on A l 2 0 3 f i l l e d epoxy has shown that the fracture toughness (or the c r i t i c a l stress intensity factor) of these, composites is independent of p a r t i c l e s i z e . The results of three-point bend tests and wedge loading tests show that this i s true irrespective of the specimen configuration employed. However, an increase in fracture toughness has been observed with increasing volume fraction of A l 2 0 3 p a r t i c l e s . Godoy maintains that this increase in fracture toughness is associated with increase in fracture surface area caused by surface roughness. In contrast, a model of linear dependence of fracture energy on volume fraction has been suggested for fine grained ceramics by Wahi et a l . 3 3 The fracture surfaces of fine grained A l 2 0 3 - T i C composite have not shown the c h a r a c t e r i s t i c wedge-shaped cleavage steps expected on 13 the b a s i s of the cra c k p i n n i n g model. In f a c t , the assumptions that l e a d to the crack i n t e r a c t i o n model imply t h a t the g r a i n s i z e of the m a t r i x i s smal l r e l a t i v e to the s i z e of the p i n n i n g p a r t i c l e s . In t h i s composite the g r a i n s i z e o f the A l 2 0 3 m a t r i x was comparable t o the average p a r t i c l e s i z e and l i t t l e i n t e r a c t i o n of the cra c k f r o n t w i t h the p a r t i c l e s c o u l d be expected. F r a c t o g r p h i c o b s e r v a t i o n s r e v e a l e d that T i C p a r t i c l e s mostly had a t r a n s p a r t i c l e f r a c t u r e . The average f r a c t u r e energy y of the composite can t h e r e f o r e be expected to l i e between the f r a c t u r e e n e r g i e s of the m a t r i x and the p a r t i c l e , v a r y i n g l i n e a r l y with the f r a c t i o n of the t o t a l f r a c t u r e s u r f a c e area o c c u p i e d by the p a r t i c l e s . The observed v a l u e s of the f r a c t u r e energy show a l i n e a r l y i n c r e a s i n g t r e n d w i t h i n c r e a s i n g volume f r a c t i o n . E x p e r i m e n t a l l y measured e l a s t i c modulus E of t h i s composite has a l s o been found to vary l i n e a r l y with the volume f r a c t i o n of the p a r t i c l e s . T h i s , and the mathematical interdependence of K , y and E suggest that the magnitude of K 2 i s a p p r o x i m a t e l y r e p r e s e n t e d by a l i n e a r f u n c t i o n of the volume f r a c t i o n . A g a in, the observed i n c r e a s e i n K has shown a very good agreement with t h i s model of l i n e a r dependence of K I C 2 o n volume f r a c t i o n . T h i s has a l s o been the e x p l a n a t i o n f o r the f r a c t u r e behaviour of a Si 3N„-SiC system s t u d i e d by L a n g e . 1 9 When the average p a r t i c l e s i z e was c l o s e to the g r a i n s i z e , l i t t l e , i f any, i n t e r a c t i o n of the c r a c k f r o n t 14 with the p a r t i c l e s was observed. Fracture energy was found to vary l i n e a r l y with the p a r t i c l e volume fraction except when the p a r t i c l e s were large. Crack interaction was considered to be a plausible mechanism only when the average p a r t i c l e size i s many times larger than the grain size of the matrix. Studies are s t i l l being made to understand in d e t a i l the fracture processes in particulate composite systems and establish quantitative expressions for more r e a l i s t i c predictions of their behaviour. Attempts have been made to v e r i f y the influence of such variables as the p a r t i c l e shape, 3"- 3 5 the i n t e r f a c i a l bond s t r e n g t h , 2 7 3 6 e l a s t i c and thermal expansion mismatch e t c . 3 6 " 3 7 on the mechanical properties of these materials. D i f f i c u l t y has been encountered in separating the effects of these variables. Besides, discrepancies between theoretical predictions and experimental data s t i l l continue to l i m i t our understanding of these materials. The p a r t i c l e f i l l e d composites discussed here and the physical processes which have been postulated to explain the fracture behaviour of these systems are b r i e f l y tabulated in Table I I. 15 Table II Summary of P a r t i c l e F i l l e d composite fracture;- Ma t r i x mater i a l F i l l e r Possible fracture c o n t r o l l i n g mechan i sms Variables which influence fracture Ref No. CERAMICS Glass Glass A1 20 3 Ni Crack front interaction plus surface roughness increases with VF and D 1 7 21 A1 20 3 TiC Transparticle fracture for smaller p a r t i c l e s depends on VF 33 Si 3N« SiC Crack front interaction for larger p a r t i c l e s increases with VF and D 34 POLYMERS Epoxy Polyester Glass Glass Crack front interact ion increases with VF and D 27 Epoxy A1 20 3 Surface Roughness increases with VF 32 Nomenclature:- VF = Volume Fraction of P a r t i c l e s D = P a r t i c l e Size 16 1.2.2 Fibre Reinforced Composites;- The c h a r a c t e r i s t i c s of a fibrous composite depend very much upon the properties of the fi b r e s and of the matrix, the nature of the i n t e r f a c i a l bond between them and the content and arrangement of fibres within the matrix. The properties of a finished composite, in pa r t i c u l a r the strength and the modulus, are to a great extent dictated by the same properties of the fibres and found to be proportional to the f i b r e volume f r a c t i o n . 3 8 " 3 9 Since a great majority of fibres are b r i t t l e , the strength values quoted for the fibres are generally the fracture strengths dependent on fracture energy, Young's modulus and the size of the largest flaw. The l a t t e r i s p a r t i c u l a r l y important as the average strength of a fibre i s determined by the presence of flaws of variable size, shape and orientation as well as by their frequency of occurrence. The interactions between fibres and matrix are very complex, and not f u l l y understood. Attempts have been made to e x p l a i n , " 0 " 4 2 the mechanics of the reinforcement processes by which fibres contribute strength, s t i f f n e s s and toughness to the matrices, in terms of several theories. These include the e l a s t i c stress transfer and s l i p mechanisms that can account for the composite strength and modulus, and several energy absorption processes for their toughness. These explanations are generally based on 17 simple models of aligned f i b r e composites and vary according to whether the matrix i s polymeric or metallic, eg., p l a s t i c deformation in metal matrices and f r i c t i o n a l s l i d i n g near the fi b r e ends in polymer and. ceramic matrices, are considered to be very s i g n i f i c a n t in composite strengthening. In view of the foregoing remarks, a word of comment i s thought to be appropriate here. Although the terms strength and toughness describe d i f f e r e n t properties, they are somewhat related. The term strength is often associated with the maximum load a given material can withstand before i t f a i l s by some means. Here, the mode of f a i l u r e may range from a gross p l a s t i c deformation to a complete macroscopic separation, or fracture due to i n i t i a t i o n , coalescence and growth of a defect in the material. The toughness, on the other hand, is related to the material's s e n s i t i v i t y . t o sharp cracks, and i s defined empirically as the minimum amount of energy required to create a unit area of fracture surface. It enables the f a i l u r e leads to be established for real engineering applications in service, when crack l i k e defects exist in the material. Many of the present day fibre composites are sensitive to sharp cracks and the resistance of these materials to b r i t t l e fracture through the propagation of sharp cracks is an important material property. Since the 18 present work is concerned with such composites and their fracture, the discussion here is mostly r e s t r i c t e d to those events that are involved in t h i s process. Although much work has been done to provide a n a l y t i c a l techniques, useful in achieving the desired strength and s t i f f n e s s in composite design," 1 r e l a t i v e l y l i t t l e progress has been made in the area of composite fracture. This i s partly due to the r e l a t i v e complexity of the f a i l u r e process resulting from the very nature of composite materials, their heterogeneity and anisotropy. In addition, the f l e x i b i l i t y in their design that has resulted in a wide variety of composite materials with a range of laminate geometries and lay-up angles, has demanded extensive studies be carr i e d out. It is l i k e l y that no unifie d approach has yet evolved from fracture mechanics pr i n c i p l e s to treat the subject of fibre composite fracture in general terms. However, an accurate a n a l y t i c a l treatment capable of characterizing their fracture behaviour i s essential i f these composites are to be designed for optimum toughness and used to their ultimate c a p a b i l i t i e s . One useful parameter that can establish the materials resistance to fracture is the fracture surface energy,Y; . Different methods of measuring Y> y i e l d conceptually d i f f e r e n t values of fracture energy, namely the G r i f f i t h s fracture surface energy Y-J- and the work of fracture Y ^ . Y T is based on the G r i f f i t h s c r i t e r i o n for 19 u n s t a b l e c r a c k p r o p a g a t i o n and i s determined by the s m a l l amount of i n i t i a l c rack p r o p a g a t i o n ; Y = _ I i v F (1.3) YI 2 3a where, V F = e l a s t i c energy s t o r e d i n the m a t e r i a l at the p o i n t of r a p i d crack p r o p a g a t i o n , a = area of the i n i t i a l crack p l a n e . The work of f r a c t u r e , Y F , on the otherhand i s o b t a i n e d by breaking a specimen i n a c o n t r o l l e d manner so th a t a l l the s t o r e d e l a s t i c energy i n the specimen-machine system goes i n t o the c r e a t i o n of f r a c t u r e s u r f a c e . T h i s i s g i v e n by where, V = A = i n t e g r a t e d area under the l o a d - c u r v e . specimen c r o s s - s e c t i o n a l a r e a . d e f l e c t i o n 20 While i s r e l a t e d to the i n i t i a l r a t e of r e l e a s e of s t o r e d e l a s t i c energy, Y F i s determined by the t o t a l s e p a r a t i o n of the two f r a c t u r e s u r f a c e s g i v i n g the absorbed energy, averaged over the whole of the f r a c t u r e p r o c e s s . The r e l a t i v e magnitudes of Yj and Y F depend upon the a c t u a l p h y s i c a l p r o c e s s e s t h a t would take p l a c e d u r i n g c r a c k i n i t i a t i o n and p r o p a g a t i o n s t a g e s . For many e n g i n e e r i n g m a t e r i a l s , Yj (or G I C , where G I C = 2 Y i c ) i s found t o be more u s e f u l i n that i t may be used as a d e s i g n parameter to p r e d i c t the f a i l u r e loads when f r a c t u r e o c c u r s by u n s t a b l e c r a c k p r o p a g a t i o n . For l i n e a r e l a s t i c i s o t r o p i c homogeneous m a t e r i a l s a c o n n e c t i o n between t h i s and the c r i t i c a l s t r e s s i n t e n s i t y f a c t o r K , has been shown to e x i s t a c c o r d i n g to the e q u a t i o n , 4 3 = G IC (plane s t r e s s ) (1.5) 2 ^ i - G i c = IC (plane s t r a i n ) (1.6) where, E Young's modulus. Poi s s o n ' s r a t i o G IC C r i t i c a l s t r a i n energy r e l e a s e r a t e . 21 For l i n e a r e l a s t i c homogeneous o r t h o t r o p i c m a t e r i a l s t h i s r e l a t i o n s h i p can be w r i t t e n as;** G I C = K I C / ( a l i a 2 2 / 2 ) / [ / < a 2 2 / a l l ) + ( 2 a 1 2 + a 6 6 > / 2 a l l l ( 1 * ? } where a 's are the c o e f f i c i e n t s of the e l a s t i c compliance i j m a t r i x . The c r i t i c a l s t r e s s i n t e n s i t y f a c t o r K , known IC as the f r a c t u r e toughness i s found to be a more u s e f u l concept than f r a c t u r e s u r f a c e energy i n e n g i n e e r i n g d e s i g n . Westergaard's e q u a t i o n s 4 5 f o r the s t r e s s d i s t r i b u t i o n around a crack t i p in a homogeneous m a t e r i a l can be w r i t t e n i n the form; 'a± = ^ ( r ^ K ) ( i , j = 1,2,3) where, r and '9 are the c y l i n d r i c a l c o - o r d i n a t e s and K i s the s t r e s s f i e l d parameter, d e f i n e d as the s t r e s s i n t e n s i t y f a c t o r . I t has been shown t h a t K = f ( a , a ) where a and a are the s t r e s s and the c r a c k l e n g t h and the f u n c t i o n a l i t y depends on the c o n f i g u r a t i o n of the c r a c k e d component and the manner i n which the loads are a p p l i e d . The b a s i c f r a c t u r e mechanics requirment f o r the onset of u n s t a b l e c r a c k p r o p a g a t i o n i n t e n s i l e opening mode i s K r e a c h i n g i t s c r i t i c a l value R . To extend the a p p l i c a b i l i t y of f r a c t u r e mechanics p r i n c i p l e s t o f i b r e r e i n f o r c e d composites, the inhomogeneity and a n i s o t r o p y of these composites have t o be taken i n t o account. In composites s e v e r a l p r o c e s s e s are 22 l i k e l y t o occur and the a c t u a l sequence of m i c r o s c o p i c a l f r a c t u r e events which take p l a c e may a l s o be important i n d e t e r m i n i n g the a p p l i c a b i l i t y of these c o n c e p t s . However, f r a c t u r e mechanics techniques developed f o r homogeneous, i s o t r o p i c m a t e r i a l s are u s u a l l y a p p l i e d to f i b r e r e i n f o r c e d composites, sometimes with e m p i r i c a l e x t e n s i o n s of l i n e a r e l a s t i c f r a c t u r e mechanics .(LEFM) to cope with the a n i s o t r o p i c response of the m a t e r i a l . With some composites a c o n s i d e r a b l e success has been a c h i e v e d with the use of LEFM and a reasonable agreement observed between d i f f e r e n t measurements on s i m i l a r m a t e r i a l s f o r v a r i o u s r e i n f o r c e m e n t , t e s t specimen and l o a d i n g geometries. In many s t u d i e s , v a l u e s of f r a c t u r e s u r f a c e energy c a l c u l a t e d u s i n g K I C and Equations 1.5 and 1.6 have shown c l o s e agreements with absorbed e n e r g i e s deduced f o r v a r i o u s . f r a c t u r e mechanisms. 4 6"* 8 On the o t h e r hand, the use of v a r i o u s s t r e s s i n t e n s i t y c a l i b r a t i o n s f o r d i f f e r e n t c r a c k geometries i n some composites has been j u s t i f i e d by c o r r e c t i n g the c r a c k l e n g t h t o a i l o w f o r c r a c k t i p d a m a ge. 4 9" 5 0 H.Harel et a l 5 1 has suggested u s i n g d i f f e r e n t K - c a l i b r a t i o n f u n c t i o n s f o r every new r e i n f o r c e m e n t geometry to o b t a i n v a l i d s t r e s s i n t e n s i t y f a c t o r s . The e f f e c t of r e i n f o r c e m e n t has been taken i n t o account i n ' t h e form K = f ( a , a , g ) , where g- i s a parameter r e f l e c t i n g the nature and geometry of the r e i n f o r c e m e n t . G e n e r a l i z a t i o n s of these approaches to d e a l 2 3 with more complex situations are s t i l l under investigation. A t y p i c a l model developed by Kanninen et a l 5 2 treats the lo c a l heterogeneity in the v i c i n i t y of a crack t i p of a unid i r e c t i o n a l fi b r e composite, assuming a homogeneous anisotropic continuum for regions away from the crack t i p . Studies on composite fracture report several energy absorption processes responsible for the increased fracture toughness." 2" 5 3 Among these the fi b r e pull-out, debonding, fibr e stress-relaxation and matrix yi e l d i n g are found to be very s i g n i f i c a n t . When broken fibres pull-out of the matrix, energy is dissipated against the f r i c t i o n a l forces at the interface. These f r i c t i o n a l forces are generally brought about by matrix shrinkage on to the fi b r e s . Debonding, or the separation of the fibres from the matrix before they f a i l may also occur as a result of the stress i n t e n s i f i c a t i o n at the crack t i p . The creation of a debonding zone has been reported for many f i b r e reinforced composites and i s analogous to the development of a p l a s t i c zone in homogeneous materials, with large amounts of energy being expended during the process. In addition the stored e l a s t i c s t r a i n energy in the debonded length of a fibre is also not recovered when i t f i n a l l y breaks. Even i f the fibres are not debonded from the matrix, e l a s t i c energy i s lost from the snapped fibre due to stress relaxation over the c r i t i c a l transfer length. With du c t i l e matrices energy is also expended through p l a s t i c deformation. 24 Marston et a l 5 * have proposed t h a t no s i n g l e mechanism d e s c r i b e d above i s r e s p o n s i b l e f o r the observed f r a c t u r e toughness of composites, but r a t h e r a number of them t a k i n g p l a c e s i m u l t a n e o u s l y . A n a l y t i c a l r e l a t i o n s have been developed f o r each of these and are found to be f u n c t i o n s of f i b r e volume f r a c t i o n and c r i t i c a l l e n g t h . Although many o b s e r v a t i o n s on f i b r e composite f r a c t u r e suggest the p u l l - o u t and debonding mechanisms to be predominant, the a c t u a l events t h a t take p l a c e seem to depend upon the bond s t r e n g t h between the f i b r e s - and the m a t r i x , and the s p e c i f i c combination of f i b r e s and the matr i x . 5 5 I t has been shown by means of model composites that the f r a c t u r e energy of a g l a s s f i b r e / p o l y e s t e r c ombination i s determined l a r g e l y by the work done a g a i n s t f r i c t i o n between the f i b r e s and the matrix a f t e r the debonding process has o c c u r e d . 5 6 S p e c i f i c a l l y , the f r a c t u r e measurements of a random g l a s s f i b r e / p o l y e s t e r composite s y s t e m 4 6 have i n d i c a t e d t hat d i f f e r e n t mechanisms c o n t r o l d i f f e r e n t stages of crack p r o p a g a t i o n and t h a t y i s determined by a debonding mechanism while y i s the sum of a debonding mechanism p l u s a p u l l - o u t c o n t r i b u t i o n . With a u n i d i r e c t i o n a l g l a s s f i b r e - e p o x y c o m p o s i t e , 5 7 y agreed with the p u l l - o u t model while y corresponded with the s u r f a c e f o r m a t i o n model, proposed by Marston et a l 5 4 i n d i c a t i n g t h at the c r e a t i o n of new f i b r e , matrix and f i b r e - m a t r i x s u r f a c e s c o n t r o l s the stage of f r a c t u r e 25 i n i t i a t i o n . Many studies have also been directed towards the understanding of the effects of specimen and testing variables on the fracture, of fi b r e reinforced composites. The measured values of fracture toughness of a given composite are found to be dependent on some or a l l of the following variables. 1. Fibre volume fractio n 2. Specimen type 3. Specimen size 4. Crack length 5. Reinforcement geometry 6. Loading rate(or s t r a i n rate) Fracture toughness measurements in glass reinforced p l a s t i c s reported by a number of researchers have been compiled by Owen and Cann. 5 8 A modified tabulation of some of these measurements is given in Table III . The measurements c l e a r l y show that the fracture toughness of some fibre reinforced composites are influenced by the type of test specimen employed, i t s dimensions and the o r i g i n a l crack size. Fracture toughness tests carried out by the same autho r s 5 8 on polyester resin, reinforced with glass chopped strand mat using a centre notch specimen configuration have indicated an increase in K I C with specimen width W at a constant a/w r a t i o , where a i s half the crack length. Only 26 Table III Fracture Toughness Test Results of some glass reinforced p l a s t i c s ; - 5 8 Composite system Spec imen geometry t (mm) a (mm) w K (mm)(MPa.m0*5) Balanced CN 0. 25 0. 25 38. 8. 4 weave 0. 25 0. 64 38. 1 1 1 . 2 fabr ic 0. 25 1 . 04 38. 1 12. 9 in epoxy 0. 25 1 . 27 38. 1 14. 8 and 0 25 1 . 70 38. 1 16. 4 polyester 0 25 2. 29 38. 1 15. 8 0 25 3. 30 38. 1 17. 8 0 2*5 4. 98 38. 1 18. 2 0 25 6. 20 38. 1 17. 8 DEN 0 25 1 . 04 38. ! 18 4 0 25 1 . 78 38. 1 18 2 0 .25 2 52 38. 1 18 2 0 .25 2 54 38. 1 18 5 0 .25 3 56 38. 1 1 6 0 0 .25 5 72 38. 1 1 8 4 0 .25 6 35 38. 1 19 3 0 .25 6 35 38. 1 20 6 Random DEN .5 1 .25 25. 0 6 .93 chopped 1 .5 2 .50 25. 0 9 68 fibres in 1 .5 3 .75 25. 0 10 .27 polyester 1 .5 3 .95 25. 0 8 . 1 5 1 .5 4 .38 25. 0 5 .99 1 .5 5 .00 25. 0 9 .35 3 .5 1 .25 25. 0 4 .39 3 .5 2 .50 25. 0 6 .04 3 .5 3 .75 25. 0 6 .58 3 .5 5 .00 25. 0 6 .41 3 .5 6 .25 25. 0 5 .59 27 Table I I I (Continued); Composite system Specimen geometry t (mm) a (mm) w K (mm)(MPa.m0,5) Random BEND 1 .5 0.30 10.0 7.9 chopped 1 .5 1 .00 10.0 8.1 fibr e s in 1 .5 1 .05 10.0 10.1 polyester 1 .5 3.05 10.0 9.4 1 .5 4.80 10.0 10.0 3.5 0.29 10.0 7.9 3.5 1 .30 10.0 9.9 3.5 1 .30 10.0 7.8 3.5 2.90 10.0 9.9 3.5 4.80 10.0 7. 1 3.5 4.85 10.0 9.4 Nomenclature:- CN Centre notch specimens DEN Double edge notch specimens BEND 3 or 4-point bend specimens t. Specimen thickness a Crack length (half crack length in CN specimens) w Specimen width K C r i t i c a l stress intensity factor (MPa.m0 5) a negligible change in K with specimen thickness has been observed, indicating that plane str a i n conditions are unlikely to occur even' in many p l i e d laminates. In a homogeneous material plane str a i n conditions are established when the less strained material adjacent to a 28 crack front prevents the contraction along the crack front of the highly strained crack t i p material. In glass reinforced p l a s t i c s the i n t e r f a c i a l and interply strength is probably too low to support ten s i l e forces along the crack front. It has also been noted that K varies IC continuously with the crack length, with a maximum occurring at crack lengths close to half the specimen width. Linear e l a s t i c fracture energy measurements of a random glass fib r e composite, containing E- glass fib r e in a polyester matrix have been reported by Beaumont and P h i l l i p s . " 6 These measurements have been carried out on 3 point bending beams and double edge notched t e n s i l e plates of two d i f f e r e n t thicknesses, at a range of crack lengths. The results of te n s i l e tests have indicated a clear variation of fracture energy ( y ) with crack size and specimen thickness, but the results of bending tests have displayed no such v a r i a t i o n . Although the mean values of Y are approximately the same for both specimen configurations, a maximum has occurred in the te n s i l e test results for an intermediate value of crack length. Further, they obtained from the thick t e n s i l e plates was less than I that obtained from the thinner plates. No st r a i n rate dependence of has been observed for any of the two specimen configurations. The results have been explained in terms of the 29 debonding model, with a s t r e s s s t a t e dependence of debonding zone s i z e and the s t r e s s f i e l d i n t e r a c t i o n with f r e e s u r f a c e s e x p l a i n i n g the v a r i a b i l i t y of the t e n s i l e t e s t d a t a . However, i t has been found d i f f i c u l t to r e c o n c i l e these ideas with the i n v a r i a b i l i t y of the bending beam r e s u l t s . In c o n t r a s t to the s t r a i n r a t e independence of Y t , the work of f r a c t u r e ( y„ ) measurements on bending beams show an i n c r e a s e with i n c r e a s i n g s t r a i n r a t e r > d i s p l a y i n g no v a r i a t i o n with c r a c k s i z e or . specimen t h i c k n e s s . T h i s has been e x p l a i n e d i n terms of a s t r a i n r a t e dependent f i n i t e i n t e r f a c i a l shear s t r e s s , which r e s i s t s the f i b r e s when they p u l l - o u t of the m a t r i x . In summary, the mechanics of the r e i n f o r c e m e n t p r o c e s s e s which account f o r the mechanical p r o p e r t i e s of f i b r e c o m p o s i t e s ; a r e based on simple models of a l i g n e d f i b r e composites. T h e r e , i s s t i l l much to be done, both t h e o r e t i c a l l y and e x p e r i m e n t a l l y , to c h a r a c t e r i z e and p r e d i c t the behaviour of these heterogeneous a n i s o t r o p i c m a t e r i a l s i n s e r v i c e . In p a r t i c u l e r , p r e d i c t i v e t e c h n i q u e s c a p a b l e of cop i n g w i t h the complexity of the f r a c t u r e p r o c e s s e s have to be e s t a b l i s h e d . S t u d i e s on f i b r e composite f r a c t u r e g i v e n i n the l i t e r a t u r e g e n e r a l l y f a l l i n t o one of the f o l l o w i n g c a t a g o r i e s . These a r e ; 1. f o r m u l a t i o n of a c c u r a t e a n a l y t i c a l t e c h n i q u e s f o r t h e i r f a i l u r e a n a l y s i s 30 2. development of various energy absorption mechanisms - l i n k i n g the microscopical fracture events with observed toughness and 3. the evaluation of the influence of specimen and testing variables on the actual toughness. The present trend in developing a n a l y t i c a l representations for f a i l u r e analysis of fib r e reinforced composites is to account for their anisotropic nature in a modified fracture mechanics formulation. The microscopical fracture events which take place are important in determining the a p p l i c a b i l i t y of these concepts. With such concepts, the effect of specimen and testing variables on fracture of these composites can be evaluated. 1.2.3 Fibre & P a r t i c l e Reinforced Composites:- Three phase composites containing both fibres and p a r t i c l e s in a matrix material have received less attention than those which contain only fibres of another material as the t h i r d phase reinforcement. 1 1 Comparative studies of resin based composites 1 2 have shown that part of the increase in the s t i f f n e s s of some three phase composite was due to the f i l l e r material. By extending theories of two phase composites Chang and Weng13 have developed an 31 a n a l y t i c a l method to determine the e l a s t i c modulus of a f i l l e d resin reinforced by randomly oriented chopped f i b r e s and have shown that their results compare well with available -experimental data. These results show that, when reinforced by the same amount of glass f i b r e s , a f i l l e d resin is often s t i f f e r than the u n f i l l e d resin, but with increasing f i b r e content the e l a s t i c modulus of the f i l l e d composite i s increased only moderately as compared to an u n f i l l e d composite. For example, a 50% increase in the fibr e content of a t y p i c a l automotive type sheet moulding compound, f i l l e d with CaC03 results in only a 10% gain in e l a s t i c modulus of the composite, while a 30% increase i s realized in case of an u n f i l l e d compound. In contrast to the b e n e f i c i a l effects of these f i l l e r materials on the f i n a l s t i f f n e s s properties of composites, a reduction in strength and work to break has been observed by Ogorkiewicz et a l . 1 4 Cawthorne and H a r r i s 1 5 have measured the fracture toughness of some model glass/resin/chalk composite systems and d i s c u s s e d 5 9 the sources of fracture energy in these materials. These model materials representing the commercial polyester dough moulding and sheet moulding compounds have been prepared by hand mixing the chopped glass fibres and chalk into the catalysed polyester resin. Single edge-notched fracture toughness testing in three- point bending have been car r i e d out to determine the t o t a l fracture work, by integrating the load-deflection curve, 32 and an apparent c r i t i c a l stress intensity factor by means of the Srawley-Brown expression. 6 0 By comparing the results with other published work they have been able to suggest that the fracture energy and the apparent fracture toughness of a wide range of glass reinforced thermosets i s a simple function of fibre content, provided the fi b r e d i s t r i b u t i o n was roughly uniform, and that the f i l l e r p a r t i c l e s have a r e l a t i v e l y l i t t l e effect on the toughness of these materials. The major contribution to the energy absorption during fracture appeared to be d i r e c t l y attributable to the fib r e debonding, the other mechanisms of fi b r e pull-out and i n t e r f a c i a l f r i c t i o n providing much smaller contributions. The addition of up to about 30 wt% of short glass fibres increases both the t o t a l fracture energy and c r i t i c a l stress intensity in roughly linear fashion, irrespective of the addition of f i l l e r p a r t i c l e s . On the other hand, they also observed that the addition of crushed, rather than precipitated, chalk f i l l e r s can lead to serious reductions in fracture toughness of these materials as a result of fibre damage by abrasion against the sharp f i l l e r p a r t i c l e s occurring during composite preparation and fracturing. 33 1 .3 PRESENT WORK:- In view of the fact that very l i t t l e progress has been made in the area of three phase resin based composites, i t was considered appropriate to investigate the simple fabrication techniques of both binary and ternary composite systems incorporating randomly di s t r i b u t e d chopped glass fibres and/or heavy metal powders in a polyester matrix, and examine their resistance to fracture. The effects of such variables as the specimen geometry, fibre and f i l l e r volume fractions, and p a r t i c l e size on the fracture of these composites have been evaluated. • «. 1.3.1 Experimental Methods;- Compact tension specimens of two phase powder composites were f i r s t prepared by a simple casting method. These specimens contained d i f f e r e n t volume fractions and p a r t i c l e sizes of iron and nickel powder. Attempts to incorporate glass fibres of very short length in to the resin by similar methods of hand mixing and casting were a l l unsuccessful due to the d i f f i c u l t y involved in wetting the fibres and removing the entrained a i r . Further, the maximum quantities of glass f i b r e s that could be added to 34 the resin were also limited to about 2-3% of volume fr a c t i o n . The glass fibres were about 2-4 mm in length and randomly oriented, as i t was o r i g i n a l l y intended to make these castings with no strong d i r e c t i o n a l i t y . It was then proposed that to make these composites, a procedure, employing high pressure i n j e c t i o n was necessary. An injection moulding unit was b u i l t and fibre composite specimens of bending beam configuration were made. But again, d i f f i c u l t i e s were encountered when the resin injected through the fibres was f i l l e d with metal powders. At high glass contents the penetration of metal powder was non-uniform and almost incomplete. Further, the frequent f a i l u r e of the f i t t i n g s and sealings in withstanding the high pressures involved and the less over a l l productivity, resulted in eventual abandonment of this method. In view of the foregoing d i f f i c u l t i e s , associated with incorporating together the metal powders and three dimensionally random short glass fibres in a resin matrix, a compromise had to be made in the non-directionality of fibre orientation. Instead of short f i b r e s , mats of randomly dispersed chopped . glass fibres were used. A reasonably good penetration of metal powders at a high fibre content was achieved s a t i s f a c t o r i l y with a simple wet lay-up technique. Layers of glass mats, after wetting with f i l l e d or u n f i l l e d l i q u i d resin, were l a i d on top of each 35 other and r o l l e d down with a r o l l e r brush to make castings, from which the bending beam test specimens were cut. Although unsuitable as a means of producing nearly isotropic composites, i t was the only way a greater control over the volume fractions of constituent fibres and p a r t i c l e s was gained with l i t t l e or no voids. A series of bend specimens containing d i f f e r e n t volume fractions of metal powders and/or glass fibres were made and tested for their fracture toughness. The metal powders used were either coarse iron powder or fine nickel powder. Standard plane s t r a i n fracture mechanics techniques were used throughout the testing and evaluation and the results compared with those of an experimental compliance c a l i b r a t i o n procedure. The experimental work summarized above is presented here in separate sections with the descriptions of equipment, specimen preparation, testing and analysis of any one of the specimen geometries or d i f f e r e n t fabrication techniques put together. However, a chronological presentation of the work done is not attempted; rather, the most comprehensive study on cast bending beams is presented at the beginning followed by the studies on injection moulded bending beams and cast double cantilever beams. The common materials used in th i s work are a l l described below. 36 1.3.2 Materials Used:- Polyester Resin;- The resin used for the matrix material of a l l the composites was the Vi b r i n P-35/15 general purpose polyester supplied by Fibreplast Products, Burnaby, B.C. This was used with MEK (methyl ethyl ketone) peroxide catalyst produced by Noury Chemical Corporation, Burlington.,NY, in the r a t i o of 3 drops (approximately 0.12 ml) of catalyst per ounce of pure resin. This is the normal proportion suggested by the supplier which provided s u f f i c i e n t gel time (20-30 min.) for mixing and moulding while preventing s e t t l i n g out of the s o l i d constituents of the composite. The density of the cured resin was found to be 1.21 g/cm3. Iron Powder;- Atomet 95 high purity, =325 mesh iron powder supplied by the Quebec Metal Powders Ltd., Sorel, Quebec, was screened in the laboratory to obtain powders of less than 45 y m diameter. (-325 mesh size.) The density of the powder was determined by a simple immersion technique and found to be approximately 7.19 g/cm3. Nickel Powder:- This was used in two di f f e r e n t p a r t i c l e sizes. 37 N i c k e l Powder;- T h i s was used i n two d i f f e r e n t p a r t i c l e s i z e s . The f i n e r 1 y m diameter p a r t i c l e s are the N i c k e l ( S u p e r f i n e ) S h e r r i t t grade NF-1M, s u p p l i e d by the S h e r i t t Gordon Mines L t d . , Saskatchewan, A l b e r t a . E x p e r i m e n t a l l y determined d e n s i t y of t h i s powder was 6.23 gm/cc. The c o a r s e r p a r t i c l e s of p a r t i c l e s i z e 40-45v m were o b t a i n e d by s c r e e n i n g the S h e r i t t grade C n i c k e l powders s u p p l i e d by the same company. These p a r t i c l e s had a d e n s i t y of 8.85 gm/cc. G l a s s F i b r e s : - A 50 i n . wide r o l l of chopped s t r a n d E - g l a s s mat s u p p l i e d by F i b r e p l a s t Products in Burnaby, B.C., was used to c u t r e c t a n g u l a r p i e c e s of mats r e q u i r e d f o r random f i b r e composite l a m i n a t e s . T h i s mat weighed approximately 450 gm/m2 and c o s t $0.96 per pound. The r o v i n g of E - g l a s s f i b r e s used to make chopped s h o r t f i b r e segments f o r random f i b r e composites ( i n c l u d i n g i n j e c t i o n moulded specimens) was o b t a i n e d from F i b r e g l a s s Canada Inc., Burnaby, B.C. The f i b r e diameter "was a p p r oximately 10 ym. i n both types and i t s d e n s i t y was taken as 2.55 gm/cc. 38 I I . CAST BENDING BEAMS. A bending beam specimen configuration was used to study the mechanical properties of composites containing the following p a r t i c l e s and/or fibres over a range of volume fractions in a polyester matrix. (I) . Coarse iron powder (II) . Coarse nickel powder (III) . Fine nickel powder (IV) . Coarse iron & fine nickel powder (V) . Randomly oriented glass fib r e mat (VI) . Randomly oriented glass f i b r e mat & coarse iron powder (VII) . Randomly oriented glass f i b r e mat & fine nickel powder Castings containing each of these in a polyester matrix were made for the volume fractions of interest using a mould. Test pieces were then cut from these castings. 39 2.1 PREPARATION OF COMPOSITES;- A wooden mould enclosed in a rectangular wooden box was made in two parts as shown in Fig.1. The inside of the bottom half of the mould contained the mould cavity lined with a layer of s i l i c o n e rubber, approximately 1/2 in.thick, to give a smooth inner surface. Two drain channels were made close to the two ends of a lengthwise edge, to allow for flow of resin into and away from the mould. The inside of the top half of the mould was also lined with s i l i c o n e rubber to give a smooth f l a t surface. Two metal clamps that could sli d e around the assembled mould held the assembly together. The mould was used both as a closed v e r t i c a l mould 'with drain holes running v e r t i c a l l y up through the top surface and as an open mould in a horizontal position with the holes running horizontally through one of the s idewalls. Composites that contained only the powders were made by mixing a weighed quantity of powder, predetermined for the intended approximate volume fraction as explained in Appendix B., with a weighed quantity of l i q u i d resin catalysed just before the addition of powders. The resulting mixture was s t i r r e d manually for 5 to 10 minutes to provide a uniform slurry which was then cast into the mould, the mould being kept closed in i t s v e r t i c a l position. Care was taken throughout the process to avoid introducing a i r bubbles into the mixture. The mould surfaces were coated with a mould release agent to 40 M O U L D TOP WOODEN MOULD FIG, 1-. The mould used f o r the f a b r i c a t i o n of cast specimens. 41 f a c i l i t a t e the removal of the cast composite plate after 24 hours of curing at room temperature. Further ageing at room temperature for at least one week was allowed before making test specimens from the casting. Composites that contained glass fibres were made in an open mould. Rectangular pieces of glass mat, with planar dimensions s l i g h t l y less than the dimensions of the mould cavity, were cut from the randomly oriented glass fibr e mat. The l i q u i d mixture was prepared as explained before with or without the metal powder. After 5 to 10 minutes of s t i r r i n g to give a uniform mixture, i t was placed in a wide plate lined with a thin aluminium f o i l . The layers of glass f i b r e mats were then dipped in this bath allowing the l i q u i d mixture to wet the fibres well. The wetted mats were l a i d on top of each other inside the open mould, taking precautions to prevent a i r bubbles from creeping into the layup. The layup was r o l l e d down with a r o l l e r brush after every 3 or 4 layers of mat, placing a thin sheet of polythene on top to prevent contact of l i q u i d resin mixture with the surface of the brush. The polythene sheet was then peeled off c a r e f u l l y and the process continued. When the layup was complete the mould was closed and the clamps were slipped into position and tightened. As the clamps were tightened the excess resin mixture squeezed out through the drain holes. The casting was then allowed to cure for at least 24 hours at room temperature, before removing from the mould. Test specimens were prepared from these castings after at least one week of curing at room temperature. 42 P O a 3 - 5 a = 0-7 3 - 5 L 5-6 p / 2 '2 8 = 0- 7 ALL DIMENSIONS IN CMS B E N D I N G B E A M G E O M E T R Y FIG. 2. The dimensions of the bending beam f r a c t u r e toughness tes t specimens used. 43 2.2 FRACTURE TOUGHNESS TESTING:~ 2.2.1 Specimen Preparation;- Test specimens were cut from the cast plates with a diamond wheel, and the surfaces were ground with Grit 320 s i l i c o n e carbide paper. This was done in order to achieve the dimensions of a standard three point bending beam as set by Sec.7.2 of ASTM E399-78a. As shown in Fig.2, the nominal dimensions of the specimens for the purpose of this work were selected to be 7.0x1.4x0.7 cm. and the surfaces were ground c a r e f u l l y to be within ±0.020 cm. in i t s cross- sectional dimensions. A centre notch of 0.7 cm. nominal depth was made using a Norton Diamond Wheel of 0.3 mm. thick. The t i p of the notch was sharpened by pressing a single edge blade against the t i p of the notch. A small hand press was used for th i s purpose. 2.2.2 Testing & Measurements:- A minimum of 4 specimens were made for each volume fr a c t i o n , except in the case of coarse iron powder polyester specimens. The width and thickness of each specimen were measured using a Vernier c a l i p e r , to the 44 nearest 0 . 0 2 5 mm. The thickness, t was measured at three positions between the crack t i p and the unnotched edge of the beam and the average of these measurements was taken as the actual thickness. The width W, was measured at three positions near the centre notch and the average of these measurements was taken as the actual width. The test specimens were loaded in three point bending on a servo-hydraulic testing machine (hereafter referred to as MTS) using a span of 5 . 6 cm. between the centres of the support r o l l s . The two support r o l l s were mounted on a j i g that was attached to the movable, lower arm of the MTS. The central loading r o l l which was attached to the fixed upper arm of the MTS was positioned exactly midway between the two support r o l l s . The specimen was positioned with the crack t i p midway between the two support r o l l s and loaded under a constant loading rate of 4 4 . 5 N/sec. This produced at the t i p of the crack a stress intensity increase r a t e , s i i g h t l y higher than the minimum rate ( 0 . 5 5 MPa.m°* 5/sec.) specified in Sec.8.3 of ASTM E3.99-78a. The specimen was loaded u n t i l i t f a i l e d and the load- displacement curves were obtained on a Honeywell recorder and an X-Y p l o t t e r . The crack length was measured to the nearest 0 . 0 2 5 mm. using a c a l i p e r after the specimen was fractured. The average of three measurements made along the crack front (one at the centre and the others midway between the centre and the end 4 5 . 7 .>^ of the c r a c k f r o n t on each s i d e ) was taken as the a c t u a l c r a c k l e n g t h . For composites c o n t a i n i n g o n l y powders, the i n i t i a l e s t i m a t e s of t h e i r volume f r a c t i o n s were assumed to be t r u e volume f r a c t i o n s . A d e t a i l e d e x p l a n a t i o n f o r t h i s i s g i v e n i n Appendix B. But i n composites c o n t a i n i n g f i b r e s no such p r i o r e s t i m a t e of the f i b r e content c o u l d be made and the i n c o r p o r a t i o n of these f i b r e s s i g n i f i c a n t l y a l t e r e d the i n i t i a l e s t i m a t e s of powder volume f r a c t i o n s . Hence, as e x p l a i n e d i n Appendix B., an a l t e r n a t i v e method of burning a s m a l l sample of composite was used to determine both the f i b r e and f i l l e r volume f r a c t i o n s of a l l f i b r e composites. 2.2.3 C a l c u l a t i o n & D i s c u s s i o n o f R e s u l t s : - Pure p o l y e s t e r and a l l composites which c o n t a i n e d only powders, e x h i b i t e d a l i n e a r l o a d - displacement behaviour upto the p o i n t of f r a c t u r e , as shown i n F i g . 3 . The l o a d a t f r a c t u r e was taken f o r the c a l c u l a t i o n of c r i t i c a l s t r e s s i n t e n s i t y f a c t o r , K I C. The composites which c o n t a i n e d g l a s s f i b r e s always e x h i b i t e d a s l i g h t d e v i a t i o n from i n i t i a l l i n e a r i t y of l o a d - displacement r e c o r d b e f o r e r e a c h i n g the f i n a l f r a c t u r e p o i n t . A t y p i c a l l o a d - d e f l e c t i o n curve i s shown i n DISPLACEMENT FIG. 3. A typical'load-displacement curve of type 1. B 0 DISPLACEMENT FIG. 4 . A t y p i c a l load-displacement curve of type 2 . 48 Fig.4. For these composites both the maximum load at fracture and the 5% o f f s e t value, were used for the c a l c u l a t i o n of c r i t i c a l stress i n t e n s i t y factor, K I C. This r e s u l t e d in two d i f f e r e n t values of K I C , and are referred to as Kmax & Kq respectively in t h i s work. In determining the 5% o f f s e t value the procedures described in Sec.9.1.1 of ASTM E399-78a were followed. For the c a l c u l a t i o n of c r i t i c a l stress i n t e n s i t y factor in units of MPa.m0'5 the following equation given in Sec.9.1.3 of ASTM E399-78a was used. = —,/,- f (a/W) (2.1) where, f (a/W) = 3/(a/W) [ 1'.99-(a/W) (1-a/W) (2 .15-3 .93a/W +2.7a 2/W 2)] 2(l+2a/W)(1-a/W) 3 / 2 where, B = Specimen thickness (cm) a = Grack length (cm) S = Span (cm) W = Width of the specimen (cm) P = Load in kN determined as explained above. Appendix C. l i s t s some of the re s u l t s obtained. The c a l c u l a t e d values of c r i t i c a l stress i n t e n s i t y factor 49 for a l l these composites have been plotted against the approximate volume fr a c t i o n s of constituent components and are shown in Figs.5-12. The curves drawn were plotted using a computer routine (see Appendix D.) that employs a parabolic curve f i t through the averages of stress i n t e n s i t y factors derived at each volume f r a c t i o n . For p a r t i c l e f i l l e d composites the use of Equation 2.1 to c a l c u l a t e the values of K I C was j u s t i f i e d by the observed homogeneity and isotropy of these composites and the values c a l c u l a t e d are considered to be representative of t h e i r fracture toughness. But with composites containing f i b r e s no such observation could be made, and the accuracy of the Equation 2.1 in c a l c u l a t i n g c r i t i c a l stress i n t e n s i t y factor had to be v e r i f i e d by a compliance method. The methods involved and the r e s u l t s observed are described, in Section 2.2.4. It has been shown that the Kq values calculated using the 5% o f f s e t load values are in close agreement with the values obtained using the compliance method. Hence the values of Kq .are considered to be representative of the fracture toughness of composites, containing randomly oriented giass f i b r e s . As can be seen from Fig.5 the c r i t i c a l stress i n t e n s i t y factor of the pure resin i s increased progressively by about 100-150% by the addition of 20-25% volume f r a c t i o n of coarse powder. S p e c i f i c a l l y , the add i t i o n of 25% volume f r a c t i o n of iron powder has  F R A C T U R E T O U G H N E S S OF P O W D E R C O f l R S E I R O N P L U S F I N E N I C K E L C O M P O S I T E S a F I N E N I C K E L I— 2.5 I— S.O — 1 — 7.S — i r 1 r i 10 0 12.5 15.0 17.5 20.0 VOLUME FRACTION(7) 22.S 25.0 Bending beam fracture toughness of fine nickel and coarse iron plus fine nickel composites.  53 i n c r e a s e d the f r a c t u r e toughness from 0.7 MPa.m0*5 to 1.8 MPa.m°* 5 whereas 20% of n i c k e l powder has r a i s e d t h i s v a l u e to a p p r o x i m a t e l y 1.4 MPa.m 0* 5. Fi g . 6 on the otherhand i n d i c a t e s t h a t f i n e Ni powder has a l e s s pronounced e f f e c t on f r a c t u r e toughness, y i e l d i n g an average v a l u e of 0.9 MPa.m 0* 5 f o r K ̂  at 20% volume f r a c t i o n . The val u e of K I C i s i n c r e a s e d c o n t i n u o u s l y over the i n i t i a l 12% a f t e r which t h e r e seems t o be no e f f e c t of powder a d d i t i o n on the toughness of t h i s system. When both coarse i r o n and f i n e n i c k e l a re pr e s e n t in the r e s i n the toughness i n c r e a s e s but tends to l e v e l o f f near 20% volume f r a c t i o n of coarse i r o n powder. The t o t a l volume content of f i n e n i c k e l powder i n these composites i s kept c o n s t a n t at 5% i r r e s p e c t i v e of the amount of i r o n powder added. Here the value of c r i t i c a l s t r e s s i n t e n s i t y f a c t o r at 20% volume f r a c t i o n of i r o n powder i s l i t t l e over 1.4 MPa.m 0* 5, a value l e s s than t h a t of a system c o n t a i n i n g 20% of i r o n powder alone i n r e s i n . As shown i n F i g . 7 , the apparent f r a c t u r e toughness of g l a s s r e i n f o r c e d composites i s g r e a t l y i n f l u e n c e d by the amount of f i b r e s p r e s e n t . Over 100% i n c r e a s e i n toughness i s o b t a i n e d simply by d o u b l i n g the volume f r a c t i o n of f i b r e s . At n e a r l y 16.8% volume f r a c t i o n of f i b r e s a value of 6.5 MPa.m0'5 was recorded f o r Kq wh i l e at 33.7% i t was n e a r l y 13.8 MPa.m0*5 A continuous a p p r o x i m a t e l y l i n e a r v a r i a t i o n of Kq was observed w i t h i n 54 this range of volume fractions. However, i t is evident from Fig.8 that the addition of fine nickel powder does not s i g n i f i c a n t l y affect the toughness of these composites. The c r i t i c a l stress intensity factor of the resulting three phase composite remains almost unaltered within a wide range of powder volume fractio n s . At higher f i b r e contents however, a s l i g h t decrease was observed with increasing amounts of powder additions. The effect of powder additions on the toughness of three phase composites just discussed, seems to be somewhat diff e r e n t in the case of coarse powders. The results of the fracture toughness tests of a series of three phase composites containing up to 16% volume fraction of iron powder are depicted in Figs.9-11. For c l a r i t y Kq values are shown separately in Fig.12. It is s i g n i f i c a n t to note that, unlike the fine nickel powder, the coarse iron powder tends to increase the fracture toughness at lower concentrations of glass f i b r e . The c r i t i c a l stress intensity factor of a composite containing 16.8% volume fraction of fibres increases with increasing amounts of iron powder up to about 6% powder volume f r a c t i o n . But, as the fi b r e content is increased, the effect of powder additions on the toughness of these composites seems to be somewhat detrimental. At 33.7% volume fraction of glass f i b r e s , the fracture toughness of the resulting composite F R A C T U R E T O U G H N E S S OF T H R E E P H A S E C O M P O S I T E S P A R T I C L E F I L L E R » F I N E N I C K E L — , 1 1 1 1 1 1 1 1 l .S 3.0 *».S 6.0 7.S 9.0 10.5 12.0 13.S VOLUME FRRCrJON(7) Bending beam fracture toughness of glass reinforced nickel f i l l e d composites. FIG. 9, F R A C T U R E T O U G H N E S S OF T H R E E P H A S E C O M P O S I T E : G L A S S CONTENT = 1 6 . 8 V O L * P A R T I C L E F I L L E R = C O A R S E I R O N - i 1 r 6 . 0 "J .3 9 . 0 VOLUME FRACTION(7) Bending beam fracture toughness of glass r e i n f o r c e d i r o n f i l l e d composite. Glass volume f r a c t i o n i s 16.8%. ON F R A C T U R E T O U G H N E S S OF fl T H R E E P H A S E C O H P O S I T E F I B R E CONTENT = 2 4 . 2 V O L X P A R T I C L E F I L L E R = C O A R S E I R O N . 10. Bending beam frac t u r e toughness of glass r e i n f o r c e d i r o n f i l l e d composite. Glass volume f r a c t i o n i s 24.2%. FRACTURE TOUGHNESS OF fl THREE PHASE COMPOSITE GLASS CONTENT = 3 1-1 VOLX PARTI C L E F I L L E R = COARSE IRON , , 1 1 1 1 —r i 1 i OO I S 3 0 1.5 6.0 1.5 9.0 10.3 12.0 13.5 15.0 VOLUME FRACTION[J) FIG. 11. Bending beam fracture toughness of glass r e i n f o r c e d i r o n f i l l e d composite. Glass volume f r a c t i o n i s 31.1%. CO FIG. 12. Comparison of K values of glass reinforced i r o n f i l l e d composites. U l 6 0 is reduced by approximately 25%, when the volume content of iron powder is increased from 0 to 16%. 2.2.4 Microscopic Observations;- Micrographic observations of a l l the composites mentioned before were made on polished i n t e r i o r surfaces. The micrographs shown in Figs.13-14 indicate the nature of p a r t i c l e d i s t r i b u t i o n observed in powder f i l l e d composites. In coarse powder composites a uniform d i s t r i b u t i o n of p a r t i c l e s was observed. In contrast, aggregates of p a r t i c l e s were observed within the matrix of fine nickel f i l l e d composites. These aggregates or clumps of fine nickel were also observed in composites containing both iron and nickel together. Micrographs Of three phase composites show the d i s t r i b u t i o n of p a r t i c l e s , as well as f i b r e s , within the resin matrix. Here again, clumping was observed in composites incorporating fine nickel powder. Regions of di f f e r e n t d i s t r i b u t i o n densities were observed on polished surfaces of these composites. Fractographic observations were made using a scanning electron microscope. Matrix cracking and fracture along the paths of particle-matrix interfaces were ( a ). 5.0 volume % fine Nickel ( X 200) FIG. 13. Micrographs showing the nature of p a r t i c l e d i s t r i b u t i o n i n powder composites. ( a ) . 24.2 volume % Glass (X 200) ( b ) . 24.2 volume % Glass plus 25.0 volume % f i n e Nickel(X 200) FIG. 14. Micrographs showing the nature of f i b r e d i s t r i b u t i o n and p a r t i c l e d i s t r i b u t i o n i n f i b r e reinforced composites. 63 ( a ) . 25.0 vol% coarse iron magnification = 200 ( b ). 25.0 v o l % coarse iron magnification = 800 C c ). 20.0 vol% coarse nickel magnification = 80 ( d ). 20.0 v o l % fine nickel magnification = 800 FIG. 15. Fractured surfaces of powder composites. 64 ( c ). 13.9 v o l % i r o n plus 24.2 v o l % Glass magnification = 200 ( d ). 14.1 v o l % f i n e n i c k e l plus 24.2 v o l % Glass magnification = 200 FIG. 16. Fractured surfaces of f i b r e r e i n f o r c e d composites. 65 prominent in two phase powder composites. Fracture steps were seen on the surfaces of coarse nickel composites. These steps, associated with some of the p a r t i c l e s , were present on the side opposite to that which faced the moving crack front. In fib r e composites f i b r e pull-out was usually observed. The pull-out length varied extensively. Fibres sti c k i n g out at d i f f e r e n t angles from fracture surfaces were always observed on these composites. In three phase composites loose p a r t i c l e s were observed on the surfaces of pulled out f i b r e s . The f a i l u r e of the matrix surrounding the fibres exhibited features similar to that observed in two phase powder composites. 2.2.5 Compliance Method of Fracture Toughness Determination;- As mentioned previously in Section 2.2.3, a compliance c a l i b r a t i o n of stress intensity was done in order to check the accuracy of Equation 2.1, in c a l c u l a t i n g the c r i t i c a l stress intensity of presumably anisotropic composites of glass f i b r e . The c a l i b r a t i o n was done for the entire range of volume fractions of composites containing only glass fibres and for composites containing glass fibres and nickel powder, up to a volume fraction of 3% in 6 6 the l a t t e r . Specimens for c a l i b r a t i o n were cut from the same o r i g i n a l castings used to make fracture toughness test specimens of the above compositions and volume fractions. These were prepared in exactly the same way as described in Section 2.2.1 maintaining the same dimensional accuracy of ±0.020 cm. in cross-sectional dimensions. The i n i t i a l centre notch made was much less deep than that mentioned in Section 2.2.1 and was around 0.400 cm. The crack length was measured from the notched edge of the specimen to the crack front on each side, using a t r a v e l l i n g microscope and the average of these values was recorded. * The specimens were loaded on the MTS using the same fixture mentioned in Section 2.2.2 and a span of 5.6 cm. Loading was continued up to about 40 l b f . and a load- displacement record was obtained on a Honeywell recorder. The specimen was removed and the centre notch was extended using the Diamond wheel. After measuring the new crack length i t was loaded again as before, and another record of load- displacement was obtained. This was repeated several times extending the crack by at least 0.1 cm. each time, except near the regions of nominal crack length used for actual fracture toughness testing, when steps of approximately 0.05 cm. were used. The records thus obtained for load- displacement were used to calculate the compliance, by measuring the slope of the linear portion of 67 the plot, neglecting the i n i t i a l non-linearity. For each crack length a compliance value was computed, and a similar set of values generated for a l l composites mentioned e a r l i e r . In order to v e r i f y whether the displacements recorded on the Honeywell plots had re f l e c t e d the true specimen displacements, the recorded displacements were compared with an accurate, independent measurement of the specimen deflections. A t r a v e l l i n g microscope was used to measure the v e r t i c a l deflections of the mid-point along the centre l i n e of an unnotched specimen during loading. The machine was stopped several times during loading and a quick measurement of the deflection was obtained on the microscope. At the same time the corresponding displacement on the Honeywell plot was also recorded. After repeating th i s several times up to a t o t a l specimen deflection of about 0.3 mm. the two sets of values were compared. A close agreement was found to exist between the two methods of specimen displacement measurements. Accordingly, the displacements recorded on the Honeywell plots which were used to compute the compliance were considered to r e f l e c t the actual specimen displacements. The compliance plots shown in Figs.17-18 were obtained by f i t t i n g in each, a polynomial function through the set of experimental values of the compliance and the crack length, using a least squares technique. The choice 68 of a l e a s t squares technique i s appropriate when the random errors in the dependent variable have a normal d i s t r i b u t i o n . F i r s t derivatives of these polynomial functions were then computed for measured crack lengths of specimens used for actual fracture toughness t e s t i n g , mentioned in Section 2.2.2, and substituted in the following equation to obtain the c r i t i c a l s t r a i n energy release rate, G IQ . A derivation of t h i s formula is given in Appendix E. P 2 G I C = - | - ' B* ( dC^/da ) (2.2) In Thickness of the specimen used for compliance c a l i b r a t i o n . Thickness of the specimen used for actual fracture toughness t e s t i n g . Fracture load. Compliance of a specimen of thickness B. The values of Young's modulus determined experimentally, as described in Section 2.3 were used in conjunction with c r i t i c a l s t r a i n energy release rates to compute the c r i t i c a l stress i n t e n s i t y factors, according to the formula, where, B* = B =  C O M P L I A N C E P L O T OF A T H R E E P H A S E C O M P O S I T E G L A S S CONTENT = 2^\.2 V O L X N I C K E L CONTENT = 2 . S V O L * 0.35 ~ i — 0.4 -1 0.45 ~1 O.S 1 1 1 1 1 1 0 55 0.6 0.65 0.7 0.75 0.8 CRACK LENGTH (CM) 18. A t y p i c a l experimental compliance pl o t f o r a glass r e i n f o r c e d n i c k e l f i l l e d composite. 71 K i c = / < E G i c ) / / ( 1 " v } (2.3) A value of 0.3 was assumed for the Poisson's r a t i o v. The values of K calculated accordingly, for composites containing only glass f i b r e s and composites of glass and n i c k e l , have been plotted against the volume f r a c t i o n s of glass and n i c k e l respectively, in Figs.19-20. The corresponding values of Kmax and Kq have also been included in these diagrams for comparison. The curves drawn pass through the averages of these values and show the best parabolic f i t for ' regions in between the experimental values. It i s evident from these diagrams that in composites for which t h i s c a l i b r a t i o n was done, a good c o r r e l a t i o n e x i s t s between the calculated values of Kq and the values of stress i n t e n s i t y obtained by the compliance method. For example, at 24% volume f r a c t i o n of glass f i b r e s the compliance values were within ±18% of Kq of these specimens containing upto 3% of nickel powder. They seem to agree in terms of their order of magnitudes. Assuming that i t holds true for a l l composites containing both glass and metal powders, the values of Kq can be considered to r e f l e c t the actual resistance of these materials to crack propagation./ at 5« CO to U J — . o S2 F R A C T U R E T O U G H N E S S OF F I B R E C O M P O S I T E S ~i 1 r 22.0 24.0 26.0 VOLUME FRACTION(J) r 28 .0 —\ 3 0 . 0 3 2 . 0 3 4 . 0 FIG. 19. Comparison of experimental values of fra c t u r e toughness of glass f i b r e composites with the corresponding compliance values. K3 i DC". <_>r- K-max K-compliance FRACTURE TOUGHNESS OF THREE PHASE COMPOSITES P A R T I C L E F I L L E R = F J N E N I C K E L G L A S S CONTENT = 2U .2 V O L * i 2.5 0 . 0 -I 1 1 1 1 R~ 0.2S O.S 0.7S 1.0 1.25 1.5 VOLUME FR f lC r iONm 1 .75 - 1 — 2.0 FIG. 20. Comparison of experimental values of f r a c t u r e toughness of g lass r e i n f o r c e d n i c k e l f i l l e d composites with the corresponding compliance v a l u e s . 74 2.3. DETERMINATION OF YOUNG'S MODULUS:- The e l a s t i c moduli of some fi b r e composites were determined experimentally, in order to calculate the c r i t i c a l stress intensity factors using the compliance c a l i b r a t i o n procedures described in Section 2.2.4. This was done for the entire range of volume fractions of composites containing only glass fibres and for composites containing glass fibres and nickel powder, up to a volume fraction of 3% in the l a t t e r . Test specimens were cut from the o r i g i n a l castings used to make bending beam specimens for fracture toughness testing. These were prepared in exactly the same way as described in Section 2.2.1 maintaining the same dimensional accuracy of ±0.020 cm. in cross-sectional dimensions. The cross sectional dimensions of each specimen were measured accurately using a Vernier c a l i p e r , to the nearest 0.025 mm. The specimens were loaded on the MTS using the same fixture mentioned in Section 2.2.2 and a span of 5.6 cm. The specimen was loaded at a constant loading rate and a load- displacement record was obtained on a Honeywell recorder. A t r a v e l l i n g microscope was also used to measure the v e r t i c a l deflections of the mid-point along the centre li n e of the unnotched specimen. The machine was stopped several times during loading and a quick measurement of the deflection was obtained on the microscope. At the same time the corresponding 75 load recorded on the Honeywell plot was also noted. This was repeated several times up to a maximum load of about 150 l b f . These values were then used to make a plot of load on specimen against the deflection and the slope of the straight l i n e which passes through these points was used to calculate the young's modulus E, according to the formula, 1 3 E = S L 0 P E - 4 B W3 ( 2 ' 4 ) where, 1 = Span W = Width of the specimen B = Specimen thickness The e l a s t i c moduli of the composites used for the compliance c a l i b r a t i o n are l i s t e d in table IV. Table IV. E l a s t i c Moduli of some Fibre Composites:- Fibre Composite Elast ic Modulus (GPa) 1 6 .8 Vol% Glass 4.60 24 .2 Vol% Glass 5.87 31 . 1 Vol% Glass 7.35 33 .7 Vol% Glass 8.89 24 .2 Vol% Glass + 0.4 Vol% Ni 6.32 24 .2 Vol% Glass + 0.8 Vol% Ni 6.28 24 .2 Vol% Glass + 2.5 Vol% Ni • 4.77 77 I I I . INJECTION MOULDED BENDING BEAMS A bending beam specimen configuration was used to study the fracture toughness of injection moulded composites containing randomly oriented chopped glass fibres of 3 mm. average length in a polyester matrix. A high pressure injection moulding technique had to be employed to achieve high volume fractions in chopped f i b r e s . A number of attempts were made to fabricate these composites by means of a simple moulding process, but none of them was successful in producing a sat i s f a c t o r y casting that contained a high volume fraction of glass fibres with l i t t l e or no voids. Incomplete wetting of fib r e s too was a problem that could not be avoided on many occasions. Hence a high pressure injection moulding technique was proposed and an equipment was b u i l t to fabricate composite specimens of a bending beam geometry. This proved to be a sat i s f a c t o r y way of making these chopped fibre resin composites. Specimens were made containing fibres of volume fractions ranging from about 10% to 30% and tested in the as cast condition. 78 3.1 PREPARATION OF COMPOSITES:- 3.1.1 Description of Equipment;- An inj e c t i o n moulding unit was b u i l t and used to make rectangular beam specimens of 6.0x1.4x0.7 cm. dimensions. Fig.21 shows the whole assembly put together and i d e n t i f i e s various parts. The main parts of th i s set up are; a. A c y l i n d r i c a l hopper that holds the catalysed l i q u i d resin mixture and delivers i t to the system. b. A pressure gauge connected to the i n l e t of the injecting cylinder. c. An injector consisting of a piston and a cylinder. d. The mould consisting of a main specimen chamber and a top chamber to accumulate the excess resin, plus a slider-clamp arrangement to ram the fibres i n . For a detailed description of the parts and i t s assembly procedures the interested reader should refer the Appendix F. CENTRE P L A T E NOT TO S C A L E INJECTION MOULDING UNIT FIG. 21. A d e t a i l e d view of. the i n j e c t i o n moulding u n i t . 80 3.1.2 Specimen P r e p a r a t i o n : - F i b r e s f o r the specimen were prepared by chopping a r o v i n g of continuous g l a s s f i b r e s t r a n d s i n t o s h o r t segments of 2-4 mm. i n l e n g t h , each s t r a n d being about lOym i n d i a m e t e r . These were kept i n a c l o s e d c o n t a i n e r and a b l a s t of compressed a i r was sent i n through an opening near the bottom. The t u r b u l a n c e so c r e a t e d caused these f i b r e s to s w i r l around and o r i e n t themselves in a random manner. The c o n t a i n e r was covered on top with a s i e v e of mesh s i z e -325 i n order to prevent the f i b r e s from e s c a p i n g . A weighed q u a n t i t y of these chopped g l a s s f i b r e s , which y i e l d the intended volume f r a c t i o n , was then packed i n s i d e the specimen chamber of the moulding u n i t . The s l i d e r was pushed i n t o , p o s i t i o n & clamped and the u n i t was mounted i n s i d e a fume hood. The p a r t s of the mould were spra y e d with a mould r e l e a s e agent, before being assembled, i n order to f a c i l i a t e the disassembly and removal of the c a s t i n g . The c y l i n d e r was a t t a c h e d to the base of the mould and the p r e s s u r e gauge and the hopper were connected to i t s i n l e t . The v a l v e s were l e f t open and the p i s t o n was brought near the t o p c l o s i n g the i n l e t p o r t . A s u f f i c i e n t q u a n t i t y of c a t a l y s e d r e s i n was poured i n t o the hopper and the p i s t o n was cranked down, a f t e r c l o s i n g the o u t l e t v a l v e of the c y l i n d e r . T h i s caused 81 the resin to be sucked into the cylinder. The piston was cranked down to i t s lowest position, making certain that the hopper was not l e f t empty. The i n l e t valve was closed and the outlet valve was opened. The piston was then cranked up quickly u n t i l the pressure b u i l t up to at least 350 l b f / i n 2 . During the subsequent injection the pressure was maintained between 300 and 600 l b f / i n 2 by means of intermittent cranking. This was continued u n t i l the excess resin f i l l e d the top chamber completely. The outlet valve was closed and the i n l e t was opened to release the pressure inside the injector. The hopper, pressure gauge and the injector were removed and cleaned with acetone. The mould was l e f t undetached inside the fume hood for over 24 hours, allowing the specimen to cure at room temperature. When i t was complete the mould was taken apart and the specimen was removed. Fracture toughness tests were carried out on these specimens after at least one week of further curing at room temperature. 3.2 FRACTURE TOUGHNESS TESTING Since the specimens were tested as cast no machining except the cutting of a centre notch was required. A centre notch of 0.7 cm. nominal depth was made using a diamond wheel of approximately 0.3 mm. thick. The notch was sharpened by 82 pressing a single edge blade against the t i p of the notch, using a small hand press. 3.2.1 Testing & Measurements;- A minimum of 2 specimens were made for each volume fraction selected. The width and the thickness were measured to the nearest 0.025 mm. using a vernier c a l i p e r . The actual width was taken as the average of three measurements made near the centre notch. The thickness was measured at three positions between the crack t i p and the unnotched edge of the beam and the average of these measurements was taken as the actual thickness. The specimens were loaded in three point bending on an MTS, using a span of 5.6 cm. between the centres of the support r o l l s . The procedure was exactly the same as that adopted for bending beams described in Section 2.2.2 of the previous chapter. Again a constant loading rate of 44.5 N/sec, which produced, at the crack t i p , a stress intensity increase rate higher than the minimum rate specified in Sec. 8.3 of ASTM E399-78a, was used. The specimen was loaded to fracture and the load- displacement curves were obtained on a Honeywell recorder and an X-Y plo t t e r . The crack length was measured to the nearest 0.025 mm. using a cal i p e r and the average of three measurements 83 made a l o n g the crack f r o n t , one at the c e n t r e and the o t h e r s midway between the c e n t r e and the end of the c r a c k f r o n t on each s i d e , was taken as the a c t u a l c r a c k l e n g t h . 3.2.2 C a l c u l a t i o n & D i s c u s s i o n of R e s u l t s ; - A l l specimens e x h i b i t e d a s l i g h t d e v i a t i o n from i n i t i a l l i n e a r i t y of l o a d - displacement r e c o r d before r e a c h i n g the f i n a l f r a c t u r e p o i n t , as shown i n Fig.4 f o r one such specimen. Hence, both the maximum loa d at f r a c t u r e and the 5% o f f s e t value were used f o r the c a l c u l a t i o n of c r i t i c a l s t r e s s i n t e n s i t y f a c t o r , K I C . T h i s r e s u l t e d i n two d i f f e r e n t v a l u e s of K r e f e r r e d to as Kmax, and Kq r e s p e c t i v e l y . The 5% o f f s e t v alue was determined a c c o r d i n g to the procedures d e s c r i b e d i n Sec. 9.1.3 of ASTM E399-78a and the E q u a t i o n 2.1 i n S e c t i o n 2.2.3 of the p r e v i o u s c h a p t e r was used to c a l c u l a t e the c r i t i c a l s t r e s s i n t e n s i t y f a c t o r i n u n i t s of Mpa.m 0* 5. The c a l c u l a t e d v a l u e s of c r i t i c a l s t r e s s i n t e n s i t y f a c t o r have been p l o t t e d a g a i n s t the volume f r a c t i o n of g l a s s f i b r e s and are shown i n F i g 22. The c u r v e s were drawn using a computer r o u t i n e that employs a p a r a b o l i c curve f i t through the averages of the c r i t i c a l s t r e s s i n t e n s i t y f a c t o r s d e r i v e d a t each volume f r a c t i o n . A l though a l a r g e s c a t t e r of v a l u e s i s apparent from t h i s 84 figure the Kmax values show a s l i g h t increase with increasing volume fraction of glass f i b r e s . While Kq remain r e l a t i v e l y unchanged at or near 3 Mpa.m0*5 within the range of volume fractions from 10-30% nearly a four-fold increase over the toughness of pure polyester has been observed. However, the toughening of the polyester by these fibres appears to be much lower than that due to random glass mats discussed in the previous chapter. FIG. 22. Fracture toughness of injection' moulded bend beam specimens. 86 IV. CAST COMPACT TENSION SPECIMENS A compact tension specimen configuration was used to study the fracture toughness of composites containing following particle's over a range of volume fractions in a polyester matr i x. (I) . Coarse iron powder. (II) . Coarse nickel powder. (III) . Fine nickel powder. (IV) . Coarse iron & fine nickel powder. Castings containing each of these in a polyester matrix were made for the volume fractions of interest using a mould and the test pieces were cut from these castings. The same specimen configuration was used to study the effe c t of ageing on the toughness properties of pure polyester. Castings of pure polyester, cured for d i f f e r e n t lengths of time, were used to cut the test specimens. 87 4.1 PREPARATION OF COMPOSITES:- The same mould which was used to make the castings described in Section 2.1 was used again. The mould was kept closed in i t s v e r t i c a l position. A weighed quantity of powder, predetermined for the intended approximate volume fr a c t i o n , was mixed with a weighed quantity of l i q u i d resin catalysed just before the addition of powder. The mixture was s t i r r e d manually for 5 to 10 minutes to give a uniform mixture and cast into the mould while taking precautions to prevent a i r bubbles from creeping into the mixture. The mould surfaces were coated with a mould release agent to f a c i l i t a t e the removal of cast composite plate after 24 hours of curing at room temperature. Test specimens were prepared from these castings after at least one week of curing at room temperature. The castings of pure polyester, which were used to make the test specimens for the ageing test, were made by casting a s u f f i c i e n t quantity of catalysed l i q u i d resin into the mould. These were again removed from the mould after 24 hours and allowed to cure at room temperature for di f f e r e n t time in t e r v a l s . 88 4.2 FRACTURE TOUGHNESS TESTING;- 4.2.1 Specimen Preparation:- Compact tension specimens of 7.5x7.5 cm. planar dimensions were cut from the cast plates with a diamond wheel. Fig.23 shows the geometry of these specimens with the nominal dimensions of the notch and the loading holes. The notch was made using a diamond wheel and sharpened by pressing a single edge blade against the t i p of the notch. The holes were d r i l l e d through the plate, at the positions shown, using a 1/2 in. diameter d r i l l . 4.2.2 Testing & Measurements:- A minimum of 3 specimens were made for each volume fraction of the powder composites and each curing time of the aged polyester. The thickness B of the specimen was measured to the nearest 0.025 mm. using a vernier c a l i p e r , at three positions between the crack t i p and the unnotched edge of the specimen, and the average value was recorded. The width, W, from the plane of the centerline of the loading holes to the far edge was measured to the nearest 0.025 mm., at three positions near the notch 89 if) W= 6-0 7-5 a =30 ALL DIMENSIONS IN CMS. COMPACT TENSION S P E C I M E N FIG. 23. The dimensions of the compact tension specimen used, 90 location, and the average of these measurements was taken as the actual width. The specimens were loaded on an MTS and were gripped by a c l e v i s and pin arrangement, at both the top and bottom of the specimen, which allowed rotation as the specimen was loaded. E c c e n t r i c i t y of loading that could result from the incorrect positioning of the specimen was eliminated by centering the specimen with respect to the c l e v i s opening. The specimen was loaded under a constant loading rate of 44.5 N/sec. u n t i l f a i l u r e and a load displacement curve was obtained on the Honeywell recorder. After the specimen was fractured the crack length was measured to the nearest 0.025 mm. at three positions; one at the centre and the others midway between the centre and the end of the crack front on each side, and the average of these measurements was recorded. 4.2.3 Calculation & Discussion of Results;- A l l specimens exhibited a linear e l a s t i c behaviour up to the point of fracture. A t y p i c a l load- deflection curve is similar to that shown in Fig.3. The load at fracture was taken for the c a l c u l a t i o n of c r i t i c a l 91 stress i n t e n s i t y factor, in units of Mpa.m0"5, using the following equation given in Sec. 9.1.4 of ASTM E399-78a. K i c " ̂ 7 2 - £< a / w> < 4 - ' ) where, f(a/W) = (2+a/W)(0.886+4.64a/W-13.3a2/W2+14.7a3/W3-5.6a4/W4) ( l - a / W ) 3 / 2 where, B = Specimen thickness (cm) a = Crack length (cm) W = Width of the specimen P = Maximum load at fracture (kN) The Figures 24-26 show the values of c r i t i c a l stress i n t e n s i t y factor against the volume fr a c t i o n s of p a r t i c l e f i l l e r s . The Fig.27 shows the e f f e c t of curing time on the fracture toughness of pure polyester. A smooth curve that passes through the averages of stress i n t e n s i t y factors has been drawn in each, using a parabolic curve f i t routine. It i s clear from Fig.24 that with the addition of a very small amount of coarse powder the c r i t i c a l stress i n t e n s i t y factor of the r e s u l t i n g composite drops sharply C O A R S E I R O N .0 FIG. 24. Compact tension fracture toughness of coarse i r o n and coarse n i c k e l composites. ^£3 1 2 « in U J to to Qi l — c to . CC O O S " . F R ACT URE TOUGHNESS OF POWDER COMPOSITES FINE NICKEL — i — 1 8 . 0 4.0 —I 1 —I 8 . 0 1 0 . 0 1 2 . 0 VOLUME FRRCTIONm 1 4 . 0 1 6 . 0 2 0 . 0 FIG. 25. Compact tension fracture toughness of f i n e n i c k e l composites. FIG. 26. Compact tension fracture toughness of coarse i r o n plus f i n e n i c k e l composites. -p- 95 from that of the u n f i l l e d polyester matrix. This i n i t i a l reduction is quite d i s t i n c t and observed in both composites of coarse iron and coarse nickel powder. With further additions the average c r i t i c a l stress intensity factor goes through a period of minimum before increasing again. This increase is about 40% over an average minimum when the f i l l e r content is increased to 20% volume f r a c t i o n . In contrast, a continuous decrease in fracture toughness i s observed for those composites which contain only fine nickel powder. Here the decrease i s over 50% for 20% increase in volume f r a c t i o n . When both types of p a r t i c l e s (coarse iron and fine nickel) are present together the overall toughness appears to be lower than that of coarse powder composites, but increased in roughly the same fashion by the addition of the iron powder. In these the volume content of fine nickel powder has been kept constant at 5%. After the i n i t i a l d i s t i n c t reduction in fracture toughness approximately 60-70% increase over an average value of 0.8 MPa.m0*5 is observed when the volume fraction of iron powder increases from 5% to 20%. Comparing these results with the bending beam toughness values of Chapter II, i t can be inferred that a d i s t i n c t increase in toughness is observed in a l l these composites when using a compact tension specimen configuration. At f i r s t , there is a marked difference in 96 fracture toughness observed for the u n f i l l e d resin matrix. With compact tension configuration nearly a three-fold increase in fracture toughness over that of the bending beam geometry has been observed. Unlike the bending beam toughness values, the results of the compact tension tests show a decrease in toughness with increasing volume fraction of metal powder. This decrease i s more or less continuous in the case of fine nickel powder while an i n i t i a l reduction plus a subsequent gain i s observed in the case of coarse powder composites. The l a t t e r is true of a l l composites containing either coarse iron, or coarse n i c k e l , or coarse iron plus fine n i c k e l . However, the calculated values of c r i t i c a l stress intensity factor in any of these composites, do not in general f a l l below that of the bending test even at high volume fractions of f i l l e r mater i a l . Fig.27 which shows the effect of curing time on the fracture toughness of pure polyester indicates that the curing of the resin would take at least 6-7 days before i t leads to stable toughness properties. Therefore i t can safely be assumed that the curing process i s complete for the purpose of toughness measurements on composites based on polyester resin after at least one week of post-curing. FIG. 27. The e f f e c t of curing time on fracture toughness of pure polyester. 98 4.2.4 Microscopic Observations;- After the specimens were fractured the fracture surfaces were observed with a scanning electron microscope. The fracture surface topography observed for these composites was e s s e n t i a l l y same as that observed for bending beam specimens. The discussion of microscopical features of bend specimens, given in Section 2.2.4, applies to these specimens as well. 4.3 CHARPY IMPACT TESTING;- 4.3.1 Specimen Preparation;- Test specimens of the dimensions shown in Fig.28 were cut from the CTS specimens that have been fractured. The surfaces were ground with Grit 320 s i l i c o n e carbide paper, in order to achieve the dimensions of a standard subsize charpy impact test specimen within the permissible variations set by ASTM E23. A centre notch of the dimensions shown in Fig.28 was made on those specimens that were to be used for the notched impact t e s t . 99 55-0 mm 7- 5 mm 8 0 mm 10-0 mm 7 E 5 Details at the notch C H A R P Y I M P A C T T E S T S P E C I M E N FIG. 28. The dimensions of. the charpy impact t e s t specimens. 100 4.3.2 Testing & Measurements:- A minimum of 4 specimens were prepared for each volume fraction of powder composites, out of which 2 were notched. The specimens were centered in the an v i l with the notched surface or the specimen width lying v e r t i c a l and the blow was struck on the opposite face fracturing the specimen. The angle of swing of the hammer was measured to the nearest 1/2° degree. 4.3.3 Calculation & Discussion of Results:- The energy absorbed by test specimens during fracture was calculated using the angle measured in above. An allowance was made for the f r i c t i o n a l loss which was assumed to be independent of the swing angle. This was estimated by measuring the angle made in a free swing and converting that into energy terms. The impact energies absorbed per unit area of fracture surface of both notched and unnotched charpy specimens have been plotted against the volume fraction of iron powder in Fig.29. For notched specimens these values are calculated on the basis of remaining cross sectional area at the notch. 101 IMPACT ENERGY OF F e - P O L Y E S T E R VOLUME FRACTION OF Fe POWDER (%) FIG. 29. The impact energy of iron powder composites. 1 02 Despite the large scatter of values, a s i g n i f i c a n t difference in notched and unnotched energies has been observed at lower volume fractions of iron powder. This difference is smaller at higher volume fractions, as with the addition of powder the notched values are increased with a corresponding reduction in unnotched energy. However, i t is important to note that a l l these values are much higher than the fracture surface energies calculated on the basis of experimentally determined K I C values or those reported in the l i t e r a t u r e . For example, a fracture surface energy of 220 J/m2 is reported for polyester resin based on work of fracture measurements, 6 1 which involves fracturing a specimen in a controlled manner and integrating the area under the load-deflection curve. If the t e n s i l e modulus of polyester is taken as 1.32 GPa, an average value of 0.7 MPa.m0*5 estimated for K I C (from bending results of Chapter II) w i l l y i e l d a fracture surface energy of 185 J/m2. These values are much smaller than that of the corresponding notch impact test result, which i s nearly 2200 J/m2. 103 V. DISCUSSION Injection moulded bend specimens have been prepared only with short glass fibres and the results indicate a r e l a t i v e l y unaffected fracture toughness over the entire range of fib r e volume fracti o n s . Although the fracture toughness of these specimens is 4 - 6 times that of the pure resin i t was only a fract i o n ( 1 / 6 to 1 / 3 ) of that obtained for multi-layer composites of glass f i b r e mats. This was thought to be due to the smaller load carrying capacity of individual fibres resulting from their smaller aspect r a t i o s , ( f i b r e length to radius ratio) The bundling or the clustering of fibres during fabrication may also result in a lower toughness. Increasing amounts of fibres incorporated in these composites do not seem to contribute to the fracture toughness. In the following sections the fracture toughness test results of the cast compact tension and bending beam specimens are discussed. In view of the variety of mechanisms that may be operative in di f f e r e n t material systems, the p a r t i c l e f i l l e d composites are discussed f i r s t . Then follows the discussion of results obtained for f i b r e reinforced composites and three phase composites incorporating both p a r t i c l e s and f i b r e s . 104 5.1 Fracture Toughness of P a r t i c l e F i l l e d Polyester:- There are various mechanisms which might be responsible for the observed fracture behaviour of particulate composites; 2 1" 3 4 (1) An increase in r e l a t i v e fracture surface area due to surface roughness may increase the surface energy and in turn the fracture toughness. (2) Energy absorption by transparticle fracture may lead to increased fracture toughness. (3) Crack front interaction with the second phase dispersion may increase the fracture energy and the resulting fracture toughness. (4) The formation of a microcrack zone in the v i c i n i t y of the crack t i p may also increase the t o t a l r e l a t i v e fracture surface area and hence the fracture toughness of a particulate composite. Surface roughness:- It has been shown by Lange, 1 7 that the f r a c t i o n a l surface area increase per unit of apparent area of a particulate composite depends only on the volume fraction of the dispersed p a r t i c l e s . This has been found by means of a 105 p l a ne s u r f a c e model a n a l y s i s u s i n g c u b i c p r o t r u s i o n s to r e p r e s e n t the p a r t i c l e s . One s i g n i f i c a n t r e s u l t of t h i s a n a l y s i s was t h a t only a smal l i n c r e a s e i n f r a c t u r e s u r f a c e a r e a can be o b t a i n e d by i n c r e a s i n g the volume content of the p a r t i c l e s . T h i s may range from 0.1 to 1.5 f o r 10% to 50% volume f r a c t i o n s of the second phase d i s p e r s i o n r e g a r d l e s s of p a r t i c l e s i z e . T h i s and the o b s e r v a t i o n that the e l a s t i c modulus of powder composites i s independent of p a r t i c l e s i z e 3 2 suggest a s i z e independent c o n t r i b u t i o n from s u r f a c e roughness to the f r a c t u r e toughness of these composites. But the toughness of the composites i n v e s t i g a t e d i n the p r e s e n t work was found to be dependent on p a r t i c l e s i z e . T h i s was observed f o r both compact t e n s i o n and bending beam specimen geometries. I n . a d d i t i o n , a decrease i n toughness with i n c r e a s i n g volume f r a c t i o n i s a l s o observed f o r some composites when u s i n g the compact t e n s i o n specimen c o n f i g u r a t i o n . T r a n s p a r t i c l e f r a c t u r e : - On the b a s i s of t r a n s p a r t i c l e f r a c t u r e the average f r a c t u r e energy of a p a r t i c l e f i l l e d composite i s expected to l i e between the f r a c t u r e e n e r g i e s of the matrix and the p a r t i c l e , 3 3 - 3 4 v a r y i n g l i n e a r l y with the f r a c t i o n of the t o t a l f r a c t u r e s u r f a c e area o c c u p i e d by the p a r t i c l e s . I t has been shown 3 3 t h a t i f the e l a s t i c modulus a l s o v a r i e s l i n e a r l y with the volume f r a c t i o n of the p a r t i c l e s the magnitude of 2 can a p p r o x i m a t e l y be r e p r e s e n t e d by a l i n e a r f u n c t i o n of the volume 106 f r a c t i o n . The results obtained here are not in agreement with th i s type of functional behaviour. Also, the fracture surfaces of powder composite specimens do not show clear evidence for t r a n s p a r t i c l e fracture. Crack front interactions:- It has been found that the fracture behaviour of many particulate composite systems can be explained in terms of a concept of crack front interaction with the second phase d i s p e r s i o n . 1 7 2 3 3 1 When a crack front meets an array of p a r t i c l e s present on the crack plane, i t bows out between each pair of p a r t i c l e s increasing i t s t o t a l length. This leads to an increase in fracture energy(see Section 1.2.1) as well as fracture toughness of a p a r t i c l e reinforced composite. Combining Equation 1.1 and 1 .2 in Section 1.2.1 and neglecting the higher order terms of volume fraction (<)>), i t can be shown that for a given p a r t i c l e size the fracture energy of a particulate composite should be approximately a linear function of the p a r t i c l e volume f r a c t i o n . If the e l a s t i c modulus E of this composite were also to be a linear function of the volume f r a c t i o n 3 2 the expression for Kj. 2 from Equation 1.5 could be written as follows; 2(. AE.* + E ) (. AY.<j> + Y T ) 1 07 2 2 K I C = 2[ (AE. Y ] L+ Ay E1)4>+E1Y1+AE.AY$ ] Neglecting the term AEAy $2 , which is small compared to other terms the expression for K 2 can be written as a li n e a r function of the volume f r a c t i o n 2 (5.1) K I C = 2[ (AE.y1+Ay.E1)(f>+E1Y1 ] E-̂  and are the e l a s t i c modulus and fracture energy of the matrix material and ^ E and AY are the differences between these values of f i l l e r and the matrix. The squares of the average c r i t i c a l stress i n t e n s i t y factor values obtained in the present work were pl o t t e d as a function of p a r t i c l e volume f r a c t i o n s . None of the composites however resulted in a li n e a r plot with a l l the points l y i n g on a str a i g h t l i n e . Fig.30 for example i l l u s t r a t e s t h i s for the coarse iron-polyester system. The behaviour of these composites over the enti r e range of volume fractions can not thus be explained by a single model based on the in t e r a c t i o n of a crack front with dispersed p a r t i c l e s . Also, this mechanism can not be responsible for the difference in fracture toughness observed f o r the two specimen geometries. Nevertheless, the concept of crack front i n t e r a c t i o n can. not t o t a l l y be excluded for these composites, e s p e c i a l l y in view of the c h a r a c t e r i s t i c cleavage 0 0 FIG. 30. 5-0 10-0 I V O L U M E F R A C T I O N (%) 5-0 20 -0 A p l o t of the square of the average K of coarse i r o n composites aga ins t p a r t i c l e o Co volume f r a c t i o n . 109 steps observed on the fracture surfaces of coarse n i c k e l composites. There i s evidence of such steps in other p a r t i c u l a t e systems 1 7 3 1 formed as a consequence of the bowing of crack front between the p a r t i c l e s and eventual reunion of i t s segments. Shrinkage stresses;- To resolve this and forward an adequate explanation for the observed fracture behaviour, other mechanisms which might contribute to the toughness of these composites have been considered. When thermosets are used as the matrix material, a s i g n i f i c a n t shrinkage of the matrix occurs during the manufacture of the composite. With polyester the lin e a r cure shrinkage could be as high as 4% a i although considerable deviations from t h i s value may be observed i n - p r a c t i c e . As a r e s u l t , a large difference between the e l a s t i c moduli of the dispersed phase and the matrix may give r i s e to high residual stresses around the p a r t i c l e s . The magnitude and d i s t r i b u t i o n of these stresses are unknown, but a rough evaluation can be made by assuming a r i g i d c y l i n d r i c a l inclusion embedded in an i n f i n i t e l y large continuum. From the e l a s t i c stress solutions for c y l i n d r i c a l o b j e c t s , 6 2 the values of the p r i n c i p a l stresses o"r , o-Qand cr at a point outside the inclusion along the r a d i a l , c i r c u m f e r e n t i a l and a x i a l d i r e c t i o n s (see Fig.31) respectively can be written as; 110 \ FIG. 31. P r i n c i p a l shrinkage stresses around a r i g i d c y l i n d r i c a l i n c l u s i o n . a = A + B / r 2 r a Q= A - B / r 2 a - v(a +a ) z r o where A and B are c o n s t a n t s determined by the boundary c o n d i t i o n s and r i s the r a d i a l d i s t a n c e to a p o i n t w i t h i n the m a t r i x . I t i s seen t h a t f o r a continuum w i t h a s t r e s s f r e e boundary the v a l u e of A i s z e r o . The c o n s t a n t B can be e v a l u a t e d by c o n s i d e r i n g the hoop s t r a i n induced i n the m a t r i x j u s t o u t s i d e the i n t e r f a c e , which would be n u m e r i c a l l y equal to t h e l i n e a r s h r i n k a g e of the m a t r i x . I f e i s the l i n e a r s h r i n k a g e , E the Young's modulus and v the p o i s s o n ' s r a t i o of t h e m a t r i x m a t e r i a l , i t can be shown t h a t 111 E e = 0 - - v ( a + o ) (5.3) 8 r z S u b s t i t u t i n g (5.2) in (5.3), B = "^- r0 1+v where r 0 i s the radius of the c y l i n d r i c a l i n c l u s i o n . This value of B y i e l d s the following expression for r a d i a l and c i r c u m f e r e n t i a l stresses; -E e , , ,2 (5,4) CTr = -°e • 1+7" ' ( r o / r ) The p r i n c i p a l stresses would vary as the inverse square of the distance from the centre of the i n c l u s i o n . Polyester with 4% l i n e a r cure shrinkage and a Poisson's r a t i o of 0.34 may give r i s e to stresses as high as E/33 at the i n t e r f a c i a l boundary. According to t h i s expression, the t e n s i l e hoop st r e s s i s equal in magnitude to the compressive r a d i a l s t r e s s at any point around"the i n c l u s i o n . It i s also evident that the magnitude of these stresses at the i n t e r f a c i a l boundary i s independent of the i n c l u s i o n s i z e . Although the s i t u a t i o n i s somewhat d i f f e r e n t when these incl u s i o n s are spherical, a stress d i s t r i b u t i o n which w i l l c l o s e l y resemble the above can be expected. The symmetry of the spherical inclusions however implies that the two 1 12 tangential stresses, which are both orthogonal to the p r i n c i p a l r a d i a l stress, should be t e n s i l e and equal in magnitude reaching a maximum near the interface. The ra d i a l stresses around the inclusion would s t i l l be compressive and also reach their maximum at the inner boundary. In view of the assumptions and approximations involved and the exact nature of the p a r t i c l e d i s t r i b u t i o n , their shape and r i g i d i t y , the actual values of stresses that are realized in practice may not be so high. However, they may be large enough to influence the crack t i p stress d i s t r i b u t i o n or produce microcrac.ks around the p a r t i c l e s in the presence of an external stress f i e l d . The l a t t e r i s p a r t i c u l a r l y important as i t w i l l increase the fracture toughness of a composite through an increase in t o t a l fracture surface area. The microcracks are often formed by decohesion of weakly bonded internal boundaries or f a i l u r e of the matrix along planes which are r a d i a l and subject to maximum normal t e n s i l e stresses. The formation of such zones has been reported for concrete and other m a t e r i a l s . 6 3 " 6 " Increase in fracture toughness through the formation of microcrack zones;- It i s then conceivable that in particulate composites the formation of microcrack zones may'contribute s i g n i f i c a n t l y to their fracture toughness, and that an increase in thi s value can be expected with increasing volume fraction of p a r t i c l e s . 1 1 3 In the presence of a given stress f i e l d , the t o t a l fracture surface area associated with microcracks w i l l s t a t i s t i c a l l y be proportional to the t o t a l volume of material, subject to residual t e n s i l e stresses of magnitude higher than a c r i t i c a l value. Using the model of c y l i n d r i c a l inclusion, i t can be shown that t h i s volume of material is proportional to the t o t a l volume fraction of p a r t i c l e s present in the matrix, and that for a given volume frac t i o n , i t i s independent of the p a r t i c l e s i z e . The results of bending beam fracture toughness tests i l l u s t r a t e d in Figs.5-12 are consistent with the concept of microcrack formation around the second phase inclusions. As expected, an increase in fracture toughness has been observed with increasing volume fractions of metal powders. The lower toughness of fine nickel composites, as opposed to coarse powder composites, appears to be a direct consequence of the clus t e r i n g of fine nickel p a r t i c l e s . When th i s happens, the residual stresses around the p a r t i c l e s would overlap with each other, the tangential t e n s i l e stresses being counterbalanced by the overlapping compressive r a d i a l stresses. The overall result of t h i s would be a reduction in the t o t a l amount of microcracks produced and thus in the material's resistance to fracture. A similar effect i s observed again at higher volume fractions, when interactions of the residual stress f i e l d s with each other may occur. This could mean a slower rate of increase in fracture toughness, with increasing amounts of p a r t i c l e s at high volume fractions. The results of both the fine nickel and 1 14 fine nickel plus coarse iron composite series show thi s very c l e a r l y . In explaining the above results the mechanism of crack interaction with dispersed p a r t i c l e s can not be completely excluded. Even in terms of previously discussed concept of matrix shrinkage, i t can be expected that the residual compressive stresses around the p a r t i c l e s may tend to hinder the progression of a crack front by i n h i b i t i n g i n t e r f a c i a l separation. The c h a r a c t e r i s t i c fracture steps i d e n t i f i e d on fracture surfaces of coarse powder composites confirms the prevalence of such interactions. The p a r t i c l e size dependence of fracture toughness can also partly be attributed to t h i s mechanism. Although the observed dependence of fracture toughness on volume fraction and p a r t i c l e size is in agreement with the above hypothesis, i t s actual contribution to fracture of these composites is unknown. Interactions of residual stresses with the crack t i p stress f i e l d i - As mentioned e a r l i e r , the residual stresses that are developed during matrix shrinkage may also severely af f e c t the crack t i p stress f i e l d along the ligament of a loaded specimen. The tangential stresses around the p a r t i c l e s would intensify the p r i n c i p a l t e n s i l e stresses in regions near the crack t i p , even causing premature f a i l u r e of a specimen. This effect may be very pronounced in specimens of compact tension geometry, 1 1 5 where the crack t i p te n s i l e stresses extend deep into the specimen. A lowering of the apparent fracture toughness of compact tension specimens can therefore be expected. In bend specimens however, the absolute length of the ligament i s much smaller than that of the compact tension specimen, l i m i t i n g the extent of such stress magnification. The pa r t i c u l a r loading geometry associated with bending beams which develops compressive stresses on the unnotched side of the beam w i l l also r e s t r i c t this e f f e c t . Thus, the mechanism of stress i n t e n s i f i c a t i o n may not be as s i g n i f i c a n t in bend specimens as in compact tension specimens. The discrepancy between the results of compact tension and bending beam geometries can now be explained. The curves drawn in Figs.32-34 compare the experimental results obtained for these two specimen geometries. At f i r s t , the higher apparent fracture toughness of pure polyester -compact tension specimens can be associated with the existence of a larger microcrack zone at the crack t i p . This is analogous to the difference in toughness observed with plate thickness in metals, which arise due to the differences in p l a s t i c zone size depending on whether plane stress (thin plate) or plane strain (thick plate) conditions e x i s t . As metal powders are added to polyester a decrease in c r i t i c a l stress intensity factor for compact tension tests is observed i n i t i a l l y . It is possible that the effects of residual stress f i e l d interactions with the crack t i p stress f i e l d might 0.0 COARSE IRON (8EN0) COARSE NICKEL (BENO) FRACTURE TOUGHNESS OF POWOER COMPOSITES 2.5 3.0 I 7.5 )0.0 12.S 15.0 V O L U M E F R A C T I O N S ) n.s 20.0 22.5 -1 25.0 FIG. 32. A comparison of the fracture toughness test r e s u l t s of coarse i r o n and coarse n i c k e l composites obtained f o r the two specimen geometries, FRACTURE TOUGHNESS OF POWDER COMPOSITES S 35 • to to UJ cr o Oo FINE NICKEL (CTS) FINE NICKEL IB END) 1 1 1 1 1 1 0.0 2.5 5.0 7.5 10.0 12.5 15.0 VOLUME FRACTIONm 17.5 I 20.0 22.5 25.0 FIG. 33. A comparison of the fracture toughness te s t r e s u l t s of f i n e n i c k e l composites obtained for the two specimen geometries. FIG. 34 . A comparison of the fracture toughness test results of coarse iron plus fine nickel composites obtained for the two specimen geometries. 00 119 be responsible for th i s observation. The contribution of microcrack formation around the p a r t i c l e s (at low volume fractions) is probably not s u f f i c i e n t to compensate for this reduction in toughness. However as the volume fraction of p a r t i c l e s i s increased, the l a t t e r may predominate over the specimen's response to fracture and consequently a gain in apparent fracture toughness i s observed. The results of compact tension tests i l l u s t r a t e d in Figs.24-26 are a l l consistent with thi s concept of stress magnification coupled with microcrack formation. Composites containing either coarse iron or coarse nickel powder exhibit a sharp drop in the c r i t i c a l stress intensity factor at very low volume fractio n s . This then, goes through a minimum and increases again with further additions of powder, u n t i l i t reaches a value close to the o r i g i n a l fracture toughness of pure polyester. In contrast to this behaviour, the composites which contained fine nickel powder have shown a continuous reduction in fracture toughness, subsequent to a sharp i n i t i a l drop. This is perhaps due to a reduction in microcrack formation at high volume fractions resulting from clumping of fine nickel p a r t i c l e s . In any event, the overal l toughness resulting from compact tension tests can be higher than the bending beam toughness values of each material, at any volume frac t i o n , due to the continued presence of a larger microcrack zone at the crack t i p . This is evident from a comparison of fracture toughness test results of both compact tension and bending beam specimen geometries. The fracture of composites which contained both iron 120 and nickel powder exhibited the cumulative effect of the addition of these powders. This material can be regarded as a nickel based matrix f i l l e d with varying amounts of iron powder. The fracture toughness of these composites have shown similar variations with volume fraction as in iron powder composites except for the corresponding contributions of nickel powder. In explaining the results of compact tension fracture toughness tests, the a p p l i c a b i l i t y of the mechanism of crack front interaction is found to be inadequate. Neither the reduction in fracture toughness at low volume fractions nor the difference in toughness observed for the two specimen geometries could be accounted for. Although i t can not alone be responsible for the fracture behaviour of these composites, the* p o s s i b i l i t y of a f r a c t i o n a l contribution of th i s mechanism can not be excluded. In summary, the fracture behaviour of p a r t i c l e f i l l e d composites investigated in the present work is consistent with a concept based on microcrack formation and residual shrinkage stresses. Of the other mechanisms, crack front interaction with dispersed p a r t i c l e s is also partly in accordance with the observed behaviour. These explanations are based on the following points; (1) The difference in apparent fracture toughness of the u n f i l l e d polyester obtained for di f f e r e n t specimen configurations can only be explained in terms of a varying 121 microcrack zone size associated with each geometry. (2) The results obtained for f i l l e d composites using a compact tension specimen configuration are in general higher than those of the bending beam configuration. This can also be explained in terms of a larger microcrack zone size associated with each geometry. (3) Within each of the composite series, the va r i a t i o n of fracture toughness with constituent p a r t i c l e volume fraction i s consistent with the concepts of microcrack formation and stress f i e l d interactions. (4) The apparent p a r t i c l e size dependence of fracture toughness can be attributed to varying degree of clumping effects associated with d i f f e r e n t p a r t i c l e s . 5.2 Fracture Toughness of Fibre Reinforced Polyester:- As discussed previously in Section 1.2.2 the theoretical models of fracture which have been postulated to account for the fracture toughness of fib r e reinforced composites are generally based on mechanisms of fibre pull-out, debonding, f i b r e stress relaxation, matrix yielding and the creation of new fracture surfaces. A n a l y t i c a l formulae developed for energy ab s o r p t i o n 5 3 5 4 6 5 through these 122 mechanisms are given in Table V. These formulae express the fracture energy in terms of volume f r a c t i o n (V f) and c r i t i c a l t r a nsfer length (1 ) of the r e i n f o r c i n g f i b r e . An a n a l y t i c a l r e l a t i o n s h i p for matrix p l a s t i c deformation i s not included here as i t was considered to be of no relevance in the present context. In fundamental mechanics of f i b r e reinforcement" 1 the c r i t i c a l t r a n s f e r length of a f i b r e for stress transfer by s l i p , i s defined as that length of the f i b r e which corresponds to the c r i t i c a l aspect r a t i o . The c r i t i c a l aspect r a t i o i s the minimum f i b r e length to radius r a t i o required to be able to stress the f i b r e to i t s breaking-point. Thus, the c r i t i c a l t r a n s f e r length is given by; ( 5 . 5 ) 1 = a, r / T c f 1 where, a = t e n s i l e strength of the f i b r e r = radius of the f i b r e T i s the i n t e r f a c i a l shear stress brought about by f r i c t i o n a l s l i p , i e ; T . = u a l r ( 5 . 6 ) 1 23 Table V. Models of Energy Absorption:- Mechanism of energy absorption A n a l y t i c a l expression Pull-out Debonding Stress-relaxation Surface formation Nomenclature:- Fibre diameter Volume fraction of fibres Tensile strength of fibr e E l a s t i c modulus of fibr e C r i t i c a l transfer length of fibr e Debonded length of fibr e Fracture energy of the matrix 1 24 where, u i s the c o e f f i c i e n t of f r i c t i o n and a is the normal stress at the fi b r e matrix interface, which results mainly from matrix cure shrinkage. Since the l a t t e r can be in the neighbourhood of 20-30 MPa, and y can be taken as 0.2,"1 the i n t e r f a c i a l shear stress T i s around 5 MPa. Using this value of T in Equation 5.5 and a value of 2000 MPa for the strength of the fibres an approximate c r i t i c a l transfer length was estimated for the composites. This was 2.0 mm. for 10 ym. diameter fibres incorporated in the present composite. In order to compare the experimental observations with the proposed theoretical models of energy absorption, this value of 1 = 2.0 mm. was substituted in the formulae of Table c V. In doing so, the t e n s i l e strength and modulus of the fibre were taken as 2000 MPa and 70 GPa, respectively. In the calcu l a t i o n of v a value of 0.185 kJ/m2 was used for the s fracture energy of polyester. This was derived from the average fracture toughness of pure polyester obtained for bending beam configuration, (refer Section 4.3.3) The debonded length l d which appears in the expression for debonding was taken as l c / 2 (=1.0 mm.). A rationale for thi s is given by Gershon & Marom.57 The c r i t i c a l stress intensity factors derived for the series of glass fibr e composites have been converted to fracture energies using Equation 1.6 and compared with the theoretical models predicting fracture in Fig.35. The average values of fracture energy calculated for the set of composites exhibit a l i n e a r l y increasing trend with volume f r a c t i o n . A 1 25 between these values and the t h e o r e t i c a l models reveals that the surface formation model provides the best explanation for the observed fracture behaviour. The values predicted by the pull-out mechanism are too high to account for the experimental r e s u l t s . The models of stress relaxation and debonding on the other hand, do not provide s u f f i c i e n t l y high values. This r e s u l t i s in agreement with the r e s u l t s of a u n i d i r e c t i o n a l glass fibre-epoxy composite investigated by Gershon & Marom. 5 7 The general agreement of the surface formation model with the experimental values proposes that the creation of new f i b r e , matrix and fi b r e matrix interf a c e s i s the main contribution to the fracture toughness of these composites. According Marston et a l 5 4 the creation of new surfaces includes the process of energy absorption through debonding, i n d i c a t i n g that v d is i m p l i c i t in the expression for Y . It i s expected that an even better agreement would p r e v a i l i f (1) an allowance was made for the random d i s t r i b u t i o n of f i b r e alignment (2) an accurate estimate was made for the c r i t i c a l transfer length of the f i b r e s . The f i r s t i s j u s t i f i a b l e because in a random f i b r e composite, not a l l the f i b r e s w i l l contribute to toughness in a given d i r e c t i o n . The expressions given in Table 5.1 have been 12+ VOLUME FRACTION (%) FIG. 3 5 . A comparison of the experimental values of f r a c t u r e energy of glass f i b r e composites with t h e o r e t i c a l models. 1 27 The f i r s t i s j u s t i f i a b l e because in a random fi b r e composite, not a l l the fib r e s w i l l contribute to toughness in a given d i r e c t i o n . The expressions given in Table 5.1 have been developed for idealized systems of u n i d i r e c t i o n a l l y reinforced f i b r e composites. In a random fi b r e composite only a fraction of fibres w i l l actually contribute to toughening through debonding and surface formation, resulting a lower e f f e c t i v e volume f r a c t i o n . The second of the above can only be achieved through an accurate estimate of the physical parameters involved. The magnitude of the i n t e r f a c i a l shear stress T used in Equation 5.5 i s dependent upon the values used for the c o e f f i c i e n t of f r i c t i o n and normal stress at the fibre-matrix interface. The actual t e n s i l e strength a£ of the fibre may also be reduced due to surface damage caused during handling and laying-up. If i t i s assumed that the observed pull-out length varies between 0 and l c / 2 the mean fibre pull-out length w i l l approximately be equal to 1 c/4. l c then becomes a s t a t i s t i c a l concept and can be estimated experimentally by measuring the pull-out lengths of fibres sticking out from the fracture surfaces. Unlike in a unidir e c t i o n a l fi b r e composite, in the present composite i t was d i f f i c u l t to make a s t a t i s t i c a l estimate of the c r i t i c a l transfer length due to the random nature of fibre alignment. 128 5.3 Fracture Toughness of P a r t i c l e & Fibre Reinforced Polyester;- The results obtained for three phase composites are self-consistent, displaying only a s l i g h t v a r i a t i o n of c r i t i c a l stress intensity factor with powder volume fr a c t i o n , (see Figs.8-12) The addition of metal powder to f i b r e reinforced composites does not in general affect the fracture toughness s i g n i f i c a n t l y . This is due to the r e l a t i v e l y smaller influence of powder additions on the toughness of the matrix material. The f i b r e reinforcement on the other hand has a greater influence on fracture and results in an increased fracture toughness for higher contents of glass f i b r e . It i s thought that the p a r t i c l e s and f i b r e have their individual contributions to the resulting fracture toughness. These contributions are cumulative, especially at low volume fractions of constituent components. But, as the t o t a l volume fraction of the reinforcement increases the resulting fracture toughness seems to be more influenced by other interactions. Let us for example, consider the results of three phase composites containing nickel powder. At low glass content the composite fracture toughness is v i r t u a l l y unaltered by the presence of p a r t i c l e s . But at f i b r e volume fractions over 30%, the addition of nickel powder tend to increase the toughness i n i t i a l l y and then reduce i t d r a s t i c a l l y . As observed e a r l i e r , a nickel powder dispersion in a matrix of polyester does not 1 29 alone constitute a composite of high fracture toughness. It can therefore be expected that the addition of nickel powder at r e l a t i v e l y low volume fractions of fi b r e w i l l not s i g n i f i c a n t l y a l t e r the toughening due to fibre reinforcement. As the volume fraction of fibre increases interactions between the two reinforcement may occur and as a result a strong dependence of fracture toughness on these materials can be expected. S p e c i f i c a l l y , the addition of nickel powder may have a detrimental effect on the toughening character of fibre reinforcement. The fibres contribute to fracture toughness through the formation of new fracture surfaces which includes the processes of debonding. It i s possible that, during the fracture of glass f i b r e - r e s i n composites, the presence of nickel p a r t i c l e s on fibre surfaces may affect the fibre-matrix i n t e r f a c i a l shear stress. In Table V the expressions which include energy absorption through debonding are a l l based on the assumption that the fibre-matrix i n t e r f a c i a l shear stress f a l l to zero on debonding. The presence of p a r t i c l e s on the fib r e surfaces may reduce the maximum i n t e r f a c i a l shear stress prior to debonding, or decrease i t not to zero but to some f i n i t e value on debonding. In any event, the result would be a reduction in energy dissipation and the resulting fracture toughness. As the volume fractions of constituent components are increased greater reductions in fracture toughness can be expected. The mechanisms which might have led to the i n i t i a l increments of fracture toughness are not very c l e a r . However, 130 the resulting increase in e f f e c t i v e volume fractions of the individual components with respect to the base matrix may also have contributed s i g n i f i c a n t l y to this behaviour. In fact, i t is easy to reconcile this idea with the variations observed for iron powder-glass composites. The results of two phase powder composites (Section 2.2.3) indicate that the coarse iron powder has a greater influence on toughness than the fine nickel powder and 25% volume fraction of iron powder increases the fracture toughness of polyester by a factor of approximately 2.5. This may explain why there i s an i n i t i a l increment in fracture toughness in three phase materials due to coarse iron powder, even at lower glass contents. The results for three phase composites containing iron powder can be analysed in the following way. At f i r s t , with increasing amounts of glass f i b r e or iron powder, contributions from each would tend to increase the fracture toughness. Opposing this would be the effects of f i b r e - p a r t i c l e interactions operative at high volume fractions. The net result would be an i n i t i a l increase in fracture toughness prior to a subsequent reduction, with increasing amounts of iron powder. This i s exactly what the series of composites containing approximately 16% volume fraction of glass f i b r e exhibits. Volume fractions over 30% in glass fib r e result in an immediate reduction in fracture toughness when powder is added. At intermediate amounts of glass content, a r e l a t i v e l y constant region appears before any reduction due to the additions. 131 VI. SUMMARY AND CONCLUSIONS One of the important mechanical properties in modern resin matrix composites is their resistance to b r i t t l e fracture. The incorporation of reinforcing materials such as p a r t i c l e s and/or f i b r e s can greatly influence the resistance of these materials to fracture. An understanding of the nature and extent of thi s influence is an important element in engineering design, i f these composites are to be u t i l i z e d for optimum toughness and used to their ultimate c a p a b i l i t i e s . Through the use of linear e l a s t i c fracture mechanics, the c r i t i c a l stress intensity factor can sometimes be used as a quantitative test parameter to compare and characterize the behaviour of composite materials in fracture. An attempt has been made in the present work to investigate the fracture behaviour of some composites incorporating randomly oriented chopped glass fibres and/or heavy metal powders in a polyester matrix, employing standard fracture mechanics techniques available for metallic materials. The effects of such variables as the specimen geometry, f i b r e and f i l l e r volume fractions, and p a r t i c l e size on the fracture of these composites have been evaluated. Two phase and three phase powder composites 1 32 containing d i f f e r e n t volume fractions and p a r t i c l e sizes of iron and nickel powder were prepared by a simple casting method. These castings were then used to make compact tension and beading beam specimens for standard fracture toughness tests. A wet lay-up technique was employed to fabricate composites reinforced with glass f i b r e , with or without an additional reinforcement in metal powder. These were again used to make standard bend beam test specimens. Attempts to make bending beam specimens of short fibr e reinforced composites using high pressure injection have not been very successful. The two specimen geometries employed for powder composites resulted in d i f f e r e n t c r i t i c a l stress intensity factors for similar materials. The difference in fracture toughness was largest for the u n f i l l e d resin and a gradual reduction in this difference was observed with increasing amounts of p a r t i c l e additions. The compact tension specimens always resulted in higher toughness values, suggesting that a specimen and loading geometry dependent mechanism might "be responsible for the fracture behaviour of these composites. It was found that a reasonable explanation for the observed experimental results can be advanced based on an hypothesis of stress f i e l d interaction and microcrack formation coupled with the concept of crack front interactions with dispersed p a r t i c l e s . The effects of stress f i e l d interaction and microcrack formation would be more intense in compact tension configuration. For both geometries, and within each composite series the variation of fracture toughness with constituent 1 33 p a r t i c l e volume fraction is shown to be consistent with the above- hypothesis, while the lower toughness of fine nickel composites has partly been attributed to clumping effects of the nickel powder. Composites of glass f i b r e have shown a l i n e a r l y increasing fracture toughness with increasing fib r e volume fraction and the results agreed well with the surface formation model of energy absorption. This suggests that the creation of new f i b r e , matrix and fibre-matrix interfaces is the main contribution to fracture toughness of these composites. The resulting toughness due to fibr e reinforcement however, is much higher than that due to p a r t i c l e dispersions in powder composites mentioned e a r l i e r . The results obtained for three phase composites are consistent with those of two phase powder and fibr e composites. Although the powder dispersions in general have r e l a t i v e l y less influence on fracture, they seem to affect s i g n i f i c a n t l y the fracture toughness of three phase composites at high volume contents of reinforcing materials. This can be attributed to fibre p a r t i c l e interactions which may reduce the energy absorption through debonding, by aff e c t i n g the fibre matrix i n t e r f a c i a l shear stress. The main conclusions which can be drawn from the present study are; 134 (1) . Linear e l a s t i c fracture mechanics can successfully be applied to compare q u a l i t a t i v e l y the behaviour of resin based composites in fracture. (2) . The loading geometry and the specimen configuration are both important in establishing a suitable test specimen geometry for quantitative fracture toughness determination of resin based composites. (3) . The residual stresses due to matrix shrinkage may lead to increased fracture toughness through the formation of microcracks in p a r t i c l e f i l l e d composites. Crack front interactions with p a r t i c l e s may also partly contribute t o the fracture resistance of these composites. (4) . The creation of new fracture surfaces which includes debonding, i s mainly responsible for the fracture behaviour of glass f i b r e reinforced polyester composi tes. (5) . The toughness of three phase p a r t i c l e f i l l e d , glass f i b r e reinforced resin composites i s primarily governed by the f i b r e reinforcement. Heavy metal dispersions do not s i g n i f i c a n t l y affect the fracture toughness at low volume fractions of fibres and p a r t i c l e s . At high volume fractions however, the 135 addition of metal p a r t i c l e s may have a, detrimental ef f e c t on the toughening character of f i b r e reinforcement. 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Load bearing fibr e composites, M.R.Piggott, International series on the strength & fracture of materials & structures, Pergamon Press, 1980, p 62-140. 42. The fracture toughness of fibre composites, D.C.Phillips, A.S.Tetelman, Composites, Sept.1972, p 216-223. 140 43. Elements of fracture mechanics,chapter 8, Deformation and fracture mechanics of engineering materials, R.W.Hetzberg, John Wiley & sons, p 255-295. 44. Fracture toughness of composites, K.G.Kreider, L.Dardi, Failure modes in composites edited by Instvan Toth, TRW Equipment Laboratories, p 193-230. 45. Bearing pressures and cracks, H.M.Westergaard, Trans ASME, Journal of Applied Mechanics, 61, 1939, p 49-53 46. The fracture energy of a glass f i b r e composite, P.W.R.Beaumont, D.C.Philips, Journal of Materials S c i . , 7(1972), p 682-686. 47. Cracking and fracture in composites, G.A.Cooper, M.R.Piggott, advances in research on the strength of fracture of materials, Vol 1, edited by D.M.R.Taplin, Pergamon Press, p 557 48. C r i t i c a l stress intensity factors applied to glass reinforced polyester resin, M.J.Owen, P . T .Bishop, Journal of Composite Materials., Vol 7, Apr 1974, p 146-159. 49. Macroscopic fracture mechanics of glass reinforced polyester resin laminates, A.W.Holdsworth, M.J.Owen, Journal of Composite Materials., Vol 8, A p r i l 1974, p 117- 1 29. 50. The development of a damage zone at the t i p of a crack in a glass reinforced polyester resin, S.Gaggar, L.J.Broutman, International journal on fracture, 10(1-974), p 606-616. 51. Effect of reinforcement geometry on stress intensity factor c a l i b r a t i o n s in composites, H.Harel, G.Marom, S.Fischer, I.Roman, Composites, A p r i l 1980, p 69-72. 52. Preliminary development of a fudamental analysis model crack growth in a fibre reinforced composite material, M.F.Kanninen, E.F.Rybicki, W.L.Griffth, ASTM STP 617, 1977. 53. The fracture toughness of composites reinforced with weakened fi b r e s , G.A.Cooper, Journal of Materials S c i . , 5(1970), p 645-654. 141 54. I n t e r f a c i a l fracture energy and the toughness of composites, T.U.Marston, A.G.Atkins, D.K.Felbeck, Journal of Materials S c i . , 9(1974), p 447-455 55. Tensile stregth of notched carbon f i b r e and glass fib r e composites, Journal of Composite Materials., Vol. 6, Jan.1972, p 32-46. 56. Fracture mechanisms in glass reinforced p l a s t i c s , B.Harris, J.Morley, D.C.Phillips, Journal of Materials S c i . , 10(1975), p 2050-2061 . 57. fracture toughness and mechanical properties of glass fib r e epoxy composites, B.Gershon, G.marom, Journal of Materials S c i . , 10(1975), p 1549-1556. 58. Fracture toughness and crack growth measurements in GRP, M.J.Owen, R.J.Cann, Journal of Materials S c i . , 14(1979), 1982-1996. 59. Dynamic e l a s t i c moduli and toughness of dough moulding compounds, D.Cawthorne, B.Harris, Composites, Jan.1975, p 25-29. 60. Fracture toughness testing methods, J.E.Srawley, W.F.Brown, ASTM special publication, 381(1965), p 133-196. 61. A note on the fracture of polyester resin, B.Harris, F.E..de Moncunill, Journal of Materials S c i . , 4(1969), p 1023-1026. 62. Theory of e l a s t i c i t y , S.Timoshenko, J.N.Goodier, 2nd ed., McGraw-Hill, New York, 1951. 63. Influence of microstructure on fracture propagation in rocks, R.G.Hoagland, G.T.Hann, A.R.Rosenfeld, Rock Mechanics, 5(1973), p 77. 64. Fracture mechanics of ceramics, D.J.Green, P.S.Nicholson, J.D.Embury, Vol. 2, edited by R.C.Bradt, Plenum Press, New York, 1974, p 541. 65. Theoretical estimation of fracture toughness of fibrous composites, M.R.Piggott, Journal of Materials S c i . , 142 5(1970), p 669-675. 66. Composite flywheel stress analysis and materials study, G.F.Morganthaler, S.P.Bonk, Advances in structural composites, 12th annual symposium, Soc. of Aerospace Material & Process Engineers, 1967. 67. Kinetic energy storage of off-peak e l e c t r i c i t y , L.A.Simpson, I.E.Oldaker, J.Stermscheg, Assesment report- Atomic energy of Canada Ltd., AECL-5116, sep. 1973. 68. Flywheels, R.F.Post, S.F.Post, S c i e n t i f i c American, Vol 229, No 6, Dec. 1973, p 17-23. 143 APPENDIX A. High Energy Density Flywheels. Flywheels have t r a d i t i o n a l l y been made of conventional materials, p a r t i c u l a r l y high strength s t e e l . The amount of energy that can be stored in such a flywheel, per unit weight of flywheel material, is s i g n i f i c a n t l y limited due to the high density of s t e e l . However, recent progress in materials technology has led to the design of flywheels that are capable of storing very large amounts of energy per unit of mass. It has been shown that the maximum amount of kinetic energy that can be stored per unit weight of flywheel material is proportional to the materials strength divided by i t s density. As reviewed at the end of this Appendix, a diff e r e n t constant of proportionality, often referred to as the shape factor is associated with each flywheel configuration. In view of t h i s , i t appears that the materials with high strength and low densities are mostly suited for high energy density flywheels. Many fibre composites, being several times lower in density than steel 144 and some even ex h i b i t i n g strengths higher than those of the strongest s t e e l s , have exactly the properties required. In order to take advantage of these properties in designing composite flywheels several flywheel configurations, that are appropriate to composites, have been studied during the past decade. 9 1 0 6 6 6 7 of these, the concentric multi-ring flywheel, o r i g i n a l l y suggested by Rabenhorst 1 0 and P o s t 6 8 is of p a r t i c u l a r i n t e r e s t . It comes clos e r to e f f e c t i v e u t i l i z a t i o n of a f i b r e composite representing a p r a c t i c a l configuration of a high volume e f f i c i e n c y , i e ; nearly a l l of the swept volume stores energy. This comprises a set of concentric rings, coupled with bonded bands of rubber-like material placed in the gaps between the rings. Flywheels incorporating several rings of c i r c u m f e r e n t i a l l y wound fib r e s in resin have been constructed. 9 The design minimizes the r a d i a l stresses preventing r a d i a l delamination and d i s t r i b u t e s the cir c u m f e r e n t i a l stresses more evenly across the thickness. The magnitudes of these stresses, at a radius r, in a ring of inner radius a and outer radius b are given b y , 6 2 3 + v 2 , 2 2 a 2b 2 2 ( A 1 } a = — - — poo ( a + b - — 7 T ~ - r ; V A I ; r • 8 r2 3 + v 2 , 2 , ,2 , a V 1 + 3v 2 ( A 2 ) a Q = - j - pa) ( a + b + - j - ^ - r ) KAZ) 1 45 where, o r CO = r a d i a l stress = circumferential stress = Poisson's r a t i o = angular v e l o c i t y = density of the flywheel material The d i s t r i b u t i o n of these b i a x i a l stresses are p l o t t e d in F i g . 3 6 s 7 for d i f f e r e n t values of a, af t e r 2 2 normalizing by d i v i d i n g by pui r It i s evident from these expressions that as the thickness of the rim i s reduced, the r a d i a l stresses become very small and the stress d i s t r i b u t i o n approaches a u n i a x i a l s i t u a t i o n . The problem of r a d i a l delamination of a u n i d i r e c t i o n a l f i b r e composite can thus be avoided by making the i n d i v i d u a l rings thin enough to minimize the internal r a d i a l stresses. However, since a l l the rims must be constrained to the maximum allowable angular v e l o c i t y of the outer one, the inner rings are now less stressed with respect to -the outer ones and so, do not u t i l i z e t h e i r f u l l capacity of energy storage. The multirim flywheel does not therefore achieve the optimum unless t h i s problem i s overcome by s u i t a b l e material design. Rabenhorst 1 0 has suggested adding increasing amounts of a dense loading material, such as lead powder, to the inner rings to increase the loading (and stored energy). The main purpose would be to d i s t r i b u t e the stresses more evenly from ring to ring as 3 6 . RADIAL AND CIRCUMFERENTIAL STRESS DISTRIBUTIONS IN A DISC FLYWHEEL VS RATIO OF INNER TO OUTER R A D I I . STRESSES ARE NORMALIZED BY D I V I D I N G BY p R u l THE CIRCUMFERENTIAL STRESS IN A THIN R I M . 1 47 well as within the in d i v i d u a l rings, and maximize the t o t a l amount of energy stored in the flywheel. Physics of Flywheels:- . The moment of i n e r t i a about the axis of rotation of a s o l i d disc of radius r, thickness t and density p i s given by, r 2 I = J r pt.2irr dr 0 1 4 2 P t . • irr 1 2 - mr where, z . m = t o t a l mass of the d i s c . The k i n e t i c energy stored in the disc when i t rotates at an angular v e l o c i t y <*> i s K . E . = j I u 2 1 2 2 = r (A3) The maximum hoop stress at the centre of the disc i s 3 + v 2 2 (A4) a = — 5 — pu r max 8 1 48 where, v = Po i s s o n ' s r a t i o From (A3) and (A4) i t i s found t h a t , K.E. / m <* a / p max and k i n e t i c energy per u n i t mass can now be expressed as; a , „ max K.E. / m = S. — — ( A 5 ) where, S = shape f a c t o r a s s o c i a t e d with the f l y w h e e l geometry. K i n e t i c energy per u n i t volume i s ; K - E ' ' V = S ' °max U 6 ) For the s o l i d d i s c c o n f i g u r a t i o n the shape f a c t o r S, i s found t o be s = 2 3 + v = 0.606 for v = 0.3 I t can be shown that f o r rod and t h i n rim c o n f i g u r a t i o n s the v a l u e of the shape f a c t o r i s 1/3 and 1/2 r e s p e c t i v e l y . APPENDIX B. Volume Fraction Determination. An i n i t i a l estimate of the volume fraction of each constituent component was made before the actual fabrication of the composite. These i n i t i a l estimates were based on the requirement of a f i n a l set of data points that extend over the whole range of interest. At the same time physical limitations to these workable ranges were set by certain parameters that were inherent in the par t i c u l a r fabrication technique used. For instance, the thickness or the v i s c o s i t y of a resin powder mixture increased with increasing amounts of powder additions, u n t i l i t became too thick for proper i n f i l t r a t i o n of glass mats or to be used in a simple casting process without much porosity being introduced. The weight proportions of powder(s) and the l i q u i d resin to be mixed were determined for the intended volume fraction(s) of powder(s) using a simple relationship of the form; 1 50 where, Wp = Weight of powder in gms. W = Weight of resin in gms. Vp = Volume f r a c t i o n of powder. V = Volume f r a c t i o n of resin matrix. R Dp = Density of powder in gms/cc D R = Density of the cured resin in gms/cc The resin was catalysed (3 drops per oz. of resin) before the addition of powders and i t was assumed that the c a t a l y s t does not make any s i g n i f i c a n t difference in the volume f r a c t i o n ( s ) of powder(s) present. Nevertheless i t was thought that the volume f r a c t i o n of the constituent powder(s) may have been al t e r e d s l i g h t l y by segregation e f f e c t s and weight losses in polyester due to evolved gasses, during the curing reactions. Hence a correctio n to the i n i t i a l estimates of volume f r a c t i o n s was thought to be appropriate and done accordingly, as explained l a t e r in t h i s section. The r e s u l t s showed a less than 5% drop in the i n i t i a l estimates of volume fr a c t i o n s for 20% V.F. and 2% for 1% V.F. in single powder polyester composites. This was considered to be too small a corr e c t i o n to be applied with any p r a c t i c a l s i g n i f i c a n c e to 151 actual functional behaviour discussed here. Hence for composites containing only powders, the i n i t i a l estimates of volume fractions were assumed to be true volume frac t i o n s . In other words Equation (B1) was used with s u f f i c i e n t accuracy to determine the quantities of powder and resin that had to be mixed in order to achieve any desired volume f r a c t i o n . The same equation was used to calculate the quantities by weight of powder and resin to arrive at di f f e r e n t volume fractions of powder in composites, containing both glass fibres and metal powders. But here the incorporation of glass fib r e mats s i g n i f i c a n t l y changed the i n i t i a l values of powder volume fractions used in Equation (B1) for computing the weight proportions of powder and resin. Besides no prior estimate of the glass fibre volume fraction could be made and d i f f e r e n t volume fractions in glass were obtained simply by incorporating d i f f e r e n t number of layers in the layup. An alternative method of estimating both the powder and the glass fib r e volume fractions was therefore required for these composites. The method used was to burn a small sample of composite at a temperature of 600°. It was l e f t in an oven overnight and the weight loss noted. Although the polyester that was burnt off reduced the ov e r a l l weight of the sample, oxidation of the metal powders resulted in a sl i g h t 1 52 ga i n i n weight. An allowance f o r the weight g a i n due to o x i d a t i o n was made by e s t i m a t i n g the f r a c t i o n a l g a i n i n weight of a sma l l sample of powder, p l a c e d i n s i d e the oven f o r the same p e r i o d of time. I f the f r a c t i o n a l weight g a i n thus determined i s given by C and the o r i g i n a l r a t i o by weight of powder and r e s i n mixed together i s given by R, an e x p r e s s i o n f o r the t o t a l weight l o s s dW can be w r i t t e n as f o l l o w s . dW = W_ - W . RC R R hence, W = dW '/ 1 - RC W = W .R = dW.R / 1 - RC " (B2) P R wp = W - (wR+wp) where, . , W ,W ,W are- the weights of r e s i n , powder and R P F f i b r e p r e s e n t i n the sample. These weights together with c o r r e s p o n d i n g d e n s i t i e s were . then used to c a l c u l a t e the i n d i v i d u a l volume f r a c t i o n s of c o n s t i t u e n t components. These a r e .the true approximate volume f r a c t i o n s used f o r composites c o n t a i n i n g both g l a s s f i b r e s and metal powders. For composites c o n t a i n i n g o n l y g l a s s f i b r e s . the c a l c u l a t i o n s were f u t h e r s i m p l i f i e d , and the above e x p r e s s i o n s would become; dW = W r and Wf = W - WR. (B3) 153 APPENDIX C. FRACTURE TOUGHNESS TEST RESULTS OF THREE-POINT BENDING BEAMS:- The following nomenclature has been used:- VOL%= P a r t i c l e or fi b r e volume fractio n B = Specimen thickness A = Crack length W = Specimen width PM = Maximum load at fracture PQ = 5% offset load at fracture KM = C r i t i c a l stress intensity factor calculated using PM in units of MPa.m0*5 KQ = C r i t i c a l stress intensity factor calculated using PQ in units of Mpa.m0*5 1 54 Coarse Iron in Polyester;- CODE VOL B A W PM KM NO % (CM) (CM) (CM) (LB) (MPA) 21 3.0 0.690 1 .027 1 .400 4.2 0.641 22 3.0 0.685 0.635 1 .395 20.0 1 .024 31 5.0 0.695 0.935 1 .400 6.8 0.737 32 5.0 0.700 0.630 1 .390 19.3 0.967 41 8.0 0.690 0.627 1 .395 24.0 1 .200 4 2 8.0 0.695 0.623 1 .385 15.6 0.784 51 12.0 0.690 0.630 1 .390 28.6 1 .454 52 12.0 0.700 0.640 1 .400 27. 1 1.359 61 13.0 0.700 0.635 1 .395 28.5 1 .429 62 13.0 0.705 0.643 1 .400 27.5 1 .378 71 16.0 0.705 0.633 1 .395 31.8 1 .576 72 16.0 0.700 0.627 1 .390 28.5 1.419 81 25.0 0.700 0.640 1 .400 36.0 1 .805 82 25.0 0.700 0.643 1 .400 36.2 1 .827 1 5 5 Coarse N i c k e l i n P o l y e s t e r : - CODE VOL B A W PM KM NO % (CM) (CM) (CM) (LB) (MPA) 1 1 1 1 . 0 0 . 6 9 5 0 . 7 1 8 1 . 3 9 0 1 0 . 2 0 . 6 2 6 1 1 2 1 . 0 0 . 7 0 0 0 . 5 9 8 1 . 3 5 5 2 0 . 5 1 . 0 3 1 1 1 3 1 . 0 0 . 6 9 5 0 . 6 3 7 1 . 4 0 0 2 1 . 8 1 . 0 9 4 1 1 4 1 . 0 0 . 6 9 5 0 . 6 1 5 1 . 3 8 0 2 0 . 0 0 . 9 9 8 121 3 . 0 0 . 6 9 5 0 . 6 3 5 1 . 4 0 0 1 9 . 9 0 . 9 9 4 1 2 2 3 . 0 0 . 7 0 0 0 . 6 3 8 1 . 4 0 0 1 9 . 5 0 . 9 7 4 1 2 3 3 . 0 0 . 6 9 5 0 . 6 4 0 1 . 4 0 0 2 1 . 6 1 . 091 1 24 3 . 0 0 . 6 9 0 0 . 6 3 0 1 . 4 0 0 2 0 . 6 1 . 0 2 6 131 5 . 0 0 . 7 0 0 0 . 6 3 0 1 . 3 9 5 2 0 . 0 0 . 9 9 2 1 32 5 . 0 0 . 6 9 5 0 . 6 3 3 1 . 3 9 5 2 0 . 0 1 . 0 0 5 1 3 3 5 . 0 0 . 6 9 0 0 . 6 3 8 1 . 4 0 0 2 1 . 2 1 . 0 7 4 1 34 5 . 0 0 . 7 0 0 0 . 6 3 0 1 . 3 9 5 1 5 . 6 0 . 7 7 4 141 1 0 . 0 0 . 6 8 5 0 . 6 3 2 1 . 4 0 0 2 2 . 6 1 . 1 3 9 1 4 2 1 0 . 0 0 . 7 0 0 0 . 6 2 6 1 . 3 9 0 2 2 . 6 1 . 1 2 3 1 4 3 1 0 . 0 0 . 6 9 0 0 . 6 3 7 1 . 4 0 0 2 2 . 0 1 . 1 1 2 1 44 1 0 . 0 0 . 6 9 5 0 . 6 0 5 1 . 3 6 0 2 0 . 1 1 . 0 2 3 Continued., CODE VOL B A W PM KM NO % (CM) (CM) (CM) (LB) (MPA) 151 15.0 0.680 0.630 1 .392 22.2 1 . 140 1 52 15.0 0.695 0.628 1 .382 23.5 1 .200 1 53 15.0 0.695 0.630 1 .392 24.2 1.216 1 54 15.0 0.700 0.635 1 .390 21.4 1 .084 161 20.0 0.680 0.628 1 .382 28.0 1 .462 1 62 20.0 0.695 0.626 1 .380 31.0 1 .583 1 63 20.0 0.695 0.557 1 .315 24.9 1 .253 1 64 20.0 0.690 0.638 1 .400 28.2 1 . 428 157 F i n e N i c k e l i n P o l y e s t e r ; - CODE VOL B A W PM KM NO % (CM) (CM) (CM) (LB) (MPA) 21 1 1 . 0 0 . 6 9 5 0 . 6 1 1 1 . 3 8 0 1 9 . 0 0 . 9 4 0 2 1 2 1 . 0 0 . 7 0 0 0 . 6 3 7 1 . 4 0 0 1 3 . 0 0 . 6 4 8 2 1 3 1 . 0 0 . 6 8 5 0 . 7 2 7 1 . 4 0 0 9 . 4 0 . 5 8 5 2 1 4 1 . 0 0 . 7 0 0 0 . 6 9 0 1 . 3 9 6 1 1 . 1 0 . 6 2 6 221 5 . 0 0 . 6 9 5 0 . 6 4 8 1 . 4 0 0 1 9 . 5 1 . 0 0 2 2 2 2 5 . 0 0 . 6 9 5 0 . 6 2 8 1 . 3 8 2 1 8 . 2 0 . 9 3 0 2 2 3 5 . 0 0 . 7 0 0 0 . 6 4 0 1 . 4 0 0 1 2 . 2 0 . 6 1 2 2 2 4 5 . 0 0 . 6 9 5 0 . 6 3 5 1 . 3 9 5 1 3 . 4 0 . 6 7 6 231 1 6 . 0 0 . 6 9 0 0 . 6 3 0 1 . 3 9 5 1 4 . 0 0 . 7 0 4 2 3 2 1 6 . 0 0 . 6 9 5 0 . 6 3 5 1 . 3 9 2 1 9 . 9 1 . 0 1 1 2 3 3 1 6 . 0 0 . 6 9 5 0 . 6 3 0 1 . 3 9 5 1 8 . 8 0 . 9 3 9 2 3 4 1 6 . 0 0 . 6 8 0 0 . 6 4 0 1 . 4 0 0 2 0 . 0 1 . 0 3 2 241 2 0 . 0 0 . 6 9 5 0 . 6 2 3 1 . 3 9 0 1 8 . 7 0 . 9 3 0 2 4 2 2 0 . 0 0 . 6 9 0 0 . 6 2 2 1 . 3 9 8 1 7 . 2 0 . 8 4 6 2 4 3 2 0 . 0 0 . 7 0 0 . 0 . 6 3 8 1 . 4 0 0 1 8 . 2 0 . 9 0 9 2 4 4 2 0 . 0 0 . 6 9 5 0 . 6 3 8 1 . 4 0 0 1 8 . 5 0 . 9 3 0 158 Coarse Iron plus Fine Nickel in Polyester;- CODE VOL B A W PM KM NO % (CM) (CM) (CM) (LB) (MPA) 261 5.0 0.695 0.621 1 .383 23.8 1 . 1 95 262 5.0 0.700 0.623 1 .386 21.7 1.080 263 5.0 0.695 0.597 1 .363 19.2 0.954 264 5.0 0.700 0.503 1 .255 14.3 0.719 271 12.0 0.700 0.633 1 . 393 26.3 1.318 272 12.0 0.700 0.621 1 .388 25.9 1 .278 273 12.0 0.700 0.625 1 .392 26.6 1.313 274 12.0 0.700 0.624 1 .395 27.8 1 . 36-1 281 20.0 0.695 0.610 1 . 380 27.8 1 .372 282 20.0 0.700 0.606 1 . 380 31.0 1 .507 283 20.0 0.695 0.628 1 .392 28.4 1.421 284 20.0 0.695 0.622 1 .388 29.3 1 .460 G l a s s F i b r e i n P o l y e s t e r : - CODE VOL B A W PQ PM KQ KM NO % (CM) (CM) (CM) (LB) (LB) (MPA) (MPA) 31 1 1 6 . 8 0 . 7 0 0 0 . 6 3 0 1 .3 -95 1 3 7 . 5 1 6 0 . 5 6 . 819 7 . 9 6 0 3 1 2 1 6 . 8 0 . 7 0 0 0 . 6 3 5 1 . 3 9 6 1 2 5 . 0 1 5 1 . 2 6 . 2 5 3 7 . 5 6 3 3 1 3 1 6 . 8 0 . 7 0 0 0 . 6 3 8 1 . 3 9 8 1 2 5 . 0 1 5 6 . 5 6 . 2 6 7 7 . 8 4 6 3 1 4 1 6 . 8 0 . 7 0 0 0 . 6 3 1 1 . 3 9 5 1 3 6 . 3 1 5 3 . 4 6 . 7 7 4 7 . 6 2 4 32 1 2 4 . 2 0 . 7 0 0 0 . 6 3 5 1 . 3 9 8 1 6 0 . 0 2 2 6 . 0 7 . 9 7 1 1 1 . 2 5 9 3 2 2 2 4 . 2 0 . 6 9 5 0 . 6 2 5 1 . 3 9 0 1 5 3 . 6 2 3 5 . 8 7 . 6 6 9 1 1 . 7 7 3 3 2 3 2 4 . 2 0 . 7 0 0 0 . 6 3 3 1 . 3 9 8 1 6 8 . 8 2 2 5 . 3 8 . 3 7 4 1 1 . 1 7 6 3 2 4 2 4 . 2 0 . 6 9 2 0 . 6 2 7 1 . 3 8 8 1 8 0 . 0 2 1 3 . 8 9 . 1 0 2 1 0 . 8 1 1 331 3 1 . 1 0 . 6 9 0 0 . 6 2 5 1 . 3 9 2 2 3 0 . 0 2 4 7 . 5 1 1 . 5 2 0 1 2 . 3 9 7 3 3 2 3 1 . 1 0 . 6 9 5 0 . 6 2 5 1 . 3 9 3 231 . 2 2 7 6 . 0 11 . 4 7 4 1 3 . 6 9 7 3 3 3 3 1 . 1 0 . 6 9 5 0 . 6 3 0 1 . 3 9 3 2 3 6 . 8 281 . 2 11 . 8 7 7 1 4 . 1 0 4 3 3 4 3 1 . 1 0 . 7 0 0 0 . 6 4 6 1 . 3 9 8 2 0 8 . 8 2 7 7 . 2 1 0 . 6 4 8 1 4 . 1 3 7 341 3 3 . 7 0 . 6 9 2 0 . 6 3 2 1 . 3 9 5 2 8 0 . 2 3 0 9 . 2 1 4 . 1 1 7 1 5 . 5 7 8 3 4 2 3 3 . 7 0 . 6 9 2 0 . 6 1 8 1 . 3 8 5 2 5 7 , . 6 3 0 2 . 4 1 2 . 8 5 8 1 5 . 0 9 4 3 4 3 3 3 . 7 0 . 7 0 0 0 . 6 3 5 1 . 3 9 5 2 7 2 . 5 3 0 2 . 8 1 3 . 6 5 9 1 5 . 1 7 7 3 4 4 3 3 . 7 0 . 6 8 5 0 . 6 3 1 1 . 3 9 5 2 8 0 . 8 3 2 8 . 0 1 4 . 2 6 1 1 6 . 6 5 8 1 60 Fine N i c k e l i n P o l y e s t e r C o n t a i n i n g 2 4 . 2 V o l % G l a s s ; - CODE VOL B A W PQ PM KQ KM NO % (CM) (CM) (CM) (LB) (LB) (MPA) (MPA) 361 0 . 4 0 . 7 0 0 0 . 6 3 8 1 . 3 9 7 2 0 9 . 2 2 2 7 . 0 1 0 . 5 1 0 1 1 . 4 0 4 3 6 2 0 . 4 0 . 6 9 0 0 . 6 2 5 1 . 3 9 2 1 6 9 . 2 1 9 0 . 5 8 . 4 7 5 9 . 5 4 2 3 6 3 0 . 4 0 . 7 0 0 0 . 6 2 7 1 . 3 9 0 1 6 8 . 4 1 8 8 . 0 8 . 3 8 4 9 . 3 5 9 3 6 4 0 . 4 0 . 7 0 0 0 . 6 2 9 1 . 3 7 0 1 6 8 . 8 1 8 0 . 0 8 . 7 9 6 9 . 3 7 9 37 1 0 . 8 0 . 7 0 0 0 . 6 3 5 1 . 4 0 0 1 7 2 . 4 2 1 5 . 2 8 . 5 5 4 1 0 . 6 7 7 3 7 2 0 . 8 0 . 6 8 0 0 . 6 3 5 1 . 4 0 6 1 8 0 . 0 2 0 5 . 6 9 . 1 9 3 1 0 . 5 0 1 3 7 3 0 . 8 0 . 6 9 8 0 . 6 2 5 1 . 3 9 0 2 2 4 . 0 2 4 0 . 4 1 1 . 1 3 6 1 1 . 9 5 2 3 7 4 0 . 8 0 . 7 0 0 * 0 . 6 6 7 1 . 3 9 7 1 6 0 . 8 1 8 5 . 2 8 . 6 0 0 9 . 9 0 5 381 2 . 5 0 . 6 9 5 0 . 6 3 8 1 . 4 0 0 1 6 7 . 6 1 8 8 . 0 8 . 4 2 9 9 . 4 5 5 3 8 2 2 . 5 0 . 6 9 8 0 . 6 1 8 1 . 3 8 0 1 7 0 . 8 1 8 8 . 0 8 . 5 3 8 9 . 3 9 8 3 8 3 2 . 5 0 . 7 0 0 0 . 6 3 7 1 . 3 9 0 1 7 7 . 0 2 0 3 . 0 9 . 0 0 2 1 0 . 3 2 4 3 8 4 2 . 5 0 . 6 9 0 0 . 6 2 2 1 . 3 7 5 1 8 0 . 0 1 9 9 . 0 9 . 2 7 5 1 0 . 2 5 4 391 6 . 6 0 . 7 0 0 0 . 6 4 4 1 . 3 8 9 1 7 4 . 0 1 7 8 . 8 9 . 0 0 2 9 . 2 5 0 3 9 2 6 . 6 0 . 6 9 6 0 . 6 3 7 1 . 3 8 5 1 6 0 . 4 1 8 4 . 0 8 . 2 9 0 9 . 5 0 9 3 9 3 6 . 6 0 . 7 0 0 0 . 6 4 0 1 . 3 7 8 1 7 8 . 8 1 8 9 . 0 9 . 3 8 4 9 . 9 1 9 3 9 4 6 . 6 0 . 6 9 0 0 . 6 4 3 1 . 3 9 5 1 5 6 . 3 1 6 4 . 7 8 . 0 8 5 8 . 5 1 9 161 Continued., CODE VOL B A W PQ PM KQ KM NO % (CM) (CM) (CM) (LB) (LB) (MPA) (MPA) 401 14.1 0.695 0.641 1 .390 1 57 .8 177.0 8. 153 9.145 402 14.1 0.700 0.640 1 .393 161.0 1 79.4 8. 190 9.126 403 14.1 0.700 0.646 1 .398 1 69.2 185.6 8.629 9.465 404 14.1 0.690 0.635 1 .388 159.0 186.0 8.202 9.595 162 Coarse Iron in Polyester Containing 24.2 Vol% Glass:- CODE VOL B A W PQ PM KQ KM NO % (CM) (CM) (CM) (LB) (LB) (MPA) (MPA) 51 1 0.8 0 .690 0 .636 1 .384 163.2 174.6 8.507 9.101 512 0.8 0 .690 0 .640 1 .390 183.4 207.0 9. 523 10.749 513 0.8 0 .695 0 .645 1 .395 182.5 202.0 9.412 10.418 514 0.8 0 .695 0 .642 1 .395 148.6 181.0 7.615 9.275 521 2.5 0 .695 0 .643 1 .396 187.5 206.5 9.609 10.583 522 2.5 0 .700 0 .636 1 . 392 151.5 176.0 7.657 8.895 523 2.5 0 .680 0 . 644 1 . 392 161.6 1 88.3 8. 553 9.966 524 2.5 0 .695 0 .648 1 .398 1 62.8 186.4 8.398 9.616 531 6.5 0 .700 0 .639 1 .390 195.3 206.4 9.975 10.542 532 6.5 0 .690 0 .642 1 .392 135.3 185.4 7.027 9.629 533 6.5 0 .695 0 . 636 1 .395 189.0 221 .4 9. 562 11.201 534 6.5 0 .695 0 .638 1 .390 202 .2 216.0 10.379 11.088 541 13.9 0 .690 0 .640 1 .393 106.5 185. 1 5. 496 9. 552 542 •13.9 0 .690 0 . 642 1 .390 135.3 178.2 7.056 9.293 543 13.9 0 .695 0 .647 1 .395 131.7 195.0 6.822 10.100 544 13.9 0 .700 0 .645 1 .392 96.0 176.4 4.946 9.089 1 63 Fine Nickel in Polyester Containing 16.8 Vol% Glass:- CODE VOL B A W PQ PM KQ KM NO % (CM) (CM) (CM) (LB) (LB) (MPA) (MPA) 561 2.6 0.700 0.665 1 .385 123.0 132.0 6.720 7.211 562 2.6 0.697 0.698 1 .392 99.0 1 22.0 5.762 7.101 563 2.6 0.690 0.695 1 .400 126.3 138.0 7.246 7.917 564 2.6 0.695 0.689 1 .383 126.5 139.6 7.379 8. 1 44 571 14.2 0.696 0.672 1 .387 114.5 143.0 6.362 7.946 572 14.2 0.695 0.696 1 .387 1 09.0 1 32.0 6.404 7 .755 573 14.2 0.695 0.675 1 .395 118.5 1 58.0 6. 525 8.700 574 14.2 0.690 0.687 1 .383 105.5 126.2 6.171 7.382 1 64 Coarse Iron in Polyester Containing 16.8 Vol% Glass:- CODE VOL B A W PQ PM KQ KM NO % (CM) (CM) (CM) (LB) (LB) (MPA) (MPA) 581 2.7 0.695 0.698 1 .394 1 45.7 160.0 8.467 9.298 582 2.7 0.695 0.696 1 .387 161.0 180.0 9.459 10.576 583 2.7 0.695 0.685 1 .385 142.4 1 68. 0 8. 1 95 9.669 584 2.7 0.692 0.715 1 .394 157.5 175.5 9.559 10.651 591 14.3 0.695 0.685 1 .388 115.7 149.0 6.615 8.519 592 14.3 0.700 0.679 1 . 391 1 50.2 1 67.8 8.357 9.336 593 14.3 0.695 0.688 1 .400 135.6 179.0 7 .603 10.037 594 14.3 0.695 0.685 1 .400 122.0 171.8 6.795 9.569 165 Fine Nickel in Polyester Containing 31.1 Vol% Glass;- CODE VOL B A W PQ PM KQ KM NO % (CM) (CM) (CM) (LB) (LB) (MPA) (MPA) 61 1 0.7 0.695 0 .628 1 .390 235.2 271 .6 11.818 13.648 612 0.7 0.700 0 .640 1 .400 266.0 282.0 13.338 14.141 613 0.7 0.695 0 .642 1 .400 244.8 270.8 12.416 13.735 614 0.7 0.695 0 .632 1 . 386 255.2 266. 5 13.040 13.617 621 9.8 0.695 0 .698 1 . 388 200.0 233.0 11 .778 13.722 622 9.8 0.690 0 .705 1 .393 178.4 211.0 10.634 12.578 623 9.8 0.695 0 .707 1 . 395 166.0 204.0 9.825 12.074 624 9.8 0.690 0 .698 1 .398 177.4 1 97.2 10.292 11.441 1 66 Coarse Iron in Polyester Containing 31.1 Vol% Glass:- CODE VOL B A W PQ PM KQ KM NO % (CM) (CM) (CM) (LB) (LB) (MPA) (MPA) 631 2.4 0 .695 0 .691 1 .393 209.3 249.6 11.997 14.307 632 2.4 0 .695 0 .690 1 .395 187.4 238.0 10.671 13.552 633 2.4 0 .686 0 .687 1 .394 192.6 243.6 11.060 13.989 634 2.4 0 .695 0 .685 1 .393 192.0 240.0 10.858 13.572 642 13.2 0 .688 0 .670 1 .387 1 56.0 194.6 8.730 10.890 643 13.2 0 .695 0 .698 1 .397 144.8 171.6 8.359 9.906 644 13.2 0 .695 0 .651 1 .381 1 55.2 189.6 8.351 10.202 646 13.2 0 .890 0 .685 1 .420 196.0 258.0 8. 1 69 10.753 647 13.2 0 .885 0 .702 1 .420 210.0 244.0 9. 1 36 10.615 167 APPENDIX D. COMPUTER PROGRAMS:- The following programs were used to calculate various parameters involved, and to produce the plots using the UBC computing f a c i l i t y . A brief description of each program i s given in appropriate comment f i e l d s . C ********************************************* C C THIS IS A PROGRAM TO CALCULATE THE CRITICAL STRESS C INTENSITY FACTOR OF BRITTLE POLYMER COMPOSITES USING C A BENDING BEAM SPECIMEN CONFIGURATION. STANDARD C EQUATIONS FOR PLANE STRAIN FRACTURE TOUGHNESS OF C METALLIC MATERIALS GIVEN IN ASTM E399-78A ARE USED. C C **************************************************** c C DEFINE VARIABLES. C C VF = VOLUME FRACTION (%) C B = SPECIMEN THICKNESS (CM) C A = CRACK LENGTH (CM) C W = SPECIMEN WIDTH (CM) C PM = MAXIMUM LOAD AT FRACTURE (LBS) C PQ = 5% OFFSET LOAD AT FRACTURE (LBS) C 1 READ(5,2)N 2 FORMAT(12) IF(N.EQ.0)GOTO 7 WRITE(6,5) 5 FORMAT(/////,2X,'CODE*,8X,'VOL',4X,'B',6X,'A',6X,'W', 16X,'PM',8X,'KM',6X,'A/W') WRITE(6,6) 6 FORMAT(/,3X,'NO*,10X,'%',4X,'(CM)',3X,'(CM)',3X,'(CM)' 1,3X,'(LB)',5X,'(MPA)',/) GOTO 10 168 7 WRITE(6,8) 8 FORMAT(/////,2X,'CODE',8X,'VOL',4X,'B',6X,'A',6X,'W', 16X,'PQ',4X,'PM',6X,'KQ',5X,'KM', 5X,'PM/PQ', 6X,'A/W') WRITE(6,9) 9 FORMATC/,3X,'NO',10X,'%',4X,'(CM)*,3X,'(CM)',3X,'(CM)' 1,3X,'(LB)',2X,'(LB)',3X,'(MPA)',2X,'(MPA)',/) C 10 READ(5,12,END=120)1,J,VF,B,A,W,PM,PQ 12 F0RMAT(I2,I3,F5.1,3F6.3,2F6.1) REAL KQ,KM C C ASSIGN THE VALUE OF SPAN S IN CM C S = 5.6 C C=S/(B*W**1.5) CQ=PQ*C*4.448E-3 CM=PM*C*4.448E-3 C F1=(3*SQRT(A/W))*(1.99-(A/W)*(1-A/W)*(2.15~3.93*(A/W) 1+2.7*(A/W)**2.0)) F2=2*(1+2*(A/W))*(1-(A/W))**1.5 F=F1/F2 Z=A/W IF(PQ.EQ.0)GOTO 18 KQ=CQ*F KM=CM*F R=PM/PQ GOTO 28 C 18 KM=CM*F WRITE(7,19)VF,KM 19 FORMAT(F8.1,F14.3) IF(I.LE.0)GOTO 21 WRITE(6,2 0)J,VF,B,A,W,PM,KM,Z 20 F0RMAT(//,I5,F12.1 ,3F7.3,F7.1 ,F10.3,F9.3) IF(I)1 ,10, 10 21 WRITE(6,22)J,VF,B,A,W,PM,KM,Z 22 FORMAT(/,I5,F12.1 ,3F7.3,F7. 1 , F10 . 3,F9.3) IF(I ) 1 , 10, 10 C 28 WRITE(7,29)VF,KQ,KM 29 FORMAT(F8.1,2F7.3) IF(I.LE.0)GOTO 31 WRITE(6,3 0)J,VF,B,A,W,PQ,PM,KQ,KM,R,Z 30 FORMAT(//,I5,F12.1,3F7.3,F7.1,F6.1,F8.3,F7.3,F8.1,F11.3)• IF(I)1 , 10 , 10 31 WRITE(6,32)J,VF,B,A,W,PQ,PM,KQ,KM,R,Z 32 FORMAT(/,I5,F12.1,3F7.3,F7.1,F6.1,F8.3,F7.3,F8.1,F11.3) IF (I ) 1 , 1 0 , 1 0 1 20 STOP END 1 69 Q *********************************************** c C THIS IS A PROGRAM TO PLOT THE EXPERIMENTAL VALUES C OF CRITICAL STRESS INTENSITY FACTOR AGAINST THE C VOLUME FRACTION OF A SECOND PHASE FILLER MATERIAL IN C POLYMER COMPOSITES.THIS PROGRAMME PLOTS A SMOOTH CURVE C THROUGH THE AVERAGE VALUES OF STRESS INTENSITY FACTORS C USING A PARABOLIC CURVE FITTING ROUTINE. THIS PROGRAM C HAS THE FLEXIBILITY OF COMBINING NUMBER OF PLOTS C TOGETHER OR PLOTTING AT A PRE-CHOSEN SCALE. C Q ****************************************************** c c DIMENSION X(300),Y(300),Z(300),AVEX(100),AVEY(100) 1 READ(5,2)M 2 FORMAT(12) IF(M.EQ.0)GOTO 300 C 10 N=0 C C READ THE CALCULATED VALUES OF CRITICAL STRESS C INTENSITY FACTORS AND THE EXPERIMENTALLY C DETERMINED VOLUME FRACTIONS C DO 100 1=1,300 READ(5,50,END=200)L,X(I),Y(I),Z(l) 50 FORMAT(I 2,F6.1 ,2F7.3) N=I K=2*N C IF(L.NE.0)GOTO 200 100 CONTINUE 200 IF(N.EQ.0)GOTO 300 DO 250 1=1,100 AVEX(I)=0.0 250 AVEY(I)=0.0 INP=0 CALL XNUM(X,N,INP) C C START PLOTTING A CURVE THROUGH N DATA POINTS C CALL GRAPH(X,Y,Z,N,K,L,AVEX,AVEY,INP) IF(M.NE.1)GOTO 1 300 CONTINUE CALL PLOTND STOP END SUBROUTINE GRAPH(X,Y,Z,N,K,L,AVEX,AVEY,INP) DIMENSION X(N),Y(N),Z(N),W(300),AVEX(INP),AVEY(INP) C NTEST=0 DO 2 I=1,N 170 IF(Y(I).EQ.0)NTEST=1 2 CONTINUE C IF(L.LT.10)GOTO 3 IF(L.EQ.11)GOTO 30 IF(L.EQ.21)GOTO 30 GOTO 40 C C SET THE SCALES FOR THE PLOT C 30 XMI=0.0 DDX=2.5 YMI=0.4 DDY=0.2 CALL AXIS(0.0,1.0,'VOLUME FRACTION(%)', -18,10.0 1,0.0,XMI,DDX) CALL AXIS(0.0,1.0,'CRITICAL STRESS INTENSITY(MPA.M1/2)' 1,35,8.0,90.0,YMI,DDY) 40 J = 2 LL=0 IF(L.LT.20)GOTO 41 LL=L L=L-10 41 IF(L.EQ.16)J=0 IF(L.EQ.17)J=1 IF(L.EQ.18)J=3 IF(L.EQ.19)J=11 JJ=J+1 DO 42 1=1,N 42 X(I)=(X(I)-XMI)/DDX IF(NTEST.EQ.1)GOTO 60 DO 52 1=1,N 52 Y(I)=(Y(I)-YMI)/DDY+1.0 60 DO 62 1=1,N 62 Z(I)=(Z(I)-YMI)/DDY+1.0 I F (NTEST. EQ.. 1 )GOTO 80 DO 7 2 1=1,N 72 CALL SYMBOL(X(I),Y(I),0.07,JJ,0.0,-1) CALL CURVE(X,Y,N,AVEX,AVEY,INP) 80 DO 82 1=1,N 82 CALL SYMBOL(X(l),Z(I),0.07,J,0.0,-1) CALL CURVE(X,Z,N,AVEX,AVEY,INP) IF(LL.LT.20)GOTO 90 CALL PLOT(12.0,0.0,-3) 90 RETURN C 3 IF(NTEST.EQ.1)GOTO 10 C DO 4 I=1,N W(I)=Y(I) 4 W(N+I)=Z(I) C CALL SCALE(W,K,8.0,YMIN,DY,1) CALL AXIS(0.0,1.0,'CRITICAL STRESS INTENSITY(MPA.M1/2)' 171 1,35,8.0,90.0,YMIN,DY) DO 6 I = 1 , N Y(I)=W(I) 6 Z(I)=W(N+I) GOTO 1 1 10 CALL SCALE( Z , N , 8 . 0 ,YMIN,DY,I) CALL AXIS(0.0,1.0,'CRITICAL STRESS INTENSITY(MPA.M1/2)' 1,35,8.0,90.0,YMIN,DY) 11 CALL SCALE(X,N,10.0,XMIN,DX,1) CALL AXIS(0.0,1.0,'VOLUME FRACTION (%)* , - l 8 , lO .O , 10.0,XMIN,DX) J=1 IF(L.EQ.6)J=0 IF(L.EQ.7)J=1 IF(L.EQ.8)J=3 IF(L.EQ.9)J=11 IF(NTEST.EQ.1)GOTO 19 DO 18 1=1,N Y(I)=Y(I) + 1 .0 18 CALL SYMBOL(X(l),Y(I ),0.07,J,0.0,-1 ) CALL CURVE(X,Y,N,AVEX,AVEY,INP) 19 DO 20 1=1,N Z(I)=Z(I ) + 1 .0 20 CALL SYMBOL(X(l),Z(I ),0.07,4,0.0,-1 ) CALL CURVE(X,Z,N,AVEX,AVEY,INP) CALL PLOT(12.0,0.0,-3) RETURN END SUBROUTINE CURVE(X,Y,N,AVEX,AVEY,INP) DIMENSION X(N),Y(N),AVEX(INP),AVEY(INP) EXTERNAL PARAB IND=0 IN=0 DO 100 J=1,INP IND=IND+IN XX=X(IND+1) NN=N-IND DO 1 I=1,NN IF(X(IND+I).NE.XX)GOTO 2 1 IN=I 2 SUMY=0.0 DO 4 1 = 1 , IN 4 SUMY=SUMY+Y(IND+I ) AVEX(J)=XX AVEY(J)= SUMY/1N 100 CONTINUE 200 CALL SKETCH(AVEX,AVEY,INP,25,1,1.5,PARAB) RETURN END SUBROUTINE XNUM(X,N,INP) DIMENSION X(N) IND=0 IN=0 300 IND=IND+IN IF(lND.GE.N)GOTO 500 NN=N-IND DO 350 1=1,NN IF(X(IND+I).NE.X(IND+1))GOTO 360 IN=I 350 CONTINUE 360 INP=INP+1 400 GOTO 300 500 RETURN END 173 Q ***************************************** C C THIS IS A PROGRAM TO CALCULATE THE CRITICAL STRESS C INTENSITY FACTORS OF POLYMER COMPOSITES USING A C COMPLIANCE METHOD. A LEAST SQUARE POLYNOMIAL CURVE C FITTING ROUTINE IS USED TO FIT THE COMPLIANCE DATA. C £ ****************************************************** C c IMPLICIT REAL*4 (A-H rO-Z) DIMENSION X(50),Y(50),YF(50),YD(50),WT(50),S(11), 1 SIGMA(11),A(10),B(10),P(11),XX(25),YY(25),YYD(25) DIMENSION XXP(600),YYP(650),YYDP(600)J(25),VF(25), IBB(25),PM(25),GC(25),TC(25),TIC3(25),TIC5(25) LOGICAL LK C 1 READ(5,5)K,N,BBS 5 FORMAT(/,2I2,F6.3) IF(N.EQ.0)GOTO 100 C C READ THE COMPLIANCE VALUES AND THE CORRESPONDING C CRACK LENGTHS C DO 21 I=1,N R E A D ( 5 , 2 0 , E N D = 2 1 ) X ( l ) , Y ( l ) 2 0 FORMAT(2X,2F8.3) 21 CONTINUE READ(5,2 5)M,E 2 5 FORMAT(I 4,E11.3) DO 41 1=1,M READ(5,40,END=41)J(I),VF(I),BB(I),XX(I),PM(I) 40 FORMAT(2X,I3,F5.1,2F6.3,6X,F6.1) 41 CONTINUE C NWT=0 LK=.FALSE. C C CHOOSE THE BEST FITTING CURVE OF POLYNOMIAL OF DEGREE C LESS THAN OR EQUAL TO K C CALL OLSF(K,N,X,Y,YF,YD,WT,NWT,S,SIGMA,A,B,SS,LK,P) CALL OLINT(XX,YY,YYD,M) C C SEE THE PLOT ON THE SCREEN C CALL SEE(X,Y,XXP,YYP,YYDP,N) C=2.54E-6 C WRITE(6,70)K 70 FORMAT(////,2X,'TOUGHNESS USING COMPLIANCE METHOD',3X, 1'K=',12,/) DO 90 1=1,M 174 GC(I)=(PM(I)**2./(2.*BB(I)**2.))*YYD(l)*BBS TC(I)=SQRT(GC(I)*E*C)*1.099E-3 TIC3(I)=TC(I)/SQRT(0.9l ) TIC5(I)=TC(I)/SQRT(0.75) WRITE(6,80 ) J ( I ),TC ( I),TIC3(I),TIC5 ( I ) 80 FORMAT(/,15,3X,3F10.3) WRITE(7,81)VF(I),TIC3(I ) 81 FORMAT(F8.1,F1 4.3) 90 CONTINUE GOTO 1 100 STOP END SUBROUTINE SEE(X,Y,XXP,YYP,YYDP,N) DIMENSION X(N),Y(N),XXP(600),YYP(650),YYDP(600) CALL PLCTRL('SCAL',0.7) CALL AXCTRL('YORI',1.0) CALL AXCTRL('LABE',1) CALL AXCTRL('SYMS',0.118) DDX=(X(N)-X(1))/599 DO 200 1=1,600 200 XXP(I)=X(1)+DDX*(I-1) CALL OLINT(XXP,YYP,YYDP,600) DO 2 01 I = 1 ,N 201 YYP(I+600)=Y(I ) NN=600+N CALL SCALE(XXP,600,10.0,XMIN,DX,1) CALL SCALE(YYP,NN,7.5,YMIN,DY,1) CALL AXPLOT('CRACK LENGTH (cm);',0.0,10.0,XMIN,DX) CALL AXPLOT('COMPLIANCE (cm/lbf);',90.0,7.5,YMIN,DY) DO 208 1=1,N X(I)=(X(I)-XMIN)/DX YYP(l+600)=YYP(l+600)+1.0 . 208 CALL SYMBOL(X(l),YYP(I+600),0.1,4,0.,-1) DO 210 1=1,600 YYP(I)=YYP(I)+1.0 IF(I.GT.1)GOTO 209 CALL PLOT(XXP(l),YYP(I),+3) GOTO 210 209 CALL PLOT(XXP(l),YYP(I),+2) 210 CONTINUE CALL PLOT(10.0,0.0,-3) RETURN END 175 APPENDIX E. STRAIN ENERGY RELEASE RATE ANALYSIS. The s t r a i n energy r e l e a s e r a t e f o r a l i n e a r e l a s t i c i s o t r o p i c specimen of u n i t t h i c k n e s s i s gi v e n b y ; 4 3 2 G I C = ~ ( dC/da ) (C1 ) where, G = C r i t i c a l s t r a i n energy r e l e a s e r a t e P = Load to f r a c t u r e a specimen of u n i t t h i c k n e s s C = Compliance f o r u n i t t h i c k n e s s a = Crack l e n g t h * I f a specimen of t h i c k n e s s B i s used f o r the compliance c a l i b r a t i o n , and the compliance of t h i s specimen * i s found to be C R , then 1 76 * A . d( C B ) dC/da = da = B * ( dC* / da ) (C2) 15 where, C * b = Compliance of a specimen of t h i c k n e s s B I f a l o a d ? B i s r e q u i r e d to f r a c t u r e a specimen of t h i c k n e s s B, the l o a d P r e q u i r e d f o r a u n i t specimen t h i c k n e s s i s g i v e n by; P = ! B (C3) B S u b s t i t u t i n g (C2) and (C3) i n ( C I ) , 2 G I C = —| B ( dC B / da ) = ~ 2 - B ^ ^ / d a ) 177 APPENDIX F. INJECTION MOULDING UNIT. The injection moulding unit shown in Figs.21 and 37 which was b u i l t to make rectangular beam specimens of chopped fibre reinforced composites, mainly consisted of; a. A c y l i n d r i c a l hopper that holds the catalysed l i q u i d resin mixture and delivers i t to the system. b. A pressure gauge connected to the in l e t of the injecting cylinder. c. An injector consisting of a piston and a cylinder. d. The mould consisting of a main specimen chamber and a top chamber to accumulate the excess resin, plus a slider-clamp arrangement to ram the fibres i n . A f l a t bottom c y l i n d r i c a l hopper was made out of mild s t e e l , and through a small hole at the centre of the bottom, a delivery tube was provided. This passed through an i n l e t valve and was connected at the end to the i n l e t of FIG. 3 7 . Injection Moulding Unit. 179 the injector system. The i n l e t of the injector was again a short segment of steel tubing with connections to a pressure gauge through i t s sides. The pressure gauge was connected through a copper U-tube, that was permanently attached to the pressure gauge. The gauge could read pressures up to 1000 l b f / i n 2 The injector consisted mainly of a piston and a cylinder. The bearing surfaces of these were machined very accurately and a c i r c u l a r groove was provided on the piston for an O-ring. The piston was connected to a cranking device by means of a threaded piston rod. This rod passed through a set of threads made in the cylinder cap and provided the necessary piston movements when i t was cranked in the proper d i r e c t i o n . The piston end of the rod was made to rotate freely on i t s bearing surfaces. This allowed for straight piston movements without any rotation. The piston cap which screwed on to the cylinder and carried the piston rod, f a c i l i t a t e d the removal of the piston, piston rod and crank assembly for cleaning purposes. The cylinder was open on both sides and had threads on the outside surface of one end for the fastening of the cap. The other end had a thick c i r c u l a r r i b surrounding the cylinder. This provided room for 3 equally spaced holes, d r i l l e d p a r a l l e l to the cylinder axis and another c i r c u l a r groove, machined on the f l a t edge and inside of the 3 holes. A set of bolts passing through these holes secured the mould in position and a good sealing between the base of the mould and the cylinder 180 was achieved by an O-ring placed in the c i r c u l a r groove. The i n l e t to the cylinder was through a steel tube, connected to the r i b , which also had provisions for pressure gauge connections. The other end of the i n l e t tube was connected to the hopper as explained e a r l i e r . The mould, a 3-piece assembly consisting of a central plate and two side plates, was supported on a c i r c u l a r base plate which had 3 holes that match with those in the c i r c u l a r r i b of the cylinder. These holes were used to assemble the mould and cylinder together, as mentioned e a r l i e r . A short segment of a 3/4 i n . diameter steel rod, located at the centre with i t s axis perpendicular to the plane of the c i r c u l a r base plate, was welded on to the base plate. This structure was used to support the mould and provide an i n l e t to the main specimen chamber. In addition i t also provided room for another control valve between the cylinder and the mould. The centre plate of the mould was welded on to this.support structure and the mould i n l e t , a 1/8 i n . diameter hole, was d r i l l e d through. The mould contained the main specimen chamber and another top chamber to c o l l e c t the excess resin. These were milled on the central plate with the planar dimensions of the specimen chamber being accurate to within ±0.005 cm. The thickness of the centre plate was the same as the required specimen thickness and the width of the specimen chamber was made equal to the length of the f i n a l specimen. 181 It was also made deep enough to pack the fibres loosely at the beginning before being pressed tight by means of a slider-clamp mechanism. The central plate was covered on the sides with two f l a t plates that were bolted on to the central plate. The two chambers were connected through a small hole of about 0.01 i n . in diameter which was d r i l l e d p a r a l l e l to the in l e t hole, across the centre arm, separating the two chambers. This was the outlet of the main specimen chamber through which a l l excess resin flowed under pressure, leaving behind the glass f i b r e s . The fibres were packed inside the specimen chamber and pressed in to position using a s l i d e r and a clamping device. The s l i d e r , a plate of steel of the same thickness as the centre plate of the mould, was machined accurately along the two edges which would be in contact with the surfaces of the specimen chamber, to obtain a perfect s l i d i n g f i t . The dimensions of the s l i d e r were such that, when s l i d in u n t i l i t s shoulders sat against the outer edge of centre plate, i t formed the mould cavity. No clearance was l e f t between the contact surfaces of the s l i d e r and the mould plates, in order to prevent any leakage of excess resin through these under the injection pressure. The clamp was used to push the s l i d e r in through the specimen chamber, pushing the loosely packed fibres into a cavity of known dimensions. As the parts of the injection moulding set up were subjected to per i o d i c a l disassembly as well as a high service pressure, a type of f i t t i n g that would withstand 182 repeated tight reconnections had to be employed. A 3-piece steel tube f i t t i n g consisting of body, nut and sleeve was used to join the end of the delivery tube of the hopper to the i n l e t of the injector system. The end of the U-tube of the pressure gauge was also connected to the i n l e t of the injector through a 45° f l a r e type two piece f i t t i n g . Pipe threads were furnished on the connecting end of the injector i n l e t and the U-tube end was f l a r e d and clamped between the former and a short length union nut. The mould was mounted on top of the cylinder and the base plate of the mould was bolted on to the c i r c u l a r r i b of the cylinder. A good rad i a l sealing was achieved by means of a standard O-ring of Buna-N ( N i t r i l e ) , which was placed in the c i r c u l a r groove of the r i b surface, as explained e a r l i e r . A standard O-ring of Buna-N ( N i t r i l e ) was also used on the bearing surfaces of the piston. The copper U-tube connected to the pressure gauge was designed to prevent the catalysed resin flowing in to the gauge. This was done by evacuating a i r from inside the gauge and U-tube and f i l l i n g i t with water. The less compressible water provided a medium to transmit the hydrostatic pressure of the l i q u i d resin into the gauge, without the column of water being s i g n i f i c a n t l y compressed, preventing the flow of resin into the U-tube. The sleeves of the i n l e t and outlet valves were thick walled steel cylinders of about 1/2 i n . inner 1 8 3 diameter, which were welded in position with their axes lying perpendicular to the respective delivery holes. The delivery holes were extended into and across the valve sleeves. A short length of a 1 / 2 in. diameter teflon rod was pushed into each of these sleeves and a diametrical hole d r i l l e d across the t e f l o n , was brought in li n e with the delivery holes. This l e f t the valve in i t s open position and a handle attached to one end of the teflon rod was used to rotate and bring i t in to a closed position.

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