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Fracture toughness of a carbon fibre-epoxy composite material Radford, Donald W. 1982

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FRACTURE TOUGHNESS OF A CARBON FIBRE-EPOXY COMPOSITE MATERIAL by DONALD W. RADFORD B.A.Sc, University Of B r i t i s h Columbia , 1980 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 Metallurgy We accept th i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August 1982 © Donald W. Radford, 1982 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree that p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of M e t a l l u r g y The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date: August 25, 1982 A b s t r a c t T e s t i n g has been undertaken to study the a p p l i c a b i l i t y of l i n e a r e l a s t i c f r a c t u r e mechanics to a carbon f i b r e -epoxy laminate system. Hercules AS/3501-6 carbon f i b r e -epoxy prepreg was used to produce laminates which were subsequently cut i n t o specimens of v a r i o u s geometries, s i z e s , and t h i c k n e s s e s . Plane s t r a i n equations were used to c a l c u l a t e values of f r a c t u r e toughness as the notch p r o p o r t i o n , specimen s i z e , geometry, and t h i c k n e s s were v a r i e d . The r e s u l t s i n d i c a t e that the toughness i s independent of specimen geometry, s i z e , and t h i c k n e s s ; however, the toughness i s seen to f a l l d r a m a t i c a l l y at i n c r e a s i n g values of notch proport i o n . To s u b s t a n t i a t e these trends compliance c a l i b r a t i o n s were c a r r i e d out f o r the v a r i o u s specimens. The trends a r r i v e d at through the compliance c a l i b r a t i o n show c l o s e agreement with those found using the plane s t r a i n method. Together these r e s u l t s i n d i c a t e that f o r a narrow range of notch p r o p o r t i o n s (a/W = 0.2 to 0.5) l i n e a r e l a s t i c f r a c t u r e mechanics can be a p p l i e d , y i e l d i n g a value of f r a c t u r e toughness which behaves as a m a t e r i a l constant comparable to K j C . i i i Table of Contents A b s t r a c t i i L i s t of Tables v L i s t of F i g u r e s v i I. INTRODUCTION 1 1. THE COMPOSITE MATERIAL 2 2. FRACTURE TOUGHNESS 4 3. LEFM APPLIED TO ANISOTROPIC COMPOSITE MATERIALS ..6 11 . PROCEDURE 9 1. MATERIAL TYPE AND PREPARATION 9 2. SPECIMEN GEOMETRY AND SIZE 14 3. TESTING EQUIPMENT AND CONDITIONS 16 4. EVALUATION TECHNIQUES 17 I I I . C-T GEOMETRY 22 1. GLASS FIBRE-EPOXY SPECIMENS 22 1.1 Specimen Geometry And S i z e 22 1.2 T e s t i n g Equipment And C o n d i t i o n s 23 1.3 E v a l u a t i o n Techniques 23 1 .4 R e s u l t s 23 1.4.1 Q u a s i - I s o t r o p i c 23 1.4.2 C r o s s p l y 24 1.4.3 Load Curve A n a l y s i s 26 2. CARBON FIBRE EPOXY SPECIMENS 28 2.1 Specimen Geometry And S i z e 28 2.2 T e s t i n g Equipment And C o n d i t i o n s 28 2.3 E v a l u a t i o n Techniques 29 2 . 4 R e s u l t s 30 2.4.1 Load Curve A n a l y s i s 30 2.4.2 Q u a s i - I s o t r o p i c 31 2.4.3 C r o s s p l y 31 3. SUMMARY OF RESULTS 34 IV. DEN GEOMETRY 35 1. QUASI-ISOTROPIC SPECIMENS 37 1.1 Specimen Geometry And Siz e 37 1.2 T e s t i n g Equipment And C o n d i t i o n s 37 1.3 E v a l u a t i o n Techniques 38 1 . 4 R e s u l t s 38 1.4.1 F r a c t u r e Morphology 38 1.4.2 Toughness Measurements 40 1.4.3 Accuracy Of Measured Toughness 42 2. CROSSPLY SPECIMENS 43 3. INSTRON TESTING 4 3 3.1 Specimen Geometry And Siz e 43 3.2 T e s t i n g Equipment And C o n d i t i o n s 44 3.3 E v a l u a t i o n Techniques 44 3.4 R e s u l t s 45 3.4.1 F r a c t u r e Morphology 45 3.4.2 Toughness Measurements 47 3.4.3 Accuracy Of Measured Toughness 49 4. MTS TESTING 50 4.1 Specimen Geometry And S i z e 50 4.2 T e s t i n g Equipment And C o n d i t i o n s .50 i v 4.3 E v a l u a t i o n Techniques . ... 52 4.4 R e s u l t s ; (0/90) Specimens 53 4.4.1 F r a c t u r e Morphology ........53 4.4.2 Toughness Measurement (LEFM) 55 4.4.3 Accuracy 59 4.4.4 Toughness Measurement (Compliance) 59 4.5 R e s u l t s ; (90/0) Specimens 62 4.5.1 F r a c t u r e Morphology 62 4.5.2 Toughness Measurement (LEFM) 63 4.5.3 Accuracy Of Measured Toughness 66 4.5.4 Toughness Measurement (Compliance) 66 5. SUMMARY OF RESULTS 68 V. 4BND GEOMETRY 72 1. TESTING EQUIPMENT AND CONDITIONS 7 3 2. GROUP 1 TESTING 7 5 2.1 Specimen Geometry And S i z e 75 2.2 Eva l u a t i o n . Techniques 76 2.3 R e s u l t s 77 2.3.1 F r a c t u r e Morphology 77 2.3.2 Toughness Measurements (LEFM) 79 2.3.3 Accuracy Of Measured Toughness 83 2.3.4 Toughness Measurement (Compliance) 83 3. GROUP 2 TESTING 85 3.1 Specimen Geometry And S i z e 85 3.2 E v a l u a t i o n Techniques 85 3 . 3 R e s u l t s . . 86 3.3.1 F r a c t u r e Morphology 86 3.3.2 Toughness Measurements (LEFM) 88 3.3.3 Accuracy Of Measured Toughness 90 3.3.4 Toughness Measurement (Compliance) 90 4. SUMMARY OF RESULTS 94 VI. DISCUSSION 96 1. MORPHOLOGY RELATED TO LEFM 96 2. DELAMINATION WIDTH 97 3. TRENDS OF RESULTS 99 4. APPLICABILITY OF LEFM 103 V I I . CONCLUSIONS 105 1. GENERAL CONCLUSIONS (THEORETICAL) 105 1.1 A p p l i c a b i l i t y Of LEFM 105 1.2 Relevance Of K l c As A M a t e r i a l Property 106 2. GENERAL CONCLUSIONS (EXPERIMENTAL) 107 2.1 M a t e r i a l T e s t i n g 107 2.2 M a t e r i a l Production 110 3. SPECIFIC CONCLUSIONS 110 BIBLIOGRAPHY 112 APPENDIX A - AUTOCLAVE 116 APPENDIX B - MATERIAL PROPERTIES 130 APPENDIX C - EXPERIMENTAL RESULTS (LEFM AND COMPLIANCE) .134 APPENDIX D - A REVIEW OF PERTINENT LITERATURE 225 V L i s t of Tables I . Q u a s i - I s o t r o p i c DEN (LEFM) Values 41 II . Cr o s s p l y DEN (LEFM) Values 48 I I I , LEFM Toughness R e s u l t s (h = 6.4mm) 89 IV. LEFM Toughness R e s u l t s (h = 12.8mm) 89 V. Compliance Toughness R e s u l t s (h = 6.4mm) 93 VI . Compliance Toughness R e s u l t s (h = 12.8mm) 93 VII . Comparative F r a c t u r e Toughness Data 101 v i L i s t of F i g u r e s 1. S t a c k i n g Sequence 12 2. Autoclave Cure Schematic 13 3. S t a r t e r Notch O r i e n t a t i o n 15 4. Compact T e n s i l e Geometry 15 5. F a i l e d G l a s s Fibre-Epoxy C-T Specimens 25 6. Load Curve f o r Glass Fibre-Epoxy , 27 7. Load Curve f o r Carbon Fibre-Epoxy 27 8. F a i l e d Carbon Fibre-Epoxy C-T Specimen ...32 9. DEN Specimen Geometry (Var ious S i z e s ) ...36 10. F r a c t u r e Morphology of Q u a s i - I s o t r o p i c DEN Specimens .39 11. Q u a s i - I s o t r o p i c DEN (LEFM) R e s u l t s 41 12. F a i l e d C r o s s p l y DEN Specimen Showing Surface Delamination 46 13. C r o s s p l y DEN (LEFM) R e s u l t s 48 14. I n s t r o n S t r a i n Gauge Mounted on DEN Specimen 51 15. F r a c t u r e Morphology of 0/90 C r o s s p l y DEN Specimens ...54 16. LEFM R e s u l t s f o r 0/90 DEN Specimens (MTS) 56 17. Notch S e n s i t i v i t y of the (0/90) AS/3501-6 CFRP 58 18. Compliance C a l i b r a t i o n f o r (0/90) DEN 60 19. Toughness R e s u l t s (Compliance) f o r (0/90) DEN Specimens 61 20. F r a c t u r e Morphology of (90/0) DEN Specimens 64 21. Toughness R e s u l t s (LEFM) f o r (90/0) DEN Specimens ....65 22. Compliance C a l i b r a t i o n f o r (90/0) DEN 67 23. Toughness R e s u l t s (Compliance) f o r (90/0) DEN Specimens 69 24. 4BND Setup and Instrumentation 74 25. F a i l e d 4BND Specimens of Vario u s Thicknesses 78 26. 4BND Group 1 Re s u l t s (2.95mm t h i c k n e s s ) 80 27. 4BND Group 1 R e s u l t s (7.62mm t h i c k n e s s ) 81 28. 4BND Group 1 Toughness V a r i a t i o n with Aspect R a t i o ...82 29. Compliance C a l i b r a t i o n f o r Group 1 4BND 84 30. F a i l e d 4BND Specimens of Vario u s Notch P r o p o r t i o n s ...87 31. 4BND Group 2 Toughness R e s u l t s (LEFM) 89 32. Compliance C a l i b r a t i o n f o r Group 2 4BND .....92 33. 4BND Group 2 Toughness R e s u l t s (Compliance) 93 34. Autoclave - Exploded View 118 35. Autoclave, Stand, and Door Layout 119 36. Autoclave - E a r l y Heating and Vacuum Systems 120 37. Autoclave - Vacuum Bagging 122 38. Autoclave - M o d i f i e d Base P l a t e s 124 39. Autoclave - F i n a l Cure Frame Assembly 125 v i i Ac knowledgement Too many people have helped me throughout t h i s t h e s i s to thank everyone; however, a few must not go unmentioned. I would l i k e to give s p e c i a l thanks to f i v e people who i n no way should be h e l d r e s p o n s i b l e f o r my e r r o r s but were of great a s s i s t a n c e i n the completion of t h i s work. My s p e c i a l thanks t o : Roger Bennett Fred Bradley Carol-Ann Drope Ewe-Ann F l e t c h e r Peter Gorog 1 I. INTRODUCTION The measurement and d e f i n i t i o n of f r a c t u r e toughness in composite m a t e r i a l s i s important today due to the ever i n c r e a s i n g use of these m a t e r i a l s . Because of the high m a t e r i a l c o s t and the type of a p p l i c a t i o n s o f t e n encountered i t i s imperative that accurate toughness data be a v a i l a b l e to the designer f o r use in determining the design c r i t e r i a . The measurement of toughness in composite m a t e r i a l s i s a s u b j e c t which has a t t r a c t e d much a t t e n t i o n in the recent p a s t . T y p i c a l l y r e s e a r c h e r s have a p p l i e d both the experimental p r a c t i s e s and the data r e d u c t i o n methods d e r i v e d f o r homogeneous l i n e a r e l a s t i c i s o t r o p i c m a t e r i a l s to these a n i s o t r o p i c f i b r e composite systems. Specimen geometries, which for more common m a t e r i a l s work w e l l , introduce modes of improper l o a d i n g and other d i f f i c u l t i e s which to some extent can be termed "mechanical" problems. To complicate these "mechanical" problems to a g r e a t e r extent are m a t e r i a l e f f e c t s . M a t e r i a l e f f e c t s can be s a i d to i n c l u d e p l y , or lamina o r i e n t a t i o n , s t a c k i n g sequence, and other m a t e r i a l p r o p e r t i e s of v a r i o u s f i b r e matrix systems. 2 To c l a r i f y the preceding mechanical and m a t e r i a l e f f e c t s the remainder of the i n t r o d u c t i o n i s separated i n t o three s e c t i o n s : i . The Composite M a t e r i a l i i . F r a c t u r e Toughness i i i . L i n e a r E l a s t i c F r a c t u r e Mechanics A p p l i e d to A n i s o t r o p i c Composite M a t e r i a l s . 1 . THE COMPOSITE MATERIAL A composite m a t e r i a l as used i n today's technology can be best d e s c r i b e d as a m a t e r i a l which i s made up of two or more simpler m a t e r i a l s , a c t i n g together to give a more d e s i r a b l e product than any of the base m a t e r i a l s . The two major components of any composite m a t e r i a l can be d e s c r i b e d as the matrix, or binder, and the reinforcement. The composite type d e a l t with throughout t h i s d i s c u s s i o n i s more s p e c i f i c a l l y a " f i b r e " composite system as compared to a p a r t i c l e or a p l a t e l e t composite. The most common man made f i b r e composite m a t e r i a l i s f i b r e g l a s s . The two major c o n s t i t u e n t s are the g l a s s f i b r e s and the r e s i n matrix. The drawn g l a s s f i b r e s are f r a g i l e but extremely strong due to the absence of su r f a c e flaws and as the r e i n f o r c i n g m a t e r i a l , they are the load c a r r y i n g component of the composite. The weaker matrix m a t e r i a l serves as a c a r r i e r , p r o t e c t o r , and load t r a n s f e r medium f o r the f r a g i l e f i b r e s . The newest, so c a l l e d advanced composites, began with 3 the p r o d u c t i o n of boron f i l a m e n t s i n the e a r l y '1960's. Due to the c o n s i d e r a b l y higher s t r e n g t h and s t i f f n e s s of these f i l a m e n t s , as compared to g l a s s f i b r e s , the term advanced composite m a t e r i a l s evolved. Included i n the group of advanced composites i s the m a t e r i a l of primary i n t e r e s t i n the f o l l o w i n g d i s c u s s i o n . Carbon fibr e - e p o x y composite m a t e r i a l s are f i n d i n g widespread use in many modern a p p l i c a t i o n s due to the high s p e c i f i c s t i f f n e s s and s t r e n g t h . F i b r e s are used i n composite m a t e r i a l s in p r i m a r i l y two forms: d i s c o n t i n u o u s and continuous. In g e n e r a l , and i n the case of the f o l l o w i n g d i s c u s s i o n , advanced composite m a t e r i a l s are made up of continuous f i b r e s or f i l a m e n t s . A f i l a m e n t a r y composite i s g e n e r a l l y made up of s e v e r a l p l i e s or laminae. In these high s t r e n g t h m a t e r i a l s one lamina c o n s i s t s of one row of p a r a l l e l f i l a m e n t bundles surrounded by matrix m a t e r i a l . U n i - d i r e c t i o n a l f i b r e composites are found i n some l i m i t e d cases; i n general however, s t r e n g t h and s t i f f n e s s are r e q u i r e d i n m u l t i p l e d i r e c t i o n s . T h i s leads to laminates which are composed of laminae stacked with v a r i o u s o r i e n t a t i o n s of the filam e n t d i r e c t i o n . T h i s v a r i a t i o n of the d i r e c t i o n of f i l a m e n t s i n su c c e s s i v e laminae leads to a great dependence of composite m a t e r i a l p r o p e r t i e s upon not only m a t e r i a l c o n s i d e r a t i o n s but a l s o upon geometrical c o n s i d e r a t i o n s . For t h i s reason i t i s imperative to denote a composite m a t e r i a l by both the 4 primary m a t e r i a l s and a l s o by the s t a c k i n g sequence, or p l y o r i e n t a t i o n . The standard n o t a t i o n used to denote the p l y o r i e n t a t i o n of a composite m a t e r i a l i s given i n the form [ © i / © 2 / © 3 . . . . / © T J ys• Each angle © r e f e r s to the o r i e n t a t i o n of a s p e c i f i c p l y . The v a r i o u s angles, ©, , through 6n , w i t h i n the bra c k e t s form a s p e c i f i c o r i e n t a t i o n group. The s u b s c r i p t " s" d e s c r i b e s the m a t e r i a l as being symmetric about an imaginary mid-plane and the s u b s c r i p t "y" denotes the number of o r i e n t a t i o n groups on each side of the plane of symmetry. The angles are given, s t a r t i n g at the su r f a c e and working towards the plane of symmetry, with the 0 ° d i r e c t i o n corresponding to the p r i n c i p a l t e s t i n g d i r e c t i o n . When c o n s i d e r i n g a c o n v e n t i o n a l m a t e r i a l , i t has been found that s p e c i f y i n g the common m a t e r i a l parameters, such as s t r e n g t h and s t i f f n e s s , may not be s u f f i c i e n t . P a r t i c u l a r l y f o r more b r i t t l e m a t e r i a l s a value of f r a c t u r e toughness i s a l s o necessary i n the c a t e g o r i z i n g of a mater i a l . 2 . FRACTURE TOUGHNESS The concept of f r a c t u r e toughness has been developed d u r i n g t h i s century to deal with the dramatic e f f e c t flaws and c r a c k s have on the f a i l u r e s t r e n g t h of m a t e r i a l s . For the case of toughness measurements in i s o t r o p i c homogeneous 5 m a t e r i a l s , the I r w i n 1 and G r i f f i t h 2 crack t h e o r i e s both lead to the idea that the energy of f r a c t u r e i s d i s s i p a t e d in the formation of new " f r a c t u r e " s u r f a c e s . These t h e o r i e s l e a d to the c l a s s i c a l approach i n v o l v i n g L i n e a r E l a s t i c F r a c t u r e Mechanics which i n t h i s d i s c u s s i o n w i l l be denoted LEFM. For LEFM to apply, the flaw or crack must grow in a s e l f - s i m i l a r f a s h i o n . To be s e l f - s i m i l a r the r e s u l t i n g crack must propagate in a d i r e c t i o n c o l l i n e a r to the i n i t i a l flaw or s t a r t e r notch. D e v i a t i o n s from t h i s s e l f - s i m i l a r crack growth make the a p p l i c a t i o n of LEFM q u e s t i o n a b l e . B a s i c a l l y two methods of t e s t i n g may be a p p l i e d . One such method y i e l d s the plane s t r e s s f r a c t u r e toughness. The r e s u l t s of t h i s method y i e l d data that p e r t a i n only to the s p e c i f i c sample that was t e s t e d (with respect to specimen geometry, s i z e , t h i c k n e s s , crack t i p r a d i u s , e t c . ) . The second method y i e l d s a more general value of toughness, known as the plane s t r a i n f r a c t u r e toughness. T h i s measure i s independent of geometry and s i z e , and due to i t s d e f i n i t i o n (regarding c r i t i c a l minimum t h i c k n e s s ) y i e l d s c o n s e r v a t i v e values which can be used as m a t e r i a l c o n s t a n t s . Standardized methods of t e s t i n g f o r many m a t e r i a l s are given by the ASTM 3 . The m a t e r i a l constant g e n e r a l l y r e l a t e d to t h i s theory i s denoted K I C. The K denotes f r a c t u r e toughness, while the Roman numeral " I " 6 d e s c r i b e s an opening mode f a i l u r e t e s t " , and the "c" shows that the value i s c r i t i c a l with r a p i d u n c o n t r o l l e d crack propagation imminent. T h i s constant has found widespread use as not only a value q u a n t i f y i n g the f r a c t u r e toughness, or crack r e s i s t a n c e of a m a t e r i a l , but a l s o as an important f a c t o r i n modern en g i n e e r i n g d e s i g n . I t t h e r e f o r e f o l l o w s that a parameter of t h i s nature f o r composite m a t e r i a l systems would be h i g h l y d e s i r a b l e . 3. LEFM APPLIED TO ANISOTROPIC COMPOSITE MATERIALS When LEFM concepts are a p p l i e d to a n i s o t r o p i c f i b r e composites a multitude of problems can be encountered. For example, in f i l a m e n t a r y composite systems, some of the energy of f r a c t u r e i s d i s s i p a t e d not only i n the formation of new f r a c t u r e s u r f a c e s but a l s o in delamination and p u l l -out of f i b r e s from the matrix m a t e r i a l . Further problems i n c l u d e propagating a s e l f - s i m i l a r crack, the m a t e r i a l a n i s o t r o p y i t s e l f , and other m a t e r i a l r e l a t e d e f f e c t s . Thus the a p p l i c a t i o n of LEFM to these a n i s o t r o p i c systems has been questioned by many research groups. 5 6 7 8 For example, a number of r e s e a r c h e r s have shown that specimen geometry may be important in toughness measurement of composite m a t e r i a l s . Beaumont and P h i l l i p s 9 p o i n t e d to a p o s s i b l e dependence of toughness values in u n i -d i r e c t i o n a l composites upon both notch l e n g t h and crack t i p r a d i u s . A l s o , the work of K o n i s h 1 0 1 1 brought out more dependencies, p r i m a r i l y that of toughness (or more 7 s p e c i f i c a l l y notch strength) upon both specimen s i z e and geometry. T h i s study d e a l s with the p o s s i b l e dependence of t r a n s l a m i n a r f r a c t u r e toughness values upon specimen geometry and notch p r o p o r t i o n , p r i m a r i l y f o r a carbon f i b r e - e p o x y system. These f r a c t u r e toughness v a l u e s are c a l c u l a t e d using both c l a s s i c a l i s o t r o p i c concepts and a compliance c a l i b r a t i o n technique. One p r i n c i p a l d i f f e r e n c e between t h i s work and many e a r l i e r s t u d i e s such as d e s c r i b e d above i s that angle p l y composite m a t e r i a l s were examined r a t h e r than u n i - d i r e c t i o n a l f i b r e composites. Thus, the major o b j e c t i v e s of t h i s work are; i . To gain i n s i g h t i n t o the problems of f r a c t u r e toughness t e s t i n g -in a n i s o t r o p i c f i l a m e n t a r y composites and; i i . To determine i f a toughness value can be found which i s a m a t e r i a l constant ( K 1 C ) and thus can be used i n design c a l c u l a t i o n s . In attempting to achieve these goals the r e s e a r c h has been undertaken i n a number of segments. With a general d i r e c t i o n i n mind, the f i r s t group of t e s t s d e a l i n g with compact t e n s i l e geometry specimens was begun. The r e s u l t i n g problems encountered and ideas i n i t i a t e d l e d to the second group of t e s t s which i n v o l v e d a l a r g e number of double edge notched t e n s i l e coupons. 8 T h i s second s e c t i o n of the r e s e a r c h produced c o n s i d e r a b l e i n s i g h t i n t o the e f f e c t s of specimen s i z e and notch l e n g t h . With t h i s i n s i g h t came many more ques t i o n s i n v o l v i n g the e f f e c t s of specimen geometry, t h i c k n e s s , and the v i s i b l e stages of f a i l u r e . In an attempt to probe some of these q u e s t i o n s two more groups of t e s t i n g were c o n t r i v e d . The t h i r d group of t e s t s was put i n t o p r a c t i c e much as planned, i n v o l v i n g both a new t e s t specimen geometry, the four p o i n t bend geometry, and more double edge notched specimens. The bend t e s t s were introduced p r i m a r i l y as a b r i e f check of specimen geometry e f f e c t s and t h i c k n e s s e f f e c t s while the f a m i l i a r double edge notched specimens were used in c o n j u n c t i o n with photographic equipment to look at any v i s i b l e s u r f a c e e f f e c t s . The l a s t group of t e s t s i n v o l v e d i n t h i s work was planned to i n c l u d e a f i n a l look at the compact t e n s i l e geometry and a d e t a i l e d study of the e f f e c t s surveyed i n the four p o i n t bend t e s t s of the t h i r d group of t e s t s . Due to l i m i t a t i o n s of time, only the four p o i n t bend t e s t s were undertaken. These four groups of r e s e a r c h c o n s t i t u t e the t e s t i n g d e s c r i b e d i n t h i s work which w i l l form the b a s i s of the d i s c u s s i o n r e g a r d i n g the two major o b j e c t i v e s l i s t e d p r e v i o u s l y . The m a j o r i t y of the d i s c u s s i o n w i l l be segmented p r i m a r i l y by the three specimen types. 9 I I . PROCEDURE 1 . MATERIAL TYPE AND PREPARATION T h i s r e s e a r c h d e a l s p r i m a r i l y with a carbon f i b r e -epoxy prepreg system s o l d by Hercules and designated AS/3501-6. The d e s i g n a t i o n AS/3501-6 d e s c r i b e s the m a t e r i a l as being made up of a high s t r e n g t h (AS) carbon f i b r e and an epoxy matrix (3501-6) rated to maintain the m a j o r i t y of i t s mechanical p r o p e r t i e s to 175 C (350°F). T h i s m a t e r i a l i s r e c e i v e d as a u n i - d i r e c t i o n a l prepreg tape. "Prepreg" means that as r e c e i v e d the m a t e r i a l i s i n r o l l form, l o o k i n g and f e e l i n g much l i k e a black f l y paper with the f i b r e s running the l e n g t h of the r o l l , embedded si d e by s i d e i n a semi-cured epoxy matrix m a t e r i a l . To f a b r i c a t e the completed composite m a t e r i a l the prepreg must be stacked i n the d e s i r e d sequence and cured. F a b r i c a t i o n of r e p r o d u c i b l e , good q u a l i t y m a t e r i a l was purported to be a s t r a i g h t forward o p e r a t i o n . T h i s o p e r a t i o n however proved to be a time consuming problem throughout much of the r e s e a r c h . At the beginning of t h i s r e s e a r c h the standard means f o r c u r i n g t h i s prepregged m a t e r i a l was not a v a i l a b l e and thus such equipment had to be c o n s t r u c t e d before the m a t e r i a l c o u l d be p r o p e r l y produced. An autoclave i s the standard t o o l in composite m a t e r i a l p r e p a r a t i o n which allows both pressure and heat to act on the prepreg to o b t a i n the d e s i r e d cure, while any 10 v o l a t i l e s are removed through an i n t e g r a l vacuum system. The u n i t that was subsequently f a b r i c a t e d was a smal l autoclave b u i l t to resemble the l a r g e r commercial u n i t s . The f i n a l i n t e r i o r dimensions of t h i s a u t o c l a v e were a 230 mm diameter and a 360 mm l e n g t h . The au t o c l a v e was i n i t i a l l y o p e r a t i v e i n J u l y of 1980 and had at that time been s a f e l y t e s t e d to 1.4 MPa (200 p s i ) i n t e r n a l p r e s s u r e . Leakage of p r e s s u r i z e d n i t r o g e n gas i n t o the vacuum system was the major cause of the many problems encountered d u r i n g the use of t h i s a u t o c l a v e . For more d e t a i l s of the c o n s t r u c t i o n and e v o l u t i o n of t h i s a u t o c l a v e i n t o i t s f i n a l form as a r e l i a b l e p r o d u c t i o n t o o l f o r small r e s e a r c h samples see Appendix A. T h i s appendix d e t a i l s the many problems encountered i n producing c o n s i s t e n t m a t e r i a l in the au t o c l a v e and how the autoclave system was subsequently m o d i f i e d to r e c t i f y these problems. In general the technique used to produce a complete composite sample p l a t e from the raw prepreg i s as f o l l o w s . A predetermined number of sheets of a s p e c i f i e d s i z e and o r i e n t a t i o n are cut from the prepreg. These sheets are stacked at p a r t i c u l a r angles to make the s p e c i f i e d p l y o r i e n t a t i o n sequence. In t h i s work, two d i s t i n c t l y d i f f e r e n t f i b r e o r i e n t a t i o n s were produced; ( 0 / 9 0 ) 1 S c r o s s p l i e d and ( 0 / ± 4 5 / 9 0 ) , s q u a s i - i s o t r o p i c . Using the terminology as 11 d e s c r i b e d i n the i n t r o d u c t i o n i s to simply r e a l i z e that the o r i e n t a t i o n group i s given i n s i d e the b r a c k e t s . The laminate i s shown to have mid-plane symmetry by the s u b s c r i p t "s" and the number of o r i e n t a t i o n groups on each s i d e of the imaginary mid-plane are given by a number in plac e of the s u b s c r i p t "n" as i n f i g u r e 1. Once the lay-up i s complete i t has a r e l e a s e f i l m a p p l i e d to both top and bottom and a c a u l p l a t e followed by bleeder p l i e s are stacked on top as shown in f i g u r e 2. The c a u l p l a t e i s used to produce an even top s u r f a c e , while the bleeder p l i e s are necessary to c o l l e c t the excess epoxy and prevent plugging of the vacuum passages. T h i s lay-up i s then vacuum bagged onto the aluminum base p l a t e and i s ready f o r i n s e r t i o n i n t o the a u t o c l a v e . Once i n s i d e the autoclave the vacuum l i n e , thermocouple, and power are connected, followed by the c l o s i n g and s e c u r i n g of the a u t o c l a v e door. To complete the laminate the pressure and temperature are c y c l e d in accordance with the s p e c i f i e d cure c y c l e (See Appendix B). No post cure heat treatment was c a r r i e d out. F i n a l l y , the m a t e r i a l i s removed from the autoclave and then from the vacuum bag, to be cut to s i z e and shape using a diamond c u t t i n g wheel. In a few cases a type 1003 g l a s s f i b r e - e p o x y system by 3M was t e s t e d . T h i s m a t e r i a l was produced i n the same manner as that d i s c u s s e d for the carbon f i b r e - e p o x y system. The only d i f f e r e n c e between the d e s c r i p t i o n s of the g l a s s and g r a p h i t e i s the a c t u a l cure c y c l e used in p r o d u c t i o n and the appearance of t h i s 12 COMPOSITE PLY ORIENTATION ( 0 / + 45 / 90 ) s F i g u r e 1 - S t a c k i n g Sequence 13 AUTOCLAVE CURE SCHEMATIC VACUUM BAG BLEEDER PLIES I- CAUL PLATE RELEASE FILM SAMPLE RELEASE FILM BASE PLATE Figure 2 - Autoclave Cure Schematic 1 4 prepregged m a t e r i a l . The g l a s s fibre-epoxy prepreg i s not black, but i s a pale yellow c o l o u r . 2 . SPECIMEN GEOMETRY AND SIZE A l l t e s t s were performed in a way such that the notch was p o s i t i o n e d to y i e l d t r a n s l a m i n a r crack propagation as i l l u s t r a t e d in f i g u r e 3 . T h i s means that the t e s t s of t h i s work deal with the f r a c t u r e of f i b r e s and not simply d e l a m i n a t i o n , s i n c e t h i s r e s e a r c h d e a l s with angle p l y and not u n i - d i r e c t i o n a l m a t e r i a l s . The American S o c i e t y for T e s t i n g and M a t e r i a l s (ASTM) sets out s t a n d a r d i z e d t e s t methods for many m a t e r i a l s ; however, in the case of f i b r e composites, no such method has yet been agreed upon. T h i s means that i f comparison to p r e v i o u s l y p u b l i s h e d data i s to be made, a l l specimen s i z e s and t e s t r a t e s must be the same as those used in the p r e v i o u s work. U n f o r t u n a t e l y , the l a c k of any s t a n d a r d i z e d procedures a l s o means that few of the groups i n v o l v e d in r e s e a r c h on these m a t e r i a l s maintain any i n t e r - g r o u p c o n s i s t e n c y . The three t e s t specimen geometries used in t h i s work were the compact t e n s i l e (C-T), the double edge notched t e n s i l e (DEN), and the four p o i n t bend beam ( 4 B N D ) specimens. Of these three geometries, only the C-T geometry i s recognized as a standard ASTM specimen. The other geometries were used, as d i s c u s s e d i n the f o l l o w i n g s e c t i o n s , to give comparisons to p u b l i s h e d works and to INTER L A M I N A R T R A N S L A M I N A R F i g u r e 4 - Compact T e n s i l e G e o m e t r y 1 6 allow f o r p r o p e r t i e s p e c u l i a r to the m a t e r i a l under i n v e s t i g a t i o n . 3. TESTING EQUIPMENT AND CONDITIONS Two l o a d i n g machines were used d u r i n g the course of t e s t i n g . The I n s t r o n t e n s i l e t e s t i n g machine used i s of the l e a d screw type with a 2 0 , 0 0 0 l b . load c e l l i n p l a c e . R e s u l t s were t a b u l a t e d on the i n t e g r a l c h a r t recorder as a p l o t of load versus crosshead displacement. No d i r e c t measurement of the specimen s t r a i n was attempted. The second l o a d i n g device used was the M a t e r i a l s T e s t i n g System (MTS) apparatus. The MTS h y d r a u l i c l o a d i n g system was used i n a constant ram (crosshead) rate mode known as stroke c o n t r o l . E l o n g a t i o n s and d e f l e c t i o n s were measured using an I n s t r o n c l i p - o n type s t r a i n gauge connected to the MTS through the s t r a i n channel g i v i n g a v o l t a g e s i g n a l as the s t r a i n output. A 5 metric ton l o a d c e l l was used. The other measurement technique employed in the t e s t i n g of s e v e r a l specimens was a 35 mm SLR camera and motor d r i v e u n i t capable of exposing 5 frames per second. T h i s photographic system was a l s o meant to look at any s u r f a c e d e l a m i n a t i o n , v i s i b l e crack propagation, or other v i s i b l e f e a t u r e s evident d u r i n g t e s t i n g . A d i g i t a l stopwatch photographed i n each frame was used to c o r r e l a t e these photographic r e s u l t s with the r e s u l t s recorded on the newly a c q u i r e d Bascom-Turner Data A c q u i s i t i o n System. A l l 1 7 load and s t r a i n data were recorded on the d i s c storage of the Bascom-Turner as v o l t a g e s from the MTS. These values can be withdrawn and manipulated at any time f o r e v a l u a t i o n . 4. EVALUATION TECHNIQUES P r i m a r i l y two major e v a l u a t i o n techniques were used to a r r i v e at values of f r a c t u r e toughness. A l l samples were eval u a t e d by plane s t r a i n LEFM methods, while some DEN and a l l 4BND specimens were a l s o evaluated using the plane s t r e s s compliance technique. A l l specimens were t e s t e d to f a i l u r e and the corresponding peak loads were recorded and used to determine values 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 ( K t c ) in each e v a l u a t i o n technique. Using the LEFM method, f i n i t e width c o r r e c t i o n f a c t o r s d e r i v e d f o r i s o t r o p i c m a t e r i a l s were used. The equations were: f o r C-T specimens 3; K a= P ( a 1 / 2 ) t ~ 1 W ~ 1 ( Y ) where, Y = 29.6 - I85.5(a/W) + 655.7(a/W) 2-I0l7(a/W) 3+ 638.9(a/w)« f o r DEN s p e c i m e n s 1 2 ; KGl= P ( a 1 / 2 ) t " 1W 1 (Y) where, Y = 1.98 + 0.36(2a/W) - 2.12(2a/W) 2+ 3.42(2a/W) 3 18 f o r 4BND specimens 1 3 . K a= [ ( P 2 l 2 t " 2 W - 3 ) ( Y ) ] 1 / 2 where, Y = 34 .7U/W) - 55.2(a/W) 2 + 1 9 6 U/W) 3 P peak load t specimen t h i c k n e s s W width (or height f o r 4BND) 1 beam len g t h a notch l e n g t h f o r C-T and 4BND 2a t o t a l notch l e n g t h f o r DEN While the l i m i t a t i o n s of using equations of t h i s type, m a t e r i a l are c l e a r l y acknowledged, the r e s u l t s do c o n s t i t u t e an i n i t i a l i n d i c a t i o n of the e f f e c t of the many v a r i a b l e s encountered. In f a c t i t should again be p o i n t e d out that a primary o b j e c t i v e of t h i s work i s to determine the a b i l i t y of the LEFM s o l u t i o n to q u a n t i f y f r a c t u r e toughness i n t h i s m a t e r i a l . The second method used f o r the det e r m i n a t i o n of q u a n t i t a t i v e values of f r a c t u r e toughness was the compliance technique. T h i s technique d i f f e r s from the f i r s t method i n that two parameters, the load (P) and the e l a s t i c l o a d versus displacement slope (dP/ds), must be determined. The compliance technique does not r e l y on m a t e r i a l i s o t r o p y s i n c e each specimen i s c a l i b r a t e d based upon energy c o n s i d e r a t i o n s , for t h i s a n i s o t r o p i c 19 i n d i v i d u a l l y . The compliance c a l i b r a t i o n f o r a given specimen s i z e and geometry i s c a r r i e d out by beginning with a number of unnotched specimens and i n c r e m e n t a l l y notching each specimen to i t s f i n a l t e s t notch l e n g t h . At the beginning, and at each intermediate notch l e n g t h , the specimen i s loaded i n i t s e l a s t i c range and the load versus e l o n g a t i o n ( d e f l e c t i o n ) r e s u l t s are recorded. Most specimens t e s t e d in t h i s way r e q u i r e a f i n a l notch p r o p o r t i o n of 0.8 and are notched i n 0.1 notch p r o p o r t i o n increments u n t i l t h i s f i n a l value i s reached. The compliance technique i s based upon the equation; G I C= (P 2/2t)(dC/da) where, G T C = K 1 C 2 / E ' equals the energy of f r a c t u r e P = peak load t = t h i c k n e s s C= ds/dP = compliance dC/da = change in compliance with notch length E' = experimental m a t e r i a l modulus = dP/ds f o r the unnotched t e s t . Thus, compliance values p l o t t e d a g a i n s t the notch p r o p o r t i o n are used to a r r i v e at the slope (dC/da) and with that value known, the energy of f r a c t u r e (G) can be c a l c u l a t e d . 20 The p a r t i c u l a r v a r i a t i o n of t h i s technique that i s a p p l i e d uses a program w r i t t e n f o r t h i s work and the UBC Amdahl 470 V/8-II computer to f i t the values of compliance versus notch p r o p o r t i o n to a polynomial i n notch p r o p o r t i o n . The best f i t i s chosen by checking polynomials of orders one through ten and choosing the f i t with the l e a s t e r r o r a s s o c i a t e d . T h i s f u n c t i o n i s then p l o t t e d . The computer next d i f f e r e n t i a t e s t h i s polynomial and m u l t i p l i e s each value by the average experimental modulus (E') d i v i d e d by 2 and p l o t s these values a g a i n s t the corresponding notch p r o p o r t i o n . The r e s u l t i n g p l o t of (E'/2)dC/d(a/W) versus a/W f o r the 4BND geometry, or (E'/2)dC/d(2a/W) versus 2a/W f o r the DEN geometry, becomes the compliance c a l i b r a t i o n curve. A c a l i b r a t i o n curve of t h i s type i s produced f o r each geometry-and s i z e v a r i a t i o n . To a r r i v e at a f r a c t u r e toughness value f o r a s p e c i f i c specimen from the corresponding compliance c a l i b r a t i o n curve the value of (E'/2)dC/d(a/W) i s found corresponding to the specimen notch p r o p o r t i o n . The equation: [ (E'/2) (dC/d(a/W) ) ( P 2 f 'vr 1 ) ] 1 / 2 = K a \ i s then used to y i e l d the q u a n t i t a t i v e toughness value. These values are a u t o m a t i c a l l y t a b u l a t e d by the computer. The major drawback of t h i s technique i s that a new c a l i b r a t i o n curve must be generated f o r every change in specimen s i z e or geometry. 21 The f i n a l e v a l u a t i o n technique used i n t h i s work was p r i m a r i l y q u a l i t a t i v e in nature. The photographs taken were i n s p e c t e d with the idea of being able to observe the sequence of events l e a d i n g to f a i l u r e and comparing these events f o r v a r i o u s specimen geometries. I t was a l s o hoped that these photographs would give some i n s i g h t i n t o the v e l o c i t y of s u b - c r i t i c a l crack growth and the shape of the deforming crack t i p . 22 I I I . C-T GEOMETRY Th i s s e c t i o n i s d i v i d e d i n t o two major t o p i c s r e l a t e d to the m a t e r i a l used on t e s t i n g . The compact t e n s i l e (C-T) geometry shown i n f i g u r e 4 was used f o r t e s t s of both the type 1003 3M Scot c h p l y prepregged g l a s s fibre-epoxy m a t e r i a l and the AS/3501-6 Hercules high s t r e n g t h prepregged carbon fib r e - e p o x y m a t e r i a l . In both cases, the C-T geometry was used to give a q u a l i t a t i v e i n d i c a t i o n of the f r a c t u r e behaviour of these composite m a t e r i a l s . T h i s i n i t i a l group of t e s t s i n c l u d e d only 16 g l a s s f i b r e - e p o x y specimens and 8 carbon fib r e - e p o x y specimens. The C-T geometry was chosen f o r the i n i t i a l t e s t s s i n c e i t i s an ASTM standard LEFM t e s t geometry. In a l l t e s t s of t h i s geometry the specimen s i z e and notch p r o p o r t i o n remained constant at W = 53 mm and a/W = 0.4 1 . GLASS FIBRE-EPOXY SPECIMENS P r e l i m i n a r y t e s t s were done with the g l a s s f i b r e composite m a t e r i a l s i n c e i t was f e l t that t h i s m a t e r i a l would be more e a s i l y produced and t e s t e d than the carbon fi b r e - e p o x y m a t e r i a l . 1 .1 Specimen Geometry And S i z e The g l a s s f i b r e samples c o n s i s t e d of e i t h e r 16 or 24 p l i e s i n both the c r o s s p l y [(0/90)„ 5 , ( 0 / 9 0 ) 6 S ] and the q u a s i - i s o t r o p i c [ ( 0 / ± 4 5 / 9 0 ) 2 s , (0/±45/90) 3 s] o r i e n t a t i o n s , y i e l d i n g t h i c k n e s s e s of 3.5 mm and 5.1 mm r e s p e c t i v e l y . 23 The specimen width and notch p r o p o r t i o n were, as noted p r e v i o u s l y , W = 53 mm and a/W = 0 . 4 . The notch root r a d i u s was 0 . 2 5 mm as produced with a sharpened hacksaw blade. 1.2 T e s t i n g Equipment And C o n d i t i o n s The I n s t r o n t e s t i n g equipment, as d e s c r i b e d i n the general procedure, was used f o r t e s t of the g l a s s f i b r e m a t e r i a l . The cross-head r a t e was set at 1.27 mm/min and d e v i c e s with 7.9 mm diameter pin s were used to apply the lo a d . 1.3 E v a l u a t i o n Techniques With the exception of v i s u a l examination dur i n g and a f t e r t e s t i n g , the LEFM method f o r f i n d i n g f r a c t u r e toughness using f i n i t e width c o r r e c t i o n f a c t o r s was the only e v a l u a t i o n technique employed. The s p e c i f i c equation used was as given i n the general procedure. The equation i s w r i t t e n here f o r c l a r i t y : K5l= P ( a 1 / 2 ) t - 1W~ 1 (Y) where, Y= 29 .6 - I85.5(a/W) + 6 5 5 . 7(a/W) 2-I 0 l7(a/W) 3+ 638.9(a/W)«. 1.4 R e s u l t s 1.4.1 Q u a s i - I s o t r o p i c T e s t i n g of the t h i n n e r 16 p l y q u a s i - i s o t r o p i c samples i n d i c a t e d that specimens of i n s u f f i c i e n t t h i c k n e s s would 24 f a i l in a combination of opening and shearing modes, l e a d i n g to the t w i s t i n g of the sample. To a l l e v i a t e t h i s problem the t h i c k e r 24 p l y specimens where used, with good r e s u l t s . The f a i l e d specimens show a damage zone extending from the notch t i p i n both 45° d i r e c t i o n s to a width of approximately 10 mm. When loaded c o n s i d e r a b l y past the poi n t of damage zone i n i t i a t i o n a crack i s fo r c e d across the f u l l width of the specimen. T h i s propagated crack tends to be s e l f - s i m i l a r with a damage zone width of 10 mm for the e n t i r e l e n g t h of the crack as seen i n f i g u r e 5 ( a ) . The f a i l e d specimens show debonding and f i b r e p u l l - o u t from the surrounding matrix m a t e r i a l . Many of these specimens a l s o show a zone of s u r f a c e delamination approximately 5 mm wide at the notch t i p . 1.4.2 C r o s s p l y The t h i n n e r 16 p l y c r o s s p l y samples d i d show a small tendency to t w i s t as was noted i n the t h i n q u a s i - i s o t r o p i c specimens. T h i s tendency was not as severe as i n the q u a s i - i s o t r o p i c specimens and disappeared i n the t h i c k e r 24 p l y c r o s s p l y specimens. The f a i l e d specimens show a damage zone of equal width and l e n g t h as compared to the elongated damage zone of the q u a s i - i s o t r o p i c samples. The damage zone seems to spread away from the notch t i p , simultaneously along the 0° and 25 Figu r e 5 (a) - F a i l e d 0/145/90 Glass Fibre-Epoxy Geometry (b) 0/90 C-T Specimens Geometry 26 the 90° f i b r e d i r e c t i o n s as seen i n f i g u r e 5(b). No samples were loaded to d e s t r u c t i o n and thus the degree of f i b r e p u l l - o u t was not noted. No su r f a c e d e l amination was e v i d e n t . 1.4.3 Load Curve A n a l y s i s In both the q u a s i - i s o t r o p i c and the c r o s s p l y specimen the a n a l y s i s of the l o a d i n g curves f o r t h i s g l a s s f i b r e -epoxy m a t e r i a l c o n t i n u a l l y gave d i f f i c u l t i e s . The middle p o r t i o n of the l o a d i n g curve, as seen i n f i g u r e 6, shows a d e f i n i t e d e v i a t i o n from l i n e a r e l a s t i c behaviour. During the i n i t i a l p o r t i o n of the load a p p l i c a t i o n , unloading does allow the specimen to re t u r n to the i n i t i a l s t a t e . The l a t t e r p o r t i o n of the l o a d i n g curve shows a t o t a l departure from r e v e r s i b l e e l a s t i c behaviour as the f i b r e s i n the specimen f a i l and y i e l d i n g takes p l a c e . The use of peak loads i n LEFM equations from l o a d i n g curves of t h i s type i s not j u s t i f i e d , due to the non-l i n e a r i t y of the l o a d i n g curve to f a i l u r e . For t h i s reason the a p p l i c a t i o n of LEFM concepts i s very q u e s t i o n a b l e and no q u a n t i t a t i v e values are presented f o r the t e s t s of t h i s mater i a l ' . Due to the many problems encountered i n the t e s t i n g of the g l a s s f i b r e composite, no f u r t h e r t e s t s of t h i s m a t e r i a l were undertaken. Instead, t e s t s were i n i t i a t e d on the m a t e r i a l of primary i n t e r e s t i n t h i s work. 27 G L A S S F I B R E - E P O X Y < O C R O S S H E A D D I S P L A C E M E N T C A R B O N F I B R E - E P O X Y 7 < O C R O S S H E A D D I S P L A C E M E N T F i g u r e 6 - Load Curve t o r G l a s s F i b r e - E p o x y F i g u r e 7 - Load Curve f o r Carbon F i b r e - E p o x y 28 2. CARBON FIBRE EPOXY SPECIMENS The C-T geometry was f e l t to be a good s t a r t i n g p o i n t f o r the t e s t i n g of the carbon fibre-epoxy m a t e r i a l s i n c e much p u b l i s h e d work e x i s t s on v a r i o u s m a t e r i a l s t e s t e d i n t h i s c o n f i g u r a t i o n . T h i s geometry a l s o allows the use of a v a r i e t y of techniques f o r viewing and measuring s u b c r i t i c a l crack propagation. 2.1 Specimen Geometry And S i z e The carbon f i b r e samples were made up of 24 p l i e s , again i n both the c r o s s p l y [ ( 0 / 9 0 ) 6 S ] and the q u a s i -i s o t r o p i c [(0/±45/90) 3s] o r i e n t a t i o n s , y i e l d i n g a t h i c k n e s s of 3.5 mm. The specimen width and notch p r o p o r t i o n were maintained at W = 53 mm and a/W = 0.4. The notch root r a d i u s a l s o was the same as f o r the g l a s s f i b r e specimens, a t 0.2 5 mm. 2.2 T e s t i n g Equipment And C o n d i t i o n s The I n s t r o n t e s t i n g equipment was used i n the same way as that d e s c r i b e d f o r the g l a s s f i b r e specimens. The l o a d i n g r a t e was again 1.27 mm/min. In an attempt to measure the rate of change of the crack p o s i t i o n d u r i n g the t e s t p r e l i m i n a r y work was done using a Fractomat commercial crack displacement measurement d e v i c e . T h i s system uses a type of e l e c t r i c a l r e s i s t a n c e f o i l bonded to the specimen su r f a c e at the crack t i p . If the s u r f a c e crack i s i n d i c a t i v e of the true crack p o s i t i o n 29 through the sample t h i c k n e s s t h i s method i s known to be q u i t e a c c u r a t e . During the l i m i t e d t e s t i n g of t h i s Fractomat system on the C-T specimens the major problem that arose, and destroyed the v a l i d i t y of these t e s t s , was the s u r f a c e delamination e f f e c t s s i m i l a r to those .discussed in the g l a s s f i b r e m a t e r i a l . Another e l e c t r i c a l r e s i s t a n c e method was a p p l i e d at a very b a s i c l e v e l . Much p r e l i m i n a r y t e s t i n g , was performed to i n v e s t i g a t e the use of the carbon f i b r e s i n the composite as an e l e c t r i c a l r e s i s t a n c e matrix. T h i s procedure was aborted when d i f f i c u l t i e s i n i n s u l a t i n g the specimen became overwhelming. Nei t h e r method was used in p r a c t i c e , f o r the above reasons, and no f u r t h e r attempts were made to adapt these techniques. 2.3 E v a l u a t i o n Techniques As i n the t e s t s of the g l a s s f i b r e specimens, other than a v i s u a l examination of the sample, only the LEFM method was used in o b t a i n i n g f r a c t u r e toughness. The equation used i s as shown in the s e c t i o n d i s c u s s i n g the g l a s s f i b r e samples. No crack lengths were measured by the e l e c t r i c a l r e s i s t a n c e techniques d i s c u s s e d i n the p r e v i o u s s e c t i o n due to the d i f f i c u l t i e s s t a t e d . 30 2.4 R e s u l t s 2.4.1 Load Curve A n a l y s i s Loading curves f o r the carbon f i b r e - e p o x y m a t e r i a l immediately showed b e t t e r correspondence to l i n e a r e l a s t i c i t y than the curves f o r the g l a s s f i b r e . The l o a d i n g curves f o r the carbon f i b r e m a t e r i a l are g e n e r a l l y l i n e a r to f a i l u r e . Past the peak load the crack seems to advance in steps with a new, s m a l l e r , e l a s t i c slope preceding each advance as seen in f i g u r e 7. These l o a d i n g curves allowed the use of the peak lo a d value f o r a l l f u t u r e toughness c a l c u l a t i o n s . Minor p e r t u r b a t i o n s on the l i n e a r l o a d i n g ramp were encountered throughout the t e s t i n g . These d i s t u r b a n c e s were c o i n c i d e n t with b u r s t s of a u d i b l e a c o u s t i c emission from the sample. T h i s noise and these p e r t u r b a t i o n s were to be evident throughout the t e s t i n g of a l l specimen types beginning at a load of approximately 50% of the f a i l u r e l o a d . No attempt was made to measure emission r a t e s . These p e r t u r b a t i o n s , preceding the peak load value, are followed by a l o a d i n g ramp of the same slope as that before the p e r t u r b a t i o n o c c u r r e d . T h i s e q u i v a l e n t slope i n d i c a t e s that the e f f e c t i v e crack l e n g t h of the specimen has not changed. For t h i s reason these d i s t u r b a n c e s preceding the peak lo a d may best be d e s c r i b e d as the f a i l u r e of f i b r e s p a r t i a l l y cut during notching or by a p o s s i b l e s l i p p a g e or deformation of the l o a d i n g p o i n t s . 31 4.2 Q u a s i - I s o t r o p i c No t w i s t i n g problems were encountered i n the t e s t i n g of the carbon f i b r e ( 0 / ± 4 5 / 9 0 ) 3 S q u a s i - i s o t r o p i c C-T spec imens. Due to the nature and c o l o u r of the carbon f i b r e - e p o x y m a t e r i a l no damage zone can be seen. The f a i l e d specimens, as shown i n f i g u r e 8 ( a ) , do not show s e l f - s i m i l a r crack p r o p a g a t i o n . The f r a c t u r e tends to fo l l o w the 45° p l i e s . The f a i l e d specimens show debonding and f i b r e p u l l - o u t from the surrounding matrix m a t e r i a l of a degree not q u i t e as s u b s t a n t i a l as that of the corresponding g l a s s f i b r e specimen. L i t t l e s u r f a c e delamination i s present at the notch t i p . Even though the crack growth was not s e l f - s i m i l a r the corresponding l o a d i n g curves d i d i n d i c a t e that the use of the LEFM was p o s s i b l e . The average value obtained f o r the four specimens, using the f i n i t e width c o r r e c t i o n equation given i n the preceding s e c t i o n was 32.4 MPa/m. The range of r e s u l t s was from 27.6 MPa/m. to 44.2 MPa/m; however, three of the four toughness values range from 27.6 MPa/m to 29.0 MPa/m. 4.3 C r o s s p l y As i n the q u a s i - i s o t r o p i c specimens no t w i s t i n g problems were encountered i n the t e s t i n g of the (0/90) c r o s s p l y C-T specimens. 32 E O E U) = O = LP = Ul E O = 0) E O = s i | _ 0 E 00 E O E CD E O ^ I E— O E vlQ E 0 3 E - 0 3 E O i ru E O E CJ E • E _ J > E • E Cfl E • E 0) E O = N» E 03 F i g u r e 8 - F a i l e d Carbon Fibre-Epoxy C-T Specimen (a) 0/±45/90 Geometry (b) 0/90 Geometry (c) Compressive F a i l u r e of 0/90 Geometry 33 The extent of the damage zone can again not be a s c e r t a i n e d due to the m a t e r i a l appearance. The f a i l e d specimens, as shown i n f i g u r e 8(b), d e f i n i t e l y do show m a c r o s c o p i c a l l y s e l f - s i m i l a r crack growth. The f a i l e d specimens show debonding and f i b r e p u l l - o u t from the surrounding matrix m a t e r i a l . P r i m a r i l y , f i b r e p u l l - o u t i s o c c u r r i n g near the notch t i p while the debonding i s concentrated i n the s e c t i o n of the sample nearer the f r e e edge. F a i l u r e at the edge opposite the notch t i p i s p r i m a r i l y compressive f a i l u r e due to a hin g i n g e f f e c t o c c u r r i n g i n t h i s specimen geometry. T h i s compressive f a i l u r e i s seen in f i g u r e 8 ( c ) . The change from compressive to t e n s i l e f a i l u r e seems to occur near the midpoint of the unnotched ligament. No surface delamination i s present at the notch t i p . The LEFM method was used to c a l c u l a t e the f r a c t u r e toughness with good agreement between the f r a c t u r e morphology and the shape of the lo a d i n g curve. The average toughness value obtained f o r these four c r o s s p l y specimens i s 32.9 MPa/m. The range of r e s u l t s was from 29.2 MPa/m to 34.9 MPa/m with three of the four toughness values w i t h i n 2 MPa/m, from 32.9 MPa/m to 34.9 MPa/m. 34 3. SUMMARY OF RESULTS No q u a n t i t a t i v e r e s u l t s are presented f o r the g l a s s f i b r e - e p o x y , C-T specimens. Even though the samples do show m a c r o s c o p i c a l l y s e l f - s i m i l a r crack growth, the load curves i n d i c a t e that the LEFM method i s not a p p l i c a b l e . For the carbon f i b r e - e p o x y specimens the c r o s s p l y samples show s e l f - s i m i l a r crack growth while the q u a s i -i s o t r o p i c samples f r a c t u r e along the 45° f i b r e s . Both geometries do produce l o a d i n g curves which r e a d i l y allow the LEFM method to be a p p l i e d . F r a c t u r e toughness val u e s c a l c u l a t e d using the f i n i t e width c o r r e c t i o n f a c t o r are approximately 32.5 MPa/m for both laminate o r i e n t a t i o n s . E l e c t r i c a l r e s i s t a n c e methods f o r f i n d i n g the p o s i t i o n of the crack f r o n t at any time were i n v e s t i g a t e d . V a r i o u s problems i n v o l v e d with the a p p l i c a t i o n of such r e s i s t a n c e methods l e d to t h e i r d e l e t i o n from t e s t i n g . No crack propagation r a t e s were measured. 35 IV. DEN GEOMETRY Thi s s e c t i o n d e s c r i b e s the t e s t i n g and e v a l u a t i o n of f r a c t u r e toughness using a double edge notch (DEN) specimen geometry. The s e c t i o n i s d i v i d e d i n t o two major c a t e g o r i e s : q u a s i - i s o t r o p i c and c r o s s p l y ; and the c r o s s p l y segment i s f u r t h e r s u b d i v i d e d i n t o two e v a l u a t i o n techniques: LEFM and compliance c a l i b r a t i o n . The DEN geometry decreases the amount of m a t e r i a l necessary and allows the specimen s i z e to be v a r i e d more e a s i l y than does the C-T geometry. While t h i s i s not an ASTM standard specimen, i t s e f f e c t i v e n e s s has been shown by previous r e s e a r c h e r s . 1 0 1 2 1 * A l l the samples of t h i s and the f o l l o w i n g t e s t specimen geometry were produced from Hercules AS/3501-6 carbon f i b r e - e p o x y prepreg. No f u r t h e r g l a s s f i b r e - e p o x y samples were made. These DEN specimens as shown in f i g u r e 9 were cut i n the form of r e c t a n g u l a r t e n s i l e coupons of width o n e - f i f t h t h e i r l e n g t h . A l l specimens c o n s i s t e d of 8 p l i e s , i n both the q u a s i - i s o t r o p i c [(0/±45/90) s] o r i e n t a t i o n and two c r o s s p l y [ ( 0 / 9 0 ) 2 s and (90/0) 2 s3 o r i e n t a t i o n s , each y i e l d i n g a t h i c k n e s s of approximately 1.15 mm. G r i p areas were r e i n f o r c e d with p h e n o l i c doublers bonded to the specimens using epoxy cement, l e a v i n g a gauge le n g t h between the doublers of j u s t over twice the specimen width. A notch root r a d i u s of 0.025 mm was produced with reasonable c o n s i s t e n c y , for a l l 156 specimens, by the use Figure 9 - DEN Specimen Geometry(Various Sizes) 37 of razor blades. 1. QUASI-ISOTROPIC SPECIMENS Te s t s of 65 q u a s i - i s o t r o p i c DEN carbon f i b r e - e p o x y specimens were c a r r i e d out to i n v e s t i g a t e the e f f e c t of specimen s i z e and notch p r o p o r t i o n on the f r a c t u r e toughness. The use of the t e n s i l e specimen geometry was expected to a l l e v i a t e the t w i s t i n g problems p r e v i o u s l y a s s o c i a t e d with t h i n n e r laminates. 1.1 Specimen Geometry And S i z e To i n v e s t i g a t e p o s s i b l e s i z e e f f e c t s , four specimen widths were used: 19.1, 25.4, and 31.1 mm. To i n v e s t i g a t e the e f f e c t of notch p r o p o r t i o n , four notch p r o p o r t i o n s were a l s o used: 2a/W = 0.2, 0.4, 0.6, and 0.8. A l l combinations of notch p r o p o r t i o n and s i z e were produced with t y p i c a l l y four r e p e t i t i o n s of each specimen. As noted p r e v i o u s l y , the samples a l l had a gauge l e n g t h of j u s t i n excess of twice t h e i r width, a t h i c k n e s s of approximately 1.15 mm and a notch root r a d i u s of 0.025 mm. 1.2 T e s t i n g Equipment And C o n d i t i o n s The Instron t e s t i n g equipment, as d e s c r i b e d i n the general procedure, was used f o r the t e s t s i n v o l v i n g a l l q u a s i - i s o t r o p i c DEN carbon fib r e - e p o x y specimens. The crosshead r a t e was 1.27 mm/min and the load was t r a n s f e r r e d to the specimen doublers. R e s u l t s were p l o t t e d on the i n t e g r a l chart recorder as load versus crosshead d i splacement. 38 Any specimen s i z e measurements were made with a micrometer while the l e n g t h of the sharpened notch was measured using a t r a v e l l i n g microscope. 1 .3 E v a l u a t i o n Techniques With the exception of v i s u a l examination d u r i n g and a f t e r t e s t i n g , the LEFM method for f i n d i n g f r a c t u r e toughness using f i n i t e width c o r r e c t i o n f a c t o r s was the only e v a l u a t i o n technique employed. The corresponding equation f o r the DEN geometry i s repeated here; K a= P ( a 1 / 2 ) t - 1 W " 1 ( Y ) where, Y= 1.98 + 0.36.(2a/W) - 2.12(2a/W) 2+ 3.42(2a/W) 3 . 1.4 R e s u l t s 1.4.1 F r a c t u r e Morphology The DEN q u a s i - i s o t r o p i c carbon f i b r e - e p o x y specimens show l i t t l e s i g n of crack propagation preceding f a i l u r e . No crack propagation i s evident i n the outer p l i e s and only the opening of the notch t i p i n d i c a t e s that l o a d i s being a p p l i e d . A f t e r f a i l u r e much debonding and f i b r e p u l l - o u t i s evident as seen i n f i g u r e 10. S e l f - s i m i l a r crack growth can only be s a i d to occur on the most macroscopic s c a l e . Throughout much of the sample f r a c t u r e has f ollowed the 45° p i i e s . G e n e r a l l y , l i t t l e d i f f e r e n c e i s seen when comparing mm OOIIO 2 iiiiliiiiliiit nu O mi 3 mi o mi 4 mi o mi T F i g u r e 10 - F r a c t u r e Morphology of Q u a s i - i s o t r o p i c DEN Spec imens 40 the f r a c t u r e s u r f a c e s of samples of v a r i o u s s i z e and notch p r o p o r t i o n . There does seem to be more delamination and p u l l - o u t i n the specimens with small notch p r o p o r t i o n s as compared to those of l a r g e r notch p r o p o r t i o n but some crack g u i d i n g by the 45° p l i e s i s evident i n a l l cases. 1.4.2 Toughness Measurements The LEFM method was a p p l i e d , even though much damage occur r e d at f r a c t u r e , as mentioned p r e v i o u s l y . The corresponding l o a d i n g curves showed a l i n e a r l o a d i n g ramp with few small d i s t u r b a n c e s , as noted i n the C-T geometry d i s c u s s i o n . The peak lo a d values were used to c a l c u l a t e the f r a c t u r e toughness (Kq) as the f a i l u r e and corresponding load drop were instantaneous. • The averages of the K a values f o r any of the s i z e s or notch p r o p o r t i o n s t e s t e d are shown g r a p h i c a l l y i n f i g u r e s 11(a) and 11(b). The curves of f i g u r e 11(a) i n d i c a t e that l i t t l e v a r i a t i o n of K a occurs with changing notch p r o p o r t i o n . Due to the s c a t t e r a s s o c i a t e d with these v a l u e s , any of the curves c o u l d be i n t e r p r e t e d as being h o r i z o n t a l l i n e s f o r the complete range of notch proport i o n s . F i g u r e 11(b) presents the e f f e c t of specimen s i z e on the v a l u e s . The K^ values i n c r e a s e , f o r a l l notch p r o p o r t i o n s with i n c r e a s i n g specimen s i z e . In general the i n c r e a s e i n K a i s the g r e a t e s t between the 19 mm and 25.4 mm specimens. Over t h i s range the average toughness 41 K Q VS. SIZE. C O N S T ) . 19 2o W 0 4 0 6 0 2 0 8 ( 0 / ± 4 5 / 9 0 ) 25 4 SIZE 3ie mm. 36 (a) 7 0 6 0 -50 4 0 E z S 3 0 2 0 h I O h K vs. ^ o w • 1 » 19mm. 2 • 2 5 4mm. 3 - 318mm. 4 • 38 mm. _l_ JL 0 2 (0/145/90). _i_ 0 4 0 6 2a W 0 8 (b) K 0 = f ( S I Z E , 2 £ ) (c) •(< lW "'^  ( 0 / ± 4 5 / 9 0 ) s T A B L E I ( 0 / ± 4 5 / 9 0 ) \ 2 f i 02 0 . 4 0.6 0 . 8 19 35.9 39.5 37.0 32.3 2 5 43.2 48.4 48.3 41.7 31 NA 49.9 47-6 41.2 3 8 45.6 58.3 55.8 44.9 SIZE AVE. 41.6 49.0 472 40.0 £• w A V E . 36.2 45.4 46.2 51.2 44.6 UNITS OF TOUGHNESS, MPtVni F i g u r e 11 - Q u a s i - i s o t r o p i c DEN (LEFM) R e s u l t s Table I - Q u a s i - i s o t r o p i c DEN (LEFM) Values 42 i n c r e a s e s from 36.2 MPa/m to 45.4 MPa/m. In comparison, the v a r i a t i o n of average toughness over the complete range of s i z e s t e s t e d was from 36.2 MPa/m at 19 mm to 51.2 MPa/m at 38 mm. Table I gi v e s the complete set of averaged toughness values f o r a l l s i z e s and notch p r o p o r t i o n s of the q u a s i - i s o t r o p i c DEN specimens t e s t e d . 1.4.3 Accuracy Of Measured Toughness The r e s u l t s of t e s t i n g the DEN q u a s i - i s o t r o p i c specimens as shown in f i g u r e s 11(a) and 11(b) and as t a b u l a t e d i n t a b l e I are the averages of 65 specimens of v a r y i n g s i z e and notch p r o p o r t i o n . E r r o r s are generated by v a r i a t i o n s i n the alignment of the specimen i n the wedge-l i k e g r i p s and by m a t e r i a l i n c o n s i s t e n c i e s . A major source of e r r o r i s the nature of the production method employed. Because of the small s i z e of the au t o c l a v e used f o r sample p r o d u c t i o n , each of the samples used as r e p e t i t i o n s was o f t e n from d i f f e r e n t p r o d u c t i o n runs. T h i s procedure tends to in c r e a s e the s c a t t e r of each set of val u e s , but avoids weighting a given p o i n t in the r e s u l t s as would be the case i f repeated samples from the same pro d u c t i o n run were used. Thus, using the above procedure, the s c a t t e r i s not of the same magnitude throughout the range of r e s u l t s . As an example, the values of K Q f o r the q u a s i -i s o t r o p i c 25.4 mm, 2a/W = 0.4 specimens range from 26.2 MPa/m to 42 .7 MPa/m ;however, three of the four values are between 37.2 MPa/m and 42.7 MPa/m. Another example to 43 show the variation in the magnitude of the error is the quasi-isotropic, 31.8 mm, 2a/W = 0.4 specimens. In thi s case 8 repetitions were performed and a l l values of K a f e l l between 46.8 MPa/m and 52.5 MPa/m. 2. CROSSPLY SPECIMENS Tests of 55 crossply DEN carbon fibre-epoxy specimens were carried out to investigate the effect of specimen size and notch proportion on the fracture toughness. This testing and evaluation was the same as that used in the previous section. Tests of another 36 crossply DEN carbon fibre-epoxy specimens were c a r r i e d out using the MTS loading system, an Instron s t r a i n gauge, and a 35 mm SLR camera. This group of tests was incorporated to investigate the surface phenomena occurring during testing and to obtain elongation values to be used in deriving K Q / values from a compliance technique. The following discussion w i l l be divided into the two groups of testing as noted above. 3. INSTRON TESTING 3.1 Specimen Geometry And Size To investigate the possible size e f f e cts for the (0/90) crossply material the same four specimen widths were used as for the quasi-isotropic specimens: 19.1, 25.4, 31.8, and 38.1 mm. To investigate the effect of notch proportion, again, four notch proportions were used: 44 2a/W = 0.2, 0.4, 0.6, and 0.8. A l l combinations of notch p r o p o r t i o n and s i z e were produced with t y p i c a l l y four r e p e t i t i o n s of each specimen. The samples again have a gauge l e n g t h of j u s t i n excess of twice t h e i r width, a t h i c k n e s s of approximately 1.15 mm, and a notch root r a d i u s of 0.025 mm. 3.2 T e s t i n g Equipment And C o n d i t i o n s The I n s t r o n t e s t i n g equipment, as d e s c r i b e d in the general procedure, was used f o r these c r o s s p l y t e s t s . The crosshead rate was once again 1.27 mm/min and the load was t r a n s f e r r e d to the specimen doublers through the same wedge-like g r i p s used f o r the q u a s i - i s o t r o p i c specimens. R e s u l t s were p l o t t e d on the i n t e g r a l c h a r t recorder as load versus crosshead displacement. Any specimen s i z e measurements were made with a micrometer while the length of the sharpened notch was measured using a t r a v e l l i n g microscope. 3.3 E v a l u a t i o n Techniques The LEFM method f o r f i n d i n g f r a c t u r e toughness again gave the only numerical r e s u l t s f o r t h i s s e c t i o n . The equation used and f i n i t e width c o r r e c t i o n f a c t o r s are the same as those used f o r the DEN q u a s i - i s o t r o p i c samples. The only other e v a l u a t i o n technique used was the v i s u a l examination of the specimen s u r f a c e d u r i n g and a f t e r t e s t i n g . 45 3 . 4 R e s u l t s 3 . 4 . 1 F r a c t u r e Morphology In c o n t r a s t to the q u a s i - i s o t r o p i c specimens, the c r o s s p l y DEN specimens do show some outer p l y c r a c k i n g , c o l l i n e a r to the notch, preceding f a i l u r e . In c o n j u n c t i o n with the v i s i b l e f r a c t u r e propagation, there was a q u i t e c o n s i s t e n t zone of delamination of the outer p l i e s near the notch t i p . As seen i n f i g u r e s 12(a) and 12(b) the width of t h i s d e l a m i n a t i o n zone i s r e l a t i v e l y independent of the specimen s i z e and notch p r o p o r t i o n . T h i s c o n s i s t e n c y of the d e l a m i n a t i o n width over the whole sample p o p u l a t i o n l e d to much s p e c u l a t i o n regarding a correspondence between t h i s d e l a m i n a t i o n zone width and the len g t h of s u b c r i t i c a l crack growth. . T h i s p o s s i b l e correspondence was a major reason behind the d e c i s i o n to use photography i n the f o l l o w i n g group of t e s t s . No d i f f e r e n c e i s seen when comparing the f r a c t u r e s u r f a c e s of samples of v a r i o u s s i z e and notch p r o p o r t i o n s . A l l specimens show minimal debonding or f i b r e p u l l - o u t and the f r a c t u r e surface i s r e l a t i v e l y smooth compared to that of the q u a s i - i s o t r o p i c DEN specimens of the previous s e c t i o n . S e l f - s i m i l a r crack growth i s a l s o very apparent in c o n t r a s t to the jagged f r a c t u r e of the q u a s i - i s o t r o p i c samples. Figure 12 - F a i l e d C r o s sply DEN Specimen Showing Surface Delamination 47 3.4.2 Toughness Measurements The LEFM method was again used for the measurement of toughness. For these c r o s s p l y samples the confidence was much gr e a t e r than i t had been f o r the q u a s i - i s o t r o p i c samples p r e v i o u s l y d i s c u s s e d due to the greater degree of s e l f - s i m i l a r crack growth. The l o a d i n g curves again show a l i n e a r ramp preceding f a i l u r e , with a massive load drop o c c u r r i n g at f a i l u r e . Due to the shape of the l o a d i n g curve the peak load values were once again used to c a l c u l a t e the f r a c t u r e toughness ( K Q ) . The averages of the K A values f o r any of the s i z e s or notch p r o p o r t i o n s of the c r o s s p l y specimens t e s t e d are shown g r a p h i c a l l y in f i g u r e s 13(a) and 13(b). The curves of f i g u r e 13(a) show that the f r a c t u r e toughness decreases d r a m a t i c a l l y at higher values of notch p r o p o r t i o n . R e f e r r i n g to the value s averaged from a l l four specimen s i z e s , as shown i n t a b l e I I , i t i s seen the toughness values remain r e l a t i v e l y constant at a l l but the highest notch p r o p o r t i o n . The curves and the t a b l e i n d i c a t e that f r a c t u r e toughness decreases d r a m a t i c a l l y at the highest notch p r o p o r t i o n . For example, f o r the s i z e averages, the toughness value i s approximately 56 MPa/m from 2a/W = 0.2 to 2a/W = 0.6 and drops to 38.6 MPa/m at 2a/W = 0.8. Fig u r e 13(b) presents the e f f e c t of specimen s i z e on the KQ values f o r the c r o s s p l y specimens. The KQ values i n c r e a s e , f o r a l l notch p r o p o r t i o n s , with i n c r e a s i n g 48 DEN. K = f(SIZE,2g) (c) (0/90) *s TABLE II ( 0 /90 ) 0.2 0.4 0.6 0.8 19 51.8 51.3 47-2 34.1 25 49.9 49.8 52.0 33.0 31 55.5 71.0 57.9 37.4 38 59.3 58.0 66.8 49.6 SIZE AVE. 54.1 57.5 56.0 38.6 t- w AVE. 46.1 46.2 55.5 58.5 51.6 UNITS OF TOUGHNESS, MPa ym Figure 13 Table II - Crossply DEN (LEFM) Results - Crossply DEN (LEFM) Values 49 specimen s i z e . In general the inc r e a s e i s r e l a t i v e l y constant from a specimen s i z e of 25.4 to 38.1 mm with the K Q values below 25.4 mm showing l i t t l e s i z e e f f e c t . As seen i n t a b l e I I , f o r the values averaged over a l l notch p r o p o r t i o n s , the toughness i n c r e a s e s from 46.2 MPa/m at a s i z e of 25.4 mm to 58.5 MPa/m at 38.1 mm. 3.4.3 Accuracy Of Measured Toughness The r e s u l t s of t e s t i n g these DEN c r o s s p l y specimens are the averages of 55 specimens of v a r y i n g s i z e and notch p r o p o r t i o n . The e r r o r s i n t r o d u c e d are from the same sources as those d i s c u s s e d i n the previous s e c t i o n with respect to the DEN q u a s i - i s o t r o p i c m a t e r i a l . With the v a r i o u s r e p e t i t i o n s coming from d i f f e r e n t m a t e r i a l p r o d u c t i o n runs, s c a t t e r e x i s t s at a l l p o i n t s , but no one s i z e or notch p r o p o r t i o n i s unduly weighted. As an example of the magnitude of the s c a t t e r i n v o l v e d , the values of K Q f o r the c r o s s p l y , 19 mm, 2a/W = 0.6, specimens range from 40 MPa/m to 50.6 MPa/m; however, three of the four v a l u e s are between 49 MPa/m and 50.6 MPa/m. The magnitude of the e r r o r i s the same whether the m a t e r i a l i s of a c r o s s p l y or a q u a s i - i s o t r o p i c laminate or i e n t a t i o n . 50 MTS TESTING 1 Specimen Geometry And S i z e DEN c r o s s p l y carbon f i b r e - e p o x y specimens [ ( 0 / 9 0 ) 2 S and ( 9 0 / 0 ) 2 S ] of a s i n g l e width (25.4 mm) were used to 'i n v e s t i g a t e the v i s i b l e e f f e c t s d u r i n g t e s t i n g . Notch lengths of 2a/W = 0.0, 0.2, 0.4, 0.6, and 0.8 were t e s t e d to allow comparison to the previous t e s t i n g performed on the Instr o n and to allow the use of a compliance methods f o r determining f r a c t u r e toughness. The sample gauge l e n g t h , t h i c k n e s s , and root r a d i u s are the same as those of the previous specimens. 2 T e s t i n g Equipment And C o n d i t i o n s The MTS t e s t i n g equipment, as d e s c r i b e d in the general procedure, was used f o r the 36 DEN c r o s s p l y carbon f i b r e -epoxy specimens. T h i s s e r v o - h y d r a u l i c equipment was used i n a constant stroke mode with a stroke r a t e of 1.0 mm/min. The same s e r r a t e d wedge-like g r i p s were used i n t h i s t e s t i n g as had been employed i n the previous DEN t e s t s . To measure the specimen e l o n g a t i o n two techniques were used on many of the samples. Attached to each specimen durin g t e s t i n g was a 12.7 mm, 50%, Instron c l i p - o n type s t r a i n gauge as shown i n f i g u r e 14. T h i s gauge was connected to the MTS through the s t r a i n channel as d e s c r i b e d e a r l i e r , s u p p l y i n g a vo l t a g e s i g n a l as the s t r a i n output. A motor d r i v e n 34mm camera was a l s o used to not 51 F i g u r e 14 - Instron S t r a i n Gauge Mounted on DEN Specimen 52 only check the specimen e l o n g a t i o n , but a l s o to r e c o r d v i s i b l e s u r f a c e e f f e c t s which were o c c u r r i n g during t e s t i n g . R e s u l t s of load and e l o n g a t i o n were recorded on the f l o p p y d i s c storage of the Bascom-Turner data system. Specimen s i z e measurements were made with a micrometer while the l e n g t h of the sharpened notch was measured using a t r a v e l l i n g microscope. 4.3 E v a l u a t i o n Techniques For these DEN specimens two methods were used to a r r i v e at q u a n t i t a t i v e values of the f r a c t u r e toughness. As in a l l the previous t e s t s the LEFM method was used. The equation used and the f i n i t e width c o r r e c t i o n f a c t o r s are the same as those used in the previous DEN t e s t s . That i s ; R a= P ( a 1 / 2 ) f 1 W " 1 ( Y ) where, Y = 1.98 + 0.36(2a/w) - 2.12(2a/W) 2+ 3.42(2a/W) 3 . The second method used to o b t a i n numerical toughness values was the compliance c a l i b r a t i o n technique. T h i s technique was e x p l a i n e d e a r l i e r , and i n v o l v e s p l o t t i n g the slope of the e l o n g a t i o n versus load c h a r t s , recorded i n the Bascom-Turner, versus notch p r o p o r t i o n . The p l o t i s the compliance curve. T h i s p l o t i s then d i f f e r e n t i a t e d p o i n t by p o i n t , m u l t i p l i e d by one h a l f the measured e l a s t i c modulus (E') of an unnotched sample, and the r e s u l t s are p l o t t e d once again a g a i n s t notch p r o p o r t i o n . T h i s p l o t i s 53 the compliance c a l i b r a t i o n or toughness curve. To arrive at the value of KQ' for a specified notch proportion one simply finds the corresponding value of (E' /2)dC/d(2a/W), from the c a l i b r a t i o n plot, and multiplies i t by the f a i l u r e load squared and divided by the width and thickness. The square root of this product i s the fracture toughness. A linear regression program b u i l t into the Bascom-Turner allows rapid, accurate measures of the i n i t i a l slopes with the remaining work carried out by the computer program. The sequenced photographic technique was employed to attempt to note surface delamination preceding f a i l u r e . The photographs were keyed by a timer to the load and elongation curves stored in the Bascom-Turner. 4.4 Results ; ( 0 / 9 0 ) Specimens 4.4.1 Fracture Morphology Photographs were taken of 6 of the 28 DEN [ ( 0 / 9 0 ) 2 S ] crossply specimens. These samples did not consistently delaminate as had the previous group of crossply DEN specimens tested on the Instron. For this reason the photographs do not y i e l d s u f f i c i e n t results to allow measurement of delamination widths. Some surface fractures were noted prior to f a i l u r e , but as shown in figure 15, the fracture takes place over a much shorter period of time than the 0 . 20 second intervals of the photographs. The f a i l u r e surfaces are much l i k e those of the previous DEN crossply tests, showing s e l f - s i m i l a r crack growth with very 54 Tl ME (min.,sec.,l/IOOsec.) F i g u r e 15 - Fr a c t u r e Morphology of 0/90 C r o s s p l y DEN Specimens 55 l i t t l e debonding or f i b r e p u l l - o u t . Throughout the photographic sequence; however, the crack can be seen to be opening. T h i s crack opening tends to produce some sign s of debonding or f i b r e p u l l - o u t l e a d i n g to what looks l i k e crack t i p b l u n t i n g . 4.4.2 Toughness Measurement (LEFM) The LEFM equation and f i n i t e width c o r r e c t i o n f a c t o r s used are the same as those used i n a l l p r e v i o u s d i s c u s s i o n s of the DEN geometry. The average values of f o r the DEN (0/90)25 c r o s s p l y o r i e n t a t i o n and the corresponding curve from the I n s t r o n t e s t i n g are presented i n f i g u r e 16. Two curves are p l o t t e d f o r the (0/90) 2s o r i e n t a t i o n , r e p r e s e n t i n g samples from two separate p r o d u c t i o n runs. The v a r i a t i o n due to m a t e r i a l p r o d u c t i o n i n c o n s i s t e n c i e s can be r e a d i l y seen; however, i t i s a l s o noteworthy that the e f f e c t s due to the v a r i a t i o n of notch p r o p o r t i o n do not change. The tr e n d towards lower toughness at the g r e a t e s t notch p r o p o r t i o n i s i n keeping with p r e v i o u s f i n d i n g s and q u a n t i t a t i v e values are i n the same range as those of the prev i o u s s e c t i o n . Unnotched c r o s s p l y t e n s i l e coupons were a l s o t e s t e d to f a i l u r e i n t h i s group of t e s t s of the DEN specimen geometry. These s p e c i f i c samples were t e s t e d , along with some samples produced from e a r l i e r m a t e r i a l , to a r r i v e at an experimental value of the t e n s i l e s t r e n g t h of t h i s m a t e r i a l . The average experimental value compiled 80 56 K Q v s . 2 ~ (LEFM) W= const. = 25-4 mm 60 h 50 1 £ 4 0 o 30 20 10 O PREVIOUS INSTRON TEST VALUES A MTS TEST-SPECIMENS 24A • MTS T E S T - S P E C I M E N S 2.1 B (0/90) 2S I 0-2 0-4 0-6 0-8 F i g u r e 16 - LEFM R e s u l t s f o r 0/90 DEN Specimens (MTS) 57 throughout t e s t i n g i s 750 MPa. Comparison of t h i s unnotched t e n s i l e s t r e n g t h (<»-u) with values of notched s t r e n g t h , c o r r e c t e d using f i n i t e width f a c t o r s , allow an understanding of the magnitude of the m a t e r i a l notch s e n s i t i v i t y . The method used to a r r i v e at the notch s e n s i t i v i t y curve f o r the 25.4 mm c r o s s p l y DEN specimens of t h i s and the pre v i o u s s e c t i o n , as shown i n f i g u r e 17, d e a l s with a f i n i t e width c o r r e c t i o n of the "gross" s e c t i o n s t r e s s . 7 The "gross" s e c t i o n s t r e s s i s d e f i n e d as the f a i l u r e l o a d of a notched specimen d i v i d e d by the unnotched c r o s s -s e c t i o n a l a r ea. The f i n i t e width c o r r e c t i o n , given by the equat i o n : Y = 1 + 0.128(2a/W) - 0.28(2a/W) 2+ 1.525(2a/W) 3, i s used as a c o r r e c t i o n f o r l o c a l d i s t u r b a n c e s i n the s t r e s s f i e l d near the notch t i p . Thus to c a l c u l a t e a c o r r e c t e d notched specimen s t r e s s (tfN°°), the "gross" s e c t i o n s t r e s s i s found and i s then m u l t i p l i e d by the value of Y f o r the corresponding notch p r o p o r t i o n . The r e s u l t i n g curve of f i g u r e 17 shows that the r a t i o of c o r r e c t e d notched specimen s t r e s s to unnotched t e n s i l e s t r e n g t h (c tT/a^ ) decreases with i n c r e a s e d notch p r o p o r t i o n . 1 5 1 6 1 7 NOTCH SENSITIVITY AS/3501-6 ( 0 / 9 0 L c F i g u r e 17 - Notch S e n s i t i v i t y of the (0/90) AS/3501-6 CFRP 59 4.4.3 Accuracy As was noted, i n the d i s c u s s i o n of e r r o r in the DEN c r o s s p l y specimens of the Instron s e c t i o n , major i n c o n s i s t e n c i e s can come from v a r i a t i o n s i n pro d u c t i o n techniques. T h i s i s g r a p h i c a l l y obvious i n f i g u r e 16 where the ( 0 / 9 0 ) 2 s DEN samples from two d i f f e r e n t p r o d u c t i o n runs were p l o t t e d s e p a r a t e l y . S c a t t e r of the r e s u l t s w i t h i n a specimen group was much more pronounced at the lower notch p r o p o r t i o n s than at the higher notch p r o p o r t i o n s . For example, in sheet 24A, the v a r i a t i o n of the three t e s t s at 2a/W = 0.2 ranged from 42.1 MPa/m to 56.3 MPa/m, while at 2a/W = 0.8 the three t e s t span was only from 39.1 MPa/m to 40.4 MPa/m. 4.4.4 Toughness Measurement (Compliance) Compliance c a l i b r a t i o n as d e s c r i b e d i n the procedure was c a r r i e d out for a l l of the DEN c r o s s p l y samples t e s t e d on the MTS. Figu r e 18(a) shows the compliance versus notch p r o p o r t i o n p l o t s f o r the two groups of (0/90) 2s DEN t e s t s . These p l o t s , being both polynomials of f i f t h order, correspond c l o s e l y to each other. The r e s u l t i n g compliance c a l i b r a t i o n p l o t s ((E'/2)dC/d(2a/w) versus 2a/W) are shown in f i g u r e 18(b). These c a l i b r a t i o n p l o t s y i e l d f r a c t u r e toughness (Kq') values, as shown in f i g u r e 19, which are c o n s i s t e n t l y higher than the corresponding LEFM K<j values but with the same trends r e g a r d i n g notch p r o p o r t i o n . Once again, K a' i s c a l c u l a t e d by f i n d i n g , from the c a l i b r a t i o n Q-2 0-4 9 -5. 0-6 0-8 c w F i g u r e 18 - Compliance C a l i b r a t i o n f o r (0/90) DEN 61 T 80 70 60 1 o CL 50h 40 A K Q v s 2rjr; (compliance) W= const. = 2 5-4 mm a 30h 20 10 A MTS TEST— SPECIMENS 24A • MTS TEST—SPECIMENS 2IB (0/90) Jl L _ -I 1— 2S 0-2 0-4 0-6 0-8 10 F i g u r e 19 - Toughness R e s u l t s (Compliance) f o r (0/90) DEN Specimens 62 curve, the value of (E'/2)dC/d(2a/W) corresponding to the p a r t i c u l a r notch p r o p o r t i o n . The value of (E'/2)dC/d(2a/W) i s then m u l t i p l i e d by P 2W~ 1t~ 1 and the square root of the sum i s taken, y i e l d i n g K a'. Therefore the r e l e v a n t equation i s ; ((E'/2)(dC/d(2a/W))(P 2W- 1t" 1) =K Q'. E r r o r in these compliance r e s u l t s may be a t t r i b u t e d to the DEN specimen geometry which, due to the high inherent r i g i d i t y , makes accurate measurement of such small displacements d i f f i c u l t . Due to the d i f f i c u l t i e s i n v o l v e d in measuring the extremely small r e s u l t i n g e l o n g a t i o n s , the DEN geometry i s recognized as one of the poorest f o r t h i s type of t e s t i n g . 1 8 The average experimental modulus (E' ) values c a l c u l a t e d f o r t h i s carbon f i b r e - e p o x y m a t e r i a l i n the DEN geometry, and used in c a l c u l a t i o n s of K a ' , i s 53 GPa. Compared to the accepted value of modulus for t h i s m a t e r i a l and p l y o r i e n t a t i o n (73 GPa) the experimental value seems too low to be simply m a t e r i a l i n c o n s i s t e n c i e s . T h i s e r r o r in modulus a l s o seems to stem from the d i f f i c u l t i e s i n v o l v e d i n a c c u r a t e l y measuring the specimen e l o n g a t i o n . 4 . 5 R e s u l t s ; ( 9 0 / 0 ) Specimens 4 . 5 . 1 F r a c t u r e Morphology Photographs were taken of 3 of the 8 DEN [ ( 9 0 / 0 ) 2 S ] 63 c r o s s p l y specimens. These samples showed much the same e f f e c t s with respect to crack opening as was seen i n the ( 0 / 9 0 ) 2 5 DEN specimens. The p r i n c i p a l f e a t u r e s were sig n s of debonding or f i b r e p u l l - o u t l e a d i n g to what looked l i k e crack t i p b l u n t i n g . The ( 9 0 / 0 ) 2 5 DEN geometry, i n c o n t r a s t to the ( 0 / 9 0 ) 2 5 specimens, d i d produce i n t e r - f i b r e s u r f a c e c r a c k s that were r e a d i l y v i s i b l e i n the photographs. F i g u r e 20 shows a photographic sequence f o r the ( 9 0 / 0 ) 2 s o r i e n t a t i o n . Comparison of the photographic sequences of f i g u r e s 1 5 and 2 0 shows a dramatic d i f f e r e n c e i n the amount of s u r f a c e d e l a m i n a t i o n . R e l a t i v e l y no su r f a c e delamination i s present i n the ( 9 0 / 0 ) 2 s specimens as compared to that of the ( 0 / 9 0 ) 2 S specimens. 4 . 5 . 2 Toughness Measurement (LEFM) The LEFM equations are again the same as those used throughout a l l p r e v i o u s t e s t i n g of DEN specimens i n t h i s work. The average values of KQ_ f o r the ( 9 0 / 0 ) 2 5 DEN specimens are p l o t t e d i n f i g u r e 21 along with the ( 0 / 9 0 ) 2 s DEN curves from the previous s e c t i o n . The r e s u l t s presented f o r the ( 9 0 / 0 ) 2 % geometry are based on only 8 specimens and as such only general trends and values can be d i s c u s s e d . Regardless of p l y o r i e n t a t i o n , the q u a n t i t a t i v e values of K A , as seen i n f i g u r e 21 f o r these and the ( 0 / 9 0 ) 2 S DEN specimens, f a l l i n t o the same range as the ( 0 / 9 0 ) 2 S DEN 6 4 TIME (min.,sec.,l/IOOsec.) F i g u r e 20 - Fr a c t u r e Morphology of (90/0) DEN Specimens 65 D Q. 80 70 60h 501 401 30T K Q vs 2 ~ (LEFM) We const.= 25-4 mm 2 0 8 10 -O A • 0-2 INSTRON T E S T ( 0 / 9 0 ) 2 s MTS T E S T 24A ( 0 / 9 0 ) 2 s MTS T E S T 21B (0/90) 2s MTS TEST 24 B (90/0) 2 S 0-4 _0_ W 0-6 0-8 F i g u r e 21 - Toughness R e s u l t s (LEFM) f o r (90/0) DEN Spec imens 66 specimens from the previous I n s t r o n t e s t i n g . The range of values i s from approximately 35 MPa/m to 60 MPa/m. Due to s i m i l a r i t i e s i n the specimen s i z e , geometry, and in the q u a n t i t a t i v e f r a c t u r e toughness r e s u l t s , the unnotched t e s t s of the ( 9 0 / 0 ) 2 S DEN specimens were combined with the (0/90)2s DEN r e s u l t s f o r the dete r m i n a t i o n of notch s e n s i t i v i t i e s . Thus the r e s u l t s d i s c u s s e d i n the previ o u s s e c t i o n , r egarding notch s e n s i t i v i t y , a l s o p e r t a i n to t h i s (90/0)25 o r i e n t a t i o n . T h i s means that as p r e v i o u s l y d i s c u s s e d , the notch s e n s i t i v i t y i n c r e a s e s with i n c r e a s i n g notch p r o p o r t i o n . 4.5.3 Accuracy Of Measured Toughness For the (90/0) 2s DEN specimens l i t t l e comment can be made regarding experimental s c a t t e r s i n c e the o b j e c t i v e of t h i s s e c t i o n was p r i m a r i l y to observe the su r f a c e e f f e c t s . 4.5.4 Toughness Measurement (Compliance) Compliance c a l i b r a t i o n , as d e s c r i b e d i n the procedure and in the preceding s e c t i o n , was c a r r i e d out f o r a l l 8 t e s t specimens of t h i s s e c t i o n . F i g u r e 22(a) shows the compliance versus notch p r o p o r t i o n p l o t f o r t h i s (90/0) 2s c r o s s p l y DEN laminate along with the curves, which were p r e v i o u s l y presented f o r the (0/90) 2s c r o s s p l y DEN specimens. These three p l o t s are i n good agreement with the r e s u l t s f o r the ( 9 0 / 0 ) 2 S DEN specimens, being f i t t e d to a t h i r d order polynomial while the two curves from the preceding s e c t i o n are f i f t h order polynomials. The K Q Calibration . 21B 0-2 0-4 ? J L 0-6 0-8 W F i g u r e 22 - Compliance C a l i b r a t i o n f o r (90/0) DEN 68 corresponding compliance c a l i b r a t i o n p l o t s ((E'/2)dC/d(2a/W) versus 2a/W) are shown in f i g u r e 22(b). As was the case i n the preceding s e c t i o n , these c a l i b r a t i o n p l o t s y i e l d f r a c t u r e toughness (Ks,') values, as shown i n f i g u r e 23, which are c o n s i s t e n t l y higher than the corresponding LEFM K Q v a l u e s . The.same trends are noted with respect to notch p r o p o r t i o n . Once again, e r r o r s may be a t t r i b u t e d to the extreme s t i f f n e s s of the DEN geometry. A l l the same e f f e c t s r e g a r d i n g measurement d i f f i c u l t i e s p e r t a i n i n g to the i n h e r e n t l y high s t i f f n e s s are as di s c u s s e d i n the previous s e c t i o n . 5. SUMMARY OF RESULTS Q u a n t i t a t i v e values of f r a c t u r e toughness f o r the samples t e s t e d on the Instr o n were d e r i v e d from a LEFM method. No compliance techniques were used s i n c e the only measure of e l o n g a t i o n was the crosshead displacement. T h i s displacement was l a t e r found to be an order of magnitude gr e a t e r than that found using a s t r a i n gauge. Toughness r e s u l t s f o r the q u a s i - i s o t r o p i c DEN specimens t e s t e d on the Instr o n show no r e l i a n c e on notch p r o p o r t i o n , y i e l d i n g an average K^ value of 44.6 MPa/m. These specimens do however show a tr e n d towards higher toughness with i n c r e a s e d specimen s i z e . The f r a c t u r e s urface f o r the q u a s i - i s o t r o p i c sample shows much debonding and f i b r e p u l l - o u t but the lo a d i n g curve i n d i c a t e s an e l a s t i c behaviour to f a i l u r e . o Q_ 801 70 60 50 40 - or K l v s 2-S- (Compliance) 30 20 A + MTS T E S T 24A ( 0 / 9 0 ) 2 S MTS T E S T 2IB ( 0 / 9 0 ) 2 s MTS T E S T 24B ( 9 0 / 0 ) 2 S 02 0-4 „ 0-6 ^ W 0-8 gure 23 - Toughness R e s u l t s (Compliance) f o r (90/0) DEN Specimens 70 For the c r o s s p l y specimens t e s t e d on both the Instron and the MTS the toughness values c a l c u l a t e d by LEFM techniques show e f f e c t s r e l a t e d to both specimen s i z e ' and notch p r o p o r t i o n . These specimens tend to show a decrease in toughness at the higher notch p r o p o r t i o n . From 2a/W = 0.2 to 0.6 the average K Q value i s approximately 56 MPa/m but at 2a/W = 0.8 the average K a value has dropped below 39 MPa/m. The s i z e dependency i s much the same as that of the q u a s i - i s o t r o p i c specimens with a tendency towards higher toughness at inc r e a s e d s i z e s . The compliance method was a l s o used to a r r i v e at toughness values f o r the c r o s s p l y laminates t e s t e d on the MTS. The values c a l c u l a t e d from t h i s method were c o n s i s t e n t l y higher than the corresponding values found using a LEFM method. The trends of the r e s u l t s f o r the compliance technique do compare favourably to those found by the LEFM method. The d i f f e r e n c e in the q u a n t i t a t i v e values of toughness are d i s c u s s e d with respect to the inherent s t i f f n e s s of the DEN geometry which leads to d i f f i c u l t i e s i n making accurate measures of the specimen e l o n g a t i o n . The idea of notch s e n s i t i v i t y i s introduced and i s shown to inc r e a s e with i n c r e a s i n g notch p r o p o r t i o n . T h i s i n c r e a s e in notch s e n s i t i v i t y i n d i c a t e s an expected decrease in f r a c t u r e toughness at gr e a t e r notch proport i o n s . 71 The f r a c t u r e s urface f o r the c r o s s p l y specimens shows very l i t t l e debonding or f i b r e p u l l - o u t . The crack growth i s d e f i n i t e l y c o l l i n e a r to the s t a r t e r notches. In the (0/90) 2 5 DEN specimens a smal l zone of s u r f a c e d e l a m i n a t i o n was noted at each notch t i p . Photographic s t u d i e s were undertaken to check f o r a correspondence of t h i s d e l a m i n a t i o n zone to the l e n g t h of s u b - c r i t i c a l crack growth, but no c o n c l u s i o n s were reached due to i n c o n s i s t e n t m a t e r i a l behaviour. The (90/0) DEN specimens showed no. su r f a c e d e l a m i n a t i o n , but d i d show s t a b l e outer p l y crack growth preceding f a i l u r e . T h i s i s compared, i n g e n e r a l , to only crack opening being v i s i b l e before c a t a s t r o p h i c f a i l u r e takes p l a c e i n the ( 0 / 9 0 ) 2 5 specimens. 72 V. 4BND GEOMETRY Thi s s e c t i o n d e s c r i b e s the de t e r m i n a t i o n and e v a l u a t i o n of f r a c t u r e toughness using a four p o i n t bending beam (4BND) geometry. The s e c t i o n i s d i v i d e d i n t o two segments. Group 1 t e s t s d e a l t with many v a r i a b l e s i n c l u d i n g specimen s i z e , t h i c k n e s s , notch p r o p o r t i o n , and aspect r a t i o but went i n t o l i t t l e d e t a i l and used few, i f any, r e p e t i t i o n s . Group 2 t e s t i n g was an outgrowth of the Group 1 t e s t s and v a r i e s only s i z e , t h i c k n e s s , and notch p r o p o r t i o n . T h i s group of t e s t s goes i n t o d e t a i l of the same order as that of the DEN specimens bf Chapter 4. The procedures used i n Groups 1 and 2 are e s s e n t i a l l y the same and w i l l thus be d i s c u s s e d in d e t a i l before the chapter i s subd i v i d e d . The 4BND specimen geometry was chosen due to i t s a p p l i c a b i l i t y to compliance t e s t i n g . The l a r g e midspan d e f l e c t i o n s allow accurate measurements to be made; however, the load o f t e n becomes extremely low f o r the 5 metric ton load c e l l used on the MTS. The 4BND geometry was chosen i n s t e a d of the c o n v e n t i o n a l ASTM standard three p o i n t bend geometry 3 because of load p o i n t c o n s i d e r a t i o n s . In some of the low aspect r a t i o beams, concern e x i s t e d r e g a r d i n g deformation at the l o a d i n g p o i n t of the three p o i n t bend geometry. The 4BND geometry allows the load to be spread over two l o a d i n g p o i n t s and thus a l l e v i a t e s the deformation problem. 73 The m a t e r i a l used was again Hercules AS/3501-6 prepregged carbon f i b r e - e p o x y . A l l beams t e s t e d were of the (0/90) c r o s s p l y o r i e n t a t i o n with the 0° d i r e c t i o n c orresponding to the length of the beam. No doublers were necessary on the specimens but guides were p r o v i d e d on the MTS bending j i g to ensure that the specimen remained u p r i g h t . A l l samples were notched with a 0.3 mm diamond saw and were advanced to a c o n t r o l l e d root r a d i u s of approximately 0.025 mm using razor blades. 1. TESTING EQUIPMENT AND CONDITIONS A l l 4BND t e s t s were performed i n e s s e n t i a l l y the same manner. In a l l cases the l o a d was a p p l i e d using the MTS and the Bascom-Turner was used to record the values of load and d e f l e c t i o n onto d i s c . The MTS stroke was c o n t r o l l e d at a r a t e of 10 mm/min. The l o a d i n g p o i n t s were 12.7 mm diameter r o l l s set up i n such a way that the two l o a d i n g r o l l s were attached to the 5 m e t r i c ton load c e l l as i n f i g u r e 24(a). The supporting r o l l s , d e f i n i n g the beam l e n g t h , were attached to the h y d r a u l i c l o a d i n g ram. A "pogostick" with an I n s t r o n c l i p - o n type s t r a i n gauge mounted, as shown in f i g u r e 24(b), was used to measure the midspan d e f l e c t i o n of the beam. The t e s t s of Group 1 used the same 12.7 mm, 50%, s t r a i n gauge as the DEN t e s t s while the t e s t s of Group 2 used a 25.4 mm, 50%, s t r a i n gauge, again connected through the s t r a i n channel of the MTS. These v o l t a g e s along with the loads were 4 B N D S T R A I N G A U G E F i g u r e 24 - 4BND Setup and Instrumentation 75 monitored and st o r e d on the Bascom-Turner. In a d d i t i o n , 8 of the 35 4BND specimens of Group 1 were photographed i n a manner s i m i l a r to that used i n the t e s t s of the DEN geometry. These photographs were again keyed to the Bascom-Turner using a d i g i t a l stopwatch f i l m e d in each frame. 2. GROUP 1 TESTING Tes t s of 35 4BND specimens were performed to gain i n s i g h t i n t o the v a r i a t i o n of f r a c t u r e toughness with specimen s i z e , notch p r o p o r t i o n , t h i c k n e s s , and aspect r a t i o . 2.1 Specimen Geometry And S i z e . Many v a r i a t i o n s and few r e p e t i t i o n s were produced f o r t h i s group of 4BND t e s t s . The specimens c o n s i s t e d of e i t h e r 24 p l i e s (2.94 mm) or 60 p l i e s (7.71 mm) i n a c r o s s p l y o r i e n t a t i o n [ ( 0 / 9 0 ) 6 S and ( 0 / 9 0 ) 1 5 5 ] . Three notch p r o p o r t i o n s were used: a/W = 0.0, 0.4, and 0.6. The other v a r i a b l e s i n v o l v e d were specimen height and beam l e n g t h . The beam lengths used r e f e r to the d i s t a n c e between the supports of the bend j i g and, in each case, the d i s t a n c e between the load a p p l i c a t i o n r o l l s i s one t h i r d of the beam leng t h as shown in f i g u r e 24(a). The specimen length was t y p i c a l l y 15% greater than the beam l e n g t h . Three beam lengths were used; 87 mm, 127 mm, and 254 mm, along with three beam h e i g h t s ; 6.32 mm, 13.3 mm, 76 and 25.7 mm. When combined these y i e l d e d specimens of the two t h i c k n e s s e s noted, separated i n t o e i g h t groups by the beam l e n g t h to beam height r a t i o s . (The s h o r t e s t l e n g t h and g r e a t e s t height were not combined.) The r e s u l t i n g aspect r a t i o s t e s t e d were 13.8, 20.1, and 40.2 f o r the lowest beam height, 6.54, 9.55, and 19.1 f o r the intermediate beam he i g h t , and 4.94 and 9.88 f o r the maximum beam h e i g h t . 2.2 E v a l u a t i o n Techniques The p r i n c i p a l techniques used, in t h i s Group 1 study, were v i s u a l and photographic f o r comparison with p r e v i o u s specimen types and LEFM f o r q u a n t i t a t i v e values and tren d s . The photographic technique was as d e s c r i b e d p r e v i o u s l y f o r the DEN specimens. The LEFM method uses the equation given in the gen e r a l e v a l u a t i o n s e c t i o n and repeated here; K„ = [ ( P 2 l 2 t ~ 2 W ~ 2 ) ( Y ) ] 1 / 2 where, Y = 34.7(a/W) - 55.2(a/W) 2+ I96(a/W) 3 . Compliance c a l i b r a t i o n s were a l s o c a r r i e d out f o r a l l the 4BND specimens. These specimens were used to i n v e s t i g a t e the c h a r a c t e r i s t i c s of t h i s method. P r i m a r i l y the problem i n v o l v e d i n using the compliance technique i n t h i s group of t e s t s i s that the t y p i c a l compliance curve was only a p p l i c a b l e to e i t h e r two or three specimens due to the l a r g e number of v a r i a b l e s i n v o l v e d . The compliance 77 curves and the c a l i b r a t i o n curves f o r t h i s s e c t i o n are in c l u d e d i n Appendix C, but the LEFM techniques were found s u f f i c i e n t f o r r e v e a l i n g the trends i n v o l v e d . 2.3 R e s u l t s 2.3.1 F r a c t u r e Morphology The photographic records of these 4BND specimens were taken to i n v e s t i g a t e any obvious d i f f e r e n c e s due to a v a r i a t i o n i n specimen t h i c k n e s s and s i z e . F i g u r e 25 shows no v i s i b l e d i f f e r e n c e s due to the v a r i a t i o n i n t h i c k n e s s . These photographs a l s o allow comparison between the modes of f a i l u r e of the 4BND and the DEN specimens. Comparing the f a i l u r e of the 4BND and the DEN specimens immediately shows the c a t a s t r o p h i c r e l e a s e of energy in the DEN geometry and the l e s s dramatic f a i l u r e of the 4BND geometry which, i f l o a d i n g i s continued, i s fo l l o w e d by debonding and f i b r e p u l l - o u t . In a m a j o r i t y of the 4BND specimens f a i l u r e o c c u r r e d without the complete s e v e r i n g of the beam. In these cases, which tended to be the specimens of grea t e r notch p r o p o r t i o n , c o n s i d e r a b l e p u l l - o u t and delamination were prese n t . The remaining 4BND specimens show a r e l a t i v e l y c l e a n f r a c t u r e s urface with very l i t t l e p u l l - o u t or del a m i n a t i o n . In these cases complete f a i l u r e was n e a r l y instantaneous and the behaviour was much l i k e that of the c r o s s p l y DEN specimen t e s t s . 78 F i g u r e 25 - F a i l e d 4BND Specimens of V a r i o u s T h i c k n e s s e s 79 2.3.2 Toughness Measurements (LEFM) Figures 26, 27, and 28 show the trends of fracture toughness (K Q) for the 4BND geometry with respect to notch proportion and aspect r a t i o . Each point shown represents a single specimen tested as no repetitions were performed in this limited group of tests. For both thicknesses, figures 26 and 27 show trends of decreasing toughness with increasing notch proportion. For example, figure 26 shows a drop from 54.7 MPa/m to 38.4 MPa/m for samples 22BM (a/W = 0.40) and 22BN (a/W = 0.59) respectively. Figures 26 and 27 also show trends which indicate a decrease of KQ with increasing thickness, and an increase of KQ with increasing height (W). Values of KQ for the thinner (2.95 mm) samples range from 30 MPa/m to 70 MPa/m, while the values for the thicker (7.62 mm) samples range only from approximately 30 MPa/m to 50 MPa/m. Figure 28 shows the var i a t i o n of K Q with aspect r a t i o for various specimen heights, thicknesses, and notch proportions. The general trend throughout is toward a decrease in K<j with increasing aspect r a t i o . This trend seems to decrease at higher notch proportions and i s in fact r e l a t i v e l y constant from 20:1 upwards. This plateau effect has been noted by previous researchers. 1 9 r K Q v s £ 80 —r 1— 4 B N D G R O U P ) 80 70 6 0 4 0 h 10 o + A Q X SAMPLE Y h^ m m*0 22B(0,P) 5 0 25 22B(Q) 100 25 22B(H,J) 6-6 12-7 22B(M,N)I98 12-7 22B(K,L) 9-6 42-7 0 22B(B,C) 13-8 6-3 V 22B(D,E) 20-6 6-3 © 22B(F,G)4l-0 6-3 1 I _ L "I ( 0 / 9 0 ) 6S 0-2 0-4 w 0-6 0-8 10 Figure"26 - 4BND Group 1 R e s u l t s (2.95mm t h i c k n e s s ) 81 T 1 — i •—r— K n vs 4BND GROUP I I 80 70 6 0 r IE 5( a CL j 30 20 10 SAMPLE - r h(mmT* 0 23(N,0) 4-9 25 + 23(P) 9-8 25 — A 23(1 ,J) 6-3 1 2 7 X 23(K,L) 9-6 23(B) 130 12-7 6-3 V 23(D,E) 2 0 0 6-3 O 23(F,G) 3 9 0 6-3 (0 /90) | 5 S 0-2 0-4 0-6 a 0-8 I-w F i g u r e 27 - 4BND Group 1 R e s u l t s (7.62mm t h i c k n e s s ) ' 80 82 4BND GROUP I 70 60 50 h ^ 401-3or 20 101-a W h t A 0-4 6-3 2-94 O 0-6 6-3 2-94 0-4 6-3 7-71 G 0-4 12-7 2-94 0-6 127 2 94 • I 0-4 25-4 » 2-94 10 20 L 2 (0/90) 30 40 50 F i g u r e 28 - 4BND Group 1 Toughness V a r i a t i o n with Aspect R a t i o 83 2.3.3 Accuracy Of Measured Toughness For these 4BND specimens l i t t l e comment can be made regar d i n g the experimental s c a t t e r s i n c e no r e p e t i t i o n s were performed. T h i s i s the case s i n c e the o b j e c t i v e s of t h i s group of t e s t s were to observe s u r f a c e e f f e c t s p h o t o g r a p h i c a l l y , to t e s t new experimental techniques, and to view trends present i n a new specimen geometry. 2.3.4 Toughness Measurement (Compliance) Compliance versus notch p r o p o r t i o n p l o t s were a l s o generated f o r each of the 4BND specimens. As mentioned e a r l i e r , due to the many v a r i a t i o n s i n specimen height (W) and length (1), a t o t a l of 15 d i f f e r e n t compliance versus notch p r o p o r t i o n p l o t s and the corresponding c a l i b r a t i o n curves were a r r i v e d a t . F i g u r e s 29(a) and 29(b) show the r e s u l t s f o r one of the ( 0 / 9 0 ) 6 5 specimens as an example of the curves obtained f o r t h i s 4BND geometry. (For the complete set of curves, see Appendix C.) Much c l o s e r agreement e x i s t s between the values and the KQ/ values f o r the 4BND geometry than f o r the DEN geometry; however, too few samples were t e s t e d to give any f i r m q u a n t i t a t i v e v a l u e s . T h i s 4BND geometry i s recognized as one of the two best geometries a v a i l a b l e f o r compliance t e s t i n g 1 8 due to the r e l a t i v e l y l a r g e amounts of d e f l e c t i o n at f a i l u r e . The average experimental modulus (E') values c a l c u l a t e d f o r t h i s carbon f i b r e - e p o x y m a t e r i a l in the 4BND geometry i s 65 GPa. C o n s i d e r i n g that many of the a c t u a l 012 0-24 0-36 0-48 F i g u r e 29 - Compliance C a l i b r a t i o n f o r Group 1 4BND 85 values were above as w e l l as below the accepted value (73 GPa) of modulus f o r t h i s m a t e r i a l and p l y o r i e n t a t i o n , the experimental value seems q u i t e a c c e p t a b l e . T h i s kind of correspondence to the t h e o r e t i c a l value of modulus allows b e t t e r c o n f i d e n c e , as would be expected, i n the compliance r e s u l t s r e l a t e d to the 4BND geometry. 3. GROUP 2 TESTING Tests of 69 4BND specimens were performed to give more d e t a i l e d q u a n t i t a t i v e i n f o r m a t i o n r e g a r d i n g a more s p e c i f i c group of v a r i a b l e s , i n c l u d i n g notch p r o p o r t i o n , t h i c k n e s s , and h e i g h t . 3.1 Specimen Geometry And S i z e The 69 specimens c o n s i s t e d of three t h i c k n e s s e s : 4.54 mm (36 p l i e s ) , 6.33 mm (48 p l i e s ) , and 7.88 mm (60 p l i e s ) . The p l y o r i e n t a t i o n s were (0/90) 9 S- , (0/90) 1 2 s and (0/90),5 5 r e s p e c t i v e l y . F i v e notch p r o p o r t i o n s were produced: a/W =0.0, 0.2, 0.4, 0.6, and 0.8. Only two specimen h e i g h t s were used: 6.4 mm and 12.8 mm. These two beam hei g h t s were combined with beam lengths of 127 mm and 254 mm in such a way that the beam len g t h to beam height r a t i o remained constant at 19.8:1. The notch root r a d i u s was again c o n t r o l l e d at 0.025 mm us i n g a razor blade. 3.2 E v a l u a t i o n Techniques The methods of LEFM and compliance c a l i b r a t i o n were both used i n the Group 2 t e s t i n g . The equation used i n the LEFM was the same as that quoted i n the d i s c u s s i o n of 86 Group 1 t e s t i n g . The compliance technique i s handled in the same way as i n the DEN t e s t i n g with the exception that the specimen height f o r the 4BND geometry r e p l a c e s the width f o r the DEN geometry. The r e s u l t s of both methods are p l o t t e d and compared. To deal with the f r a c t u r e morphology only v i s u a l examination was performed d u r i n g and a f t e r f a i l u r e . No sequenced photographic work was done in t h i s s e c t i o n s i n c e the primary i n t e r e s t was the q u a n t i t a t i v e t r e n d s . 3.3 R e s u l t s 3.3.1 F r a c t u r e Morphology Examples of the f a i l e d 4BND specimens are shown in f i g u r e 30. The f r a c t u r e s u r f a c e s tend to have a r e l a t i v e l y smooth t e x t u r e , much l i k e the DEN specimens of the same c r o s s p l y o r i e n t a t i o n , with l i t t l e or no f i b r e p u l l - o u t v i s i b l e . In the case of a l l t h i c k n e s s e s and both h e i g h t s the type of f a i l u r e seems to change near the a/W = 0.6 notch p r o p o r t i o n . A l l specimens with a lower notch p r o p o r t i o n than 0.6 and some of the a/W = 0.6 specimens, show a c a t a s t r o p h i c energy r e l e a s e at f a i l u r e . These are the specimens that show a r e l a t i v e l y smooth f r a c t u r e s u r f a c e with l i t t l e d e l a m i n a t i o n . Specimens having a notch p r o p o r t i o n of a/W = 0.8 and the remaining a/W = 0.6 specimens do not f a i l c a t a s t r o p h i c a l l y . These specimens show a f a i l u r e that r e s u l t s i n a load drop to a value of approximately 20% of the f a i l u r e l o a d . Any f u r t h e r l o a d i n g Figure 30 - F a i l e d 4BND Specimens of Various Notch Proportions 88 produces f u r t h e r d e f l e c t i o n which makes the f i b r e p u l l - o u t and debonding present much more obvious. A l l specimens show macroscopic s e l f - s i m i l a r crack growth. That i s , the p r i n c i p a l d i r e c t i o n of the f r a c t u r e i s p e r p e n d i c u l a r to the 0° d i r e c t i o n , c o l l i n e a r to the s t a r t e r notch, not c o n s i d e r i n g the v a r i o u s amounts of f i b r e p u l l - o u t occurr i n g . In c o n j u n c t i o n with these d i f f e r e n t f a i l u r e s u r f a c e s , there i s a d i f f e r e n c e i n the type of a u d i b l e noise emitted. L i t t l e a u d i b l e noise precedes f a i l u r e i n the samples with the lower values of notch p r o p o r t i o n . The samples with the gr e a t e r notch p r o p o r t i o n s tend to emit some a u d i b l e noise beginning at approximately 50% of the f a i l u r e load and, of course, there i s c o n s i d e r a b l e noise present a f t e r the post-f a i l u r e load drop has oc c u r r e d . 3.3.2 Toughness Measurements (LEFM) t The averages of the LEFM f r a c t u r e toughness r e s u l t s , f o r any one s i z e and notch p r o p o r t i o n , are shown i n f i g u r e s 31(a) and 31(b) and t a b u l a t e d i n t a b l e s III and IV. F i g u r e 31(a) shows the average r e s u l t s f o r each of the three t h i c k n e s s e s of the 6.4 mm high beams, while f i g u r e 31(b) shows s i m i l a r r e s u l t s f o r the 12.8 mm high beams. Both f i g u r e s show dramatic drops in the f r a c t u r e toughness (K^) as the notch p r o p o r t i o n surpasses a/W = 0.5. For example, the 4.5 mm t h i c k , 12.8 mm high beams show an average K Q f o r a/W = 0.4 of 51.2 MPa/m and f o r a/W = 0.8 of 70 60 "I a CL 2d-10 4BND GROUP 2 h = 6-4 mm 89 ( 0 / 9 0 ) 70-eo* o CL O C 20 101 K Q V S W « i i 4BND GROUP 2 h=l2-8 mm ( 0 / 9 0 ) * 0 2 0-4 a 0-6 0-8 7 W TABLE III LEFM Ca) 0-2 0 4 a. 0-6- 0-8 - 'w TABLE IV LEFM (b) \t(mm] V \ 4-5 6-4 7-9 0-2 45-1 42-7 40-6 0-4 43-5 37-5 391 0/6 ..35-4 26-8 2 6 8 0-8 16-7 13-0 13-8 AVE. 35-2 30-0 301 t AVE. 42-8 4 0 0 29-7 14-5 1 a CL 2 cr 31-8 V s 4-5 6-4 7-9 0 2 51-6 47-6 49-5 0-4 51-2 42-2 45-1 0-6 3 7 0 310 326 0-8 15-2 15-2 16-4 AVE. 38 8 34 0 35-9 t AVE. 49-6 46-2 33-5 5-6 s. 5 36-2 F i g u r e 31 - 4BND Group 2 Toughness R e s u l t s (LEFM) Table I I I - LEFM Toughness R e s u l t s (h = 6.4mm) . Table IV - LEFM Toughness R e s u l t s (H = 12.8mm) 90 15.2 MPa/m. A l l curves show t h i s kind of toughness drop with i n c r e a s e d notch p r o p o r t i o n , while no c o n s i s t e n t trend, can be observed regarding t h i c k n e s s v a r i a t i o n s . At the lower notch p r o p o r t i o n s the Kft values f o r the higher (12.8 mm) beams are on average approximately 7 MPa/iii g r e a t e r than those f o r the lower (6.4 mm) beams. 3.3.3 Accuracy Of Measured Toughness The r e s u l t s p l o t t e d i n f i g u r e s 31(a) and 31(b) represent 60 4BND specimens of v a r y i n g s i z e , t h i c k n e s s , and notch p r o p o r t i o n . Specimen aspect r a t i o remains r e l a t i v e l y c o n s t a n t . In the case of the 12.8 mm beams two r e p e t i t i o n s were performed f o r each notch p r o p o r t i o n and t h i c k n e s s while three r e p e t i t i o n s were performed f o r each of the corresponding 6.4 mm high beams. Prod u c t i o n run i n c o n s i s t e n c i e s are at a minimum throughout these samples due to improved temperature c o n t r o l and vacuum s e a l i n g techniques. E r r o r seems much reduced, with the maximum s c a t t e r f o r three r e p e t i t i o n s of the same notch p r o p o r t i o n being from 22.1 MPa/iii to 29.7 MPa/iii. T h i s was f o r the case of the t h i c k e s t 6.4 mm high beam at a notch p r o p o r t i o n of a/W = 0.64. 3.3.4 Toughness Measurement (Compliance) Six i n d i v i d u a l compliance versus notch p r o p o r t i o n curves and the corresponding compliance c a l i b r a t i o n curves ((E'/2(dC/d(a/W) versus a/W). are p l o t t e d . Each set of p l o t s r e f e r to a s p e c i f i c beam height and t h i c k n e s s as 9 1 shown i n f i g u r e s 3 2 ( a ) and 3 2 ( b ) . A l l the compliance versus notch p r o p o r t i o n p l o t s are p l o t t e d as f i f t h or gre a t e r order polynomials. The compliance c a l i b r a t i o n curves y i e l d a complete set of f r a c t u r e toughness ( K Q ' ) v a l u e s . The averages of these values are p l o t t e d i n f i g u r e s 3 3 ( a ) and 3 3 ( b ) and presented n u m e r i c a l l y i n t a b l e s V and VI. These K Q ' values are approximately equal to the LEFM K A values over the notch p r o p o r t i o n range from a/W = 0 . 2 to a/W = 0 . 5 but do not decrease as d r a m a t i c a l l y as the LEFM values at the higher notch p r o p o r t i o n s . In g e n e r a l , the R Q' value s decrease from approximately 5 5 MPa/m at a/W = 0 . 2 to 3 5 MPa/m at a/W = 0 . 8 . The s c a t t e r and what seem to be i n c o n s i s t e n c i e s i n the KQ ' versus notch p r o p o r t i o n values most l i k e l y stem from l o c a l areas of extreme s e n s i t i v i t y i n the compliance c a l i b r a t i o n curves. In c e r t a i n cases a small s h i f t in notch p r o p o r t i o n on the compliance c a l i b r a t i o n curve i n a segment that has zero, or a constant slope can produce a lar g e change i n the value of (E' / 2)dC/d(a/W). For example, in the range of a/W = 0 . 1 6 to 0 . 2 4 f o r the c o r r e l a t i o n curve corresponding to a beam height of 1 2 . 8 mm and a th i c k n e s s of 4 . 5 mm, the change i s from 2 6 0 0 i n " 1 to 3 5 0 0 i n - 1 . T h i s l a r g e v a r i a t i o n i n what appears to be a h o r i z o n t a l l i n e e x i s t s because the o v e r a l l range of such a c a l i b r a t i o n curve i s from approximately 0 to 4 0 0 , 0 0 0 i n " 1 . 92 0 0-2 0-4 J5_ 0-6 0-8 W 0 0-2 0-4 trg- 0-6 0-8 F i g u r e 32 - Compliance C a l i b r a t i o n f o r Group 2 4BND —a L - — 70 6 Of o CL - o 4-20f 10 0* K / a QVS"V7 T 1 1 4BND GROUP 2 93 t (mm) • 4*5 A 6-4 © 7 - 9 L_ (0/90) 7 0 6 0 | D 0_ 0-2 0-4 n 0-6 0-8 2 0 --\ ioh o K « v s w T 1 1 4BND GROUP 2 t (mm) a 4-5 A 6-4 o 7-9 » 1  X (0/90) » w (a) T A B L E V Compliance 0-2 0-4 a 0-6 0-8 \ (b) T A B L E V I , Compliance a/\ 'wX 4-5 6-4 7-9 0-2 501 54-6 48-6 0-4 61-8 45-3 48-3 0-6 47-6 43-5 43-8 0-8 40-7 3 5 6 36<5 / w AVE. 50-1 44-8 44-3 t AVE. 51-51-8 45-0 37-6 a a. 2 - <3 46-4 a/X 4-5 6-4 7-9 0-2 46-5" 50-6 69-9 0-4 56-3 42« 8 31-2 0-6 48-9 34-7 43-0 0-8 46-6 31-2 2 8-5 / w AVE. 49-6 3 9 8 43-2 t AVE. 55-7 43-4 42>2 35-4 o Q_ •sOf 44-2 F i g u r e 33 - 4BND Group 2 Toughness R e s u l t s (Compliance) Table V - Compliance Toughness R e s u l t s (h = 6.4mm) Table VI - Compliance Toughness R e s u l t s (h = 12.8mm) 94 Other types of curve f i t s may a l l e v i a t e t h i s problem. The average experimental modulus (E') value found i n these t e s t s i s 63 GPa. As i n the Group 1 4BND t e s t s t h i s value i s q u i t e a c c e p t a b l e f o r t h i s m a t e r i a l system and leads to in c r e a s e d confidence i n the general magnitude of the K Q ' v a l u e s . 4. SUMMARY OF RESULTS The r e s u l t s of the Group 1 t e s t s show that the f r a c t u r e toughness f o r the 4BND geometry decreases with i n c r e a s i n g specimen aspect r a t i o . L e v e l l i n g of t h i s trend seems to occur from an aspect r a t i o of approximately 20:1 upwards. For t h i s reason the Group 2 beams were produced to have an aspect r a t i o - o f 20:1. The i n v e s t i g a t i o n of the he i g h t , t h i c k n e s s , and notch p r o p o r t i o n e f f e c t s on K A l e d to the f o l l o w i n g r e s u l t s ; i . A d e f i n i t e decrease in K A at notch p r o p o r t i o n s gr e a t e r than a/W = 0.5. i i . No s u b s t a n t i a l e f f e c t of beam t h i c k n e s s on the f r a c t u r e toughness. i i i . A small increase i n K Q with i n c r e a s e d height ( s i z e ) , p a r t i c u l a r l y at the low notch proport i o n s . The use of the compliance technique f o r d e r i v i n g f r a c t u r e toughness showed some s c a t t e r but, in g e n e r a l , r e s u l t e d i n values of toughness e q u i v a l e n t to those 95 c a l c u l a t e d by LEFM methods up to a notch p r o p o r t i o n of approximately a/W =0.5. At gr e a t e r notch p r o p o r t i o n s the compliance c a l i b r a t i o n r e s u l t s do not drop as d r a m a t i c a l l y as the corresponding LEFM toughness v a l u e s . The i n v e s t i g a t i o n of the f r a c t u r e s u r f a c e s of the 4BND specimens p o i n t s to a p o s s i b l e change i n the mode of f r a c t u r e with i n c r e a s i n g notch p r o p o r t i o n . Up to a value of a/W = 0.6 t h e - f r a c t u r e s u r f a c e shows r e l a t i v e l y l i t t l e debonding or f i b r e p u l l - o u t and the corresponding f a i l u r e i s c a t a s t r o p h i c l e a v i n g two separate beam h a l v e s . In c o n t r a s t , the f r a c t u r e s u r f a c e s of the samples with notch p r o p o r t i o n s g r e a t e r then a/W = 0.6 show more f i b r e p u l l -out, debonding, and delamination and a r e s u l t i n g beam that i s s t i l l i n t a c t . In e i t h e r case the crack growth i s m a c r o s c o p i c a l l y s e l f - s i m i l a r . 96 VI. DISCUSSION 1 . MORPHOLOGY RELATED TO LEFM The morphology of the f r a c t u r e s u r f a c e s i s s u b s t a n t i a l l y d i f f e r e n t f o r each of the p l y o r i e n t a t i o n s t e s t e d . The f a i l u r e of the c r o s s p l y samples show, with few e x c e p t i o n s , r e l a t i v e l y smooth f r a c t u r e s u r f a c e s with l i t t l e debonding or f i b r e p u l l - o u t . T h i s r e s u l t p o i n t s to b e t t e r correspondence with the concepts of l i n e a r e l a s t i c f r a c t u r e mechanics f o r the c r o s s p l y specimens than f o r the q u a s i -i s o t r o p i c DEN specimens. L i n e a r e l a s t i c f r a c t u r e mechanics i s based on the idea that when a crack i s introduced i n t o a s t r e s s e d p l a t e , a balance must be r e a l i z e d between the decrease in p o t e n t i a l energy and the i n c r e a s e i n s u r f a c e energy r e s u l t i n g from the formation of the two new f r a c t u r e s u r f a c e s . Thus i t can be seen that the f a i l u r e of the q u a s i - i s o t r o p i c specimens evolve energy in forms other than the simple formation of two new f r a c t u r e s u r f a c e s to a g r e a t e r extent than do the c r o s s p l y specimens. Even w i t h i n the group of c r o s s p l y specimens with which t h i s work i s p r i m a r i l y concerned, there are some v a r i a t i o n s i n morphology. The t e s t i n g of 4BND specimens showed a d e f i n i t e change away from the smooth f r a c t u r e s u r f a c e d e s c r i b e d , towards a s u r f a c e of much gr e a t e r debonding and f i b r e p u l l - o u t , as the notch p r o p o r t i o n i n c r e a s e d past a/W = 0.6. F o l l o w i n g s i m i l a r reasoning as before t h i s p o i n t s to a b e t t e r correspondence to l i n e a r e l a s t i c 97 f r a c t u r e mechanics f o r specimens with small to intermediate notch p r o p o r t i o n s than f o r specimens with l a r g e notch p r o p o r t i o n . Another f e a t u r e that would seem to d e t r a c t from the correspondence with the concepts of l i n e a r e l a s t i c f r a c t u r e mechanics i s the s u r f a c e delamination, p r i m a r i l y near the notch t i p , which i s present i n many f a i l e d spec imens. 2. DELAMINATION WIDTH The r e l a t i v e p r o p o r t i o n of surface delamination and f i b r e p u l l - o u t in the (0/90) 2s D E N specimens near the notch t i p was shown in f i g u r e 12. T h i s zone of delamination seems to be of s i m i l a r width r e g a r d l e s s of specimen s i z e . The e f f e c t of notch p r o p o r t i o n seems l e s s d i s t i n c t but from the r e l a t i v e l y small number of samples i t seems that the delamination zone width i s independent of notch p r o p o r t i o n . The width of t h i s zone of delamination i s equal to the le n g t h of the crack v i s i b l e d u r i n g t e s t i n g immediately p r i o r to c r i t i c a l propagation. The second set of DEN t e s t s were performed in an attempt to s u b s t a n t i a t e the correspondence between c r i t i c a l crack l e n g t h and the width of su r f a c e d e l a m i n a t i o n . The photographic study was i n c o n c l u s i v e s i n c e the expected delamination took p l a c e on the opposite s i d e of the sample, but in most cases the narrow zones of delamination near the notch t i p were not present. Instead of r e i n f o r c i n g the idea that the width of the zone of delamination i s equal to 98 the l e n g t h of s u b c r i t i c a l crack growth t h i s second group of DEN specimens i n d i c a t e d that the e f f e c t may be due to p r o d u c t i o n techniques. In almost a l l t h i s second set of DEN t e s t s the delamination took p l a c e on what was the top s u r f a c e (the s u r f a c e away from the base p l a t e ) of the specimen dur i n g the cure process i n d i c a t i n g p o s s i b l e s u r f a c e i n c o n s i s t e n c i e s . More complete t e s t i n g with higher speed photography plu s t i g h t e r specimen c o n t r o l i s necessary i f a c o n c l u s i o n i s to be made i n t h i s area. A c o n s i d e r a b l e d i f f e r e n c e e x i s t s between the s u r f a c e s of the ( 0 / 9 0 ) 2 S and (90/0) 2s D E N c r o s s p l y specimens as seen by comparing f i g u r e s 15 and 20. In c o n t r a s t to the previous d i s c u s s i o n of s u r f a c e delamination corresponding to crack movement, the (90/0) 2s specimens show no s u r f a c e d e l a m i n a t i o n . T h i s occurrence i n d i c a t e s a b e t t e r correspondence with the concepts of l i n e a r e l a s t i c f r a c t u r e mechanics i n ( 9 0 / 0 ) 2 S specimens than i n the ( 0 / 9 0 ) 2 5 specimens. Q u a n t i t a t i v e l y , however, the two o r i e n t a t i o n s y i e l d values of K Q which, fo r the small number of t e s t s performed, are the same. Thus i t would seem that the energy r e l e a s e d through s u r f a c e delamination does not s i g n i f i c a n t l y a l t e r the toughness values as compared to an o r i e n t a t i o n where the s u r f a c e p l i e s are c o n s t r a i n e d and d e l a m i n a t i o n does not occur. 99 3. TRENDS OF RESULTS The trends of toughness versus notch l e n g t h are s a t i s f a c t o r i l y represented by the values obtained using LEFM techniques. Confidence i n t h i s technique as an i n d i c a t i o n of trends i s d e r i v e d from the s i m i l a r i t y of the trends observed when compliance c a l i b r a t i o n values of toughness are used. The dependence of toughness values on s i z e and notch p r o p o r t i o n appears to correspond favourably with the work of Wright et a l . 3 8 , P h i l l i p s 2 1 , A d s i t and Waszczak 1 2, and others who have noted s i m i l a r s i z e and notch p r o p o r t i o n dependence. In p a r t i c u l a r , Wright et a l . examining boron fibre-aluminum, present r e s u l t s that are s i m i l a r to the DEN r e s u l t s of t h i s work. The same decrease in toughness with i n c r e a s i n g notch p r o p o r t i o n and d e c r e a s i n g specimen s i z e i s noted. The use of d i f f e r e n t p l a t e s of m a t e r i a l i n the DEN t e s t i n g f o r d i f f e r e n t specimen s i z e s makes the s i z e e f f e c t in these samples q u e s t i o n a b l e . However, the 4BND t e s t s used the same run of m a t e r i a l f o r d i f f e r e n t s i z e s and d e f i n i t e l y showed a s i z e e f f e c t at lower values of notch p r o p o r t i o n . Group 1 t e s t i n g of the 4BND specimen geometry shows a d e c r e a s i n g dependence of upon aspect r a t i o as the aspect r a t i o i n c r e a s e s . At aspect r a t i o s of 20:1 and 100 above, there i s l i t t l e or no dependence remaining. Based on t h i s r e s u l t , the 4BND specimens of Group 2 were produced with a constant (20:1) aspect r a t i o . T e s t s of l a r g e r aspect r a t i o s were not performed; however, both the trends and q u a n t i t a t i v e values are expected to be equal to those r e p o r t e d i n the Chapter 5, Group 2 t e s t i n g . Throughout the t e s t s of v a r i o u s specimen geometries t h i s work shows a d e f i n i t e decrease in toughness values at the higher notch p r o p o r t i o n s . The 4BND t e s t s show a change in the mode of f a i l u r e at the higher notch p r o p o r t i o n s which may add some i n s i g h t i n t o the dramatic toughness decrease. In c o n j u n c t i o n with t h i s , the i n c r e a s i n g notch s e n s i t i v i t y shown i n the r e s u l t s must be co n s i d e r e d . The combination of these f a c t o r s would seem to i n d i c a t e that a decrease in toughness at higher notch p r o p o r t i o n s , as ex p e r i m e n t a l l y recorded, would be expected. Numerical toughness values a l r e a d y p u b l i s h e d by groups such as Caprino et a l . 1 4 f o r the same carbon f i b r e - e p o x y m a t e r i a l are given as approximately 31 MPa/m f o r both the c r o s s p l y and q u a s i - i s o t r o p i c laminates at intermediate notch p r o p o r t i o n s (2a/W = 0.33). R e s u l t s of t h i s work y i e l d values at the intermediate and low notch p r o p o r t i o n s f o r both DEN and 4BND geometries of approximately 50 MPa/m. The experimental v a l u e s f o r the C-T geometry average to 32.5 MPa/m fo r both o r i e n t a t i o n s . The comparison of these AUTHOR FRACTURE TOUGHNESS (0/9,0) • (0/*45/90) SPECIMEN MATERIAL TYPE Caprino, Halpin, and N i c o l a i s 40.3 s 35.6 s DEN AS/3501 25.0 s 25.1 s C-N AS/3501 24.6 4s 32.8 2s C-N AS/3501 42.0 4s 33.2 2s C-N T 300 Konish, Swedlow, and Cruse 24.2 s 3BND MORG 11/5206 Cruse 22.6 s Hole NARMCO/5208-2 Slepetz and Carlson 29.5 2s C-T MODMOR 11/5208 Radford 50.6 2s 44.6 s DEN AS/3501-6 47,5 ns 4BND AS/3501-6 ALL TOUGHNESS VALUES ARE CONVERTED TO MPa/m See Appendix D 1 02 numerical r e s u l t s leads to another area of i n t e r e s t . The DEN specimens of Caprino et a l . were only 50% of the t h i c k n e s s used f o r DEN specimens in t h i s work. T h i s means that the Caprino specimens have only four p l i e s . The two l o a d c a r r y i n g 0° p l i e s are both surface p l i e s and thus have an e x t r a degree of freedom compared to an i n t e r n a l p l y . The two 90° p l i e s are i n c o n t a c t at the symmetric mid-plane. The photographs of Chapter 4 show delamination o c c u r r i n g i n the outer p l i e s . T h i s s u r f a c e delamination i n d i c a t e s a v a r i a t i o n in the s t r e s s s t a t e which leads to premature f a i l u r e of the s u r f a c e p l i e s . T h i s r e s u l t i n d i c a t e s that the d i s c r e p a n c y i n toughness values between t h i s work and the work of Caprino et a l . may be t r a c e d to the r e l a t i v e p r o p o r t i o n of the number of s u r f a c e p l i e s to the t o t a l number of p l i e s . As the number of s u r f a c e p l i e s becomes small compared with the t o t a l number of p l i e s the toughness value should approach a maximum. The specimens of Caprino et a l . would then be the worst case, y i e l d i n g low toughness v a l u e s . Comparison of the f r a c t u r e toughness v a l u e s , of t h i s work, f o r the DEN and C-T geometries a l s o shows a marked d i f f e r e n c e . The much lower toughness values of the C-T specimens i n d i c a t e a p o s s i b l e specimen geometry dependence. If t h i s were the case i t would make the determination of a m a t e r i a l constant very d i f f i c u l t . T ests i n v o l v i n g the 4BND 103 geometry were undertaken to gain some i n s i g h t i n t o the cause of t h i s toughness v a r i a t i o n . Toughness values found i n terms of LEFM f o r the 4BND geometry are i n the same range as those i n d i c a t e d f o r the DEN specimens which d i s c r e d i t s the idea of a specimen geometry e f f e c t . The lack of s u b s t a n t i a l v a r i a t i o n with respect to changes i n t h i c k n e s s of the 4BND specimens seems to correspond to the idea of su r f a c e p l y e f f e c t . Since a l l 4BND specimens have a l a r g e p r o p o r t i o n of i n t e r i o r p l i e s , l i t t l e d e v i a t i o n with an in c r e a s e d number of p l i e s i s expected. Thus i t i s d e f i n i t e that f u r t h e r C-T t e s t s must be performed to give s u f f i c i e n t i n f o r m a t i o n on the v a r i a t i o n s observed. For present a p o s s i b l e m a t e r i a l p r o d u c t i o n v a r i a t i o n or i n c o n s i s t e n c y of t e s t i n g i s the only obvious e x p l a n a t i o n . 4. APPLICABILITY OF LEFM For the complete spectrum of s i z e and notch p r o p o r t i o n v a r i a t i o n s , t h e concepts of LEFM are unable to y i e l d values which c o n s t i t u t e m a t e r i a l constants f o r the AS/3501-6 carbon fib r e - e p o x y m a t e r i a l . In c o n t r a s t , c o n s i d e r i n g the lack of v a r i a t i o n of toughness with specimen s i z e and th i c k n e s s f o r the c r o s s p l y m a t e r i a l i n the two primary specimen geometries t e s t e d (DEN and 4BND), the concept of LEFM does, however, seem a p p l i c a b l e over a narrowed range of notch p r o p o r t i o n s . I t i s t h e r e f o r e reasonable to i n t e r p r e t the r e s u l t s i n a way such t h a t , f o r t h i s 1 04 m a t e r i a l , a constant value of toughness e x i s t s f o r notch p r o p o r t i o n s i n the range 0.2 to 0.5. In t h i s range an average value of toughness would be 45 - 50 MPa/m and i s s u b s t a n t i a t e d by the v a l u e s c a l c u l a t e d from the compliance c a l i b r a t i o n f o r the 4BND geometry. The r e s u l t s of the C-T t e s t i n g do not agree with t h i s value; however, few t e s t s , were performed with t h i s geometry. As an a l t e r n a t i v e , the compliance c a l i b r a t i o n curves determined during t e s t i n g may be used to a t t a i n f r a c t u r e toughness values ( K a ' ) . The use of t h i s method, however, means that a s p e c i f i c curve i s necessary f o r each specimen v a r i a t i o n other than notch p r o p o r t i o n . T h i s , of course, i s expected due to the nature of t h i s technique. 1 05 VII. CONCLUSIONS 1 . GENERAL CONCLUSIONS (THEORETICAL) 1.1 A p p l i c a b i l i t y Of LEFM The tests of this work show that for the s p e c i f i c cases examined, many of the necessary conditions for the application of LEFM are observed. The observation of these conditions for th i s modest group of tests is not, however, s u f f i c i e n t to prove the relevance of LEFM in a l l f i b r e -composite systems. These conditions include: i . Notch S e n s i t i v i t y - Tests of the DEN crossply specimens show a d e f i n i t e notch s e n s i t i v i t y ( f f iH D / f fu ) which implies that flaws do affe c t t h i s ma t e r i a 1 . i i . S e l f - s i m i l a r Crack Growth - LEFM theory r e l i e s on the a b i l i t y to propagate a s e l f - s i m i l a r crack through the material of interest. For f i b r e -composite systems, in general, the crack follows an i n t e r - f i b r e path which may or may not be c o l l i n e a r to the starter notch. In the tests of this work the specimens do show macroscopically s e l f - s i m i l a r crack growth regardless of the laminae orientation considered. In the case of the quasi-isotropic material tested, the general di r e c t i o n of the crack was c o l l i n e a r to the starter notch, even though the path followed was jagged and corresponded, at certain locations, to 106 the ±45° d i r e c t i o n s . The c r o s s p l y specimens have a major i n t e r - f i b r e a x i s in the d i r e c t i o n of s e l f - s i m i l a r crack growth and thus show c o l l i n e a r growth with l i t t l e d e v i a t i o n , i i i . Energy of F r a c t u r e - An o r i g i n a l e x p e c t a t i o n i n the use of LEFM was that a l l of the energy introduced i n t o the specimen duri n g l o a d i n g went i n t o the formation of two new smooth f r a c t u r e s u r f a c e s . 2 The c r o s s p l y specimens behave i n much t h i s way, with l i t t l e energy given o f f i n the form of s u r f a c e delamination and f i b r e p u l l -out. The q u a s i - i s o t r o p i c specimens show a gre a t e r p r o p o r t i o n of damage o c c u r r i n g , i n d i c a t i n g poorer c o r r e l a t i o n with the theory of LEFM than the c r o s s p l y specimens. I t i s expected that the c r o s s p l y o r i e n t a t i o n w i l l be the most a p p l i c a b l e , of any of the m u l t i - p l y f i b r e -composites, to LEFM. The preceding c o n d i t i o n s show th a t , f o r the m a t e r i a l and c o n d i t i o n s of the t e s t s performed i n t h i s work, the concepts of LEFM allow a v i a b l e method f o r the a n a l y s i s of the toughness of c e r t a i n carbon f i b r e - e p o x y laminates. 1.2 Relevance Of K As A M a t e r i a l Property Once i t i s e s t a b l i s h e d that the concept of LEFM can be a p p l i e d to a m a t e r i a l system, i t i s then important to know whether a m a t e r i a l p r o p e r t y l i k e R, a l s o e x i s t s and i f 1 07 c o n v e n t i o n a l equations f o r i s o t r o p i c m a t e r i a l s can be used. The t e s t s of t h i s work have p o i n t e d to few dependencies r e g a r d i n g specimen s i z e and geometry. The use of LEFM K i C equations to a r r i v e at toughness values does, however, show a d e f i n i t e dependence of toughness on notch p r o p o r t i o n . The toughness drops at higher notch p r o p o r t i o n s . Up to a notch p r o p o r t i o n of approximately 0.5, however, the toughness remains r e l a t i v e l y c o n s t a n t . These trends with respect to specimen geometry, s i z e , t h i c k n e s s , and notch p r o p o r t i o n are s u b s t a n t i a t e d by values f o r the same specimens found using a plane s t r e s s compliance c a l i b r a t i o n technique. Both the toughness values and trends are s i m i l a r i r r e g a r d l e s s of the data r e d u c t i o n method used. T h i s p o i n t s , over a narrow range of notch p r o p o r t i o n s , to the a p p l i c a b i l i t y of the plane s t r a i n K 1 C e v a l u a t i o n technique f o r t h i s s p e c i f i c m a t e r i a l . Thus, for notch p r o p o r t i o n s between 0.2 and 0.5, the t e s t s of t h i s work i n d i c a t e that the concepts of LEFM and a m a t e r i a l toughness constant are a p p l i c a b l e and y i e l d a toughness value of 47.5 MPa/m for the c r o s s p l y AS/3501-6 carbon fibre-epoxy m a t e r i a l . 2. GENERAL CONCLUSIONS (EXPERIMENTAL) 2.1 M a t e r i a l T e s t i n g Both the I n s t r o n and MTS t e s t i n g equipment work s a t i s f a c t o r i l y . The Bascom-Turner data a q u i s i t i o n system 108 i s much s u p e r i o r to the s t r i p c h a r t recorder a l l o w i n g much more f l e x i b i l i t y i n the c o l l e c t i o n and e v a l u a t i o n of the r e s u l t s . A s t r a i n gauge i s necessary f o r compliance c a l i b r a t i o n s s i n c e a d i r e c t measurement of e l o n g a t i o n ( d e f l e c t i o n ) i s needed to overcome e r r o r s due to s l i p p a g e and l o a d p o i n t i n d e n t a t i o n . Each of the three specimen geometries t e s t e d were s u i t a b l e f o r t e s t i n g of d i f f e r e n t v a r i a b l e s . i . C-T - The C-T geometry i s l i k e l y to be the most u e s f u l of the three f o r examining slow crack propagation. During the t e s t s of t h i s work, however, t h i s geometry n e c e s s i t a t e d t h i c k specimens to overcome t w i s t i n g . In a l l cases deformation of the l o a d i n g holes took p l a c e . The C-T specimen proved to be d i f f i c u l t to produce and makes s i z e v a r i a t i o n d i f f i c u l t . i i . DEN - The DEN geometry allows the t e s t i n g of t h i n n e r lay-ups than e i t h e r the C-T or the 4 B N D geometries; however, samples must remain s u f f i c i e n t l y t h i c k to overcome e f f e c t s due to s u r f a c e p l y c o n t r i b u t i o n s . A p r a c t i c a l upper l i m i t to the number of p l i e s a l s o e x i s t s due to d i f f i c u l t i e s i n g r i p p i n g the specimen as the u l t i m a t e f a i l u r e l o a d i n c r e a s e s . Specimen alignment, with the l o a d i n g d i r e c t i o n , i s a l s o d i f f i c u l t and misalignment o f t e n leads to the opening of only one of the two 109 notches. The s i z e can be v a r i e d r e a d i l y and the a b i l i t y to use t h i n n e r laminates a l l o w s the use of l e s s m a t e r i a l . The toughness values found using i s o t r o p i c c o r r e c t i o n f a c t o r s are e q u i v a l e n t to those found for the 4BND specimens. Conversely, the toughness values using the compliance technique do not c o i n c i d e . T h i s i s because the DEN geometry i s i n h e r e n t l y poor f o r compliance s t u d i e s due to i n h e r e n t l y h i g h s t i f f n e s s r e s u l t i n g i n d i f f i c u l t y i n measuring the small e l o n g a t i o n s produced, i i i . 4BND - The aspect r a t i o in the 4BND t e s t s i s important, but due to the small a u t o c l a v e s i z e the p r o d u c t i o n of l a r g e aspect r a t i o samples i s d i f f i c u l t . Conversely, the use of low aspect r a t i o specimens leads to much loa d p o i n t deformation. Again, the 4BND geometry cannot be used f o r the t e s t i n g of extremely t h i n laminates s i n c e the r e s u l t i n g f a i l u r e i s i n f l e x u r e . The 4BND geometry i s extremely easy to produce, and s i z e and t h i c k n e s s v a r i a t i o n s are r e a d i l y accomplished ( w i t h i n the c o n s t r a i n t s of the autoclave s i z e ) . T h i s geometry lends i t s e l f extremely w e l l to compliance c a l i b r a t i o n techniques due to the r e l a t i v e l y h i g h compliance of the specimens. 110 Aspect r a t i o s of 20:1 and g r e a t e r are necessary to o b t a i n constant toughness v a l u e s . Thus, the most s u c c e s s f u l geometry f o r the purposes of t h i s work was the 4BND geometry, s i n c e i t allowed comparison between toughness values found by i s o t r o p i c c o r r e c t i o n methods and compliance techniques. 2 M a t e r i a l Production Most of the s c a t t e r i n the r e s u l t s of t h i s work has been due to m a t e r i a l i n c o n s i s t e n c i e s most l i k e l y i n t r o d u c e d d u r i n g the production c y c l e . The problems encountered are d i s c u s s e d i n d e t a i l i n Appendix A. I t i s recommended that any f u t u r e e f f o r t s towards the refinement of the m a t e r i a l p r o d u c t i o n process be c o n c e n t r a t e d on the a q u i s i t i o n of a l a r g e r a u t o c l a v e . T h i s i s imperative s i n c e a l l the c o m p l e x i t i e s that have become necessary to o b t a i n specimen r e p r o d u c i b i l i t y stem d i r e c t l y or i n d i r e c t l y from the i n s u f f i c i e n t s i z e of the present a u t o c l a v e . SPECIFIC CONCLUSIONS i . F r a c t u r e toughness values are dependent upon notch p r o p o r t i o n f o r the c r o s s p l i e d AS/3501-6 carbon fibr e - e p o x y m a t e r i a l . P a r t i c u l a r l y at l a r g e r notch p r o p o r t i o n s the toughness drops d r a m a t i c a l l y with i n c r e a s e d notch p r o p o r t i o n . i i . F r a c t u r e toughness values are independent of specimen t e s t i n g geometry and t h i c k n e s s f o r the 111 c r o s s p l y o r i e n t a t i o n , comparing the DEN and 4BND geometries. F r a c t u r e toughness v a l u e s show only a minor dependence upon specimen s i z e f o r both the q u a s i -i s o t r o p i c DEN specimens and a l l the c r o s s p l y specimens. In both cases a s l i g h t r i s e i n toughness with i n c r e a s i n g s i z e i s apparent. A r e l a t i o n seems to e x i s t between the delaminated s u r f a c e zone of the (0/90) DEN specimens and the length of s u b - c r i t i c a l crack propagation. The premature f a i l u r e of the sur f a c e p l i e s may e f f e c t the toughness v a l u e s . Laminate t h i c k n e s s must be s u f f i c i e n t so that t h i s s u r f a c e e f f e c t i s not a major c o n t r i b u t i o n . Crack growth i n the sur f a c e p l i e s of the (90/0) DEN specimens was observed. T h i s c r a c k i n g i s i n t e r - f i b r e i n nature, but i n s u f f i c i e n t t e s t s were performed to determine whether t h i s crack growth i s i n d i c a t i v e of the crack length through the specimen t h i c k n e s s . F r a c t u r e toughness values decrease with i n c r e a s i n g aspect r a t i o , f o r the 4BND specimens, to reach a minimum value at r a t i o s of 20:1 and g r e a t e r . 1 1 2 BIBLIOGRAPHY 1. Irwin, G. R. , Trans., ASME, Appl. Mech. , 24, 1957, p. 361. 2. G r i f f i t h , A. A., Transact ions , Royal S o c i e t y of London , V o l . 221, 1920. (This a r t i c l e has been r e p r i n t e d with a d d i t i o n a l commentary in Trans., ASM, 61, 1968, p. 871.) 3. ANSI/ASTM, E 399-74 : P l a n e - s t r a i n F r a c t u r e Toughness of M e t a l l i c M a t e r i a l s , E 399,1974. 4. Hertzberg, R. W., Deformation and F r a c t u r e Mechanics of E n g i n e e r i n g M a t e r i a l s , 1976, p. 262. 5. H a r r i s , B. and B u n s e l l , A. R., Impact P r o p e r t i e s of Glass F i b r e / Carbon F i b r e H y b r i d Composites, Composites , September 1975, p. 197. 6. Awerbuch, J . and Hahn, H. T., C r a c k - T i p Damage and F r a c t u r e Toughness of Boron-Aluminum Composites, J .  Composite M a t e r i a l s , V o l . 13 ( A p r i l 1979), p. 82. 7. Bader, M. G. and E l l i s , R. M., The E f f e c t of Notches and Specimen Geometry on the Pendulum Impact St r e n g t h of U n i a x i a l CFRP, Composites , November 1974, p. 253. 8. Ueng, C. E. S., Aberson, J . A. and L a f i t t e , B. A., T e n s i l e A n a l y s i s of an Edge Notch i n a U n i - D i r e c t i o n a l Composite, Composite M a t e r i a l s , V o l . 11 ( A p r i l 1977), p. 222. 9. Beaumont, P. W. R. and P h i l l i p s , D. C , T e n s i l e Strength of Notched Composites, Composite M a t e r i a l s , V o l . 6 (January 1972), p. 32. 10. Konish, H. J . , J r . , Mode I S t r e s s I n t e n s i t y F a c t o r s f o r Symmetrically Cracked O r t h o t r o p i c S t r i p s , F r a c t u r e  Mechanics of Composites , ASTM STP 593, ASTM, 1975, p. 99. 11. Konish, H. J . , J r . , Swedlow, J . R., and Cruse, T. A., Experimental I n v e s t i g a t i o n of F r a c t u r e i n an Advanced F i b e r Composite, J ^ Composite M a t e r i a l s , V o l . 6 (January 1972), p. 114. 12. A d s i t , N. R. and Waszczak, J . P., F r a c t u r e Mechanics C o r r e l a t i o n of Boron-Aluminum Coupons C o n t a i n i n g S t r e s s R i s e r s , F r a c t u r e Mechanics of Composites , ASTM STP 593, ASTM, 1975, p. 163. 13. Srawley, J . E. and Brown, W. F., F r a c t u r e Toughness T e s t i n g and I t ' s A p p l i c a t i o n s , ASTM STP 381 , ASTM, 1964. 1 13 14. Caprino, G., H a l p i n , J . C. and N i c o l a i s , L., F r a c t u r e Toughness of Graphite-Epoxy Laminates, Composites , A p r i l 1980, p. 105. 15. Nuismer, R. J . and Whitney, J . M., U n i a x i a l F a i l u r e of Composite Laminates C o n t a i n i n g S t r e s s C o n c e n t r a t i o n s , F r a c t u r e Mechanics of Composites , ASTM STP 593, 1975, p. 117. 16. O c h i a i , S. and Peter s , P. W. M., T e n s i l e F r a c t u r e of Centre-Notched Angle P l y (0/±45/90) s and (0/90) 2 s G r a p h i t e -Epoxy Composites, M a t l s . Sc. ,17, 1982, p. 417. 17. Pipes, R. B., Wetherhold, R. C. and G i l l e s p i e , J . W., J r . , Notched Strength of Composite M a t e r i a l s , Composite  M a t e r i a l s , V o l . 13, ( A p r i l 1979), p. 148. 18. Experimental Techniques i n F r a c t u r e Mechanics, SESA , 1973, p. 76. 19. Parry, T. V. and Wronski, A. S., Kinking and T e n s i l e , Compressive and Int e r l a m i n a r Shear F a i l u r e i n Carbon-Fibre-R e i n f o r c e d P l a s t i c Beams Tested i n F l e x u r e , J_^ _ Ma11 s. Sc . , 16, 1981, p. 439. 20. Wright, M. A. and Iann u z z i , F. A., The A p p l i c a t i o n s of the P r i c i p l e s of Lin e a r E l a s t i c F r a c t u r e Mechanics to U n i -D i r e c t i o n a l F i b r e R e i n f o r c e d Composite M a t e r i a l s , J .  Composite M a t e r i a l s , V o l . 7 (October 1973), p. 430. 21. P h i l l i p s , D. C , The F r a c t u r e Mechanics of Carbon F i b r e Laminates, Composite M a t e r i a l s , V o l . 8 ( A p r i l 1974), p. 130. 22. Sanford, R. J . and S t o n e s i f e r , F. R., F r a c t u r e Toughness Measurements i n U n i - D i r e c t i o n a l G l a s s - R e i n f o r c e d - P l a s t i c s , J . Composite M a t e r i a l s , V o l . 5 ( A p r i l 1971), p. 241. 23. Waddoups, M. E., Eisenmann, J . R. and Kaminski, B. E., Macroscopic F r a c t u r e Mechanics of Advanced Composite M a t e r i a l s , Composite M a t e r i a l s , V o l . 5 (October 1971), p. 446. 24. S l e p e t z , J . M. and C a r l s o n , L., F r a c t u r e of Composite Compact Tension Specimens, F r a c t u r e Mechanics of Composites , ASTM STP 593, ASTM, 1975, p. 143. 25. S i h , G. C. and Chen, E. P., F r a c t u r e A n a l y s i s of Uni-D i r e c t i o n a l Composites, Composite M a t e r i a l s , V o l . 7, ( A p r i l 1973), p. 230. 26. W i l l i a m s , J . G. and B i r c h , M. W., Mixed Mode F r a c t u r e i n A n i s o t r o p i c Media, Cracks and F r a c t u r e , ASTM STP 601, ASTM, 1976, p. 125. 1 1 4 27. Swedlow, J . L., C r i t e r i a f o r Growth of the Angled Crack, Cracks and F r a c t u r e , ASTM STP 60.1, ASTM, 1976,. p. 506. 28. Zweben, C , The Strength of Notched and Damaged Composites, J . Composite M a t e r i a l s , V o l . 3, (October 1969), p. 713. 29. D e v i t t , D. F., Schapery, R. A. and Bradley, W. L., A Method f o r Determining the Mode I Delamination F r a c t u r e Toughness of E l a s t i c and V i s c o e l a s t i c Composite M a t e r i a l s , J . Composite M a t e r i a l s , V o l . 14 (October 1980), p. 270. 30. Bascom, W. D., B i t n e r , J . L., Moulton, R. J . and S i e b e r t , A. R., Composites , January 1980, p. 9. 31. Cruse, T. A., T e n s i l e S trength of Notched Composites, J .  Composite M a t e r i a l s , V o l . 7 ( A p r i l 1973), p. 218. 32. Holdsworth, A. W. , Owen, M. J . and M o r r i s , S., Macroscopic F r a c t u r e Mechanics of Glass R e i n f o r c e d P o l y e s t e r Resin Laminates, J ^ Composite M a t e r i a l s , V o l . 8 ( A p r i l 1974), p. 117. 33. Zimmer, J . E.,' F r a c t u r e Mechanics of a F i b e r Composite, J .  Composite M a t e r i a l s , V o l . 6 ( A p r i l 1972), p. 312. 34. Owen, M. J . and Bishop, P. T., 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 A p p l i e d to Glas s R e i n f o r c e d P o l y e s t e r Resin, J .  Composite M a t e r i a l s , V o l . 7 ( A p r i l 1973), p. 146. 35. Mandell, J . F., McGarry, F. J . , Wang, S. S. and Im, J . , S t r e s s I n t e n s i t y F a c t o r s f o r A n i s o t r o p i c F r a c t u r e Test Specimens of S e v e r a l Geometries, J_^ Composite M a t e r i a l s , V o l . 8 ( A p r i l 1974), p. 106. 36. Jea, L. and Felbeck, D. K., Increased F r a c t u r e Toughness of Graphite-Epoxy Composites through I n t e r m i t t e n t I n t e r l a m i n a r Bonding, J ^ Composite M a t e r i a l s , V o l . 14 ( J u l y 1980), p. 245. 37. Morris,D. H. and Hahn,H. T., F r a c t u r e R e s t i s t a n c e C h a r a c t e r i z a t i o n of Graphite-Epoxy Composites, Composite  M a t e r i a l s : T e s t i n g and Design (Fourth Conference), ASTM STP 617,ASTM,1977, p. 5. 38. Wright, M. A., Welch, D. and J o l l a y , J . , The F r a c t u r e of Boron F i b r e R e i n f o r c e d 6061 Aluminum A l l o y , F r a c t u r e of  Composite M a t e r i a l s , Ed; G. C. S i h and V. P. Tamues, V o l . 18, 1978, p. 221. 39. Brinson, H. F. and Yeow, Y. T., An Experimental Study of the F r a c t u r e Behaviour of Laminated Graphite-Epoxy Composites Composite M a t e r i a l s : T e s t i n g and Design (Fourth Conference), ASTM STP 617, ASTM, 1977, p. 18. 1 15 Perry, J . L. and Adams, D. F., Charpy Impact Experiments on Graphite-Epoxy Hybrid Composites, Composites , J u l y 1975, p. 166. 1 1 6 APPENDIX A - AUTOCLAVE INTRODUCTION Th i s r e p o r t was requested i n December 1980 f o r the purpose of d e t a i l i n g the progress i n the c o n s t r u c t i o n and development of the U.B.C. Department of M e t a l l u r g y Composites Research Autoclave. The matter has come up at t h i s time due to recent m o d i f i c a t i o n s which have brought r e p r o d u c i b i l i t y of sample p r o p e r t i e s to an ac c e p t a b l e l e v e l . T h i s r e p o r t w i l l break the apparatus i n t o three b a s i c sub-systems which are i n v o l v e d i n the c u r i n g of f i b r e - r e s i n prepregged lay-ups. The sub-systems a r e : i . The Heating System: As i n i t i a l l y c o n t r i v e d , the hea t i n g system was to heat the complete aluminum inner l i n e r and, by heat t r a n s f e r phenomena, the sample was to be heated through the v a r i o u s temperature cure c y c l e s . i i . The Pressure System: T h i s system, i s simply the i n c l u s i o n of the necessary f i t t i n g s so that high pressure gas can be b l e d i n t o the pressure v e s s e l to allow the a p p r o p r i a t e pressure on the su r f a c e of the f i b r e - r e s i n lay-up. i i i . The Vacuum System: T h i s system i s i n c l u d e d to evacuate the immediate area of the f i b r e - r e s i n lay-up. The lay-up technique d i c t a t e s the vacuum system. That i s , the vacuum bag i s sealed around the sample and an o u t l e t passes from the bag, through the pressure v e s s e l w a l l , to a vacuum pump. F i n a l l y , the v a r i o u s sub-systems are i n t e r r e l a t e d , and some f u t u r e proposals are noted, l e a d i n g to the recommendation of continued refinement. DESCRIPTION of CONSTRUCTION The composites research a u t o c l a v e , f o r the main p a r t , was not newly c o n s t r u c t e d . The pressure v e s s e l e x i s t e d p r e v i o u s l y as a v e r t i c a l a u t o c l a v e and, due to the o r i g i n a l use, i s c o n s t r u c t e d p r i m a r i l y from s t a i n l e s s s t e e l . During r e c o n s t r u c t i o n , the stand was mo d i f i e d to support the c y l i n d e r i n a h o r i z o n t a l o r i e n t a t i o n to f a c i l i t a t e l o a d i n g of composite lay-ups. At t h i s time, a heated c y l i n d e r i c a l aluminum inner l i n e r surrounded by one 1 1 7 inch preformed f i b r e g l a s s i n s u l a t i o n was i n s e r t e d . A l l thermocouple and power leads e x i t the chamber through pressure t i g h t f i t t i n g s in the back as. shown in f i g u r e 34. To complete the m o d i f i c a t i o n s to the pressure v e s s e l , the heavy door was mounted to a s e l f - a l i g n i n g hinge system to ease alignment and c l o s i n g as seen in f i g u r e 35. In a d d i t i o n to the above m o d i f i c a t i o n s was the i n c l u s i o n of a gas i n l e t and a copper pipe to be used as the m a n i f o l d f o r the inner vacuum system. To f a c i l i t a t e c o n t r o l of the h e a t i n g , a v a r i a c and a temperature c o n t r o l l e r were mounted on the lower s h e l f of the s u p p o r t i n g stand. EVOLUTION of the HEATING SYSTEM The i n i t i a l h e a t i n g system, as mentioned e a r l i e r , c o n s i s t e d of p e r i p h e r a l h e a t i n g elements around the inner aluminum c y l i n d e r . These elements were a i d e d by an a d d i t i o n a l h e a t i n g element on each end of the c y l i n d e r . By using t h i s system the p r e l i m i n a r y plan was to heat the p r e s s u r i z e d gas which would give a thermally constant environment in much the f a s h i o n of an oven. During e a r l y t e s t i n g i t was noted that s i n c e the f l a t c e n t r a l l y mounted f i b r e - r e s i n lay-up was r e c e i v i n g heat through gas c o n v e c t i o n , the lay-up temperature was t r a i l i n g the w a l l temperature by approximately 90°F. T h i s c o n v e c t i o n induced temperature l a g made c o n t r o l d i f f i c u l t , however more importantly, with the l a g i n the system s p e c i f i e d h eating r a t e s c o u l d not be maintained w i t h i n the given e r r o r margins. To a l l e v i a t e t h i s problem, some thought was i n i t i a l l y given to the i n s t a l l a t i o n of a fan u n i t to produce f o r c e d c o n v e c t i o n . A system of t h i s nature however seemed to be adding unnecessary c o m p l i c a t i o n and bulk p a r t i c u l a r l y when the a u t o c l a v e would p r i m a r i l y produce f l a t samples. With these thoughts in mind a r e v i s e d base p l a t e was produced with an i n t e g r a l h e a t i n g element. The heated p l a t e , as shown in f i g u r e 36(a), heats the sample by conduction, and due to the c l o s e p r o x i m i t y of the sample, any l a g i s thus minimized. T e s t i n g has r e v e a l e d t h a t the p l a t e , as expected due to the conductive p r o p e r t i e s of the aluminum and the extremely small area of p l a t e in qontact with the aluminum c y l i n d e r , i s e s s e n t i a l l y i s o t h e r m a l . The present system thus allows the use of e i t h e r , or both, the p e r i p h e r a l or p l a t e h e a t e r s . T y p i c a l l y , only the p l a t e heater i s used. In t h i s case, the c y l i n d e r w a l l temperature tends to l a g the sample 118 T - CYLINDER THERMOCOUPLE T - END CAP THERMOCOUPLE b F i g u r e 34 - Autoclave - Exploded View 119 F i g u r e 35 - A u t o c l a v e , S t a n d , and D o o r L a y o u t 1 20 I H E A T I N G S Y S T E M F i g u r e 36 - A u t o c l a v e - E a r l y Heating and Vacuum Systems 121 temperature by approximately 90°F which allows p r e c i s e t r a n s i t i o n s from h e a t i n g to constant temperature due to a high heat f l u x from the p l a t e to the w a l l . M o d i f i c a t i o n s throughout the l a t e r h a l f of 1981 and i n t o 1982 have allowed the use of twin base p l a t e s . The m o d i f i c a t i o n to the h e a t i n g system of the a u t o c l a v e i n c l u d e d the d e l e t i o n of 50% of the w a l l heaters and the use of these power connections f o r the heater of the second base p l a t e . The power leads have been provided with plug in connectors which mate to sockets mounted f l u s h with the inner aluminum l i n e r . Of f i n a l note, i n t h i s s e c t i o n , are t e s t s of December 1980 which c o n f i r m that there i s a temperature g r a d i e n t a c r o s s the sample t h i c k n e s s . T e s t s performed on g l a s s f i b r e - e p o x y samples show an approximate g r a d i e n t of 5°F per m i l l i m e t e r . Carbon fibre-epoxy samples have not yet been t e s t e d , but are expected to show a much lower g r a d i e n t due to a p p r e c i a b l y higher thermal c o n d u c t i v i t y v a l u e s . The vacuum system i s i n c l u d e d to evacuate the immediate area around the sample. As such, the o r i g i n a l system used a Duo-seal vacuum pump with an i n l i n e vacuum meter connected through a pressure t i g h t f i t t i n g to the i n s i d e of the a u t o c l a v e . The vacuum p i p i n g i n s i d e the autoclave i s formed from 1/8 i n . copper tubing and l e d to two i n t e r c o n n e c t e d p o r t s on opposing corners of the heated base p l a t e as seen i n f i g u r e 36(b). The b a s i c vacuum system was then completed by the a p p l i c a t i o n of a p u t t y -l i k e s e a l a n t on the p l a t e s u r f a c e around the perimeter. F i g u r e 37(a) shows how the nylon f i l m was a p p l i e d to the upper s u r f a c e of the s e a l a n t to form a vacuum "bag" surrounding the lay-up. N e g l e c t i n g the continuous low l e v e l leakage of p r e s s u r i z e d gas i n t o the vacuum bag, (to be d i s c u s s e d i n d e t a i l i n the s e c t i o n f o l l o w i n g ) the only problem of i n t e r e s t was the drawing of epoxy i n t o the vacuum p o r t s and l i n e s . T h i s problem was inherent i n the system due to the use of "down-draft" vacuum p o r t s . That i s , as the epoxy flowed due to the pressure and vacuum e f f e c t s , g r a v i t y g r e a t l y aided in d i r e c t i n g the epoxy to the p o r t s . During the course of t e s t i n g s e v e r a l methods have been used in attempts to a l l e v i a t e t h i s problem without changing from the "down-draft" o r i e n t a t i o n . A vacuum t r a p was i n i t i a l l y added, however due to the remote l o c a t i o n of the t r a p the connecting l i n e s were apt to plug with congealed epoxy. Next, the epoxy was d i r e c t e d through a longer pathway with excess bleeder m a t e r i a l , by way of a s p e c i a l double bag, double bleeder lay-up system as shown in f i g u r e 37(b) and the vacuum t r a p was d e l e t e d . T h i s system seemed to 1 22 S I N G L E B A G D O U B L E B A G ( b ) F i g u r e 37 - A u t o c l a v e - Vacuum Bagging 1 23 work a c c e p t a b l y ; however, the adoption of the added p r o t e c t i o n of an i n t e g r a l vacuum t r a p u n i t was s t i l l c o n s i d e r e d . Further c o n s i d e r a t i o n l e d to the change of the base p l a t e to a system with a s i n g l e r a i s e d vacuum p o r t . T h i s m o d i f i c a t i o n as shown in f i g u r e 38(a) allowed the sample to be c o n s i d e r a b l y l a r g e r s i n c e no d i s t a n c e had to be maintained between the samples and the vacuum p o r t . With the port mounted at the f r o n t on the r a i s e d p o r t i o n of the p l a t e above the top of the sample, r e s i n no longer had the a i d of g r a v i t y i n f i n d i n g i t s way to the vacuum p o r t . T h i s method maintained the use of vacuum bag s e a l a n t and the double bleeder lay-up system. A l s o at t h i s time a second copper vacuum l i n e was i n s e r t e d i n t o the a u t o c l a v e to allow the use of one vacuum pump f o r each p l a t e . T h i s high mounted vacuum port worked acc e p t a b l y w e l l , however vacuum-pressure leaks continued to plague the system. In response to t h i s c o n t i n u a l problem, in the summer of 1981, the prototype f o r the l a t e s t system was designed and produced. The prototype as shown in f i g u r e 38(b) r e t a i n e d a 0.25 i n . aluminum base p l a t e with an i n t e g r a l heater element. To t h i s base p l a t e was b o l t e d a r i s e r frame, with i n t e g r a l vacuum passages and t r a p s , and an aluminum frame supp o r t i n g the reusable s i l i c o n e rubber vacuum bag. Copper tubing remained as vacuum l i n e s and the connections continued to be made v i a f l a r e f i t t i n g s . Most of the m a t e r i a l f o r DEN t e s t i n g was produced using t h i s system with good success and c o n s i s t e n c y . Some vacuum leakage continued however, and was f i n a l l y t r a c e d to the vacuum bag s e a l a n t used to s e a l the thermocouple wires. The lay-up technique at t h i s time r e v e r t e d to a s i n g l e bag system, with the bleeder p l i e s d i r e c t l y below the reusable vacuum bag. The f i n a l frames were designed in September of 1981. Two p a i r s of top and bottom frames were produced and ready for i n s t a l l a t i o n i n l a t e January of 1982. F i g u r e 39 shows t h i s f i n a l design which i s long enough f o r the uncut width of the 12 i n . prepreg to be used and has lower r i s e r s to decrease the vacuum bag deformation when c u r i n g t h i n specimens. Problems continued to plague t h i s design and a double bag technique was again i n s t i t u t e d . To ease the clean-up of excess epoxy the i n t e r i o r faces of a l l components of the vacuum frames are now sprayed with an epoxy mold r e l e a s e agent before each use. The l a t e s t changes of method seem f i n a l l y to have cured any vacuum leakage and epoxy overflow. The f i n a l bagging sequence wraps the sample in r e l e a s e p l i e s , then adds a r i g i d c a u l p l a t e f o l l owed by bleeder p l i e s numbering no l e s s than 35% the number of p l i e s i n the sample. Nylon R A I S E D V A C U U M P O R T VACUUM PORT VACUUM BAG SEALANT BASE PLATE TO VACUUM PUMP ( a ) R E - U S E A B L E V A C U U M B A G S Y S T E M TO VACUUM PUMP SECTION A-A VACUUM TROUGH VACUUM BAG FRAME RISER WITH INTEGRAL VACUUM SYSTEM (b ) F i g u r e 38 - Autoclave - M o d i f i e d Base P l a t e s F I N A L P L A T E D E T A I L TOP PLATE BOTTOM PLATE F i g u r e 39 - Autoclave - F i n a l Cure Frame Assembly 1 26 i s wrapped around t h i s lay-up and s e a l e d . A s l i t i s provided in the top of t h i s nylon "bag" through which the vacuum can reach the sample. On top of t h i s nylon "bag" are placed two bleeder p l i e s and bleeder m a t e r i a l i s i n s e r t e d i n t o the vacuum channels on three s i d e s of the r i s e r . A sheet of nylon i s p l a c e d on top of t h i s completed lay-up and the vacuum bag and frame are b o l t e d down. T h i s technique e f f e c t i v e l y stops excess epoxy from being troublesome. The cure f o r the vacuum-pressure leakage seems to have been the simple replacement of the vacuum bag s e a l a n t as a s e a l f o r the thermocouples. At present, s i l i c o n e s e a l e r i s a p p l i e d and allowed to cure before any a u t o c l a v e run. At the same time as the newest p l a t e s were being r e a d i e d f o r use the vacuum system i n s i d e and o u t s i d e the a u t o c l a v e r e c e i v e d e x t e n s i v e m o d i f i c a t i o n . I n s i d e the a u t o c l a v e the f l a r e f i t t i n g s were r e p l a c e d with Swagelock .1/4 i n . quick connect f i t t i n g s . Each p l a t e r e c e i v e d a corresponding male quick connect plug connected to the p l a t e by new f l e x i b l e , b r a i d e d , s t a i n l e s s s t e e l covered t e f l o n pressure hose. Copper tubing remained through the bulkhead to the atmosphere s i d e of the a u t o c l a v e . F l e x i b l e rubber pressure hose r e p l a c e d the vacuum hose formerly going to the vacuum pumps. These pressure hoses were connected to two v a l v i n g blocks on a newly c o n s t r u c t e d vacuum c o n t r o l p a n e l . T h i s i n c l u s i o n allows the pressure leakage from any p o s s i b l e vacuum bag f a i l u r e to be shut o f f by a valve on the panel thus p r e v e n t i n g any adverse e f f e c t to the second vacuum system i n s i d e the a u t o c l a v e . Each vacuum system has a separate vacuum gauge mounted on the c o n t r o l panel. A f i n a l c o n s i d e r a t i o n d e a l s with the a c t u a l magnitude of the a p p l i e d vacuuming. Due to the nature of the system, the o r i g i n a l vacuum was approximately two orders of magnitude greater than the s p e c i f i e d v a l u e . No t e s t i n g has been c a r r i e d out i n t h i s regard; however, i t i s b e l i e v e d that t h i s "over vacuuming" c o u l d account f o r i n c r e a s e d amounts of epoxy being b l e d from the sample and i n t o the vacuum p o r t s , producing a sample of lower comparative epoxy content. To a l l e v i a t e t h i s p o s s i b l e problem the vacuum c o n t r o l panel has v a l v e s which allow the operator to bleed t h i s excess vacuum. Vacuum can now be a d j u s t e d to values s p e c i f i e d by the r e s p e c t i v e cure c y c l e . When the s h u t - o f f v a l v e i s c l o s e d i n the case of a vacuum bag f a i l u r e , t h i s bleed valve must a l s o be c l o s e d . I n t e r a c t i o n Between the Pressure and Vacuum System The pressure and vacuum systems were c o n s t r u c t e d to be completely separate, however due to i n i t i a l vacuum bag s e a l i n g problems the two systems d i d i n t e r a c t . High pressure gas c o n t i n u o u s l y leaked in small amounts to the 1 27 i n t e r i o r of the vacuum bag, there to be scavenged by the vacuum pump. With the vacuum system f u n c t i o n i n g c o r r e c t l y , t h i s seemed to pose no s e r i o u s problems except f o r the use. of g r e a t e r q u a n t i t i e s of gas than would have been otherwise necessary. The problem that can, and d i d a r i s e however, was the c l o g g i n g of the vacuum l i n e s c a using a l o s s of vacuuming. T h i s l o s s of vacuum would seem to allow the i n t e r i o r of the bag to reach an e q u i l i b r i u m pressure with the surroundings, l e a d i n g to what would seem to be an extreme l o s s of e f f e c t i v e pressure on the sample s u r f a c e . R e s u l t i n g samples have shown a much higher r e s i n content than samples in which the vacuum system was f u n c t i o n i n g c o r r e c t l y . T h i s s i t u a t i o n has f i n a l l y been c o r r e c t e d as d e t a i l e d i n the p r e v i o u s s e c t i o n . The autoclave p r e s e n t l y uses l i t t l e i f any excess gas and the vacuum can be maintained e a s i l y at a l l times. The leakage encountered throughout a l l the e a r l y work can now be a t t r i b u t e d to the type of vacuum bag se a l a n t used. The quoted temperature r a t i n g of t h i s vacuum bag putty i s 450°F; however, o b s e r v a t i o n s at o p e r a t i n g temperatures have shown the l o s s of s e a l i n g p r o p e r t i e s . At o p e r a t i n g temperatures the v i s c o s i t y has dropped d r a m a t i c a l l y making displacement of the s e a l a n t occur at the e l e v a t e d p r e s s u r e . A higher temperature se a l a n t i s a v a i l a b l e at approximately 10 times the cost but i s at t h i s time unnecessary. Autoclave C o n t r o l s O r i g i n a l l y vacuum was u n c o n t r o l l e d with the vacuum pump being e i t h e r on or o f f . The pressure was c o n t r o l l e d u s ing a r e g u l a t o r and any excess pressure was bled by hand. C o n t r o l of temperature was c a r r i e d out by a combination of manual c u r r e n t adjustment f o r the heating ramps and t h e r m o s t a t i c c o n t r o l of the temperature p l a t e a u s . The f i r s t change in t h i s c o n t r o l system was the a d d i t i o n of v a r i a b l e vacuuming as d e t a i l e d i n the s e c t i o n " E v o l u t i o n of the Vacuum System". No f u r t h e r c o n t r o l m o d i f i c a t i o n s were made u n t i l June of 1982 when the programmable system c o n t r o l l e r was added. T h i s microprocessor based u n i t , produced by Leeds and Northrop, i s p r e s e n t l y being used to simply c o n t r o l the temperature by a p r e s e t program. A l l ramps and p l a t e a u s are c o n t r o l l e d by t h i s program. In the f u t u r e t h i s present c o n t r o l system w i l l be permanently i n s t a l l e d and connected so that complete i n t e r a c t i v e c o n t r o l of a l l systems w i l l be handled by the programmer. A l l necessary microprocessor e l e c t r o n i c s have been obtained. With the i n c l u s i o n of s o l e n o i d a c t u a t e d v a l v i n g t h i s system w i l l be complete. M u l t i p l e programs 1 28 may be s t o r e d on the reuseable memory storage c a s s e t t e s . Autoclave Operation Once the lay-up i s prepared, as d i s c u s s e d i n the s e c t i o n " E v o l u t i o n of the Vacuum System", and the frames are s e a l e d and b o l t e d t i g h t l y together the a c t u a l o p e r a t i o n of the composites r e s e a r c h autoclave i s q u i t e simple. The standard procedure i s as f o l l o w s : i . S l i d e i n the completed lower vacuum frame. i i . Plug i n the bottom vacuum l i n e quick connect f i t t i n g and switch vacuum pump on. Check and c o r r e c t any vacuum l e a k s . i i i . S l i d e in the completed upper vacuum frame. i v . Plug i n t o the top vacuum connector and repeat ( i i . ) f o r the top frame. v. Plug i n upper and lower power and thermocouple l e a d s . v i . Replace inner aluminum door and then press i n the two i n s u l a t i o n d i s c s . v i i . Close the pressure v e s s e l door and torque the se c u r i n g nuts. v i i i . Raise pressure to the maximum value to be a p p l i e d d u r i n g the cure and check vacuum gauges fo r any l o s s of vacuum. I f a s i g n i f i c a n t l o s s does e x i s t , the aut o c l a v e must be d e p r e s s u r i z e d and opened to c o r r e c t the leakage. Steps ( v i . ) through ( v i i i . ) are then repeated u n t i l vacuum i s s a t i s f a c t o r y . When s a t i s f a c t o r y vacuum has been a t t a i n e d a d j u s t pressure to the necessary s t a r t i n g v a l u e . i x . Switch the programmer and c o n t r o l l e r s on, and i f in use switch on the c h a r t r e c o r d e r . x. Adjust the vacuum gauges to the p r e s c r i b e d i n i t i a l v a l u e s . x i . S t a r t program running. R e p r o d u c i b i l i t y of Sample P r o p e r t i e s O r i g i n a l t e s t i n g gave very i n c o n s i s t e n t r e s u l t s , p a r t i c u l a r l y with respect to s u r f a c e q u a l i t y . With the i n i t i a t i o n of the new vacuum frame system, the use of a 1 29 r i g i d c a u l p l a t e , and the a c q u i s i t i o n of the t e f l o n impregnated g l a s s f i b r e c l o t h , the r e s u l t s have become q u i t e c o n s i s t e n t whether the lay-up be of carbon f i b r e -epoxy or of g l a s s f i b r e - e p o x y . 1 30 APPENDIX B - MATERIAL PROPERTIES MAGNAMITE GRAPHITE PREPREG TAPE AS/3501-6 Magnamite AS/3501-6 g r a p h i t e prepreg tape i s an amine-cured epoxy r e s i n r e i n f o r c e d with u n i - d i r e c t i o n a l g r a p h i t e f i b r e s . The reinforcements are Hercules continuous type AS (high strength) g r a p h i t e f i l a m e n t s that have been s u r f a c e -t r e a t e d to in c r e a s e the composite shear and t r a n s v e r s e t e n s i l e s t r e n g t h . Hercules 3501-6 r e s i n was developed to operate i n temperature environments of 350°F. AS/3501-6 prepreg i s recommended f o r general-purpose s t r u c t u r a l a p p l i c a t i o n s . TYPICAL COMPOSITE PROPERTIES RM. TEMP. 3 50°F 0° FLEXURAL STRENGTH, P S I X 1 0 3 260 180 0° FLEXURAL MODULUS, PSI X 10 6 17.5 17.0 0° TENSILE STRENGTH, PSI X 10 3 230 0° TENSILE MODULUS, PSI X 1 0 6 20 .0 0° TENSILE STRAIN, % 1.15 90° TENSILE STRAIN, % 0.63 CURED PLY THICKNESS, MILS 5.2 FIBRE VOLUME, % 62 TYPICAL PREPREG CHARACTERISTICS WIDTH, IN. CURED PLY THICKNESS, MILS LENGTH/UNIT WEIGHT, FT/LB RESIN CONTENT, WT % FLOW, WT % GEL TIME, MIN, AT 350°F VOLATILES, WT % TACK, MIN 12.00 5.2 20 42 25 1 0 1% MAXIMUM 30 MINIMUM 1 32 3M Scotchply PREPREG TAPE type 1003 Scotc h p l y R e i n f o r c e d P l a s t i c Type 1003 i s a non-woven f i b r e g l a s s r e i n f o r c e d epoxy r e s i n m a t e r i a l designed f o r high performance s t r u c t u r a l a p p l i c a t i o n s . The f i b r e g l a s s used i s continuous f i l a m e n t "E" type. T h i s m a t e r i a l i s s u p p l i e d i n r o l l s and i s approved under MIL-P-25421B. The r e s i n meets the requirements of MIL-R-9800B. The maximum continuous o p e r a t i n g temperature i s 250°F (121 C). TYPICAL COMPOSITE PROPERTIES RM. TEMP. 250°F 167 90 6.0 5.4 140 10.8 5.7 5.2 11.0 10.0 64 12.00 10.0 10.6 30 0° FLEXURAL STRENGTH, PSI X 10 3 0° FLEXURAL MODULUS, PSI X 10 6 0° TENSILE STRENGTH, PSI X 10 3 0° TENSILE MODULUS, PSI X 10 6 SHORT BEAM SHEAR STRENGTH, PSI X 10 3 CURED PLY THICKNESS, MILS FIBRE VOLUME, % TYPICAL PREPREG CHARACTERISTICS WIDTH, IN. CURED PLY THICKNESS, MILS LENGTH/UNIT WEIGHT, FT/LB GEL TIME, MIN, AT 350°F Cure C y c l e (3M 1003) 1 34 APPENDIX C - EXPERIMENTAL RESULTS (LEFM AND COMPLIANCE) The f o l l o w i n g pages l i s t the p e r t i n e n t specimen c o n d i t i o n s and a l l experimental r e s u l t s . A l l compliance and compliance c a l i b r a t i o n curves not i n c l u d e d i n the text are a l s o given, as are the l i s t i n g s f o r the programs used to o b t a i n these r e s u l t s . The page immediately f o l l o w i n g t h i s b r i e f i n t r o d u c t i o n g i v e s a flow c h a r t f o r a r r i v i n g at the compliance c a l i b r a t i o n c u rves. For the purposes of t h i s appendix, E*/2(dC/d(a/W)) and E'/2(dC/d(2a/W)) w i l l be denoted C . 135 Flow Chart (Compliance) P Load Curves Compliance Curve K Calibration Curve L i s t i n g of DEN a t 04:55 P.M. on JULY 12, 1982 f o r CC1d=RADD PAGE 1 1 C D E N 2 C 2 £ + + + * + + + + * * * * + < p * * * * * * + * * * * * * + • * * * * * + + * + * * * + * * * 4 C 5 C THIS PROGRAM TABULATES AND CALCULATES COMPLIANCE.TENSILE STRESS 6 C ,MODULUS AND FRACTURE TOUGHNESS FOR DOUBLE EDGE NOTCHED 7 C SPECIMENS. 8 C 9 C 10 C TO RUN PROGRAM SET UP DATAFILE; 11 C LINE #1 12 C LINE 2+ 13 C LINE ++ tt OF COMPLIANCE DATAS, tt OF FAILURE DATAS, n SAMPLE CODE NOTCH PROPORTION.COMPLIANCE, O SAMPLE CODE HEIGHT,THICKNESS,FAILURE LOAD(LBS ) , ^ 14 C NOTCH PROPORTION, (D 15 C LAST : GAUGE LENGTH (FOR STRAIN CALCULATION), 3 16 C ON M T S 17 C RUN *FTN SCARDS=DEN ™ 18 C RUN -LOAD 5=DATAFILE (6=*PRINT*) % 19 C TO P L O T 20 C RUN PLOT:Q PAR=-PLOT* O 21 C § 22 A * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 23 c in 24 DIMENSION XX(200),YY(200),YYD(200),YP(200),XP( 200) " ^ 25 DIMENSION Y(200),X(200),YF(200).YD(200).WT(200) O 26 DIMENSION S(2 1 ) ,SIGMA(21),A(21),B(21),PP(21) M -27 DIMENSION W(200),T(200),P(200),AWG(200),AMOD(200) 3 28 DIMENSION CD(10) 3 29 INTEGER SN(200).SG(200) , w 30 LOGICAL LK 31 COMMON/CC 1 /ND,NG,NK 32 C0MM0N/CC2/SN,X,Y,AMOD 33 C0MM0N/CC3/SG,W,T,P,AWG 34 COMMON/CC4/CD,AVMOD 35 COMMON/CC5/GL,WAV,TAV 36 COMMON/PP1/XP,YP 37 CALL DATAC 38 K=10 39 N=ND 40 LK=.FALSE. 4 1 NWT=0 42 C OLSF IS A CANNED PLOT ROUTINE 43 CALL OLSF(K,N,X,Y,YF,YD,WT,NWT,S,SIGMA,A,B,SS,LK,PP) _ 44 KF=K+1 oo 45 NK=K CTi 46 NDER=50 47 STEP = (X(ND)-X(1))/FLOAT (NDER) 48 M=NDER+1 L i s t i n g of DEN a t 04:55 P.M. on JULY 12, 1982 f o r CC 1 d = RADD 49 SUM=X(1) 50 DO 100 I = 1,M 51 XX(I)=SUM 52 SUM=SUM+STEP 53 100 CONTINUE 54 C OLINT IS A CANNED PLOT ROUTINE 55 CALL OLINT(XX,YY,YYD,M) 5G SUMW=0. 57 SUMT=0. 58 D0200 I=1.NG 59 SUMW=5UMW+W(I) 60 SUMT=SUMT+T(I) 6 1 200 CONTINUE 62 C CALCULATES AVERAGE WIDTH AND THICKNESS. 63 WAV=SUMW/FLOAT(NG) 64 TAV=SUMT/FLOAT(NG) 65 CONM=GL/(WAV+TAV) 66 KK = 0 67 SUM=0. 68 D0300 I=1.ND 69 AMOD(I)=0. 70 IF(X(I).EO.O.)GOTO 310 7 1 GOTO 300 72 C CALCULATES RTHE MODULUS USING THE COMPLIANCE AND CONM. 73 310 AMOD(I)=CONM/Y(I) 74 KK=KK+1 75 SUM=SUM+AMOD(I) 76 300 CONTINUE 77 AVMOD = SUM/F LOAT(KK) 78 D0400 I=1,M 79 XP(I)=XX(I) 80 YP(I)=YY(I) 81 400 CONTINUE 82 CALL PLTC(M) 83 D0500 1 = 1 ,M 84 XP(I)=XX(I) 85 YP(I)=YYD(I)*AVM0D/2. 86 500 CONTINUE 87 CALL PLTD(M) 88 D0600 I=1.NK 89 0=1+1 90 C O ( I ) = P P ( J ) + F L O A T ( I ) 91 600 CONTINUE ' 92 CALL TAB 1 93 CALL TAB2 94 WRITE(6,700)(PP(I),I=1.KF) 95 700 FORMAT('1',10F12.7) 96 STOP 97 END PAGE 2 T3 i-t O OJ 3 M l O a Cd z in Xi fD O I-1-3 fD tn CO L i s t i n g of DEN a t 04:55 P.M. on JULY 12, 1982 f o r CC i d=RADD 98 SUBROUTINE DATAC 99 C THIS SUBROUTINE READS THE DATA. 100 DIMENSION AW(200),A(200),CD(10),C(200),W(200),T(200),P(200), 101 *AWG(200) 102 INTEGER S(200),SG(200) 103 COMMON/CC1 /ND,NG,NK 104 C0MM0N/CC2/S, AW.CA 105 C0MM0N/CC3/SG,W,T,P,AWG 106 COMMON/CC4/CD,AVM 107 C0MM0N/CC5/GL.WAV.TAV 108 READ(5,10)ND,NG 109 10 F0RMAT(2I5) 1 10 DO 100 I = 1,ND 111 READ(5,20)S(I),AW(I),C(I) 112 20 FORMAT(A4,2F10.4) 113 100 CONTINUE 114 D0200 I=1,NG 1 15 READ(5,30)SG(I),W(I),T(I),P(I),AWG(I) 116 30 FORMAT(A4,4F10.4) 117 200 CONTINUE 118 READ(5,40)GL 119 40 F0RMAT(F10.4) 120 RETURN 12 1 END PAGE 3 T3 O \a ft) 3 l-h o 1 a w z cn •a fD o 3 fD D tn oo L i s t i n g of DEN a t 04:55 P.M. on JULY 12,- 1982 f o r CC 1d=RADD 122 SUBROUTINE PLTD(M) 123- C THIS SUBROUTINE PLOTS (E/2 ) (DC/D(2A/W)) VS. 2A/W 124 DIMENSION XP(200).YP(200) 125 COMMON/PP i/XP,YP 126 CALL PLOT(12..0..-3) 127 CALL SCALE(YP,M,8..YMIN.DY.1) 128 CALL SCALE(XP,M.10..XMIN.DX,1) 129 CALL AXISIO. ,0. . '2A/W .-4, 10. ,0. ,XMIN.DX) 130 CALL AXISfO. .0. , '(E/2 ) *DC/D(2A/W) (1/IN.)',+25,8. ,90..YMIN 131 *DY ) 132 CALL LINE(XP,YP.M,+1) 133 CALL PLOTND 134 RETURN 135 END ] PAGE 4 T3 t-i O l O f-l 0) 3 l-h O 1-1 a ra z tn Xi ro o 3 (0 D cn C O <J3 L i s t i n g of DEN a t 04:55 P.M. on JULY 12, 1982 f o r CC1d=RADD 136 SUBROUTINE PLTC(M) 137 C THIS SUBROUTINE PLOTS C VS. 2A/W 138 DIMENSION XP(200),YP(200) 139 COMMON/PP1/XP,YP 140 CALL SCALE(YP,M,8..YMIN.DY,1) 141 CALL SCALE(XP,M,10.,XMIN,OX,1) 142 CALL AXIS(0.,0.,'2A/W,-4,10.,0..XMIN.DX) 143 CALL AXIS(0.,0.,'COMPLIANCE (IN/KIP)'.+20,8.,90.,YMIN,DY 144 CALL LINE(XP,YP.M,+1) 145 RETURN 146 END PAGE 5 •t O i£> i-t 0). 3 i-ti o *1 a w z cn T J tt> O 3 n> D in if* o L i s t i n g of DEN at 04:55 P.M. on JULY 12.'1982 f o r CC1d=RADD 147 SUBROUTINE TAB 1 148 C THIS SUBROUTINE SETS UP A TABLE OF COMPLIANCES. 149 DIMENSION AW(200),C(200).AMD(200) 150 INTEGER SN(200) 15 1 COMMON/CC1/ND,NG,NK 152 COMMON/CC2/SN,AW,C,AMD 153 C0MM0N/CC5/GL,WAV,TAV 154 CALL HEADC 155 CONC=.17512644 156 C0NM=6.892079 157 DO 100 I=1,ND 158 CE=C(I) 159 CM=CE*CONC 160 AM=AMD(I) 16 1 AMM=AM*CONM 162 WRITE(6,200)SN(I),AW(I).CM, CE 163 200 FORMAT(' ' ,T38,A4,T47,F4.2,T52.2F1 164 IFUM.EQ.O. )GOTO 100 165 WRITE(6,300)AMM,AM 166 300 FORMAT('+'.T76.F9.1.T87.F9.1 167 100 CONTINUE 168 RETURN 169 END ) <-t O i Q n 0) 3 hti O a z to n o 3 (D D cn L i s t i n g of DEN at 04:55 P.M. on JULY 12, 1982 f o r CC i d = RADD 170 SUBROUTINE TAB2 171 C THIS SUBROUTINE SETS UP A TABLE OF TOUGHNESS AND STRESS. 172 DIMENSION W(200),T(200),AA(200),P(200) 173 DIMENSION C0(10),FS(200) 174 INTEGER SG(200) 175 COMMON/CC1/ND.NG,NK 176 C0MM0N/CC3/SG.W,T,P.AA 177 C0MM0N/CC4/CP,AVM 178 COMMON/CC5/GL,WAV,TAV 179 CALL HEADT 180 CPR=1.098739 181 CPA=6.892079 182 DO 100 1=1,NG 183 WT=W(I)*T(I) 184 A=AA(I) 185 Y= 1 .98+.36*A-2. 12*A**2 + 3 . 42*A**3 186 SA=SORT(A*W(I)/2.) 187 TLE=P(I)*SA*Y/(WT*1000.) 188 TLM=CPR*TLE 189 AD=CD(1) 190 DO 200 J=2,NK 191 dJ=J-1 192 FAC=CD(d)*A**JJ 193 AD=AD+FAC 194 200 CONTINUE 195 TC = SQRT(AVM*AD/(2.*WT))*P(I )/ 1000. 196 TCM=TC*CPR 197 FL=P(I)/(WT*(1.-A)*1000.) 198 F LM = F L *CPA 199 WRITE(6,30)SG(I).A,W(I),T(I),P(I),FLM,FL,TLM,TLE,TCM,TC 200 30 FORMAT( ' ' , T 1 1 ,A4,T 16,2F8.3,T35.F7.4,T45,F8. 1,T57,3F9. 1,T84 201 *3F12.1) 202 100 CONTINUE .203 RETURN 204 END PAGE 7 f-« O iQ f-l 0> 3 f-h O »-t D ta CO TJ (D O 3 n> 3 L i s t i n g of DEN a t 04:55 P.M. on J U L Y 12, 1982 f o r CC i d = RADD PAGE 8 2 0 5 S U B R O U T I N E HEADT 2 0 6 C T H I S S U B R O U T I N E S E T S UP H E A D I N G S FOR THE TOUGHNESS AND 2 0 7 C S T R E S S T A B L E . 2 0 8 W R I T E ( 6 , 5 ) 2 0 9 5 FORMAT( ' 1 ' , T 7 , ' T O U G H N E S S R E S U L T S ' , / ) 2 1 0 W R I T E ( 6 , 1 0 ) 2 1 1 10 F O R M A T ( ' + ' , T 1 1 1 , ' D . W . R A D F O R D ' , / / ) 2 1 2 W R I T E ( 6 , 2 0 ) 2 1 3 2 0 F O R M A T ( ' ' , T 7 . ' S P E C I M E N T Y P E - DEN , ' ) 2 14 WRITE ( 6 , 3 0 ) tjj 2 1 5 3 0 F O R M A T ( ' + ' , T 3 2 , ' L E F M EON USED : - K = 0 A * * . 5 ( Y ) ; ' ) n 2 1 6 W R I T E ( 6 , 4 0 ) O 2 1 7 4 0 FORMAT( ' + ' , T 6 3 , ' Y = 1 . 9 8 + 0 . 3 6 ( 2 A / W ) - 2 . 1 2 ( ( 2 A / W ) * * 2 ) + 3 . 4 2 ( ( 2 A / W ) ^ 2 1 8 * * + 3 ) ' , / ) Q, 2 1 9 W R I T H 6 . 5 0 ) 3 2 2 0 5 0 F O R M A T ( ' ' , T 7 , ' L A M I N A T E G E O M E T R Y - ( 0 / 9 0 ) 2 S ' , / ) 2 2 1 W R I T E ( 6 , 6 0 ) £T 2 2 2 6 0 FORMAT ( ' ' . T 2 5 , ' R E S U L T S ' ) i-( 2 2 3 W R I T E ( 6 , 7 0 ) 2 2 4 7 0 F O R M A T ( ' + ' . T 7 4 . ' C A L C U L A T E D V A L U E S ' . / ) § 2 2 5 W R I T E ( 6 , 8 0 ) § 2 2 6 8 0 FORMAT( ' ' ,T 1 0 , ' S A M P L E ' , T 2 0 , ' 2 A / W ' , T 2 7 , ' W I D T H ' ) 2 2 7 W R I T E ( 6 , 9 0 ) CO 2 2 8 9 0 FORMAT( ' + ' , T 3 5 . ' T H I C K N E S S ' , T 4 6 . ' F A I L U R E ' ; T 5 9 , ' F A I L U R E ' ) *0 2 2 9 W R I T E ( 6 , 1 0 0 ) O 2 3 0 1 0 0 F O R M A T ( ' + ' , T 6 8 , ' F A I L U R E ' , T 7 7 , ' T O U G H N E S S ' , T 8 9 , ' T O U G H N E S S ' ) w 2 3 1 W R I T E ( 6 . 1 1 0 ) 3 2 3 2 1 1 0 F O R M A T ( ' + ' , T 1 0 1 . ' T O U G H N E S S ' , T 1 1 3 . ' T O U G H N E S S ' ) ™ 2 3 3 W R I T E ( 6 . 1 2 0 ) |j, 2 3 4 1 2 0 FORMAT( ' ' . T 4 6 , ' L O A D ' , T 5 9 , ' S T R E S S ' , T 6 8 , ' S T R E S S ' , T 7 7 , ' L E F M ' ) 2 3 5 W R I T E ( 6 . 1 3 0 ) 2 3 6 1 3 0 F O R M A T ( ' + ' , T 8 9 . ' L E F M ' . T 1 0 1 , ' C O M P L I A N C E ' ,T1 1 3 . ' C O M P L I A N C E ' , / ) ^237 W R I T E ( 6 , 1 4 0 ) ]238 1 4 0 FORMAT( ' ' , T 2 7 , ' ( I N . ) ' , T 3 7 , ' ( I N . ) ' , T 4 7 , ' ( L B . ) ' , T 6 0 , ' ( M P A ) ' ) 2 3 9 W R I T E ( 6 , 1 5 0 ) 2 4 0 1 5 0 FORMAT( ' + ' , T 6 9 , ' ( K S I ) ' , T 7 8 , ' ( M P A / M ) ' , T 8 9 , ' ( K S I / I N ) ' ) 241 W R I T E ( 6 , 1 6 0 ) 2 4 2 1 6 0 F O R M A T ( ' + ' , T 1 0 2 . ' ( M P A / M ) ' , T 1 1 3 , ' ( K S I / I N ) ' , / ) 2 4 3 R E T U R N 2 4 4 END Co L i s t i n g of DEN at 04:55 P.M. on JULY 12, 1982 f o r CCid=RADD PAGE 245 SUBROUTINE HEADC 246 C THIS SUBROUTINE SETS UP HEADINGS FOR THE COMPLIANCE TABLE. 247 COMMON/CC5/GL,WAV,TAV 248 WRITE(6,10) 249 10 FORMAT('-',T7, 'COMPLIANCE RESULTS',/) 250 WRITE(6,20) 25 1 20 FORMAT(' + ' ,T111 , 'D.W. RADFORD',/) 252 WRITE(6,30) 253 30 FORMAT(' ',T7, 'SPECIMEN TYPE- DEN',/) 254 WRITE(6,40) 255 40 FORMAT(' ',T7, 'LAMINATE GEOMETRY- (0/90)2S') 256 WRITE(6,50)WAV 257 50 FORMAT('+',T45 ,'WIDTH-',T52,F6.4.T59.'IN. ;') 258 WRITE(6,60)TAV 259 60 FORMAT('+',T65 , 'THICKNESS-' ,T76,F6.4 , T83 , 'IN. ; ' ) 260 WRITE(6.70)GL 261 70 FORMAT(' + ',T89, 'GAUGE LENGTH-',T103.F6.3 , T 1 10, ' IN.',/) 262 WRITE(6,80) 263 80 FORMAT(' ',T37 ,'SAMPLE',T47,'2A/W',T53,'COMPLIANCE') 264 WRITE(6.90) 265 90 FORMAT('+',T65 .'COMPLIANCE MODULUS MODULUS',/) 266 WRITE(6,100) 267 100 FORMAT(' ',T55 , '(M/N)' ,T66, '(IN/KIP)') 268 WRITE(6,110) 269 1 10 F0RMAT('+',T78 ,'(MPA) ',T89,'(KSI)' ./) 270 RETURN 27 1 END TJ i-l O Cu 3 O a z cn TJ fD O !-•• 3 fD D cn L i s t i n g of 4BEND a t 04:54 P.M. on JULY 12. 1982 f o r CC1d=RADD 1 C 4 - B E N D 2 C 3 Q* ******** * * * * * * * * * * * * * * * * * * * * * * , * * * * * * * * * * * * Il * * * * * * * * * * * * * 4 5 c C T H I S PROGRAM T A B U L A T E S AND C A L C U L A T E S C O M P L I A N C E , S H E A R S T R E S S , 6 C M O D U L U S . AND F R A C T U R E TOUGHNESS FOR 4 POINT BEND S P E C I M E N S WITH 7 8 9 C c A L O A D I N G P O I N T S P R E A D OF ONE T H I R D THE BEAM L E N G T H . \j C TO R U N T H I S P R O G R A M , SET UP THE D A T A F I L E ; 10 C L I N E H\: H OF C O M P L I A N C E D A T A S ,ft OF F A I L U R E D A T A S , 1 1 C L I N E 0 2 + : S A M P L E CODE NOTCH P R O P O R T I O N , C O M P L I A N C E 12 c ( E F O R M A T ) , 13 c LINE/! '++ : S A M P L E CODE H E I G H T , T H I C K N E S S . F A I L U R E LOAD 14 c ( L B S ) , NOTCH P R O P O R T I O N , 15 c L A S T : B E A M L E N G T H ( B E T W E E N S U P P O R T S ) 16 c 17 c ON M T S 18 c RUN * F T N S C A R D S = 4BEND 19 c RUN - L O A D 5 = D A T A F I L E ( 6 = + P R I N T * ) 2 0 c 2 1 c TO P L O T 2 2 c C V S . A / W AND E / 2 ( D C / D ( A / W ) ) V S . A /W 2 3 c 24 c RUN P L O T : 0 P A R = - P L O T # 2 5 c 2 6 c 2 7 c 2 8 c 2 9 D I M E N S I O N X X ( 2 0 0 ) , Y Y ( 2 0 0 ) , Y Y D ( 2 0 0 ) , Y P ( 2 0 0 ) , X P ( 2 0 0 ) 3 0 D I M E N S I O N Y ( 2 0 O ) , X ( 2 0 0 ) , Y F ( 2 0 0 ) . Y D ( 2 0 0 ) , W T ( 2 0 0 ) 31 D I M E N S I O N S ( 2 1 ) , S I G M A ( 2 1 ) , A ( 2 1 ) . B ( 2 1 ) , P P ( 2 1 ) 32 D I M E N S I O N W ( 2 0 0 ) , T ( 2 0 0 ) , P ( 2 0 0 ) , A W G ( 2 0 0 ) . A M O D ( 2 0 0 ) 3 3 D I M E N S I O N C D ( 1 0 ) 34 I N T E G E R S N ( 2 0 0 ) , S G ( 2 0 0 ) 3 5 L O G I C A L LK 3 6 C O M M O N / C C 1 / N D , N G . N K 3 7 C 0 M M 0 N / C C 2 / S N . X , Y . A M O D 3 8 C O M M O N / C C 3 / S G , W , T , P , A W G 3 9 C O M M O N / C C 4 / C D , A V M O D 4 0 C O M M O N / C C 5 / G L , W A V , T A V 4 1 C O M M O N / P P 1 / X P , Y P 4 2 C A L L DATAC 4 3 K= 10 44 N = ND 4 5 L K = . F A L S E . 4 6 NWT=0 4 7 c O L S F I S A CANNED P L O T R O U T I N E 4 8 C A L L O L S F ( K , N , X , Y , Y F , Y D , W T , N W T , S , S I G M A , A , B , S S , L K , P P ) PAGE 1 TJ O iQ t~l O 3 l-h o Cd Z a m Xi fD n 3 fD D in L i s t i n g of 4BEND a t 04:54 P.M. on JULY 12, 1982 f o r CC1d=RADD 49 KF=K+1 50 NK = K 51 NDER=50 52 STEP=(X(ND)-X(1))/FLOAT(NDER) 53 M=NDER+1 54 SUM=X(1) 55 DO 100 1 = 1 ,M 56 XX(I)=SUM 57 SUM=SUM+STEP 58 100 CONTINUE 59 C OLINT IS A CANNED PLOT ROUTINE 60 CALL OLI NT(XX,YY,YYD,M) 61 SUMW=0. 62 SUMT=0. 63 D0200 I=1,NG 64 SUMW=SUMW+W(I) 65 SUMT=SUMT+T(I) 66 200 CONTINUE 67 C CALCULATE AVERAGE HEIGHT AND THICKNESS 68 WAV=SUMW/FLOAT(NG) 69 TAV = SUMT/F LOAT (NG) 70 CONM=(23.*GL**3)/((TAV*WAV+*3)*108.) 7 1 KK=0 72 SUM=0. 73 D0300 I=1,ND 74 AMOD(I)=0. 75 I F ( X ( I ) .EO.O.)GOTO 310 76 GOTO 300 77 C CALCULATES THE MODULUS USING THE COMPLIANCE AND CONM. 78 310 AMOD(I)=CONM/Y(I) 79 KK=KK+1 80' SUM=SUM+AMOD(I) 8 1 300 CONTINUE 82 AVMOD=SUM/FLOAT(KK) 83 D0400 I=1,M 84 XP(I)=XX(I) 85 YP(I)=YY(I) 86 400 CONTINUE 87 CALL PLTC(M) 88 D0500 1=1,M 89 XP(I)=XX(I) 90 YP(I )=YYD(I)*AVMOD/2. 91 500 CONTINUE 92 CALL PLTD(M) 93 D0600 I=1,NK 94 J=I+1 95 CD(I )=PP(J)*FLOAT(I) 96 600 CONTINUE 97 CALL TAB 1 PAGE 2 O in Cu 3 i-ii O n W a in fD O (-•• 3 fD D cn L i s t i n g of 4BEND a t 04:54 P.M. on JULY 12. 1982 f o r CC i d = RADD 103 SUBROUTINE DATAC 104 C THIS SUBROUTINE READS THE DATA. 105 DIMENSION AW(200).A(200),CD(10).C(200),W(200).T(200),P(200) 10S *AWG(200) 107 INTEGER S(200).SG(200) 108 C0MM0N/CC1/ND,NG,NK 109 C0MM0N/CC2/S,AW.C,A 110 C0MM0N/CC3/SG,W.T,P,AWG 111 COMMON/CC4/CD,AVM 112 COMMON/CC5/GL.WAV.TAV 1 13 READ(5 , 10)ND.NG 114 10 F0RMAT(2I5) 115 DO 100 I = 1,ND 116 READ(5,20)S(I).AW(I);C(I) 117 20 F0RMAT(A4,2F10.4) 118 100 CONTINUE 119 D0200 I=1,NG 120 READ(5,30)SG(I),W(I),T(I),P(I),AWG(I) 121 30 FORMAT(A4.4F10.4) 122 200 CONTINUE 123 READ(5,40)GL 124 40 F0RMAT(F10.4) 125 RETURN 126 END ) PAGE 4 o iQ i-t CU 3 l-h O >-| >P» tu 2 D co n (V o 3 n> D cn L i s t i n g of 4BEND at 04:54 P.M. on JULY 12, 1982 f o r CC1d=RADD PAGE 3 98 CALL TAB2 99 WRITE(6,700)(PP(I),I=1,KF) 100 700 FORMAT(' 1 ', 10F12.7) 101 STOP 102 END T3 >-! o lO >-1 0> 3 i-h O 1-1 tu 2: a CO T3 o y->-3 ro D w L i s t i n g of 4BEND a t 04:54 P.M. on JULY 12. 1982 f o r CC1d=RADD PAGE 5 127 SUBROUTINE PLTD(M) 128 C THIS SUBROUTINE PLOTS (E/2)(OC/D(A/W)) VS. A.W 129 DIMENSION XP(200),YP(200) 130 C0MM0N/PP1/XP,YP 131 CALL PLOT( 12.,0. .-3) 132 CALL SCALE<YP,M,8..YMIN.DY,1) 133 CALL SCALE(XP.M,10..XMIN.DX,1) 134 CALL AXIS(0.,0.,'A/W',-3,10.,0.,XMIN.DX) 135 CALL AX IS(0. ,0. . '(E/2)*DC/D(A/W ) (1/IN.)',+25.8. .90. .YMIN. ^ 136 *DY) '-I 137 CALL L I N E U P , YP.M.+1 ) ° 138 CALL PLOTND 7| 139 RETURN CD 140 END a o >-t to z a cn •O (D o 3 fD 3 CO L i s t i n g o f 4BEND a t 04:54 P.M. on JULY 12. 1982 f o r CC i d = RADD 141 SUBROUTINE PLTC(M) 142 C THIS SUBROUTINE PLOTS C VS. A/W. 143 DIMENSION XP(200) ,YP(200). 144 COMMON/PP1/XP,YP 145 CALL SCALE(YP.M,8..YMIN.DY,1) 14G CALL SCALE(XP,M.10..XMIN.DX,1) 147 CALL AXIS(0..0..'A/W'.-3.10..0..XMIN.DX) 148 CALL AXIS(0..0.,'COMPLIANCE (IN/KIP)',+20,8.,90..YMIN.DY 149 CALL LINE(XP.YP.M.+1) 150 RETURN 151 END j PAGE 6 i-1 O L Q 0> 3 M l o *> W a CO TJ a» o H 1 -3 n> cn cn o L i s t i n g of 4BEND a t 04:54 P.M. on JULY 12, 1982 f o r CC 1d=RADD 152 SUBROUTINE TAB 1 153 C THIS SUBROUTINE SETS UP A TABLE OF COMPLIANCES. 154 DIMENSION AW(200),C(200),AMD(200) 155 INTEGER SN(200) 156 C0MM0N/CC1/ND,NG,NK 157 COMMON/CC2/SN,AW,C,AMD 158 C0MM0N/CC5/GL,WAV,TAV 159 CALL HEADC 160 CONC=.17512644 161 C0NM=6.892079 162 DO 100 1=1.ND 163 CE=C(I) 164 CM=CE*CONC 165 AM=AMO(I) 166 AMM=AM*CONM 167 WRITE(6,200)SN(I).AW(I),CM,CE 168 200 FORMATC ',T38,A4,T47,F4.2,T52,2F1 169 IF(AM.EO.0.)GOTO 100 170 WRITE(6,300)AMM,AM 171 300 FORMAT('+',T76,F9.1.T87.F9.1 172 100 CONTINUE 173 RETURN 174 END 13 >-« O i Q 0> 3 l-h o n w z, a CO n> o M -3 ft) 3 L i s t i n g of 4BEND a t 04:54 P.M. on JULY 12. 1982 f o r CC i d = RADD PAGE 8 175 SUBROUTINE TAB2 176 C THIS SUBROUTINE SETS UP A TABLE OF TOUGHNESS AND LOAD. 177 DIMENSION W(200).T(200),AA(200),P(200) 178 DIMENSION CD(10).FS(200) 179 INTEGER SG(200) 180 COMMON/CC1/ND.NG.NK 181 C0MM0N/CC3/SG,W,T,P,AA 182 COMMON/CC4/CD,AVM 183 COMMON/CC5/GL.WAV.TAV ^ 184 CALL HEADT i l 185 CPR=1.098739 O 186 CPA=6.892079 \0 187 DO 100 I=1.NG 2 188 WT=W(I)*T(I) g 189 A=AA(I) 190 Y = 34.7*A-55.2*A** :2+196. *A**3 ™ 191 T L E = ( ( ( P ( I ) * G L / ( 1 0 0 0 . * T ( I ) ) ) * * 2 ) + Y / ( 4 . * ( W ( I ) * * 3 ) ) ) * * . 5 ° 192 TLM=CPR*TLE . 193 AD = CD(1) 194 DO 200 J=2,NK W 195 JJ=J-1 § 196 FAC=CD(J)*A**JJ 197 AD=AD+FAC W 198 200 CONTINUE ^ 199 TC=SQRT(AVM*AD/(2.*WT))*P(I)/1000. ^ 200 TCM=TC*CPR M -201 FL=(2 . * P ( I ) * G L ) / ( 1 0 0 0 . * T ( I ) * ( W ( I ) * ( 1 . - A ) ) + *2) 3 202 FLM=FL*CPA 2> 203 . WRITE(6,30)SG( I).A.W(I ) , T ( I ) , P ( I ).FLM,FL,TLM,TLE.TCM.TC ^ 204 30 FORMAT( ' ' . T 1 1 ,A4,T 16,2F8.3,T35.F7.4.T45,F8. 1 . T57 , 3F9. 1 . T84, 205 *3F 12 . 1 ) 206 100 CONTINUE ^207 RETURN J208 END O i IS) L i s t i n g of 4BEND at 04:54 P.M. on JULY 12, 1982 f o r CC i d = RADD PAGE 209 SUBROUTINE HEADT 2 10 C THIS SUBROUTINE SETS UP HEADINGS FOR TOUGHNESS AND STRESS TABLE. 211 WRITE(6,5) 212 5 FORMAT('1',T7,'TOUGHNESS RESULTS',/) 213 WRITE(6,10) 214 10 FORMAT( ' + ' ,T111, 'D.W. RADFORD',//) 215 WRITE(6,20) 216 20 FORMAT(' '. T7,'SPECIMEN TYPE- 4BEND ,') 217 WRITE(6,30) 218 30 FORMAT(' + ',T32, 'LEFM EON USED :- K =(P*L)**2*(Y)/T**2*H**3; ' ) 219 WRITE(6,40) T) O 220 40 FORMAT(' + ' ,T77. 'Y = 34.7(A/W)-55.2((A/W)**2)+196( ( A/W)**3) ' , / ) iQ 221 WRITE(6,50) £ 222 50 FORMAT( ' ',T7,'LAMINATE GEOMETRY- (0/90)2S',/) g 223 WRITE(6,60) 224 60 FORMAT(' ',T25.'R E S U L T S') ™ 225 WRITE(6,70) ° 226 70 FORMAT( ' + ' ,T74 . 'C A L C U L A T E D V A L U E S',/) 227 WRITE(6,80) 228 80 FORMAT( ' ' , T 10, 'SAMPLE ' .T20, 'A/W' ,T26, 'HE IGHT') W 229 WRITE(6,90) § 230 90 FORMAT*' + ',T35. 'THICKNESS',T46,'FAILURE',T59,'FAILURE') 231 WRITE(6,100) t/) 232 100 FORMAT(' + ' ,T68, 'FAILURE',T77, 'TOUGHNESS',T89.'TOUGHNESS') ^ 233 WRITE(6,110) 234 1 10 FORMAT(' + ' ,T101, 'TOUGHNESS',T113, 'TOUGHNESS') 235 WRITE(6.120) 236 120 FORMAT( ' '. T46,'LOAD',T59,'STRESS',T68,'STRESS',T77,'LEFM') 2> 237 WRITE(6.130) 238 130 FORMAT('+',T89,'LEFM',T101,'COMPLIANCE',T113,'COMPLIANCE',/) 239 WRITE(6.140) 240 140 FORMATC ' ,T27,'(IN. )',T37, ' ( I N . ) ' ,T47, '(LB.)',T60, '(MPA ) ' ) 241 WRITE(6,150) 242 150 FORMAT( ' + ' , T6S, '(KSI )',T78, '(MPA/M)',T89, '(KSI/IN)') 243 WRITE(6.160) 244 160 FORMAT(' + ',T102,'(MPA/M)',T113,'(KSI/IN)',/) 245 RETURN 246 END ft) O (->• 3 fD D tn L i s t i n g of 4BEND a t 04:54 P.M. on JULY 12, 1982 f o r CC1d=RADD PAGE 10 247 SUBROUTINE HEADC 248 C THIS SUBROUTINE SETS UP HEADINGS FOR THE COMPLIANCE TABLE 249 COMMON/CC5/GL,WAV,TAV 250 WRITE(6, ,10) 251 10 FORMAT(' '-',T7, 'COMPLIANCE RESULTS'./) 252 WRITE(6, , 20) 253 20 FORMAT(' ' + ' ,T111, 'D.W. RADFORD' ./) 254 WRITE(6, , 30) 255 30 FORMAT(' ' ',T7,'SPECIMEN TYPE- 4BEND',/) 256 WRITE(6, ,40) 257 40 FORMAT( ' ',T7.'LAMINATE GEOMETRY- (0/90)2S') 258 WRITE(6, ,50)WAV 259 50 FORMAT( ' + ',T44.'HEIGHT-' , T52 , F6 . 4,T59. 'IN. ; ' ) 260 WRITE(6,60)TAV 261 60 FORMAT( ' + ' ,T65, 'THICKNESS-' ,T76,F6.4,T83, 'IN. ; ') 262 WRITE(6, ,70)GL 263 70 FORMAT(' '+',T90.'BEAM LENGTH-',T103,F6.3,T110,'IN.',/) 264 WRITE(6, ,80) 265 80 FORMAT( ' ' ,T37, 'SAMPLE' ,T47, 'A/W' ,T53, 'COMPLIANCE') 266 WRITE(6, ,90) 267 90 FORMAT( '+',T65,'COMPLIANCE MODULUS MODULUS',/) 268 WRITE(6. , 100) 269 100 FORMAT(' ' ',T55,'(M/N)',T66,'(IN/KIP)') 270 WRITE(6. .110) 27 1 1 10 FORMAT(' ' + ' ,T78, '(MPA ) ' ,T89 , ' (KSI ) ' ,/) 272 RETURN 273 END ft O lO n cu 3 O r-l if* W •z a CO Xi CD o t-i' 3 CD 3 cn TOUGHNESS RESULTS D.W. RADFORD SPECIMEN TYPE- DEN , LEFM EON USED :- K=0"A** . 5( Y ) ; LAMINATE GEOMETRY- (0/90)2S SAMPLE R E S U L T S 2A/W WIDTH THICKNESS FAILURE Y=1.98+0.3G(2A/W)-2.12((2A/W)**2)+3.42((2A/W) C A L C U L A T E D V A L U E S FAILURE FAILURE TOUGHNESS TOUGHNESS '3) LOAD STRESS STRESS LEFM LEFM ( I N . ) ( I N . ) ( L B . ) (MPA) ( K S I ) (MPA/M) ( K S l / l N ) 6ab O. 280 0. . 770 0 .0435 2420 .0 691 .6 100. . 3 51 , 9 47 , . 2 6ah 0. 220 0, ,766 0 . 0440 2700 .0 707 , .8 102 , 7 50. .9 46 . 3 u rrl' Gal 0. 230 0. , 752 0 .0440 2580 .0 697 , .9 101 . 3 50. .2 45 .7 6ac 0. 4 20 0. .767 0 .0465 2100, ,0 699. . 7 101 . , 5 52 , . 2 47 , . 5 6a 1 0. .420 0. ,764 0 .0460 2040, .0 689 .8 100, . 1 51 , .4 46 . 7 6am 0. .430 0. .747 0 .0455 1950, .0 693, . 7 100, , 7 50, .9 46, . 3 i—t —\ 6ad 0. ,630 0. ,745 0 .0450 1380, .0 766 .8 111, .3 48 , .7 44 , . 3 %—> U) 6af 0. .640 0. .765 0 .0450 1400 .0 778 .6 113, .0 49. .5 45 .0 rt 6 a j 0. .640 0. ,759 0 .0455 1440 .0 798, , 3 1 15, 8 50, .5 46 .0 •™t 6an 0. 630 0. ,742 0 .0445 1 120, .0 631 , .8 91 . ,7 40, ,0 36, .4 O 6aa 0. 820 0. . 747 0 .0445 540 .0 622 .0 90, . 2 27 , .0 24 , .6 6ae 0. ,840 0. , 762 0 .0460 700 .0 860, . 2 124 , 8 34, .9 31 . 8 6ag 0. .840 0. .763 0 .0450 620. .0 777 .8 112, .9 31 , .6 28 .8 6ak 0. 860 0. ,750 0 .0450 670 .0 977 . 3 141 , 8 35, ,9 32 , .7 4aa 0. ,210 0. .997 o .0470 1520 .0 283 .0 4 1 . 1 23, .0 20 .9 4ae 0. , 2 10 1, .010 0 .0485 3460 .0 616 . 2 89, .4 50, .4 45 . 9 5ad 0. ,200 1. ,006 0 .0425 3050, .0 614, .6 89. , 2 49, .6 45, . 1 4ab 0. 410 0. ,993 0 .0485 2410 .0 584 .6 84 , .8 49, .8 45 .3 5af o. , 400 0, ,984 0 .0440 2200 .0 583 . 7 84 , . 7 49, .6 45, .2 5ag 0. ,400 1, .003 0 .04 30 2730 .0 727 . 1 105, , 5 62, .4 56 .8 4ac o. .600 0, .993 0 .0485 1420 .0 508 .0 73 . , 7 38, . 4 34 .9 4af 0. .610 1 .008 0 .0480 1680 .0 613 .6 89 .0 46, . 3 42 . 1 5aa 0. , 620 1, .013 0 .0420 1780 .0 758 .8 1 10 . 1 56 , . 8 51 . 7 5ae 0. .610 1, .000 0 .0445 1795 .0 7 12 . 8 103 . ,4 53 . 5 48 . 7 4ad 0. .830 1. .000 0 .0490 875 .0 724 .0 105 , .0 35 , 1 31 .9 4ag 0, ,820 1 .012 0 .0495 845 .0 645 . 9 93 , .7 32 .7 29 . 7 5ab 0 .800 1 .006 0 .0430 980 .0 780 . 7 113 . 3 42 .0 38 .3 5ac 0. .800 0 .988 o .0435 740 .0 593 . 3 86, . 1 31 . 7 28, .8 TOUGHNESS RESULTS D.W. RADFORD SPECIMEN TYPE- DEN , LEFM EON USED : - K=0~A* * . 5( Y ) ; LAMINATE GEOMETRY- (0/90)2S R E S U L T S Y=1 .98+0.36(2A/W)-2.12((2A/W)**2) + 3.42( (2A/W) C A L C U L A T E D V A L U E S -3) MPLE 2A/W WIDTH THICKNESS FAILURE FAILURE FAILURE TOUGHNESS TOUGHNESS LOAD STRESS STRESS LEFM LEFM ( IN. ) (IN. ) (LB. ) (MPA) (KSI) (MPA/M) (KSl/TKl) 4ai 0. .210 1 .256 0. .0480 4200. ,0 607 . 8 88 . 2 55. .4 50. 4 5ah 0. .430 1 .246 0, .0440 3380. ,0 745. .5 108. . 2 70, .6 64 . 3 a 5a i 0. ,410 1 .250 0, .0440 3500. ,0 743. .4 107. .9 71 , .0 64 . 7 4ah O. .610 1 . 252 0. .0480 1500. 0 441 . 1 64 .0 37 , . 1 33. .7 4ak 0. .610 1 . 257 0 .0480 2300. ,0 673, . 7 97 .7 56, .7 51 . 6 5aj 0. .610 1 . 250 0. .0440 2300. 0 739. .0 107 . 2 62 . 0 56 . 5 i—< 5al O. .610 1 . 259 0. .0435 2050. 0 661 .5 96 .0 55 . 7 50. . 7 Ui 4aj 0. .810 1 . 253 0 .0485 1 150. ,0 686 .4 99 .6 40 .0 36. . 4 rf 4al 0, ,810 , 1 .261 0. .0480 1000. ,0 599. .3 87 .0 35. .0 31 . ,9 f-l 5ak 0. 800 1 . 249 0. .0435 980. ,0 621 , .6 90 . 2 37 .3 33 9 O 5ba 0. . 180 1 .515 0. .0460 4340. ,0 523 . 4 75 .9 50 .4 45. .9 5bb 0. . 180 1 .510 0 .0465 3750. ,0 448 .9 65 . 1 43 . 2 39. 3 6ao 0 . 190 1 .520 0 .0455 5270. ,0 648 .4 94 . 1 63 .5 57 . 8 6ba 0. . 180 1 .514 0 .0455 5380. ,0 656 .4 95 . 2 63 . 2 57 . , 5 5bf 0. . 400 1 .511 0 .0470 3470. 0 561 . 3 81 .4 59 . 1 53 , 8 5bg 0. . 390 1 .505 0 .0470 3020. .0 482 .4 70 .0 50 .8 46 , 3 6aq 0. .390 1 .507 O .0450 3650. ,0 608 . 1 88 . 2 64 . 1 58, . 4 6be O . 390 1 .510 0 .0440 4370. .0 743 . 1 107 .8 78 . 5 71 ,  4 5be 0 .610 1 .512 0 .0460 2670 .0 678 . 4 98 . 4 62 .6 57 .0 6ap 0 .610 1 .495 0 .0455 2700 .0 701 .5 101 .8 64 .4 58 , 6 6bb 0 .600 1 .512 0 .0460 2920 .0 723 .4 105 .0 67 .5 61 , .4 6bf 0 .600 1 .512 0 .0465 2900 ,0 710 .7 103 . 1 66 .3 60. . 3 5bc 0 .800 1 .513 0 .0470 1360 ,0 659 . 1 95 .6 43 .5 39, .6 5bd 0 .800 1 .511 0 .0450 1470 .0 745 .0 108 . 1 49 . 2 44 , . 7 6bc 0 .800 1 .511 0 .0460 1690, .0 837 .9 121 .6 55 .3 50 .3 6bd 0 .800 1 .510 0 .0460 1640 .0 813 .6 1 18 . 1 53 . 7 48 , .9 6bg 0 .810 1 .514 0 .0445 1350 .0 726 .8 105 . 5 46 .5 42, . 3 TOUGHNESS RESULTS SPECIMEN TYPE- DEN .LEFM EON USED :- K=tfA**.5(Y); Y= 1 . 98+0.3G(2A/W)-2.12((2A/W)**2) + 3.42((2A/W) LAMINATE GEOMETRY- (0/+45/-45/90)S R E S U L T S c A L C U L A T E D V A L U E S SAMPLE 2A/W WIDTH THICKNESS FAILURE FAILURE FAILURE TOUGHNESS TOUGHNESS LOAD STRESS STRESS LEFM LEFM (IN. ) (IN. ) (LB.) (MPA) (KSI) (MPA/M) (KSI/TN) 9aa 0. 230 0. 763 0. 0490 2030. 0 486. 0 70. 5 35. 2 32.0 . 9ae 0. 240 0. 769 0. 0480 2010. 0 493. 8 71 . 6 36 . 2 32.9 9a 1 0. 230 0. 766 0. 0480 1840. 0 447 . 9 65. ,0 32 . 5 29.6 9an 0. 210 0. 756 0. 0495 2250. 0 524 . 5 76. 1 37 . 1 33.8 9ab 0. 450 0. 725 0. ,0500 1060. 0 366. 4 53. 2 26 . 3 23.9 9af 0. 410 0. 786 0. 0480 1645. 0 509. 3 73. 9 38. 6 35. 1 9aj 0. 420 O. 766 0. 0490 1585. 0 501 . 8 72 . 8 37 . 4 34 . 1 9ao 0. 410 0. 758 0. 0480 1785. 0 573. 1 83 . 2 42 . 6 38.8 9ac 0. 630 0. 765 0. .0475 1250. 0 640. 8 93. ,0 41 . , 2 37 . 5 9ag 0. 630 0. 760 0. ,0500 1 175. 0 576. 0 83. 6 36 . 9 33.6 9a 1 0. 640 0. 762 0. .0480 1040. 0 544 . 4 79. ,0 34 , 5 31.4 9ap 0. 620 . 0. 756 0, ,0480 1070. 0 534 . ,8 77 . 6 34 . 6 31.5 9ar 0. 620 0. 761 0, ,0500 1240. 0 591 . 1 85. .8 38 , .3 34.9 9ad 0. 830 0. .762 0. .0480 690. 0 764 . 8 111. ,0 32 . ,3 29.4 9ah 0. 820 0. 759 0. ,0485 680. 0 707 . ,3 102 , 6 31 . 0 28 . 2 9ak 0. 820 0. 760 0. .0485 710. 0 737 . 5 107. ,0 32 . 3 29.4 9am 0. 840 0. 770 0, .0495 765 . 0 864. ,6 125 , .4 35 . 3 32 . 1 9aq O. 830 0. 764 0, .0485 660. 0 722 . 1 . 104 . 8 30, .6 27 . 8 7ad 0. 220 1. .014 0. .0445 2450. 0 479. ,8 69 , .6 39 , . 7 36. 1 8af 0. 210 1. .01 1 0, ,0450 2750. ,0 '527. , 3 76, ,5 43. . 1 39.3 8bh 0. 200 1. .005 0. .0435 2780. .0 547 . ,8 79. .5 44 , .2 40. 2 9bh O. 200 1. .006 0 .0430 2800. ,0 557 , 6 80, .9 45 , .0 40.9 7ac 0. .400 1. .013 0, .0445 2200. .0 560, ,6 81 , . 3 48 , .4 44 .0 8ah 0. 400 1. ,008 0 .0450 2260. ,0 572. .3 83 .0 49, .2 44.8 8bf 0. .400 1. .008 0, .0440 2030. .0 525. ,8 76, .3 45 .2 41.2 8bg 0. ,390 1. .004 0 .0440 2380, .0 608, , 7 88, .3 52 .4 47.7 9bg 0. .400 1. .015 0 .0440 2070. .0 532 , .4 77 .3 46 .0 41.8 7aa 0. .600 1, .017 0 .0460 1630, ,0 600 .3 87, . 1 45 .9 41.8 7ab 0 . 600 1 .015 0 .0450 1740. .0 656 . 4 95 .2 50 . 2 45.6 8ag 0. .600 1 .008 0 .0455 1720, .0 646 .2 93 .8 49 .2 44 . 8 8bt 0 .610 1 .007 0 .0450 1495, .0 583 .0 84 .6 43 .9 40.0 9be 0 .610 0 .965 0 .0450 1760 .0 716 .2 103 .9 52 .8 48. 1 8ae o .800 1 .009 0 .0465 980, .0 719 .8 104 .4 38 .8 35.3 8a 1 o .800 1 .015 0 .0455 1 100 .0 820 .8 1 19 . 1 44 .4 40. 4 8be 0 .800 1 .006 0 .0450 1 140 .0 867 .8 125 . 9 46 . 7 42.5 9bf 0 .800 1 .002 0 .0435 910 .0 7 19 .5 104 . 4 38 . 7 35 . 2 9b 1 o .810 o .998 0 .0440 908 .0 750 . 1 ' 108 .8 39 .0 35 . 5 TOUGHNESS RESULTS SPECIMEN TYPE- DEN ,LEFM EON USED : - K=dA**.5(Y) LAMINATE GEOMETRY- (0/+45/-45/90)S R E S U L T S SAMPLE 2A/W WIDTH THICKNESS FAILURE LOAD (IN. ) (IN. ) (LB. ) 7af 0. 420 1 , .259 0. 0460 2650. 0 7ag 0. 410 1 , .255 0. ,0453 2400. 0 8aa 0. 420 1 , .258 0. 0460 2550. 0 8ab O. 400 1 , .245 0. ,0460 2500. 0 8bb O. 410 1 , .250 0. ,0440 2550. 0 8bc O. 400 1 , . 246 0. ,0440 2330. 0 9bb 0. 420 1 .256 0, ,0440 2650. 0 9bd 0. 420 1 .266 0, ,0450 2550. 0 7ah O. 610 1 .255 O 0460 1840. 0 8ad 0. 620 1 .255 0, .0460 1755 . 0 8bd 0. 620 1 .263 0, .0440 1770. 0 9ba 0. 600 1 .258 0 .0420 1725. 0 7a1 0. 800 1 . 253 0, .0460 1250. .0 8ac 0. ,820 1 . 245 0, .0465 1115, ,0 8ba 0. ,800 1 .218 0, .0445 990, .0 9bc 0. ,790 1 .248 0 .0445 1470, ,0 10bd 0. 170 1 .502 0 .0440 3380, .0 10bf 0. , 140 1 .475 0, .0440 4200, ,0 11ad 0. , 180 1 .510 0 .0445 4120, .0 10bb 0. ,400 1 .504 0 .0435 2930, .0 10bc 0, ,390 1 .509 0 .0440 3470, ,0 11ae 0. .390 1 .506 0 .0450 3300, .0 11aa 0. .610 1 .520 0 .0460 2160, .0 11ac 0 .610 1 ,504 0 .0450 2420 .0 11af 0 .600 1 .517 0 .0440 2420 .0 10ba 0 .820 1 .513 0 .0430 1340 .0 10ba 0 .800 1 .488 0 .0430 1180 .0 11ab 0 .800 1 .516 0 .0450 1020 .0 Y=1.98+0.36(2A/W)-2.12((2A/W)**2)+3.42((2A/W) C A L C U L . A T E D V A L U E S FAILURE FAILURE TOUGHNESS TOUGHNESS STRESS STRESS LEFM LEFM (MPA) (KSI ) (MPA/W) (KSl/Tfi) 543. 7 78 . 9 52 . 0 47.3 493 . 1 7 1 . 6 47 . 2 43 .O 523. 6 76. 0 50. .0 45.5 501 . 4 72 . 8 48 . 0 43.6 541 . , 6 78 . 6 51 . 8 47 . 1 488 . ,2 70. 8 46 . , 7 42 .5 569. ,8 82 . 7 54 . 4 49.5 531 . 9 77 . 2 51 . 0 46.4 563. ,3 81 . 7 47 , 4 43 . 1 551 . ,4 80. 0 45. .9 41.8 577 . , 7 83 . 8 48. .2 43 .9 562. ,5 81 . 6 47 . 9 43.6 747 , 3 108 . 4 44 . 9 40.9 737 , .4 107 . 0 41 , .4 37 .6 629 .4 91 . 3 37 , . 3 33 .9 868 , .7 126 . 0 53 .7 48.8 424 , .7 61 . 6 40 . 1 36.5 518 , .6 . 75. 2 45 .7 41.6 515 .3 74 . 8 49 .6 45. 1 514 .4 74 . 6 54 . 1 49.2 590 .5 85 . 7 62 . 3 56.7 550 .2 79. ,8 58 .0 52.8 545 .9 79. 2 50 .5 46.0 631 .9 91 . 7 58 .2 53.0 624 .7 90. 6 58 .4 53 . 1 788 .6 1 14. ,4 48 .8 44.4 635 .5 92, ,2 41 .6 37.9 515 .2 74. 8 34 . 1 31.0 COMPLIANCE RESULTS D.W. RADFORD SPECIMEN TYPE- DEN LAMINATE GEOMETRY- (0/90)2S WIDTH- 0.9900 IN. : THICKNESS- 0.0434 IN. GAUGE LENGTH- 0.500 IN. SAMPLE 2A/W COMPLIANCE COMPLIANCE MODULUS MODULUS (M/N) (IN/KIP) (MPA) (KSI) 21BI 0. .0 0, .000292 0. .001670 48016. .2 6966 21BI 0. . 12 0. .000343 0. .001960 21BI 0. ,21 0, .000427 0. .002440 21BI 0. .31 0, .000578 0. .003300 21BI 0. .41 0. .000718 0. .004100 21BI 0. .51 0, .000853 0. .004870 21BI 0. .61 0, .001086 0. .006200 21BM 0, ,0 0. .000291 0. .001660 48305. .5 7008 21BM 0. .07 0 .000336 0. ,001920 21BM 0. . 17 0. .000461 0. .002630 21BM 0. .30 0, .000571 0. .003260 21BM 0. .39 0. .000583 0. .003330 21BM 0. .60 0, .000762 0. .004350 21BN 0. .0 0. .000254 0. .001450 55301 .4 ' 8023 21BN 0, . 1 1 0. .000313 0. .001790 21BN 0. .80 0. .001658 0. .009470 o w z -a CO cn TOUGHNESS RESULTS D.W. RADFORD SPECIMEN TYPE- DEN , LEFM EON USED :- K=0"A * * . 5 ( Y ) ; Y = 1 . 98+0 . 36 ( 2A/W)-2 . 12 ( ( 2A/W) * * 2 )+ 3 . 42 ( ( 2 A/W) LAMINATE GEOMETRY- (0/90)2S R E S U L T S C A L C U L A T E D V A L U E S •3) SAMPLE 2A/W WIDTH THICKNESS FAILURE LOAD FAILURE FAILURE TOUGHNESS STRESS STRESS LEFM TOUGHNESS LEFM TOUGHNESS . TOUGHNESS COMPLIANCE COMPLIANCE (IN.) (IN.) (LB. ) (MPA) (KSI) (MPA/M) (KSI/TN") (MPA/M) ( K S l / f N ) 21BA 0. .380 0.992 0.0445 1800.0 453. 3 65.8 38, .9 35. .4 44, .3 40.4 21BB 0. ,210 0.993 0.0430 2245.0 458. 7 66 .6 37 .2 33 , 8 59, .3 53.9 21BC 0. ,800 1 .001 0.0435 820.0 648. 9 94.2 34 .9 31 , 7 48. .5 44 . 1 21BD 0. .0 0.974 0.0440 4710.0 757 . 5 109.9 21BE 0. .0 0.980 0.0430 5200.0 850. 5 123.4 21BG 0. . 200 0.996 0.0445 2220.0 431 . 5 62.6 34 , .6 31 . 5 57 , .4 52.2 21BH 0. . 380 0.980 0.0430 2065.0 544 . 7 79.0 46 .4 42, , 3 52, . 1 47.4 21BI 0. ,610 0.985 0.0435 1434.0 591 . 4 85 .8 44, . 1 40, , 1 49, .8 45.4 21BL 0. , 200 1 .000 0.0420 2770.0 568. 2 82.4 45 . 7 41 . 6 73, .6 67 .0 2 1BM 0. ,600 0.981 0.0425 1362.0 562. 9 81.7 42 .3 38. .5 46, .7 . 42.5 21BN 0. ,800 1 .008 0.0440 778.0 604. 5 87.7 32, .6 29. .7 45, .6 41.5 CTi o COMPLIANCE RESULTS D.W. RADFORD SPECIMEN TYPE- DEN LAMINATE GEOMETRY- (90/0)2S WIDTH- 1.0093 IN. ; THICKNESS- 0.0431 IN. ; GAUGE LENGTH- 0.500 IN. SAMPLE 2A/W COMPLIANCE COMPLIANCE MODULUS MODULUS (M/N) (IN/KIP) (MPA) (KSI) 24BB 0. .0 0. .000308 0. .001760 45026. . 1 6533 24BB 0. . 11 0. .000322 0. .001840 24BB 0. ,21 0, .000415 0. .002370 24BB 0. ,30 0, .000490 0. .002800 24BB 0. ,42 0. .000615 0. ,003510 24BE 0. ,0 0, .000240 0. .001370 57843. .7 8392 24BE 0. , 1 1 0. .000303 0. .001730 24BE 0. .21 0, .000438 0. .002500 24BE 0. .30 0, .000576 0. .003290 24BE 0. ,39 0. .000753 o: .004300 24BE 0. .52 0 .000905 0 .O0517O 24BE 0 .60 0 .001119 0, .006390 24BF 0. .0 0. .000249 0 .001420 55807 .0 8097 24BF 0. .21 0 .000454 0. .002590 24BF 0 .42 0. .000772 0 .004410 24BF 0 .62 0 .001145 0 .006540 24BF 0, .82 0 .001755 0 .010020 a z 3 -3 TOUGHNESS RESULTS D.W. RADFORD SPECIMEN TYPE- DEN .LEFM EON USED :- K=OA**.5(Y); Y=1.98+0.36(2A/W)-2.12((2A/W)**2)+3.42((2A/W) **3) LAMINATE GEOMETRY- (90/0)2S R E S U L T S C A L C U L A T E D V A L U E S SAMPLE 2A/W WIDTH THICKNESS FAILURE FAILURE FAILURE TOUGHNESS TOUGHNESS TOUGHNESS TOUGHNESS LOAD STRESS STRESS LEFM LEFM COMPLIANCE COMPLIANCE (IN. ) (IN. ) (LB. ) (MPA) (KSI) (MPA/M) (KSI/TTT) (MPA/M") (KSI/TN) 24BA 0. .220 1 .005 0.0430 2745.0 561 .3 81.4 46.2 42. 1 72.3 65.8 24BB 0. . 420 1 .008 0.0430 1495 .0 409.9 59.5 35 . 1 31.9 50.0 45.5 24BC 0. .0 1.013 0.0430 4820.0 762 .6 1 10.7 24BD 0. ,0 1.017 0.0435 4960.0 772 . 7 112.1 24BE 0, .600 1 .005 0.0430 1460.0 582. 1 84.5 44.3 40.3 56.7 51.6 24BF 0, .820 1 .008 0.0430 834 .0 736.7 106 .9 37.2 33.8 37 .0 33.7 -3 cn COMPLIANCE RESULTS SPECIMEN TYPE- DEN D.W. RADFORD LAMINATE GEOMETRY- (0/90)2S WIDTH- 0.9907 IN. THICKNESS- 0.0437 IN. SAMPLE 2A/W COMPLIANCE COMPLIANCE MODULUS (MPA) (M/N) (IN/KIP) 24AC 0. .0 0, .000263 0 .001500 24AC 0. . 14 0, .000340 0 .001940 24AC 0, .21 0, .000475 0 .002710 24AC 0. .30 0, .000602 0 .003440 24AC 0 .40 0, .000722 0 .004120 24AD 0. .0 0. .000273 0 .001560 24AD 0. . 1 1 0, .000299 0 .001710 24AD 0, .20 0. .000440 0 .002510 24AD 0. .30 0, .000550 0 .003140 24AD 0. .41 0, .000720 0 .004110 24AD 0. .52 0, .000884 0 .005050 24AD 0, .61 0. .001130 0 .006450 24AE 0. .0 0. .000247 0 .001410 24AE 0. . 1 1 0. .000333 0, .001900 24AE O. . 20 0. .000473 0 .002700 24AE 0, .30 0. .000473 0 .002700 24AE 0. .40 0. . 000713 0, .004070 24AE 0. .51 0. .000837 0, .004780 24AE 0. .61 0. .001107 0, .006320 24AE 0. 71 0. .001345 0, .007680 24AE 0. .81 0. ,001727 .0. .009860 24AJ 0. 0 0. ,000235 0 .001340 24AU 0. . 14 0. .000347 0. .001980 24AJ 0. .20 0. .000450 0 .002570 24AJ 0. ,29 6. ,000578 0, .003300 24AJ 0. .38 0. ,000665 0, .003800 24AJ 0. 50 0. ,000879 0, .005020 24AU 0. ,60 0, ,000979 0, .005590 24AU 0. ,71 0, ,001343 0, .007670 24AJ 0. 79 0. ,001730 0. ,009880 53046.6 51006.3 ; GAUGE LENGTH- 0.500 IN. MODULUS (KSI) 7696.8 7400.7 D W Z 3 CO 56432.6 8188.0 59380.5 8615.8 CO TOUGHNESS RESULTS D.W. RADFORD SPECIMEN TYPE- DEN ,LEFM EON USED LAMINATE GEOMETRY- (0/90)2S R E S U L T S K=(7A**.5(Y); Y=1.98+0.36(2A/W)-2.12((2A/W)**2)+3.42((2A/W) **3) C A L C U L A T E D V A L U E S SAMPLE 2A/W WIDTH THICKNESS FAILURE FAILURE FAILURE TOUGHNESS TOUGHNESS TOUGHNESS TOUGHNES LOAD STRESS STRESS LEFM LEFM COMPLIANCE COMPLIAN (IN.) (IN. ) (LB.) (MPA) (KSI) (MPA/M") (KSI/TfT) (MPA/M) (KSI/TN) 24AA 0. .0 0. 940 0 .0435 3940.0 664 . 1 96.4 24AB 0. , 220 1 . 000 0 .0435 3050.0 619 . 5 89.9 50. .9 46 . 3 86 . ,5 78 , 7 24AC 0. .400 1 . .008 0 .0435 2860.0 749. 2 108.7 64 . ,5 58 , .7 86 . 1 78 , 3 24AD 0. .610 0. ,999 0 .0435 1896.0 771 . 0 111.9 57 . ,9 52, .7 72. 5 66, .0 24AE 0. ,810 1 . .010 0 .0450 940.0 750. 2 108 .9 39 . , 2 35, .7 52 . 1 47 , .4 24AF 0. . 190 0. .984 0 .0450 2780.0 534. 2 77 .5 42. . 1 38 . 3 76 . , 7 69, .8 24AG 0. .420 0. ,994 0 .0430 1825 .0 507 . 4 73 .6 43. . 1 39, .2 56. .2 51 , . 2 24AH 0, .0 0. .947 0 .0435 3880.0 649 . 1 94 .2 24AI 0 .610 0. ,994 0 .0430 1832 .0 757 . 5 109 .9 56 , .7 51 , .6 70. ,7 64 .3 24AJ 0. .790 0. ,995 0 .0430 956.0 733. 3 106.4 40, .4 36 .8 52. . 4 47 .7 24AK 0. .210 0. ,994 0 .0440 3480.0 694 . 2 100.7 56, .3 51 .3 97 . 8 89 .0 24AL 0 .410 0. .996 0 .0450 2630.0 685. 5 99.5 58 , .5 53 .2 78 . 7 71 .6 24AM 0 .620 1 . .003 0 .0440 1838.0 755. 4 109.6 56, . 2 51 .2 71 , .0 64 .6 24AN 0 .800 1 , .006 0 .0425 900.0 725. 4 105.3 39, . 1 35 .5 50, .4 45 .9 a -3 to COMPLIANCE RESULTS D.W. RADFORD SPECIMEN TYPE- 4BEND LAMINATE GEOMETRY- (0/90)6S HEIGHT- 0.2470 IN. SAMPLE THICKNESS- 0.1153 IN. A/W COMPLIANCE COMPLIANCE MODULUS (MPA) 72806.3 79487.3 (M/N) (IN/KIP) 22BB 0. 0 0. 081259 0. 464000 22BB 0. . 10 0. ,085462 0. . 488000 22BB 0. . 19 0. .0914 16 O. .522000 22BB 0. .29 0. ,102799 O. .587000 22BB 0. 39 0. .123989 0 .708000 22BC 0, 0 0. .074429 0. .425000 22BC 0. 1 1 0. .077581 0. .443000 22BC 0. . 20 0. ,084761 0. .484000 22BC 0. .30 0. .096 144 0, .549000 22BC 0. .40 0. . 1 16984 0, .668000 22BC 0. .50 0. .149033 0. .851000 22BC 0. .60 0. .203147 1. .160000 ; BEAM LENGTH- 3.420 IN. MODULUS (KSI ) 10563.8 1 1533. 1 4=» til 25 a o o c T3 TOUGHNESS RESULTS D.W. RADFORD SPECIMEN TYPE- 4ESEND .LEFM EON USED LAMINATE GEOMETRY- (0/90)6S R E S U L T S SAMPLE A/W HEIGHT THICKNESS K=(p*L)**2*(Y)/T+*2*H**3; Y=34.7(A/W)-55.2((A/W)**2)+196((A/W)**3) 22BA 22BB 22BC 0.0 O. 390 0.600 (IN. ) 0.242 0. 247 0.252 (IN. ) 0. 1 180 O . 1 150 0. 1 130 FAILURE LOAD (LB. ) 280.0 91.0 51.5 C A L C U L A T E D V A L U E S FAILURE STRESS ( MPA ) 1910.1 1643.2 2114.5 FAILURE STRESS (KSI ) 277 . 1 238.4 306 .8 TOUGHNESS LEFM (MPA/M) 49.6 44 .5 TOUGHNESS LEFM ( K S l / l N ) 45. 1 40.5 TOUGHNESS COMPLIANCE (MPA/M) 52.3 45.4 TOUGHNESS COMPLIANCE (KSI/IN) 47 .6 41.4 O i-t O c cn COMPLIANCE RESULTS D.W. RADFORD SPECIMEN TYPE- 4BEND LAMINATE GEOMETRY- (0/90)6S HEIGHT- 0.2430 IN. THICKNESS- O.1145 IN. BEAM LENGTH- 5.000 IN. SAMPLE A/W COMPLIANCE COMPLIANCE MODULUS MODULUS (M/N) (IN/KIP) (MPA) (KSI) 22BD 0. 0 0. 229416 1 .310000 85244 .9 12368 22BD 0. 1 1 0. .238172 1 .360000 22BD 0. .20 0. ,250431 1 .430000 22BD 0. 30 0. .278451 1 .590000 22BD 0. 40 0 316979 1 .810000 22BE 0. 0 0. .239923 1 .370000 81511 .6 1 1826 22BE 0. 10 0. . 248680 1 .4 20000 22BE 0. 21 0. .266192 1 .520000 22BE 0. 30 0. 285456 1 .630000 22BE 0. 40 0. ,327486 1 .870000 22BE 0. 49 0. .40279 1 2 .300000 22BE 0. 60 0. .497359 2 .840000 z a O C-Xi TOUGHNESS RESULTS D.W. RADFORD SPECIMEN TYPE- 4BEND .LEFM EON USED : - K=(P*L)**2*(Y) /T**2*H**3: LAMINATE GEOMETRY- (0/90)6S R E S U L T S Y = 34 .7(A/W)-55.2((A/W)**2) + 196((A/W)**3) C A L C U L A T E D V A L U E S SAMPLE 22BD 22BE A / W 0.400 0.600 HEIGHT (IN. ) O. 246 0.240 THICKNESS (IN. ) 0. 1 150 0. 1 140 FAILURE LOAD (LB. ) 52 .8 23 . 2 FAILURE STRESS (MPA) 1452 . 5 1521 .9 FAILURE STRESS (KSI) 2 10. 7 220.8 TOUGHNESS LEFM (MPA/M) 43.4 31.3 TOUGHNESS LEFM (KSI/IN) 39.5 28.5 TOUGHNESS COMPLIANCE (MPA/M) 48.5 31.3 TOUGHNESS COMPLIANCE (KSI/IN) 44. 1 28.5 tn Z a a I-I o c TJ CTi C O COMPLIANCE RESULTS D.W. RADFORD SPECIMEN TYPE- 4BEND LAMINATE GEOMETRY- (0/90)6S HEIGHT- 0.2440 IN. ; THICKNESS- 0.1165 IN. SAMPLE A/W COMPLIANCE COMPLIANCE MODULUS BEAM LENGTH- 10.000 IN. MODULUS (M/N) (IN/KIP) (MPA) (KSI ) 22BF 0. .0 1 .908877 10. .900O0O 79566.9 1 1544 22BF 0. . 10 1 .873853 10. .700000 22BF 0. .20 1 .936898 1 1 . .060000 22BF 0. .30 2 .085755 1 1 , ,910000 22BF 0. .41 2 .227608 12. ,720000 22BG 0. .0 1 . 796797- 10. ,260000 84530.1 12264 22BG 0. 12 1 .823066 10. ,4 10000 22BG O. , 24 1 .879107 10. ,730000 22BG 0. .30 1 .938649 1 1 . , 070000 22BG 0. . 40 2 . 14.1796 12 . , 230000 22BG 0. .48 2 .41 1490 13 . 770000 22BG 0. . 59 3 .075219 17 . ,559998 tn 55 O O O C Xi o TOUGHNESS RESULTS D.W. RADFORD SPECIMEN T Y P E - 4BEND .LEFM EON USED : - K = ( P * L ) * * 2 * ( Y ) / T * * 2 * H * * 3 ; LAMINATE GEOMETRY- (O/90)6S R E S U L T S Y = 3 4 . 7 ( A / W ) - 5 5 . 2 ( ( A / W ) * *2) + 196 ( (A /W) * *3 ) C A L C U L A T E D V A L U E S SAMPLE 22BF 22BG A/W 0 . 4 1 0 0 . 590 HEIGHT ( IN. ) 0 .244 0 . 244 THICKNESS FAILURE LOAD ( IN. ) O. 1 180 0 . 1 150 ( L B . ) 24 .0 11.0 FAILURE STRESS (MPA) 1352.8 1317.4 FAILURE TOUGHNESS STRESS LEFM (KSI ) 196.3 191.2 (MPA/M) 39.8 28 . 1 TOUGHNESS LEFM ( K S I / I N ) 36 .2 25 .6 TOUGHNESS TOUGHNESS COMPLIANCE COMPLIANCE (MPA/M) 48 .6 35. 1 ( K S I / T N ) 44 . 2 3 1 . 9 W z a o o c X) COMPLIANCE RESULTS SPECIMEN TYPE- 4BEND D.W. RADFORD LAMINATE GEOMETRY- (0/90)6S HEIGHT- 0.5193 IN. ; THICKNESS- 0.1157 IN. ; BEAM LENGTH- 3.420 IN. SAMPLE A/W COMPLIANCE COMPLIANCE MODULUS MODULUS (M/N) (IN/KIP) (MPA) (KSI ) 22BH 0. .0 0. ,012434 0. ,071000 51042.1 7405 22BH 0. . 10 0. .012784 0, .073000 22BH 0. . 19 0. .014185 0. ,081000 22BH 0, .29 0. .017162 0, ,098000 22BH 0. .40 0. .021716 0. ,124000 22BJ 0. .0 0, .009982 0. .057000 63578.7 9224 22BJ 0. . 10 0, ,010508 0, ,060000 22BJ 0. .20 0, .012259 0. .070000 22BJ 0. .30 0. ,014886 0, .085000 22BJ 0. .39 0. .019789 0. .113000 22BJ 0. .49 0. .026619 0, ,152000 22BU 0. GO 0. ,041855 0. . 2390O0 w z a o i o c co TOUGHNESS RESULTS D.W. RADFORD SPECIMEN TYPE- 4BEND ,LEFM EON USED LAMINATE GEOMETRY- (0/90)6S R E S U L T S K=(P*L)*+2*(Y)/T**2*H**3; Y=34.7(A/W)-55.2((A/W)*+2)+196((A/W)**3) SAMPLE 22BH 22BI 22BJ A/W 0.400 0.0 0.600 HEIGHT (IN. ) 0.506 0.517 0.535 THICKNESS (IN. ) 0. 1 170 0. 1 150 0. 1 150 FAILURE LOAD (LB. ) 347 .0 922 .0 170.0 FAILURE STRESS (MPA) 1516.9 1414.0 1521.7 C A L C U L A T E D V A L U E S FAILURE STRESS (KSI) 220. 1 205.2 220.8 TOUGHNESS LEFM (MPA/R) 64.9 46.7 TOUGHNESS LEFM (KSI/IN) 59. 1 42.5 TOUGHNESS COMPLIANCE (MPA/M) 60.8 45 . 1 TOUGHNESS COMPLIANCE ( K S l / f N ) 55.3 41 .0 a 25 o o l-l o c T J 175 W 4BND (Group 1 ) C O M P L I A N C E R E S U L T S S P E C I M E N T Y P E - 4 B E N 0 D . W . RADFORD L A M I N A T E G E O M E T R Y - ( 0 / 9 0 ) 6 S H E I G H T - 0 . 5 2 0 5 I N . S A M P L E T H I C K N E S S - 0 . 1 1 6 5 I N . A /W C O M P L I A N C E C O M P L I A N C E MODULUS ( M P A ) 6 6 4 7 6 . 4 7 0 2 3 9 . 3 ( M / N ) ( I N / K I P ) 2 2 B K 0 . . 0 0 . . 0 2 9 4 2 1 0 . 1 6 8 0 0 0 2 2 B K 0 . . 10 0 . 0 3 0 4 7 2 0 . 1 7 4 0 0 0 2 2 B K 0 . .21 0 . . 0 3 4 3 2 5 0 . 1 9 6 0 0 0 2 2 B K 0 . . 2 8 0 . . 0 3 8 8 7 8 0 . 2 2 2 0 0 0 2 2 B K 0 . . 4 0 0 . 0 5 0 6 1 2 0 . 2 8 9 0 0 0 2 2 B L 0 . 0 0 , . 0 2 7 8 4 5 0 . 1 5 9 0 0 0 2 2 B L 0 . 10 0 . 0 2 9 2 4 6 0 . 1 6 7 0 0 0 2 2 B L 0 . . 2 0 0 . . 0 3 3 2 7 4 0 . 1 9 0 0 0 0 2 2 B L 0 . . 3 0 0 . 0 3 9 2 2 8 0 . 2 2 4 0 0 0 2 2 B L 0 . . 3 9 0 . 0 5 0 2 6 1 0 . 2 8 7 0 0 0 2 2 B L 0 . . 5 0 0 . . 0 6 9 0 0 0 0 . 3 9 4 0 0 0 2 2 B L 0 . . 5 9 0 . . 0 9 6 6 7 0 0 . 5 5 2 0 0 0 ; B E A M L E N G T H - 5 . 0 0 0 I N . MODULUS ( K S I ) 9 6 4 5 . 3 1 0 1 9 1 . 3 HI Z O l-t O c TOUGHNESS RESULTS D.W. RADFORD SPECIMEN TYPE- 4BEND .LEFM EON USED LAMINATE GEOMETRY- (0/90)6S R E S U L T S K=(P+L)**2*(Y)/T+*2*H**3; Y=34.7(A/W)-55.2((A/W)**2)+196((A/W)**3) C A L C U L A T E D V A L U E S SAMPLE 22BK 22BL A/W 0.400 0.590 HEIGHT (IN. ) 0.516 0.525 THICKNESS (IN. ) 0. 1 190 0. 1 140 FAILURE LOAD (LB. ) 199.0 103.0 FAILURE STRESS (MPA) 1202.4 1344 .0 FAILURE STRESS (KSI) 174 .5 195.0 TOUGHNESS LEFM (MPA/M) 52 .0 42 .0 TOUGHNESS LEFM (KSI/TN) 47 . 3 38.3 TOUGHNESS COMPLIANCE (MPA/M) 55.4 47.8 TOUGHNESS COMPLIANCE (KS l / lN ) 50. 5 43.5 cd 23 O O I-I O c TJ COMPLIANCE RESULTS SPECIMEN TYPE- 4BEND LAMINATE GEOMETRY- (0/90)6S HEIGHT- 0.5050 IN SAMPLE THICKNESS- 0.1155 IN A/W COMPLIANCE COMPLIANCE MODULUS (MPA) 75902.5 61287.8 (M/N) (IN/KIP) 22BM 0. .0 0. 227664 1 . 300000 22BM 0. . 1 1 0. .241674 1 .380000 22BM 0. .40 0. ,322233 1 .840000 22BN 0. ,0 0. ,281953 1 .610000 22BN 0. . 14 0. ,280202 1 . 600000 22BN 0. .22 0. 299466 1 .710000 22BN 0, ,32 0. 329238 •1 .880000 22BN 0. .42 0. 383527 2 .190000 22BN 0. .51 0. 462334 2 .640000 22BN 0, .59 0. ,569161 3 .250000 D.W. RADFORD BEAM LENGTH- 10.000 IN. MODULUS (KSI) 11013 .O 8892.5 a o O c T O U G H N E S S R E S U L T S D . W . R A D F O R D S P E C I M E N T Y P E - 4 B E N D , L E F M EON U S E D L A M I N A T E G E O M E T R Y - ( O / 9 0 ) 6 S R E S U L T S K = ( P * L ) * * 2 * ( Y ) / T * * 2 * H * * 3 ; Y = 3 4 . 7 ( A / W ) - 5 5 . 2 ( ( A / W ) * * 2 ) + 1 9 6 ( ( A / W ) * * 3 ) C A L C U L A T E D V A L U E S S A M P L E 2 2 B M 2 2 B N A / W 0 . 4 0 0 0 . 5 9 0 H E I G H T T H I C K N E S S ( I N . ) 0 . 5 2 0 0 . 4 9 0 ( I N . ) 0 . 1 180 0 . 1 130 F A I L U R E L O A D ( L B . ) 1 0 5 . 0 4 2 . 0 F A I L U R E S T R E S S ( M P A ) 1 2 S 0 . 0 1 2 6 9 . 4 F A I L U R E S T R E S S ( K S I ) 182 . 8 1 8 4 . 2 T O U G H N E S S L E F M ( M P A / M ) 54 . 7 3 8 . 4 T O U G H N E S S L E F M ( K S I / T N ) 4 9 . 8 3 4 . 9 T O U G H N E S S C O M P L I A N C E ( M P A / M ) 6 4 . 4 4 2 . 3 T O U G H N E S S C O M P L I A N C E ( K S I / T N ) 5 8 . 6 3 8 . 5 Cd 25 a o O c TJ oo o COMPLIANCE RESULTS SPECIMEN TYPE- 4BEND D.W. RADFORD LAMINATE GEOMETRY- (0/90)6S HEIGHT- 1.0030 IN. THICKNESS- O.1155 IN. BEAM LENGTH- 5.000 I N . SAMPLE A/W COMPLIANCE COMPLIANCE MODULUS MODULUS (M/N) (IN/KIP) (MPA) (KSI) 22BO 0 .0 0 .006129 0 .035000 44979.3 6526.2 22B0 0. . 10 0 .006655 0 .038000 22B0 0 .20 0 .007530 0 .043000 22BO 0. .30 0 .009282 0 .053000 22BO 0. . 39 0 .011733 0. .067000 22BP 0. 0 0 .006129 0. .035000 44979.3 6526.2 22BP 0. 10 0. .006655 0. .038000 22BP 0. 2 1 0. .007881 0. .045000 22BP 0. 30 0. .009457 0. 054000 22BP 0. 40 0. .012259 0. 070000 22BP 0. 50 0. .017338 0. 099000 22BP 0. 60 0. .026619 O. 152000 cd 25 D O i-i O C TJ CO IV) TOUGHNESS RESULTS D.W. RADFORD SPECIMEN T Y P E - 4BEND ,LEFM EON USED LAMINATE GEOMETRY- (0 /90 )6S R E S U L T S SAMPLE A/W HEIGHT THICKNESS K = ( P * L ) * * 2 * ( Y ) / T * * 2 * H * * 3 ; Y = 3 4 . 7 ( A / W ) - 5 5 . 2 ( ( A / W ) * * 2 ) + 1 9 6 ( ( A / W ) * *3) 22BO 22BP 0 . 390 0 . 6 0 0 ( IN . ) 1 .01 1 0 .995 ( IN. ) 0 . 1 150 O. 1 160 FAILURE LOAD ( L B . ) 737 .0 265 .0 FAILURE STRESS (MPA) 1161.3 994 .0 C A L C U L A T E D V A L U E S FAILURE STRESS 168.5 144 . 2 TOUGHNESS LEFM (KSI ) (MPA/M) 70 .9 41 .6 TOUGHNESS LEFM (KS I / T N) 6 4 . 5 37 .9 TOUGHNESS COMPLIANCE TOUGHNESS COMPLIANCE (MPA/M) ( K S I / I N ) 61.1 4 0 . 5 55 .6 36 .9 z o o 1-1 o c CO co COMPLIANCE RESULTS SPECIMEN TYPE- 4BEND LAMINATE GEOMETRY- (0/90)6S HEIGHT-SAMPLE A/W 22B0 22B0 22B0 22BQ 22BO 1.0020 IN. : THICKNESS- 0.1165 IN. COMPLIANCE COMPLIANCE MODULUS (IN/KIP) 0.0 0.11 0.21 0.31 0.41 (M/N) 0.032749 0.034150 0.038528 0.045007 0.056216 0.187000 0.195000 O.220000 0.257000 0.321000 (MPA) 66970.6 D.W. RADFORD BEAM LENGTH- 10.000 IN. MODULUS (KSI) 9717.0 Cd Z o a o c TJ co cn TOUGHNESS RESULTS D.W. RADFORD SPECIMEN TYPE- 4BEND ,LEFM EON USED : - K=(P*L)**2*(Y) ' /T**2*H**3; Y=34.7(A/W)-55.2((A/W)**2)+196((A/W)**3) LAMINATE GEOMETRY- (0/90)6S R E S U L T S C A L C U L A T E D V A L U E S SAMPLE A/W HEIGHT THICKNESS FAILURE FAILURE FAILURE TOUGHNESS TOUGHNESS TOUGHNESS TOUGHNESS LOAD STRESS STRESS LEFM LEFM COMPLIANCE COMPLIANCE (IN.) (IN.) (LB.) (MPA) (KSI) (MPA/M) (KS l / lN ) (MPA/M) (KSI/IN) 22B0 0.410 0.996 0.1140 322.0 1127.5 163.6 67.1 61.0 63.5 57.8 § 22BR 0.0 1.008 0.1190 837.0 954.2 138.4 ' O O O c 4BND ( G r o u p 1 ) COMPLIANCE RESULTS SPECIMEN TYPE- 4BEND LAMINATE GEOMETRY- ( 0 / 9 0 )15S HEIGHT- 0 .2G10 IN. ; SAMPLE A/W COMPLIANCE (M/N) 23 -B 0. o 0. 032749 23 -B 0. . 11 0. .034325 23 -B 0. 20 • 0. .035726 23 -B O. . 29 0. .035726 23 -B 0. .40 0. .040104 23 -C 0. ,0 0. .041855 23 -C 0. 09 0. .042731 23 -C 0. 23 0. .046058 23 -C 0. , 30 0. .053589 23 -C 0. .40 0. .063921 THICKNESS- 0.3055 IN COMPLIANCE MODULUS (IN/KIP) (MPA) 0.187000 57804.1 0.196000 0.204000 O.204000 0.229000 0.239000 45227.5 0.244000 O.263000 O.306000 0.365000 D.W. RADFORD BEAM LENGTH- 3.420 IN. MODULUS (KSI ) 8387 .0 6562.2 CO 25 a o O C TJ co co TOUGHNESS RESULTS D.W. RADFORD SPECIMEN T Y P E - 4BEND ,LEFM EON USED : - K = ( P * L ) * * 2 + ( Y ) / T * * 2 * H + * 3 : LAMINATE GEOMETRY- (0 /90 )15S R E S U L T S Y = 3 4 . 7 ( A / W ) - 5 5 . 2 ( ( A / W ) * * 2 ) + 1 9 G ( ( A / W ) * * 3 ) C A L C U L A T E D V A L U E S SAMPLE 23-A 23-B A/W 0 . 0 0 . 4 0 0 HEIGHT (IN.) 0.271 0.251 THICKNESS FAILURE LOAD ( IN . ) 0 . 2990 0 .3120 ( L B . ) 873 .0 202 .0 FAILURE FAILURE TOUGHNESS STRESS STRESS LEFM (MPA) 1874.2 1345.7 (KSI) 271 .9 195 . 3 (MPA/M) 40. G TOUGHNESS LEFM ( K S I / T N ) 36 .9 TOUGHNESS TOUGHNESS COMPLIANCE COMPLIANCE (MPA/M) ( K S I / T N ) 22 .O 20 .0 W z a o o c TO-C O IX ) COMPLIANCE RESULTS SPECIMEN TYPE- 4BEND D.W. RADFORD LAMINATE GEOMETRY- (0/90)15S HEIGHT- 0.2495 IN. THICKNESS- 0.2955 IN. BEAM LENGTH- 5.000 IN. SAMPLE A/W COMPLIANCE COMPLIANCE MODULUS MODULUS (M/N) (IN/KIP) (MPA) (KSI) 23-D 0. 0 0. .085287 0. 487000 82085.4 11910.1 23-D 0. . 10 0, 086688 0. 495000 23-D 0. 20 0. .097020 0. 554000 23-D 0. 30 0. ,105076 0. 600000 23-D 0. 40 0, , 121713 0. 695000 23-E 0. 0 0. .118736 0. 678000 58961.1 8554.9 23-E 0. 12 0. 126967 0. 725000 23-E 0. 21 0. . 132220 0. 755O00 23-E 0. 30 0. 141502 0. 808000 23-E 0. 4,0 0. . 159540 0. 911000 23-E 0. 50 0. . 185634 1 . 060000 23-E 0. 59 0. .241674 1 . 380000 td 23 a o r-t o c-VD TOUGHNESS RESULTS O.W. RADFORD SPECIMEN TYPE- 4BEND .LEFM EON USED LAMINATE GEOMETRY- (0/90)15S R E S U L T S K=(P*L)+*2*(Y)/T**2*H**3; Y = 34.7(A/W)-55.2((A/W)**2)+196((A/W)**3) C A L C U L A T E D V A L U E S SAMPLE 23-D 23-E A/W 0.400 0.590 HEIGHT (IN. ) 0.264 0.235 THICKNESS (IN. ) 0. 2970 0.2940 FAILURE LOAD (LB. ) 129.0 54.0 FAILURE STRESS (MPA) 1 193. 1 1363.6 FAILURE STRESS 173 . 1 197 .9 TOUGHNESS LEFM 36.9 28.5 TOUGHNESS LEFM (KSI) (MPA/M) (KSI/IN) 33.6 26.0 TOUGHNESS COMPLIANCE TOUGHNESS COMPLIANCE (MPA/M) (KSI/TN) 46.8 34.2 42.6 31 . 1 cd 25 D O c TJ VD 193 0 0-12 0-24 _c_ 0-36 0-48 W 4BND (Group 1) COMPLIANCE RESULTS SPECIMEN TYPE- 4BEND D.W. RADFORD LAMINATE GEOMETRY- (0/90)15S HEIGHT- 0.2575 IN. THICKNESS- 0.3110 IN. BEAM LENGTH- 10.000 IN. SAMPLE A/W COMPLIANCE COMPLIANCE MODULUS MODULUS (M/N) (IN/KIP) (MPA) (KSI) 23-F 0. .0 0 .535887 3 .060000 90331.9 13106.6 23-F 0. . 12 0 .516623 2 .950000 23-F 0. , 18 0 .546394 3 .120000 23-F 0. . 28 0 .569161 3 .250000 23-F 0. 42 0. .579669 3 .310000 23-G 0. .0 0, .621699 3. .550000 .77863.5 11297.5 23-G 0. 12 0, .639211 3. .650000 23-G 0. 21 0, ,674237 3 . 850000 23-G 0. 30 0. .679491 3. .880000 23-G 0. 41 0. .742536 4 . 240000 23-G 0. 46 0. .782815 4. .470000 23-G 0. 60 0. .875632 5. .000000 1^ to z a o o c T3 TOUGHNESS RESULTS D.W. RADFORD SPECIMEN TYPE- 4BEND ,LEFM EON USED LAMINATE GEOMETRY- (0/90)15S R E S U L T S K=(P*L)**2*(Y)/T**2*H**3; Y=34.7(A/W)-55.2((A/W)**2)+196((A/W)**3) C A L C U L A T E D V A L U E S SAMPLE 23-F 22-G A/W 0.420 0.600 HEIGHT (IN. ) O. 253 0.262 THICKNESS (IN. ) 0. 3100 0. 3120 FAILURE LOAD (LB. ) 53 .0 40.0 FAILURE STRESS (MPA) 1094.5 1609.0 FAILURE STRESS (KSI ) 158 .8 233.5 TOUGHNESS LEFM (MPA/M) 32.5 34.6 TOUGHNESS LEFM (KSI/TN) 29.6 31.4 TOUGHNESS COMPLIANCE (MPA/M) 33 . 3 30. 3 TOUGHNESS COMPLIANCE (KSI/IN) 30. 3 27.5 cd Z a o o c TJ VD cn 1 96 4BND (Group 1) COMPLIANCE RESULTS SPECIMEN TYPE- 4BEND LAMINATE GEOMETRY - (0/90)15S HEIGHT- 0.5440 IN. ; THICKNESS- 0.3000 IN SAMPLE A/W COMPLIANCE COMPLIANCE MODULUS (M/N) (IN/KIP) (MPA) 23-1 0.0 0.004203 0.024000 50652.9 23-1 0.09 0.004378 0.025O0O 23-1 0. 19 0.005079 0.029000 23-1 0.29 0.006305 0.036000 23-1 0. 39 0.007706 0.044000 23-d 0.0 0.004378 0.025000 48626.8 23-d 0.28 0.005604 0.032000 23-d 0.39 0.006830 .0.039000 23-d 0.50 0.009632 0.055000 23-d 0.60 0.014886 0.085000 D.W. RADFORD BEAM LENGTH- 3.420 IN. MODULUS (KSI) 7349.4 7055.5 if* tn z o o I-I o c Xi TOUGHNESS RESULTS D.W. RADFORD SPECIMEN T Y P E - 4BEND ,LEFM EON USED LAMINATE GEOMETRY- (0 /90 )15S R E S U L T S K = ( P * L ) * * 2 * ( Y ) / T * * 2 * H * * 3 ; Y = 3 4 . 7 ( A / W ) - 5 5 . 2 ( ( A / W ) * * 2 ) + 1 9 6 ( ( A / W ) * * 3 ) C A L C U L A T E D V A L U E S SAMPLE 23-H 23-1 2 3 - J A/W 0 . 0 0 . 390 0 . 6 0 0 HEIGHT (IN. ) 0 .535 0 . 535 0 .562 THICKNESS (IN. ) 0. 2990 0 .3050 0 . 2960 FAILURE LOAD (LB. ) 2910.0 627 .0 342 .0 FAILURE STRESS (MPA ) 1603.0 909 .9 1077.8 FAILURE STRESS (KSI ) 232.6 132 .0 156.4 TOUGHNESS LEFM (MPA/M) 40. 4 33 .9 TOUGHNESS LEFM ( K S I / I N ) 36 .8 30 .9 TOUGHNESS COMPLIANCE TOUGHNESS COMPLIANCE (MPA/M) (KS I /TN) 29 .7 35 .6 27 . 1 32 .4 Cd 53 a o o c i 1 • VD CO 199 1 0 012 0-24 - ° - 0-36 0-48 W 4 B N D (Group 1) COMPLIANCE RESULTS D.W. RADFORD SPECIMEN TYPE- 4BEND LAMINATE GEOMETRY- (0/90)15S SAMPLE HEIGHT- 0.5205 IN. ; THICKNESS- 0.3030 IN. ; BEAM LENGTH- 5.000 IN. A/W COMPLIANCE COMPLIANCE MODULUS (MPA) (M/N) (IN/KIP) 23 -L 0. .0 0, ,012959 0. 074000 23 -L 0. . 10 0. .014535 0. 08300O 23 -L 0. . 19 0. ,016287 0. 093000 23 -L 0. . 30 0. ,019614 0. , 1 1200O 23 -L 0. .40 0. ,024518 0. 140000 23 -K 0. .0 0. .015061 0. .086000 23 -K 0. .09 0. .016112 0, ,092000 23 -K 0. . 20 0, ,017338 0, ,099000 23 -K 0. .30 0. .020840 0. ,119000 23 -K 0, ,40 0. ,026269 0. ,150000 23 -K 0. .51 0. .035551 0 .203000 23 -K 0 .60 0 .051137 0. .292000 58026.8 49930.0 MODULUS (KSI) 8419.3 7244.6 tn O o 1-1 o c TJ TOUGHNESS RESULTS D.W. RADFORD SPECIMEN TYPE- 4BEND ,LEFM EON USED LAMINATE GEOMETRY- (0/90)15S R E S U L T S K=(P*L)**2*(Y)/T**2*H**3; Y = 34.7(A/W)-55.2((A/W)**2)+196((A/W)**3) SAMPLE 23-K 23-L A/W 0.600 0.400 HEIGHT (IN. ) 0.506 0.535 THICKNESS (IN. ) 0. 2990 0.3070 FAILURE LOAD (LB. ) 168.0 344.0 FAILURE STRESS (MPA) 945 . 3 749.5 C A L C U L A T E D V A L U E S FAILURE STRESS (KSI) 137.2 108.7 TOUGHNESS LEFM 28 .2 33.0 TOUGHNESS LEFM (MPA/W) (KSI/TN) 25 . 7 30.0 TOUGHNESS COMPLIANCE TOUGHNESS COMPLIANCE (MPA/M) (KSI/IN) 32.8 36.3 29.8 33. 1 W Z a o >-i o c o 202 COMPLIANCE RESULTS SPECIMEN TYPE- 4BEND LAMINATE GEOMETRY- (0/90)15S SAMPLE 23-M 23-M 23-M 23-M 23-M HEIGHT- 0.5350 IN. ; THICKNESS- 0.3080 IN. A/W COMPLIANCE COMPLIANCE MODULUS (M/N) (IN/KIP) (MPA) 0.0 O. 10 0.20 0. 30 0. 39 0.076180 0.078457 0.083185 0.091591 O. 106127 0.435000 0.448000 0.475000 0.523000 0.606000 71540.6 D.W. RADFORD BEAM LENGTH- 10.000 IN. MODULUS (KSI) 10380. 1 til a o O c Ti tv) O co TOUGHNESS RESULTS D.W. RADFORD SPECIMEN TYPE- 4BEND ,LEFM EON USED :- K=(P*L)**2*(Y)/T+*2*H +*3; Y=34.7(A/W)-55.2((A/W)**2)+196((A/W)**3) LAMINATE GEOMETRY- (0/90)15S C A L C U L A T E D V A L U E S R E S U L T S SAMPLE A/W HEIGHT . THICKNESS FAILURE LOAD (IN.) (IN.) (LB.) 23-M 0.390 0.535 0.3080 227.0 FAILURE FAILURE TOUGHNESS TOUGHNESS TOUGHNESS TOUGHNESS STRESS STRESS LEFM LEFM COMPLIANCE COMPLIANCE (MPA) (KSI) (MPA/M) (KSI/TN) (MPA/M) (KSl/lN) 953.9 138.4 42.4 38.6 47.3 43.0 tt* W 53 D CD i-t O c Xi to o >f* 205 0 0-096 0192 _g_ 0-288 0-384 4BND (Group 1 COMPLIANCE RESULTS SPECIMEN T Y P E - 4ESEND LAMINATE GEOMETRY- ( 0 / 9 0 ) 1 5 S HEIGHT- 1.0225 I N . THICKNESS- 0 . 3 0 2 0 IN SAMPLE 23 -N 23 -N 23 -N 23 -N 2 3 - N A/W COMPLIANCE COMPLIANCE MODULUS 0 . 0 0 . 0 9 0 . 19 0 . 29 0 . 4 0 (M/N) 0 .002452 0 .002627 0 .002977 0 .002802 0 .003327 ( I N / K I P ) 0 . 0 1 4 0 0 0 0 . 0 1 5 0 0 0 0 . 0 1 7 0 0 0 0 . 0 1 6 0 0 0 0 . 0 1 9 0 0 0 (MPA) 4 0 5 9 1 . 9 D.W. RADFORD BEAM LENGTH- 5 . 0 0 0 I N . MODULUS ( K S I ) 5 8 8 9 . 7 4=. CO z o CD o c TJ O CTi TOUGHNESS RESULTS D.W. RADFORD SPECIMEN TYPE- 4BEND ,LEFM EON USED LAMINATE GEOMETRY- (0/90)15S R E S U L T S SAMPLE A/W HEIGHT K=(P*L)**2*(Y)/T* + 2*H**3; Y = 34 .7(A/W)-55.2((A/W)**2)+196((A/W)**3) 23-N 23-0 0. 400 0.600 (IN.) 1 .020 1 .025 THICKNESS FAILURE LOAD (IN. ) O. 3060 0. 2980 (LB. ) 1380.0 735.0 C A L C U L A T E D V A L U E S FAILURE FAILURE TOUGHNESS STRESS STRESS LEFM (MPA) 829.9 1011.2 (KSI) 120. 4 146.7 (MPA/TO) 50. 4 43 .0 TOUGHNESS LEFM (KSI/TN) 45 .9 39. 1 TOUGHNESS TOUGHNESS COMPLIANCE COMPLIANCE (MPA/M-) 15.5 8.3 (KSI/TN) 14.1 7.6 Cd O O C tv) O COMPLIANCE RESULTS SPECIMEN TYPE- 4BEND LAMINATE GEOMETRY- (0/90)155 1.0225 IN. ; THICKNESS- 0.3100 IN. COMPLIANCE COMPLIANCE MODULUS (M/N) (IN/KIP) (MPA) 23-P 0. .0 0. ,012784 0. ,073000 23-P 0. . 10 0. .013660 0. 078000 23-P ' 0. .20 0. .015061 0. ,086000 23-P 0. .30 0. ,018213 0. ,104000 23-P 0. .40 0. .022416 0. , 128000 HEIGHT-SAMPLE A/W D.W. RADFORD BEAM LENGTH- 10.000 IN. MODULUS (KSI) 8803.0 Cd 55 a o o c TJ ts> O VD TOUGHNESS RESULTS D.W. RADFORD SPECIMEN TYPE- 4BEND .LEFM EON USED LAMINATE GEOMETRY- (0/90)15S R E S U L T S : - K=(P*L)**2*(Y)/T**2*H**3; Y = 34.7(A/W)-55.2((A/W)* *2) + 196((A/W)**3 ) SAMPLE 23-P 23-0 A/W 0.400 O.O HEIGHT (IN.) 1 .020 1 .025 THICKNESS (IN. ) 0.3090 O. 31 10 FAILURE LOAD (LB. ) 592.0 3540.0 FAILURE STRESS (MPA) 705. 1 1493.4 C A L C U L A T E D V A L U E S FAILURE STRESS (KSI ) 102.3 216.7 TOUGHNESS LEFM (MPA/M) 42 .9 TOUGHNESS LEFM (KSI/IN) 39.0 TOUGHNESS COMPLIANCE (MPA/M) 40.2 TOUGHNESS COMPLIANCE (KSI/IN) 36 .6 >f* Cd 25 D O O c T3 21 1 0 0 0 9 6 0192 J _ 0-288 0-384 4BND (Group 1) COMPLIANCE RESULTS SPECIMEN TYPE- 4BEND LAMINATE GEOMETRY- (0/90)12S SAMPLE 31 AE 31AE 31AE 31 AE 31AE 3 1 AE 31AE 31AE 31AE 31 Ad 31Ad 31Ad 31Ad 31Ad 3 1Ad 31Ad 31Ad 31Ad 31AN 31AN 31AN 31AN 3 IAN 31AN 31 AN 31AN 31AN D.W. RADFORD HEIGHT- 0.2551 IN. ; A/W COMPLIANCE (M/N) 0 .0 0, .147807 0 .844000 0. . 12 0, . 149558 O .854000 0 .24 0, .163218 0 .932000 0 .31 0. ,175477 1 , .002000 0. .41 0, .203147 1 . 160000 0. .50 0, .245878 1 . 404000 0 .60 0 .329588 1 , .882000 0, 71 0. . 526080 3 .004000 0. .81 1 , . 138321 6 .500000 0. .0 0. . 124340 0, .710000 0. . 1 1 0, . 129243 0, .738000 0. , 22 0. . 137649 0, .786000 0. .31 0, , 152710 O .872000 0. .42 0, .182131 1 , .040000 0. .51 0. .225213 1 , .286000 0. .61 0. ,319431 1 , ,824000 0. .71 0. .535186 3 . 056000 0. 81 1. ,108550 6 .330000 0. 0 0. ,132045 0, ,754000 0, 1 1 0. , 135548 0, ,774000 0. . 23 0. ,146406 0. ,836000 0. 32 0. 162868 0, ,930000 0. 39 0. 184933 1 . 056000 0. .51 0. 238522 1 . ,362000 0. .60 0. 325035 1 . ,856000 0. 69 0. 534136 3 . 050000 0. ,81 1. 21 1174 6. 916000 THICKNESS- 0.2494 IN. COMPLIANCE MODULUS (IN/KIP) (MPA) 52472 .0 ; BEAM LENGTH-MODULUS (KSI) 7613.4 5.000 IN. 62375.2 9050.3 Cd a o o c ro 58735 . 3 8522.1 to TOUGHNESS RESULTS O.W. RADFORD SPECIMEN TYPE- 4BEND ,LEFM EON USED :- K=(P*L)**2*(Y)/T**2*H**3; Y=34.7(A/W)-55.2((A/W)**2)+196((A/W)**3) LAMINATE GEOMETRY- (0/90)12S R E S U L T S C A L C U L A T E D V A L U E S SAMPLE A/W HEIGHT THICKNESS FAILURE FAILURE FAILURE TOUGHNESS TOUGHNESS TOUGHNESS TOUGHNESS LOAD STRESS STRESS LEFM LEFM COMPLIANCE COMPLIANCE (IN. ) (IN. ) (LB. ) (MPA) (KSI) (MPA/M) ( K S l / l N ) (MPA/M) (KSI/TN) 31AA 0. O O. .289 0 . 2500 634 .0 2092 . 7 303 . 6 31AB O. 300 0. 297 0 . 2500 204 .0 1301 . 2 188 . 8 45. .4 41 . 3 50. .4 45.9 31AC 0. . 420 0. 248 0 .2500 84 .0 1119. 3 162. 4 32 . 9 29 .9 36 , .9 33 .6 31 AD 0. , 580 0. , 234 0 . 2470 44 .0 1271 . 1 184 . 4 27 .3 24 .8 31 , .6 28.7 31AE 0. .810 ' 0. 242 0 .2500 15 .0 1956. 0 283 . 8 13 .6 12, . 3 32. . 1 29.2 31AF 0. .0 0, ,238 0 .2480 365 .0 1790. 8 259 . 8 31AG 0. ,200 0. . 264 0 .2500 221 .0 1365. 9 198 . 2 44 .9 40 .9 48, .6 44 .2 31AH 0. .420 0. , 256 0 .2490 107 .0 1343. 4 194 . 9 40 . 1 36 .5 46. . 4 42.2 31AI 0. ,620 0. , 250 0 .2520 43 .0 1303 . 1 189. 1 25 . 7 23 .4 34 . 7 31.6 31AJ 0. .810 0. , 249 0 . 2490 15 .0 1855 . 0 269 . 1 13 . 1 1 1 .9 31 .7 28.8 31AK 0. . 160 0. ,251 0 . 2490 207 .0 1288. 9 187 . 0 40 .4 36 .7 52, .6 47.9 31AL 0. .420 0. ,252 0 .2490 103 .0 1334. 5 193. 6 39 .5 36 .0 45, .0 41 .0 31AM O. ,620 o . ,255 0 .2500 47 .0 1379. 9 200. 2 27 . 5 25 .0 37 , .7 34 .3 31 AN 0. .810 0. ,247 0 . 2490 14 .0 1759. 5 255. 3 12 .3 1 1 .2 29, .7 27 .0 COMPLIANCE RESULTS D.W. RADFORD SPECIMEN TYPE- 4BEND LAMINATE GEOMETRY- (0/90)12S HEIGHT- 0.5041 IN. THICKNESS- 0.2489 IN. SAMPLE A/W COMPLIANCE COMPLIANCE MODULUS (MPA) 63059.2 BEAM LENGTH- 10.000 IN. MODULUS (M/N) (IN/KIP) 31A0 0. 0 0. 127842 0. 730000 3 1AQ 0. 11 0. 130995 0. ,748000 31AQ 0. 21 0. 139401 0. 796000 31AQ 0. 31 0. 155863 0. 890000 31AQ 0. 41 0. 182131 1 . 040000 31AQ 0. 52 0. 232918 1 . 330000 31 AO 0. 61 0. 317679 1 . ,814000 31AV 0. 0 0. 127842 0. 730000 31AV 0. 13 0. 131695 0. 752000 31AV 0. 24 0. 144654 0. 826000 31AV 0. 34 0. 163218 0, .932000 31AV 0. 43 0. 194040 1 , 108000 31AV 0. 51 0. 232568 1 . ,328000 31AV 0. 60 0. 317679 1 . ,814000 31 AW 0. 0 0. 131695 0. .752000 31AW 0. 1 1 0. 135548 0, .774000 31AW 0. 21 0. 145705 0 .832000 31AW 0. 30 0. 161116 0, .920000 31AW 0. .39 0. 187035 1, .068000 31AW 0. .50 0. 232918 1. .330000 31AW 0. .60 0. 317329 1 .812000 31AW 0. ,69 0. ,501562 2 ,864000 31AW 0. ,79 1 . ,041652 5, .948000 31AR 0. ,0 0. 1 15233 0. .658000 31AR 0. .09 0. , 118035 0. .674000 31AR 0. ,20 0, , 126791 0, .724000 31AR 0. ,30 0. , 139401 0 .796000 31AR 0. ,40 0. , 164269 0, .938000 31AR 0. 50 0. ,204197 1 , .166000 31AR 0. ,60 0. 277400 1 , . 584000 31AR 0. 70 0. ,457080 2 , .610000 31AR 0. ,80 0. ,963896 5, .504000 (KSI) 9149.5 63059.2 9149.5 61214.4 8881.9 69959.3 10150.7 Z a o >-« o c TJ to TOUGHNESS RESULTS D.W. RADFORD SPECIMEN T Y P E - 4BEND ,LEFM EON USED : - K = ( P * L ) * * 2 * ( Y ) / T * * 2 * H * * 3 ; Y = 3 4 . 7 ( A / W ) - 5 5 . 2 ( ( A / W ) * * 2 ) + 1 9 6 ( ( A / W ) * * 3 ) LAMINATE GEOMETRY- (0 /90 )12S R E S U L T S C A L C U L A T E D V A L U E S 5AMPLE A/W HEIGHT THICKNESS FAILURE FAILURE FAILURE TOUGHNESS TOUGHNESS TOUGHNESS TOUGHNESS LOAD STRESS STRESS LEFM LEFM COMPLIANCE COMPLIANCE ( IN. ) ( IN. ) (LB . ) (MPA) (KSI ) (MPA/M) ( K S I / I N ) (MPA/M) ( K S I / T N ) 31A0 0 . 2 3 0 0 .507 0 .2500 282 .0 1020.2 148.0 46 .8 42 .6 57 . 1 52 .0 31 AP 0 . 4 3 0 0.506 0 .2500 148 .0 981 .0 142 . 3 40 .7 37 . 1 44 .0 4 0 . 0 31AQ 0 . 6 1 0 0.502 0 .2490 78 .0 1 126.5 163.5 32 .5 29 .6 46 .3 42.1 31AR 0 . 8 0 0 0 .510 O.2500 30 .0 1589.9 230.7 17.4 15.9 41 .5 37 .8 31AS 0 . 0 0 .507 0 .2490 853 .0 1837 .0 266.5 31AT 0 . 2 0 0 0 .496 0 .2490 305.0 1072.4 155.6 48 . 4 44 .0 5 2 . 0 47 . 3 31AU 0 . 4 3 0 0 .499 0 .2490 155 .0 1060.6 153.9 43 .7 39 .8 46 .5 4 2 . 3 31AV 0 . 6 0 0 0 .503 0 .2480 72 .0 988 .6 143.4 29.4 26 .8 40 .7 37 .0 31AW 0 . 7 9 0 0 .507 0 .2460 22 .0 1087.5 157.8 12.9 11.7 29 .6 26 .9 cd Z O O O c TJ r o COMPLIANCE RESULTS D.W. RADFORD SPECIMEN TYPE- 4BEND LAMINATE GEOMETRY- (0/90)9S HEIGHT- 0 .2509 IN. ; THICKNESS- 0 .1783 IN. SAMPLE A/W COMPLIANCE COMPLIANCE MODULUS (M/N) (IN/KIP) (MPA) 65394 .5 69586.4 32--E 0 . 0 0 . 174426 0 . 996000 32 -E 0 . 12 0 . 185984 1 . 062000 32 -E 0. 23 O. 199294 1 . 138000 32 -E 0. 32 0 . 220659 1 . 260000 32 -E 0. 40 0 . 247979 1 . 4 16000 32 -E 0. 50 0 . 321182 1 . 834000 32 - J 0. 0 0 . 163918 0 . 936000 32 - u 0 . 14 0 . 169522 0 . 968000 32 - d 0. 21 0 . 178979 1 . 022000 32 - J 0. .30 0 . 202796 1 . ,158000 32 - d 0. 39 0 . 235370 1 . 344000 32 - d 0. ,51 0. 3005 17 1 . ,716000 32 - d 0. ,60 0. 408045 2 . 330000 32 - d 0. .70 0. 654623 3, .738000 32 - d 0. . 79 1 . .403813 8 . 016000 32 -N 0 .0 0. . 152710 0. .872000 32 -N 0 . 12 0, , 158314 0 .904000 32 -N 0 . 23 0. . 168822 0 . 964000 32 -N 0 .31 0. , 188786 1 .078000 32 -N 0 .41 0 .235720 1 . 346000 32 -N 0 .48 0 .31 1725 1 .780000 32 -N 0 .58 0 .413999 2 .364000 32 -N 0 .70 0 .711013 4 .060000 32 -N 0 .81 .1 .644787 9 .392000 ; BEAM LENGTH- 5.000 IN. MODULUS (KSI) 9488.4 10096.6 W 25 a o o c Xi M 74693.7 10837.6 CTl TOUGHNESS RESULTS D.W. RADFORD SPECIMEN T Y P E - 4BEND ,LEFM EON USED : - K = ( P * L ) * * 2 * ( Y ) / T * * 2 * H * * 3 ; Y=34 .7 (A /W) -55 .2 ( (A /W) * *2 )+196 ( (A /W) *+3 ) LAMINATE GEOMETRY- ( 0 /90 )9S R E S U L T S C A L C U L A T E D V A L U E S SAMPLE A/W HEIGHT THICKNESS FAILURE FAILURE FAILURE TOUGHNESS TOUGHNESS TOUGHNESS TOUGHNESS LOAD STRESS STRESS LEFM LEFM COMPLIANCE COMPLIANCE ( IN. ) ( IN . ) ( L B . ) (MPA) (KSI ) (MPA/M) ( K S I / T N ) (MPA/M) ( K S I / I N ) 32-A 0. 0 0. 247 0 . 1780 282 .0 1789. 7 259. 7 32-B 0. . 230 0. 244 0 . 1800 128 .0 1388 . 4 201 . 5 44 , . 2 40. , 2 44 , .8 40 .7 32 -C 0. .450 0. 260 0 . 1770 79 .0 1504 . 3 218. 3 43, , 7 39. , 7 57 . .0 51 .9 32-D 0. .610 0. 249 0 . 1780 41 .0 1683 . 4 244 . 3 34 , .2 31 . , 1 46, .9 42 .6 3 2 - E 0. ,500 0. 250 0 . 1770 62 .0 1545. 1 224 . 2 40 ,8 37 . , 1 49. , 2 44 .8 32 -F 0. ,0 0. 256 0 . 1770 317 .0 1883 . 5 273. 3 32 -G 0. . 230 0. 250 O . 1780 133 .0 1389 . 7 201 . 6 44 , 8 40. ,8 46 . 2 42 .0 32-H O. 410 0. 248 0 . 1790 8 1 .0 1456 . 7 2 11. 4 43 . 2 39. , 4 55 .9 50 .9 32-1 0. 610 0. 243 0 . 1780 4 1 .0 1767 . 6 256. 5 35, . 5 32 . , 3 47 .4 43 .2 3 2 - J 0. , 790 0. 258 0 . 1750 15 .0 2012 . 5 292 . 0 17 .0 15. .5 46, .0 41 .8 32-K 0. , 230 0. 252 0 . 1800 141 .0 1433. 9 208. 0 46 .4 42 . . 2 48 . 5 44 . 1 3 2 - L 0. 420 0. 249 0 . 1790 80 .0 1476. 8 214. 3 43, .5 39. ,6 56, . 1 51 .0 32-M 0. 620 0. 252 0 . 1800 44 .0 1837 . 2 266 . 6 36 .4 33. , 1 52, . 3 47 .6 32-N 0. ,810 0. ,255 0 . 1800 14 .0 2283 . 6 331 . 3 16 . 3 14 . ,8 47 . 1 42 .9 COMPLIANCE RESULTS SPECIMEN TYPE- 4BEND LAMINATE GEOMETRY - (0/90)9S SAMPLE 32 -0 32 -0 32 -o 32 -0 32 -o 32 -o 32 -R 32 -R 32 -R 32 -R 32 -R 32 -R 32 -R 32 -R 32 -R 32 -V 32 -V 32 -V 32 -V 32 -V 32 -V 32 -V 32 -W 32 -W 32 -W 32 -W 32 -W 32 -W 32 -W 32 -W 32 -W D.W. RADFORD HEIGHT- 0.5051 IN. THICKNESS- O.1799 IN. BEAM LENGTH- 10.000 IN. A/W COMPLIANCE (M/N) COMPLIANCE MODULUS (IN/KIP) (MPA) 0. 11 0. 17 1974 0. .982000 0. 20 O. 183533 1 . ,048000 0. 3 1 0. 203847 1 . .164000 0. 42 0. 241674 1 , .380000 0. 50 0. 295613 1 . 688000 0. 60 0. 4 15050 2, .370000 0. 0 0. 16742 1 O, .956000 0. 13 0. 171274 0, .978000 0. 23 0. 182482 1 , .042000 0. 31 0. 200695 1 . 146000 0. 42 0. 238522 1 . .362000 0. 51 0. 299816 1 . .7 12000 0. 60 0. 399989 2. .284000 0. 70 0. 630455 3. .600000 0. 80 1. 342169 7 . 664000 0. 0 0. 16742 1 0, .956000 0. 10 0. 172324 0, .984000 0. 20 0. 183883 1 , .050000 0. 31 0. 206649 1 , .180000 0. ,41 0. 241674 1 .380000 0. 51 0. 30612 1 1 .748000 0. 61 0. 429410 2 , .452000 0. 0 0. 178279 1 .018000 0. 1 1 0. 182131 1 , .040000 0. 20 0. 192639 1 .100000 0. 30 0. 212603 1 , .214000 0. 40 0. 252883 1 .444000 0. ,50 0. 318380 1 , .818000 0. ,60 0. 441319 2 .520000 0. ,71 0. 726775 4, .150000 0. 80 1. 591 198 9, .086000 MODULUS (KSI) 66226.6 9609.1 ** W a o O c •a tv) 66226.6 9609.1 62193.2 9023.9 tv) 00 TOUGHNESS RESULTS D.W. RADFORD SPECIMEN T Y P E - 4BEND .LF.FM EON USED : - K = ( P * L ) * * 2 * ( Y ) / T * * 2 * H * * 3 ; Y = 3 4 . 7 ( A / W ) - 5 5 . 2 ( ( A / W ) * * 2 ) + 1 9 6 ( ( A / W ) * * 3 ) LAMINATE GEOMETRY- ( 0 /90 )9S R E S U L T S C A L C U L A T E D V A L U E S SAMPLE A/W HEIGHT THICKNESS FAILURE FAILURE FAILURE TOUGHNESS TOUGHNESS TOUGHNESS TOUGHNESS LOAD STRESS STRESS LEFM LEFM COMPLIANCE COMPLIANCE ( IN. ) ( IN. ) (LB . ) (MPA) (KSI) (MPA/M) ( K S I / I N ) (MPA/M) (KSI/TN) 32-0 0. .210 0 .515 0 . 1800 250 .0 1156.6 167.8 53 .3 4 8 . 5 46 .3 42 .2 32-P 0. ,400 0 .502 0 . 1800 148 .0 1249.3 181.3 53 . 3 4 8 . 5 64 .8 59 .0 32 -0 0. ,600 0 .506 0 . 1810 65 .0 1208.4 175.3 36 . 1 32 .8 46 .3 42 . 1 32-R 0. .800 0. 505 0 . 1800 21 .0 1576.5 228 . 7 17.2 15.7 46. 1 4 2 . 0 32 -S 0. 0 0 .509 0 . 1810 558 .0 1640.2 238.0 32-T 0. 180 0 .503 0 . 1800 246 .0 1107.3 160.7 49 .8 4 5 . 3 53 .8 4 9 . 0 32-U 0. , 390 0 .500 0 . 1790 138 .0 1142 .4 165 .8 49 .0 44 .6 58 .7 53 .4 32-V 0. 610 O.502 0 . 1780 65 .0 1313.2 190.5 37 .9 34 . 5 4 8 . 9 44 . 5 32-W 0. ,800 0 .504 0 . 1800 16 .0 1205.9 175.0 13. 1 12.0 35 .2 32 .0 COMPLIANCE RESULTS D.W. RADFORD SPECIMEN TYPE- 4BEND LAMINATE GEOMETRY- (0/90)15S HEIGHT- 0.2489 IN. ; THICKNESS- 0.3102 IN. ; BEAM LENGTH- 5.000 IN. SAMPLE A/W COMPLIANCE COMPLIANCE MODULUS MODULUS (M/N) (IN/KIP) (MPA) (KSI) 33 -E 0. 0 0. 134847 0. 770000 33 -E 0. 14 0. 139401 0. 796000 33 -E 0. 22 0. 146406 0. 836000 33 -E 0. .31 0. 159365 0. ,910000 33 -E 0. 39 0. 175827 1 . ,004000 33 -E 0. .50 0. 213304 1 . ,218000 33 -E 0. .60 0. 283004 1 . 6 16000 33 -E 0. .67 0. 436765 2 , 494000 33 -E 0. .81 1 . 023088 5 , 84 2000 33 -N 0. .0 0. 100172 0, .572000 33 -N 0. . 10 0. 102274 0, ,584000 33 -N 0. 22 0. 110330 0. .630000 33 -N 0. . 30 0. 120487 0. .688000 33 -N 0. .39 0. 140101 0. .800000 33 -N 0. .51 0. 178979 1 .022000 33 -N 0. .61 0. 241674 1 , .380000 33 -N 0. .70 0. 378273 2 .160000 33 -N 0. .81 0. 808384 4 .616000 33 - J 0. .0 0. 107177 0 .612000 33 - J 0, . 16 0. 112081 0 .640000 33 - d 0 . 22 0. 1 16634 0 .666000 33 - d 0 . 30 0. 125040 0 .714000 33 - d 0 .38 0. , 142903 0 .816000 33 - d 0 .50 0. .176878 1 .010000 33 - d 0 .60 b. .241674 1 .380000 33 - d 0 .70 0, ,382126 2 .182000 33 - d 0 .83 0. ,957591 5 .468000 49795.5 7225.0 67032.3 9726.0 Cd 55 O O o c TJ 62651.1 9090.3 to to O TOUGHNESS RESULTS D.W. RADFORD SPECIMEN TYPE- 48END ,LEFM EON USED :- K=(P*L)**2*(Y)/T**2*H**3; LAMINATE GEOMETRY- (0/90)15S R E S U L T S Y = 34.7(A/W)-55.2((A/W)**2)+196 ( (A/W)**3) C A L C U L A T E D V A L U E S SAMPLE A/W HEIGHT THICKNESS FAILURE FAILURE FAILURE TOUGHNESS TOUGHNESS TOUGHNESS TOUGHNES LOAD STRESS STRESS LEFM LEFM COMPLIANCE COMPLIAN (IN.) (IN.) (LB. ) (MPA) (KSI) (MPA/M) (KSI/IN) (MPA/M) (KSl/TFl) 33-A 0. .0 0. . 266 0 .3100 621 .0 1951 . 3 283. 1 33-B 0. . 230 0. 265 0 .3130 223 .0 1 179 . 317 1 . 1 39. , 1 35 .6 63. .8 58, , 1 33-C 0. .450 0. 270 0 .3100 1 15 .0 1 159. 4 168 . 2 34 . ,3 31 . 2 31 . , 1 28 , 3 33-D 0. .650 0. 266 0 .3100 47 .0 1205. 6 174 . 9 22 . , 1 20 . 1 38. , 2 34 . 8 33-E 0, .810 0. 233 0 .3080 17 .0 194 1 . 0 281 . 6 13. ,2 12 .0 26. .0 23. .6 33-F 0 .0 0. 236 0 .3100 428 .0 1708 . 5 247 . 9 33-G 0. . 150 0. 232 0 .3120 254 .0 1442 . 8 209 . 3 43. .0 39 .2 75. 5 68 , 7 33-H 0. .420 0. 242 0 . 3090 120 .0 1358. 6 197 . 1 39 . 4 35 .9 29. , 4 26 , .7 33-1 0, .640 0. . 246 0 .3100 55 .0 1559 . 1 226 . 2 28. . 5 26 .0 44 . 5 40, .5 33-d 0 .830 0. . 245 0 .3100 19 .0 2435. 1 353 . 3 14 , . 1 12 .8 29 . ,9 27 . 2 33-K 0, , 180 0. 247 0 .3100 232 .0 1257 . 3 182 . 4 39 . 6 36 . 1 70. ,5 64 , 2 33-L 0 .420 o. . 245 0 .31 10 136 .0 1492 . 6 216 . 6 43 . 6 39 .7 33, ,0 30, ,0 33-M 0 .640 0. . 245 0 .3100 57 .0 1629. 0 236 . 4 29 . 7 27 . 1 46. . 2 42 , . 1 33-N 0, .810 0. 247 0 . 3100 20 .0 2018. 9 292 . 9 14 . 1 12 .9 29 , .6 26 , 9 Cd ss a o o c • a K> r o COMPLIANCE RESULTS SPECIMEN TYPE- 4BEND LAMINATE GEOMETRY- (0/90)155 D.W. RADFORD HEIGHT- 0.5004 IN. THICKNESS- 0.3101 IN. BEAM LENGTH- 10.000 IN. A/W COMPLIANCE COMPLIANCE MODULUS (MPA) 64663.4 (M/N) (IN/KIP) 0. 0 0. 102274 0. 584000 0. 11 0. 103675 0. 592000 0. 22 0. 1 12081 0. 640000 0. 32 0. 12574 1 0. 718000 0. 43 0. 148507 0. 848000 0. 53 0. 188436 1 . 076000 0. 62 0. 262339 1 . 498000 0. 0 0. 101573 0. 580000 0. 1 1 0. 100873 0. 576000 0. 21 0. 108929 0. 622000 0. 31 0. 120487 0. 688000 0. 41 0. 138350 0. 790000 0. 50 0. 165670 0. .946000 0. 60 0. 230817 1. .318000 0. 71 0. 373019 2. .13O000 0. 80 0. 7061 10 4 .032000 0. 0 0. 1 15233 0. .658000 0. 12 0. 121888 0 .696000 0. 21 0. 127842 0 .730000 0. .31 0. 141502 0 .808000 0, ,41 0. 164969 0 .942000 0. .51 0. 208400 1 .190000 0. .61 0. 279151 1 .594000 0 .0 0. 1 14533 0 .654000 0 . 12 0. . 123989 0 .708000 0 . 23 0. 135898 0 .776000 0 . 33 0. 146406 0 .836000 0 .43 0. . 176177 1 .006000 0 .51 0. .208O50 1 .188000 0 .62 0 .280553 1 .602000 0 .71 0 .475293 2 .714000 0 .80 0 .909957 5 .196000 MODULUS (KSI ) 9382.3 65109.3 9447.0 4=. t d z a o >-i o c Xi to 57391.2 8327.1 57742 .2 8378. 1 TOUGHNESS RESULTS D.W. RADFORD SPECIMEN T Y P E - 4BEND .LEFM EON USED LAMINATE GEOMETRY- (0 /90 )15S K = ( P * L ) * * 2 * ( Y ) / T + * 2 + H * * 3 ; Y = 3 4 . 7 ( A / W ) - 5 5 . 2 ( ( A / W ) * * 2 ) + 1 9 6 ( ( A / W ) * * 3 ) SAMPLE R E S U L T S A/W HEIGHT. THICKNESS C A L C U L A T E D V A L U E S ( IN. ) ( IN. ) FAILURE LOAD ( L B . ) FAILURE STRESS (MPA) FAILURE STRESS (KSI ) TOUGHNESS LEFM TOUGHNESS LEFM (MPA/M) (KS I /TN) TOUGHNESS TOUGHNESS COMPLIANCE COMPLIANCE (MPA/M) ( K S I / T N ) 33-0 0. 280 0. .528 0. 3130 350 .0 1066 .5 154 . . 7 49 .8 45. .4 65 , .2 59, .3 33-P 0. 430 0. . 498 0. 3110 193 .0 1061 .6 154 . .0 43 . 7 39 .8 46. ,4 42 . , 2 33 -0 0. .620 0. .499 0. 31 10 103 .0 1269 .7 184 . . 2 35 .4 32, . 2 48, .6 44 , .2 33-R 0. 800 0. .499 0. 3120 36 .0 1596 .9 231 . 7 17 . 3 15, .8 38 . ,9 35, ,4 33-S 0. 0 0. 501 0. 3100 1008 .0 1785 . 7 259 , . 1 33 -T 0. .210 0. 493 0. 31 10 373 .0 1089 .9 158 . . 1 49 . 2 44, .7 48 . 6 44, .3 33-U 0. 420 0. 498 0. 3120 211 .0 1117 .4 162. . 1 46. .5 42, , 3 50, . 1 45, .6 33-V 0. 610 O. 493 0. 3080 86 .0 104 1 , . 1 151 . , 1 29 .8 27 , . 1 39, ,0 35 , .5 33-W 0 . 800 0. 495 0. 3030 31 .0 1438 .9 208. 8 15. .5 14 , , 1 34. , 1 31 , .0 Cd z a o O C T J fO GO 224 Polynomial Equations f o r the Compliance versus Notch P r o p o r t i o n , Curves IE) -rs CO v—s t~-o s r + i n L D rs rs 2: . rs co ON + -3-3: 3= rs rs rs •—\ rs CO CO •—s '—• o ON • • m CO CO cn s r + + m m m — s y—* sr s r < N rs rs cO CO —• —' vO 00 m m m r ~ vD cn o O • • o o + + CO cn /—V rs rs S—V rs /— rs rs CO CO cfl cfl •—' — rH cn rH VO oo 00 s r r~ 00 CN m sr r ~ m ON cn r-. CN cn r-l rH CN + + + + cn cn cn cn cn cn cn /—v S—V *— Cfl CO cd CO '—s v—' cn • • • • 00 ON o CN vO CN s r 00 t-~ rH 00 s r rH 1 + I I sr s r s r s r ^—v ^—\ c o c ^ t r > c o c ^ c o c o r o o o r o ro /-~N /• \ /—\ \ - V —S /-—-v. /—\ /""N /" N. /-—V /—S r s r s r s r s r s r s r s r s rs r s r s r s cfl- CO CO CO CO CO CO CO Cfl cfl cfl cfl CO Cfl o. sr NO rH cn m cn m m m cn r ~ m CN <—i m vD o 00 cn CN CN O 00 ON rH CN rH . VD CN CN sr o r ~ CN m o o ST 00 00 sr O ON rH ON m vO 00 00 cn m ON O O o m r» • ON cn • I-- ON vO rH r» o o cn m m o CN rH o O NO rH rH CN 1 1 + + + + i + 1 + + 1 1 + cfl CO Cfl cfl cfl cfl — ' ^ — ' ^ — ' — ' v—^ O VD m m s r cn • • • « CN • O CN oo vD • cn o 00 s r cn 00 r -NO rH m rH rH m rH + 1 + + + 1 cn cn cn cn cn cn r—v ' — s ' N C N C N C N C N C N C N C N C N C N C N C N C N C N C N C N C N CN o S S S S S S S - S S S S - : s rs" rs : s rs —< Cfl cfl CO CO cfl cfl cfl Cfl Cfl cfl CO cfl CO co cfl cfl CN 00 00 cn o CN cn m o vD vD 00 vD vO 00 r-^  cn ON rH CN ON r-^  rH rH ON m ON s r ON m a s r cn ON CN sr rH cn vD r~ cn m rH sr cn CN 00 cn CN o cn CN sr cn 00 m o ON as o 00 s r o o o o vD CN • CN rH CN cn cn CO o m sr cn o o o o O rH O rH s r o O CN vD o o o cfl cfl cfl CO cfl Cfl — ' * — ' N ' v—J m ON s r o 00 rH • m • • rH vD ON - m cn • • rH cn m o vO sr CN ON rH s r vO ON 1 + 1 i 1 + cfl vD C N C N C N C N C N 00 '—^ ^—N ^—V /^V C N rs rs rs rs rs s r cn o + + + 1 + 1 1 + 1 + + 1 + + + 1 + r ^ ? r s s r s N 5 S r 5 N r s N r s ^ r s s ? . ^ ^ r s v ^ r s , 5 ^ r s ' CO vy TO —^' cfl —^ CO Cfl Cfl N—^ r -s r vD cn s r CN ON rH s r cn ON 00 cn r -rH o CN vD VD m CN ON rH + 1 + + + 1 m 00 r~~ rH s r rH o o rH VO sr m vD CN m cn sr m s r rs rs rs rs rs rs sr o O r - 00 s r o ON CN o rH cn cn ON sr m o rH o 'CN CN O i n cn cn rH s r CN vD o o ON ON vO rH rH cfl cfl cfl cfl cfl cfl o o o O o ON r - cn ON o cn o VO m cn CN sr rH o N S —^^  —' '—' o o o cn cn m o o rH o o CN vO 00 o o rH o o CN o VO rH cn rH CN cn CN CN cn o o o o o CN o o rH o o o O o o o o o o CN cn vD r ~ VD + + + + + + + I + + + + + I I + + + 1 CN rH o cn CN rH o sr CN rH ON vO rH sr m CN rH ON vO o s r vO vO 1 + 1 1 1 + vO sr m vD ON r-» ON vO O o o ON i n m s r r ~ O s r i—i rH rH CN cn cn C  cn vO m vD CN cn 00 s r o s r s r cn O s r sr ON s r m o o o sr s r m vD vD m cn 00 O rH CN 00 cn rH r-~ rH cn vO rH o o o sr cn • O rH s r o rH CNI m cn o o sr o o ON ON vO vD o o o o rH rH O o rH o O o o cn o o o o o O O o o o O II ll ll ll II II II II II II II II II ll ll ll ll ll II II II II II II II u o o o a U U u u o u O u c_> CJ CJ u CJ o O a CJ CJ CJ u ; j Q P Q Q Q Q O P P P p P Q P P a Q P P p P l"H Z Z Z Z Z z Z Z z Z Z z Z z Z z z Z z Z Z >* W P3 PQ PQ cq Pd PQ pq pq pq pq pq pq PQ eq pq pq PQ pq PQ pq Q O Q sr s r sr sr sr s r sr sr s r s r sr s r s r s r s r s r s r s r s r s r s r i d rH CJ z Z U W o rJ z PM • pq w a •"3 1 1 1 I I rv 1 «N < <c < < P fn SB s o o* < p fa rc pq < pq pq pq pq pq PQ PQ PQ pq rH sr s r CN CN CN CN CN CN CN CN cn <n cn cn cn CN CN CN CN CN CN CN CN CN CN CM CN CM CN CM CN cn CN o c z 1 rs I z 1 rs Z rs P M < 1o 1 < 1 o 1 < 1 o < < cn cn rH rH CN CN cn cn CN CM cn cn cn cn cn cn 225 APPENDIX D - A REVIEW OF PERTINENT LITERATURE T h i s appendix i s i n c l u d e d to give the reader an i n depth view of the l i t e r a t u r e p r e s e n t l y a v a i l a b l e . I t a l s o d e s c r i b e s v a r i o u s techniques attempted and used in the r e s e a r c h of f r a c t u r e mechanics i n f i l a m e n t a r y composite mater i a l s . The i n t e n t i o n of t h i s appendix i s not to l i s t a l l p u b l i c a t i o n s i n the s p e c i f i c area, but to d i s c u s s a group of papers which have made major impacts upon the author. Many of the papers i n c l u d e d were used as an i n i t i a l i n d i c a t i o n f o r the d i r e c t i o n t h i s work, while others were s t u d i e d f o r t h e i r techniques in data a n a l y s i s . Even more were read with great i n t e r e s t due to t h e i r c o r r o b o r a t i o n with work a l r e a d y completed by t h i s author. In a l l , the f o l l o w i n g appendix g i v e s a r e l a t i v e l y complete overview of the present s t a t e of the r e s e a r c h in t h i s a r e a . U n i - d i r e c t i o n a l Composites T h i s f i r s t segment of the d i s c u s s i o n of toughness measurement in f i b r e composite m a t e r i a l s deals with u n i -d i r e c t i o n a l composites. V a r i o u s u n i - d i r e c t i o n a l m a t e r i a l s have been the o b j e c t s of a great deal of r e s e a r c h . As noted by R. J . Sanford and F. R. S t o n e s i f e r 2 2 , the f a i l u r e of u n i - d i r e c t i o n a l f i b r e composites can be analysed with the e x i s t i n g theory of f r a c t u r e mechanics. T h i s theory s u f f i c e s , s i n c e crack extension i s achieved by the formation of plane s u r f a c e s and can be completely d e s c r i b e d by the s i n g l e parameter, crack l e n g t h . In a d d i t i o n , the u n i - d i r e c t i o n a l composite i s l i k e l y a more s e n s i t i v e i n d i c a t o r of the i n f l u e n c e of changes in m a t e r i a l s v a r i a b l e s than any other lay-up angle, s i n c e there i s l i t t l e f i b r e r e i n f o r c i n g e f f e c t . The major reason, however, for the great number of papers i n v o l v i n g u n i - d i r e c t i o n a l m a t e r i a l s probably stems from e a r l y work by Wu. 2 3 Wu d i s c o v e r e d that under s p e c i f i c c o n d i t i o n s the techniques of i s o t r o p i c f r a c t u r e mechanics can be d i r e c t l y a p p l i e d to composite m a t e r i a l s . The c o n d i t i o n s were: i . The o r i e n t a t i o n of the flaw with respect to the p r i n c i p a l a x i s of symmetry must be f i x e d . i i . The s t r e s s i n t e n s i t y f a c t o r s d e f i n e d f o r the a n i s o t r o p i c cases must be c o n s i s t e n t with the i s o t r o p i c case i n s t r e s s d i s t r i b u t i o n and i n crack displacement modes. 226 i i i . The c r i t i c a l o r i e n t a t i o n c o i n c i d e s with one of the p r i n c i p a l d i r e c t i o n s of e l a s t i c symmetry. U n i - d i r e c t i o n a l m a t e r i a l s would seem to s a t i s f y a l l of these r e s t r i c t i v e c o n d i t i o n s . Many m a t e r i a l systems have been evaluated using a v a r i e t y of t e s t specimen geometries. The most popular t e s t specimen would seem to be the notched t e n s i l e specimen of which there are three b a s i c types. These three notched t e n s i l e specimens a r e : the s i n g l e edge notch (SEN), the double edge notch (DEN), and the c e n t r e notch (CN) geometries. Other specimen geometries i n c l u d e the three and four p o i n t bending beam, the compact t e n s i o n specimen, and the Charpy Impact specimen. Beaumont and P h i l l i p s 9 , using v a r i o u s f i b r e - e p o x y systems, found that notch s e n s i t i v i t y i s dependent upon the shear s t r e n g t h s of the m a t e r i a l s . For the most p a r t , they found that the untreated carbon f i b r e s and the S-glass f i b r e composites are notch i n s e n s i t i v e due to low shear s t r e n g t h s . The s u r f a c e t r e a t e d carbon f i b r e system shows notch s e n s i t i v i t y and c o r r e s p o n d i n g l y higher shear s t r e n g t h s . T h i s notch i n s e n s i t i v i t y i s o f t e n c h a r a c t e r i z e d , d u r i n g notched t e n s i l e t e s t i n g , by f r a c t u r e p e r p e n d i c u l a r to the notch ( p a r a l l e l to the f i b r e s ) . T h i s f r a c t u r e s t a r t s from the notch root and propagates to the g r i p p i n g area without y i e l d i n g c r o s s f i b r e crack propagation. Wright and I a n n u z z i 2 0 note t h i s same p a r a l l e l f r a c t u r e in t h e i r t e s t i n g of a carbon fibre-epoxy system. Of i n t e r e s t i n t h i s work i s that the f i b r e type i s unmodified, however the volume f r a c t i o n of f i b r e i s v a r i e d . There are l a r g e d i f f e r e n c e s i n the f a i l e d samples. The specimens with g r e a t e r volume f r a c t i o n s show shear f a i l u r e s of the type noted by Beaumont and P h i l l i p s while t e s t i n g untreated f i b r e m a t e r i a l s . The samples with the lower volume f r a c t i o n , i n c o n t r a s t , show behaviour much more l i k e the notch s e n s i t i v e , t r e a t e d f i b r e m a t e r i a l of Beaumont and P h i l l i p s . T h i s i n t e r - f i b r e shear or debonding i s a l s o seen i n notched impact specimens. 5 In t h i s case f i b r e s ahead of the notch remain unbroken while s p l i t t i n g ' o c c u r s on e i t h e r s i d e of the notch. T h i s p a r t i c u l a r specimen geometry e f f e c t i s a l s o noted i n three p o i n t bending beam samples where the shear s t r e n g t h i s low. To complete t h i s d i s c u s s i o n of t e s t i n g problems r e l a t e d to specimen geometry, the compact t e n s i l e specimen geometry should be touched upon. Very few authors have 227 used the compact t e n s i l e specimen geometry, p a r t i c u l a r l y i n d e a l i n g with u n i - d i r e c t i o n a l m a t e r i a l s . S l e p e t z and C a r l s o n 2 " d i s c o v e r e d t h a t , while v a r y i n g the f i b r e , o r i e n t a t i o n with respect to the l o a d i n g a x i s , the f r a c t u r e always progresses p a r a l l e l to the f i b r e s . Thus, using both g l a s s and carbon f i b r e , they found that any attempt to f r a c t u r e across the f i b r e only leads to the breakage of one of the two l o a d i n g arms. In f a c t , with the f i b r e o r i e n t e d i n the l o a d i n g d i r e c t i o n and the l o a d i n g arms r e i n f o r c e d the f a i l u r e continues to be the shearing of one of the l o a d i n g arms. T h i s o b s e r v a t i o n i s i n keeping with the r e s u l t s noted in the notched t e n s i l e specimens. One f i n a l note regarding these i n t e r - f i b r e shear f a i l u r e s o r i g i n a t e s in a paper by Awerbach and Hahn 6 concerning a boron-aluminum composite. I t was found that with i n c r e a s i n g l o a d , a d d i t i o n a l crack extension and a d d i t i o n a l l o n g i t u d i n a l p l a s t i c zones are observed. The spacing between adjacent a x i a l p l a s t i c zones approximately equals the f i b r e spacing. T h i s of course leads to a b l u n t i n g of the crack t i p and makes measurement of notched t e n s i l e s t r e n g t h d i f f i c u l t . T h i s i n f o r m a t i o n of a l o n g i t u d i n a l p l a s t i c zone in the r e l a t i v e l y d u c t i l e aluminum matrix does seem to correspond to the i n t e r - f i b r e f a i l u r e i n the p r e v i o u s l y d e s c r i b e d r e s i n matrix system. Another "mechanical" v a r i a b l e of i n t e r e s t i s the crack t i p r a d i u s . T y p i c a l l y , t h i s i s not c o n s i d e r e d to be of great consequence i n the f i b r e composite due to the d i s c o n t i n u o u s nature of the m a t e r i a l . Problems regarding the i n t r o d u c t i o n of a sharp crack of small r a d i u s are compounded by the aforementioned deformation at the crack t i p . Beaumont and P h i l l i p s found that even though i t i s d i f f i c u l t to repeatedly induce a sharp crack t i p , i t i s c l e a r that such sharpening does y i e l d a decrease i n s t r e n g t h . The authors note t h a t , none of the K 1 C or G I C/2 values are lower than the t h e o r e t i c a l values and i t appears that as the r e l a t i v e crack sharpness (the crack l e n g t h d i v i d e d by the crack t i p r a d i u s ) i n c r e a s e s , the data f a l l s c l o s e r to that p r e d i c t e d by LEFM. T h i s leads to the t e n t a t i v e suggestion that "sharp" cracks w i l l tend to obey LEFM. With respect to t h i s same v a r i a b l e , Bader and E l l i s 7 , u sing a Charpy Impact system, note a c r i t i c a l value f o r the span-to-notch depth r a t i o . These authors found that at span-to-depth r a t i o s below the c r i t i c a l v alue, the f r a c t u r e mode i s one of e x t e n s i v e d e l a m i n a t i o n , whereas above the c r i t i c a l value a compression i n i t i a t e d f l e x u r a l f a i l u r e i s observed. These same authors f e e l that the notch t i p r a d i u s i s not important. Using the c r i t e r i o n as d e s c r i b e d by Beaumont and P h i l l i p s , however, the r e l a t i v e crack sharpness i s changed with each new notch l e n g t h . 228 Bader and E l l i s conclude that due to energy c o n s i d e r a t i o n s , the Charpy Test i s of very d o u b t f u l v a l i d i t y f o r composite m a t e r i a l t e s t i n g . A l l other authors d i s c u s s e d i n t h i s s e c t i o n have concluded that the t e s t specimens used give reasonable r e s u l t s . Wright and Iannuzzi even go so f a r as to conclude that the p r i n c i p l e s of LEFM can be used to d e s c r i b e the f a i l u r e of carbon r e i n f o r c e d epoxy specimens r e s p e c t i v e of whether the specimens f a i l by t r a n s v e r s e crack propagation or by l o n g i t u d i n a l s p l i t t i n g . The q u e s t i o n of whether or not LEFM can be a p p l i e d to the measurement of toughness i n u n i - d i r e c t i o n a l composite m a t e r i a l s can now be d i s c u s s e d . As mentioned i n i t i a l l y , Wu s t a t e d the f o r the case of u n i - d i r e c t i o n a l f i b r e composite m a t e r i a l s LEFM would apply. Some authors agree with t h i s statement and have gone ahead, with l i t t l e or no q u e s t i o n , to apply t h i s t h e o r y . 2 0 2 2 Conversely, Beaumont and P h i l l i p s note that under s p e c i f i c circumstances LEFM may apply. They, along with o t h e r s 5 6 7 8 , b e l i e v e that depending upon the f r a c t u r e mode, other c o n d i t i o n s are prese n t . For i n s t a n c e , Beaumont and P h i l l i p s conclude that the work of f r a c t u r e of carbon f i b r e composites i s more c l o s e l y approximated by a model i n which the i n t e r f a c i a l shear s t r e s s i s maintained during p u l l - o u t , than a debonding model. The reverse ,they s t a t e , i s true f o r the S-glass f i b r e composites. More than.one paper concerns i t s e l f with attempting to analyze the r e s u l t s i n more than one way to check f o r c o n s i s t e n c y . In general however, the main p o i n t at which most authors tend to q u e s t i o n the a p p l i c a t i o n of Mode 1 f r a c t u r e i s when crack e x t e n s i o n i s not c o l l i n e a r with the i n i t i a l pre-machined notch. When t h i s n o n - c o l l i n e a r crack growth becomes apparent, a common t o p i c of d i s c u s s i o n i s the use of mixed mode, or S c theory. T h i s theory does not r e l y on the l i m i t i n g process f o r d e r i v i n g the energy r e l e a s e e x p r e s s i o n and re p r e s e n t s a fundamental departure from the c l a s s i c a l concept. I t i s based on the crack t i p energy d e n s i t y reaching a c r i t i c a l value at f r a c t u r e i n i t i a t i o n which can account f o r the a r b i t r a r y v a r i a t i o n of load p o s i t i o n , f i b r e d i r e c t i o n , volume f r a c t i o n , a n d other p h y s i c a l parameters present i n the composite as a f u n c t i o n of the d i r e c t i o n of crack i n i t i a t i o n . 2 5 2 6 2 7 T h i s method seems promising, however, l i t t l e experimental work has been done in c o n j u n c t i o n with the S c theory. In f a c t , once the composite i s no longer u n i - d i r e c t i o n a l t h i s theory g i v e s i n c r e a s i n g problems. 229 Thus, i t would seem that three basic approaches are available: i . a s t a t i s t i c a l theory to predict the number of cut fibres in a composite structure and to investigate what effect these cut fibres w i l l have on structural s t r e n g t h 2 8 ; i i . extention of linear e l a s t i c fracture mechanics theory to orthotropic or anisotropic materials and then to fibrous composites; and i i i . a study of cracks in a heterogeneous material or at an interface and the extension of that theory to the case of a fibrous composite. 8 Delamination of Uni-directional Composites Delamination toughness of u n i - d i r e c t i o n a l fibre composite materials i s actually a s p e c i f i c case in the toughness of uni-directional composites. In this case, testing is done with the f i b r e d i r e c t i o n perpendicular to the direction of loading. Of the three major breakdowns of orientation discussed here, the interlaminar fracture toughness seems the least applicable to a general determination of fracture toughness in angle-ply materials. This mode must be considered however, since in most cases mul t i - d i r e c t i o n a l materials do include p l i e s of this orientation with respect to the major load axis. Devitt, Schapery, and B r a d l e y 2 9 , in discussing the importance of this delamination mode, state that the growth of interlaminar flaws (delamination) is an important part of the f a i l u r e process in many laminates. Compressive fatigue appears to be an especially severe type of loading in producing delaminations, and out-of-plane stresses developed through compressive loading and l o c a l buckling are thought to be the primary cause of such delamination type fractures. These observations indicate that the delamination fracture toughness may be the c r i t i c a l toughness parameter for fatigue stressing where in-plane stresses are compressive. These same authors use an a x i a l l y s p l i t beam geometry as a test approach to obtain the fracture toughness for the opening mode of delamination in a u n i - d i r e c t i o n a l glass-epoxy composite. This thin s p l i t beam geometry gives stable crack growth and is therefore suited to the determination of a relationship between slow crack speed and the energy release rate. Bascom, Bitner, Moulton, and S i e b e r t 3 0 also use an a x i a l l y s p l i t beam geometry. This double cantilever beam specimen i s , however, width tapered for a constant change 230 in compliance with crack l e n g t h . The use of t h i s type of specimen allows the c a l c u l a t i o n of f r a c t u r e energy without the s p e c i f i c knowledge of the. crack l e n g t h . T h i s i s based on the general e x p r e s s i o n : G 5= (P 2/2b)(dC/da) where, f o r i d e a l e l a s t i c beams; dC/da = 2 4 a 2 E " 1 h ' 3 b " 1 and thus; G l c= 1 2 P 2 a 2 E " 1 h " 3 b " 1 I f the specimen i s then width tapered to g i v e a constant r a t i o of a/b, then G I C can be determined from P and E a l o n e . In a small s e c t i o n of a d i s c u s s i o n of toughness in u n i - d i r e c t i o n a l f i b r e composites, S l e p e t z and C a r l s o n 2 4 i n v e s t i g a t e the 90° or i n t e r l a m i n a r mode. They s t a t e that only when e = 90°, would crack growth be expected to be by Mode 1 f r a c t u r e o nly. T h i s statement would seem obvious s i n c e i n t h i s case the f r a c t u r e i s p r i m a r i l y c o n s t r a i n e d i n a homogeneous e l a s t i c medium, the i n t e r - f i b r e matrix. Experiments using a compact t e n s i l e specimen geometry show, however, the e x i s t e n c e of f i b r e b r i d g i n g behind the advancing crack t i p . Through f u r t h e r experiments t h i s group r e a l i z e d that t h i s f i b r e b r i d g i n g a c t i o n tends to increase both the specimen s t i f f n e s s and toughness . Thi s e f f e c t seems much more s i g n i f i c a n t i n the S-glass specimens than in the corresponding g r a p h i t e f i b r e specimens. The authors a t t r i b u t e t h i s v a r i a t i o n to the higher s t i f f n e s s of the g r a p h i t e f i b r e s . T h i s work would then seem to p o i n t to a g r e a t e r i n f l u e n c e of i n t e r l a m i n a r toughness than would be i n i t i a l l y be expected. In f a c t , in t h e i r c o n c l u s i o n s r e g a r d i n g the S-glass system, S l e p e t z and C a r l s o n note that in u n i - d i r e c t i o n a l specimens, f r a c t u r e toughness i s dependent on crack l e n g t h i n the e a r l y stages of crack growth due to the development of the network of f i b r e s b r i d g i n g the crack plane behind the advancing t i p . Even though Bascom et a l . were b a s i c a l l y i n t e r e s t e d i n modifying the p r o p e r t i e s by adding e l a s t o m e r i c toughening agents, they d i d take note of trends corresponding to specimen s i z e v a r i a t i o n s . From the l i m i t e d data used, t h i s group saw an apparent trend towards higher G I C values with i n c r e a s i n g specimen l e n g t h and d e c r e a s i n g h e i g h t . In c o n t r a s t , D e v i t t et a l , using a non-l i n e a r beam theory to s u b s t a n t i a t e t h e i r experimental r e s u l t s , note that the accuracy of the a n a l y s i s used i s supported by the experimental r e s u l t s from each of the 231 three specimen t h i c k n e s s e s . C o n s i d e r i n g the amount of data presented by each group of authors, i t would seem u n l i k e l y that any f i r m c o n c l u s i o n c o u l d be drawn regarding e f f e c t s of specimen s i z e and geometry. Each of the specimen types do however allow the e s t i m a t i o n of the instantaneous crack l e n g t h , which i s of great value p a r t i c u l a r l y i n opaque m a t e r i a l s . U t i l i z i n g a t h e o r e t i c a l approach to the energy r e l e a s e r a t e f o r a n o n - l i n e a r beam combined with the e f f e c t of v i s c o e l a s t i c behaviour, D e v i t t et a l . make comparisons with t h e i r experimental v a l u e s . Using the a n a l y s i s and s e v e r a l measured values the instantaneous crack l e n g t h may be c a l c u l a t e d . T h i s c a l c u l a t e d value i s shown to be extremely c l o s e to the crack l e n g t h values measured. Thus these authors do f o l l o w LEFM theory with p a r t i c u l a r emphasis on the i d e a l i z e d v i s c o e l a s t i c crack growth theory. It would seem from these papers, that f o r delamination f r a c t u r e , the authors r e l y on the use of LEFM only q u e s t i o n i n g the importance of f i b r e b r i d g i n g . Angle-Ply Composites The p r e v i o u s two s e c t i o n s have d e a l t with work devoted to the measurement of f r a c t u r e toughness in u n i - d i r e c t i o n a l f i b r e composite m a t e r i a l s . These m a t e r i a l s , as noted i n the e a r l i e s t s e c t i o n , have been t e s t e d p r i m a r i l y s i n c e e a r l y r easearch concluded that they met r e s t r i c t i v e c o n d i t i o n s which allowed the use of LEFM. U n i - d i r e c t i o n a l m a t e r i a l s are however of l i t t l e design i n t e r e s t i n s t r u c t u r e s and thus f r a c t u r e c r i t e r i a have remained r e l a t i v e l y unobtainable f o r p r a c t i c a l laminates. Beaumont and P h i l l i p s d i s c u s s e d r e s u l t s of an author named G i l l i l a n d r e garding notch s e n s i t i v i t y . They p o i n t out r a t i o s of t e n s i l e and shear s t r e s s e s with respect to u n i - d i r e c t i o n a l m a t e r i a l s and give c r i t i c a l r a t i o s f o r notch s e n s i t i v i t y . If t h i s d i s c u s s i o n were extended f u r t h e r the r e s u l t would be a r e a l i z a t i o n that in angle-p l i e d m a t e r i a l s the r a t i o would i n d i c a t e obvious notch s e n s i t i v i t y . T h i s p o i n t i n i t s e l f g i v e s evidence f o r the p o s s i b i l i t y of the a p p l i c a t i o n of LEFM to a n g l e - p l i e d m a t e r i a l s . Subsequent res e a r c h by v a r i o u s groups has i n c l u d e d c o n s i d e r a b l e work i n v o l v i n g m a t e r i a l notch s e n s i t i v i t y . In most cases regarding carbon f i b r e - e p o x y 7 1 6 1 7 1 8 2 6 and boron-aluminum 2 7 the r e s e a r c h e r s have noted that notch s e n s i t i v i t y i n c r e a s e s as the notch length i s extended. Much i n i t i a l r e s e a r c h on a n g l e - p l i e d composite m a t e r i a l s p e r t a i n e d to e i t h e r the t e n s i l e f a c t o r s r e l a t e d 232 to c e n t r a l c i r c u l a r h o l e s . 1 0 1 2 2 3 3 1 3 2 3 3 3 4 3 5 Test specimen geometries vary, but i n essence are the same as those d i s c u s s e d with respect to the u n i - d i r e c t i o n a l m a t e r i a l s . Most of these papers expand along the l i n e s used in u n i - d i r e c t i o n a l t e s t i n g . Thus, depending upon the s p e c i f i c a n a l y s i s , the author e i t h e r attempts to prove or d i s p r o v e the use of LEFM by a d i s c u s s i o n of areas such as energy of f a i l u r e . K o n i s h 1 0 views the s i t u a t i o n from a d i f f e r e n t vantage point and uses a t h e o r e t i c a l base to d i s c u s s the t o p i c of s t r e s s i n t e n s i t y f a c t o r s ( S I F ) . I t was found, with t e s t s s u b s t a n t i a t i n g the theory, that the i n f l u e n c e of i s o t r o p i c m a t e r i a l p r o p e r t i e s on the SIF i s c l o s e l y coupled with that of specimen geometry. Using a numerical a n a l y s i s method, to l a r g e l y c o r r e c t f o r boundary e f f e c t s , the author o b t a i n s very accurate r e s u l t s . Separate models are r e q u i r e d f o r the c e n t r e notched and double edge notched specimens due to d i f f e r e n c e s i n the degrees of i m p l i c i t symmetry. I t i s i n t e r e s t i n g to note that the e f f e c t of v a r i a b l e crack l e n g t h on Konish's a n i s o t r o p y f a c t o r i s much d i f f e r e n t i n the two specimen types. That i s , the i n f l u e n c e of m a t e r i a l a n i s o t r o p y i n c r e a s e s with crack l e n g t h i n the c e n t r e notched specimens and decreases with crack l e n g t h i n the double edge notch specimens. T h i s leads to the assumption that the e f f e c t s of a n i s o t r o p y i n c r e a s e as the crack t i p approaches a specimen boundary. The c o n c l u s i o n s of Konish's work tend to p o i n t to the a p p l i c a t i o n of i s o t r o p i c SIF, and t h e r e f o r e LEFM, to angle-p l y composite m a t e r i a l s . In p a r t i c u l a r , t h i s c o n c l u s i o n i s i n t e r e s t i n g i n that i t s t a t e s that some r e d u c t i o n of a n i s o t r o p i c i n f l u e n c e s may occur simply because a n g l e - p l y laminates are l e s s d i r e c t i o n a l than are c r o s s p l y laminates. The c o n c l u s i o n a l s o p o i n t s to the c o n t r o l of specimen geometry as a method of reducing a n i s o t r o p y e f f e c t s . In f a c t , s i n g l e edge notch t e n s i l e specimens or bending beam specimens are suggested as being p r e f e r r e d due to the fewer number of degrees of i n - p l a n e symmetry. In e a r l i e r work, Konish has c o l l a b o r a t e d with Swedlow and C r u s e 1 1 i n the use of a three p o i n t bend specimen. The two major reasons fo r the use of t h i s geometry, at that time, were the ease of a p p l i c a t i o n and the e x i s t e n c e of an ASTM T e n t a t i v e Method of t e s t i n g . The group d i d however show t h a t , as noted i n the s e c t i o n on u n i - d i r e c t i o n a l m a t e r i a l s , the f r a c t u r e mechanism seems crack dominated. T h i s crack dependence leads Konish et a l . to conclude that i n many cases the procedures of LEFM can be a p p l i e d . S e v e r a l papers d e s c r i b e the use of the compact t e n s i l e specimen or a d e r i v a t i v e of that geometry. S l e p e t z and C a r l s o n , in comparing a g l a s s f i b r e - e p o x y system and a carbon fib r e - e p o x y system, found a great d i f f e r e n c e i n the 233 damage zones. The damage zone, in the g l a s s fibre-epoxy t e n s i l e specimen, i s c o n s i d e r a b l y l a r g e r than the p l a s t i c zone ahead of the crack t i p in a metal specimen and tends to dominate subsequent behaviour. T h i s ever expanding damage zone seems to extend to f a i l u r e without the development and growth of a through c r a c k . Thus, with no i n d i c a t i o n of crack propagation, the a p p l i c a t i o n of LEFM to such a g l a s s fibre-epoxy system seems i n a p p r o p r i a t e . Conversely, the same authors were ab l e to propagate a crack i n the carbon f i b r e - e p o x y systems. Other damage mechanisms i n c l u d i n g debonding, delamination, and some load d i r e c t i o n a l s p l i t t i n g at the l e a d i n g edge of the propagating crack were a l s o observed. These damage mechanisms seem to be secondary modes. Thus, from the r e s u l t s , S l e p e t z and C a r l s o n conclude that while the work of f r a c t u r e i n a n g l e - p l y laminates does vary with load o r i e n t a t i o n , the same carbon f i b r e - e p o x y specimens do not e x h i b i t a dependence of toughness on crack l e n g t h . Before l e a v i n g the matter of specimen geometry and i t s e f f e c t s , i t i s i n t e r e s t i n g to take note of a unique specimen m o d i f i c a t i o n . Due to mechanical e f f e c t s , the p r e v i o u s authors and others have found that the standard compact t e n s i l e specimen i s l e s s than p e r f e c t when a p p l i e d to f i b r e composites. In many cases the compact t e n s i l e specimens are modified by e i t h e r reinforcement of the l o a d i n g arms, or by the i n t r o d u c t i o n of s i d e grooves. Jea and F e l b e c k 3 6 on the other hand use a unique metal compact t e n s i l e framework which holds the specimen and applys the l o a d to the t h i n notched beam shaped laminate. T h i s geometry i s expected to use l e s s m a t e r i a l than e i t h e r a c o n v e n t i o n a l compact t e n s i l e specimen or a bending beam specimen and due to the l a c k of t h i c k n e s s , g i v e s f a i l u r e at more e a s i l y a p p l i e d l o a d s . For each of the many specimen types i n use, and e f f e c t s noted, there seem as many v a r i o u s methods for i n t e r p r e t i n g the b a s i c r e s u l t s . P h i l l i p s 2 1 , c o n t i n u i n g with a n g l e - p l y specimens where he and Beaumont l e f t o f f , uses an e f f e c t i v e modulus term E*. T h i s e f f e c t i v e modulus i s a f u n c t i o n of the e l a s t i c compliance tensor of a given m a t e r i a l and thus f o r a crack propagating i n a s p e c i f i c d i r e c t i o n , E* can be c a l c u l a t e d . The idea behind t h i s e f f e c t i v e modulus term i s that the use of the Young's modulus, while a p p l y i n g to e l a s t i c a l l y i s o t r o p i c m a t e r i a l s , does not apply to e l a s t i c a l l y a n i s o t r o p i c m a t e r i a l s . P h i l l i p s a l s o proposed that the use of a (0/90) laminate p l y o r i e n t a t i o n allows the g r e a t e s t p o s s i b i l i t y f o r the a p p l i c a t i o n of LEFM to a n g l e - p l y f i b r e composite m a t e r i a l s . T h i s seems to be born out by the f a c t that authors using other laminate o r i e n t a t i o n t y p i c a l l y have d i f f i c u l t y p ropagating a crack i n the d e s i r e d path. T h i s problem, as i n u n i - d i r e c t i o n a l systems, leads to attempts to apply 234 mixed mode t h e o r i e s . In a paper d i s c u s s i n g mixed mode f r a c t u r e of g r a p h i t e -epoxy composites M o r r i s and Hahn 3 7 d e s c r i b e the major work to date in mixed mode f r a c t u r e . In g e n e r a l , the work was p r e v i o u s l y generated for u n i - d i r e c t i o n a l composites with a crack p a r a l l e l to the f i b r e d i r e c t i o n . For t h e i r work i n a n g l e - p l y specimens, M o r r i s and Hahn decided upon the use of a simple model based on the idea of an e f f e c t i v e normal crack of a p p r o p r i a t e l e n g t h . To a t t a i n toughness values t h i s l e n g t h i s then s u b s t i t u t e d i n t o an equation developed for normal c r a c k s . A method now seeing e x t e n s i v e a p p l i c a t i o n to these composite m a t e r i a l systems i n the two parameter compliance technique. O c h i a i and Peters and o t h e r s 3 7 3 8 use t h i s technique to f i n d crack propagation r e s i s t a n c e values from e x p e r i m e n t a l l y determined compliance curves. The i n t e r e s t i n g aspect of the r e s i s t a n c e , K^, technique i s that some authors f e e l that a m a t e r i a l constant of design importance may be developed. T h i s i s d i f f e r e n t from the common compliance technique in which c a l i b r a t i o n curves must be generated f o r each new specimen geometry, p l y o r i e n t a t i o n , t h i c k n e s s , and s i z e . V a r i o u s other methods have been used to a r r i v e at numerical values from t e s t r e s u l t s . These i n c l u d e the breakdown of the energy of f a i l u r e i n t o sub-groups such as p u l l - o u t , delamination surface and main crack s u r f a c e e n e r g i e s 3 6 , the use of notched and unnotched r e s u l t s to a r r i v e at notch s e n s i t i v i t y c o r r e c t i o n s , and even c o r r e c t i o n s to l i n e a r i z e a n o n - l i n e a r s t r e s s s t r a i n curve. These and more methods are a p p l i e d throughout the l i t e r a t u r e d e a l i n g with f r a c t u r e toughness of composite m a t e r i a l s . I t would seem, however, that due to the great number of v a r i a b l e s i n v o l v e d , no one method of t e s t i n g , or for that matter, of i n t e r p r e t i n g the r e s u l t s has been found. In most cases i n d i v i d u a l s f i n d methods which can, t y p i c a l l y with some c o r r e c t i o n , be a p p l i e d to the s p e c i f i c system of i n t e r e s t . I n c o n s i s t e n c i e s do appear, however, i n cases where more than one m a t e r i a l system or t e s t i n g method i s used. Conclu s i o n s It would seem q u i t e easy to obt a i n s t r e n g t h and toughness values f o r s p e c i f i c t e s t specimens, however i f t h i s data cannot be simply and a c c u r a t e l y a p p l i e d to many s i t u a t i o n s r e g a r d l e s s of s i z e , specimen geometry or laminate o r i e n t a t i o n then the values are of l i t t l e use as design c r i t e r i a . Making the task even more d i f f i c u l t i s the f a c t that t y p i c a l l y these m a t e r i a l s are at a premium and due to the type of a p p l i c a t i o n s in which they are used, s a f e t y f a c t o r s are n e c e s s a r i l y low. T h i s i n d i c a t e s that i f 235 a m a t e r i a l constant i s to be generated and used, the technique must be of high enough q u a l i t y and r e p r o d u c i b i l i t y to ensure extreme accuracy. Researchers to date have shown the a p p l i c a b i l i t y of s p e c i f i c t e s t methods and data r e d u c t i o n schemes for c e r t a i n f i b r e composite systems. The depth of work accomplished however and the immense number of v a r i a b l e s i n v o l v e d continues to keep an o v e r a l l s o l u t i o n out of reach. T h i s i s not to say that the r e s u l t s to the present have given no i n s i g h t i n t o the o v e r a l l problem. Work by C r u s e 3 1 3 8 i n p a r t i c u l a r would seem to i n d i c a t e t h a t , f o r a graphite-epoxy system, there appears to be no s i g n i f i c a n t amount of independent crack growth in any p l y p r i o r to f r a c t u r e . R e s u l t s of t h i s type l e a d to the p o s s i b i l i t y of not only t r e a t i n g the m a t e r i a l as a homogeneous body, but a l s o to the a p p p l i c a t i o n of procedures such as a damage zone c o r r e c t i o n f a c t o r . The work of K o n i s h 1 0 would seem to give a b a s i c guide f o r specimen geometry. T h i s work giv e s preference to s i n g l e notched specimens fo r symmetry reasons as w e l l as t e s t s i m p l i c i t y . A l s o of i n t e r e s t i n t h i s area are the v a r i o u s methods methods of d e r i v i n g and a p p l y i n g a n i s o t r o p y and f i n i t e width c o r r e c t i o n f a c t o r s . The major drawbacks, however, to even t h i s work, are the e f f e c t s of p l y o r i e n t a t i o n and v a r i o u s f i b r e - m a t r i x systems. Since f a i l u r e modes change with f i l a m e n t o r i e n t a t i o n , the f r a c t u r e energy i s a n t i c i p a t e d to be a f u n c t i o n of laminate conf i g u r a t i o n . While much promising work has been done using t r e a t e d carbon fibre-epoxy composites, other f i b r e systems give great d i f f i c u l t i e s . For g l a s s f i b r e s and even untreated carbon f i b r e s the amount of f i b r e p u l l - o u t and the l a r g e damage zone makes c o n v e n t i o n a l a n a l y s i s q u e s t i o n a b l e at best. Models of the mechanisms t a k i n g p l a c e have been p r e s e n t e d 1 8 3 6 3 7 3 9 but too l i t t l e data i s a v a i l a b l e to give a good i n d i c a t i o n of the accuracy of these types of a n a l y s i s. It would seem that a p o s s i b l e method of modelling the o v e r a l l s i t u a t i o n would be to determine how the toughness of an u n i - d i r e c t i o n a l p l y changes with o r i e n t a t i o n . Using t h i s knowledge, the model would then determine a method of adding p l i e s , and the corresponding p r o p e r t i e s , to a r r i v e at a s i n g l e value f o r the completed laminate. T h i s idea of the summation of the e f f e c t s of i n d i v i d u a l p l i e s does not seem to have been c o n s i d e r e d by the m a j o r i t y of r e s e a r c h e r s . Thus, i n c o n c l u s i o n , i t would seem that f o r the most part too few r e s u l t s are p r e s e n t l y a v a i l a b l e and too l i t t l e work i s being done in any one p a r t i c u l a r d i r e c t i o n to 2 3 6 a r r i v e a t any one s o l u t i o n t o the measurement of toughness i n c o m p o s i t e m a t e r i a l i n the immediate f u t u r e . A good u n d e r s t a n d i n g of the f r a c t u r e mechanisms i n v o l v e d f o r a.few-s p e c i f i c systems has been a t t a i n e d but due t o the immense number of v a r i a b l e s much more work i s needed f o r a broader u n d e r s t a n d i n g of the s u b j e c t . 

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