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Fatigue damage propagation in graphite/epoxy composites Yavuz, Ömer 1984

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FATIGUE DAMAGE PROPAGATION IN GRAPHITE/EPOXY COMPOSITES by OMER YAVUZ B.Sc, The University Of Manchester Institute Of Science And Technology, Manchester, England, 1982 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 t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA February 1984 © Omer Yavuz, 1984 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements fo r an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I further agree that permission for extensive copying of t h i s t h e s i s for scholarly purposes may be granted by the head of my department or by h i s or her representatives. I t i s understood that copying or publication of t h i s thesis f o r f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of n e r A L L _ U » Q . G I C _ A L " £ . M & i * J £ £ . A . I * J c The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date DE-6 (3/81) i i Abstract A series of tests was performed to determine the increase in the crack length or fatigue damage of graphite/epoxy composites under tension-tension fatigue using t r a v e l i n g microscope, tetrabromoethane enhanced radiography and compliance techniques. Hercules As/3501-6 graphite fibre/epoxy prepreg was used to produce laminates which were subsequently cut into compact tension sample geometry. [90/0] 8 i ply configuration was used in the preparation of the laminates. Fatigue damage was observed to be in the form of a 'damage zone' rather than a single crack, which increased in size in both the 0° and 90° di r e c t i o n s during fatigue. The damage followed three stages, during the whole fatigue l i f e . The f i r s t stage was the acceleration; the intermediate stage was the deceleration and the f i n a l stage was the reacceleration of the damage. As a resu l t of t h i s behaviour the Paris approach was found to be non-valid for t h i s material. Change in the compliance was observed during fatigue and this change revealed the same three stages as the development of the damage zone. i i i Table of Contents Table Of Contents i i i L i s t of Tables iv L i s t of Figures v CHAPTER I. INTRODUCTION 1 1.1 General Review ..1 1.2.1 Tension-Tension And Tension-Compression Fatigue 3 1.2.2 E f f e c t Of Frequency On Fatigue 6 1.2.3 E f f e c t Of Manufacturing On Fatigue 7 1.2.4 E f f e c t Of Stacking Sequence On Laminate Strength 8 1.2.5 Micromechanisms Of Fatigue 10 1.2.6 Damage Zone Detection Methods And Crack V e l o c i t y Studies 13 1.2.7 Formulating The Decay In S t i f f n e s s During Fatigue 16 1 .3 Theory 18 1.3.1 Fracture Toughness Equations 18 1.3.2 Fatigue Testing Equations 19 1.3.3 Compliance Tests 21 1.4 Purpose . 22 CHAPTER I I . PROCEDURE 23 2.1 Laminate And Sample Preparation 23 2.2 S t a t i c Tensile Fracture Testing 25 2.3 Fatigue Testing 26 2.4 Compliance Testing 29 2.5 Determining The Weight And Volume Fraction Of The Fibres 31 CHAPTER I I I . RESULTS 33 3.1 Tensile Fracture And Load Curve Analysis 33 3.2 Fatigue Testing Results 35 3.2.1 Fatigue L i f e Of The Material 35 3.2.2 Fatigue Crack Length Measurements 36 3.2.3 Change In The Compliance During Fatigue 39 3.2.4 Paris Plot Of The Material 41 3.2.5 Radiographs Of The Fatigued Samples 42 3.2.6 F i n a l Fracture Morphology 44 CHAPTER IV. DISCUSSION 46 4.1 S t a t i c Tests 46 4.2 Fatigue Tests .47 i ) Fatigue L i f e 47 i i ) Fatigue Damage Propagation 48 i i i ) Compliance Data 51 iv) F i n a l Fracture Morphology 52 CHAPTER V. CONCLUSIONS 54 REFERENCES 57 iv L i s t of Tables I . F r a c t u r e Toughness v a l u e s f o r samples of Laminate 2 us i n g ASTM compact t e n s i o n sample equation (eqn. 3) .111 I I . F r a c t u r e Toughness v a l u e s f o r samples of Laminate 4 us i n g ASTM compact t e n s i o n sample equation (eqn. 3) .112 I I I . F a t i g u e T e s t i n g Data f o r Laminates 1,2,3,4, and 7 ...113 I V . Compliance Test R e s u l t s 116 V. Weight and Volume F r a c t i o n of the F i b r e s f o r Each Laminate 118 V L i s t of Figures 1. Increase in the crack length during compression fatigue for u n i d i r e c t i o n a l and [0/90] cross-ply graphite/epoxy composite. 2 6 61 2. S t i f f n e s s decay during fatigue. This i s the data of Smith (22.5° to the weave) used in the development of Poursartip's t h e o r y . 2 7 61 3. Compact tension specimen used in the experiments 62 4. ( i ) Curing Treatment of graphite/epoxy composite 63 4. ( i i ) The p o s i t i o n of the compact tension samples and t h e i r notches as they were cut from a laminate 64 5. T y p i c a l t e n s i l e loading pattern of the test samples leading to fracture using Instron t e s t i n g machine. ...65 6. The method of drawing new C-a 3 l i n e s i f the compliances of the samples have the same notch length from the same laminate are d i f f e r e n t from each other 66 7. Load-deflection data of sample F € for various notch lengths 67 8. Change in the compliance with the notch length for Sample F e 68 9. V a r i a t i o n of the compliance with the cube of notch length for sample F 6 69 10. Fatigue L i f e data 70 11. Crack Length vs cycles for sample J 3 max. load=4446N, min. load=222N,a0 = 24 . 5mm .'....71 12. Crack length vs. cycles for sample K 3. max. load=4528N, min. load=240N, a 0 = 24.8mm ...72 13. a vs N for sample L 3 . max. load=4688N, min. load=142N, a o = 2 5mm 73 14. a vs N for sample B 5. max. load=4466N, min. load=l51N, ao = 24. 5mm 74 15. a vs N for sample C 5. max. Ioad-=4101N, min. load=7lN, a 0 = 25mm. Low stress fatigue test 75 16. a vs N for sample E 5 . max. load=4822N, min. load=338N, a 0 = 25mm 76 v i 17. a vs N for sample F 5 max. load=507lN, min. load=53N,a 0 e25mm 77 18. a vs N for sample H 5 . max. load=4857N, min. load=80N, a 0 = 24 . 5mm 78 19. a vs N for sample K 5 . max. load=3932N, min. load=80N, a0=24.5mm. T y p i c a l low s t r e s s f a t i g u e . Sample d i d not f a i l 79 20. a vs N for Sample A 6 . max. load=5204N, min. load=80N. High s t r e s s fat igue 80 21. ( i ) a vs N for Sample C 6 . max. load=3692N, min. load= 142N,a 0 = 24 . 5mm 81 21. ( i i ) a vs N for sample g 6 . max. load=5249N, min. load=80N, a 0 = 24.45mm 81 22. a vs N for Sample E 6 . max. load=5266N, min. load=l228N, a 0 = 24.8mm 62 23. a vs N for Sample K 6 . max. load=4902N, min. load=142N, ao = 24.1 mm 83 24. a vs N for Sample L 6 . max. load=5071N, min. load=142N, a 0 = 24.3mm. High s t r e s s fa t igue 84 25. a vs N for Sample C 6 . max. load=4573N, min. load=15lN. a0=24.9mm. Sample was not fat igued up to f i n a l f a i l u r e . A t y p i c a l medium s t r e s s fat igue 85 26. a vs N for Sample F 7 . max. load=499lN, min. load=7lN, a0=24.5mm. High s t ress f a t i g u e . E f f e c t i v e crack length showed a higher increase in ve loc i t y than the o t h e r s . 86 27. a vs N for Sample I7. max. load=5l60N, min. load=80N, a o = 2 4. 5mm 87 28. Change in the load - d e f l e c t i o n curves during fa t igue of samples L 6 and H 6 88 29. Increase in the compliance of Sample C 5 during f a t i g u e . 89 30. Increase in the compliance of Sample E 5 dur ing f a t i g u e . 90 31. Increase in the compliance of Sample F 5 dur ing f a t i g u e . 91 vi i 32. Increase in the compliance of H 5 during fatigue 92 33. Increase in the compliance of J 6 during fatigue 93 34. Increase in the compliance of Sample K s during fatigue. 94 35. Increase in the compliance of Sample E 6 during fatigue. 95 36. Increase in the compliance of K 6 during fatigue 96 37. Increase in the compliance of I 7 and F 7 during fatigue. 97 38. Load d e f l e c t i o n data of a t e n s i l e fractured sample ( f a i l e d a ccidentally) 98 39. Paris Plot for Samples E 5 and K 5 99 40. Sample C 6 1 00 41 . Sample E 6 101 42 . Sample G 6 1 03 43. Sample K 6 1 04 44. Sample L 6 106 45. Sample C« 107 46. A sample f a i l e d by delamination. Notice the f a i l u r e i s caused from the damage in the two perpendicular d i r e c t i o n s that i s v i s i b l e in the radiographs 109 47. F a i l e d sample geometry showing delamination, f i b r e debonding and pull-out -109 48. Sample f a i l e d from the hole 110 49. Sample fractured under Instron incremental t e n s i l e loading 110 v i i i Acknowledgement The author i s g r a t e f u l for the advice and encouragement given by Dr. J.S. Nadeau and Dr. E. Teghtsoonian. Thanks are also extended to my fellow graduate students and faculty members in the Department of M e t a l l u r g i c a l Engineering. The assistance of the technical s t a f f of t h i s department, in p a r t i c u l a r Mr. R.C. Bennett and Miss N. Talebian, i s greatly appreciated. F i n a n c i a l assistance received in the form of an a s s i s t a n t s h i p under National Research Council of Canada i s g r a t e f u l l y acknowledged. 1 Chapter I INTRODUCTION 1 .1 General Review It was just in the early 70's that carbon f i b r e reinforced p l a s t i c s (CFRP) made their debut as an i n d u s t r i a l material. Given the variety of matrices, in which carbon f i b r e could work, p l a s t i c s had already emerged as the one supporting material offering the most immediate promise. Since then the wide variety of application in aerospace, sports goods and industry, involving a l l the primary CFRP c h a r a c t e r i s t i c s have emphasised the v e r s a t i l i t y of CFRP. These materials have great promise in reduction of weight and freedom from fatigue and corrosion. They also permit the designer to t a i l o r the material to match the applied loading. There are, on the other hand, serious problems to be overcome; the cost of the material, i t s b r i t t l e nature, i t s s u s c e p t i b i l i t y to erosion, the v a r i a b i l i t y between apparently i d e n t i c a l components and the d i f f i c u l t y of making j o i n t s between sub-assemblies. One sometimes wonders how many materials would never have been developed i f a l l the f a u l t s had been determined at the time of their discovery. Fr'om a simple measurement of t e n s i l e strength as the main guide to a material's usefulness researchers have gradually become accustomed to considerations of fracture toughness, stress corrosion resistance and an 2 everlengthening l i s t of other mechanical, p h y s i c a l , chemical and e l e c t r i c a l properties. The evaluation of fatigue resistance i s a t y p i c a l example of t h i s trend towards a deeper understanding of material p r o p e r t i e s . As these materials have v i t a l a p p l i c a t i o n s the fatigue property should be c l e a r l y understood. 3 1.2.1 Tension-Tension And Tension-Compression Fatigue Ramani and Williams 1 worked on 'notched and unnotched fatigue behavior of angle-ply graphite/epoxy composites'. Their i n v e s t i g a t i o n on the unnotched [0/±30] 3 graphite/epoxy revealed that f a i l u r e occurred at stress l e v e l s that were 40% lower than the average s t a t i c strength. This behavior i s in sharp contrast to the e s s e n t i a l l y fatigue i n s e n s i t i v e behavior exhibited by u n i d i r e c t i o n a l graphite/epoxy at r e l a t i v e l y high stress l e v e l s . 2 It was observed that the fatigue l i m i t (in terms of the percent of the s t a t i c ultimate strength) increases with increasing percentage of 0-degree p l i e s in the laminate and tension-compression cycling damage growth was d i f f e r e n t from the tension-tension c y c l i n g . 1 According to Awerbuch and Hahn3 when a laminate contains a s u f f i c i e n t number of 0-degree p l i e s i t s s t a t i c and fatigue t e n s i l e strengths are controlled by these 0-degree p l i e s . Temperature measurements were made during c y c l i n g and the temperature was observed to increase asymptotically to a constant value within several thousand cycles and to remain the same u n t i l immediately before the f i n a l f racture. In contrast, Owen and Morris 4 have indicated that the graphite f i b r e - r e i n f o r c e d composites do not show any s i g n i f i c a n t temperature r i s e even at the high test frequency of 7000 cycles per minute at which structural steels become very hot. 4 A l s o , L ibe r and D a n i e l 5 observed that these m a t e r i a l s do not e x h i b i t any s i g n i f i c a n t d e t e r i o r a t i o n of mechanical p roper t ies such as l o s s of s t i f f n e s s and st rength dur ing f a t i g u e . Compressive s t rengths have been found to be much lower than the t e n s i l e strengths and hence t h e i r f l e x u r a l fa t igue i s c o n t r o l l e d by the compressive s t rength . Dharan 6 s tudied the fat igue of g raph i te/po lyester in tension/compression and in reversed bending between imposed stroke l i m i t s . At l e s s than 75% of the u l t imate s t r a i n no f a i l u r e was observed at 4x10 s r e v e r s a l s . Resul ts from the tension/compression f a t i g u e tes ts ind icated that f a i l u r e always occurred dur ing the compression port ion of the c y c l e . The e f f e c t of reversed bending was observed to be l e s s severe than in tension/compression. Bader and Johnson 7 studied the f l e x u r a l fa t igue of u n i d i r e c t i o n a l CFRP specimens. They observed two zones ( t e n s i l e and compressive) on the f rac tu red sur face . For t h e i r study, the presence of these two zones was in accord with expectat ions , because the compression s ide of the specimen was always in compression and the tens ion s ide always in tension dur ing the fat igue l o a d i n g . Beaumont and H a r r i s 8 showed that under repeated pure tension l o a d i n g , carbon/polyester composites exh ib i ted no f rac tu res in 107 c y c l e s for s t ress l e v e l s l e s s than 0.9 of the s t a t i c f a i l u r e s t r e s s . Th is was a lso observed by Owen and Morr is .* Both studies a l s o showed that the mater ia l s behaved 5 well under f l e x u r a l loading; f a i l u r e occurred in 10 7 cycles only at flexure stresses above 0.66 of the s t a t i c f a i l u r e s t r e s s . Also o f f - a x i s loads were found to reduce the s t i f f n e s s s i g n i f i c a n t l y under c y c l i c loading. Ryder and Walker 9 studied the fatigue behavior of graphite/epoxy composites using p l a i n and notched specimens and found that generally tension-compression loading was more severe than tension-tension or compression-compression l o a d i n g . 1 * 9 * 1 0 Schutz and his co-workers 1 1 observed that stress concentrations reduce the fatigue strength of graphite/epoxy composites and although the s t a t i c strength of the high modulus f i b r e composite was lower than for the high strength f i b r e composite, the fatigue strength of both appeared to be the same. 6 1 . 2 . 2 E f f e c t Of Frequency On Fatigue Stinchcomb and his co-workers 1 2 studied the e f f e c t of frequency during fatigue c y c l i n g of composites. The frequency parameter was found to be a major factor governing the extent and severity of fatigue damage in the Boron/Aluminium composite samples tested. High frequency t e s t i n g of Boron/Aluminium composite did appear to produce s u b s t a n t i a l l y l e s s cracking than in the low frequency case. i . e . fatigue damage appeared to be more dispersed at high frequencies and more l o c a l l y concentrated at low frequencies for that material. The phenomena which combined in d i f f e r e n t ways to produce the d i f f e r e n t fracture modes at d i f f e r e n t frequencies also produced d i f f e r e n t fatigue response and intermediate f a i l u r e events. S t a t i c and dynamic s t i f f n e s s of the sample was even reduced by 50% in some cases. Therefore i t was concluded that frequency of c y c l i n g can influence or even control the in t e r a c t i o n and combination of f a i l u r e modes such as f i b r e breakage, debonding, delamination and matrix cracking. 7 1.2.3 E f fec t Of Manufacturing On Fat igue The defects and i r r e g u l a r i t i e s introduced dur ing the product ion of composites have a large ro le in the f a t i g u e performance of the m a t e r i a l . P a p i r n o 1 3 worked on doubly notched [0/ -60/60] s graphite/epoxy specimens to adapt a photomicrographic technique, p rev ious ly developed for metals in which the camera was observing the ins ide of the notch . Examination of photomicrographs, automat ica l l y exposed at p e r i o d i c i n t e r v a l s dur ing the t e s t s , revealed that f a t i g u e c racks developed ear l y in the t e s t . The photos a l s o revealed manufacturing i r r e g u l a r i t i e s and d e f e c t s ; non-uniform d i s t r i b u t i o n of f i b r e s with many r e s i n - r i c h areas in the 60-degree p l i e s ; voids at the p ly i n t e r f a c e s ; non-uniform p ly th icknesses e s p e c i a l l y of the 0-degree outer p l i e s . The e f f e c t of these would be to randomize the sequence of l o c a l f a i l u r e events which led to general f a i l u r e . If the notches were located in a .region with few d e f e c t s , the s t a t i c strength of the specimen would be h igh ; i f there were many defects and i r r e g u l a r i t i e s in the notch region lower s t a t i c strengths were expected. Therefore there would be scat te r in f a i l u r e data and fa t igue l i f e of s i m i l a r samples. Papirnos ' argument i s that t h i s m a t e r i a l as fabr i ca ted i s a poor candidate for s t r u c t u r a l a p p l i c a t i o n s . He a l so suggests that s t a t i c notch tes ts should be performed to screen a given lo t of composite mater ia l before time-consuming and expensive fat igue programs are i n i t i a t e d . 8 1.2.4 Effect Of Stacking Sequence On Laminate Strength Several authors have studied the influence of stacking sequence on laminate strength. Faye and Baker 1" dealt with the t e n s i l e fatigue strength of combined angle-ply [±15°,±45°] boron-epoxy laminates in which the positions of the ±15° and ±45° groups were reversed. The effect was a pronounced difference in strength throughout the entire S-N curve. The t h e o r e t i c a l explanation of the above phenomenon i s beyond the scope of lamination theory (LT), since in t h i s formulation, the predicted stresses in symmetric composites under membrane loading are independent of stacking arrangement. More rigorous solutions presented in [Reference 15,16] indicate that while LT gives a very r e a l i s t i c portrayal of the stress f i e l d in regions remote from a boundary, i t f a i l s in boundary layer regions, where s i g n i f i c a n t interlaminar stresses are developed. It i s therefore a strong p o s s i b i l i t y that the unique behavior can be a t t r i b u t e d to the degradation caused by delamination triggered by these interlaminar stresses. Severe delaminations have, in fact, been witnessed by Foye and Baker, who ident i f y progressive delamination as the primary source of strength degradation in fatigue. Another possible mechanism which can explain strength dependence on stacking sequence i s the constraining influence of adjacent layers on the propogation of a crack in a given layer or at an interface. A n a l y t i c a l r e s u l t s for a problem of t h i s type are presented by Chen and S i n 1 7 for a laminate consisting 9 of i s o t r o p i c l a yers. According to Pagano and P i p e s 1 8 there are several p o s s i b i l i l i t e s for optimization of laminate strength by varying the stacking order. The stacking arrangement should avoid interlaminar tension in the free edge zone and should minimize interlaminar shear resultants. Interlaminar compressive stresses should be introduced to minimize the detrimental e f f e c t of the shear stresses. In the case of a [0/90] b i d i r e c t i o n a l laminate, i t was argued that putting 90° layers at the outer surface would give a stronger laminate. 10 1.2.5 Micromechanisms Of Fatigue Prakash 1 9 studied the tension-compression fatigue of CFRP. His explanation for crack propogation in CFRP i s as follows: During fatigue, heat i s generated due to hysteresis of the polymer matrix. Heat accumulation leading to a l o c a l r i s e in temperature occurs. Generation of heat in certain portions of the sample becomes greater than the d i s s i p a t i o n of heat from that portion, because there are r e s i n - r i c h areas, broken f i b r e s , voids, cracks, delaminations on which the rate of heat d i s s i p a t i o n i s less than in the regions containing the spe c i f i e d amount of carbon fibres which are good thermal conductors. With heat accumulation, a r i s e in temperature occurs leading to a higher damping within the specimen which leads to a further r i s e in temperature. After some time the matrix shear modulus f a l l s to a low l e v e l . This permits l o c a l buckling of the fibres (stated simply: l o c a l heating causes l o c a l softening of the matrix and allows adjacent f i b r e s to buckle normally). As carbon f i b r e s are very b r i t t l e , the buckled f i b r e s break and produce a s l o t (or crack) in the composite. This newly created s l o t , i t s e l f a bad conductor of heat, causes further l o c a l heat accumulation. Furthermore, broken f i b r e s produce enough elevation of stress to give r i s e to f a i l u r e of the adjacent f i b r e s , which leads to a deepening of the crack. F i n a l l y t o t a l f a i l u r e r e s u l t s when the remaining cross-section cannot carry any more str e s s . 11 The cumulative f i b r e f a i l u r e process described above i s in accordance with the fatigue f a i l u r e c r i t e r i o n suggested by Hashin and Rotem 2 0. According to t h i s c r i t e r i o n , i f 9 represents the angle between the d i r e c t i o n of loading and the f i b r e d i r e c t i o n (for uni d i r e c t i o n a l material) for 0°^|(9<|2°, the specimen f a i l s by the process of cumulative f i b r e f a i l u r e ( i . e . f i b r e f a i l u r e mode). For larger values of 6, the f a i l u r e mode i s that of crack growth through the matrix, p a r a l l e l to the f i b r e s ( i . e . matrix f a i l u r e mode). Whitcomb 2 1 investigated fatigue damage in notched [0/45] and [45/90/0] type graphite/epoxy laminates. Delamination and ply cracking were found to be the dominant types of fatigue damage. In general, ply cracks did not propagate into adjacent p l i e s of d i f f e r i n g f i b r e o r i e n t a t i o n . Off-axis s t a t i c and fatigue behavior of AS-3501-5A graphite/epoxy was studied by Awerbuch and Hahn 2 2 in an e f f o r t to characterize the matrix/interface-controlled f a i l u r e . Seven d i f f e r e n t o f f - a x i s angles between 0° and 90° were tested. Fatigue f a i l u r e occurred without any warning or v i s i b l e damage. Matrix f a i l u r e c h a r a c t e r i s t i c s varied with o f f - a x i s angle and appeared in the form of serrations and a x i a l and transverse cracks. Large scatter in l i f e was observed at a l l o f f - a x i s angles. Micrographs of fracture surfaces showed a combination of several independent f a i l u r e modes such as fracture of individual f i b r e s and f i b r e tows, matrix serration (shear f a i l u r e ) , matrix cleavage and matrix/interface cracking p a r a l l e l to the f i b r e s . 12 Matrix serrations increased with longitudinal shear s t r e s s . In the absence of the shear stress, a cleavage type of f a i l u r e prevailed. Fracture surfaces which consisted of matrix-dominated and interface-dominated regions were not planar. F i n a l l y the sudden death behavior was at t r i b u t e d to rapid crack growth immediately before the f i n a l fracture. The appearance of serrations and microcracks in the matrix material possibly created high stress concentrations along the f i b r e s causing them to f a i l along some weak spots. 13 1.2.6 Damage Zone Detection Methods And Crack Veloc i t y  Studies Mandell and McGarry 2 3 studied the crack v e l o c i t y in graphite/epoxy specimens for s t a t i c t e s t s . To determine the crack v e l o c i t y the specimen was f i r s t coated with a non-conductive layer and s i l v e r s t r i p s were then painted ahead of the notch at several i n t e r v a l s . The s t r i p s were connected in a c i r c u i t with an oscilloscope, so that a drop in voltage was recorded when each s t r i p was broken by the crack. The system seemed to be successful, but i t i s not c e r t a i n whether t h i s method can be used for fatigue tests. Chang, Gordon and his co-workers 2 4 used a modified x-ray non-destructive evaluation (NDE) technique to observe the position of the crack in graphite/epoxy samples during s t a t i c and c y c l i c tests . The NDE monitoring was conducted in re a l time while the fracture specimens were under t e n s i l e ramp loading and constant amplitude c y c l i c loading. Tetrabromoethane (TBE) was applied as an x-ray opaque additive at the t i p s of a s l i t in the center of the specimens to enhance the flaw image. Damage i n i t i a t o n , growth and f a i l u r e mechanisms were observed from sequences of x-ray pictures recorded during t e s t i n g . Some similar studies in composites have been l i m i t e d to real-time surface damage studies or post-fracture evaluation, but using TBE gave a better chance to observe the entire damaged region. 14 Sendeckyj and Maddux 2 5 made side-by-side comparisons of damage indications obtained by using TBE enhanced x-ray, through transmission ultrasonic C-scan, and holographic non-destructive inspection methods of various composite specimens containing d i f f e r e n t amounts of damage. It was concluded that TBE enhanced x-ray photography gave the most d e t a i l e d information of the nature and planar d i s t r i b u t i o n of damage in graphite/epoxy composites. Holography using thermal loading showed delaminations and cracks in the surface p l i e s and was capable of finding both matrix cracks and f i b r e fractures in the surface p l i e s and providing information on the through-the-thickness d i s t r i b u t i o n of the delaminations, but more work needs to be done in interpretation of fringe pattern anomalies and selection of loading methods for damage re s o l u t i o n . Through-transmission ultrasonic c-scans showed the planar extent of delamination without giving any information on either matrix cracks or fractured f i b r e s . The r e s u l t s of x-ray radiography using tetrabromoethane gave the best picture of damage, so i t was advised that t h i s method be used in studying damage in graphite/epoxy composites. Kunz and Beaumont 2 6 investigated crack extension in graphite/epoxy composites in notched beams under c y c l i c compressive loading. They used cross-ply and u n i d i r e c t i o n a l specimens and observed that crack propogation underwent periods of deceleration and a c c e l e r a t i o n . Fatigue crack extension in 15 uni d i r e c t i o n a l composites was a result of a x i a l cracking and frequently resulted in crack arrest. Crossplied [0/90] composites had lower compressive strengths and through-specimen fractures resulted from s p l i t t i n g of the 0° p l i e s , transverse cracking in the 90° p l i e s and delamination between the p l i e s . Plots of crack length vs number of cycles were drawn for [0] and [0/90] samples using a t r a v e l l i n g microscope (see f i g . 1). The curves showed two stages of crack growth. Region I corresponded to i n i t i a l crack acceleration, then deceleration; Region II represented crack reacceleration. Crack growth in [0/90] composites followed the same pattern as in u n i d i r e c t i o n a l composites, but i t was more rapid in the former. Paris plots were then drawn showing large scatter in crack v e l o c i t i e s . Most of the samples had straight l i n e s and negative slopes in th e i r Paris p l o t s . It was noted that during c y c l i n g corresponding to Region I the crack that had i n i t i a t e d at the machined notch grew rapidly under the applied stress and then v i s i b l y slowed down. Continued cy c l i n g produced cracks that originated at the newly created fracture surface and grew p a r a l l e l to the f i b r e s in the a x i a l d i r e c t i o n . After some time cracks proceeded again across the fi b r e s with a v i s i b l e increase in v e l o c i t y which corresponds to Region I I . Cracks either propogated through the specimen u n t i l f a i l u r e occurred or decelerated again and remained arrested. 16 1 .2 .7 Formulating The Decay In S t i f f n e s s During Fat igue P o u r s a r t i p , Ashby and Beaumont 2 7 s tud ied the damage accumulation during fat igue of composite m a t e r i a l s . The damage was monitored by measuring the e l a s t i c modul i , because being a tensor of the fourth rank, the moduli o f f e r the p o s s i b i l i t y of d i s t i n g u i s h i n g and monitoring d i f f e r e n t components of damage. They represented the v e l o c i t y of damage a s : dD/dN = f (Ao,D) (1) where D i s a var iab le which represents fa t igue damage, Ao* i s the s t ress amplitude and N i s the number of c y c l e s . The above equation can be in tegrated to give the fa t igue l i f e : N f " L_i5 (2) where D± and D f are the i n i t i a l and f i n a l amounts of damage r e s p e c t i v e l y . To evaluate dD/dN they used an equation based on experimental measurement of s t i f f n e s s versus number of c y c l e s . The data were S m i t h ' s 2 8 which revealed three regions of s t i f f n e s s decay dur ing fat igue l i f e . The i n i t i a l damage growth phase was found to be both st ress and s t r a i n dependent. The intermediate damage phase with constant damage growth was only s t r e s s dependent, and in the f i n a l phase, the damage rate increased with s t r a i n amplitude and had l i t t l e s t r e s s dependence. The s t i f f n e s s curves a l l fol lowed an exponential form. See F i g 2. 17 In agreement with the method of Poursar t ip et a l , Kunz and Beaumont 2 6 found that the incrase in crack length fol lowed the same pat tern as the change in s t i f f n e s s during f a t i g u e . 18 1.3 Theory While studying the f r a c t u r e of composite mater ia l s some researchers have used L inear E l a s t i c F racture Mechanics equat ions d i r e c t l y , as in the form of being used for i s o t r o p i c m a t e r i a l s , and some others e i t h e r converted these equations for composite mater ia ls or created new equat ions . 1.3.1 Fracture Toughness Equat ions I n i t i a l l y , i t was decided to use Compact tension samples for the present p r o j e c t . The f r a c t u r e toughness equation for t h i s kind of geometry from ASTM standards i s : 2 9 " 3 0 K = _ i _ ^ [ 2 9 . 6 - 1 8 5 . 5 ( a / w ) + 6 5 5 . 7 ( a / w ) 2 - 1 0 1 7 . 0 ( a / w ) 3 + 6 3 8 . 9 ( a / w ) A ] (3 ) I C wt where, P=applied l o a d ; a=crack l e n g t h ; w=width; t=th ickness . (See f i g . 3) In other words, K i c - - ! r f < a / w > <*> In f rac tu re mechanics, s t ra in energy re lease rate i s def ined a s : « <« where, 5 C / 6 a i s the change in compliance with crack length . For plane s t r e s s , G I C - ^ ( 6 ) , hence K * = £(§f)E (7 ) where E i s the Young's modulus of the m a t e r i a l , but, for a homogenous an iso t rop ic mater ia l the r e l a t i o n i s 2 * 1-1 n G i c • K i c m te) 1/2 1 1 / 2 + 2 b 1 2 + b 6 6 2 b l l J - (8) To use t h i s equation the crack has to co inc ide with one of the p r i n c i p a l axes of mater ia l symmetry such that i t extends s t r a i g h t ahead. In t h i s case, the system must necessar i l y be o r thot rop ic in nature and the e l a s t i c c o e f f i c i e n t s in 19 equation 8 can be expressed in terms of the p r i n c i p a l modulus of e l a s t i c i t y and the po isson 's r a t i o : 3 5 11 1 E, 1 2 1 " V12 b22 = I2 ( 1 " V23 >» b12 12 < 1 + V23>' b66 12 where subsc r ip ts 1,2 and 3 are p r i n c i p a l x,y and z d i r e c t i o n s r e s p e c t i v e l y ; v=poisson's r a t i o , /i=shear modulus. (Note that E,=E 2 for a [90/0] composite.) The term E in equation 7 i s replaced by E' for composite mater ia l which i s c a l l e d the ' E f f e c t i v e Modulus' and i s equal t o : E' = i and b l l b 22j .2 1/2 T/v \ ov ^ 1L/2^- l fh_22\+ 2 b 12 + b 66 Vbll/ 2 b n T / 2 V 1} K I - n ( f i ) E ' <9» 1.3.2 Fat igue Test ing Equations In c y c l i n g i f a and a are the maximum and minimum max min s t resses r e s p e c t i v e l y , the fo l lowing terms are important in d e s c r i b i n g the fat igue c y c l e . St ress Amplitude, o = a (o max -a min )/2 Mean S t r e s s , a = m (a max +a min )/2 St ress Rat io , R = a min /o max Stress Range, 0 max a min - - - - (10) 20 To draw an S-logN graph e i the r Aa or a can be used as S. max Usual ly crack length (a) vs number of c y c l e s " p l o t s are drawn to determine the rate and behavior of crack propogation dur ing f a t i g u e . The slope of the curves (da/dN) i s a funct ion of the app l ied s t ress and the crack l e n g t h . 3 6 Quite o f t e n , for metals t h i s r e l a t i o n assumes the form of a simple power r e l a t i o n s h i p wherein: da m n _ ( i i ) • a & - o a - - - - - - ^ ' where m 2 - 7 , n =* 1 - 2 3 6 Par is postulated that the ' s t r e s s i n t e n s i t y factor range' was the o v e r a l l c o n t r o l l i n g factor in the fat igue crack propagation process . This r e l a t i o n i s | | . A A K ° - - - - - - - - - ( 1 2 ) where A i s a constant and AK=Stress i n s t e n s i t y factor range=K max K where K i s c a l c u l a t e d using the max. load and K i s min max min c a l c u l a t e d using the min. t e n s i l e load . E i the r equation 3 or equation 9 can be used for these c a l c u l a t i o n s while using composite m a t e r i a l s . A lso the constants A and m are funct ions of mater ia l v a r i a b l e s , environment, frequency, temperature and s t ress r a t i o . The Par i s plot i s usual ly drawn in l o g - l o g form and i t i s usua l l y argued that the crack growth rate (da/dN) i s s e n s i t i v e to the i n d i v i d u a l values of K or R , and the s t ress r a t i o . max min 21 1.3.3 Compliance Tests It i s necessary to measure the compliance of the tes t samples in order to be able to use equations (7) and (9) . A tes t sample i s t e n s i l e loaded to a ce r ta in f r a c t i o n of i t s f rac tu re load and the d e f l e c t i o n of the sample along the loading l i n e can be measured using var ious methods (e .g . using a c l i p - g a g e ) . Loading should be performed in the e l a s t i c range of the m a t e r i a l . The inverse slope of the produced l i n e w i l l g ive the compliance of the sample for that notch length . The test can be c a r r i e d out for a number of notch lengths on the same sample and the compliance vs notch length graph can be drawn. The slope of t h i s curve gives (6C/6a) which i s used in equations (7) and (9) . 22 1.4 Purpose As can be seen from the l i t e r a t u r e survey, researchers have used d i f f e r e n t techniques to determine the fatigue damage in graphite f i b r e reinforced composites. In the present work, i t was decided to determine the crack v e l o c i t y and damage in graphiteepoxy composites during fatigue, using t r a v e l l i n g microscope, radiography and compliance techniques. The 'compact tension sample' geometry was found to be suitable for t h i s purpose (See F i g . 3). Due to the l i m i t e d c a p a b i l i t y of the equipment i t was decided to work on tension-tension fatigue only. The laminate having the construction [ 90/3 j 8s. was used, because t h i s is a simple laminate to make and yet, i t approximates the properties of more complex laminates. 23 Chapter II PROCEDURE 2.1 Laminate And Sample Preparation The Hercules AS3501-6 high strength graphiteepoxy prepreg material was used in the preparation of the laminates. 'AS' corresponds to high strength f i b r e s and '3501-6' means that the epoxy matrix was rated so that i t maintains i t s mechanical properties up to 350°F. The prepreg material was in the form of a r o l l with the fi b r e s running along the length of the r o l l . The intention was to prepare [90|0]B* type of laminates where 90° i s the d i r e c t i o n perpendicular co the loading l i n e and 0° i s along the loading l i n e . The u n i d i r e c t i o n a l prepreg was cut into sixteen rectangular 90° and sixteen 0° p l i e s which would be joined together and then cured to produce the laminate. After the lay-up procedure was finished by s t i c k i n g the p l i e s together following the above ply sequence, a release f i l m was applied to both top and bottom of the laminate and a caul plate followed by bleeder p l i e s were stacked on top. The caul plate was used to produce a smooth surface and the function of the bleeder p l i e s was to c o l l e c t the epoxy that was squeezed out of the p l i e s during the heat treatment. The laminate was then vacuum bagged onto an aluminum base plate. Heating tapes were present under the plate in order to heat the laminate when i t was inside the autoclave. (The d e t a i l e d operation and the 24 a p p a r a t u s i s d e s c r i b e d i n d e t a i l i n r e f e r e n c e 3 7 ) . The p r e p a r e d a s s e m b l y was t h e n h e a t e d i n t h e p r e s e n c e o f vacuum i n t h e b a g a n d p r e s s u r e i n t h e a u t o c l a v e f o l l o w i n g t h e c u r e c y c l e recommended by H e r c u l e s ( s e e f i g . 4 ( i ) ) . A p r e s s u r e o f 80 p s i was a p p l i e d d u r i n g t h e 240°F t e m p e r a t u r e a n d 100 p s i was a p p l i e d u n t i l t h e end o f t h e t r e a t m e n t . No p o s t - c u r i n g was u s e d (A ±10°F e r r o r was a l l o w a b l e d u r i n g t h i s o p e r a t i o n ) . When t h e a u t o c l a v e c o o l e d down t h e a s s e m b l y was t a k e n o u t a n d t h e l a m i n a t e was r e m o v e d . I t was t h e n c u t i n t o c o m p a c t t e n s i o n s a m p l e s ( f i g . 3 ) u s i n g a 1.25mm t h i c k d i a m o n d saw. The s a m p l e s w ere g i v e n c o d e numbers a s shown i n f i g . 4 ( i i ) . D u r i n g d r i l l i n g t h e h o l e s o f t h e C.T.S., a p l a s t i c m a t e r i a l was p u t u n d e r t h e s a m p l e t o a v o i d i n t r o d u c i n g c r a c k s a r o u n d t h e h o l e s . A f t e r c u t t i n g a n o t c h i n e a c h s a m p l e w i t h t h e d i a m o n d saw a s h a r p c r a c k was p r o d u c e d u s i n g a r a z o r b l a d e . A g r o o v e was c u t a t t h e b e g i n n i n g o f t h e n o t c h i n o r d e r t o be a b l e t o p l a c e a c l i p gage on t h e s a m p l e t o m e a s u r e i t s d e f l e c t i o n d u r i n g a t e n s i l e l o a d i n g ( f i g . 3 ) . A b o u t s e v e n l a m i n a t e s w e re p r e p a r e d i n t h e a b o v e manner a n d t w e l v e s a m p l e s c o u l d be c u t f r o m e a c h l a m i n a t e a s shown i n f i g . 4 ( i i ) . 25 2.2 S t a t i c Tens i le Fracture Test ing In accordance with the advice of P a p i r n o 3 i t was decided to determine the f racture toughness of samples from var ious parts of the laminate . The d i r e c t i o n of the notches were va r ied to see whether the crack d i r e c t i o n a f f e c t e d the toughness (see f i g . 4 ( i i ) ) . Laminates 2 and 4 were used for t h i s purpose. For the former laminate the notches were cut by a diamond saw and no sharp cracks were introduced by the razor blade whereas sharp cracks were intoduced to the samples of laminate 4. The s t a t i c t e n s i l e tes ts were performed by using the Instron t e s t i n g machine with a load c e l l of 0-8896N loading-range and a crosshead-displacement rate of 0.25mm/sec. A t y p i c a l loading curve i s shown in f i g . 5. The maximum load to f racture was recorded for each sample. 26 2.3 Fatigue Test ing The MTS servo -hydraul ic machine was used for the fa t igue t e s t s . Only tens ion - tens ion loading was used as the machine was not designed to apply compression fat igue l o a d i n g . Stroke c o n t r o l was used for the s ix samples of laminate 1, but i t was changed to load cont ro l for the remaining samples. Samples of laminate 1 were fa t igue tested without watching the increase in the crack lengths . The stroke c o n t r o l l e d samples gave very short fat igue l i f e . S t a r t i n g with laminate 3 a t r a v e l l i n g microscope was p laced in f ront of the tes t ing assembly to watch the crack propagation during the t e s t s . The crack lengths were recorded at c e r t a i n i n t e r v a l s with an accuracy of ±0.2mm. It was d iscovered that there were usual ly two cracks running from the notch . Most ly , the la rges t crack was fo l lowed. Surface cracks on the other s ide of the samples were a lso checked by stopping the test and p lac ing the other side of the sample in front on the t r a v e l l i n g microscope. To observe the damage zone ins ide the sample which could not be seen by the naked eye, a radiographic technique was used. Tetrabromoethane was put into the crack t i p by an in jec to r during the fat igue t e s t . Due to the dynamic motion of the sample the l i q u i d penetrated into the damage zone. The t e s t i n g was then stopped and the sample was removed from the MTS and placed in f ront of a P h i l l i p s x -ray machine equipped with a copper t a r g e t . 27 The x - ray machine was then adjusted to 16 k i l o v o l t s and 6mi l l i amps . A c i r c u l a r column of x - rays i r r a d i a t e d the sample producing the image of the damage zone on a f i l m placed just behind the sample. The x - rays were app l ied for 15 seconds and during t h i s short time tetrabromoethane p r e f e r e n t i a l l y absorbed the x - r a y s . The f i lms were then developed, f i xed and p o s i t i v e p r i n t s were made. Crack lengths were then measured e i ther by using the f i lms or the p r i n t s . Af ter t h i s , the sample was s t a t i c a l l y t e n s i l e tested while measuring i t s d e f l e c t i o n to determine i t s compliance and i t was put back into the MTS assembly for further f a t i g u e . This descr ibed procedure was repeated severa l times for each sample. A frequency of 10Hz was used in the tes ts as higher f requencies gave r i s e to a temperature increase in the samples. Around 20 mm notch length was used in the f i r s t laminate, but seeing that no sample was f a i l e d (under load cont ro l ) i t was changed to 24.5±1mm to enable the fat igue cracks or damage to grow. Some samples were subjected to high loads c lose to t h e i r f rac tu re load ( e . g . loads greater than or equal to 4700 N) whereas other samples were subjected to medium loads (e.g.4500<Load<4700N) and low loads (Load<4500N). High load fat igue tes ts ran for about one or two days, whereas the others could run from two to nine days. The longest per iod of time was taken by sample C 5 which f a i l e d at 7.5x10 s c y c l e s . Some samples d i d not f a i l for a long per iod of t ime, so they were not 28 fat igued fur ther . Sample E 6 was tested with a r e l a t i v e l y high minimum load and a high maximum load (which was c lose to the f a i l u r e load range) in order to see whether graphiteepoxy i s maximum st ress or s t ress range s e n s i t i v e . 29 2.4 Compliance Test ing The main aim in using the compliance method was to determine the ' e f f e c t i v e crack length ' and to measure the increase in compliance of the samples dur ing fat igue t e s t i n g . The Instron or the MTS machines were used for th i s purpose. The Instron was used in the 0-4448N load range with a crosshead-displacement rate of 0.25mm/minute whereas the MTS was used with the same load range and displacement rate while i t was operated under stroke c o n t r o l . The sample was placed in the machine and incremental t e n s i l e loading was appl ied while d e f l e c t i o n was recorded by a c l i p - g a g e which was posi t ioned on the sample ( f i g . 3 ) . The c l i p -gage measured the d e f l e c t i o n at the beginning of the notch. The 'Thales t r i a n g l e ' r e l a t i o n was used to f i n d out the d e f l e c t i o n at the loading l i n e . The compliance was then c a l c u l a t e d by taking the inverse slope of the l o a d - d e f l e c t i o n curve in the e l a s t i c range. Th is procedure was appl ied severa l times to a sample from each laminate by cu t t ing several notch lengths within the same sample (see f i g . 7 ) . The ca lcu la ted compliances were then p l o t t e d versus t h e i r notch lengths ( f i g . 8 ) . The slope of t h i s curve could then be used to determine the f racture toughness (equations 7 and 9) of the sample or i t could be used to determine the ' e f f e c t i v e crack length ' of another sample i f i t s compliance value were known. To make the l a t t e r c a l c u l a t i o n e a s i e r , compliance of the reference sample was p lo t ted versus 30 the cube of the notch length , g i v ing a s t ra ight l i n e up to a c e r t a i n notch length (see f i g s 6 and 9 ) . When the compliances of a l l the samples had been measured before the fat igue t e s t s i t was seen that there was a sca t te r in the values for samples with the same notch lengths. Then the method descr ibed in f i g . 6 was used to compute the apparent crack length of a specimen for which only the compliance was known. If the middle curve belongs to the reference sample A with a compliance value C 0 at the notch length (a) p a r a l l e l s were drawn to i t for other samples B and C with compliances C, and C 2 with the same notch lengths . Hence, when sample B was fa t igued and there was an increase in i t s compliance due to the damage introduced, i t s ' e f f e c t i v e crack length ' could be c a l c u l a t e d by the new l i n e s t a r t i n g from C , . The same i s true for sample C. 31 2.5 Determining The Weight And Volume F rac t ion Of The  F ib res Af te r a l l the tes ts were f i n i s h e d small p ieces were cut from a sample of each laminate. These p ieces were then b o i l e d in concentrated N i t r i c a c i d at 100°C for ha l f an hour to remove the r e s i n from the f i b r e s . The f i b r e s were then washed with water severa l times and d r ied in a furnace at a r e l a t i v e l y low temperature. The f i b r e s were weighed by a s e n s i t i v e sca le which could read the weight to an accuracy of ±0 .1mg. E r ro rs could be introduced to the readings due to presence of some r e s i n l e f t between the f i b r e s . Equations 13,14,15 and 16 were used to determine the weight and volume f r a c t i o n of the f i b r e s : w = w £ + w - - - - - - - - - ( 1 3 ) c r m where w c ' w f a n c ^ w m a r e t* i e w e i 9 n t o f t n e composite, wt. of the f i b r e s and weight of the matrix epoxy r e s p e c t i v e l y . P „ - P f v f + P V - - - - - - - - ( 1 4 ) c i r mm where p , p and p are the density of the composite f i b r e s and c f m matrix r e s p e c t i v e l y . V and V are volume f r a c t i o n of the f i b r e s £ m and matr ix . Equation 14 can be rewritten a s : p c = p f V f + pm ( 1 -V - - - - - - - (15) To determine the volume f r a c t i o n of the f i b r e s i t i s necessary to know the volume of the composite and dens i ty of the epoxy. Then, m m_ m £ v = — , v r = — m P m f Pf m t 32 a n d v = vc + v c f m where v i s the ac tua l volumes and V_ =v./v r i c The data are given in table V. 33 Chapter III RESULTS 3.1 Tens i le Fracture And Load Curve Analys is The f racture load and f rac ture toughness values of the samples from Laminate 2 and 4 are shown in Tables I and II r e s p e c t i v e l y . The ASTM compact tension sample equation (eqn. 3) was used for the toughness c a l c u l a t i o n s . No sharp cracks were introduced into the samples of Laminate 2. As a resu l t the f rac ture loads were higher than the samples (with sharp cracks) of Laminate 4. A lso there was a large scat ter in f racture loads ranging from 4893N to 9118N. Sample L 2 might be considered except ional as no other sample approached that l e v e l of f rac ture load . Samples A 2 , B 2 , C 2 , J 2 and K 2 seemed to have low f rac ture loads with respect to the samples near the center of the laminate, but samples D 2 , F 2 , G 2 , and I2 which were a lso on the edges were not so weak (See f i g . 4 ( i i ) ) . The d i r e c t i o n of the notches for the samples near the edges PS and QR of the laminate d id not seem to e f f e c t the f rac ture l o a d . I n i t i a l damage at the t i p of the notch would s tar t very c lose to the center of the sample whether the notch was cut towards the center of the laminate or towards the edge. Fracture toughness values fol lowed the sample pattern and sca t te r as the f racture load of the samples as K J C i s s t rongly dependant to the f racture load ( i t i s the highest parameter in 34 eqn. 3 ) . In laminate 4 there was l e s s scat ter in the f rac tu re loads which gave some encouragement for the fat igue t e s t s . The sca t te r was ±670N. Fracture toughness resu l t s a l s o seemed to be reasonable except that they were lower than the r e s u l t s of Laminate 2 perhaps due to the presence of the sharp c r a c k s . A l s o , the edge samples have resu l t s c loser to those of the center ones i r r e s p e c t i v e of the pos i t i on of the notch. In both laminates th icknesses var ied s l i g h t l y throughout the p l a t e , with the resu l t that the volume f r a c t i o n of the f i b r e s var ied from region to reg ion . This was be l ieved to be the main source of scat ter in the toughness va lues . As shown in f i g . 5 the loading curves of the samples were l i n e a r . Cracking noise was heard at about 85% of the maximum load which corresponds to a l i t t l e peak shown. Af ter the maximum l o a d , several peaks occurred which meant that the cracked sample d id not lose i t s load bearing c a p a c i t y . Complete f rac tu re was achieved a f te r 1.5-2 minutes for most of the samples. 35 3.2 Fatigue Tes t ing Results 3.2.1 Fat igue L i f e Of The Mate r ia l There seemed to be a large sca t te r in the fa t igue l i f e of the samples. As most of the samples were f a i l e d by damage around the holes few data po ints were l e f t to draw the Ao vs log N graph (see f igu re 10). Most of the samples of Laminate 1 were fat igued below 22MPa and no f a i l u r e was observed in the f i v e samples tes ted , under load c o n t r o l . Samples f a i l e d q u i c k l y under stroke cont ro l as shown in Table I I I , but they were not put on the fat igue l i f e p l o t . Samples of laminate 3 mostly f a i l e d below 3x10 s c y c l e s whereas i t took longer time for the other laminate . Only one f a i l u r e was observed below 31.69 MPa (Sample C 6 ) . Sample E 6 was tested to determine whether fat igue l i f e depends on the maximum st ress or the s t ress range. Hence a high maximum st ress c l o s e to the f racture s t ress and a low s t ress range was used. That i s i f the mater ia l was maximum s t ress sens i t i ve i t would not survive so long and i f the mater ia l was s t ress range s e n s i t i v e i t would surv ive for a very long time as a low st ress range was a p p l i e d . It was seen that the sample d id not f a i l up to 5x10 6 c yc les and the operat ion was stopped. This suggests that Ao i s the important fac tor in the fa t igue of t h i s m a t e r i a l , but fu r ther experiments are necessary in order to be c e r t a i n about i t . 36 3 .2 .2 Fatigue Crack Length Measurements Most of the crack length measurement data are shown in f i g s . 11 to 27. Some readings are c a l l e d 'maximum damage zone length ' which corresponds to the length measured from the x - ray p r in t or f i l m . As there was not a s ing le crack propagating but in general a number of c racks , the maximum length was measured. The damage zone was v i s i b l e at the i n i t i a l stage of fat igue l i f e , that i s fat igue damage s tar ted ear l y in the t e s t s . This damage zone propagated very l i t t l e with respect to i t s i n i t i a l s i ze at the intermediate and longest stage of fat igue c y c l i n g . Then c lose to f a i l u r e i t increased aga in , but at a slower rate than the i n i t i a l ra te . In samples J 3 , K 3 , F 5 and L 6 damage zone lengths increased with a r e l a t i v e l y higher speed then the other samples in the intermediate stage of the fat igue l i f e , but in general i t can be said that the intermediate stage i s a crack dece le ra t ion stage. For samples B 5 , H 5 , A 6 , C 7 , F 7 and I7 the crack running on the surface of the sample was detected on the x - ray f i l m . That i s why the surface readings are very c lose to the max. damage zone leng th . The qua l i t y of the x - ray f i l m a l s o a f fec ted the readings. The sur face crack lengths are represented as ' t r a v e l l i n g microscope reading ' in the a vs N graphs. They a lso followed three stages in the fat igue l i f e . An i n i t i a l high v e l o c i t y in the f i r s t s tage; decelerat ion in the intermediate stage and r e a c c e l e r a t i o n in the f i n a l stage. The values were usual ly lower 37 than the corresponding maximum damage zone lengths. In sample B 5 , one crack s ta r ted to propogate at the i n i t i a l stage of f a t i g u e , but a second crack s tar ted la te r from the edge of the notch and took the l e a d . A lso in samples F 5 and C 7 cracks on the other s ide of the sample s tar ted to grow f a s t e r and became c lose to the maximum damage zone length . The ' e f f e c t i v e crack length ' which was c a l c u l a t e d by the compliance method a l s o showed three stages during f a t i g u e , but the values were considerably lower than those given by the other two types of data (In t h i s method the fat igue crack i s considered to be a notch) . Th is could probably be explained by the behavior of sample I s which was a c c i d e n t a l l y t e n s i l e loaded by using a high crosshead displacement rate instead of a low one and f rac tu red . The r e s u l t i n g crack was measured and i t was found to be 42mm long on the specimen sur face . When the compliance test was performed i t was r e a l i z e d that I5 was s t i f f e r than a sample which had a notch length of 40.1mm (see f i g . 38) ; i . e . the f ractured sample was showing a br idging e f f e c t which gave the sample some load bearing c a p a c i t y . When a saw cut was made in t h i s sample to a depth of 43.8mm the slope of compliance curve f e l l considerably behaving l i k e a normal notch. Th is might be the case for fat igued samples. The br idging e f f e c t around the damage zone does not l e t the fat igue crack or damage behave as a notch of equivalent length does. That i s why the values of e f f e c t i v e crack lengths were lower than the measured crack lengths . For samples E 5 , F 5 , H 5 , E 6 and F 7 these values are 38 p lo t ted on a larger scale (Figures 16, 17, 18, 22 and 26 r e s p e c t i v e l y ) . 39 3 . 2 . 3 Change In The Compliance During Fat igue . Most of the resu l t s are shown on F i g s . 28 to 37. When the compliance t e s t s were performed on the fat igued samples they showed the behavior that can be seen from f i g . 28. Whatever the app l ied s t resses were, the compliance of the samples increased in the i n i t i a l stage of fat igue l i f e . This increase slowed down in the t e s t s for the intermediate stage and c lose to f a i l u r e , the compliance increased considerably aga in . As the damage increased the l o a d - d e f l e c t i o n l i n e changed from the s t r a i g h t l i n e form to a s l i g h t curve. The inverse slope increased as loading proceeded. There was not so much d i f fe rence in the compliance for d i f f e r e n t cyc les at low loads e . g . around 500N to 1000N. This might be due to the br idg ing e f f e c t caused by the mater ia l surrounding the damage zone or c r a c k s . Normalized compliance (C/C 0) values vs number of cyc les were p l o t t e d for most of the samples. The data revealed that there are three stages of fat igue l i f e of th i s composite. Region 1 occurred at an average value of 0.2105 of the fat igue l i f e (N ) with an average increase of 0.168 in C/C 0 . Region 2 took the longest time during 0.49 of the samples l i f e with an average increase of 0.115 in C/C 0 whereas region 3 showed an increase of 0.35 in C/C 0 [0.25 in C/C 0 i f sample J 5 i s exc luded] . Sample F 5 which was fat igued under a high s t ress showed a continuous increase in i t s normalized compliance during the intermediate stage i . e . high s t ress gave quicker and more severe 40 o damage. Sample J s c l e a r l y showed the three stages of f a t i g u e . The f i n a l f a i l u r e region for t h i s sample i s very t y p i c a l (The sample was pref ractured in the Instron at a very low s t r a i n rate to determine i t s f racture l o a d ) . Sample K5 and E 6 which are t y p i c a l of low s t r e s s fa t igue d i d not show an increase beyond 1.3 in C/C 0 . As they were not fat igued up to the f a i l u r e , t h e i r f i n a l stage i s not shown. Sample E 5 which was fat igued under medium s t ress showed a very low increase in the intermediate stage l i k e sample J 5 whereas sample I7 revealed a d e f i n i t e increase in compliance dur ing the intermediate stage. Sample F 7 from the same laminate c l o s e l y fol lowed the pattern of I7. 41 3 . 2 . 4 P a r i s P lo t Of The Mater ia l The P a r i s P l o t s drawn for samples E 5 and K 5 are shown in f i g . 39. Th is type of p lot in tests of metals and ceramics, usua l l y has a p o s i t i v e s lope . In the present system the mater ia l does not fo l low that pattern as can be seen from the f i g u r e . Crack v e l o c i t y decreases during the f i r s t and intermediate stage of fa t igue l i f e , then shows an increase c lose to f a i l u r e . For sample K 5 the f i n a l stage i s not shown as i t was not cyc led to f i n a l f a i l u r e , but there i s a v i s i b l e incremental decrease in v e l o c i t y dur ing f a t i g u e . Both p lo ts were drawn using the x-ray data . If the p l o t s were drawn using the t r a v e l l i n g microscope reading or the e f f e c t i v e crack length , these methods would give d i f f e r e n t l i n e s . There would a lso be large s c a t t e r from sample to sample which can be understood by examining the a vs N data of a l l the samples. Equation 9 was used to ca l cu la te the s t r e s s in tens i t y factor ranges (AK) of the two samples shown in f i g . 39. 42 3 . 2 . 5 Radiographs Of The Fatigued Samples The p r i n t s produced from the x - ray f i lms are shown in f i g s . 40 to 45 in a l p h a b e t i c a l order of the samples. F igure 40 shows the increase in the damage zone of sample C 6 dur ing f a t i g u e . This sample had a sudden increase in crack length at the very beginning of the fat igue t e s t . Notice that damage in the 0° d i r e c t i o n s t a r t s at some distance from the sharp crack meaning that fat igue damage s tar ted a f te r t h i s i n i t i a l increase in the crack length . F i g . 41 shows a 'low s t ress range' fat igue of sample E 6 . The damage zone d id not increase much, even a f t e r 4.22x10 s cyc les revea l ing that the sample was far from f a i l u r e , but damage increased more in the 0° d i r e c t i o n than in the perpendicular d i r e c t i o n . F i g s . 22 and 35 of the same sample revealed that there i s damage proceeding, but at a low magnitude. Sample G 6 ( f i g . 42) which was fat igued under a high s t ress showed a quicker increase in the damage zone un l ike E 6 . The damage had propagated extensively in both d i r e c t i o n s a f t e r 2 . 7X1 0 5 c y c l e s . The cracks that were detected by the t r a v e l l i n g microscope were d i s t ingu ishab le in the damage zone of the radiographs. F i g . 43 shows another high s t ress f a t i g u e . Not ice the increase in length of the two cracks in the 2 .17x l0 6 cyc les i n t e r v a l , which was a l so v i s i b l e on the surface of the sample. 43 Normalized compliance data of t h i s sample a l s o revealed t h i s increase (see f i g . 36) . Sample L 6 ( f i g . 44) which was a l s o fat igued by a high s t r e s s again shows an increase in crack length a l s o in the d i r e c t i o n of the notch as wel l as a damage zone inc rease . F i g . 28 of sample L 6 ( l o a d - d e f l e c t i o n data) reveals t h i s change. F i g . 45 shows the p e c u l i a r behavior of the medium s t ress fat igued sample, C 7 . Not only the two cracks s t a r t i n g from the corners of the notch but other cracks p a r a l l e l but away from the notch increased in length during f a t i g u e . In a l l of the samples the damage zone grew qu ick l y in the i n i t i a l stage of fat igue l i f e which i s cons is tent with the S-N and C/C 0 -N da ta . Also the i n d i v i d u a l cracks were c l e a r l y v i s i b l e in the high s t ress fat igue t e s t s ; whereas, in the low s t ress f a t i g u e , the damage was in the form of a zone of cracks rather than a s ing le c rack . 44 3 . 2 . 6 F i n a l Fracture Morphology The f i n a l geometry of the t e n s i l e and fat igue f a i l e d samples i s shown in F i g s . 46 to 49. The separation of the fat igued samples into two star ted from the corners and not from the center of the notch. This was in good agreement with the radiographs. As mentioned before, most of the samples f a i l e d from the ho le . The f a i l e d region was near the edge of the sample where the pin was pushed upwards by the MTS machine. i . e . impact loading was probably occurr ing on the upper half of the ho le . This impact would be severe i f the hole was larger than the p i n . (See f i g . 48). The geometry in f i g . 46 is a t y p i c a l delamination f a i l u r e . Only some layers of the sample seemed to be delaminated. The sample was not d iv ided into equal ha lves , but some part of the lower port ion was l e f t . This geometry, ind icates that the damage which was seen in the 0° d i r e c t i o n in the radiographs i s a lso p lay ing a big ro le in the f a i l u r e of the ply c o n f i g u r a t i o n . F i g . 47 reveals delaminat ion, f ib re debonding and p u l l - o u t in the fat igued region of the f ractured sur face . The fat igued region i s c l e a r l y d is t ingu ishab le from the f i n a l f racture reg ion . The l a t t e r region i s smoother than the former. Fatigue f rac ture again started from the corner of the notch not from the sharp c rack . 45 The t e n s i l e f ractured samples showed the smoothest f a i l u r e . Un l ike the fat igued samples (see f i g . 49) f rac ture s ta r ted exact l y in the center of the notch along the sharp c rack . 46 Chapter IV DISCUSSION 4.1 S ta t i c Tests The s t a t i c t e n s i l e t e s t s revealed that the f racture load and the f racture toughness of the samples that were cut from the same laminate were not uniform. The scat te r was worst on the samples of Laminate 2 poss ib l y because no sharp cracks were int roduced. The scat ter was not so bad on Laminate 4. The average f racture toughness values for laminate 2 and laminate 4 were 40.18 and 29.9 MPa/m respect i ve l y using the ASTM compact tension sample equation (Sample L 2 i s excluded as i t was an except ional case ) . The d i f f e r e n c e in the toughness values i s probably due to the presence of a sharp crack in the samples of laminate 4. A l s o , when the th icknesses of the seven prepared laminates were measured, i t was seen that there was scat te r in the values from laminate to laminate (±0.6mm) and within the sample p l a t e . Hence the res in content and f i b r e volume f r a c t i o n was not uniform even within the same laminate. Therefore as d iscussed by Papirno the scat te r in the s t a t i c t e s t s would cause a sca t te r in the fat igue t e s t i n g of t h i s m a t e r i a l . 47 4.2 Fatigue Tests  i ) Fatigue L i f e Scatter was observed in the fat igue l i f e of the samples that were t e s t e d . Fat igue f a i l u r e s occurred below 3x10 s c y c l e s for laminate 3 which was thinner than the laminates 6 and 7 (the th icknesses of laminates 5, 6, and 7 were 4 . 1 , 4 .45, and 4.9 mm respect i ve ly ) whereas i t was above 3x10 s cyc les for the other laminates. Specimens with higher res in content appeared to have longer fat igue l i f e . If 5560N i s taken as the normal f racture load , a l l of the f a i l u r e s occurred when c y c l i c load range was above 71.2% of the f racture load . This i s not in agreement with the work of Beaumont and H a r r i s . 8 According to those workers the mater ia l does not f a i l in 107 c y c l e s for s t ress l eve l s less than 0.9 of the s t a t i c f a i l u r e s t r e s s . No s t ress vs cyc les to f a i l u r e curve was drawn us ing the test p o i n t s , as there was scat ter in the data and too few test points (as most samples f a i l e d from the h o l e s ) , but i t was observed to be a shallow l i n e as descr ibed by Dharan 6 ; Awerbuch and H a h n 2 2 ; and Owen. 3 8 In f i g . 39 the s t ress range was p lo t ted rather than the maximum s t ress because of the behavior of sample E 6 which had a very high maximum load (c lose to the average f racture load) with a high minimum load (hence, low s t ress range) during f a t i g u e . 48 The a-N and compliance data for thi s specimen showed that the maximum load d i d not affect the sample at a l l , because of the low stress range and the sample did not f a i l in 5x10 6 cycles. Therefore the material can be said to be stress range se n s i t i v e , but more work i s necessary to be ce r t a i n . i i ) Fatigue Damage Propagation Although there was scatter in the s t a t i c tests and fatigue l i f e data the measurement of crack propogation c l e a r l y revealed the character of the fatigue process. Most researchers have used one method to measure fatigue damage. On the other hand, using three methods ( i . e . t r a v e l l i n g microscope, radiography and compliance methods) increased the scope of the data and the methods complimented one another. It was observed that there are three stages of crack propagation during fatigue. An i n i t i a l acceleration in the f i r s t stage; deceleration in the intermediate stage (small amount of reacceleration towards the f i n a l stage may or may not occur); and reacceleration of the crack length, close to f a i l u r e . This is a very d i f f e r e n t behavior than in metals and in glassepoxy composites, in which cracks usually accelerate or stay steady during fatigue. The crack length measurement using x-ray films or pr i n t s produced an a vs N curve that was higher than obtained by the other methods because the x-ray technique not only reveals the cracks on the surface, but also the cracks produced in the inner 49 l a y e r s . The radiographs showed a damage zone (rather than the two cracks seen on the surface) which was propagating not only at right angles to the loading d i r e c t i o n , but along the loading d i r e c t i o n as well. When high stresses were used in the tests, the individual cracks that were v i s i b l e on the surface could be distinguished on the x-ray films and these cracks seemed to be growing faster than the damage zone. In the low stress fatigue tests the growth was in the form of a damage zone rather than well defined cracks. The size of the damage zone was considerably larger at the i n i t i a l stages of fatigue, revealing that fatigue damage sta r t s early in the test which was also observed by Papirno. 1 3 Fracture noise was also heard at the f i r s t few thousand cycles of the test. The i n i t i a l cracking i s known to consist of cracking in the 90° p l i e s (transverse cracks) as only the resin r e s i s t s the load in t h i s d i r e c t i o n . Reifsnider and Jamison 3 9 showed that the number of these cracks increases rapidly with load, in the f i r s t cycle and that with increasing cycles the spacing of transverse cracks approaches a value equal to the ply thickness. Thus the f i r s t stage of rapid change in the crack length and compliance must correspond to t h i s rapid increase in the number of transverse cracks. The presence of the transverse cracks in the 90° p l i e s causes two things to happen in the zero degree p l i e s . i . S p l i t s (resin cracks) occur p a r a l l e l to the f i b r e s , i i . Delaminations begin to grow between the two p l i e s . 50 The intermediate stage of fatigue probably corresponds to gradual growth of the delaminations as well as a steady projection of the transverse cracks p a r a l l e l to the main crack l i n e . The f i n a l f a i l u r e occurs when the delaminations link-up causing large sections of the specimen to separate. Delaminations were clear in some radiographs e s p e c i a l l y in f i g . 4 3 ( i i i ) . TBE penetrated more into the delaminated areas revealing i t s e l f as a continuous dark zone in the pri n t s of the x-ray f i l m s . The 'effective crack lengths' calculated using the compliance method followed the lowest pattern in the a-N data, because the compliance c a l i b r a t i o n was based on notches, whereas fatigue cracks are regions that are not completely severed and are therefore considerably tougher than a notch of the same length (see f i g . 38). Nevertheless e f f e c t i v e crack length followed the same pattern as the other two methods revealing the three stages of fatigue. The Paris plot drawn for the two tested samples did not follow the pattern of the metals (fig.39). The curves were plotted using the x-ray data and the crack v e l o c i t y showed continuous deceleration and a f i n a l acceleration. Hence the material does not obey Paris law. Similar Paris plots drawn for t h i s composite by Kunz and Beaumont 2 5 had a negative slope (for compression fatigue). 51 There i s not much previous work a v a i l a b l e which determined crack extension during fat igue except the work of Kunz and Beaumont 2 6 ; and K i m . * 0 F ig .1 shows the data of Kunz and Beaumont for compression f a t i g u e . This reveals the same pattern of behavior as observed in the present case . Kim's work a l s o revealed the pattern descr ibed in the present work and the dece lerat ion a f t e r the i n i t i a l growth of fa t igue was descr ibed as a mater ia l property and not dependent upon the load h i s t o r y , although change was not observed in the s t a t i c t e s t s . i i i ) Compliance Data The dependance of the compliance on the crack length obeyed a cubic r e l a t i o n s i m i l a r to metals which i s in agreement with the study of Mostovoy and h is co-workers .* 1 When a notch length c loser to the width (W) of the specimen was t e s t e d , th i s cubic r e l a t i o n was not v a l i d as the behavior of the l a s t test point shows in f i g . 9. Th is i s a lso in agreement with the LEFM theory . The normalized compliance values (C/C0) p l o t t e d vs number of cyc les revealed the decay in s t i f f n e s s dur ing fat igue in various amounts, depending upon the magnitude of the s t ress range. This i s in contrast with the work of Awerbuch and H a h n 3 ' 2 2 ; and L iber and D a n i e l . 5 They supported the idea that there i s no loss in strength or s t i f f n e s s of the mater ia l dur ing fa t igue . In reference 3 Awerbuch and Hahn even asser ted that there i s an increase in t e n s i l e modulus a f t e r f a t i g u e . There was l i t t l e observable change in s t i f f n e s s only in the samples tested at low s t resses ( i . e . compliance has the opposite e f f e c t ) l i k e 52 sample K 5 , but s t i l l the normalized compliance changed to 1.3 a f t e r 4 . 9 x l 0 6 c y c l e s (see f i g . 3 4 ) . The compliance data of the fat igue tested samples showed c l e a r l y that there are 3 stages of fat igue of t h i s m a t e r i a l . A c c e l e r a t i o n , dece le ra t ion and reacce le ra t ion of the damage. The magnitude of dece lerat ion var ied from sample to sample in the intermediate stage, but high s t resses seemed to cause d e c e l e r a t i o n and a slow reacce le ra t ion in t h i s stage. The compliance data seems to be in agreement with the r e s u l t s of P o u r s a r t i p , 2 7 and S m i t h . 2 8 iv) F i n a l Fracture Morphology Most of the samples f a i l e d from the holes of the compact tens ion specimen even though attempts were made to improve the surface f i n i s h of the ho les . Therefore the mater ia l i s very s u s c e p t i b l e to pin load ing . This i s a ser ious disadvantage e s p e c i a l l y in a i r c r a f t app l i ca t ions where var ious types of fa t igue loads could e f f e c t a pin hole of t h i s composite. Therefore more work i s necessary to improve t h i s behavior . Other than t h i s type of f a i l u r e , delamination was found to be the predominant f a i l u r e mechanism of the m a t e r i a l , which i s in agreement with the work of Whitcomb, 2 1 and Re i fsn ider and J a m i s o n . 3 9 Delamination was not found in a l l the p l i e s , but s p l i t t i n g along the 0° d i r e c t i o n c l e a r l y a f f e c t e d the f i n a l delaminat ion morphology ( f i g . 46). 53 Or. some f a i l e d samples debonding and f i b r e p u l l - o u t mechanisms were a lso v i s i b l e . The f i n a l f racture region was found to be smoother than the fat igued zone. Fatigue cracks i n i t i a t e d at the corners of the notch and/or at the corners of the sharp crack introduced whereas t ransverse c rack ing s tar ted at the center of the sharp crack lead ing to a smoother f racture surface in the s t a t i c a l l y t e n s i l e f rac tu red samples. 54 Chapter V CONCLUSIONS The fo l lowing conclus ions can be made in l i g h t of the present experimental d a t a : 1. There was a considerable scat ter found in the values of the f racture load and f racture toughness from laminate to laminate and on the samples of the same laminate, although the same manufacturing schedule was app l ied to a l l of the m a t e r i a l . There was a l s o a v a r i a t i o n of thickness and f i b r e volume f r a c t i o n in a l l the tested samples. Larger autoclaves are necessary to produce mater ia ls of uniform th ickness and p r o p e r t i e s . 2. The presence of a sharp crack and a blunt notch gave r i s e to d i f f e r e n t magnitude of the f racture loads meaning that sharpness i s an important factor in the f racture toughness of the m a t e r i a l . Sharpness increases ' s t r e s s concentrat ion factor ' . 3. As a resu l t of the scatter in the s t a t i c t e s t s , fa t igue l i f e showed a scat te r and i t appeared to be s t ress range sens i t i ve rather than maximum st ress s e n s i t i v e . 4. The t r a v e l l i n g microscope, radiography and compliance methods revealed that there are three stages of fat igue crack propagation dur ing the whole fat igue l i f e of the m a t e r i a l . In the i n i t i a l stage the crack or the damage zone a c c e l e r a t e d ; in the intermediate stage i t decelerated and in the f i n a l stage i t reacce le ra ted . The damage was in the form of a zone of 55 transverse cracks in the 90° p l i e s and s p l i t s in the 0° p l i e s . E f f e c t i v e crack length data measured by the compliance method gave the lowest a vs N curve as the fa t igue cracks were tougher than a notch of equivalent length . • » 5. . The mater ia l does not obey Par is law, _ because of the a c c e l e r a t i o n and dece le ra t ion of the fa t igue damage. The Par i s p lo t curves had a negative and vary ing slope in the f i r s t two stages of fat igue l i f e and an increase in the crack v e l o c i t y was only v i s i b l e c lose to the f i n a l f a i l u r e . 6. The normalized compliance (C/C0) p lo t ted versus number of cyc les a l so revealed the three stages of fa t igue by showing the increase in compliance or decrease in s t i f f n e s s . The compliance changed considerably during high s t r e s s range fat igue and change very l i t t l e in low s t ress f a t i g u e . 7. The compliance of the mater ia l for severa l notch lengths showed that C var ies l i n e a r l y with the cube of the notch length as i s the case for i s o t r o p i c m a t e r i a l s . 8. Most of the fat igued samples f a i l e d from the holes of the CTS specimen meaning that the mater ia l i s s e n s i t i v e to pin load ing . Delamination and res in cracking was found to be the dominant mechanism of fat igue f a i l u r e . Delamination f a i l u r e was revealed by the morphology of the f a i l e d samples. 56 Some samples f a i l e d with de laminat ion , debonding and f i b r e p u l l - o u t . The f i n a l f racture region was smoother than the fa t igued zone. A l l the fat igue cracks s tar ted at the corners of the notch or even at the corners of the sharp c rack , whereas in s t a t i c a l l y t e n s i l e f rac tured samples t ransverse cracking s tar ted at the center of the sharp crack leading to a smooth f a i l u r e . 9. More work seems to be necessary to explain the behavior of the graphite/epoxy composite under f a t i g u e . The product ion equipment should be improved in order to give uniform proper t ies to the m a t e r i a l . S t a t i c tests should be performed before the time consuming and expensive fat igue t e s t s . Al though, there i s scat ter in the s t a t i c and dynamic t e s t s of the graphite/epoxy, i t is found to be a fat igue r e s i s t a n t mate r ia l and seems promising for i t s future a p p l i c a t i o n s . 57 REFERENCES 1. Ramani, S .V . and Wi l l iams, D . P . , ' N o t c h e d and Unnotched Fatigue Behavior of Angle -Ply Graphite/epoxy Composites' , Fat igue of Fi lamentary Composite M a t e r i a l s , ASTM STP 636, 1977, pp. 27-46. 2. Kenda l l , D . P . , Journal of M a t e r i a l s , ASTM, V o l . 7, No.3, Sept. 1972, p. 430. 3. Awerbuch, J . and Hahn, H.T . , 'Fat igue and Proof Test ing of U n i d i r e c t i o n a l Graphite/epoxy Composites ' , ASTM STP 636, 1977, pp. 248-266. 4. Owen, M.J . and Mor r i s , S . , SPI, 25th Annual Technical Conference, Washington, D.C, Feb. 1970, Sect ion 8 - E . 5. L i b e r , T. and D a n i e l , I .M. , ' E f f e c t s of Tens i le Load Cyc l ing on Advanced Composite Angle -P ly Laminates ' , SPI, 31st Annual Technical Conferences, Washington, D . C , Feb. 1976, Sect ion 21 -E . 6. Dharan, C . K . H . , 'Fat igue Fa i lu re Mechanisms in Pultruded Graphite/Polyester Composites' , ASTM Symposium on Fatigue of Composites, Bal Harbor, F l a . , Dec. 1973, pp. 144-159. 7. Bader, M.G. and Johnson, M. , 'Fat igue Strength and Fa i lu re Mechanisms in Un iax ia l Carbon F ibre Reinforced Epoxy Resin System', Composites 4, No 2, March 1974, p .58. 8. Beaumont, P.W.R. and H a r r i s , B . , ' The E f f e c t of Environment on Fatigue and Crack Propogation in Carbon F ibre Reinforced Epoxy R e s i n ' , In ternat ional Conference on Carbon F i b r e s , Their Composites and A p p l i c a t i o n s , P l a s t i c s I n s t i t u t e , London, Feb. 1971 9. Ryder, J . T . and Walker, E .K . , Fatigue of Fi lamentary Composite M a t e r i a l s , ASTM STP 636, 1977, pp. 3 -26 . 10. Schutz, D. and Gerharz, J . J . , Composites, V o l . 8, No 4, Oct . 1977, pp. 245-250. 11. Schutz, D . , Gerharz, J . J . and Alschweig, E . , 'Fat igue Proper t ies of Unnotched, Notched and Jo inted Specimens of a Graphite/epoxy Composite' , Fatigue of F ibrous Composite M a t e r i a l s , ASTM STP 723, 1981, pp. 31-47. 12. Stinchcomb, W.W. and h is co-workers, 'Frequency Dependant Fatigue Damage', Fa i lu re Modes in Composites II , 1974, p.131. 13. Papirno, R., 'Fat igue Fracture I n i t i a t i o n in Notched Graphite/epoxy Specimens', Journal of Composite Mater ia l s , 58 V o l . 10, Jan. 1977, pp. 41-50. 14. Foye, R.G. and Baker, D . J . , 'Design of Or thotropic Laminates ' , 11th S t ruc tu ra l Dynamics and Mate r ia l s Conference, Denver, Colorado, 1970; Journal of Composite M a t e r i a l s , V o l . 5, Jan. 1971, p .50. 15. P ipes . R.B. and Pagano, N . J . , ' Inter laminar St resses in Composite Laminates Under Uniform and A x i a l E x t e n s i o n ' , Journal of Composite M a t e r i a l s , V o l . 4, 1970, p.204. 16. Puppo, A . H . and Evansen, H .A. , ' Inter laminar Shear in Laminated Composites Under General ized Plane S t r e s s ' , Journal of Composite M a t e r i a l s , V o l . 4, 1970, p.204. 17. Chen, E .P . and S i h , C . C , ' I n t e r f a c i a l Delamination of a Layered Composite Under Ant i -P lane S t r a i n ' , Journal of Composite M a t e r i a l s , V o l . 5, 1971, p .51. 18. Pagano, N.J . and P ipes , R . B . , 'The Influence of Stacking Sequence on Laminate S t reng th ' , Journal of Composite M a t e r i a l s , V o l . 5, 1971, p .55. 19. Prakash, R., 'A Fractographic Study of Fat igue in CFRP' , Composites, V o l . 10, No 3, July 1979, pp. 174-178. 20. Hashin, Z. and Rotem, A . , 'A Fatigue F a i l u r e C r i t e r i o n for F ibre Reinforced M a t e r i a l s ' , Journal of Composite Mater ia ls 7, Oct . 1973, p. 448. 21. Whitcomb, J . D . , 'Experimental and A n a l y t i c a l Study of Fatigue Damage in Notched Graphite/epoxy Laminates ' , Fatigue of Fibrous Composite Mater ia l s , ASTM STP 723, 1981, pp .48 -63 . 22. Awerbuch, J . and Hahn, H.T . , 'O f f -Ax i s Fat igue of Graphite/epoxy Composite ' , Fatigue of Fibrous Composite M a t e r i a l s , ASTM STP 723, 1981, pp. 243-273. 23. Mandel l , J . F . , McGarry, F . J . and Merer U . , ' F i b r e Or ien ta t ion , Crack Ve loc i t y and Cyc l i c Loading E f f e c t s on the Mode of Crack Extension in Fibre Reinforced P l a s t i c s ' , Fa i lu re Modes in Composites II, 1974, p .33. 24. Chang, F . H . , Gordon D . E . , Rodin i , B.T. and McDaniel , R . H . , 'Real Time Character i zat ion of Damage Growth in Graphite/epoxy Laminates ' , Journal of Composite M a t e r i a l s , V o l . 10, July 1976, p. 182. 25. Sendeckyj, G.P. and Maddux, G . E . , 'Comparison of Holographic, Radiographic and Ul t rasonic Techniques for Damage Detect ion in Composite M a t e r i a l s ' , Journal of Composite M a t e r i a l s , V o l . 11, Oct. 1978, pp. 1037-1056. 59 26. Kunz, S . C . and Beaumont, P.W.R. , 'Microcrack Growth in Graphite Fiber-Epoxy Resin Systems During Compressive F a t i g u e ' , Fatigue of Composite M a t e r i a l s , ASTM STP 569, 1975, pp. 71-91. 27. P o u r s a r t i p , A . , Ashby, M.F. and Beaumont, P.W.R., 'Damage Accumulation During Fat igue of Composites' , Sc r ip ta M e t a l l u r g i c a , V o l . 16, No. 5, Pergamon Press L t d . , Feb. 1982, pp. 601-606. 28. Smith, E.W., PhD Thes i s , Cambridge Un ive rs i t y , Engineering Department, U.K. , 1976. 29. Tada, H . , P a r i s , P. and I rwin, G . , The Stress Analys is of Cracks Handbook, Del Research Corporat ion, Hel lertown, Pennsylvania, 1973, pp. 2.19-2*.20. 30. Zhang, H . S . , Nadeau, J . S . and Teghtsoonian, E . , 'Fat igue Crack Propogation in Glass/epoxy Composites ' , The Un ive rs i t y of B r i t i s h Columbia, Vancouver, B . C . , 1981. 31. S i h , G . C . , 'Fracture of Composite M a t e r i a l s ' , Proc, F i r s t USA-USSR Symposium, R iga , USSR, 1978. 32. Beaumont, P.W.R. and Tetelman, S . , 'The Fracture Strength and Toughness of F ibrous Composites ' , F a i l u r e Modes in Composites, The M e t a l l u r g i c a l Soc iety , AIME, pp. 49-80. 33. K e l l y , A . , ' In ter face E f f e c t s and The Work of Fracture of a Fibrous Composite' , Proc . Royal S o c , London, A. 319, 1970, pp. 95-116. 34. Beaumont, P.W.R., 'A Fracture Mechanics Approach to F a i l u r e in Fibrous Composi tes ' , J . Aveston, Gordon and Breache Science Publ ishers L t d . , 1974, V o l . 6 , pp. 107-137. 35. S i h , G . C . , H i l t o n , P . D . , Badal iance, R., Shenberger, P .S . and V i l l a r r e a l , G . , ' F rac tu re Mechanics of Fibrous Composites ' , ASTM Spec ia l P u b l i c a t i o n s , No 521, 1973, p. 98. 36. Hertzberg, R.W., Deformation and Fracture Mechanics of Engineering M a t e r i a l s ' , John Wiley and Sons, 1976, pp. 465-472. 37. Radford, D.W., 'F racture Toughness of a Carbon Fibre/epoxy Composite M a t e r i a l ' , M.A .Sc . Thes is , The Univers i ty of B r i t i s h Columbia, Vancouver, B . C . , 1982. 38. Owen, M . J . , 'Fatigue of Carbon F ibre Reinforced Composites ' , Fracture and Fat igue , Academic Press , New York, 1974. 60 39. R e i f s n i d e r , K .L . and Jamison, R., ' F rac tu re of Fat igue -loaded Composite Laminates ' , Int . J . F a t i g u e , V o l . 4, Butterworth and Co (Publ ishers) L t d . , Oc t . 1982, pp. 187-197. -40. Kim, R .Y . , 'Experimental Assesment of S t a t i c and Fatigue Damage of Graphite/epoxy Laminates ' , U n i v e r s i t y of Dayton Research I n s t i t u t e , A i r Force Mater ia l s Laboratory , 1978. 41. Mostovoy, S . , Cros ley , P.B. and R i p l y , E . J . , 'Use of Crack l ine Loaded Specimens for Measuring Plane St ra in Fracture Toughness', Journal of M a t e r i a l s , V o l . 2 . , Sept. 1967, pp.661-681. 61 i i i 1000 * (cyclM) MOO F igure 1 - Increase in the crack length dur ing compression fa t igue for u n i d i r e c t i o n a l and [0/90] c r o s s - p l y graphite/epoxy c o m p o s i t e . 2 6 F igure 2 - S t i f f n e s s decay during f a t i g u e . T h e s e a r e t h e data of Smith ( 2 2 . 5 ° to the weave) used in the development of P o u r s a r t i p ' s t h e o r y . 2 7 62 P r — * — • 1 W=56mm, 6 =72mm, H=62mm, P = LOAD, 0 = 19 or24.5mm, d=8mm, g=32mm, Figure 3 - Compact tension specimen used in the experiments. 63 A S / 3 5 0 1 - 6 / TEMPERATURE g 1 1 hour / : i i • i ! 1 , i • i , i i J 1 2 hours 1 1 f • 1 | 1 j 200'F —^ I 3 - 5*F/nif 1 1 1 1 1 1 3|- 5*F/«jin • i J 1 - 2'F/nln | • 1 TIME Figure 4 - ( i ) Curing Treatment of graphite/epoxy composite A. 1 H. i 'i F , R c z - : - : : : 3 = LAM. 2 » i a LAM. 4 and others Figure 4 - ( i i ) The pos i t ion of the compact tension samples and t h e i r notches as they were cut from a laminate. 65 C R O S S H E A D D I S P L A C E M E N T Figure 5 - Typ ica l t e n s i l e loading pattern of the tes t samples leading to f racture using Instron tes t ing machine. 66 SAMPLE A*REFERENCE SAMPLE, Figure 6 - The method of drawing new C - a 3 l i n e s i f the compliances of the samples have the same notch length from the same laminate are d i f f e r e n t from each other . 67 DEFLECTION (8) mm Figure 7 - Load -de f lec t ion data of sample F 6 for various notch lengths. i r — " I 1 ~T5 18 22 26 3CT 34 38 42 NOTCH LENGTH (a) mm Figure 8 - Change in Compliance with notch length for Sample F s er» 00 Figure 9 - Var ia t ion of compliance with the cube of notch length for sample F 6 **1 C fD O I 0» rt C ro fl> & 0) rr 0) o m 2 ° * m S T R E S S R A N G E (AO") MPa O T 1—~1 1 o ro o T " O r o • > 13 I -m co 2 r -m o co > 2. -D a. a! 3 O 2 rn co • • • • Q i i i i i° i i i i OL S A M P L E J 1 1 1 O--MAX. DAMAGE ZONE LENGTH Q=T. MICROSCOPE READING I 4 5 h 3 4 0 i t 3 5 h o UJ 3 0 .j * 2 5 o < cc 2 0 o o • o0=24.5mm 10 15 2 0 C Y C L E S (N) ( X l O 4 ) 25 N f Figure 11 - Crack Length vs cyc les for sample J 3 max. load=4446N, min. load=222N,a0=24.5mm S A M P L E K 3 £ E O - M A X . D A M A G E Z O N E L E N G T H ••T. M I C R O S C O P E READING 0.5 LO L5 C Y C L E S (N) ( x l O 3 ) 2.0 % Figure 12 - Crack length vs . cyc les for sample K 3 . max. load=4528N, min. load=240N, a0=24.8mm. There i s cons iderable d i f f e r e n c e in the two types of readings. (N represents hole f a i l u r e ) to SAMPLE L i 1 1 1 O'MAX. DAMAGE ZONE LENGTH •=T. MICROSCOPE READING 45 ^ 4 0 X 3 5 H O z 3 0 UJ -j u o • o • N f = 93 320 cycles, O CYCLES (N) (XlO4) 8 Figure 13 - a vs N for sample L 3 . max. load=4688N, min. load=142N, a0=25mm. There i s not a rapid increase in crack speed as f a i l u r e nears . to SAMPLE B5 E E *o 40 X h- 35 O z lxl 30 1 °o < 20 o 15 , 1 1 r 0 « M A X . DAMAGE ZONE LENGTH OT. MICROSCOPE READING o*:@ — • 2ncrock - I s t crock A A « E F F E C T I V E CRACK LENGTH JL i J L 2 3 CYCLES (N) 4 -5 5 Figure 14 - a vs N for sample B 5 . max. load=4466N, min. load=151N, a 0 e 24.5mm. A second crack formed a f te r some time which had a v e l o c i t y greater than the f i r s t c rack . SAMPLE (L 9 1 1 1 r 0=MAX. DAMAGE ZONE LENGTH Q S T . MICROSCOPE READING A* E F F E C T I V E C. L E N G T H - 4 0 - O • A I -2 3 4 5 CYCLES (N) (xlO6) Ni Figure 15 - a vs N for sample C 5 . max. load=41u1N, min. load=71N, a0=25mm. Low s t ress fat igue t e s t . E E SAMPLE E, 13 X h-O 35 z UJ -J 30 25 < CC o 20 E 28 E • -J 27 • o u: 26 u. UJ O'MAX. DAMAGE ZONEi LENGTH Q- T. MICROSCOPE READING 4-y A O eff. JL I Ji 9 10 CYCLES (N) (XlO5) II 12 Figure 16 - a vs N for sample E 5 . max. load=4822N, min. load=338N, a0=25mm. X-ray values were nearly constant throughout the fat igue l i f e . a. EFF. C. LENGTH mm CRACK L. (a) mm LL £ E S 35 SAMPLE H. o 30 w 25 d 20 E E 28 0 O MAX. DAMAGE ZONE LENGTH •=T. MICROSCOPE READING 5 27 ? 26 U.' Li. Ui 25 N, 5 6 7 8 CYCLES (N) (XlO5) 10 II Figure 18 - a vs N for sample H 5. max. load=4857N, min. load=80N, a0=24.5mm. Surface and x-ray readings are the same. CO SAMPLE K. 5 Figure 19 - a vs N for sample K 5 . max. load=3932N, min. load=80N, a0=24.5mm. Typical low stress f a t i g u e . Sample d id not f a i l . V£> SAMPLE A 6 E 4 5 E -5 4 0 i i I r 0=MAX. DAMAGE ZONE LENGTH •= T. MICROSCOPE READING 3 5 x e> g 3 0 * 2 5 o < 2 0 cc o D 8 0.5 1.0 1.5 2.0 2.5 C Y C L E S (N) (XI0 ) N «4 .59x l0c . 3.0 3.5 Figure 20 - a vs N for Sample A g . max. load=5204N, min. load*80N. High s t ress fa t igue . F a i l e d normally . Two types of data are in good agreement. oo o S A M P L E C o = 1 T MAX. DAMAGE l • " ZONE ! 1 1 LENGTH 1 ' " T 1 I - T — E 4 0 - •= T. MICROSCOPE READING » -E 3 5 o d n o L 9 — D " — LJ N6TH 1 3 0 2 5 r 1 1 1 i a 0 = 24.5 mm i i i i i t i LU - J 1 2 3 4 5 6 7 8 9 10 tACK 3 5 3 0 2 5 N 0 (XlO 5) B — IX. O — Q i i i S A M P L E 1 i V 24.45 mm i - J 1 1 I 1 I L _ 0.5 1.0 1.5 2.0 2.5 3.0 3.5 C Y C L E S (N) ( X I 0 ) Figure 21 - i i ) a vs N for Sample C 6 . max. load=3692N, min. load=142N. At the very beginning, the sample had an immediate f racture and hence a shorter l i f e , i i ) a vs N for sample G 6 . max. load=5249N, min. load=80N. High s t ress f a t i g u e . SAMPLE % 40 e> i 1 1 1 OMAX. DAMAGE ZONE LENGTH 35 30 •=T. MICROSCOPE READING S 2 5 5 20 -1 O O o • •o • o • •o • J eff. -6 CYCLES (N) (x|0) Figure 22 - a vs N for Sample E f . max. load=5266N, min. load=1228N, a0=24.8mm. Sample did not f a i l . High max. s t ress and a low st ress range was used. Sample showed the behavior of a low s t ress fat igue i . e . not max. s t ress s e n s i t i v e . SAMPLE K 6 E E x —J 45 h 40 35 30 25 20 15 , 1 1 r 0 » M A X . DAMAGE ZONE LENGTH • « T . MICROSCOPE READING 8 A O • _ A'EFFECTIVE C. L 0.5 1 0 « 1-5 CYCLES (N) (XlO6) 2.0 Figure 23 - a vs N for Sample K 6 . max. load=4902N, min. load=142N. CD CO SAMPLE L s £ £ 40 X 35 H e> z 30 UJ - J 25 tt < 20 a 15 1 1 r -0 s MAX. DAMAGE ZONE LENGTH • » T . MICROSCOPE READING A = EFFECTIVE C. L. JL 10 15 CYCLES (N) 20 (XlO4) 25 Figure 24 - a vs N for Sample L 6 . max. load=5071N, min. load=142N, a0=24.3mm. High s t ress f a t i g u e . CO SAMPLE C7 § 4 0 3 3 5 - Q • A • 0=MAX. DAMAGE ZONE LENGTH •«T . MICROSCOPE READING - -Obockside T.M.R. A « E F F E C T I V E C. L o =24.9 mm o P: • A r 5 CYCLES (N) (x|0 ) a, Figure 25 - a vs N for Sample C , . max. load=4573N, min. l o a d « 1 5 1 N , >=24.9mm. Sample was not fat igued up to f i n a l f a i l u r e . A t y p i c a l medi s t ress f a t i g u e . urn 00 SAMPLE F7 35 30 25 20 26 25 24 ( , j 1 p = MAX. DAMAGE ZONE LENGTH 0 ^ 2 4 . 5 ™ ™ »T. MICROSCOPE READING ^ n • - • • 6 8 10 CYCLES (N) (X|(55) 12 Figure 26 - a vs N for Sample F 7 . max. load=4991N, min. load=71N, a0=24.5mm. High s t ress fa t igue . E f f e c t i v e crack length showed a higher increase in v e l o c i t y than the o t h e r s . 00 cr> SAMPLE l 7 E UJ(D 35 30 "P O • z UJ 25 - J 20 -< or 15 o T • •A o 0 =24.5 mm 0 • — - A Q A 0*MAX. DAMAGE ZONE LENGTH •=T MICROSCOPE READING A=EFFECTIVE C. L. 1 1 ; I L _ 0 A -8 10 12 14 CYCLES (N) (XlO5) 16 18 Figure 27 - a vs N for Sample I7. max. load=5160N, min. load=80N, a0=24.5mm. 00 1 1 1 1 I 1 1 1 I I 1 I I 1 I 1 1 1 I I DEFLECTION (8) mm Figure 28 - Change in the load - d e f l e c t i o n curves during fa t igue of samples L 6 and H 6 . 2.087x10 rnn/H N.* 7,506,660 eyes. 2 3 CYCLES 4 - « 5 (N) (XlO6) Figure 29 - Increase in the compliance of Sample C 5 dur ing fat igue , CD VO Figure 30 - Increase in the compliance of Sample E 5 dur ing f a t i g u e . vo o NORMALIZED COMPLIANCE (C/C0) £6 T 1 1 r o u 1.3 o T 1 r —i 1 r SAMPLE K. QL 2 O u 1.2 .. 1.1 C0= I.996xl0"4mm/N o LO J I I I I I I L 6 CYCLES (N) (XlO ) Figure 34 - Increase in the compliance of Sample K5 dur ing f a t i g u e . Figure 35 - Increase in the compliance of Sample E s dur ing f a t i g u e . 2 4 6 8 10 12 14 16 18 20 CYCLES (N) (XlO9) Figure 36 - Increase in compliance of K6 dur ing fat igue vo CJ I i i r 1 1 I i i i Figure 37 - Increase in the compliance of I7 and F 7 dur ing f a t i g u e . vo i 1 1 1 1 1 1 1 r DEFLECTION IS) mm Figure 38 - Load de f lec t ion data of a t e n s i l e f ractured sampl ( f a i l e d a c c i d e n t a l l y ) . CRACK VELOCITY (log da/dN) m/sec. 66 100 ( i i ) C 6 N=9xl0 5 cycles U3.6) 101 * : -1 ( i i i ) E 6 , N=4.22X10 6 cycles (x3.7) 103 Figure 4 2 Sample G 6 ( i ) N=5.3X10 1 1 cyc les (x3.3) ( i i ) G 6 N = 2 . 7 X 1 0 5 cyc les (x3.6) Figure 43 Sample K 6 ( i ) N=1.66x10 s cyc les (x3.5) ( i i ) K6 N=3.28X10 5 cyc les (x3.5) 105 ( i i i ) K 6, N=2.17X10 6 cycles (x3.5) 106 Figure 44 Sample L 6 ( i ) N=1.36x10 s c yc les (x3.3) ( i i ) L 6 N=2.07x105 cyc les (x3.6) 107 Figure 45 Sample C 7 (i) N=6.65x10* cycles (x3.6) ( i i ) C 7 N=1.93x10* cycles (x3.75) 108 ( i i i ) C 7 f N=4.2X10 5 cyc les U 3 . 7 5 ) 109 \ Figure 46 - A sample f a i l e d by de laminat ion . Not ice the f a i l u r e i s caused from the damage in the two perpendicular d i r e c t i o n s that i s v i s i b l e in the rad iographs . F igure 47 - F a i l e d sample geometry showing de laminat ion , f i b r e debonding and p u l l - o u t . Figure 49 - Sample f rac tu red under Instron incremental t e n s i l e loading . 111 Table I F r a c t u r e Toughness values f o r samples of Laminate 2 using ASTM compact t e n s i o n sample e q u a t i o n (eqn. 3) Sample Number Notch Length a (mm) Notch t o Width r a t i o a/w Th i c k n e s s t (mm) F r a c t u r e load Pf (N) F r a c t u r e Toughness ^(MPai'in) *2 18 0.321 3.985 5693 36.565 B 2 19 0.339 4.130 5071 32.867 c 2 18 0.321 4.01 5560 36.893 D 2 19 0.333 3.970 6574 43.212 E 2 19.8 0.350 4.250 7384 46.590 F 2 19.5 0.345 3.990 7006 47.406 G2 21.5 0.375 4.050 6427 45.733 H2 20.5 0.353 4.235 6503 41.566 I? 21.0 0.363 3.950 5960 41.850 J2 20.0 0.357 4.090 5271 35.915 K 2 19.8 0.350 4.010 4893 33.396 L 2 19.3 0.342 3.970 9118 61.116 112 Table I I F r a c t u r e Toughness valu e s f o r samples of Laminate 4 u s i n g ASTM compact t e n s i o n sample e q u a t i o n (eqn. 3) Sample Number Notch Length a (mm) Notch t o Width r a t i o a/w Thi c k n e s s t (mm) F r a c t u r e l o a d Pf (N) F r a c t u r e Toughness K^MPav/m) A. 18.3 0.3327 4.970 5591 30.029 B, 19.2 0.349 5.250 5898 31.093 c. 20.0 0.357 4.880 5427 30.359 D, 20.0 0.364 4.910 5471 31 .249 E» 19.4 0.353 4.895 4653 26.233 Fft 19.4 0.353 4.895 4559 25.785 G. 19.7 0.358 4.960 5471 31.060 H, 19.8 0.354 4.970 5769 32.686 I« 19.8 0.354 4.860 5493 32.697 J« 19.5 0.355 4.990 5017 28.176 Kft 20.0 0.357 5.010 5489 30.523 Lft 20.0 0.357 4.935 5293 29.882 113 Table I I I F a t i g u e T e s t i n g Data for Laminates 1,2,3,4, and 7 i ) LAMINATE 1 Sample Number Notch Length a (mm) Max. Load £>ax <N> Min. Load Pmin <»> Load Range AP(N) S t r e s s Range Ao Mpa C y c l e s t o F a i l u r e A, 18.5 4435 911 4324 19.1 6.64xl0« (NF) C, ( S O 22.0 4946 943 4003 18.3 4990 D, (SC) 21.0 4626 1059 3567 16.03 690 E, (SC) 22.0 4385 400 3985 18.83 4320 F, (SC) 21.0 4644 495 4199 18.87 1250 G, (SC) 21.0 4404 854 3550 15.95 45570 H, (SC) 21.0 4515 890 3625 16.29 4360 I i 20.0 4003 979 3024 14.2 4.24x10' (NF) J i 20.0 4359 756 3603 16.92 4.8x10' (NF) Ri 18.5 4092 778 3314 15.22 5.1x10 s (NF) L, 18.5 4510 133 4377 21.01 5x10' (NF) 'SC = Stroke C o n t r o l 'NF' = No f a i l u r e Note: Samples C,, D,, E,, F,, G,, H, were f a t i g u e d under 'Stroke C o n t r o l ' . Sample B, was t e n s i l e f r a c t u r e d . Load t o f r a c t u r e was 5756N. i ) LAMINATE 3 G 3 24.5 4484 356 4128 33.68 1 12240 I j 29.0 4048 303 3745 33.67 95640 J 3 24.5 4466 222 4224 34.28 269210 K 3 24.8 4528 240 4288 34.53 212960 (HF) L 3 25.0 4688 142 4546 37.22 93320 'SC = Stroke C o n t r o l 'NF' = No f a i l u r e 'HF' = Hole f a i l u r e Note: Sample A 3 was compliance t e s t e d . Sample C 3 f r a c t u r e d a c c i d e n t a l l y . Below samples of Laminate 3 was o n l y c y c l e d and crack l e n g t h was not measured. Most of them f a i l e d by hole f a i l u r e . B 3 19.8 4484 294 4190 28.16 1.15x10' (HF) D 3 20 6263 543 5720 38.66 38360 (HF) E 3 20 6192 712 5480 39.02 4860 (HF) F 3 24.5 4995 907 4088 31.58 38400 (HF) 114 i i i ) LAMINATE 5 Sample Number Notch Length a (mm) Max. Load P (N) max Min . Load min Load Range AP(N) Stress Range Ao Mpa Cyc les to F a i l u r e N f B s 24.5 4466 151 4315 32.17 459560 c 5 25.0 4101 71 4030 31 .69 7506660 D s 25.5 4973 80 4893 38.16 425260 (HF) E 5 25.0 4822 338 4484 34.28 1077550 (HF) F 5 25.0 5071 53 5018 38.51 431630 (HF) G 5 25.0 4617 80 4537 34.79 705630 (HF) H 5 24.5 4857 80 4777 36.02 1102290 (HF) Js 25.5 3994 80 3914 31 .28 1148910 K5 24.5 3932 80 3852 31 .04 4.9x10 s (NF) 'HF' = Hole f a i l u r e 'NF' = No f a i l u r e Note: Samples A 5 and L s were compliance tested . Sample J 5 was i n i t i a l l y loaded to i t s f r a c t u r e s t ress leve l to observe i t s Load to f racture (P £ 5 5 1 6 N ) . That i s why i t had a short l i f e with a low s t r e s s . Sample I5 was a c c i d e n t a l l y f ractured dur ing s t a t i c t e n s i l e loading. iv) LAMINATE 6 24.2 5204 80 5124 38. 18 458880 24.5 4448 80 4368 32.86 4325830 c 6 24.5 3692 1 42 3550 26.81 981380 E e 24.8 5266 1 228 4038 29.0 5X10 6 (NF) G 6 24.45 5249 80 5169 37.51 -H 6 24.5 5089 80 5009 37. 18 -K6 24. 1 4902 142 4760 33.93 -L 6 24.3 5071 142 4929 36.53 'HF' = Hole f a i l u r e ' NF' = No f a i l u r e Note: Sample F 6 was compliance t e s t e d . Sample D 6 f a i l e d at the beginning of the fat igue test in which Max. Load was 5305N. So was Sample I6. Sample J 6 was not used. Sample C 6 seemed to have an immediate cracking at the beginning of the t e s t . 1 1 5 v) LAMINATE 7 Sample Number Notch Length a (mm) Max. Load P (N) max Min. Load P (N) min Load Range AP(N) S t ress Range Ao Mpa Cyc les to F a i l u r e N f c 7 2 4 . 9 4 5 7 3 1 5 1 4 4 2 2 2 9 . 4 8 _ F 7 2 4 . 5 4 9 9 1 7 1 4 9 2 0 3 0 . 9 2 -I T 2 4 . 5 5 1 6 0 8 0 5 0 8 0 3 1 . 4 6 Note: Sample G 7 was compliance t e s t e d . Sample A 7 f rac tu red at the very beginning of the fat igue t e s t . 116 Table IV Compliance Test Resu l ts i ) Values of Compliance (C) vs Notch Length (a) and C vs a 3 for sample A 5 . Notch Length (a) Compliance (C) Cube of Notch Length mm mm/N (xlO"*) mm3 24.5 1.994 14706.13 28.0 3.066 21952.00 34.2 5.418 40001.69 39.5 8.783 61629.88 i i ) For sample again from Laminate 5 25.2 2.135 16003.00 28.47 2.884 23076.10 30.75 3.740 29076.05 32.65 4.496 34805.63 34.68 5.578 41709.72 37.3 7.566 51895.12 40.1 14.577 64481.20 43.45 17.273 82029.36 Eqn. of C vs a 3 using the f i r s t f i v e notch lengths (for L 5 ) i s : C=1.3193881x10' 7 a 3 -1.226322x10"* i i i ) For sample F 6 from Laminate 6 17.5 1.062 5359.38 24.6 1 .940 14886.94 27.05 2.543 19792.55 29.00 3.073 24389 31 .8 4.078 32157.43 34.95 5.341 42691.51 40.0 9.772 64000.00 44.0 18.080 85184 C vs a 3 equation for F 6 using the f i r s t 6 notch lengths i s : C=1.143664x10' 7 a 3 +2.9448x10'" 117 iv) For sample G 7 Notch Length (a) mm Compliance (C) mm/N (xlO-") Cube of Notch Length mm3 24.5 2.078 14706.13 26.4 2.399 18399.74 29.15 3.156 24769.41 31 .77 4.044 32066.51 33.82 4.984 38683.06 35.9 5.933 46268.28 40.5 9.837 66430.13 44.45 18.196 87824.42 C vs a 3 equation for G 7 using the f i r s t 6 data points i s : C=1.2166865x10* 7a 3+1.4785x10-" v) For sample A 3 from Laminate 3. (The resu l ts were not used for ' e f f e c t i v e crack length ' measurements. 18.8 1.18 6644.67 27.8 3.0230 21484.95 31.2 4.456 30371.33 35.0 6.519 42875 39.0 11.18 59319 118 Table V Weight and Volume F r a c t i o n of the F i b r e s for Each Laminate . Lam. Num. Comp. Mass(gm) (m c) F iber Mass(gm) (m f) Mass F r a c t i o n of f i b r e s (mf/m c) Volume of f i b r e s ( v f ) (cm 3) Volume of comp <v c) (cm3) Volume F r a c t i o n of f i b r e <vf ) 1 6.7666 5.0797 0.751 2.6735 4.0911 0.653 2 3.4900 2.6622 0.763 1.4012 2.0968 0.668 3 5.5993 4.1124 0.736 2.1644 3.4139 0.634 4 3.8129 2.6728 0.701 1 .407 2.365 0.595 5 3.5117 2.5369 0.722 1 .335 2.1542 0.620 6 6.0794 4.316 0.710 2.2716 3.7534 0.605 7 7.9994 5.6516 0.702 2.9556 4.9588 0.596 Note - p f =1.9gm/cc, ^ = 1 . 1 9 gm/cc 

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