FIBRE PRESTRESSED COMPOSITES A study of the influences of fibre prestressing on the mechanical properties of polymer

ma& composites

B y:

Siamak Motahhari

A thesis submitted to the Department of Matenals & Metailurgical

Engineering in conformity with the requirements for

the degree of Doctor of Philosophy

Queen's University

Kingston, Ontario, Canada

Match, 1998

copyright O Siamak Motahhari, 1998

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Fibre prestressing during the curing of the polymeric resin is applied in some fabrication processes of composite materials nich as filament windmg and pultrusion processes. The influences of fibre prestresshg on certain mechanical properties have been inveaigated and justified in the present thesis.

Epoxy resh with E-glass fibre and carbon fibre were used to manufacture the samples. The samples were made by applying and holding the tension on the fibres on a horizontal tensiometer machine while the resin was being cured. For glass-epoxy and carbon-epoxy samples Merent prestressing levels nom 10 to LOO MPa and 20 to 140 MPa were applied respectively during the curing of the resin. The samples were made at three Merent curing temperatures. Flexural strength, flexural modulus, and impact strength of the composites were chosen and measured as representative of the mechanical properties. It was shown that in all cases the studied mechanical properties sipificantly increased when fibre prestressing mcreased. The increase of the mechanical properties continued up to a certain fibre prestressing level. Beyond that level, however, the mechanical properties declined. The best fibre prestressing level at which the highea mechanical properties were obtained, was shown to be a fùnction of the curing temperature and the constituent materials of the composites.

In the second part ofthis thesis the effort has been taken to explain the changes of the mechanical properties caused by fibre prestressing. The residual aresses resulting 6om the fibre prestressing and resin shrinkage were responsible for the changes of the mechanical properties. A new method was developed to measure the residual stresses which were fonned in the composite during the curing process. This method was based on the evaluation of the residual strain in the fibres right after the curing process and removal of applied prestress. Using this method, it was indicated that the residual stresses in the fibre prestressed composites were a linear, increasing fùnction of the prestressing level.

Furthermore, a new method was introduced to measure the shrinkage of the polymeric resins. By the use of this method, the shrinkage of the epoxy resin was measured for the three curing temperatures, previously used to fabricate the samples. The tests were c d out on the un-remfarced polymer. In the next aep, some experiments were arranged to investigate the contribution of the resh shrinkage to the formation of the residual stresses in the reidorced polymer. To achieve this goal a bi-layer composite-neat polymer bar was made. The residual strain of the polymer was calculated by the measurement of the deflection of the bar. Comparison of the residual strain of the polymer in the bi-layer sample with the shrinkage of the polymer in the un-reinforced sample revealed that only 3.3% of the shrinkage of the resin contributes to form the residual stresses in the bi-layer sample.

The stress 6ee temperature of the bi-layer sample, the temperature at which the deflection of the sample disappeared, was determined by r e - h e a ~ g the sample and measuring the deflection of the sample at the same tirne. This temperature was the point below which the stresses were fonned in the composite. The stress fiee temperature was found to be much lower than the curing temperature which usualiy was taken as stress fiee temperature.

Acknowledgments

It is a pleasure to express my genuine gratitude to my r e ~ a r c h supervisor, Dr.

John Cameron for his extensive encouragement, guidance, support and insight. H i s t h e

and his hands-on assistance during the mvestigations were invaluable and are greatly

appreciated.

Also, 1 would lüte to thank the faculty and staff of the Queen's University

Materials & MetaUurgical Engineering Department for their support and assistance.

Among aii, Dr. V. Kristic is especiaiiy thanked for many hitful discussions.

1 gratefiiliy aclmowledge the financial support of the Iranian Ministty of Culture &

Higher Education, Queen's University and Natural Science and En-gineering Research

Council of Canada (NSERC).

n i e support of my family never wavered even through the mon difEcult times. 1

thank them aii for their understanding, love and carhg we &are together.

This study would not have been possible without the help of the above-mentioned

people.

Contents

Chapter 1: Introduction and Scope ......m....m.................................................................. 1

Chspter 2: Literature Review.. ..................................................................................... 4 2- 1: The Genesis of Glass Fibre Composites ........................................................ -4

2- 1 O 1 : Fibre Glass ......................................................................................... 4 2- 1-2: Epoxy Resin ....................................................................................... 5

2-2: Fibre Restressed Composites ........................................................................ 5 2-2- 1 : Enhancement of Composite Strength Through Appücation of

................................................................. Previously Stressed Fibres 9 2-3: Residual Stresses in Fibre Composites ........................................................ 1 1

....................................... 2-39 1 : Causes of Residual Stresses in Composites 12 ............................................................... 2-3- 1- 1: Thermal Stresses 12 .............................................................. 2-30 1-2: Fibre Pre-tension 1 2

........................................................... 2-3- 1-3 : Chemical Shrinkage 13 ........................................................ 2-3- 1-4: Moisture Absorption 1 4

2-3-2: Prediction of Residual Micro-stresses .............................................. 13 ...................................................... 2-3-2- 1: Analytical Approaches 1 4

................................................... 2-3-2-2: Finite Element Modeling 1 6 2-3 -3 : Measurement of Residual Stresses ................................................... 1 7

......................................................... 2-3-3- 1: Destructive Methods 1 s .................................................. 2-3-3- 1- 1: Tende Testing 18 .................................................. 2-3-39 1-2: Layer Removal 19

2-3-3- 1-3: Radial Cut Method ........................................... 1 9 ..................................................... 2-3-30 1-4: Hole Drilling 21

7 3 2-3-3-2: Non-Destructive Methods ............................................. ..-- 2-3-3-2- 1: Lamination Deflection ...................................... 22

77 2-3-3-2-2: X-ray Difnaction ................................ ..............-O ................................................. 2-3-3-2-3: Photoelasticity -24

................................... 2-3-3-2-4: Embedded Strain Gauge 25

Chapter 3: ~I icrosbucture of Fibrous Composites .m.........................................~......... 27 3- 1 : Fracture Mechanism in Polymer Matrk Composites ................................... -27

. 3- 1 1 : Single and Multiple Fracture ............................................................ 2 7 . . 3- 1-2: Conditions of Failure ..................... ... ............................................... -30 3-2: Crack Propagation and Toughening Mechanisms ........................................ 34 3 CI

3-3: Interface in Fibre Composite ....................................................................... 37 3-3- 1: Impact Toughness ............................................................................ 33 3-3-2: Single Fibre Pullout .......................................................................... 39

............................................... 3-3-3 : Embedded Fibre Cntical Length Test -42

iii

Chapter 4: Experimental Methods ................................m.......mm.m................................ **44 .............................................................. 4- 1: Preparation of Restressed Samples 41

.............................................................................. 4- 1- 1: Uniforni Winding -50 -CI ......................................................................................... 4-2: Mechanical Tests 33

............................................................... 4-3: Measurement of Residual Stresses 5 5 ................................................................. 4-4: Measurement of Re& Shrinkage 59

4-5: Contniution of Resin Shrinkage to Residual Stress ...................................... 62 ...................................................................................... 4-6: Large Size Samples 67

.............................................................................................. 4-7: impact Test 69

Chapter 5: Resuits and Discussion ............................................................................ *.71 ........................................... 5- 1 : Residual Stress in Fibre Prestressed Composites 71

5-2: Resin Shrinkage ........................................................................................... 79 .................................. 5-3: Contribution of Resin Shrinkage to Residual Stresses 85

5-4: Effect of Fibre Prestresshg on Mechanical Properties ................................... 88 5-4- 1 : Flexural Strength .............................................................................. 89 5-4-2: Flexural Modulus .............................................................................. 99

............................................................................. 5-4-3: Impact Strength 105 .................................................. 5-5 : Effects of Processing Conditions on BFPL 1 1 8

................................................................................... 5- 5- 1 : Type of Fibre L I S ......................................................................... 5-5-2: Curing Temperature 123

Chnpter 6: Conclusions & Contributions .............................................mm................. 1 2 9 ................................................................................ 6- 1 : Mechanical Roperties 129

6-2: Shrinkage of Polymer ................................................................................. 129 6-3: Contniution of Resin Shrinkage to Residual Stresses ................................ 120

........................................................................................ 6-4: Residual Stresses 131 ................................................................................ 6-5: Justification of Results 122

-CI ............................................................................................. 6-6: Contn'butions -1 JJ

...................................................................... 6-7: Suggestions for Future Work 154 References ................................m.................................................................................. 136

................................................................................................................. Ap pendix 1 141

List of Figures

Fig. 2-1: The ng used by Jorge et al. to manufacture the pre-stressed composite plates [Jorge 19901 .................................................................................................................. .6

Fig. 2-2: Influence of pre-stress on the tende strength [Jorge 19901 ................................. 7

............................. Fig. 2-3 : Influence of pre-stress on the tende modulus [Jorge 19901.. .7

...... Fig. 2-4: Plot of interface shear strength against the fibre pre-tension [Scherf 19921.. 8

Fig. 2-5: The radial cut method to determine circumferential and radial residual stresses in ................................. a filament-wound composite cylinder. [taken fkom Nelson 199 51.. 20

............................. Fig. 2-6: The difnaction of an x-ray beam according to Bragg's law ..2j

Fig. 3- 1: Illustration of the distinction between single and multiple fracture. proutman 19741 .......................................................................................................................... . .29

Fig. 3-2: (a) The effect of fibre concentration on hcture mode of composite with a brittle fibre in a ductile matrix. (b) The effect of fibre concentration on fracture mode of composites with a ductile fibre in a brittle matrix. [Broutman 19741 ................................ 19

Fig. 3-3: Extreme brittleness caused by too strong bond between fibre and matrix Carbon- -- fibre-reinforced carbon. [Broutman 19741.. ................................................................... J 3

Fig. 3-4: Carbon-fibre-reinforced carbon. The fibre-matrix bond strength is less than of the specimen show in Fig. 3-3, resulting in fibre pd-out and an increased fiacture toughness.

C ) - [Broutman 19741 ............................................................................................................ JJ

Fig. 3-5: Passage of crack in fibre-remforced composites involves interfacial debonding and filament fractures off the main hcture plane. Fibres bridge the crack faces in the wake of the crack fiont. [Atkins 19851 .......................................................................... .3 5

Fig. 3-6: Cook-Gordon debonding. Weak interfaces in the path of a crack debond ahead ofthe propagation crack tip, owing to a stress concentration of the stress parauel to the crack. Crack runs into debonded region, is blunted and at least slowed down, if not arrested [Atkins 19851 ................................. ,... .............................................................. .57

.............. Fig. 3-7: Single fibre pull out test. Favre-Penh resin disc variant. Favre 19721 4 1

Fig. 3-8: Single fibre pull out test. Chua-Piggott controlled embedded length variant. [Chua 19851 ................................................................................................................... 4 1

................... Fig. 3-9: Typical puil out curve obtained with glass-polyester [Chua 1 98 51 -41

Fig . 3-10: Adhesion force for non-post cured polyester.0 . Pullout; x. Fibre breakape [Chua 19851 ................................................................................................................... 42

. .............................................. Fig . 3- 1 1: Embedded fibre cntical length test [Lee 19901 43

Fig . 4- 1: Winding machine provided more uniform windhg by creation constant tension .................................................................................................................... on the fibre A 5

............................................ Fis . 4-2: Apparatus used to make prestressed composites A6

Fig . 4-3: Temperature profile in the oven. used to cure the samples ................................ 48

.......... Fig . 4-4: When tension increases. loose fibres become taut and aart to cany load 5 1

Fig . 4-5: Value of stress at point A can be used as an evidence to assess the uniforrnity of .................................................................................................................... the windiig 52

Fig . 4-6: Four point bending device. used to conduct flexural tests ................................. 31

Fig . 4-7: Monitoring the strain of the fibre during the c u h g process shows that some part of the strain of the fibres is not recovered d e r removing the extemal tension . The un- recovered strain is used to assign the fibres' residual force. Fr ., ...................................... 56

............................................ . Fig 1-8: Apparatus used to meaçure shrinkage of polymer -60

....................................................... Fig . 4-9: Sample bends due to shrinkage of polymer 63

Fig . 4- 10: Deflection of sample was eliminated when temperature mcreased ................... 64

... Fig . 4- 1 1: Shrinkage of polymer applies a shear force on the top surface of composite 66

Fig . 4- 12: Drawing bench. used to produce large ske samples ........................................ 68

Fig . 1- 13: Temperature profile in the oven. used to make the large sue samples ............. 70

Fig . 5- 1: Residual force in the fibres increases linearly as a fuoction of prestressing in glass-epoxy composite . Samples cured at 150 OC for four bours ..................................... 74

Fig . 5-2: Resîdual stress in fibres is about half of prestressing applied during curing process . Glass-epoxy composites cured at 150 OC for four hours .................................... 75

Fig . 5-3: Residual stress in matrix as a fhction of premess in glass-epoxy composites . .......................................................................... Samples cured at 150 O C for four hours 76

Fig . 5-4: Residual shear stress increases at the mterface as fibre prestress increases . Glass- epoxy composites cured at 150 O C for four ho un. .......................................................... 77

Fig. 5-5: Ratio of residual arain to total strain, created by prestressing, is constant and it does not depend on prestresshg level. Glass-epoxy composites cured at 150 O C for four hours.. ........................................................................................................................... .7S

................................. Fig. 5-6: Shrinkage of epoxy resin as a fùnction of tirne at 110 O C S 2

Fig. 5-7: Shrinkage of epoxy resin at 1 50 O C as a fiuiction of time.. .............................. .S3

.......................................... Fig. 5-8: Shrinkage of epoxy resin. Step heating was appiied 84

Fig. 5-9: Schematic diagram of force vs. deflection, during bending test, for a glass-epoxy ......................................................... un-prenressed sample cured at 110 O C for 4 hours 9 1

Fig. 5- 10: Schematic diagram of force vs. deflection, during bending test, for a glass- epolry prestressed sample prestressed at 50 MPû and cured at 1 10 O C for 4 hours ........... 92

Fig. 5-1 1: Flexural nrength vs. Prestressing level for E glass-epoxy composites. Samples cured at 110 O C .............................................................................................................. 93

Fig. 5- 12: Fîexural strength vs. Restressing level for E glass-epoxy composites. Samples cured at 150 O C .............................................................................................................. 94

Fig. 5-13: Flexural strength vs. Restressing level for E glass-epoy composites. Step heatmg appiied ............................................................................................................... 95

Fig. 5- L4: Flexural Modulus vs. fiestresshg ievei for E giass-epoxy composites. Samp les cured at 1 10 O C ........................................................................................................... 100

Fig. 5- 15: Flexural Modulus vs. Restressing level for E glass-epoxy composites. Samples ............................................................................................................ cured at 150 O C 10 1

Fig. 5-16: Flexural Modulus vs. Prestressing level for E glass-epoxy composites. Step heating applied ............................................................................................................ 102

Fig. 5-17: Vertical component o f residual force in the fibres (Fr sine) works against the bending force, resulting in increase of flexural modulus. [Afier Zhang and Cameron] .................................................................................................................... 1 05

Fig. 5- 18: Impact strength of glass-epoxy composites as a function of prearessing level. ........................................................................ Samples cured at 150 O C for four hours 109

Fig. 5-19: An un-prestressed broken sample after impact testing. Damaged zone can be seen m the middle,. ...................................................................................................... 1 1 0

Fig. 5-20: Restressed sample after breakage. 40 MPa fibre prestressing was appiied. . ..................................................................................................... Sphmg can be seen 1 I l

.... Fig . 5-2 1: Prestressed sample d e r breakage . 60 MPa fibre prestresshg was applied 1 12

Fig . 5-22: A prestressed sample a e r impact t e s h g . 80 MPa fibre prestressing was ................................................................ applied . Splitting and debonding c m be seen 113

Fig . 5-23: (a) Crack propagation in un-prestressed composite . Crack cuts the fibres to pass . (b) Crack propagation through interface and fibre breakage occur at the same time in

.................................................................................................... a prestressed sample 1 1 4

Fig . 5-24: SEM imaging fkom un-prestressed sample . The crack has crossed the fibres . The fibres are covered by the polymer and no separation can be seen between fibres and

......................................................................................................................... matrk 115

Fig . 5-25: SEM imaging nom a 40 MPa fibre prestressed sample . Fibre-matrix separation ................................................................................................................... can be seen 116

Fig . 5-26: Schematic diagram of required force for crack propagation .......................... 117

Fig . 5-27: Flexural strength of carbon-epoxy vs . fibre prestressing level ........................ 119

........................ Fig . 5-28: Flexural strength of carbon-epoxy vs . fibre prestressing level 120

Fig . 5-29: Flexural modulus of carbon-epoxy composite vs . fibre prestressing level ....... 121

. ....... Fig . 5-30: Flexural modulus of carbon-epoxy composite vs fibre p restressing leve1 122

Fig . 5-3 1: Fleniral strength vs . predressing level for glass-epoxy composites .............. -125

............... Fig . 5-3 2: Flexural modulus vs . prestressing level for glass-epoxy composites 126

........... Fig . 5-33: Flexural strength vs . prestressing level for carbon-epoxy composites -127

Fig . 5-34: R e m a l modulus vs . prestressing level for carbon-epoxy composites ............ 118

List of Tables

-.5 Table b 1: Magnitude o f curved part of stress-strain graphs in different samples ......... .. .>J

Table 4-2: Deflection of sample detennhed by two different methods. The error percentage is indicated . . . . . . .. . . . .. .. .. . .. . . . .. ...... .. .. . .. . . . . . . .. . .. . .. ......... . . . . . .. . . . . . . .. .. .. . . . . . . . . . . . . .. . . . .5 5

Table 5- 1 : Average flexural strength and standard deviation ......................................... . -96

Table 5-2: Flemal strength of un-prestressed samples compared to those at BFPL . .. ... .97

Table 5-3: Fle.wal modulus and standard deviation ..................................................... 103

Table 5-4: Rexural modulus of un-prestressed samples are compared to those at BFPL ........................................................................................................................... 104

1- Introduction and Scope

Fibre remforced composites are a vaiuable class of materials which demonstrate

both high stifniess and strength simultaneously. High ratio of strength to density and

relatively low-cost are some of the sipificant features of polymer matriv composites that

have made them the most rapidly developed materials in recent years. In spite of their

promishg fiiture, complexity of interactions between their constituent components rnakes

them a difncult subject for study. Because of the advantages and industrial applications of

composites, they have been the subject of much research. These research efforts are

concemed with Merent aspects of these materials. They include polymer science, surface

chemistry, stress analysis, and other aspects.

The present thesis examines the ginuences of fibre prestressing on the properties of

polymer matrix composites. In the first aep, the changes of flexural arength, flexural

modulus and impact strength are determined as the applied prestressing levei, maintained

d u h g the curing process, is varied. Restressing was applied on the fibres on a horizontal

tensiometer machine. The experiments show significant variation in the measured

mechanical properties. This corresponds to the results reported by other researchers

[Jorge 1990, Zhang 1992, Scherf 19921. ui the second aep, the effects of the processing

conditions are studied on the prestressing. It is shown that when either or both of the

processing conditions Vary, nich as temperature, and the constituent materials, such as

fibres, the dependence of the mechanical propenies upon prestressing is evident. This

means that the same trend in the changes of the properties can not be expected when

different processes or materials are used to make the prestressed composites.

In the next part of this study effort is taken to h d the annver to the major

question of how prestressing can cause the changes observed in the composites. T o

answer this question, there is a need to know what happens during the curing process and

how it is infiuenced by fibre pretension. In this part, it is shown that the understanding of

the formation of residual stresses is the main key to describe the observed changes of

properties. In an overd view, residual stresses m the composites corne from three

sources:

Re* shrinkage during the curing process.

The clifference benveen the coefficient of thermal expansion of the fibres and the

polymeric matrix.

In the case of fibre prestressed composites, the recoil of the fibres after removing the

tension.

On the other hand, despite the above factors, stress relaxation is known to reduce stresses

in the polymers. This can especiaiiy happen at hi& temperatures in the polymer. When the

temperature drops, the rates of stress relaxation becomes slower.

Two approaches can be used to detexmine or assess the residual stresses in the

composites. One is using mathematical methods and the other one is by using experimental

techniques. The development of a mathematical model is an extremely complicated and

Mcu l t task due to the large number of factors on which the residual stresses depend.

Therefore, a mathematical model mua necessarily be based on a large number of

assumptions, covering the misshg knowledge or the inabüity to express some of the

relevant factors. Checking the validity of these assumptions is not always easy or even

possiile.

On the other hand, the experimental methods usuaily faii to determine the micro-

residual stresses (as wili be defined in section 2-3) in composite matenals. This is because

of the smaii diameter micron size of the fibres and their unifom distribution in the sample.

Despite the mentioned di%culties, the residual stresses have been determined in

fibre pre-stressed composites m this present thesis by introducing a new method. This

method is based on the measurement of the residual main in the fibres following the

curing process and when the applied tension is removed. The residual stresses are then

calculated based on an understanding of the mechanics of the situation and the

mathematical models. Therefore this method can be called a combination of both

experimental and mathematical methods. By the use of this technique residual stresses are

detelmined in fibre prestressed composites. The known values of the residual stresses,

then, are used to explain the changes observed in the mechanical properties of the

composites.

The results, reported in the present thesis, can be used in the fabrication of fibre

composites. This is especialiy useful when the pre-stress can readily be accommodated on

the fibres such as during filament winding or pultrusion process. In other processes the

proper h u r e s have to be arranged to apply the fibre pre-tension to the specimens during

curing.

2- Literature Review

2-1: The Genesis of Glass Fibre Composites:

Natural composites, such as wood, have been available for thousands of years.

Ancieut artisans recognized the relationship between continuous and discontinuous phases

when they used pitch to bind reeds to produce composite boats 7000 years ago [Seymour

199 11.

The continuous phase, used prior to the 20th century, was based on natural

resinous products, such as pitch, casein, and albumin. The first synthetic lamhating resin

was a polyester produced by Berzelius in 1847. This was the precursor of Watson Smith's

Glyptals and Baekeland's phenolic resins, which were introduced in the early 1900s. Srnail

amount of phenolic-based paper and cloth laminates were used for several decades, but the

tme beginning of the age of composites was the production of fibre glass-reinforced

polyesters by Ellis and Rust in the late 1930s [Seymour 199 11.

2- 1- 1 : Fibre Glass:

The American Society for Teaing and Materials (ASTM), in Standard C 167-7 1,

defines glass as "an inorganic product of fusion, which has cooled to a rigid condition

without crystalbhg." Because glass is amorphous, it is isotropic, and Like other

amorphous polymers has a glass transition point rather thao a melting or fht-order

transition characteristic of crystalline products.

Glass fibre is made from molten glass forced at 1266 O C through orifices in the

base of the burhmgs to produce continuous or staple fibres. The glass is not a definite

compound, but is primarily silica producing by heating sand (SiO?), iimestone (CaCO,),

and bonc acid (&BO3) in a high temperature refiactory fiunace.

Continuous filaments are produced by ailowing the molten giass, held in platinum

aiioy tanks (busbgs), to flow by gravity through multiple orifices. The molten filaments

formed are gathered together and attenuated to specified dimensions before being

quenched by a water spray. The cooled filaments are carried on a belt where they are

coated with a lubncant or sizing and grouped together in buadles which are then wound

on spools. The arands are wound together to produce roviags[Seymour 199 11.

2- 1-1: Epoxy Resin:

Cross-iinhable epoxy resins, based on the condensation of bis-phenol A @, pr-

isopropylidene diphenol), (HOC&I&Ca (BPA) and epichiorobydrin (ClCH2CHOCH2),

were produced by DeTrey Freres in 1936. Epoxy resins may be cured at ordinary

temperatures by Lewis bases, nich as amines, which react with the terminal oxirane

(epoxy) groups. Rimary amines' react hnce as fast as secondary amines2, and this rate is

accelerated in the presence of hydroqd compounds. Epoxy resins may aiso be cured at

elevated temperatures (up to 200 OC) by the addition of cyclic anhydrides, whicli react

with hydroyl pendant groups [Seymour 199 11.

2-2: Fibre Restressed Composites:

nie effects of fibre prestressing on the mechanical properties of composite

materials is aa area which has not been extensively studied by many authors. The worli

accomplished by Jorge et al. ( 1990) is one of the mon relevant research to that which was

achieved in this thesis. In this work by Jorge, the authors used E-glass and polyester resh

to make theu unidirectional composites. They produced composite plates between two

glass plates. The rowigs were applied through two comb-like sets of aeel pins (Fig. 2- 1)

in two paraîlel sides of the lower plate mold. They made each roving no geater than 6 to

8 consecutive longitudinal paths to achieve a good unifonnity of prestressing. In these

experiments they applied the prestressing load by use of weights and puUeys on the roving

extremity, during and up to the complete curing of the composite.

F i g 2-1: The rig used by Jorge et al. to manufacnire the pre-stressed composite plates [Jorge 1990)

The tensile tests on those samples, then, revealed a considerable increase in both the

tende arength and tensile modulus As can be seen in Fig. 2-2 and 2-3, when fibre pre-

tension increases, the mechanical properties mcrease. This trend continues until a given

prestressing level, and after that those mechanical properties are stabilized or even show a

slight decrease (see the modulus data in Fig. 2-3).

Fig. 2-2: Influence of pre-stress on the tende strength (Jorge 19901

Pre - stress N 1

Fig. 2-3: Influence of pre-stress on the Young's modulus [Jorge 1990)

Scherf and Wagner (1992) studied the effect of pre-tension applied on single fibre

composites. Their resuits suggested that the fibre pre-tension significantly affected the

number of fragments as weli as the interface shear strength. They showed that the number

of fibre fragments in the tende test of a composite maeased when the fibre pre-tension

was increased. Calcdation of r, the mterface shear strength, was also canied out by

Scherf and Wagner. Their calcdation demonstrated that shear stren=gth at the interface

increases as the fibre pre-stressing increases in single fibre composites. Fig. 2-4 shows the

interface shear strength versus fibre pre-tension. 25% increase in shear strength cm be

seen as 5% pre-tension was applied to the filament. These scientists used the normalized

pre-tension in their calculation. Normalization was performed by dividing the pre-tension

load by the fibre nominal cross section and by the "strength" of the fibre, i. e., the stress at

which the first break occurs.

Fig. 24: Plot of interfixe shear strength against the fibre pre-tension [Scherf 1 9931

8

Another work was accomplished by Zhang and Cameron (1992). They produced

glass-epoxy composites with pre-stressed fibres. They maintained a known level of tension

on the fibres during the curing process. Bendmg and impact tests were then perfonned on

the composites. In this study, they reported up to 52% and 44% increase in the flexural

modulus and impact strength of the pre-stressed composites respectively when compared

to the composites made with no prestressing. They also mdicated that there was a &en

pre-stressing level at which both the flexural modulus and impact strength reached a

maximum value and after that level of prestressing was passed fùrther increase in

prestressing resulted in a reduction of the measured flemal modulus and impact strength.

2-2-1: Enhancement of Composite Strength through Application of Previously

Stressed Fibres:

Fibre prestressing can be canied out either before the incorporation of the fibres in

the composite or during the curing process of the polymeric resin. The term "previously

stressed fibre" has been used [Manders 19831 to desmie the application of the stress to

the fibres before their incorporation in the composite, while the ''fibre prestressing" term

referred to the case that the stress is applied and maintained during curing.

Small but meamable enhancement of composite strength can be achieved by

eliminating some of the weak spots or defects in the fibres. One way of attaining this goal

is to stress the fibres and to induce fracture at the defect sites before they are incorporated

into the matW [Chou 19921.

Mills and Dauksys (1973) were the f5st to adopt the concept of fibre stressing

pnor to incorporation into the resin. In their work, cabon fibre prepregs were pre-

stressed at temperatures as low as -18OC. The previous stressing of prepregs by bending

induced non-uniform tende stress which reached maximum values at the outer surfaces,

with fibres near the center of the prepreg stressed the least. They accomplished large

decreases in the statistical uncertainty in laminate test pieces through a reduction in the

fiequency of low strength defects. This r e d t was accompanied by a corresponding

increase in average strength of a boron-epoxy composite fiom 198.5 psi to 209.1 psi

(5.5% increase) using the Milis and Dauksys previous stressing method on the boron

fibres.

Manders and Chou (1983) provided a theoretical analysis of the enhancement of

strength in composites reidorced with previously stressed fibres. The basis of theu

reasoning was as follows. The failure of a fibre in an aligned composite causes a stress

wave to propagate outwards placing a dynamic overstress on the neighboring fibres. The

resulting dynamic stress concentration is generally greater than the natic stress

concentration which prevails after the syaem has settled, and increases the probability that

adjacent fibres also fail, weakening the composite. This analysis showed how weak fibres

may be prefiactured to e b a t e the dynamic overstress, thereby increasing the strength of

the composite. Manders and Chou discussed this strength enhancemeni with reference to

the level of pre-stress, fibre variability, stress concentrations, and size of' the composite.

Chi and Chou (1983) have measured in a systematic fashion the effect of ushg

previously stressed loose carbon strands on the mean strength of composites as well as the

dispersion of composite strength. They demonstrated that the arength of the composite

was enhanced after pre-bending the fibres to an appropriate level pnor to the manufacture

of the composite.

2-3: Residual Stresses in Fibre Composites

The increased use of composites in engineering applications has led to concem

about the reliability of these materials. In particular, the residual stresses introduced during

fabrication are one the moa significant features in the processing of composite structures.

Residual stress is defined as stress which exists in a structure under uniform temperature in

the absence of extemally appiied loads Mordfin 198 11. The total stress on a structure in a

service is the sum of the apptied stresses (themial, mechanicai, etc.) and the residual

stresses. Due to this superposition of stresses, residual stresses may reduce the alowable

load, and thus the effective strength of a component in service.

Several sources of residual stress in composite materials have been reported in the

literature [Nelson 1995, White 19921. DifTerences in coefficient of thermal expansion

(CTE) between the constituents of a composite matenal can result m locked-in thermal

stresses upon cooling fiom its processing temperature. Additional residual stresses in

polymer mativ composites may be formed as a remit of chernical shrinkage of the matnx

during cure and moisture absorption [Tsai 1980, Oakeshott 19941. In the processes which

involve fibre pre-stressing (e.g. filament winding) the fibre tension is also cited as a

sigmficant source of residual stress [Knight 19721.

Residual stress due to the merential contraction of the fibre and matrix is referred

to as residual micro-stress, whiie the term residud macro-stress is used to describe the

stress redting fkom the differential thermal contraction of adjacent laminates in a

composite. The prefixes micro- and macro- do not refer to the magnitude of stress, but to

the size of the region over which they act [Nelson 19951.

2-3-1: Causes of Residual Stresses in Composites:

2-3- 1- 1 : Thermal Stresses:

The source of residual stress in composites most commonly cited in the literature is

the aress which results fiom the different coefficients of thermal expansion ( C E ' S ) of the

constituent materials of the composite. When the composite is cooled fiom its processing

temperature, residual thermal stresses are produced as a result of this CTE mismatch. In a

unidirectional fibre reidorced composite, the mat* and fibre matenals may have

significantly different CTE's. For example, in a glass-epoxy composite, the CTE's of the

fibre and matrix materials are reported as aF5x lob/K and a,=54x 10%S, respectively

[Tsai 19801. For polymer mat* composites, the material is ofien assumed to be stress-

fiee at the cure temperature because the matrix is still fluid enough to aiiow aress

relaxation. Thermal residual stresses are introduced when the composite is cooled Born

the cure temperature. The stress produced due to CTE mismatch between the fibre and

matri. is generally referred to as residual micro-stress because it is M t e d to a smaii

region surroundhg the fibre. The stress aate in unidirectional composites is h h e r

complicated because the reinforcing fibres are often anisotropic, having different CTE's in

the transverse and longitudinal directions. The interaction between adjacent fibres and the

potential viscoelastic properties of the matrix also rnakes the analysis and prediction of

residual micro-stress difficult.

2-3- 1-2: Fibre Pre-tension:

Fibre pre-tension during the curing process can create residual stress in composites

when the tension is released. This is because fibres tend to recoil to their original state.

However, as a result, residual stresses are developed in the composite.

The contnTution of fibre pre-tension to residuai stresses is larger than that of the

other parameters. This is very important in those processing methods in which pre-tension

can be applied readüy on the fibres, such as during the marnent winding and pultrusion

process. The magnitude and effect of this source of residual stress will depend on the

amount of fibre tension, material properties, and processing history of the composite.

2-3- 1-3: Chernical Shrinkage:

An additional source of residual stress in polymer m a t h composites is the

chemical shrinkage which occurs due to the cross-lioking of the polymer matri\: during

cure. This shrinkage cm produce residual stresses because the reinforcing fibres are

generaiiy not chemicdy affected during curing. In order to ensure geometric compatibility

between the fibre and the mat& residual micro-stresses are fonned. Most of the literature

suggeas that since most of the cross-linking takes place at the highen processing

temperature, the mat& is stiU fluid enough to allow the residual stress to completely relax.

Thus, the cure temperature is usuaily taken as the stress-fiee temperature, and residual

stress due to chemical shrmkage is neglected [Tsai 19801. In a audy by White and Hahn

(1992), the contribution ofchemicai shrinkage to residual stress in a graphite-bismaleimide

composite was less than 4% for a typical cure cycle. Their midy indicates, however, that

residual stresses due to chemical sbrinkage may not ahvays be negligible and will depend

on the matrk matenal and cure history of the composite.

3 4 - 1-4: Moisture Absorption:

Stresses cm form in composite materials due to the absorption of moisture into the

matrix. This is esp eciaiiy significant in p olymer-matrix comp otites. When the p olymer

matrix absorbs moisture, the resuiting deformation can introduce both macro- and micro-

residual stress due to aoisotropic swehg of adjacent plies and the clifference in swelling

between the mat* and the fibres. The swelling stress due to moisture absorption

generally acts to oppose the residual stress developed due to thermal mains and chemical

shrinkage [Oakeshott 1994, Naik 19841.

2-3-2: Prediction of Residual Micro-Stresses:

2-3-2- 1: Analytical approach:

Various analytical techniques have been employed to predict the micro-stress fields

in composite materials subjected to mechanical and thermal loading. In general these

models have been created to study the effects of applied loading; however, they can be

extended to consider the case of thermal residual stresses created in a composite during

the cool down period afier curing.

Jayaraman and Reifsaider (1992) have used a simple analytical approach for the

determination of residual thermal stresses m composites, aliowing circumferential

symmetry and incorporating radial Young's Moduius gradients. The composites were

modeled by three concentric cyhders representing a fibre, interphase and matriv The

redting governhg dinérential equations, representing a 'dilute' solution, were solved

directly by Cauchy-Euler and Series Solution techniques and the Merences m local stress

States were identified.

According to Jaywaman et al. (1993, 1994), mechanics representations of the

micro-details of fibre regiforced composites have generaiiy assumed the exinence of two

phases, namely the fibre and matrk. However, in reality, an additional phase may e d a

behveen the fibre and rnatrk known as the interphase which is the local region that results

when the matris bonds with the fibre d a c e or the fibre si9ng. The interphase region is

often the product of processing conditions involved in composite manufacture. Hence the

properties of the region depend diiectly upon the chemical, mechanical and

thermodynamical nature of the bonding process between the matriv and fibre materials,

and any subsequent changes in these local conditions. As a direct result of this

dependence, the interphase may have spatialiy non-uniform properties, i.e. the properties

may Vary fiom point to point through the thickness of the interphase.

ui another study, Krempl and Yeh (1990) computed the residual stress field in two

unidirectional aiuminum matrix composites: Graphite/ 606 1-T6 A 1 and Boron/ 606 1 -T6

A 1. ui their analysis, the fibres were assumed to be transversely isotropic elastic inclusions

in an isotropic thermoviscoplastic maair Matenal constants were aiiowed to Vary with

temperature, and tirne-dependent effeas such as creep were computed. The residual

stresses in the mode1 resulted fiom thermal stresses induced during cooling at a constant

rate from a temperature of 660 O C to room temperature. Residual tende stresses in the

aluminum matrix on the order of 60 - LOO MPa were predicted This study also evaluated

the effects of the residual stress on the mechanical and thennal behavior of the composite

during service.

Mikata and Taya (1985) anaiyzed coated fibre composites (nickel-coated T3OO in

Al 606 1 and Sic-coated T300 m Al 606 1) under thermomechanical loading situations by

means of a four-phase model (fibre/coatin9/matrixl~~rro~flding composite). The fibre and

nirrounding body were assumed transversely isotropic and the matrix and coating were

considered isotropic. The thennoelastic properties of the surroundhg body were obtained

using the d e of mixtures. The composite was subjected to three independent loading

conditions: aicisymmetric temperature change, uniaxial stress applied parailel to the fibre

direction, and equal biaxial stresses applied perpendicular to the fibre direction. It was

s h o w that an increase in fibre volume fiaction and thichess of the coating resulted in a

decrease in the thermal stresses (axial and hoop) at the fibre coating interface.

2-3-2-2: Finite Element Modeling:

The finite element rnodehg method (FEM) has been used by several researchers

to compute the residual micro-stresses formed in composites d u ~ g processing

[Oakeshott 1994, Chandra 1994, Rangaswamy 19941. Finite element models have

considered regular hexagonal and square arrays of fibres with the stresses determined in

representative unit cells. The constant geometly along the fibre leugths aiiow conditions of

plane main to be assumed in the sections transverse to the fibre axes.

Rohwer and Jiu (1986) developed a tbree dimensional finite element model of a

hexagonal and square array of a unidirectionai carbon fibre reidorced plastic. Conditions

of plane strain were imposed on one transverse edge, and to simulate a traction-&e

condition at the fibre ends, zero n o m 1 stress resultant on the other. The fibre volume

fraction modeled was 60%. Results were presented in ternis of axial tangential and radial

stresses. Adams and Miller (1977) produced a two dimensional h i t e element analysis of a

square array of fibres which included moisture expansion in addition to thermal

contraction effects. The moisture expansion has the effect of counteracting and even

revershg the stresses induced by the thermal contraction. The epoxy resin properties were

ailowed to Vary with temperature and moisture content according to noalinear idealized

stress-strain relationships. The octahedral shear stress normalized by the octahedral shear

yield strength were presented under conditions of generalized plane strain.

Oakshon and Fletcher (1994) investigated the effect of fibre paclcing geometn.

interfibre distance, and fibre diameter on residual stress by use of a two-dimensional mode1

on a cross section transverse to the fibre length for a unidirectional carbon fibre relliforcrd

epoxy composite during the cool down phase of the cure cycle. The fibre and matri.

materials were assumed to behave elastically, and the temperature dependent properties of

the epoxy matrix were included. The modeling results show that the maximum principal

residual stresses are tensile in the matrix and compressive in the fibres. Also, the predicted

maximum principal stresses are mversely proportional to interfibre distance, with stresses

exceeding the yield strength of the ma& at niterfibre distances of less than 1 .O pm.

2-3-3: Messurement of Residual Stresses:

There e n a s many difTerent methods to measure the residual stresses m

composites. These methods can be divided into two groups; destructive methods and non-

destructive methods. The destructive methods of measurement of residual stresses

generaliy involved cutthg the part of mterest m such a way to relieve the residual stress.

From the manner in which the part defortus, it is possible to determine the magnitude and

direction of the stress present in the matenal piior to the cut Belson 19951.

Contrary to destructive methods, non-destructive methods are developed to

determine the residual stresses without damaging the examined pans. These methods have

the obvious advantage that they do not dearoy the part to be measured. They also allow

the residual stress in a part to be measured over t h e to asses the effects that tirne and

loading Iiiaov have on the residual stress levels.

2-3-3-1: Destructive Methods:

2-3-3- 1- I : Tende Teaing:

Novak and Decrescente (1970) attempted to determine the thermal residual

macro-stresses in graphite-epoxy composites by meaniring the effect that these stresses

have on transerse tensile strength of the laminate. In these experiments, the tensile

arength of the [&45/0/&45] cross ply laminate in the direction perpendicular to the fibres

in the O degree ply is compared to the transverse tensile strengtli of unidirectional "stress-

fiee" specimen of the same composite. These researchers reason that the dserence in

tende arength corresponds to the level of thermal pre-stress present in the material. For a

graphite reinforced flexiiilized resin composite, they determined that the transverse

residual stress was 1230 psi (8.5 MPa) using this measuring technique. This compared

favorably with a theoretical value of 1270 psi (8.7 MPa) which was computed using a

simplification of laminated plate theory. This analysis neglects the impact that residual

micro-stresses cm have on the failure of a composite. Ahhough this method of measuring

residual stress is relatively simple compared to other techniques, it provides a direct

measure of the effect of residual stress on the strength of a composite pan.

2-3-3- 1-2: Layer Removal:

In the layer removal technique, the residual stress in a layer of material is

detemiined by removing the layer, and measuring the deformation in the rea of the

specimen. This technique, although is developed for isotropie mat enals, lias been adapt ed

to measure residual macro-stresses in cross ply composites. Crasto and Kim (1992) Used

the peei-ply technique to measure processing induced residual strains in graphite-epo~y

composites. In their experiments, axial and transverse strain gauges were mounted on both

faces of several composite plates including [O JgOJ,, [Os/90r],, [O J904], and [Oi/(f60)j],

lay-ups The ciifference in arain was measured before and after separiting the outer 0°

plies t o m the laminate. A starter crack was initiated with a release film to aid in the

separation of the plies. Craao and Kim used this released main to calculste the stress-Eee

temperature of the laminate using laminate plate theory.

2-3-30 1-3: Radial Cut Method:

The radial-cut method is a simple, inexpensive, and approsimate method of

determining the residual stress state in a cyiiidncal pan. In this method, the ~g is cut in

the radial direction to release the residual stress. Measurements of the subsequent

deformation of the ring in the circumferential and radial directions give an indication of the

magnitude of the stresses present prior to the cut. Aleong and Munro (1991) used this

method to determine the residual stresses in radially-thick fdament-wound composite

rings. In their experiments, the rings were cut along the radius, and the radial and

initial cut, additional cuts at B O 0 to the original cut were made, and the n r a h readings

values were observed to remah constant. In this work, radial residual strains ranging fiom

422 Ndin to 1285 p'din were reported for the dinérent rings.

2-3-3- 1-4: Hole Drilling:

The hole d r i b g method is a common technique used to determine residual

stresses near the d a c e of isotropie materials. The technique involves the dt.illing of a

mall bünd hole into a region containhg residual stress, resulting in the removal of this

stress. By the meamring the strain on the surface of the parent matenal near the hole afier

it is drilled, the magnitude and direction of the stresses that were removed can be

calculated. Special strain gauge rossetes have been developed to measure the released

strain; however. techniques such as holography have been applied. This method can be

used to determine how the in-plane stress varies with depth in the material. The maximum

depth to wliich usehl measurements can be made is about one-half of the hole diameter.

Hole drilling is often referred to as a semi-destructive technique because the holes are

ofien very smaiî and can be repaired or ignored in some cases pelson 19951.

The hole-drillhg technique measures the combined residual stress fiom both

micro- and macro-sources. It is relatively simple to perform; however, it is not yet in

widespread use for composite materials, posnily because of the complexity of the

analysis. Disadvantages of this technique include the limited depth to which stress can be

measured. For thick composite parts with complex residual stress distributions, hole-

drilling would have limited application.

2-3-3-2: Non-Destructive Methods:

2-3-3-2- 1 : Lamination Deflection:

Residual macro-stresses are fomed in cross-ply composite laminates due to

anisotropic thermal contraction of adjacent plies upon cool down fiom the cure

temperature. One of the manifestations of this source of stress is the warping or deflection

of laminates with an unsyrnmetric lay-up. In a symmetnc laminate, the forces due to

residual stresses balance in nich a way as to prevent warping. Bending of a cotnposite

laminate can also be csused by the processing of matenal nonunSormities as weil as

temperature and m o i m e gradients through the thickness of the pan.

2-3-3-2-2: X-ray Diffraction:

X-ray f i a c t i o n is one of the moa common noii-destnictive methods to

determine residual stresses in metals. M e n a crystaliine material is irradiated with ?r-rays,

the waves are diniacted by the ctystal lattice planes of the material as indicated in Fig. 2-6.

The difiacted waves from adjacent planes travel Werent distances to the detector due to

the increased path length. These waves will interfere constructively at certain angles of

=action given by Bragg's law.

2d sin 8 = R

Where A is the wavelength of the x-ray, dis the interplanar spacing to be measured, and 0

is the angle at which constructive interference occurs.

When a stress is applied to a crystahe materiai, the interplanar spacing

change. This change wili &est itself as a change in the angle of difEaction at which an

interference peak will be observed.

As a method of measuruig residual stress, x-ray difhaction has the advantage that

it is a non-destructive, non-contact method. Also, since the x-ray beam diameter is on the

Difiacted Detector incident

Fig 2-6: The diffraction of an x-ray beant according to Bragg's law.

order of 1 mm or smaiier, relatively high spatial resolution of a stress field caii be

achieved. Limitations of this method include the fact that the x-ray beam has a depth of

penetration Limited to approxbately 0.025 mm in moa engineering matenals. Thus. the

method is ouiy usehil for measuring surface stresses. However, this tecbiiiquc can be

combined with destructive methods, such as layer removal, to obtain rcsidunl stress

gradients through the tliickness of a part. A significant limitation of the tecliiuque cornes

fkom the fact that factors such as grain size, texture, and preferred crystallographic

orientations wiiI affect the measurements.

Aithough x-ray difiaction is iimited to crystaiîine matenals. several rescarcliers

have atternpted to use iIiis technique to meanire residual stresses in polymer-inatrk

composites. Barret and Redicki (1980) proposed a method to meanve residual stress

which invoked incorporating a layer of metaiiic particles in the composite approximately

the same diameter as the reinforcing fibres, and measuring the residual strain in these

particles due to the curing process. In another study, Fenn, et al. (1993) used this

technique to study the thermal stresses in an epoxy material of the type used in fibre

reinforced composites. They chose a simple epoxy m a t h instead of a composite because

of the difnculty in interpreting the results for a three-phase system (matrix-fibre-particle).

They used nickel particles and measured the triaxial residual strains as a fuoction of cure

temperature and particle volume fiaction. Their results agreed quaütatively with predicted

results for some aspect of the experiment; however, the measurements indicated that the

mapitude of the residual stresses are much higher than predicted and that the residual

stresses decreased with increasing cure temperature. Assuming the primary source of the

stress to be the ciifference in CTE between the matrix and the particles, one would expect

an increase in residual stress with increasing cure temperature. It is ooted that chernical

shrinkage stresses could be responsi%le for the discrepancy. These researchers indicate that

more work is required to use this technique to accurately determine residual stresses in

polymer matris composites.

2-3-3-2-3: Photoelasticity:

The photoelastic method of stress meanirement is based on the fact that certain

materials have optical properties which are a fiuiction of the state of stress in the material.

Specifïcally, certain photoelastic or buefigent materials have the property that the speed

of iight in the material wilî change as a fiinction of stress. Using a polariscope, the changes

1

in speed of light (expressed in term of the index of refiaction) are manifested as patterns

of mterference f i g e s superimposed on the image of a part. From these f i g e patterns,

the stress state can be computed.

Traditional photoelasticity requhes the use of visible ligbt, and is thus limited to

transparent materials which exhibit birefiges such as plexiglass and certain polymer

resins. For opaque materials, it is possible to use reflective photoelasticity in which a thin

layer of photoelastic material is applied to the surface of a pan. Fringe patterns are

developed by passing polarized light through the lnyer, reflectins it off the surface of the

specimen, and passing it back through an analyzer. This technique is usehl for detertubhg

surface stresses in non-photoelastic materials.

One of the difnculties in using photoelasticity for composite matenûls is that

composites are ofien not transparent, and the fibre and matnv have Mereut indices of

refiaction. Knight (1972) created a transparent composite cylinder using an epoxy resin

and fibre glass with matched indices of refiaction. Knight meanired the residual

macrostresses in cylinders with a 6" inside diameter and varying wall thichesses. Radial

and circumferential stress distriiutions through the thickness of the cylinder were

measured. Maximum tende stresses occurred in the circumferential direction and had a

magnitude of 28 MPû at the inside d a c e of the ring.

2-3-3-2-4: Embedded Strain Gauge

The embedded strain gauge method was developed to measure subsurface strains

in polymer rnatrix composite laminates by Daniel, et al. (1972). ln this method,

conventional resistive strain gauges are embedded between plies in composite laminates

during processing. A technique to successfuly embed the gauges without local thickening

of the specimen was developed.

Lee and S p ~ g e r (1990) embedded strain gauges between layers of a filament

wound cylinder to ver@ their predictions of residual stress and main due to filament

winding process. The strain values measured with these gauges agreed weii with their

mode1 predictions.

3- Microstructure of Fibrous Composites

The failure of a fibre-remforced matenal is a complex process which invoives an

accumulation of micro-structural damage. UnWre homogeneous brittle matenals, fibre

composites do not contain a population of observable pre-existing defects, one of which

ultimately precipitates failure. Inaead, an accumulation of fibre or matrix fractures

develops as the material is loaded and this constitutes a critical defect in a rnacroscopic

view of the f?acture.

This chapter examines the fracture of fibre composites with respect to the

microstructure aspects. Fracture mechanism, bond strength at interface, and crack

propagation are the subjects discussed. In this chapter, it is indicated how the changes in

microstructure are reflected on overali strength of composites. This makes it possible to

predict the mechanical properties of the composite by knowledge of characteristics of

materials which are in the micron size region.

3-1 : Fracture Mechanism in Polymer Matrix Composites:

It is convenient to &de the possible failure processes mto two types, depending

on whether the failure is determined by matenal reaching some overail instability, such as a

limit of stress or grain, or whether the failtue is precipitated by the action of some discrete

fkacture nucleus, such as a broken fibre, or a notch fiom which the failure crack can grow

[Cook 1990, Broutman 19741.

3-1-1: Single and Multiple Fracture:

Most fibre-reidorced materials have at least one component which is brittle. WMe

the fibres are always stronger than the ma& they may or may not have a greater

elongation to Mure. It is thus possiile to distinguish between dinerent types of failure

processes according to the relative ductility of the components. Fig. 3-1 shows a

completely general composite. When an increment loading is applied, the failure main of

the less extensible phase wiU be reached. Taking EL > Q, we have

0 = VI El ET +V?CQ (3- 1)

Where q Y , E and 6 are tende stress, volume percentage, Young's Modulus and strain

respectively and subscriptions 1 and 2 refer to each phase. Phase 2 fails at this stress(@,

and the load which was carried by it is transferred to phase 1. This then fails if:

VI 01 < V, El ET + V , CQ (3-2)

and the composite is said to fnil by si~iglefic~c~z~re, since the faiiure zone is Limited to the

single region immediately adjacent to the zone of fira fracture. If phase I is mfticiently

arong, or is present in a sufnciently great concentration, however, the composite will not

fail completely, but will continue to bear load up to a failure stress VI 0,. D u ~ g this

subsequent loadhg, the more brittle phase wili continue to fiacture into malier and

muiller pieces. This behavior is known as niulriple fracture.

As was noted above, the less ductile phase can be either the fibre or the matris. If

the fibre is more brittle, the transition 60m single to multiple fracture of the fibre occurs

when

V , ~ m = K , o a . + Y / a / (3-3)

Where d i s the stress carried by the matrix at the failure of the fibres. Multiple fiacture of

the fibres thus occurs at concentrations less than

V A = (a, - 'A)/(q- 0 'AI (3-4)

F i s 3- 1: [Ilustration of the distinction b e ~ n single and multiple fiachire. [Broutman 19741

Fig. 3-2: (a) The effect of fiber concentration on fracture mode of composite witli a brittle fiber in a ductile matrix. (b) The effect of fiber concentration on fracture made of composites witli a ductile fiber in a brittle mairix. [Broutman 19741

which is marked by the pomt A in Fig. 5-2.

At the fibre concentration less than Y,,, strainhg the composite beyond the failure

strain of the fibres will result in their bemg broken down mto shorter and shorter lengths,

the minimum being detemiined by the maximum rate of transfer of shear stress at the

d a c e of the fibre. The value will lie between x and 2x where (considerhg a single fibre)

.Y is given by the force balance

n r a c = m2q (3-5)

fiom which

x = q r / Z t (2-6)

Wliere x, r, rand o, are fibre length and radius, shear stress and tensile stress of the fibre

respectively. This value is equal to haifthe cntical length L. [Broutman 19741.

3-1-2: Conditions of Failure:

n i e propagation of a crack under an applied tensile stress is govemed by two

independent conaraints, these being that the stress at the crack tip should excced the

failure stress of the material there, and that there should be a net energy loss to the system

as the crack grows. The latter is the weii-hown W t h energy cnterion. Although the

aress cnterion seems obvious it deserves special mention in the case of composite

materials because of their anisotropy.

n i e stress concentrations associated with an eîüptical void in an elastic isotropic

medium were first calculated by Inglis (1913). These calculations were developed for an

aeleotropic matenal (with special referme to wood) by Green and Taylor (1945), who

emphasized the possibility that the crack does not always propagate in a direction normal

to the applied stress (i.e., when a notched wood specimen is puiied in tension parallel with

the grain, there is a high probability that the crack will grow m a direction parallel with the

appiied stress, by sptitting along the gram).

Crack deflection has also been noted m laminated materials [Aimond 1969, Wang

199 11, where increases in Gracture toughness have been obtained by the crack defîection

mechanism. For an isotropie matenai, the necessary ratio of tensile strength to interlaminar

shear strength is near four. For most woods, the factor is about six, wlde for an extremely

anisotropic material, such as a carbon fibre remforced resin, the value c m be as hi& as 11

tirnes [Keily 19701. This impties that, to be sure of debonding operating as a crack-

aopping mechanism in an advanced, highly anisotropic composite, the iuterlarninar shear

arength mun be seriously reduced. This rnay be acceptable in some structures which cany

o d y simple tende loads, but if biaxial stress mua be camed, it rnay be impossible

simultaneously to assure adequate notch resistmce.

Outwater et al. (1969) have discussed the factors which decide whether a rnatriv

crack should propagate through the fibre or along the interface. Tliey considered a long

single fibre embedded in a block of mat* and debonded over a distance x from the fiee

surface.

The stress necessary to continue the debonding process is composed of two parts,

the first being that necessary to overcome the sfidmg fiction of the fibre over the distance

x as it is pulied out of the sheath of matrix after failure of the bond, and the second is the

stress necessary to cause the bond to faii:

o d = ( 2 r j / r ) + ( 4 ~ / ~ ~ / r ) ' / "

Where Gu is the work done per unit d a c e area of interface to cause failure of the bond

and r, is the fiictional shear stress between fibre and m a h after debonding.

I f x tends to zero, then the debonding stress becomes simply:

~d = (~E,G&)"~ (3- 8)

and this is the condition for debonâing to begin. It is clear fiom the form of Equation 3-8

that in a given composite, there is a fibre N e at which the debonding stress becomes

greater than the fibre failure stress:

r C ~ E / G ~ / oj2 (3-9)

and that for the fibre radü less than this value, the fibres wiü break rather than puil out of

the matrir. This implies that a crack propagation in the matrix in a direction normal to the

fibres will tend to ignore the presence of the interfice, and wiU cut across the matris and

fibre alike. An example of this type of extremely brinle failure is show in Fig. 3-3, for a

carbon-fibre-reinforced carbon matrix in which there is a very strong fibre-rnatrix bond.

Fig. 3-4 shows the fi-acture surface of a similar composite in which the bond strength has

been reduced to aliow a certain degree of debondhg and fibre puii-out during failure.

Fig 3-3: Extreme brittleness caused by too strong bond between fibre and matrix. Carbon-fibre-reinforced carbon. [Broutman 19741

Fig. 3-4: Carbon-fibre-reinforced carbon. The fibre-matrix bond strength is less than of the specimen shown in Fig. 3-3, resulting in fibre pull-out and an increased fhcture toughness. proutman 197.11

3-2: Crack Ropagation and Toughening Mecbanhms:

If'the fibres are not continuous, and there is a matrk crack originating perhaps at a

pore, dun particle or notch in the ma& approaches a discontinuous fibre nich that the

distance between the end of the fibre and the fiacture plane is less than the cntical transfer

length, it is expected that filament end to be pulled out of the matnv rather than broken.

This comes about simply because within the transfer length at the ends of filaments, the

breaking stress is not reached. On the other hand, continuous filaments of wiiform

arength will fail in the plane of the m a t h crack, with no pull out wlieu these

discontinuous filaments whose ends are embedded at distance greater than the transfer

length below the main fiacture plane. Real fibres have weak points Grom place to place

along their length, and Vary statisticaly in strength fiom fibre to fibre, so that a fibre in the

path of the crack will be broken either where it crosses the plane of the crack (i.e. where

the stress is greatest) or at a flaw in the fibre which is near, but not necessarily on, tlie

plane. Thus fiacture surfaces appear whiskery and real composites which have continuous

fdaments, but also weak points possess properties in between the two extremes shown by

those with fidl pull-out and no puil-out [Atkms 19851.

M e n a filament fiacnires off the mam fracture plane, debonding has to take place

up, down and around the filament fiacture to aliow the main crack to propagate (Fig. 3-5).

Mer tlie interfacial bond has been broken, there is an interfacial nictional stress opposing

the fibres coming out of the holes. The fiction stress may be as large as the interfacial

mess was before debonding (ifthe mterfacial break occurs by slip in the matriv adjacent

to the fibres), but it is usualiy rather less. Even so, work has to be done p d h g fibres out

as the original main crack fiont propagates. Cottrell (1964) showed that pull-out work

contniutes significantly to resistance against cracking in carbon fibre composites.

Some other contniutions to composite toughness corne fiom the work of

debonding and the creation of new surfaces, both in main hcture plane and also in the

cyiindrical areas around the pull-out nlaments. Composte fracture toughness is the mm of

ail the various dissipative work components per unit cross sectional area of fracture

referenced to the area of the main crack. As cylindncal debond areas and pull-out lengths

are related to the events off the main fracture plane, a consequence of dividing the total

work of crack propagation by merely the projected area of main matri.. crack-and not the

actual total area of new surfaces which should include the cylindrical debond areas-is that

a synergisrn in toughness occurs. That is, the toughoess of the composite is greater than

Fig. 3-5: Passage of crack in fibre-reinforcd composites involves interfacial debonding and filament fktures off the main fracture plane. Fibres bridge the crack faces in the wake of the crack front. [Atkins 19851

the nun of the toughness of the components. Thus, even though many flamentary

composites are made from components which are mdividudy brittle, the composites can

have a respectable resistance to crack propagation. The total toughness of typically laid-up

glass or carbon nbre types composites with 50 or so per cent volume fiaction of fibres

may be about 50 kJ/m2.

A feature of the cracking behavior of fïiamentaty composites which is ciiffereut

fiom moQ other situations is that partially pull-out fibres bridge the crack-openiug in the

wake of the advancing matrix crack (Fig. 3-5). The effect is enhanced the longer the pull-

out length. Cracked composites thus have an ability to hang together in situations where

other solids of similar toughness would break apart. The full contribution to toughness

given by pull-out is achieved only when the filaments have pulled al1 the way out, at wluch

t h e they no longer bridge the crack faces.

Strong interfacial bonding between the components of composite is necessary in

order to transfer the load rapidly into the reinforcing components and thereby achieve high

values of composite modulus and strength. However, it may be show that high f?acture

toughess results when the interfacial bonding is weak. When a filament fractures in a

composite having a strong interfacial bonding, a crack is formed in the matrk around the

fibres, and usually this crack is energetic enough to run through the composite, breaking

the fibres as they are met in a Ppper action. The work of fiacture can be veiy low.

One means of alleviahg the problem of low toughness is to introduce crack

stoppers which arrest the ninnmg crack. Cook and Gordon (1964) made use of the fact

that tende stresses exia parailel to a ninning crack in order to produce arrest. The

magnitude of these stresses is about one-Wh of the normal stress concentrated at the

crack fiont in an isotropic continuum, so if there are locaiiy weak interfaces in the path of

the crack which are about one-fif€h as strong as the mam body, debonding ahead of the

crack should occur and the crack be blunted into a T-shape (Fig. 3-6).

Fig. 3-6: Cook-Gordon debonding. Weak interfaces in the path of a crack debond ahead of the propagation crack tip, owing to a stress concentration of the stress parailel to the crack Crack runs into debonded region, is blunted and at Ieast slowed down, if not arrested [Atkins 19851

3-3: Lnterface in Fiber Composites:

It is well known that the fiber-matrix interface gives fiber composites their

structural iutegrity. The interface consists the bond between the fiber aiid matri\: and the

immediate region adjacent to this bond. The intedace is usually considered to be of zero

thickness for analysis proposes. At least three types of bondmg are thought to exist at the

interface. These are chemicai, electrical and mechanical.

The role of the mterface in composite structural inte- is better appreciated

when it is realized that 1 in3 ( 16.38 cm3)of 50401. % fibre composite with a fibre diameter

of 0.0003 hi (7.62 p)contains approximately 6500 in2 (4.2 m2) of interface area

proutman 19741.

The strength, aiflhess, and toughness of the interfacial bond al1 affect a

composite's ultimate properties and the mechanism by which it fails. There are several

methods which cm be used to obtain a measure of the stress state and the strength of the

bond at the interface. These methods can be d ~ d e d mto two groups. ûne group deals

with either single fibres in a matrix casting or multifibres. The other group involves

indirect measure of the bond strength at the interface. The second group can also be

viewed as a qualitative test; however, when interpreted properly it could serve as a

quantitative test. Short beam shear test (ASTM D2344), longitudinal tensile test (ASTM

D3039), and impact toughness test are the indirect methods that are used to assign the

mechanical properties of the intefiace. The short beam test, for instance, is widely used in

the composites indumy. It is a three-point flexural test on a specimen with a smal van,

which promotes failure by interlaminar shear. The use of this method is ümited by the fact

that the failed test specimens fkequently exhibit compressive damage on the top surface,

and the actual fkacture process occurs under complex conditions of combined shearing and

compression. Furthermore, the experimental values are found to depend on fibre volume,

which is not accounted for in the calcuiation, and to decrease with the concentration of

processing flaws? such as voids, intemal rnicrocracks, and dry fibre strands. Dorey and

Harvey (1988) reported that as the level of surface treatment of strand high strength

carbon fibres was increased, the hterlaminar shear strengths of theu unidirectional

composites increased rapidly, but leveled off at a value approximately equal to the shear

strength of the epoxy manix. Therefore, the fdure process mua change fiom hterfacial

to matrk çhear at the treatment level at which hterfacial bond strength equals the yield

nrength of the matrix, so that the latter value is the maximum value attainable from a shon

beam shear test.

Due to the problems that associate with indirect methods, a number of techniques

have been developed to meanire the adhesion of a single fibre to its surrounding rnatriu. In

the following section, some of these methods are reviewed.

3-3-1: Single-Fibre Pullout Test:

This test was first proposed by Broutman (1963). Two vanants can be

distinguished. Favre and Perrin (1972) cast a very thin resin disc around a fibre disc and

meawed the force required to initiate puiiout (Fig. 3-7). Chua and Piggon (1985) altered

the technique by ernbedding the fibre to a controiied depth in a solid block of resh (Fig. 3-

8); this modification is intended to reduce any tende stress resulting fiom resh

deformation at the point of entry of the fibre. The bond strength is calculated as foliows.

r=P, /d =aJ/4L (3- 1 O)

where 5, Pm,, d, L, and o, are average shear strength of the bond, maximum load applied

to the fibre, diameter of the fibre, embedded fibre length, and rna.ximum stress applied to

the fibre respectiveiy.

The tensile stress in the puli-out fibre must be less than its uttirnate tensile strength

a. if it is to pull out rather than break. The maximum embedded fibre length Lm

permitted is thus &en by:

L , = O, d / 4 r (3- 1 1)

In a typical experiment, the force on the fibre is recorded as a fiction of puil out

distance as the fibre is pded (see Fig. 3-9). The first peak on the plot is attniuted to

debonding and Wctional resistance to slipping, and later, the mialler peaks to friction and

stick-slip behavior. Altematively, experiments are conducted in which the embedded

length is increased up to the pomt of fibre fracture and the debonding force is plotted

vernis fibre length (see Fig. 3- 10)). The dope of this line is taken to be the bond strength.

Piggott (1987) states that the embedded single-fibre test is unique in its ability to give not

oniy debonding energies but also fiction coefficients and shrinkage pressures. He

concedes that this is the most diflicult of the single-fibre tests to cany out successfuliy.

Early attempts to study carbon fibre adhesion Favre 19721 were unsuccessfùi owing

primarily to the extremely short embedded lengths required by small diameter fibres with

large bond strengths. Piggott and Andison (1987) have developed the technique to the

point that fibres can be reproducibly embedded to depths of less than 0.5 mm. The method

remains tedious and subject to large data scatter.

Since, the method which was inaoduced by Chua and Piggott reduces the entrance

effects of the fibre to the mat* it is preferred over the other method by Favre and Perrin.

However, both these methods are still under development and need more study to be used

as fùiiy reliable methods.

Matrix Defonnation at Fibre Entrance

Fig. 3-7: Single fibre pull out test. Favre-Perrin resin disc variant. [Favre 19721

F i g 3-8: Single fibre pull out test. Chua-Rggon controlled embedded length variant. [Chua 19851

Fil OJ)

Fig. 3-9: Typical pullout curve obtained with Fig. 3-10: Adhesion force for non-pst cured glass-polyester [Chua 1985) polyester.0, Pull out; x. fibre breakagc [Chua

19851

3-3-2: Embedded Fibre Critical Length Test:

in this test, as first descnbed by Ongchin et al. (1972), one or more continuous

fibres are embedded longitudinaily in a resin having a failure strain greater than that of the

fibre. A tensile specimen is prepared, as depicted in Fig. 3- 11. The specimen is strained in

a tensile fumire to an elongation greater than the strain to failure of the fibre. Since the

specimen contains l e s than the critical volume fiaction of fibre, the fibre wiii break into

many d pieces. The smaiiea fragments are too short to aiiow the transfer of stress

equal io or greater than the fibre tende strength, au, and wiil break fiee of the resin. KeUy

and Tyson (1965) derived a simple expression for the ma,ximum shear stress s at the fibre-

resh boundary, as a huiction of a fibre critical length, Le :

r= cUd/2Le

Fig. 3- 1 1: Embedded fibre criticai length test. p e e 19901

The mode1 predicts that the fibre ikacture process shouid result in a narrow

distniution of fibre lengths fkom Le 12 to Le . The derivation assumes a uniform fibre

strength and diameter, which is never the case for actual fibres. A rigorous calcdation

requkes a lmowledge of the tensiie strength of the fibre at its critical length, which is a

difficult value to obtain experirnentally.

The measurement methods of interfacial strength in composites are not limited to

what are presented in this chapter. There are more methods and many of them are nil

underway (for more information see Lee 1990 ). The extensive efforts, which have been

taken to develop the measurement methods of the interfacial properties, hdicate the

si@cance of this region in the final properties of the composite materials. It appears that

having a profound understanding of the composites is not possible without a deep

Imowledge of the interface.

4- Experimental Method

In the present work, two kinds of composites were made and tested. Glass fibre-

epohy and carbon fibre-epoxy composites were made by the procedure which foliows later

in Section 4- 1.

The glass fibre used in the experiments was E-giass fibre roving AA2200 which

was obtained f?om Fibreglas Canada Inc. E-glass is a general name for the fibreglass that

is developed for electrical applications. The high tende resistance makes it a very good

option as reinforcement in plastic composites. E-glass contahs relatively high percentages

of alumina (Alz03), calcium oxide (Cao), and boric oxide (B203), in addition to silica

(SiO?). The carbon fibre was QUN1689 supplied by Hercules Inc. The epoxy resin and the

liardener were RP-4005 and RF-1500 respectively. The resh was a iow viscosity epoxy-

novalac compound. It is made by reacting phenolic resins of the novalac type with

epichlorohydrin. They were provided by MF Composite Inc. and manufactured by Ciba-

Geigy.

II : Preparation of Restressed Samples:

n i e prestressed specimens were made by winding the fibres around two grips. The

gips were two 1 318 in (3.5 cm) long and 1 118 in (2.8 cm) thick cylinders. The uniforni

winding of the fibres around the grips was an important matter. This was because if the

fibres were not W o d y woud, some fibres would have remained loose and some others

tight (i. e. some fibres would be cartying less tension than others). This prevented the

uniforni distribution of the stress on the fibres m the next step when the fibres were

stressed. To overcome this problem, a winding machine was made. The machine, which is

Rotating Frame

\ Fiber Strand

\ Spool of Glass Fiber

\ Friction Box 1

Fig. 4- 1 : Windiiig iiirichiiie provided niore uiiiforrii wviriding by creiitioii constant ierisioii on the fibre.

schematicaiiy shown m Fig. 4- 1 , helped to wind the a r e s uniformiy around the grips by

creating a constant fiction force on the fibres during winding. In Section 4-1-1, it is

show how much this machine reduced the non-uniformity of the winding of the fibres. In

the next sep, the gips and the fibres on them were transferred to a horizontal tensiometer

machine where a controilable force could be applied on the a r e s (see Fig. 4-2).

Tension +-Il!

a) Top view

Fibres -

Fig. 4-2: Apparatus used to rnake prestressed composites.

A U-cross sectional aluminum mold with a layer of the wax paper as releasing

agent was used to make the composite bars. The epoxy resin, then, was warmed up in a

microwave and mked to the hardener in a ratio of 100 to 15. WarmBig up the resin helped

with better mixing of the resin components and also with better wetting of fibres. The

mived resin was applied directly on the fibres in each experiment. Then the sample was

located inside a speciaiiy designed oven. The temperature inside the oven volume could be

read and controiled by a thermocouple comected to a controller.

The oven was designed and made to provide enough heat to cure the samples.

Shce the fibres had to be tensioned continuously d u ~ g the curing process, two ends of

the oven were open. The oven was laid directly over the sample. To rnake a uniforni

temperature profile along the oven working volume, it was well insulated using ceramic

wool. The temperature profle was determined in the oven. Fig. 4-3 shows a typical

temperature profile for the oven. As can be seen, there is a drop in the temperature close

to the ends. Due to this matter, two ends of composite bars were always cut off and were

not used. This ensured that the curing temperature was not more than f 2 O C different for

all the samples.

The fibres were wound around the cylinders, so that there was a gap between the

upper and lower layers of the fibres. These two layen were clamped together to eliminate

the gap. The clamps were made fiom soft nibber materials to avoid damaging the fibres.

In the next aep, a predetermined stress was appüed on the fibres by the

tensiometer machine. This stress level was kept constant until the end of the curing

process. When heating was staned, the stress dropped due to thermal expansion of the

fibres; however, it was kept constant by applying a nirther teasde load to the fibres.

O 2 4 6 8 10

Distance (in)

Fig. 4-3: Temperature profile in the oven, used to cure the simples.

At the end of the curing process, the oven was tumed off and the sarnple was

cooled d o m to ambient. Cooling usuaiiy took about two hours. Afienvard, the tension

was removed very slowly and the sample was taken out of the mold by cutting offthe bare

ends of the fibres.

The prepared samples were caremy milled to make a smooth top surface. During

milling, the extreme care was taken not to cut the fibres. Afier this stage, the samples were

cut to smaller pieces to produce standard specimens. The pieces, then, were used for the

mechanical tests. The giass fibre-epoxy specimens were 72 nlnl by 10 r m r and 4 mri and

the carbon fibre-epoxy çamples were 72 mm by 8 mm by 3 mm. These samples were used

for bending tests.

It was necessary to h o w the fibre cross sectional area to calculate the pretension

as stress. In order to find out the fibre strand cross sectional area, the fibres could be

assumed as long cylinders with constant diameter. This assumption was not far nom

reality. The cross sectional area of the fibre strand could, then, be calculated as follows:

Where V and I are the volume and length of the fibres respectively. On the other haod, I r

cm be written as:

where m and p are weight and density of the strand. Substitution of V in Equation 4- 1

fiom Equation 4-2 provides AI, the cross sectional area as a fùnction of the density and the

weight of the unit length as foîlows:

The weight of the unit length of strand was measured and it was found to be 2.30 gndni

and 0.76 pdnr for glass and carbon fibre arands respectively. The density of the fibre, p.

can be found nom either literature or direct meanirement. The densities of g las fibre and

carbon fibre were measured by using a picnometer and they were found to be 2500 kg/n3

and 1850 kg/nzJ respectively. B y the use of the available data the cross sectional areas of

the glass fibre strand and carbon fibre strand were calcuiated to be 0.92 mn~2/stratrd and

O . 4 1 nznz2/strutui respect ively.

The weight percent of the fibre and resin were determined by howing the length

of the fibre used in the specimen and the weight of the composite specimens. The fibre

weight percent in glass-epoxy samples were 6 0 S % and in carbon-epoxy samples 47&2%

which correspond to 42% and 36% fibre volume percentage, respectively.

4- 1 - 1 : Uniform Winding:

When making fibre prestressed composites, it is very important to have uniform

winding of fibres; otherwise, some of the fibres are aretched during the prestressing and

others remain loose and do not contnbute to the carrying of the load. Therefore, it is

necessary to have an assessrnent of the uniformity of the winding. In that regard, a test

was designed to determine the level of the uniformity of the winding. The tea was based

on this fact that glass fibres behave iinear elastically up to the yielding point. This means

that the stress-strain graph of the glass fibre mua appear as a araight line. However, when

a bundle of fibres are drawn in a tende tea, the stress-strain graph shows a curvature at

the beginning and subsequently it t m s to a straight üne. The curved part of the graph is

fomed because the fibres do not possess the same level of looseuess (or tightness) at the

beginning, so that when the loading is aarted the fibres are engaged to carry the load one

after another according to their looseness. Fig. 4-4 shows how when the tension increases

the fibres aan to participate canyhg the load. When more fibres are engaged, the slope of

the stress-strain cuve increases. The increase of the slope of the curve continues until all

the fibres are stretched. M e r that the slope remains constant (see Fig. 4-5). if the

ciifference amoag the looseness of the fibres is large, in other words, windllig is very non-

unifom, the curved part of the graph becomes significant. On the other hand, if the

winding is relatively uniform, the straight line on the graph starts at lower stresses. In the

ideal case, when the winding is perfect, the curved part disappears and the araight line

staxts right from the ongin.

Tension

Loose Fiber

Tension

Co) Tight Fiber

/

F i g 4-4: When tension increases, Iaose fibres become taut and start to carry Ioad,

/

Based on the above explmation, the curved part of the graph indicates the non-

uniformity of the winding. In Fig. 4-5, the magnitude of stress at point A can be used as

f--- , Tension

evidence to assess the uniformity of the winding. If point A is located at lower stresses

then the winding of fibres is more uniform

Fig. 4-5: Value of stress at point A can be used as an evidence to assess the unifonni ty of the winding.

In an experiment to indicate the unifodty of the winding, three samples were

wound by hand and three others by use of the winding machine which was described in

Section 4- 1 and s h o w in Fig. 4-1. The tende tests were accomplished on a tensiometer

and the stress-strain graph was created for each sample. Then, the magnitude of the stress

at point A, in Fig. 4-5, was measured. Table 4-1 shows and compares the results of the

tests. As can be seen fiom the table, the average of the magnitude of the stress of the

c w e d part of the graph has decreased fiom 23 MPa to 7.3 MPa when the machine was

used to wind the fibres. While it was not practicaiiy possible to have an ideal winding

(completely d o m ) , the use of the windhg machine significantly reduced the Ievel of

non-unifo rmity .

I Average = 23 1 Average = 7.3

1 1 I

Table 4- 1: Magnitude of curved part of stress-main graphs in different samples

4-2: Mechanical Tests:

Four point bending tests were camed out on the samples on an hstron tensile test

machine. The bending device is shown in Fig. 4-6. The tests were performed according to

ASTM D790. The cross head speed was chosen to be 0.05 i r h ~ i ~ i 11.77 nrnr/nti>$ The

flexural modulus and flexural strength, then, were calculated using the foiiowing equations

lpopov 19681:

where E, and o are flexural modulus and flexural strength, LV, and d are width and

thichess, L, s, and a are outer span, inner span, and the distance between outer and inner

spans and P, and A are the maximum load camed by the sample during the test and the

correspondent deflection respectively.

Fig. 516: Four point bending device, used to conduct flexurd tests.

To ensure that the deflection, read f?om the chart of the hstron, was accurate, the

amount of the deflection of a sample was measured by ushg both a dia1 indicator and by

using the graph of the haroa. Table 4-2 compares the values of the deflections measured

by the dia1 indicator and those which were obtained from the graph of the Instron. As can

be seen the average of the error between the two sets of data was 1.375%. This ciifference

was considered acceptable and systernatic, so that the values read fiom Instron machine

were subsequently directly used to calculate the flexural modulus of the samples.

Table 4-2: Defiection of sample determined by two different methodç. The error percentage is indicated.

1 Average of error = 1.375% 1

4-3: Messurement of Residual Stresses:

The procedure, descnbed in pan 4-1, was applied to make the samples. The only

clifference was the strain of the fibres was monitored as a huiction of applied force before,

during, and after the curing process. At the first stage when the resin was aiii Liquid, the

force-strain curve was created for the fibres by applying a pre-determined force on the

fibres and recording the strain ai the same tirne (Fig. 4-7, A-B). Since the resin was liquid,

it could not cause any resistance and the whole load was camed by the fibres. The fibres

were kept aretched and at the same tirne heating aarted. While the temperame was

rising, due to thermal expansion of the fibres, the load tended to drop; however, it was ,-

kept constant by more stretching of the fibres. Part B-C in Fig. 4-7 indicates the stretching

of the fibres to keep the tension constant. This continued until the temperature reached

150 OC, the set value. M e r that, there was no more changes in the level of load duriog the

Error (%)

2

Deflection read from graph of Instrun (in)

0.0255

Deflection read fiom dia1 mdicator (in)

0,025

Strain

Fig. 4-7: Monitoring the main of the fibre during the curîng process shows that some part of the strain of the fibres is not recovered after removing the extemal tension. The un-recovered main is used to assign the fibres' residual force. Ffi,..

heating process. At the end of the heatiag period, the oven was turned off and the sample

aarted cooling down to ambient. During cooling, the force increased due to thermal

contraction of the fibres (Fig. 4-7, C-D). When the temperature came back to room

temperature, the tension was removed very slowly and at the same time the strain was

recorded (Fig. 4-7, D-E).

From Fig. 4-7, it appears that there was a Merence between the starting and

ending points (point A and E). In other words, the main of the fibres was not hl ly

recovered. Tbis experiment proved that some pan of the fibres' arain was not recovered

after removhg the tension. This was because the fibres were held by the cured resui and

they were not able to recoil fieely. This experiment also indicated that the fibres remained

stretched in the fibre prestressed composites. It also gave the amount of un-recovered

strain of the fibres in the composites. The amount of un-recovered arain of the fibres was

used to calculate the residual tende force in the fibres. This could be accomplished by

hding the corresponding force in the fibres on the force-nrain curve. It should be noted

that the residual sirah is for that part of the length of fibres which is embedded in the

polymer; however, A-B line on Fig. 4-7 shows the force-strain relationship for the whole

length of the fibres including the part which is not embedded in the polymer. This can be

corrected by multiplying the residual strain by the ratio of the total length of the fibres to

the embedded length of the fibres in the polymer.

The nonnal and shear stresses m the fibres and matrix cm be computed f?om the

data provided for the residual forces in the fibres. The micro-residual stress in fibres, q,,

,cari be calcuiated as foUows:

Where FJ, is the residual force in the fibres and AI is the total fibres cross sectional area

in the sample. The cross sectional area for one arand of the fibre was previously evaluated

as explained in Section 4- 1 :.

q, is the tension ni the fibres. According to static equilibrium the algebraic

summation of the forces in the specimen mua be zero dong the fibre axis thus it can be

written:

Where F,,,., is the residual force in the matrix. On the other hand, it is known:

A , and O,, are the cross sectional area of matriv and matrix residual stress respectively.

Substitution of Equations 4-8 and 4-9 in Equation 4-7 provides a,, as foiiows:

Assuming the fibre diameter is constant along the specimeo then A#Am can be subaituted

with 6.j /KtI, the ratio of the fibre to matrix's volume percentages. Then the residual

normal stress in the mat* a,,, can be written as:

The minus sign indicates that normal stress in the ma& is compressive.

The residual shear stress, s-,,, at the fibre-matrix mterface, is the other parameter

which can be assessed by loiowing the axial residual forces.

Where S' is the surface area of the fibres in the specimen and can be computed as:

Sf = n D / L N (4- 13)

Where DJ L and N are filament diameter, specimen length and number of fdaments in the

composite respectively. The filament diameter, Dh was determined by SEM imaging and it

was found to be 20 p for the glass fibres used in these experiments. The number of

filaments in the composite can be calculated by dbiding the cross sectional area of the

fibres arands by the cross sectional ares of a single filament.

Substitution of Equations 4-13 and 4- 14 in Equation 4- 12 provides the following

equation:

The residual stresses were determined in the fibre prestressed composites by using

the above calculations at f i e Werent prestressing levels. The experiments were repeated

twice for each prestressing level. The results are presented in the next chapter.

4-4: Measurement of Resin Shrinkage:

Since the shrinkage of the polymer, during the curing process, was one of the

sources which introduced the residual stresses to the composites, it was necessary to have

quantitative information about t . For this reason, a test was designed to measure the

shrinkage of the polymer during curing and, d e r that, during cooling to ambient.

An alumiaum mold with a U cross section was constmcted, with hvo push rods

made of Chromel which served as markers. A guide was designed to control the

positionhg of the markers. The mold &es were 280nimx 10nimx 8nm. The two ends of

the mold were open. The guide aiiowed the markers to move independently in straight

lines. The thin markers were placed in the smali holes of the guide and the apparatus was

assembled as shown in Fig. 4-8. In order to avoid the sticking of the resh to the mold, wo

O tical Microsco e r M Guide

I

Fig. 4-8: Apparatus used to measure shrinkage of polyrner.

layers of grease and waxed paper were used as release agent inside the mold. The open

ends of the mold were closed by dams made fkom ceramic wool. These dams were

yielding enough to readily accommodate the resin dimasional changes (DC) during

curing.

The procedure next was to nU the mold with the mixed resin. The marker ends

were submerged in the re&. The other ends of the markers were placed under an optical

microscope. The microscope lem was equipped with a graticule so that the relative

movement of the marker tips could be measured. The oven was laid over the mold. The

experiment was started by heating the resin in the assembled apparatus. The marker tips'

location and the temperature were recorded as functions of tirne. When the resin expanded

or contracted, the markers moved so that the DC could be read by the distance between

the marker tips under the microscope. Since the initial distance between the hvo ends of

the markers which were implanted in the resin was known, the DC could be calculated

per unit length.

To cancel out the Uuluence of the markers' expansion, the test was repeated;

without resin and with the resin. The results obtained for the expansion of the markers,

which was mal1 compared to the dimensional changes of the resins during the tests, were

subtracted fiom that found for the resin.

The microscope magnification was x 3 5 and the scale on the graticule kvas dMded

to 100 divisious, so the maximum precision to read the marker tips was 1/35 mm. The

distance beween the two ends of the markers which were implanted in the resin at the

start of each test was measured for each test performed and was 170 mm in ali tests.

The tests were accompüshed under three different heating conditions. For the firn

test, the temperature was raised quickiy fkom room temperature to 1 LO OC continuously

and was kept at 110 O C for 4 hom. Then the oven was turned off and the assembly was

aliowed to cool down to room temperanire. The second test was carried out by the same

procedure except the temperature was raised quickly to 150 O C and was held at 150 O C

for 4 hours. The third test was achieved by applying a step heating program which was

recommended by the resin manufacturer. Here the resin was allowed to partly cure at

room temperanire for 4 Iir and then the temperature was raised to 66 O C for one hour.

This was foiiowed by 1 hour at 93 O C and 1 h o u at 120 O C and 2 hours at 150 OC. nie

second test was camed out three times to examine the reproducibiüty of the test. These

tests showed the dimensions recorded were reproducible within 10% for all meanired

dimensions referred here.

Since the reaction between the epoxy resin and the hnrdeuer was highly

exothermic, a large amount of heat was produced during the reaction. This heat increased

the temperature of the polymer above the temperanire of the oven. For the £ka hvo

samples, which were heated up quickly to the curing temperature, the heat of the reaction

was released very fast at the beginning of the curing process. in the sample cured at 150'

C, the increase of the temperature of the polymer caused some little amount of smoking

for a short period of tirne. The smoking continued for about one or two minutes and then

it stopped. For the two other samples cured at 11O0 C and the step-heated sample, no

smoke was observed.

4-5: Contribution of Resin Shrinkage to Residuai Stress:

A test was desîgned to measure the contniution of the resin rhrinkage to the

residual stress. The epoxy resh was used to make an un-prearessed composite specimen

with fibre glass. The fibre glass was laid on the bottom of a mold where the epoxy resin

was applied on that. In order to obtain a d o r m sample a very slight tension was applied

on the fibres to keep them straight and paraiiel. The use of two clamps at the ends of the

fibres also helped to hold the fibres in place at the bottom of the mold. M e r impregnation

of the fibres by the resin, a known amount of extra resin was lefi on the top W a c e of the

fibres. The assembly was then located inside an oven. The sample was cured for four

houn at 150 OC. At the end of the curing process, when the specimen was taken out of the

mold, it was observed that it had a slight curvature. The deflection at the middle of the

sample was measured by the use of a micrometer and it was found to be 1.27 ntnz. The

sample was 250 nim long and 22 mni wide.

The extra resin formed a fibre-fiee resin phase on the top. Therefore the sample

looked lüte a rectangular bar composed of wo layers. The upper layer was the un-

reidorced polymer phase and the lower layer was the composite phase. The curvature was

Neat Polymer

/ Composite

Fig. 4-9: Sarnple ben& due to shrinkage ofpolymer.

63

concave on the polymer Zde (Fig. 4-9). The formation of the cwature mdicates that the

shrinkage of the neat polymer phase at the top and that of composite phase at the boaom

were not identical during the process.

The thickness of each phase was determined by sectioning the specimen. The

composite layer and the neat polymer phase were 3 mm and 2 nrnz thick respectively.

In the next aep, the specimen was located inside an oven where the temperature

could be increased very slowly. The deflection of the sample was monitored by the use of

a dia1 indicator as shown in Fig. 4-10, It was found out that the deflection in the sample

was eliminated at 88f 1 OC. This means the sample was straight at that temperature.

Therefore, 88 O C can be inferred as the stress fiee temperature [Crasto 19931 as far as the

two adjacent layen are concerned.

Dia1 Indicator

Sample

/

Fig 4- 10: Defiection of sample was eliminated when temperature increased.

64

Having the geometrical and physical characteristics of the composite-polymer bar

and the value of the deflection, it is possible to calculate the residual force at the interface

of two layers. The shrinkage of the upper layer imposes a force along the specimen on the

top d a c e of composite phase. This is shown in Fig. 4- 1 1.

Force P' makes the sample bend concave upward. The composite phase can be treated as

shown in Fig. 4-1 la to assign a mathematical relation between the amount of deflection

and the residual force between two layers. P: in Fig. 4- 1 1 a, can be subaituted with P

which is equal to P' but has shified down in the middle of sample's thickuess and M o , a

moment that tries to bend the sample upward (Fig. 4-1 lb). hfo cm be calculated as

. follows:

where t. is the thickness of the composite phase.

The relation of deflection, v, and the distance along the specimen lengh can be

expressed by the following differential equation (see Appendiv 1 for more details):

where:

and Ec and 1, are Young's modulus and moment of inenia of the composite layer

resp ectively.

In this particular case, the boundary conditions cm be written as:

~ ( 0 ) = O , a) = O , M(0) = -bf0 ,

The solution of the above differential equation upon considering the mentioned boundary

provides the foilowiog equation, which expresses the defîection of the bar as a fùnction of

hi., and h:

The maximum deflection occurs at x = U2. Therefore, afier substituthg x with L/2 and

doing some simplification, we have:

Neat Polymer

Comoosite

(b)

Fig 4-1 1: Shrinkage of potymer applies a shear force on the top su- of composite.

Substitutmg MO in Equation 4-20 fiom Equation 4- 16 provides h. as follows:

2 2v-x A = - Arc sec[- + 11 L 4

Ec , Young's moduius of the composite, can be found by the nile of mixtures:

E, = EI yI + En V, (4-22)

where EJ E,,, . Gj, and V, are Young's modulus of fibre and polymer matriw and volume

percentage of fibre and polymer in the composite phase respectively. El and, E , are

adopted from literature pubin 1969, Lee 19671 and were considered 70, and 3 GPa

respectively. Ij , and Y,, were also measured and found to be 40 and 60% respectively.

Knowing Ec , 1, , and k, it is possible to calculate P, the residual force between the

composite and polymer layers, by the use of Equation 4- 18.

The reaction of force P keeps the neat polymer phase under tension and causes

reîidual teasile strain. The amount of the main, created in the polymer, cm be computed

according to the foliowing equation:

Where A is the cross sectional area of the polymer phase. Using the above equations and

data, P and E were found to be 96.6 Nand 7.32 x lo4 mm/nrm respectively.

4-6 : Large Size Samples:

A drawing bench was made to produce large size samples. Using this machine,

samples up to six feet long were fabricated. 'Ihe drawing bench is shown schematicaiiy in

Fig. 4- 12. The fibres were mserted between two star-shape grips. The eiectncal motor

provided mechanical work to rotate the dnua The d m p d e d the cable and placed the

fibres under tension. The amount of tension could be read fiom the load cell instaiied

dong the cable. A constant tension was maintained on the fibres until the end of the curing

process. The U shape mold with a layer of wax paper as releasing agent, then, was iocated

under the fibres and the mixed resin was applied. This was camed out very carefùiiy to

ensure the whole surface area of the fibres were wet by the resin. Then a curing oven was

located around the sample. Two ends of the oven were opened to ailow the fibres to pass

through. The temperature inside the oven was measured and controlied by a themocouple

connected to a controîier. Since the ends of the oven could not be ciosed completely and

also the heathg elements were not extended to the ends in the oven body, the temperature

DRUM LOAD CELL

MOTOR

BENCH I I CONTROL

-- PANEL - i

F i g 4-12: Drawing bench, used to produce large site samples.

68

dropped at two ends. To obtain a d o m temperature inside the oven volume, an air

circulation system was introduced to the oven. The hot air was blown inside the oven from

one end ushg a commercial heat gun. The hot air exited fiom the other exit at the other

end of the oven. The distance of the hot air blower to the oven and the site of the air exit

door was experimentally determined to gain the best uniforni temperature profile inside

the oven (see Fig. 4- 13).

Several samples were made by use of this machine. The samples were cured at

150°C for 4 hours. At the end of the curing process the sample was cooled to ambient and

then the applied tension was gradually removed and the sample was taken out. These

samples were deployed to conduct the impact tests in the next section.

4-7: Impact Test:

Using giass fibres, two samples at each of 0, 20, 40, 60 and 80 MPa prenressing

level were fabricated on the machine, described m Section 4-6. The Nes of the samples

were 96 cm x 1.9 cm x 0.6 cm The samples were next cut lengthwise to prepare the

impact test specimens. Two specimens fiom each sample were taken. The Nes of the

specimens were 8.1 cm x 1.9 cm x 0.6 cm The specimens were used unnotched on a

Tinius Olsen Charpy test machine. The maximum capacity of impact tester was 264 A.lbs

(357.7 0, nonetheless, only between 10% to 16% of the maximum capacity of the

machine was used in the experirnyts. AU the samples broke partidy according to the

ASTM definition [ASTM 19831.

5- Results and Discussion

5-1: Residual Stress in Fibre Restressed Composites:

Temperature bas greater detrimental effect s on composites than on monolithic

materials. Smce a composite consists of NO or more constituent materials having Werent

mechanical and physical properties, any change in temperature will induce stresses in each

constituent, even though the composite matenal as a whole may not be loaded extemally.

UsuaUy, all composites are fabncated at a certain higher temperature and used at lower

temperatures, so thermal residual stresses often exia before the specimens are loaded

mechanically. Sometimes the thermal residual stresses are so high that they alone can

cause some damage in the fom of microcracking. In some other circumstances properly

arranged material geometry and thermomechanical properties may be used to introduce

t h e m l residual stresses that are beneficial [Zhao 19931.

Residual stresses in fibre-remforced composites anse during processing, primarily

fiom a mismatch in the coefficients of thermal expansion between mathv and fibre. In

thermosetting matrix composites, an additional contribution c m anse fiom chemical

shrinkage of the matrix as it cures.

In the case of fibre prestressed composites the fibres' tension is also a great source

of residual stresses. The bonding between the fibres and matrix is eaablished when the

fibres are stretched so when the tension is removed, similar to a spring, the fibres tend to

recoil. This introduces a considerable compression force to the mat&

The total residual stresses in the fibre prestressed composites are the summation of

the residual stresses which are created by each of the above mentioned factors. Ch the

other han4 stress relaxation in the polymenc mtrix, especiaiiy at high temperatures or

around the T, glass transition temperature, is the main reason for reduction of the residual

stresses in polymer matrk composites.

The method and caIculations, described in section 4-3, were used to measure the

residual stresses in fibre prestressed composites. This method provided the total residual

stresses in the composites regardless of the sources and the contniutions of them. Two

tests at each of 15,40, 70, and LOO MPa prestressing level were camed out. The resulting

residual forces in the fibres were calculated based on the measued fibres' strain in each

test. Figs. 5-1 to 5-4 show the residual force in the fibres, the residual stresses in the fibre

and mat* and the shear residual stresses at the interface between the fibres and matris as

hctions of the prestressing level. The first point which is apparent nom the graphs, is

that residual stresses in the composites are linear increasing functions of prestressing level.

This means that the increase in prestreshg causes more residual stresses in the

composites. Fig. 5-2 indicates that, for this particular composite system and processing

conditions used in this study, the normal residual stresses in the fibres are almoa haif of

the fibre prestress during the process. This also can be seen in Fig. 5-5. It shows that the

ratio ofthe rendual strain of fibres to their total strain, created by prestresshg during the

process, is constant in all samples r e g d e s s of the amount of prestressing.

Fig. 5-3 &es the residual stresses in the mat&- The matrix is under normal -. compressive mess in fibre prestressed composites. The trend line, which is fitted among

the data, can be extrapolated to the zero prestressmg level. This provides the theoretical

residual stress in the matrix for the un-prestressed sample. As can be seen in the graph, the

residuai stress in un-prestressed sample was found to be -0.8 MPa. The minus sign

indicates that the matrix in un-prestressed samples is under tension rather than

compression. It may be argued that the extrapolation of the experirnental data is not a

direct method to estimate the residual stress in the un-prestressed composites. This

method does give, however, an estirnate of the amount of residual stress in un-prestressed

samples. The amount of the residual stress d e t e d e d for un-prestressed sample by this

method is comparable to the result generated by the model which was presented by

Jayaraman et al. (1993). They developed a mathematical model which was able to

calculate the residual stresses in un-prestressed composites. For a typical glass fibre-epoq

composite sample, this model predicted 0.3 MPa tende residual stress (this can be

expressed as -0.3 MPa if the compression force be considered positive) in the matrix. The

results of this elrperimental study and that provided by Jayaramao's model are nmüar.

Fig. 5-1 indicates that shear residual stress at the interface increases when fibre

prestressing rises. The increase of shear residual stress at the interface places the matrix in

greater compression force. This can cause higher resistance to fiacture in the composites

by preventing the opening of microcracks, whm the samples are subjected to the external

loads. On the other hand, the increase of shear residual forces at the interface beyond a

certain value results in debondmg of the fibres and ma& This reduces the integity of

composite and decreases its resistance agamst external loads. 7

Prc-stress (M Pa)

Fig. 5- 1; Residual force in fibers increases linearly as a function of prestressiiig in glass-epoxy composite. Saniples cured at 150 OC for four Iiours,

Pm-s tress (M Po)

Fig. 5-4: Residual sliear stress increascs at the interface as fibre prestress increases. Glass-epoxy co~iipsites cured st 1 50 "C for 4 hours.

5-2: Resin S hrinkage:

Shrinkage is the reduction in volume or in hea r dimensions which is observed

durhg the curing process. It induces stresses which can lead to early cracking. Some of

this shrinkage occurs while the epoxy-curing agent system is in a liquid state, while it is in

a thermoplastic state, and after it has gelled. in general, shrinkage occurs in the direction

toward the bulk of the matenal. Shrinkage is of two kinds: curing duinkage caused by the

reaction and rearrangement of the molecules into a more compact configuration; and

thermal shrinkage, brought about by the cooling of the specimen from higher processiog

temperatures[lee 19671. The majority of shrinkage occurs before gelation, so that the

effect can be largely offset when making open-mold castmgs by feediug in additional resiu.

This part of shrinkage does not cause residual stresses when the resin contain fiilers.

Therefore, only a smaii part of shrinkage of the resin contnbutes to the creation of residual

stresses.

As already described in section 4-4, the epoxy resh shrinkage was measured by

looking at the relative movement of two markers which were implanted in the resin. The

tests were accomplished at Merent curing temperatures. The results of the teas are

sbown in Fig. 5-6 to 5-8. Fig. 5-6 and Fig. 5-7 indicate the shrinkage values for the

samples which were heated up directly to the curing temperatures. These two graphs

show çimilar trends. A sharp and fast shrinkage occurs after 2 or 3 minutes and then a 1

relatively flat portion of the curve can be seen. These tests are evidence the major pan of

shrinliage in the resin occurs at early stage of the heating. This part of the shrinkage is

complete in less than two minutes. M e r that, the shrinkage proceeds very slowly. This

continues until the end of heating process. When the oven was t m e d off at point C and

the sample started to cool dom, more shrinkage has occwed in the sample (C-D). This

part of the shrinkage is the thermal contraction of the cured r e h . The amount of resin

shrinkage due to thermal contraction (GD) is comparable to that due to chemical reaction

at the early step of heating (A-B). For the sample cured at 1 10 OC, the ratio of the thermal

shrinkage to the chemical shrinkage is 1 :2. This ratio for the 150 OC cured sample is about

1: 1.1. When the chemical shrinkage happens at the early stage, the resin is not yet ver-

viscous to f o m residual stresses in the sample; however, when the thermal shrinkage

occurs at the end of the curing process, the resin bas been soiidified so bat the shrinkage

- in this stage is able to create intemal stresses in the sample.

The other point that should be noticed is the ratio of the total shrinkage in the two

samples made at different curing temperatures. For the 110 "C and 150 O C cured specimen

the total shrinkage has been 0.015 n i d m m and 0.022 mndnini respectively. The total

shriakage has increased 45% when curing temperature has increased fiom 110 O C to 150

O C . This demonarates that the curing temperature has a great iduence on the shrinkage

of the resin.

In addition, the cornparison of the chemical shrinkage values of the Cumes

indicates that the inmease of the curing temperature has increased the chemical sbrinltage

by 15%. On the other hand, the curing temperature increase has resulted in about 80%

mcrease in the thermal shrinkage. This indicates that the curing temperature has greater

effect on the thermal shrinkage than chemical shrinkage. Thus the increase of the curing

temperature can cause more residual stresses in the specimen.

The shrinkage trend, as shown in Fig, 5-8, is Werent for the sep-heated sample

fiom those which were heated up rapidly to the h a 1 cursig temperature. As indicated in

Fig. 5-8, there is a very small amount of shrinkage while the resin is curing at room

temperature (see A-B). Folowing that when the temperature was raised to 66 OC, fua a

naall amount of expansion is seen (B-C) and then the resin rhrinks(C-D). In the next sage

when the temperature is raised to 93 OC no expansion is observed and the resin shrinks

rapidly (D-E). Following that, when the temperature is raised to 120 O C a rapid expansion

occurs in the polymer (E-F7)and afier that whiie the temperature stays at 120 O C some

smali shrinkage recovers some part of the expansion (F'-F). And. finalIy, when the

temperature is raised to 150 O C a steep expansion cm be seen again (F-G') but while the

temperature remains at 150 O C for 1 hour, the shrinkage proceeds very slowly (G'-G). At

the end of heating process, during cooling, thermal contraction is observed (G-H). This

experiment also shows that the majority of the shrinkage is completed at 93 O C for the

sep-heated sample.

There are significant ciifferences between the step-heated sample shown in Fig. 5-5

and those which were heated up directly to the curing temperature, Fig. 5-6 and Fig. 5-7.

First, the total shrinkage for the step heated-sample is much less than that for the two

others. The total measured shrinkage value decreased to 30% comparing to the 150 O C

cured sample and it was 0.0066 mdrnrn.

The other clifference is that the thermal expansion is never seen during the c u ~ g

process of 110 O C and 150 OC cured samples but for the step-heated resh there are

periods during the cure when the resin has expanded compared to the starting point. in

Tiittc (min)

Fig. 5-8: Shrinkage of epoxy resiri, Step heatirirr. was amlied.

other words, the shrinkage cuve cornes below the zero point iine. This can be important

when using tension sensitive inclusions or brittle mold materials with this resin.

5-3: Contribution of Resin Shrinkage to Residual Stresses:

The method, which was htroduced in Section 4-3 to measure the residual stresses

in fibre prestressed composites, provides the total residual stresses in the composites

regardless of the sources which produce them In fibre prearessed composites, the

bonding between the fibre and matrk is established while the fibres are aretched.

Shrinkage occurs in the resin while it cures. Therefore, when the c u ~ g process finislies

and the temperature retums to room temperature and before removing the tension, the

matrk tends to shrink more than the fibres, so that the matrix is under tension at this tirne.

AAenvards, when the fibres' tension is removed, the recoiling of the fibres not only

compensates for the shrinkage of the matrix but also may place it under compression.

Thus the shrinkage of the matrix reduces the stresses which are produced by fibre

recoiling.

To gain a profound understanding of the prestressing mechanism, it is necessaiy to

determine the shrinkage of the ma& in the composites and consequently how much of

the fibre prestressing is neutralized by the matrix shrinkage. The information obtained on

the epoxy resin shrinkage, fkom Section 5-2, cm not be directly used here. This is because

the existence of the Wers in the resin resuits in significant changes to the observed ' 7

shrinkage. It is well known that the inclusions reduce the shrinkage of epoxy resins, so

that when the epoxy resin mcludes the a r e s , the amount of the shrinkage of the resin is

seen to be different. This point is also evident by the resuits of the shrinkage test and by

comparing these r e d t s to the r e d t s of the measurement of the residual stresses in the

composites. The magnitude of the shrinkage of the bulk resin and fires arain during pre-

tensioning are 10'* and 1 0 ~ respectively. Thus, assuming the resin shrinkage is the same in

the bulk and in the composite form, the matrix should be under tension in the prearessed

composites, whereas the measurement of the residual stresses in the composites shows

that the matrix is under compression. Therefore, the resin shrinkage in the composite mua

be much less than that measured in the bulk f o m

The test which was designed and explained in Section 4-5, determines how much

of the resin shrinkage contnbutes to the formation of residual stresses when the bulk resin

- is in contact with the composite. As already calculated in Chapter 4, the resin shnnkage is

7 . 3 2 ~ loJ mm/mm. Comparing this to 2 . 2 ~ 1om2 mndmrn, the total shrinkage of the epohy

resin 8i the bulk form, we can conclude that only 3.3% of the shrinkage in the bulk resin

interferes to produce the residual stresses. This large decrease in the resh shrinkage is

caused by the contact of only one surface of the neat polymer bar to the composite, so that

we c m expect the shrinkage of the resh along the fibre direction in the composite should

be even tess than 3.3% due to more surface area contacted to the fibres.

The slow heating of the composite-neat resh bar showed the residual stresses

benveen the layers are elirninated at 88 OC. Accordhg to the available data sheet for this

epoxy resin, the coefficient of thenna1 expansion of the cured resh is 15x10" PC.

Asniming that the coefficient of themal expansion of the composite bar is the same as the

fibre glass and it is 5 x 104 P C F e 19671, the relative thermal expansion of the polymer

bar to the composite bar at 88'C can be &en as folows:

E = ~ ~ ! ~ / , w w r r- aeanipsitJ AT ( 5 - 1)

Taking room temperature as 22 O C , the relative thermal strah (E) of polymer layer will be

6 . 6 ~ 10'' mdmm. Comparing this vahe to that what was already calculated fiom the aatic

calculations (7.32~ lo4 mmjmm), about 10% dinerence c m be observed. Bearing in mind

that some of the parameters were taken fiom literature and they may not be exact, 10%

difference is acceptable and shows the accuracy of the tests.

nie curing temperature is usuaily considered as the stress-£iee temperature in

mathematical modeling. The stresses are, then, assumed to be built up when the composite

is cooled down to room temperature. This experiment demonstrates that the stress fiee

temperature for this system is 88 O C . Bearhg in mind that the curing temperature was 150

O C , it can be concluded that no stresses have been formed between the two layers during

cooling fiom 150 O C down to 88 O C . The formation of the residual aresses, then, has

aaned when the temperature dropped below 88 O C . This can be explained by the

viscoelastic behavior of the polymer. Polyrners at high temperatures are able to relax the

stresses eanly, also stress relaxation in polymers is much faaer at higher temperatures.

Therefore a considerable part of the stresses are relaxed when the temperature is ail hi&.

In this experiment, the sample was cooled down m ai.; however, if the cooling rate is

different, it is expected that both the sample curvature and the fiee stress temperature

change. For very slow coolUlg, theisample has more tirne so that a laqer pan of stress is

relaxed. On the other hand, if the sample cools down very fia, the polyner does not haïe

enough tirne for extensive mess relaxation.

As a conclusion, the effect of the resin shrinkage on the formation of the residual

stresses is not as much as would be expected by looking at the resuit of the shrinkage of

the neat resin. This is due to two factors. First, m composites, the mterface areas between

the fibres and polymer is very large, so that the strong bondmg of the fibre-polymer does

not aliow the shrllikage along the fibre direction. The resin shrinkage can be

accommodated perpendicular to the fibres direction redting in more packhg of the

fibres. Secondly, at liigh temperatures the stress relaxation can neutralize some part of the

stresses which possibly are produced by the resin shrinkage. Therefore the effect of the

resin shrinkage to create residual stresses in the composites is not as significant as that of

fibre prestressing.

5-1: Effect of Fibre Restressing on Mechanical Roperties:

The main reason for using fibre prestressing is to improve the mechanical

properties of the composites. In this study, flexural strength, flexural modulus, and impact

arength of the composites have been chosen as the basis to determine how fibre

prestressing affects the mechanical properties. As will be show later, the experiments

Uidicated that fibre prestressing is able to improve the mentioned mechanical properties.

AU the tests showed very similar trends. The measured properties increased when the fibre

prestressing increased. This continued up to a certain prestressing level in each series.

Afterwards the properties declined. The prestressing level, at which the maxhum - - 7

mechanical properties were gamed, was not a constant value but a fùnction of the curing

temperature and constituent materials.

5-40 L : Flexural Strength:

Four point bending teas were canied out on the samples. Twelve specimens were

teaed for each prestresshg level for the samples which were made at 110 OC. For the two

other series, six specimens were teaed at each prestressing level.

The load-deflection curves, for the ali samples, showed a s d a r fonn They al1 had

a linear part at the beginning. This linear part of the c w e continued up to a ma>àmuq

then the c w e dropped to the zero point line in a senes of irregular steps. Fig. 5-9 and Fig.

5-10 show two typical stress-deflection curves for the four point bending test of an un-

prestressed and a prestressed glass-epoxy sample, respectively, used in this study.

Comparison of Fig. 5-9 and Fig. 5- 10, indicates that the un-prestressed sample 1x1s

a longer taü after the maximum. In the un-prestressed samples, the fibres are not aretched,

so that when the extemal stress increases, not all the fibres contribute to cany the load at

the same time. In fact, in the un-prestressed composites, only a smali portion of the fibres

carry the load. This results in lower strength and in formation of a long tail after the initial

breakage. On the other hand, in the fibre prestressed composites, the fibres are aretched,

so that they all, or at least a large portion of the- contn'bute to carry the load. In this

case, the a r e s in each plane of the sample break çimultaneously rather than one by one.

This results in the higher strength and the shorter tail of the curve d e r the initial

breakage. ' 7

The maximum applied force m each test has been used to calculate the flexural

strength of the samples. The flexural strength was calculated accordhg to Equation 4-5.

The test results are plotted verms presuessmg level. Fig. 5- 1 1 to Fig. 5- 13 show the

flexural strength of fibre prestressed glass-epoxy composites at three different curing

temperatures These data are also presented m Table 5- 1. As can be seen in the graphs, the

flexural strengths of the composites hcrease when fibre prestressing inmeases. This trend

continues up to a certain level in each senes and then a slight drop in the strength is

observed. The maximum strength, in step-heated samples, is located at 25 MPa fibre

prearessing. This point for the 110 OC and 150 O C cured samples is located at 40 MPa and

62 MPa prearessing resp ectively.

These results are very similar to what Jorge et al. (1990) reponed about the tende

strength of fibre prestressed glass-polyester composites. The ody clifference that exias

between these two pieces of work is they remarked that the tende arength was stabilized

after reaching the malrima, but in the present work, a slight drop in the properties cm be

observed after passing the maxima.

The standard deviation of data is show in Table 5- 1. It can be seen that the

dispersion of data is reduced around the best fibre prestressing level (BFPL) at which the

maximum strength is acquired. This trend is very obvious especially in the sep heated

glass-epoxy samples. In the two other groupe, made at Werent curing conditions,

although the trend is not clear, it still can be seen. This phenornenon was already reported

and explained by Mills et al. (1973). They, however, applied the stress to the fibres pnor

to the use of them in the composites while in this work the pretension was applied and - 3

mahtained on the fibres during the curing process. They explained that fibre prestressing

was able to reduce the fiequency of the low strmgth defects, so that the deviation of the

mechanical strength decreased.

** Cured @ 110 OC

O I O 20 30 40 50 60

Prestressing Level (MYa)

Fig. 5- 1 1 : Flexural Sirength VS. Prestressing Level for E glass-epoxy composites. Samples cured at 1 10 OC,

** Step heating

20 30

Prcstrcssing Lcvcl (hl Pri)

Fig. 5- 13: Flexural Strengtli VS. hestressing Level for E giass-epoxy coiiiposites. Step heating applied.

Group I: Step heated

Fibre Prestressing @Pa) Flexural Strength (MPa) Standard Deviation

Group II: Cured at 1 10 O C

Group Ill: Cured at 150 O C

Fibre Prestressing (AdPa)

O

Table 5- 1: Average flexural strength and standard deviations

No. of Tests

18

Fibre Prenressing (MPa) 1 No. of Tests Flexural Strength (MPa) 1 Standard Deviation 1

Flexural Strength @Pa)

5 2 0 . 8

Standard Deviation

4 2 . 6

Table 5-2 presents and compares the flexural strengths at the BFPL and the

flexural strengths of the un-prestressed samples. The strengths of the aep heated samples,

110 O C , and 150 O C have increased up to 33%, 27%, and 27% respectively. These

significant increases in the flexural strengths of the composites are brougbt about by

applying the BFPL on the fibres during the curing of the resin.

Flexural Strength of Un-

prestressed Samples (MPa)

Table 5-2: Flexural strength of un-prestressed sampfes compared to those at BFPL.

Step heated

Cured at 1 10 O C

Cured at 150 O C

It was explained earlier in this section how fibre prestressing helps to fabncate

stronger composites by making all the fibres cany the load simultaneously. Fuithemore,

fibre prestressing increases the strength of the composites by influencing the crack

propagation mechanism. When a sample is subjected to a bending force, the outer layer of

the composite d e n the greatest tende stress, so that cracks normdy a a n there. The

sample breaks when the crack gains enough energy to propagate. The state of forces at the

crack tip is very important to determine whether or not the crack starts to move through

the specimen. When the crack sans to open the fibres make bridges between the nvo

crack surfaces helping them to hold together. This is a well-known phenornenon in fibre

Maximum Flemal

Strength (M'a)

increase

(%)

501.5

521.3

462.7

670.5

663.5

59 1.2

33%

27%

27%

composites that increases the fiacnire toughness and mength of the composites. The

increase of the stress r e d t s m the rupture of the nbre bridges and the crack continues to

move on. Here, there is a basic difference between the prestressed and un-prestressed

samples. As already shown, in prestressed samples, there is a si_pificant amount of

compressive residual stress in the matrix. The compressive residual aress reduces the

tensile stress, created by the bending force, in the matrix. Therefore, more bending force is

required to provide the crack with enough energy to move. The increase of the fibre

prestressing results in the formation of more compressive residual stress in tlie matrix and

consequently more resistance againa the crack propagation provides higher flexural

strength in the composite.

In un-prestressed composites the situation is completely reversed. The teiisile

residual stress, which is caused by the sluinkage of the resin and tlie diEereuce of the

coefficients of thermal expansion of the fibres and mat* is added to the tensile stress

which is created due to bending. This increases the likelihood of the crack propagation iu

the composite. A more detailed discussion about the eEect of residual stress on the crack

propagation mechanimi can be found in reference [Atkins 19851.

The &op of the strength after the BFPL in each series can be anributed to the

fibre-matri, debonding. The increase of prestressing raises the residual shear aress at the

interface of the fibre-matrk. This, finally, results in debonding of the fibres and matrix and

reduces the overall strength of the composite. Thus, there is an optimum fibre prestressing

to obtain the maximum possible resistance to resist crack opening and before fibre-matrix

debonding reduces the effect.

It may be concluded that fibre prestressing replaces the tende rendual stress in the

matrix with a compressive stress. The compressive stress, therefore, resists the crack

opening mechanism in the composite and increases the flexural strength. The formation of

ever-increashg residual stress in the composite promotes the separation of the fibre fiom

the ma& and this at the hi& levels has a negative effect on the strength. These nvo

effects work against each other. Before reaching the BFPL, the firn effect is dominant, so

that the strength increases. Mer passing the BFPL, the second effect sans to take over,

therefore, the strength begins to decline.

5-3-2: Flexural Modulus:

Flexural moduli of the composites were calcuiated according to Equation 4-4 using

the dope of the linear part of the stress-deflection curve in each test. The results are

ploned as a fùnction of fibre prestressing in Figs 5- 14 to 5-16. Similar to the hdings for

flexural arengths, the flexural rnoduius values of the composites appear to increase with

fibre prestressing up to a certain level and decline beyond that level of prestressing. Table

5-3 shows the averages of the flexural moduius of the samples at each prestressing level.

The table aIso indicates the standard deviation of the tests. Unlike the flemiral stren-gth,

however, there is no obvious decrease in standard deviation around the BFPL. in Table 5-

4 the flexural moduli of the un-prestressed samples are compared to the flexural moduli at

the BFPL. The step heated samples exhibit 33% mcrease of the flexural modulus while

110 O C and 150 O C cured samples display 25% and 23% increase respectively.

* Step hcnting

20 30

Prestressing Level (MPa)

Fig. 5-16: Flextiral Modulus VS. Prestressing Level for E glass-epoxy coniposites. Step heating applied.

Group II: Cured nt 1 1 O O C

Group I: Step heated

Fibre Ptestressing (MPa) No. of Tests Flexural Modulus (GPa) Standard Deviation

Fibre Prestressing @Pa)

O

10

20

35

50 ;

Table 5-3: Flexural modulus and standard deviations.

No. of Tests

6

6

6

6

6

Group Ill: Cured at 150 O C

Fibre Prcstressing PlPa)

O

10

30

40

Flexural Modulus (GPa)

16.01

17.4 1

21.15

20.56

Standard Deviation

1.294

1.20 1

0.636 ,

1.054

No, of Tests

6

6

6

6

20.33 1.256

50

60

80

Flexural Modulus (GPa)

15.73

16.84

18.04

18.96

Standard Deviation

1 .263 l

1.197

0.749

1.178

6

6

6

20.0 1

18.94

18.18

0.934

1.122

0.490 I

The explanation, presented by Zhang et ai. (1992), can be used with some

modifications to justify the increase of the modulus of fibre prestressed composites. The)

asnuned that when the resin cures, it holds the fibres as they are stretched, so that after

removing the extemal load, some residual strain remains in the fibres. Thus the fibres are

under tension in the manufactured composites. The tende residual force in the fibres, F p

then, produces a component normal to the direction of the fibres. This force component

acts againa the bending force during the bendhg test (Fig. 5- 17). As a result, compared to

the un-prestressed specimen, more bending force is required to cause a certain amount of

deflection. Therefore, the flexural modulus appears to be higher. This explanation c m

rationalize the increment of the flexural modulus of the prearessed composites. However.

this point should be noted that ody a portion of the applied force remains in the fibres

after the process and not the whole tension as was discussed in Section 5- 1.

Flexural Modulus of Un-

prestressed Samples (GPa)

Table 5-1: Flexural modulus of un-prestressed samples compared to those at BFPL.

Maximum Flexural

Modulus (GPa)

Step heated

Cured at 110 O C

Cured at 150 O C

Increase

(%)

20.97

20.83

19.43

15.73 CVP

16.62

15.78

33%

25%

23%

Fig. 5- 17: VerticaI component of residuai force in the fibres (F, sine) works against the bending force, resulting in increase of flexural modulus. [After Zhmg 19931

5-43: impact Strength:

The results of impact tests are presented in Fig. 5- 18. As cm be seeo, the impact

arengtli of the prestressed composites increased when the fibre prestressing increased.

This continued up to 60 MPa fibre prestressing. The impact strength declined beyond this

point. This is very sirnilar to what was already observed for the flexural modulus and

arengh. Comparing the ma- impact strength obtained at 60 MPa prestressing to

that of un-prestressed samples, 33% increase can be observed.

Fig. 5- 19 to 5-22 show the broken samples after testing. The breakage patterns are

completely dinerent m the un-prestressed samples than those which were prestressed. The

un-prestressed samples have been d ~ d e d to either two or tluee pieces. Most of the

damage is in the middle of samples where the harnmer smick and the portions away nom

impact area are almon undamaged. These samples look like they have been shear

fiactured by the action of scissors. The fibres are broken and cut at the middle. Fibre pull

out can also be seen at the breaking points. (see Fig. 5- 19)

The prestressed samples, however, have a different appearance after fracture. in

these samples the damage area is not localized. A broken sample whicli was made at 40

MPa prestressing is show in Fig. 5-20. The sample is split into many pieces. The

thickness is fiactured into four main layers and there are some transverse spiits as weil. In

this sample ten such splits can be counted. Splitting by fracture results in the formation of

a large new surface area. According to the GdEths' theory, the formation of a iiew

surface requires the expenditure of energy. Therefore, splining consumes energy and it

increases the impact strength of the composites.

In section 5- 1, it was show that the fibre prestressing created sorne residual sliear

stresses in the rnatrix and at the fibre-matrix intefiace. The residual shear stresses were

shown to increase ünearly as a fiuiction of fibre prestressing. As was indicated, the residual

shear stresses are close to zero in the un-prestressed composites. These stresses, however,

increase to 950 Pa at 100 MPa fibre prestressing .

The residual stresses are the mai. reason for the splitting fracture mechanisim of

the composite. When a crack tip approaches a fibre, two possibilities cm be imagined as

shown in Fig. 5-23. First, the crack crosses the fibres and cuts them as weli as the matnx;

and second, the crack changes its direction and moves through the matrix parauel to the

fibres. The crack goes through the easiest way that needs less energy for M e r crack

growth. For the un-prestressed samples, as experiments show, the crack goes through the

libres and cuts them [see Fig. 5- 191. Therefore it can be concluded that cutting the fibres

is the easiea way for the crack to pass and it has a lesser propagation energy peak as

compared to the energy peak for the combined case of debonding and fibre cutting.

On the other hand, in the prestressed samples the longitudinal debonding fiacnire

is observed rather than only a transverse fracture. Thus it can be inferred that many cracks

which are created and distributed in the composite during fracture prefer to move through

the matrix along the fibres mstead of crosshg and cutting the fibres. This dEerence

bebveen the un-prestressed samples and the prestressed ones can be attributed to the

residual stresses at the fibre-matrix intefiace. These stresses make the inteface vulnerable

to the extemal loads and decrease the load canying ability of the interface. Therefore,

when the crack approaches the interface, fibre-matrix separation can occur at a lower

energy as compared to the energy needed for the cuttiug of the fibres. This causes the

crack to deviate fiom its route and it moves along the fibres rather than txying to cross

them. The SEM imaging also confirms this idea. Fig. 5-24 shows that how a crack bas

passed through the fibres in an unprestressed sample while the fibres are aill coated by the

matrk and no fibre-matrix separation is obsewed By cornpanson, Fig. 5-25 indicates

fiacture has created gaps between the fibres and the matrix in prearessed sample. The

bare fibres show the complete separation of the fibres and matrix and there is no sign of

breakage in the fibres.

More residual stresses at the intetface r e d t s in the easier path and the crack c m

be distniiuted in the composite and more splitting occurs. This creates more surface area

within the sample volume and increases the absotbed energy during the impact. However.

when the residual N e s e s at the interface increase more than a panicuiar level this

mechanism becomes easier to operate and absorbs less energy. The increase of residual

stresses at the fibre-matrix interface beyond this level r e d t s in low energy fibre-matrix

separation. The less energetic separation of the fibres Born the matm decreases the

absorbed energy and results in a lower impact strength. Therefore, although the splitting

fiactwe is also observed h 80 MPa and greater fibre prestressed samples, the impact

energy drops.

From this study, it appears that there are two fiacture mechanimis competing

against eacli other d u ~ g the impact test. At low fibre prestressing levels, the transverse

fracture has a lower bamer force as compared to that for debonding fiacture (see curves

A and B in Fig. 5-26) so that the transverse fiachire occurs. As fibre prestressing

increases, the debonding f?acture which leads to the formation of splits requires less

bamer force to aan, so that debonding hchire overcomes the transverse fiacture (see

curves A and C in Fig. 5-26). The debonding fiacture consumes more energy by creation

of more surface area within the sample volume. The increase of fibre prestressing beyond a

particular level causes the debonding fracture to occur at lower force. As a result,

although splits are stiU formed during the breakage, they consume less energy (see areas

under curves C and D in Fig. 5-26). T'us the impact strength deciines. For the glass fibre-

e p o q composites studied in these experiments, the bea fibre prestressing leveî, to obtain

the highest impact strength, is located at 60 ma. However, it is expected that this

optimum will be at Werent levels in other composite systems based on the constituent

materials and curing conditions.

Fig. 5-19: An un-prestressed broken sample after impact testing. Damaged zone can be seen in the rniddle.

Fig. 5-20: Premessed sample after breakage. 40 MPa fibre prestressing was applied. Splitting cm be seen.

F i g 5-21: Restressed sample after breakage. 60 MPa fibre prestressing was applied.

Fig. 5-22: A prestressed sample afbr impact testing. 80 MPa fibre prestressing was applied. Splitting and debondhg can be seen.

I Fibers - \

I

Crack

(b)

Fig 5-23: (a) Crack propagation in un-prestressed composite. Crack cuts the fibres to pass. (b) Crack propagation through interface and fibre breakage occur at the same tirne in a prestressed sample.

Fig. 5-23: SEM imaging Born un-prestressed broken sample. The crack has crossed the fibres. The fibres are covered by the polymer and no separation can be seen between fibres and matrix.

Fig. 5-25: SEM in~aging fiom a 10 MPa fibre prestressed sample. Fibre-itiatrix separation can be seen.

Traveling Distance of Cracks thiough composite

Fig. 5-26: Scheiiiatic diagraiil of required force for crack propagation.

5 5 : Effects of Processing Conditions on BFPL:

Since the best fibre prestressing level (BFPL), at which the m ~ u m mechanical

properties were gained, was very important from the view point of induanal applications,

the influences of the type of fibres and curing temperature were studied.

5-5- 1: Type of Fibre:

As explained in Chapter 4, carbon fibre-epoxy composites were made at two

dinerent curing temperature and dinerent fibre prestressing levels and then the bending

tests were performed on them Figs 5-27 to 5-30 show the results of the bending tests of

carbon-epoxy composites. Considering the fleniral modulus, the BFPL for the sep-heated

carbon-epoxy composites is around 50 MPa prestressing and for 150 O C cured sarnples is

around 115 MPa. These values for glass-epoxy composites are 30 MPa and 55 MPa

respectively. Comparing these resuits, it can be concluded that the BFPL's for the carboti-

ep0.y composites are located at higher fibre prestressing levels.

Carbon fibres are different fiom glass fibres in many aspects such as chemical

properties which results in different chemical bonding at the interface. However, the moa

sigdicant dinerence of these two types of fibres can be attributed to their aiffness. The

Young's modulus of the cirbon fibres is about 2.3 times more than that of glass fibres

(162 GPa and 70 GPa [Tao 1991, Lee 19671 respectbely), so that 2.2 times more stress

would be needed to bring about the same aram in the carbon fibres as in the glass fibres.

Therefore, as a general conclusion, it can be prsdicted that for the composites which

inciude a s e r fibres, the BFPL is located at higher prestressing levels.

5- 5-2: Curing Temperature:

The BFPL for the step-heated, 1 10 O C , and 150 O C cured glass-epoq composites

are located beween 20 to 30 MPa, 40 to 50 MPa, and 55 to 65 MPa prestressing levels

respectively. The BFPL for the carbon-epoxy composites is also located between 50 to 5 5

MPa and 60 to 1 15 MPa prestressing when the samples were aep heated and cured at 150

O C respectively. This cm be seen in Figs 5-3 1 to 5-34. In cases of both glass-epoxy and

carbon-epoxy composites, it is obvious that when the curing temperature increases, the

BFPL moves to higher prestressing levels. This can be explained by considering the

shrinkage of the polymer. In Section 5-2, it was shown that the increase of the curing

temperature increases the amount of the shrinkage of the epoxy resin. Wlien the polymer

shrinks. it provides some room for the a r e s to recoii, so that the residual strain in the

fibres is the fibres strain, created by fibre prestressing, minus the amount of the shrinkage

of the polymer. Therefore, when the curing temperature increases, the polymer shrinks

more and coosequently, more room is created for the fibres to recoil. This reduces the

residual main in the fibres and residual stress in the composite. Thus, to reach the same

level of the residual stress in the composite, more prestressing mua be appüed on the

fibres. As a result, the BFPL moves to higher prestressing levels.

The tests show lower strength and modulus for the samples cured at 150 O C

comparing those cured at 110 O C and the step-heated samples. As mentioned in Section 4-

4, the heat resulting tom the reaction of the epoxy resh with the hardener increased the

temperature of the polymer above the temperature that was fixed for the oven for a short

period of t h e at the begmniag of the heating. This resulted in smoking of the sample

cured at 150 OC. Smoking mdicated that the polymer has been insignificantly degraded.

The lower measured strength and modulus for the samples cured at 130 O C can be

attriiuted to the relative degradation of the polymer.

6- Conclusions & Contributions

6-1: Mechanical Properties [Motahhari 19961:

Fibre prestressing during the curing process brings about a significant increase in the

flexural strength and flexural modulus of glass-epoxy and carbon-epoxy composites. In

the present work the strength and modulus were raised as much as 33% for glass-

epoxy composites and 17% and 33% for carbon-epoxy composites respectively.

Fibre prearessing during the curing process increases the impact strength of glass-

epoxy composites. In these experiments up to 33% increase in impact strength was

mtasured as compared to the un-prestressed composites.

Beyoud a certain prestresshg level fibre prestressing decreases the mechanical

properties. A mechanism whereby this takes place has beeu proposed.

The bem fibre prestressing level (BFPL), at which the highest mechanical propenies

are obtained, is a fùnction of the curing temperature, fibre Young's Modulus, c u ~ g

shrinkage and the thermal shrinkage value of resin. Increasing the curing temperature,

resin shrinkage or fibre Young's Modulus moves the BFPL to the higher values.

The standard deviation of data decreases around the BFPL. In other words, the

composites can be manufactured with more reproducibility when the optimum level of

prearessing is camed by the fibres.

6-2: Shrinkage of Polymer (Motabhari 19971 :

A new method has been introduced to measure the dimensional changes of polymenc

resin during the curing process.

7) The total shrsikage of epoxy r e h during the curing process is cornmensurate with the

curing temperature and heatmg rate. A higher curing temperature and faaer rate of

heating cause the resin to rhrink more. The experiments show that the resin shrinkage

mcreases three times more when the temperature is raised quickly to 150 O C rather

than behg raised aep wise to the same temperature.

8) Shrinkage due to reaction and thermal expansion due to heating occur at the same time

and they compensate each other.

9) The m*um shrinkage occurred in the resin at 93 O C when the sep-heatiiig process

was used. 93 O C was one ofthe aeps on the way to 150 O C .

M)During the step-heating process, there are some penods of time when the resin has

expanded comparing to the startmg point. This phenornenon is not seen for those

samples which were heated up rapidly and continuously (at an average rate of 8

OC/min) to the final curing temperature.

6-3: Contribution of Polymer Shrinkage to Residual Stresses [Motahhari 19971:

11)The presence of the fibres in the resin bas a significant influence on the longitudinal

shrinkage of the resin. The arong bonding between the fibres aud matrix does not

allow the resin to shrink dong the fibres' direction. This suggeas that the resin shrinlis

perpendicular to the fibres' direction in unidirectionai composites.

12) Measurement of the deflection of the composite-polymer bar indicates that only 3.3%

of the total shrinkage of the polymer, mcludmg both chemical çhrinkage and thermal

contraction, has contnbuted to the creation of residual stresses at the interface of the

two phases. In other words, only 3.3% of the polymer shrinkage has remained as the

residual strain m the polymer.

1 3 ) Calculation of the p olymer ' s thermal expansion main b y assigning the stress- fiee

temperature in the composite-polymer bar and the poiymer's residual strain by the

meanirement of the deflection in the bar are in good agreement and they can be used

to vaiidate the experiments.

14) During the subsequent reheating of the composite-polymer bar the curvature is seen to

decrease up to a temperature of 88 O C when the bar is flat. This suggens that, contrary

to fmdings in the literature and in the analytical modehg [Oakeshott 1994, White

1993, Jayaraman 1993, Uemura 1979, Novak 19701, the stress-fiee temperature is

below the curing temperature.

6-4: Residunl Stresses [Motahhari 1997) :

15) The micro-residual stresses in glass fibre-epoxy composites have been evaluated when

the fibres are under some hown level of pre-tension during the curing process. n i e

force-strain cuve for the fibres before, during and after curing shows that some part

of the nbres' $train is not recovered. The un-recovered strain is used to assess the

residual stresses iu the composite.

16) The residual stresses in fibre prestressed composites are a linear fùoction of applied

fibre prestress d u ~ g cure throughout the prestressing range investigated in this wok.

17) The ratio of the residual strain in the fibres to the total arain due to prestressing is a

constant value and it does not depend on fibres' pre-tension.

18) The matriv is under compression and the fibres under tension in fibre prestressed glass-

epoxy composites.

6-5: Justification of Resuits:

19)The fibre prestresshg cm hcrease the flexural strength through two mechanimis.

First, fibre prestressing places the matrix under compressive residual forces. These

forces retard the crack opening mechanism and cancel out some pan of shear forces at

the interface and tende forces in the matrk produced during, for example, bending.

Secondly, the non-prestressed specimens have the fibres in a non-taut aate so that

initial loading serves to straighten and load them, resulting in deformation of the

matriu. When the fibres are stretched, however, before adding the resin and cunng it

around the nraight, taut fibres, the subsequent composite has fibres which are able to

contribute to carrying the load instantaneously and simultaneously. This results in

obtaining higher strength.

2 0)The flexural modulus of prestressed composites increases because the residual stress in

the fibres creates a compooent which opposes îhe bending force, so that more force is

needed to form the same deflection that was observed in the non-prestressed sample.

2 1 ) The fractured prestressed samples are iongitudinaly split dwing the impact test,

whereas the un-prestressed samples do not show such a breakage mode. Splitting

causes the formation of a large new area and consumes energy. This results in an

increase of the impact strength.

22)There is a combination of transverse fiacture and debonding fracture in the samples. At

low fibre prestressing levels, the transverse fiachire mechanism is more prevalent. As

the fibre prestresshg increases, the debonding fkacture mechanism becomes more

prevalent than the transverse fiachire. This results in the formation of a new large

surface area within the sample volume and mcreases the consumed energy during the

impact.

23)The debonhg breakage mode is promoted by the residual shear stresses in the matrix.

These stresses are caused by fibre prestressing and act in two ways. Fira they increase

the impact strength by deviating the propagating cracks along the fibres and by the

increasing of the formation of new d a c e areas within the volume of the sample.

Secondly, these residual stresses decrease the impact arength by reducing the ability of

the interface to resist shear debonding and by promoting the relatively easier separation

of the a r e s fkom the rnatrix. For the composites used in the cument experiments the

first mechanism is dominant up to 60 MPa fibre prestressing. Beyond ihis level, the

second rnechanism dominates the fira one and the impact strength drops. Therefore a

maximum point m impact strength of the teaed composites was observed in this syaem

under study at 60 MPa fibre prestressing motahhari 19981.

6-6: Contributions:

A new method is introduced to measure the micro-residual stresses in fibre prestressed

composites. This method is based on the monitoring the arain of the fibres before,

during, and after the curing process. This provides an assessrnent of the residual arain

in the fibres. The residual stresses cm be calculated f?om a knowledge of the residual

main. This is done by canying out some simple calculations, which have been

presented in this thesis.

A new method is presented to measure the shrinkage of the polymeric r e h . This

method makes possible the measurement of both chemical rhrinkage and thermal

rhrinkage at the same Ume. This measurement is based on the tracking of the relative

movement of two markers, which were implanted in the polymer and viewed under an

optical microscope.

The effects of processing conditions and constituent materials on flexural and impact

properties of composites were detemhed when prestressing was applied on the fibres

in polymer ma& composites.

It is shown that the stress-fiee temperature in polymer matrix composites is lower than

the curing temperanire.

A mechanism of fiacture during impact testing is presented which iiiustrates the role of

crack path deflection on the impact strength.

6-7: Suggestions for Future Work:

A study of the effect of the initial cooling rate fiom the curing temperature on the

residual stresses and on the stress-fiee temperature by meanirement of the deflection of

the polymer-composite bar.

Study of the geometnc characteristics of fibre on the amount of residual stresses m

composites. For this reason, giass fibre with the same chemical and mechanical

properties but different diameters should be used to measure the residual stresses in the

composites. The ratio of the total d c e area of the fibres in the composite to the

volume of fibres can influence the residual stresses in fibre prestressed composites.

Another way to perform this, is usbg the fibres wiih the cross section other than

circdar shape.

Deteminhg if the BFPL always occurs at the same level of residual stress in the

composites, made of the same constituent matenals regardless of the curing

temperature, cooling rate, etc.

Smdy of the effect of stress relaxation at room temperature in the composites for long

time periods and investigate ifthis can change the BFPL as a h c t i o n of time.

Investigate the shrinkage of the polymer perpendicular to the fibres' direction and

comparing that to the shrinkage of the polymer along the fibres in the composite.

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Appendh 1: Differential Equations for Barn-Columm (Popov 1969):

Consider an element isolated f?om beam column as s h o w in Fig. A-1. This

element is shown in its deflected position. The deflections considered in this treatment, are

smaii in relation to the span of the beam-column, which permits the following

approximations:

On this basis, the two equilibrium equations are:

IF , .=o?+, ~ d x - v + ( Y + ~ Y ) = o

The £ira one of these equations yields:

The second, on neglecting the iafinitesllnals of higher order, &es:

Therefore, for beam-columns, the shear Y, in addition to depending on the rate of change

in the moment M as in beams, also depends on the magnitude of the axial force and the

dope of the elastic curve. The latter term is the component of P along the inclined sections

s h o w in Fig. A-1.

in this development for the curvanire, the usual relation for the bending theory

bv/&' = M/(jF:r) can be employed. On subaituting equation A-2 into equation A- 1 and

rnakmg use of the above relation, one obtains two aitemative Werential equations for

beam-columns:

where for simpiicity EI is assumed to be constant and A-' = P/@l'). The homogeneous

solution of equation A-4 and several derivatives are Listed below:

v = CI siri /tu + C2 COS AX + C3 x + C4 (A-5)

v '=c , ÂcmÂx-C2Âsir~/Zx +C3 (A-6)

vn=-cl A ~ S ~ ~ ~ R ~ - C ~ A ~ C O S J . Y 04-71

v" = -CI /ZJ cm ~r + C? Â3 sin ~r (A-8)

These relations are needed in some problems to express the boundûiy conditions for

evaluating the constants Cl, C2, C,, and C4.

Now consider a slender bar of constant El which is simultaneously subjected to the

end moments Mo and an axial force P as shown in Fig. A-2. Within the span there is no

transverse load. Therefore, the right-hand term of equation A-4 is zero, and the

homogeneous solution of this equation @en by equation A-5 is the complete solution.

The boundary conditions are:

v(9) = O , va) = 0, M(0) = -Mo , and M o = -Mo

Since M = H v " , with the aid of equations A 4 and A-7 these conditions yield:

v(0) = c2 + C4 = O

v(L) =CI s inRL+C2 ccasRL+CJL+C4=0

M(o) = -c2 ~m-' = -Mo

M o = -C, E I A ~ sin AL - C2 E I ~ cos AL = -MO

Solvïng these four equations simdtaneously:

Mo C, = -c, = - and CJ=O P

Therefore, the equation of the elastic cuve is:

The maximum deflection occurs at x = L/2. After some simplifications, it is found to be:

Mo s i n 2 A L / 2 AL# vm, = -4 Mo + cos- - 1) = -(sec- - 1)

P cosÂL/2 2 P 2

The largest bending moment also occun at x = U2. Its absolute maximum is

W, Mm= = 1-Mo - Pv-l= Mo sec-

2

(A- 1 O)

(A- I l )

Fig A-1: An element ofa beam column.

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