FIBRE PRESTRESSED COMPOSITES...fibre prestressed composites were a linear, increasing fùnction of...
Transcript of FIBRE PRESTRESSED COMPOSITES...fibre prestressed composites were a linear, increasing fùnction of...
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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