kinetic and thermo-viscoelastic characterisation of the epoxy adhesive in glare
TRANSCRIPT
Composite Structures 124 (2015) 19–28
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Composite Structures
journal homepage: www.elsevier .com/locate /compstruct
Kinetic and thermo-viscoelastic characterisation of the epoxy adhesivein GLARE
http://dx.doi.org/10.1016/j.compstruct.2014.12.0690263-8223/� 2015 Elsevier Ltd. All rights reserved.
⇑ Corresponding author. Tel.: +31 15 2788673; fax: +31 15 2781151.E-mail addresses: [email protected], [email protected]
(M. Abouhamzeh).
M. Abouhamzeh a,⇑, J. Sinke a, K.M.B. Jansen b, R. Benedictus a
a Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlandsb Faculty of Industrial Design Engineering, Delft University of Technology, Landbergstraat 15, 2628 CE Delft, The Netherlands
a r t i c l e i n f o
Article history:Available online 7 January 2015
Keywords:FM-94 epoxyTemperature dependentViscoelasticTMADMA
a b s t r a c t
Epoxy FM-94 has a temperature dependent and viscoelastic response which is used for metal bondingapplications and composite laminates like GLARE. A Dynamic Mechanical Analysis is performed on theepoxy FM-94 adhesive. A master curve is produced using the time–temperature superposition principleand is modelled as a Prony series. In addition, the cure kinetics of the adhesive are measured using DSC(Differential Scanning Calorimetry) and fitted to a standard kinetic model. Both the kinetics and thethermo-viscoelastic models can be used in subsequent research to predict the cure induced and residualthermal stresses due to the composite processing steps.
� 2015 Elsevier Ltd. All rights reserved.
1. Introduction
Glass Aluminium Reinforced Epoxy (GLARE), is the most com-mon type of Fibre Metal Laminates (FMLs). Fuselage panels andleading edges of tail planes are among structural parts of aircraftin which FMLs have found applications. The most recent aerospaceapplication of GLARE is the fuselage of the Airbus A-380 in whichsingle and double curved GLARE panels are used. Constituents ofGLARE are adhered together using epoxy FM-94 that shows prop-erties that change with time and temperature. Although, theunderstanding and applications of FMLs are further developed byresearchers [1–5], the effects of the curing process of epoxyFM-94 on residual stresses and the final geometry are not studiedin detail yet. The cure process results not only in deviations fromdesigned dimensions which hamper the assembly but also inresidual stresses by which the load capacity, fatigue strength, dam-age tolerance and residual strength of the material decreases.Therefore this research, started at the Faculty of AerospaceEngineering at TU Delft (Department of Aerospace Structures andMaterials), studies the development of geometric deviations andresidual stresses during the manufacture of GLARE. As a first step,thermoelastic modelling was used considering only thermalcooling from the cure temperature to ambient conditions [6,7].As a next step, the residual stress development during curing of
GLARE as well as the viscoelastic behaviour after cure needs tobe determined.
The curing process of GLARE products consists of three stages:heating to the cure temperature, curing isothermally and cool-down to ambient temperature. Residual stresses and distortionsoccurring in GLARE panels have been studied with simple model-ling approaches in two previous papers [7,8]. In order to modelthe curing process of GLARE and predict the residual stresses, thedevelopment of cure of the epoxy should be characterised. Here,analysis of cure kinetics is performed on epoxy FM-94. The changein the degree of cure is determined within the temperature profileof the cure cycle which can be used later for predicting the residualstresses developed during the cure process.
The determination of thermo-viscoelastic response of fullycured composites is nowadays a standard procedure, e.g. [9,10].The determination of the change in viscoelastic behaviour duringcure is possible but much more challenging [11–15]. The needfor consideration of the viscoelasticity during cure of epoxyFM-94 is also investigated in this paper.
The thermo-viscoelastic response of the epoxy FM-94 presentedhere, can be used for residual stress analysis of laminates using thistype of resin or adhesive during cure and also other thermal oraging environments.
2. Thermo-dynamic analysis
For the purpose of predicting the residual stresses after cure ofGLARE panels, the structural behaviour of the constituents needs tobe characterised and modelled during the cure cycle. In the
Table 1Cure kinetic parameters for epoxy FM-94.
K0 [1/s] 3.52E+06EA [J/mole] 6.75E+04m [–] 0.558n [–] 2.508Htot [J/g] 134.9
20 M. Abouhamzeh et al. / Composite Structures 124 (2015) 19–28
temperature range of curing GLARE (up to 120 �C), the mechanicaland thermal properties of aluminium and glass fibres only changeby a small amount and the data for it is available elsewhere [16].However, the mechanical and thermal properties of the epoxyadhesive change with time (stress relaxation), temperature anddegree of cure. This includes both the isothermal part of the curecycle in which the epoxy cures and the cool-down part by whichthe cured epoxy experiences a large thermal gradient. Here, inorder to investigate the thermal expansion and the glass-transitiontemperature (Tg) of epoxy FM-94, Thermo-Mechanical Analysis(TMA) is performed. The thermo-mechanical properties are deter-mined using Dynamic-Mechanical Analysis (DMA).
2.1. Material system
FM-94 adhesive is a modified epoxy film adhesive designed forbonding metallic and composite structures [17]. FM 94 adhesiveoffers not only high temperature performance (maximum servicetemperature of 104 �C) but also good toughness and moistureresistance. As an example of this latter ability, it is used to bondto Nomex honeycomb with retention of shear properties afterpre- and post-bond humidity exposure. Within composite andmetal bonding applications, the FM-94 adhesive exhibits superiorelongation and shear strength properties. As in GLARE production,this epoxy type is used in the bonding of aluminium layers rein-forced with glass fibres to bring higher fatigue, residual strengthand damage tolerance compared to metal or full composite parts.On the other hand, due to the need for large scale laminates, metallayer overlap using FM-94 adhesive films are used to overcome thelimited width of the metal sheets. The controlled flow characteris-tics allow for its use in co-cured applications as well as in bondingpre-cured structures. Different types of reinforcing doublers orstringers are also bonded to the laminate using FM-94 adhesive.
2.2. Kinetic characterisation of the epoxy adhesive during cure ofGLARE
The cure kinetics describes the amount of reaction as a functionof time and temperature. Differential Scanning Calorimetry (DSC)is used to measure the heat flow into and from the sample. Theonset and completion of cure, degree of cure (DOC) and glass-tran-sition temperature (Tg), all can be obtained from DSC. Furthermore,cure dependent material properties can be derived using DMA dur-ing cure of pure epoxy or prepreg in a later stage of this researchwith the purpose of calculating the residual stresses during cure,considering the effects of cure shrinkage and evolution of stiffness.
2.2.1. DSC measurementsThe heat flow is the internal heat, H, generated per unit mass
and per unit of time during the cross-link reaction and is repre-sented as:
dHdt¼ Htot
dadt
ð1Þ
Htot is the total heat of reaction after complete cure. Total heat ofreaction and the cure rate can be determined using iso-conversionDSC measurements in which the sample is heated with a constantheat rate and the heat energy input to the sample is measuredversus the cure time.
In order to calculate the degree of cure for any temperature his-tory, four DSC measurements are performed with heating rates of5, 6 10 and 15 �C/min. Cure rates are measured and fitted to theKamal–Sourour reaction rate equation [18]:
dadt¼ k0e �EA=RTð Þamð1� aÞn ð2Þ
R is the universal gas constant and T is the temperature in Kelvin. EA
is the activation energy, k0 is a coefficient and m and n are twoconstants which are listed in Table 1 after the fitting procedure.
The degree of cure at any time t is calculated from integration ofthe instantaneous cure rate as:
aðtÞ ¼Z t
0
dadt
dt ð3Þ
By using the kinetic model, Eq. (2) and the parameters of Table 1,the degree of cure can be predicted for isothermal cure history.Fig. 1 shows a few examples. The standard temperature to cureGLARE is 121 �C.
In order to simulate the cure process during the heating part ofthe cure cycle of GLARE, a calculation is done for a constant heatingrate of 2 �C/min as shown in Fig. 2. A complete cure process for atypical cure cycle of GLARE is shown in Fig. 3.
It can be seen that the adhesive starts to cure during heatingjust before the isothermal part. The temperature change duringthis level of cure influences the temperature-dependent propertiesof the polymer like thermal expansion coefficient and especiallythe viscoelastic response (stress relaxation). However, the degreeof cure at the end of heating is about 0.24 (24%) which is wellbefore the epoxy gelation which is usually above 0.4. This meansthat the heating part of the cure cycle does not contribute to theresidual stress development and does not need to be included inthe structural modelling. This is due to the fact that the epoxycan only sustain stresses after gelation.
2.3. Thermo-Mechanical Analysis (TMA)
Thermo-Mechanical Analysis measures the change in thesample length as a function of temperature or time. In TMA, theposition of the instrument probe is measured. TMA can be per-formed under a small static load with different sample shapesand configurations. It is commonly used for the determination ofthe coefficient of thermal expansion and the glass transition tem-perature of the polymeric material [19]. TMA is performed oncured epoxy FM-94 since the coefficient of thermal expansion isneeded at fully cured state to predict the cooling stresses.
2.3.1. Specimens for TMAPure FM-94 epoxy layers have a thickness of 0.1 mm and were
stacked together to make a plate of 4 mm thickness. After prepar-ing for the vacuum bag, it was put in a special mould preventingthe adhesive from squeezing out during cure. The epoxy was curedin the autoclave according to the standard cure cycle used forGLARE (see Fig. 3) at a temperature of 120 �C and a pressure of6 bar. Specimens were cut out from the cured epoxy with dimen-sions 4 � 3 � 3 mm and tested in a Pyris Diamond Thermo-Mechanical Analyser, Perkin Elmer Instruments.
2.3.2. TMA resultsThe results of the TMA measurement are shown in Fig. 4. The
slope of the curve is equal to the Coefficient of Thermal Expansion(CTE). The two slopes seen in Fig. 4, represent the CTE in the solidand rubbery states which are about 110 and 360 lm=m �C,respectively. The slope change occurs at the glass-transition
0 50 100 150 200 250 300 3500
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cure time [min]
Deg
ree
of c
ure
[-]
Isothermal cure at different temperatures
60
80
100
121
Fig. 1. Predicted cure development of FM-94 for different isothermal temperatures.
0 20 40 60 80 100 120 140 160 180 2000
100
200
300
400
500
Tem
pera
ture
[° C
]
Cure time [min]0 20 40 60 80 100 120 140 160 180 200
0
0.2
0.4
0.6
0.8
1
Deg
ree
of c
ure
[-]
TemperatureDegree of cure
Fig. 2. Cure development within constant heating rate of 2 �C/min.
M. Abouhamzeh et al. / Composite Structures 124 (2015) 19–28 21
temperature (Tg) of the material. In cross-linked polymers likeepoxy thermosets, the glass transition is influenced by thecrosslinking during curing and polymerisation. Therefore, the Tg
develops during cure, as a function of degree of cure andapproaches its final value after complete curing (see e.g. [14]).The TMA measurement was done on a fully cured sample, whichyielded a Tg of about 92 �C.
2.4. Dynamic Mechanical Analysis (DMA)
Polymers are viscoelastic materials since their properties aredependent on time. Viscoelastic materials undergo creep and stressrelaxation. Dynamic Mechanical Analysis (DMA) involves applyinga small sinusoidal strain (stress) to a sample and measuring theresulting stress (strain) response [19,20]. Consequently, the
0 20 40 60 80 100 120 150 200 25020
30
40
50
60
70
80
90
100
110
120125
Tem
pera
ture
[ ° C
]
Cure time [min]0 50 100 150 200 250
0
0.2
0.4
0.6
0.8
1
Deg
ree
of c
ure
[-]
TemperatureDegree of cure
Fig. 3. Temperature and conversion during the cure cycle of GLARE.
Fig. 4. TMA result for epoxy FM-94.
22 M. Abouhamzeh et al. / Composite Structures 124 (2015) 19–28
material properties are determined as a function of temperature,time or frequency. The inputs to the analysis are the amplitudesof the stress and strain waves together with their phase lag. Foran elastic solid, the phase lag (d) is zero and for a purely viscous(ideal) liquid, it is equal to 90�, whereas a viscoelastic materialhas a phase lag in between those two limiting cases. In this study,we chose to characterise the viscoelastic properties of the epoxyresin using the DMA technique and will use the viscoelastic Pronyparameters to predict the time dependent stress–strain behaviour(see Section 2.4.4).
In Dynamic Mechanical Analysis, the sinusoidal deformationand stresses are commonly represented in complex notation. The
complex modulus is the ratio between the complex stress andstrain and is given by:
E� ¼ r0eiðxtþdÞ
e0eixt¼ r0
e0cos dð Þ þ i � sin dð Þð Þ ¼ E0 þ iE00 ð4Þ
The fundamental parameters are the storage and loss moduli (E0
and E00) and the ratio of the two, tan d = E00/E0. Note that in Eq. (4),notations are used for tensile response but the same terminologycan be used in case of shear loading (i.e. G⁄ instead of E⁄).
Recalling from theory of viscoelasticity, the behaviour of visco-elastic materials is characterised with time dependent materialfunctions and therefore, the stress becomes a function of strain
40 60 80 100 120 140 160 18010-1
100
101
102
103
104
Temperature [° C]
Log
E' &
log
E" [
MP
a]
(a)
E'
E"
T=100.4 °C
T=104.4 °C
40 60 80 100 120 140 160 1800
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Temperature [° C]
Tan
δ [-]
(b)
T=116.4 °C
Fig. 5. DMA results from temperature sweep at frequency 1 Hz-(a) Storage and loss moduli (b) tan d.
M. Abouhamzeh et al. / Composite Structures 124 (2015) 19–28 23
and will depend on the strain history rather than strain or rate ofstrain [21].
If there is no stress or strain before time t = 0, the constitutiveequation for linear viscoelastic response of the material in the timedomain can be written as:
r tð Þ ¼Z t
0Ckl
ij ðT; t � sÞ @�kl
@sds ð5Þ
where Cklij ðT; tÞ is the general relaxation stiffness matrix component
dependent on time t and temperature T.Since the polymer is cured at a higher temperature than its
glass transition and cools down to ambient temperature, stressrelaxation is relevant to be considered specially around theglass transition temperature. As discussed, viscoelasticity can be
neglected during cure. However, after complete cure, besideschange of properties with temperature, stress relaxation occursduring cool-down. Therefore, the temperature-dependent visco-elastic properties of epoxy FM-94 should be determined.
It is known that for an isotropic material, the shear and bulkmodulus should be specified in order to characterise the materialresponse. However, volumetric relaxation is often negligible formany polymers which means that the bulk modulus of the poly-mer is almost independent of time and exhibits no relaxation. Asa result, only the deviatoric relaxation modulus will define thematerial viscoelastic behaviour and the volumetric response isassumed to be elastic, although it can be temperature dependent[14]. In order to find the relaxation stiffness dependent on timeand temperature during cooling of the epoxy adhesive, tensile
Fig. 6. Storage modulus (a) and tan d (b) data from tensile DMA (temperature–frequency sweep).
24 M. Abouhamzeh et al. / Composite Structures 124 (2015) 19–28
DMA is carried out in several frequencies and temperature. Conse-quently, the thermo-viscoelastic response of the material can bemeasured within a frequency-temperature sweep. The relaxationmodulus can be used as the input of the material modellingsubroutines in finite element packages like Ansys and Abaqus.
2.4.1. Specimens and experimental details for DMA measurementsThe DMA tests are performed using a DMA Q800 Dynamic
Mechanical Analyser manufactured by TA Instruments. The epoxy
FM-94 is cured with the same cure cycle as shown in Fig. 3. Sam-ples of 40 � 6.3 � 1 mm dimensions were prepared by CNCmachining. The testing is done in tensile mode.
The elongation properties of the material are studied as a func-tion of temperature (with a constant heat rate of 1.0 �C/min). Thespecimen was exposed to a sinusoidal strain with frequencies:0.3, 1.0, 3.2, 10.0, 30.0 Hz. The temperature ranges from 37 to174 �C and at each temperature step, the frequency (time) depen-dent response of the specimen is obtained.
40 50 60 70 80 90 100 110 120-25
-20
-15
-10
-5
0
Temperature [° C]
Shi
ft fa
ctor
, log
aT [-
]
experimental valuesfitted values
Fig. 7. Shift factor for producing the mastercurve within time–temperature superposition with Tref = 120.0 �C.
100 1010 1020
102
103
Master curve
log wred
log
E' [
MP
a]
Fig. 8. Mastercurve produced after time–temperature superposition withTref = 120.0 �C.
M. Abouhamzeh et al. / Composite Structures 124 (2015) 19–28 25
2.4.2. DMA results-temperature dependencyFirst, the response of the material is studied from 37 to 174 �C at
a frequency of 1 Hz, as the most frequently used one in the detec-tion of transitions.
The storage and loss moduli and also tan d of the epoxy materialare shown in Fig. 6 as a function of temperature. A drop of the stor-age modulus can be observed near the glass transition temperatureof the material. From this figure, the glass-plateau is found to be:
Eglass MPa½ � ¼ 2690� 17:2T �C½ � for T < 80 �C ð6Þ
Fig. 5 shows that the epoxy has a glassy modulus of 2.0 GPawhich decreases with increasing temperature. The glass transitionranges from about 100–120 �C, as can be seen from the figures.During this transition, both E0 and E00 rapidly decrease [19]. For con-stant-frequency tests on amorphous polymers (like epoxies), theglass transition can be defined as the temperature at which the1 Hz tan d curve has its maximum value. This value, fromFig. 6(b) is at 116 �C which may be called Ttan d
g . This value is muchhigher than that found previously by TMA which can be explainedby the fact that the glass transition is a kinetic phenomenon and isstrongly affected by the experimental time scale (frequency) andthe measurement method. The maximum of E00 is found to be104 �C which we call it TE00
g . The determination of Tg should bebased on practical considerations. FM-94 is a network polymerwhich is used in structural applications like composite laminatesor as adhesives in bonding of panels made of FMLs or sandwichstructures. In all of these applications, the structural integrity isthe primary function of the adhesive. Accordingly, the point whereE0 begins to drop from its glassy state, is a sign of the drop in thestructural integrity of the adhesive and therefore is a good wayof assigning the maximum temperature of use. This can be identi-fied by the onset point, defined by the intersection of the glassystate curve and the transition region curve (Fig. 5). Therefore, themaximum temperature of use is found to be around 100 �C andin this paper, this will be referred to as the Tuse
max. This value iscomparable to the Tg value of 92 �C already found from TMA.
2.4.3. DMA results-time and temperature dependencyHere, the time–temperature response of the material is studied
which is needed to obtain a thermo-viscoelastic model of thepolymer.
10-10
10-5
100
105
1010
1015
1020
1025
101
102
103
104
log ωred
[rad/s]
Log
E′-s
tora
ge m
odul
us[M
Pa]
experimental valuesshifted values
Fig. 9. Shifted modulus versus reduced radial frequency from DMA.
Table 2Prony series coefficients.
sn [s] En [MPa] sn [s] En [MPa]
1.00E�24 93.6 1.00E�08 90.31.00E�23 25.9 1.00E�07 107.11.00E�22 41.9 1.00E�06 149.51.00E�21 43.3 1.00E�05 209.11.00E�20 35.7 1.00E�04 269.21.00E�19 41.1 1.00E�03 237.31.00E�18 40.9 1.00E�02 138.21.00E�17 43.2 1.00E�01 61.51.00E�16 46.3 1.00E+00 24.11.00E�15 49 1.00E+01 9.51.00E�14 50.4 1.00E+02 41.00E�13 57.4 1.00E+03 2.81.00E�12 57.1 1.00E+04 1.71.00E�11 64.9 1.00E+05 1.11.00E�10 70.1 1.00E+06 0.91.00E�09 78.8 1.00E+07 0
10-10 100 1010 1020 10300
0.1
0.2
0.3
0.4
0.5
0.6
0.7
log ωred [rad/s]
δ-ta
n de
lta [-
]
experimental valuesshifted values
Fig. 10. Tan d versus reduced radial frequency from DMA.
26 M. Abouhamzeh et al. / Composite Structures 124 (2015) 19–28
Results are shown in Fig. 6, for the storage modulus and tan dversus temperature.
2.4.4. Time–temperature superposition (TTS)By application of the time–temperature superposition (TTS)
principle [19] to the data, a mastercurve can be obtained fromwhich the frequency response of the material is extractable for awide range of temperatures. TTS is a curve fitting procedurefrom multiple frequency measurements taken at a series oftemperatures.
According to the TTS principle, the relaxation stiffness in Eq. (2)can be written as:
EðTðtÞ; tÞ ¼ EðT0; tredÞ
tred ¼t
aTðTðtÞÞð7Þ
Or in the frequency domain, where we have complex dynamicmoduli:
E0ðTðxÞ;xÞ ¼ E0ðT0;xredÞE00 T xð Þ;xð Þ ¼ E00 T0;xredð Þxred ¼ x � aTðT tð ÞÞ
ð8Þ
In the above equations, T0 is the reference temperature and aT isthe time–temperature shift factor. tred and xred stand for reducedtime and frequency, respectively.
Fig. 7 shows the shift factors versus temperature. The shift fac-tor values are fitted to the Williams–Landel–Ferry equation:
logðaTÞ ¼C1ðT � Tref ÞC2 þ T � Tref
ð9Þ
The reference temperature is Tref = 120.0 �C and a nonlinear fit isapplied to get a functions with constant values of C1 = 29.4,C2 = 185.6 for temperatures up to 120.0 �C.
If the time (frequency) in the raw data in Fig. 6 is shifted with avalue of aT, a master curve is produced that covers all the temper-atures. The master curve is obtained by superimposing the rawdata at different temperatures to a selected reference temperature,(120.0 �C in this case). Note that after shifting, the reduced fre-quency values are used in the mastercurve (Fig. 8).
10-20 10-15 10-10 10-5 100 105101
102
103
104
log time [s]
Log
E [M
Pa]
Fig. 11. E-modulus versus time, as calculated from Eq. (11).
M. Abouhamzeh et al. / Composite Structures 124 (2015) 19–28 27
The storage and loss moduli can be fitted to a Prony seriesdescribing the generalised Maxwell model in the frequencydomain as follows:
E0 xð Þ ¼ E1 þXm
1
Enx2s2n
1þx2s2n; E00 xð Þ ¼
Xm
1
Enxsn
1þx2s2n
ð10Þ
where m is the number of Maxwell elements used in the approxi-mation and E1 is the modulus at infinite frequency, i.e. rubberymodulus equal to ER = 21.2 MPa from Fig. 9. The 32 terms of theProny series are listed in Table 2. The shifted modulus together withthe approximation made by the fitted Prony series are shown inFig. 9.
From the comparison of the shifted data with the predictionsby the Prony series, it can be found that the fitting is accurateenough to be used in further material modelling (see Fig. 10).To have the time dependent modulus, Eq. (11) can be used toget Fig. 11 which can be utilised as the viscoelastic response ofthe polymer.
E tð Þ ¼ E1 þXm
1
Ene�t=sn ð11Þ
where E1 is the relaxation modulus at t =1 (rubbery modulus) andm is the number of Maxwell elements. The initial modulus can befound to be E0 = 2070.0 MPa and the rubbery modulus equal toER = 21.2 MPa.
3. Conclusion and future work
In this paper, an important step in the development of a modelfor residual stress prediction during cure of FMLs was described.The cure kinetics, thermal and viscoelastic properties of the resinused in the prepreg layers of GLARE are determined using thermaland dynamic mechanical measurements. It was shown that in thetemperature range of the cure cycle of GLARE, properties are
significantly dependent on time and temperature. As a result, thetime–temperature dependent material model for epoxy FM-94was obtained. These effects are not yet seen in the residual stresspredictions currently used in the design of the material for fatiguelife, nor in the residual strength and damage tolerance. The epoxyFM-94 studied in this paper is also used in other structural appli-cations like the bonding adhesive in sandwich structures. Theobtained thermo-viscoelastic material model of the adhesive, canbe used in the analysis of the S2-glass-epoxy prepreg layers andfor the adhesive used in bonded parts of GLARE-type structures.Attachment of adjacent GLARE laminates to produce large panelsfor fuselage of aeroplane and even bonding cycle for adding biggerexternal doublers and reinforcement stringers, are among majorapplications of epoxy FM-94.
For the future phases of this research, the change of stiffness ofthe prepreg during the cure cycle should be measured and imple-mented in the model. The modelling will also include the epoxycure shrinkage and orthotropic viscoelastic behaviour of the pre-preg layers during cool-down.
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