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epoxy laminates
Polymer Testing 62 (2017) 287e294
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Property Modelling
Numerical analysis and fiber Bragg grating monitoring of thermocuring processes of carbon fiber/epoxy laminates Qinglin Wang a, Linlin Gao a, Xiaoxia Wang b, Qi Dong a, Guoshun Wan a, Tianxiang Du a, Yunli Guo a, Chen Zhang a, *, Yuxi Jia a, ** a b
Key Laboratory for Liquid-Solid Structural Evolution & Processing of Materials, Ministry of Education, Shandong University, Jinan 250061, China School of Mechanical-Electronic and Vehicle Engineering, Weifang University, Weifang 261061, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 June 2017 Accepted 11 July 2017 Available online 14 July 2017
A three-dimensional differential viscoelastic model combining the effects of curing degree, thermal expansion, chemical shrinkage and stress relaxation for composite laminates was established and well verified. The evolution of strain and stress of composite laminates during cure was numerically simulated using the validated model. Also, fiber Bragg grating temperature and strain sensors were adjacently embedded in the composite laminate to in situ monitor the temperature and strain evolution. The monitored strain was evaluated by comparison with the corresponding simulated strain. The results reveal that the monitored temperature can reflect the actual temperature evolution in composite laminates, whereas the monitored strain cannot accurately characterize the actual strain evolution in composite laminates at the early stage of cure. However, when the resin/grating interfacial bond strength increases enough to transfer resin strain effectively, the changes in the monitored strain can match well with the actual strain changes. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Differential viscoelastic model Finite element analysis Fiber Bragg grating sensor Thermocuring characteristic
1. Introduction By virtue of light weight and high specific strength and stiffness, carbon fiber reinforced polymer (CFRP) composites have been widely used in numerous areas such as aerospace, sport equipment, medical devices and other high-performance applications. Residual strain and stress can be induced during the fabrication of CFRP composites, which can reduce mechanical performance, dimensional stability and durability of composite structures, and sometimes even cause matrix cracking. Hence, it is essential to accurately predict and monitor the evolution of strain and stress during the curing process of CFRP composites. It is well known that polymer materials exhibit typical viscoelastic response from a low viscosity material to a fully cured elastic solid during the curing process [1]. The evolution of processinduced residual strain and stress is affected by many factors such as cure cycle, chemical shrinkage, thermal expansion, tool/ part interaction and so on [2e6]. In early studies, the elastic model
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (C. Zhang), [email protected] (Y. Jia). http://dx.doi.org/10.1016/j.polymertesting.2017.07.014 0142-9418/© 2017 Elsevier Ltd. All rights reserved.
[7,8] and cure hardening instantaneously linear elastic model [9] were established to investigate the evolution of process-induced residual stress of CFRP laminates. These models either assumed that the material was stress-free before cooling or were only suitable for thin composite laminates. Later, the three-dimensional viscoelastic model for polymer composites was gradually employed in a general convolution integral form [10e13]. Ding et al. [14] investigated the effects of aluminum skins on the residual stress evolution of autoclaved composite laminates using a threedimensional differential viscoelastic model. Zobeiry et al. [15] adopted both the integral and differential viscoelastic constitutive equations to research the general material response, and the results revealed that identical material representations could be attained, but the differential form was time-saving and more convenient to implement and code with a finite-element method than the integral one. The appropriate temperature condition needs to be applied to polymer composites during the fabrication process. Although the temperature condition can be set by the temperature control device in advance, the actual temperature of polymer composites can be different from the preset temperature on account of the resin curing heat generation and imperfect temperature control stability of industrial devices. Also, limited studies have been performed to
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monitor the strain evolution of polymer composites during the entire cure cycle with accurate and effective methods, and even fewer works have been done to evaluate the effectivity of the monitored strain. In recent years, the fiber Bragg grating (FBG) has become an attractive technology for health monitoring of composite structures due to its outstanding advantages such as the immunity to electromagnetic interference, relative lightweight, durability, signal stability and suitability for wavelength multiplexing [16e19]. Lau and Zhou [20] discovered that surface mounted strain sensors could not precisely detect microcracks and delamination of a laminated composite plate, considering that the effect of shear deformation would delay the transmission of deformation from the damage zone to the plate's surface. On the contrary, embedded FBG sensors have been widely used to provide in situ monitoring of composite materials without significant effects on the global mechanical behavior of the host material in view of the extremely small physical size of an optical fiber [21e25]. In this work, a composite laminate with embedded FBG temperature and strain sensors was fabricated. The evolution of strain and stress of the composite laminate during the entire cure cycle was numerically simulated using a validated differential viscoelastic model. The monitoring results of temperature and strain of the laminate were obtained through the embedded sensors. The monitored strain was evaluated by comparison with the corresponding simulated strain. The comparison between simulated strain and monitored strain can provide a comprehensive understanding of the thermocuring characteristics of composite laminates and the monitoring characteristics of FBG sensors.
2.1.2. Differential viscoelastic constitutive model The mechanical response of a polymer material involves the characteristics of elastic and viscous behavior, especially at high temperature. A collection of Maxwell units in parallel referred to as the generalized Maxwell model is widely used to represent the viscoelastic behavior of polymer materials, as depicted in Fig. 1 [28]. In this paper, instead of the integral form, the differential viscoelastic constitutive equation is adopted in order to obtain the numerical solution. The stress in the m-th arm of the generalized Maxwell model at time t is given by Ref. [15]:
dεt dstm 1 þ t stm ¼ Cm eff dt tm dt Eq. (4) can be written in finite difference form as [28]:
εt εt1 stm st1 1 m eff þ t stm ¼ Cm eff Dt tm Dt
2.1. Finite element (FE) model and validation 2.1.1. Thermo-chemical model When a composite laminate is heated, the resin is gradually cured and reaction heat is generated. A thermo-chemical model is needed to characterize the evolution of temperature and cure degree throughout the laminate during the entire cure cycle. The process of heat transfer can be described by the Fourier's heat conduction equation as [1]:
rCp
vT v vT v vT v vT ¼ kx þ ky þ kz þQ vt vx vx vy vy vz vz
da dt
stm ¼
i h 1 Cm εteff εt1 þ st1 m eff t 1 þ Dt tm
Zt
da dt dt
(7)
Combining the stresses from all arms of the model and the equilibrium spring, the total stress at time t is written as [28]:
(1)
(2)
where rr is the resin density, Vr denotes the volume fraction of the resin, and Hr is the released total heat for the fully cured resin. da=dt represents the instantaneous cure rate of the resin. The cure degree a can be calculated by the equation:
aðtÞ ¼
(6)
where εtot is the total strain tensor; CTE and CCS are the effective thermal expansion coefficient and chemical shrinkage coefficient, respectively; DT is the change in temperature, and Da is the change in cure degree. stm is solved according to Eq. (5) as:
where r, Cp, kx, ky, kz denote the density, specific heat and anisotropy thermal conductivities of the composite, respectively. T is the temperature at time t; Q is the internal heat generation due to the resin curing reaction and can be determined by the following formulation [26,27]:
Q ¼ rr Vr Hr
(5)
t t1 t where st1 m and sm , εeff and εeff indicate stress tensors and effective strain tensors before and after the passage of a time increment Dt, respectively. ttm and Cm are the relaxation time and stiffness matrix of the m-th arm of the model at time t, respectively. The effective strain tensor εeff can be defined by the following formulation as:
εeff ¼ εtot CTE,DT CCS,Da 2. Theoretical approach
(4)
(3)
0
Fig. 1. Generalized Maxwell model [28].
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st ¼ C e εteff þ
n X
stm ¼ C e εteff
m¼1
n Cm εt εt1 þ st1 X m eff eff þ t 1 þ D t t m m¼1
(8)
Based on Eq. (8), the stress increment Dst at time t is calculated:
Dst ¼ st st1
¼ C e εteff εt1 eff
n Cm εt εt1 Dt tt st1 X m m eff eff þ t 1 þ D t t m m¼1 (9)
where Ce is the stiffness matrix of the spring and equals to C∞. The stiffness matrix Cm of the m-th arm of the model is expressed as [13,15]:
xða; TÞ Cm ¼ ðC u C ∞ ÞWm exp tm ðaÞ
(10)
In Eq. (10), Cu is the matrix consisting of unrelaxed stiffnesses of the lamina, and each stiffness in the matrix Cu is considered as the elastic stiffness. C∞ is the matrix consisting of fully relaxed stiffnesses and can be calculated through a partition factor as C∞ ¼ rCu. In this paper, r is chosen to be 0.14 for TR50S/YPH-308 material [13]. The unrelaxed and fully relaxed stiffnesses of the lamina are considered cure-independent, and the stiffnesses of composites dominated by the reinforcing fibers are considered constant [13]. Wm and tm are the weight factor and the discrete relaxation time, respectively. x denotes the reduced time and can be defined as:
x¼
Zt 0
ds aT ½a; TðsÞ
(11)
1 b2 ðT Tr Þ b1 exp a1
2.1.3. Validation of finite element model The thermo-chemical and viscoelastic constitutive models described above were accomplished in ABAQUS using the subroutines USDFLD, HETVAL, UMAT and UEXPAN. Then, a validation study was performed on the cross-ply laminate [0/90/90/0] with plate aspect ratio of a/b ¼ 4. The geometric model for the validation study is shown in Fig. 2. The cure cycle and thermo-chemical and mechanical parameters used here for AS4/3501-6 material were obtained from the literature [13]. The numerical prediction results of residual stress during cure are compared with those presented by White and Kim [13]. Fig. 3 shows the interlaminar normal stress (s3) history during the whole cure cycle at the point (0, a, 0), resulting from the present model and the model given by White and Kim. It can be seen that excellent agreement is achieved. The interlaminar normal stress (s3) distribution at x ¼ 0 and z ¼ 0 during cooling is presented in Fig. 4, and the results from the two models also show good correlation. Thus, the accuracy and reliability of finite element model are well validated. 2.2. FBG sensing principle An FBG sensor bears a periodical refractive index modulation in the optical fiber core. When a broadband light source travels through an FBG, the narrow-band light with the same wavelength is reflected back by the grating. The wavelength of the reflected light, lB, depends on the effective refractive index (neff) of the fiber core and the Bragg period (L) of the grating, according to the Bragg equation [23]:
lB ¼ 2neff L
(17)
The shift of the reflected Bragg wavelength due to the axial strain ε and temperature change DT is expressed as [23,30,31]:
h
i
DlB ¼ lB ð1 Pe Þε þ af þ x DT ¼ Kε ε þ KT DT
where aT is the shift function and is expressed as [29]:
logðaT Þ ¼
289
(12)
where b1 and b2 are constants which equal to 1.4 and 0.0712, respectively; Tr is the reference temperature which is 30 C in this case. Also, the relaxation time ttm at time t in Eq. (5) can be determined as [14,29]:
where Pe is the photoelastic coefficient, af is the thermal expansion coefficient and x is the thermo-optic coefficient. Kε and KT denote the strain and temperature sensitivity constants, respectively. For the FBG temperature sensor, the FBG is encapsulated in a steel capillary tube and is in strain-free condition [32], so Eq. (18) can be simplified in terms of only the temperature change as:
DlB ¼ lB af þ x DT ¼ KT DT
(13)
log½tm ðaÞ ¼ log½tm ðar Þ þ ½f ðaÞ ða ar Þlogðlm Þ
(14)
and
lm ¼
109:9 tm ðar Þ
(19)
An FBG that is not specially treated serves as the strain sensor,
ttm ¼ aT ½a; TðsÞtm ðaÞ
f ðaÞ ¼ 9:3694 þ 0:6089a þ 9:1347a2
(18)
(15)
(16)
where tm(ar) is the relaxation time at the reference cure degree ar. It is assumed that there is no strain and stress history before t ¼ 0 and the material is transversely isotropic in the plane perpendicular to the reinforcing fibers. Based on the previous t values of each arm stress (st1 m ), the successive values of s can be calculated according to Eq. (9).
Fig. 2. Geometric model of the laminate for the validation study.
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Fig. 3. Interlaminar normal stress (s3) history at the point (0, a, 0) during the entire cure cycle.
location where FBG sensors were embedded. Teflon tubes were used to protect the optical fiber from breaking in the egress location during the fabrication of the CFRP laminate. The temperature and strain sensitivity constants of FBG sensors were measured to be 9.6 pm/ C and 1.2 pm/mε, respectively. The laminate was fabricated by means of hot press molding. At first, the temperature was raised to 80 C from 25 C and held for a 30-min dwell (Dwell-1), and then was raised to 130 C for a 60-min dwell (Dwell-2) during the first heating cycle. After a period of cooling, the temperature was raised to 80 C again for a 30-min dwell (Dwell-3), and then was raised to 130 C for a 10-min dwell (Dwell-4) during the second heating cycle. Natural cooling was adopted during the entire cure cycle. The second heating cycle and natural cooling can help to reduce the stress concentration and improve the monitoring stability of FBG sensors. The temperature cycle was applied to the top and bottom surfaces of the CFRP laminate. The initial temperature and cure degree for this study were chosen as 25 C and 0, respectively, and the fabrication pressure was set to be 0.5 MPa. The cure kinetic formula for YPH-308 epoxy was determined based on e previous work [33]:
da=dt ¼ expð0:65 1000=T 1:52Þ a0:49 ð1 aÞ1:89 (20) The corresponding finite element model was established in ABAQUS with the same geometry, material system and temperature condition as described above for TR50S/YPH-308 material. The element type of finite element analysis was chosen to be C3D20R. The unrelaxed material properties of TR50S/YPH-308 are listed in Table 1. The relaxation time tm(ar) and the weight factor Wm at the reference cure degree are shown in Table 2.
4. Results and discussion 4.1. FBG monitoring of material temperature evolution Fig. 4. Interlaminar normal stress (s3) distribution at x ¼ 0 and z ¼ 0 during cooling stage.
and is affected by the thermal expansion of the grating itself as well as chemical shrinkage and thermal expansion of the resin around the grating. In this work, the FBG temperature sensor is laid adjacent to the FBG strain sensor in order to decouple the effect caused by the thermal expansion of the grating on the FBG strain sensor, and hence the axial strain ε from the resin around the grating can be attained from the measured wavelength shift by combining Eqs. (18) with (19). 3. Experimental The laminate analyzed in this paper consisted of 22 plies of TR50S/YPH-308 prepreg with the lay-up type of [9011/011] and dimensions of 300 mm 300 mm 2.75 mm. During the stacking process of TR50S/YPH-308 prepregs, the FBG temperature sensor (FBG-T) and FBG strain sensor (FBG-S) were longitudinally embedded between the 17th and 18th plies along the central axis of the 17th ply and were 75 mm distance from the edge of the laminate. The schematic diagrams of CFRP laminate and embedded FBG sensors are presented in Fig. 5. In Fig. 5(a), the quarter geometry of CFRP laminate with the sizes of a0 ¼ 150 mm, b0 ¼ 150 mm and c0 ¼ 1.375 mm is symmetrical with respect to the x-axis and y-axis. For convenience, the point M in Fig. 5(a) is used to represent the
The spectra of embedded FBG temperature and strain sensors before and after the fabrication process are presented in Fig. 6. It can be observed that there is no evident distortion from all the spectra, which implies that the data obtained from embedded FBG sensors is accurate and reliable. The relative shift in central wavelength on account of thermal expansion and resin chemical shrinkage can be seen from the arrows indicated in Fig. 6. The evolution of material temperature monitored by FBG-T is plotted in Fig. 7. It is clear that the temperature evolution exhibits evident undulation in all dwells, and the maximum temperature reaches 146 C in Dwell-4, which is 16 C higher than the preset temperature (130 C). The temperature undulation can be attributed to two main factors. The first is the internal heat generation due to the resin curing reaction, and the second is that the programmed temperature control of industrial devices leads to multiple heating and cooling cycles for the purpose of heat preservation. The temperature undulation in Dwell-2 is induced by the two factors, while the temperature undulation in Dwell-1, Dwell-3 and Dwell-4 is mainly affected by the second factor. Because of good accuracy and reliability of FBG-T as well as the fact that FBG-T is only affected by the temperature, FBG-T is a much more accurate and convenient approach to obtain the actual temperature evolution including the temperature undulation in the CFRP laminate than the traditional temperature testing devices. Therefore, the temperature monitored by FBG-T can be considered as the actual temperature of the CFRP laminate.
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291
Fig. 5. Schematic diagrams of CFRP laminate and embedded FBG sensors. (a) Quarter geometry of CFRP laminate which is symmetrical with respect to the x-axis and y-axis; (b) locally amplified sectional drawing of FBG-T and FBG-S.
Table 1 Unrelaxed material properties of TR50S/YPH-308 prepregs [13]. Property
Value
E1 (GPa) E2 ¼ E3 (GPa) G12 ¼ G13 (GPa) G23 (GPa) n12 ¼ n13
129.6 8.5 4.2 3.21 0.27 0.32 0.5 34.2 167.0 8810.0
n23
CTE1 (mε/ C) CTE2 ¼ CTE3 (mε/ C) CCS1 (mε) CCS2 ¼ CCS3 (mε)
Table 2 Relaxation times and weight factors at the reference cure degree (ar ¼ 0.98) [13]. m
tm (min)
Wm
1 2 3 4 5 6 7 8 9
29.2 2.92e3 1.82e5 1.10e7 2.83e8 7.94e9 1.95e11 3.32e12 4.92e14
0.059 0.066 0.083 0.112 0.154 0.262 0.184 0.049 0.025
4.2. FE analysis on thermocuring process In order to simulate the evolution of cure degree, strain and stress of the CFRP laminate, the actual temperature monitored by FBG-T is imported into ABAQUS as the temperature condition of the FE analysis on the thermocuring process. Also, since the laminate is thin enough and the temperature cycle is only applied on the top and bottom surfaces during the fabrication of the laminate, the temperature along the thickness and in-plane direction is considered uniform during the FE modelling process. The evolution of the cure degree at the point M is obtained from FE analysis and depicted in Fig. 7. It can be clearly seen that the resin curing reaction occurs mainly in Dwell-2 with a sharp increase in the cure degree. Meanwhile, the cure degree also shows a small increase in
Dwell-1 and Dwell-4. The evolution of the simulated strain and stress along the reinforcing fiber direction at the point M is plotted in Fig. 8, from which the comprehensive effects of thermal expansion and chemical shrinkage on the evolution of residual strain and stress can be seen. At first, the resin curing reaction develops slowly, and the overall strain behaves as the tensile strain mainly affected by the thermal expansion. Later, due to the rapid curing reaction in the procedure Dwell-2, the chemical shrinkage strain plays a dominant role and the overall stain gradually behaves as the compressive strain. As the curing reaction is gradually completed, the thermal expansion strain dominates again and the overall strain evolution becomes synchronous with the temperature evolution. The simulated stress follows a similar evolution trend to the simulated strain. Also, it should be noted that there is a small strain and stress undulation at about 98 min in Fig. 8, which is generated on account of the temperature undulation, considering that the cure degree is large enough at about 98 min and the effect of the chemical shrinkage on the strain and stress evolution is relatively weak. Fig. 9 illustrates the distribution of simulated strain and stress along y ¼ 0 in the 17th ply at a ¼ 0.6, 0.8, 0.96 (at the end of cure cycle). It can be seen that the strain and stress behave as the tensile strain and stress at a ¼ 0.6 but later as the compressive strain and stress at a ¼ 0.8 and 0.96. Compared with the strain and stress at a ¼ 0.6 and 0.8, the strain and stress at the end of cure cycle (a ¼ 0.96) exhibit noticeable increase, which is mainly due to the effect of cooling. Additionally, Fig. 9 shows the uniformity of strain and stress distribution along the reinforcing fibers, which corresponds to the uniform temperature distribution in the in-plane direction. 4.3. Evaluation of material strain monitored by FBG Given that the differential viscoelastic model and corresponding finite element codes used in this work have been well validated, the simulated strain is believed to effectively characterize the strain evolution of the CFRP laminate. Therefore, the strain monitored by FBG-S can be evaluated by comparison with the simulated strain. The strain comparison between FBG test and FE simulation during the entire cure cycle is presented in Fig. 10. The monitored strain shows a distinct difference from the simulated result. First, there is no obvious strain variation from the monitored
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Fig. 6. Spectra of FBG sensors before and after the fabrication process of CFRP laminate.
Fig. 7. Evolution of monitored temperature and simulated cure degree during the entire cure cycle.
Fig. 8. Evolution of simulated stress and strain at the point M during the entire cure cycle.
Fig. 9. Distribution of simulated strain and stress along y ¼ 0 in the 17th ply at a ¼ 0.6, 0.8, 0.96.
Fig. 10. Strain comparison between FBG test and FE simulation during the entire cure cycle.
Q. Wang et al. / Polymer Testing 62 (2017) 287e294
strain at the early stage of cure. This can be related to the low resin viscosity, which results in a relatively weak bond strength between the resin and FBG-S as well as poor efficiency of strain transfer from the resin to FBG-S. Second, in Dwell-2, the monitored strain exhibits frequent undulation rather than rapid development as the simulated strain, which is caused by the following reasons. As shown in Fig. 7, with the resin cure degree in Dwell-2 increasing rapidly, the bond strength between the resin and FBG-S is becoming larger and larger. Hence, the movement of air and vapor bubbles under the conditions of high temperature and pressure can be detected more and more sensitively by the FBG-S in the form of strain undulation. Also, when the bond strength between the resin and FBG-S is strong enough, the thermal strain of the resin caused by the temperature undulation can be effectively transferred to the FBG-S grating, and then can contribute to the undulation of the monitored strain, which is also slightly reflected from the undulation of the simulated strain at about 98 min. According to the evolution characteristic of the resin cure degree shown in Fig. 7, it can be concluded that effective interfacial bond between the resin and FBG-S can be established in Dwell-2 and the chemical shrinkage strain of the resin can be effectively transferred to FBG-S. However, the frequent undulation of the monitored strain in Dwell-2 makes the chemical shrinkage strain unnoticeable. At the end of the cure cycle, the monitored strain is much smaller than the simulated strain, mainly because of the absence of the early chemical shrinkage strain from the monitored strain. Since FBG-S cannot effectively monitor the strain evolution in Dwell-1 and Dwell-2, it is a reasonable choice to eliminate the effect of the early strain and then only compare the monitored strain with simulated strain after Dwell-2. Here, given that no apparent temperature undulation is noticed again and the strain evolution is also relatively stable after 125 min (onset of first cooling process), the strain at 125 min is chosen as the reference strain. The changes of monitored and simulated strains after 125 min with respect to the respective reference strain are shown in Fig. 11. The changes of the monitored strain develop faster than the simulated results at first, but later good agreement between the monitored and simulated strain changes is achieved. The faster development in the monitored strain changes can be explained by the fact that the chemical shrinkage strain in Dwell-2 is not displayed clearly as a
Fig. 11. Monitored and simulated strain changes after 125 min with respect to the respective reference strain.
293
result of the frequent strain undulation, as described above, but it takes effect during the first cooling process. 5. Conclusions (1) The monitored temperature by the FBG sensor can reflect the actual temperature evolution of the CFRP laminate, and can be used as the temperature condition of the numerical analysis on the thermocuring process, which can significantly simplify the FE analysis on the whole thermocuring process. (2) The three-dimensional differential viscoelastic model combining the effects of cure degree, thermal expansion, chemical shrinkage and stress relaxation is established and well verified, and then the evolution of cure degree, strain and stress of the CFRP laminate during the entire cure cycle is analyzed. The simulated strain can serve as the reference to evaluate the monitored strain by FBG sensor. (3) The monitored strain by the FBG sensor cannot accurately characterize the actual strain evolution of the CFRP laminate at the early stage of cure as a result of low resin viscosity, movement of air and vapor bubbles as well as temperature undulation. However, when the resin/grating interfacial bond strength increases enough to transfer resin strain effectively, the changes in the monitored strain achieve good agreement with the actual strain changes of composite laminates. Acknowledgements This work was supported by the National Natural Science Foundation of China (51373090), the China-EU Co-funded Project (MJ2015-HG-103, Horizon 2020-690638), the National Key Basic Research Program of China (JCKY2016205B007), and the Natural Science Foundation of Shandong Province (ZR2014EL013). References [1] Y.K. Kim, S.R. White, Viscoelastic analysis of processing-induced residual stresses in thick composite laminates, Mech. Compos. Mater. Struct. 4 (1997) 361e387. [2] Y. Miao, J. Li, Z. Gong, J. Xu, K. He, J. Peng, Y. Cui, Study on the effect of cure cycle on the process induced deformation of cap shaped stiffened composite panels, Appl. Compos. Mater. 20 (2013) 709e718. [3] R. Joven, B. Tavakol, A. Rodriguez, M. Guzman, B. Minaie, Characterization of shear stress at the tool-part interface during autoclave processing of prepreg composites, J. Appl. Polym. Sci. 129 (2013) 2017e2028. [4] Y. Nawab, S. Shahid, N. Boyard, F. Jacquemin, Chemical shrinkage characterization techniques for thermoset resins and associated composites, J. Mater. Sci. 48 (2013) 5387e5409. [5] J. Sun, Y. Gu, Y. Li, M. Li, Z. Zhang, Role of tool-part interaction in consolidation of L-shaped laminates during autoclave process, Appl. Compos. Mater. 19 (2012) 583e597. [6] O.G. Kravchenko, C. Li, A. Strachan, S.G. Kravchenko, R.B. Pipes, Prediction of the chemical and thermal shrinkage in a thermoset polymer, Compos. Part A Appl. Sci. Manuf. 66 (2014) 35e43. [7] A.S.D. Wang, F.W. Crossman, Edge effects on thermally induced stresses in composite laminates, J. Compos. Mater. 11 (1977) 300e312. [8] K.S. Kim, H.T. Hahn, Residual stress development during processing of graphite/epoxy composites, Compos. Sci. Technol. 36 (1989) 121e132. [9] A.A. Johnston, An Integrated Model of the Development of Process-induced Deformation in Autoclave Processing of Composites Structures, The University of British Columbia, Vancouver, 1997. [10] J. Li, X. Yao, Y. Liu, Z. Cen, Z. Kou, X. Hu, D. Dai, Thermo-viscoelastic analysis of the integrated T-shaped composite structures, Compos. Sci. Technol. 70 (2010) 1497e1503. [11] S. Clifford, N. Jansson, W. Yu, V. Michaud, J.A. Månson, Thermoviscoelastic anisotropic analysis of process induced residual stresses and dimensional stability in real polymer matrix composite components, Compos. Part A Appl. Sci. Manuf. 37 (2006) 538e545. [12] J. Magnus Svanberg, J. Anders Holmberg, Prediction of shape distortions Part I. FE-implementation of a path dependent constitutive model, Compos. Part A Appl. Sci. Manuf. 35 (2004) 711e721.
294
Q. Wang et al. / Polymer Testing 62 (2017) 287e294
[13] S.R. White, Y.K. Kim, Process-induced residual stress analysis of AS4/3501-6 composite material, Mech. Compos. Mater. Struct. 5 (1998) 153e186. [14] A. Ding, S. Li, J. Wang, L. Zu, A three-dimensional thermo-viscoelastic analysis of process-induced residual stress in composite laminates, Compos. Struct. 129 (2015) 60e69. [15] N. Zobeiry, R. Vaziri, A. Poursartip, Differential implementation of the viscoelastic response of a curing thermoset matrix for composites processing, J. Eng. Mater. Technol. 128 (2006) 90e95. [16] K.T. Lau, Structural health monitoring for smart composites using embedded FBG sensor technology, Mater. Sci. Technol. 30 (2014) 1642e1654. [17] G. Lubineau, Estimation of residual stresses in laminated composites using field measurements on a cracked sample, Compos. Sci. Technol. 68 (2008) 2761e2769. [18] R. de Oliveira, C.A. Ramos, A.T. Marques, Health monitoring of composite rot sensors, Comstructures by embedded FBG and interferometric Fabry-Pe put. Struct. 86 (2008) 340e346. [19] K.S.C. Kuang, R. Kenny, M.P. Whelan, W.J. Cantwell, P.R. Chalker, Embedded fibre Bragg grating sensors in advanced composite materials, Compos. Sci. Technol. 61 (2001) 1379e1387. [20] K.T. Lau, L.M. Zhou, The mechanical behaviour of composite-wrapped concrete cylinders subjected to uniaxial compression load, Compos. Struct. 52 (2001) 189e198. [21] A. Lamberti, G. Chiesura, G. Luyckx, J. Degrieck, M. Kaufmann, S. Vanlanduit, Dynamic strain measurements on automotive and aeronautic composite components by means of embedded fiber Bragg grating sensors, Sensors 15 (2015) 27174e27200. [22] C. Yilmaz, C. Akalin, E.S. Kocaman, A. Suleman, M. Yildiz, Monitoring Poisson's ratio of glass fiber reinforced composites as damage index using biaxial fiber Bragg grating sensors, Polym. Test. 53 (2016) 98e107. [23] K.S.C. Kuang, R. Kenny, M.P. Whelan, W.J. Cantwell, P.R. Chalker, Residual
[24]
[25]
[26] [27]
[28]
[29] [30]
[31]
[32]
[33]
strain measurement and impact response of optical fibre Bragg grating sensors in fibre metal laminates, Smart Mater. Struct. 10 (2001) 338e346. A. Riccio, F. Di Caprio, F. Camerlingo, F. Scaramuzzino, B. Gambino, Positioning of embedded optical fibres sensors for the monitoring of buckling in stiffened composite panels, Appl. Compos. Mater. 20 (2013) 73e86. G. Pereira, M. McGugan, L.P. Mikkelsen, Method for independent strain and temperature measurement in polymeric tensile test specimen using embedded FBG sensors, Polym. Test. 50 (2016) 125e134. T.A. Bogetti, J.W. Gillespie, Process-induced stress and deformation in thicksection thermoset composite laminates, J. Compos. Mater. 26 (1992) 626e660. S.R. White, H.T. Hahn, Process modeling of composite materials: residual stress development during cure. Part I. Model formulation, J. Compos. Mater. 26 (1992) 2402e2422. D. Roylance, Engineering Viscoelasticity, 2139, Department of Materials Science and Engineering-Massachusetts Institute of Technology, Cambridge MA, 2001, pp. 1e37. Y.K. Kim, S.R. White, Stress relaxation behavior of 3501-6 epoxy resin during cure, Polym. Eng. Sci. 36 (1996) 2852e2862. E. Marin, L. Robert, S. Triollet, Y. Ouerdane, Liquid resin infusion process monitoring with superimposed fibre Bragg grating sensor, Polym. Test. 31 (2012) 1045e1052. S.N. Economidou, D. Karalekas, Optical sensor-based measurements of thermal expansion coefficient in additive manufacturing, Polym. Test. 51 (2016) 117e121. M. Mulle, H. Wafai, A. Yudhanto, G. Lubineau, R. Yaldiz, W. Schijve, N. Verghese, Process monitoring of glass reinforced polypropylene laminates using fiber Bragg gratings, Compos. Sci. Technol. 123 (2016) 143e150. L. Zeng, L. Zhan, Cure kinetics of YPH-23 carbon fiber/epoxy prepreg by isothermal method, New Chem. Mater. 44 (2016) 193e195 (in Chinese).
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Property Modelling
Numerical analysis and fiber Bragg grating monitoring of thermocuring processes of carbon fiber/epoxy laminates Qinglin Wang a, Linlin Gao a, Xiaoxia Wang b, Qi Dong a, Guoshun Wan a, Tianxiang Du a, Yunli Guo a, Chen Zhang a, *, Yuxi Jia a, ** a b
Key Laboratory for Liquid-Solid Structural Evolution & Processing of Materials, Ministry of Education, Shandong University, Jinan 250061, China School of Mechanical-Electronic and Vehicle Engineering, Weifang University, Weifang 261061, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 June 2017 Accepted 11 July 2017 Available online 14 July 2017
A three-dimensional differential viscoelastic model combining the effects of curing degree, thermal expansion, chemical shrinkage and stress relaxation for composite laminates was established and well verified. The evolution of strain and stress of composite laminates during cure was numerically simulated using the validated model. Also, fiber Bragg grating temperature and strain sensors were adjacently embedded in the composite laminate to in situ monitor the temperature and strain evolution. The monitored strain was evaluated by comparison with the corresponding simulated strain. The results reveal that the monitored temperature can reflect the actual temperature evolution in composite laminates, whereas the monitored strain cannot accurately characterize the actual strain evolution in composite laminates at the early stage of cure. However, when the resin/grating interfacial bond strength increases enough to transfer resin strain effectively, the changes in the monitored strain can match well with the actual strain changes. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Differential viscoelastic model Finite element analysis Fiber Bragg grating sensor Thermocuring characteristic
1. Introduction By virtue of light weight and high specific strength and stiffness, carbon fiber reinforced polymer (CFRP) composites have been widely used in numerous areas such as aerospace, sport equipment, medical devices and other high-performance applications. Residual strain and stress can be induced during the fabrication of CFRP composites, which can reduce mechanical performance, dimensional stability and durability of composite structures, and sometimes even cause matrix cracking. Hence, it is essential to accurately predict and monitor the evolution of strain and stress during the curing process of CFRP composites. It is well known that polymer materials exhibit typical viscoelastic response from a low viscosity material to a fully cured elastic solid during the curing process [1]. The evolution of processinduced residual strain and stress is affected by many factors such as cure cycle, chemical shrinkage, thermal expansion, tool/ part interaction and so on [2e6]. In early studies, the elastic model
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (C. Zhang), [email protected] (Y. Jia). http://dx.doi.org/10.1016/j.polymertesting.2017.07.014 0142-9418/© 2017 Elsevier Ltd. All rights reserved.
[7,8] and cure hardening instantaneously linear elastic model [9] were established to investigate the evolution of process-induced residual stress of CFRP laminates. These models either assumed that the material was stress-free before cooling or were only suitable for thin composite laminates. Later, the three-dimensional viscoelastic model for polymer composites was gradually employed in a general convolution integral form [10e13]. Ding et al. [14] investigated the effects of aluminum skins on the residual stress evolution of autoclaved composite laminates using a threedimensional differential viscoelastic model. Zobeiry et al. [15] adopted both the integral and differential viscoelastic constitutive equations to research the general material response, and the results revealed that identical material representations could be attained, but the differential form was time-saving and more convenient to implement and code with a finite-element method than the integral one. The appropriate temperature condition needs to be applied to polymer composites during the fabrication process. Although the temperature condition can be set by the temperature control device in advance, the actual temperature of polymer composites can be different from the preset temperature on account of the resin curing heat generation and imperfect temperature control stability of industrial devices. Also, limited studies have been performed to
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monitor the strain evolution of polymer composites during the entire cure cycle with accurate and effective methods, and even fewer works have been done to evaluate the effectivity of the monitored strain. In recent years, the fiber Bragg grating (FBG) has become an attractive technology for health monitoring of composite structures due to its outstanding advantages such as the immunity to electromagnetic interference, relative lightweight, durability, signal stability and suitability for wavelength multiplexing [16e19]. Lau and Zhou [20] discovered that surface mounted strain sensors could not precisely detect microcracks and delamination of a laminated composite plate, considering that the effect of shear deformation would delay the transmission of deformation from the damage zone to the plate's surface. On the contrary, embedded FBG sensors have been widely used to provide in situ monitoring of composite materials without significant effects on the global mechanical behavior of the host material in view of the extremely small physical size of an optical fiber [21e25]. In this work, a composite laminate with embedded FBG temperature and strain sensors was fabricated. The evolution of strain and stress of the composite laminate during the entire cure cycle was numerically simulated using a validated differential viscoelastic model. The monitoring results of temperature and strain of the laminate were obtained through the embedded sensors. The monitored strain was evaluated by comparison with the corresponding simulated strain. The comparison between simulated strain and monitored strain can provide a comprehensive understanding of the thermocuring characteristics of composite laminates and the monitoring characteristics of FBG sensors.
2.1.2. Differential viscoelastic constitutive model The mechanical response of a polymer material involves the characteristics of elastic and viscous behavior, especially at high temperature. A collection of Maxwell units in parallel referred to as the generalized Maxwell model is widely used to represent the viscoelastic behavior of polymer materials, as depicted in Fig. 1 [28]. In this paper, instead of the integral form, the differential viscoelastic constitutive equation is adopted in order to obtain the numerical solution. The stress in the m-th arm of the generalized Maxwell model at time t is given by Ref. [15]:
dεt dstm 1 þ t stm ¼ Cm eff dt tm dt Eq. (4) can be written in finite difference form as [28]:
εt εt1 stm st1 1 m eff þ t stm ¼ Cm eff Dt tm Dt
2.1. Finite element (FE) model and validation 2.1.1. Thermo-chemical model When a composite laminate is heated, the resin is gradually cured and reaction heat is generated. A thermo-chemical model is needed to characterize the evolution of temperature and cure degree throughout the laminate during the entire cure cycle. The process of heat transfer can be described by the Fourier's heat conduction equation as [1]:
rCp
vT v vT v vT v vT ¼ kx þ ky þ kz þQ vt vx vx vy vy vz vz
da dt
stm ¼
i h 1 Cm εteff εt1 þ st1 m eff t 1 þ Dt tm
Zt
da dt dt
(7)
Combining the stresses from all arms of the model and the equilibrium spring, the total stress at time t is written as [28]:
(1)
(2)
where rr is the resin density, Vr denotes the volume fraction of the resin, and Hr is the released total heat for the fully cured resin. da=dt represents the instantaneous cure rate of the resin. The cure degree a can be calculated by the equation:
aðtÞ ¼
(6)
where εtot is the total strain tensor; CTE and CCS are the effective thermal expansion coefficient and chemical shrinkage coefficient, respectively; DT is the change in temperature, and Da is the change in cure degree. stm is solved according to Eq. (5) as:
where r, Cp, kx, ky, kz denote the density, specific heat and anisotropy thermal conductivities of the composite, respectively. T is the temperature at time t; Q is the internal heat generation due to the resin curing reaction and can be determined by the following formulation [26,27]:
Q ¼ rr Vr Hr
(5)
t t1 t where st1 m and sm , εeff and εeff indicate stress tensors and effective strain tensors before and after the passage of a time increment Dt, respectively. ttm and Cm are the relaxation time and stiffness matrix of the m-th arm of the model at time t, respectively. The effective strain tensor εeff can be defined by the following formulation as:
εeff ¼ εtot CTE,DT CCS,Da 2. Theoretical approach
(4)
(3)
0
Fig. 1. Generalized Maxwell model [28].
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st ¼ C e εteff þ
n X
stm ¼ C e εteff
m¼1
n Cm εt εt1 þ st1 X m eff eff þ t 1 þ D t t m m¼1
(8)
Based on Eq. (8), the stress increment Dst at time t is calculated:
Dst ¼ st st1
¼ C e εteff εt1 eff
n Cm εt εt1 Dt tt st1 X m m eff eff þ t 1 þ D t t m m¼1 (9)
where Ce is the stiffness matrix of the spring and equals to C∞. The stiffness matrix Cm of the m-th arm of the model is expressed as [13,15]:
xða; TÞ Cm ¼ ðC u C ∞ ÞWm exp tm ðaÞ
(10)
In Eq. (10), Cu is the matrix consisting of unrelaxed stiffnesses of the lamina, and each stiffness in the matrix Cu is considered as the elastic stiffness. C∞ is the matrix consisting of fully relaxed stiffnesses and can be calculated through a partition factor as C∞ ¼ rCu. In this paper, r is chosen to be 0.14 for TR50S/YPH-308 material [13]. The unrelaxed and fully relaxed stiffnesses of the lamina are considered cure-independent, and the stiffnesses of composites dominated by the reinforcing fibers are considered constant [13]. Wm and tm are the weight factor and the discrete relaxation time, respectively. x denotes the reduced time and can be defined as:
x¼
Zt 0
ds aT ½a; TðsÞ
(11)
1 b2 ðT Tr Þ b1 exp a1
2.1.3. Validation of finite element model The thermo-chemical and viscoelastic constitutive models described above were accomplished in ABAQUS using the subroutines USDFLD, HETVAL, UMAT and UEXPAN. Then, a validation study was performed on the cross-ply laminate [0/90/90/0] with plate aspect ratio of a/b ¼ 4. The geometric model for the validation study is shown in Fig. 2. The cure cycle and thermo-chemical and mechanical parameters used here for AS4/3501-6 material were obtained from the literature [13]. The numerical prediction results of residual stress during cure are compared with those presented by White and Kim [13]. Fig. 3 shows the interlaminar normal stress (s3) history during the whole cure cycle at the point (0, a, 0), resulting from the present model and the model given by White and Kim. It can be seen that excellent agreement is achieved. The interlaminar normal stress (s3) distribution at x ¼ 0 and z ¼ 0 during cooling is presented in Fig. 4, and the results from the two models also show good correlation. Thus, the accuracy and reliability of finite element model are well validated. 2.2. FBG sensing principle An FBG sensor bears a periodical refractive index modulation in the optical fiber core. When a broadband light source travels through an FBG, the narrow-band light with the same wavelength is reflected back by the grating. The wavelength of the reflected light, lB, depends on the effective refractive index (neff) of the fiber core and the Bragg period (L) of the grating, according to the Bragg equation [23]:
lB ¼ 2neff L
(17)
The shift of the reflected Bragg wavelength due to the axial strain ε and temperature change DT is expressed as [23,30,31]:
h
i
DlB ¼ lB ð1 Pe Þε þ af þ x DT ¼ Kε ε þ KT DT
where aT is the shift function and is expressed as [29]:
logðaT Þ ¼
289
(12)
where b1 and b2 are constants which equal to 1.4 and 0.0712, respectively; Tr is the reference temperature which is 30 C in this case. Also, the relaxation time ttm at time t in Eq. (5) can be determined as [14,29]:
where Pe is the photoelastic coefficient, af is the thermal expansion coefficient and x is the thermo-optic coefficient. Kε and KT denote the strain and temperature sensitivity constants, respectively. For the FBG temperature sensor, the FBG is encapsulated in a steel capillary tube and is in strain-free condition [32], so Eq. (18) can be simplified in terms of only the temperature change as:
DlB ¼ lB af þ x DT ¼ KT DT
(13)
log½tm ðaÞ ¼ log½tm ðar Þ þ ½f ðaÞ ða ar Þlogðlm Þ
(14)
and
lm ¼
109:9 tm ðar Þ
(19)
An FBG that is not specially treated serves as the strain sensor,
ttm ¼ aT ½a; TðsÞtm ðaÞ
f ðaÞ ¼ 9:3694 þ 0:6089a þ 9:1347a2
(18)
(15)
(16)
where tm(ar) is the relaxation time at the reference cure degree ar. It is assumed that there is no strain and stress history before t ¼ 0 and the material is transversely isotropic in the plane perpendicular to the reinforcing fibers. Based on the previous t values of each arm stress (st1 m ), the successive values of s can be calculated according to Eq. (9).
Fig. 2. Geometric model of the laminate for the validation study.
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Fig. 3. Interlaminar normal stress (s3) history at the point (0, a, 0) during the entire cure cycle.
location where FBG sensors were embedded. Teflon tubes were used to protect the optical fiber from breaking in the egress location during the fabrication of the CFRP laminate. The temperature and strain sensitivity constants of FBG sensors were measured to be 9.6 pm/ C and 1.2 pm/mε, respectively. The laminate was fabricated by means of hot press molding. At first, the temperature was raised to 80 C from 25 C and held for a 30-min dwell (Dwell-1), and then was raised to 130 C for a 60-min dwell (Dwell-2) during the first heating cycle. After a period of cooling, the temperature was raised to 80 C again for a 30-min dwell (Dwell-3), and then was raised to 130 C for a 10-min dwell (Dwell-4) during the second heating cycle. Natural cooling was adopted during the entire cure cycle. The second heating cycle and natural cooling can help to reduce the stress concentration and improve the monitoring stability of FBG sensors. The temperature cycle was applied to the top and bottom surfaces of the CFRP laminate. The initial temperature and cure degree for this study were chosen as 25 C and 0, respectively, and the fabrication pressure was set to be 0.5 MPa. The cure kinetic formula for YPH-308 epoxy was determined based on e previous work [33]:
da=dt ¼ expð0:65 1000=T 1:52Þ a0:49 ð1 aÞ1:89 (20) The corresponding finite element model was established in ABAQUS with the same geometry, material system and temperature condition as described above for TR50S/YPH-308 material. The element type of finite element analysis was chosen to be C3D20R. The unrelaxed material properties of TR50S/YPH-308 are listed in Table 1. The relaxation time tm(ar) and the weight factor Wm at the reference cure degree are shown in Table 2.
4. Results and discussion 4.1. FBG monitoring of material temperature evolution Fig. 4. Interlaminar normal stress (s3) distribution at x ¼ 0 and z ¼ 0 during cooling stage.
and is affected by the thermal expansion of the grating itself as well as chemical shrinkage and thermal expansion of the resin around the grating. In this work, the FBG temperature sensor is laid adjacent to the FBG strain sensor in order to decouple the effect caused by the thermal expansion of the grating on the FBG strain sensor, and hence the axial strain ε from the resin around the grating can be attained from the measured wavelength shift by combining Eqs. (18) with (19). 3. Experimental The laminate analyzed in this paper consisted of 22 plies of TR50S/YPH-308 prepreg with the lay-up type of [9011/011] and dimensions of 300 mm 300 mm 2.75 mm. During the stacking process of TR50S/YPH-308 prepregs, the FBG temperature sensor (FBG-T) and FBG strain sensor (FBG-S) were longitudinally embedded between the 17th and 18th plies along the central axis of the 17th ply and were 75 mm distance from the edge of the laminate. The schematic diagrams of CFRP laminate and embedded FBG sensors are presented in Fig. 5. In Fig. 5(a), the quarter geometry of CFRP laminate with the sizes of a0 ¼ 150 mm, b0 ¼ 150 mm and c0 ¼ 1.375 mm is symmetrical with respect to the x-axis and y-axis. For convenience, the point M in Fig. 5(a) is used to represent the
The spectra of embedded FBG temperature and strain sensors before and after the fabrication process are presented in Fig. 6. It can be observed that there is no evident distortion from all the spectra, which implies that the data obtained from embedded FBG sensors is accurate and reliable. The relative shift in central wavelength on account of thermal expansion and resin chemical shrinkage can be seen from the arrows indicated in Fig. 6. The evolution of material temperature monitored by FBG-T is plotted in Fig. 7. It is clear that the temperature evolution exhibits evident undulation in all dwells, and the maximum temperature reaches 146 C in Dwell-4, which is 16 C higher than the preset temperature (130 C). The temperature undulation can be attributed to two main factors. The first is the internal heat generation due to the resin curing reaction, and the second is that the programmed temperature control of industrial devices leads to multiple heating and cooling cycles for the purpose of heat preservation. The temperature undulation in Dwell-2 is induced by the two factors, while the temperature undulation in Dwell-1, Dwell-3 and Dwell-4 is mainly affected by the second factor. Because of good accuracy and reliability of FBG-T as well as the fact that FBG-T is only affected by the temperature, FBG-T is a much more accurate and convenient approach to obtain the actual temperature evolution including the temperature undulation in the CFRP laminate than the traditional temperature testing devices. Therefore, the temperature monitored by FBG-T can be considered as the actual temperature of the CFRP laminate.
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291
Fig. 5. Schematic diagrams of CFRP laminate and embedded FBG sensors. (a) Quarter geometry of CFRP laminate which is symmetrical with respect to the x-axis and y-axis; (b) locally amplified sectional drawing of FBG-T and FBG-S.
Table 1 Unrelaxed material properties of TR50S/YPH-308 prepregs [13]. Property
Value
E1 (GPa) E2 ¼ E3 (GPa) G12 ¼ G13 (GPa) G23 (GPa) n12 ¼ n13
129.6 8.5 4.2 3.21 0.27 0.32 0.5 34.2 167.0 8810.0
n23
CTE1 (mε/ C) CTE2 ¼ CTE3 (mε/ C) CCS1 (mε) CCS2 ¼ CCS3 (mε)
Table 2 Relaxation times and weight factors at the reference cure degree (ar ¼ 0.98) [13]. m
tm (min)
Wm
1 2 3 4 5 6 7 8 9
29.2 2.92e3 1.82e5 1.10e7 2.83e8 7.94e9 1.95e11 3.32e12 4.92e14
0.059 0.066 0.083 0.112 0.154 0.262 0.184 0.049 0.025
4.2. FE analysis on thermocuring process In order to simulate the evolution of cure degree, strain and stress of the CFRP laminate, the actual temperature monitored by FBG-T is imported into ABAQUS as the temperature condition of the FE analysis on the thermocuring process. Also, since the laminate is thin enough and the temperature cycle is only applied on the top and bottom surfaces during the fabrication of the laminate, the temperature along the thickness and in-plane direction is considered uniform during the FE modelling process. The evolution of the cure degree at the point M is obtained from FE analysis and depicted in Fig. 7. It can be clearly seen that the resin curing reaction occurs mainly in Dwell-2 with a sharp increase in the cure degree. Meanwhile, the cure degree also shows a small increase in
Dwell-1 and Dwell-4. The evolution of the simulated strain and stress along the reinforcing fiber direction at the point M is plotted in Fig. 8, from which the comprehensive effects of thermal expansion and chemical shrinkage on the evolution of residual strain and stress can be seen. At first, the resin curing reaction develops slowly, and the overall strain behaves as the tensile strain mainly affected by the thermal expansion. Later, due to the rapid curing reaction in the procedure Dwell-2, the chemical shrinkage strain plays a dominant role and the overall stain gradually behaves as the compressive strain. As the curing reaction is gradually completed, the thermal expansion strain dominates again and the overall strain evolution becomes synchronous with the temperature evolution. The simulated stress follows a similar evolution trend to the simulated strain. Also, it should be noted that there is a small strain and stress undulation at about 98 min in Fig. 8, which is generated on account of the temperature undulation, considering that the cure degree is large enough at about 98 min and the effect of the chemical shrinkage on the strain and stress evolution is relatively weak. Fig. 9 illustrates the distribution of simulated strain and stress along y ¼ 0 in the 17th ply at a ¼ 0.6, 0.8, 0.96 (at the end of cure cycle). It can be seen that the strain and stress behave as the tensile strain and stress at a ¼ 0.6 but later as the compressive strain and stress at a ¼ 0.8 and 0.96. Compared with the strain and stress at a ¼ 0.6 and 0.8, the strain and stress at the end of cure cycle (a ¼ 0.96) exhibit noticeable increase, which is mainly due to the effect of cooling. Additionally, Fig. 9 shows the uniformity of strain and stress distribution along the reinforcing fibers, which corresponds to the uniform temperature distribution in the in-plane direction. 4.3. Evaluation of material strain monitored by FBG Given that the differential viscoelastic model and corresponding finite element codes used in this work have been well validated, the simulated strain is believed to effectively characterize the strain evolution of the CFRP laminate. Therefore, the strain monitored by FBG-S can be evaluated by comparison with the simulated strain. The strain comparison between FBG test and FE simulation during the entire cure cycle is presented in Fig. 10. The monitored strain shows a distinct difference from the simulated result. First, there is no obvious strain variation from the monitored
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Fig. 6. Spectra of FBG sensors before and after the fabrication process of CFRP laminate.
Fig. 7. Evolution of monitored temperature and simulated cure degree during the entire cure cycle.
Fig. 8. Evolution of simulated stress and strain at the point M during the entire cure cycle.
Fig. 9. Distribution of simulated strain and stress along y ¼ 0 in the 17th ply at a ¼ 0.6, 0.8, 0.96.
Fig. 10. Strain comparison between FBG test and FE simulation during the entire cure cycle.
Q. Wang et al. / Polymer Testing 62 (2017) 287e294
strain at the early stage of cure. This can be related to the low resin viscosity, which results in a relatively weak bond strength between the resin and FBG-S as well as poor efficiency of strain transfer from the resin to FBG-S. Second, in Dwell-2, the monitored strain exhibits frequent undulation rather than rapid development as the simulated strain, which is caused by the following reasons. As shown in Fig. 7, with the resin cure degree in Dwell-2 increasing rapidly, the bond strength between the resin and FBG-S is becoming larger and larger. Hence, the movement of air and vapor bubbles under the conditions of high temperature and pressure can be detected more and more sensitively by the FBG-S in the form of strain undulation. Also, when the bond strength between the resin and FBG-S is strong enough, the thermal strain of the resin caused by the temperature undulation can be effectively transferred to the FBG-S grating, and then can contribute to the undulation of the monitored strain, which is also slightly reflected from the undulation of the simulated strain at about 98 min. According to the evolution characteristic of the resin cure degree shown in Fig. 7, it can be concluded that effective interfacial bond between the resin and FBG-S can be established in Dwell-2 and the chemical shrinkage strain of the resin can be effectively transferred to FBG-S. However, the frequent undulation of the monitored strain in Dwell-2 makes the chemical shrinkage strain unnoticeable. At the end of the cure cycle, the monitored strain is much smaller than the simulated strain, mainly because of the absence of the early chemical shrinkage strain from the monitored strain. Since FBG-S cannot effectively monitor the strain evolution in Dwell-1 and Dwell-2, it is a reasonable choice to eliminate the effect of the early strain and then only compare the monitored strain with simulated strain after Dwell-2. Here, given that no apparent temperature undulation is noticed again and the strain evolution is also relatively stable after 125 min (onset of first cooling process), the strain at 125 min is chosen as the reference strain. The changes of monitored and simulated strains after 125 min with respect to the respective reference strain are shown in Fig. 11. The changes of the monitored strain develop faster than the simulated results at first, but later good agreement between the monitored and simulated strain changes is achieved. The faster development in the monitored strain changes can be explained by the fact that the chemical shrinkage strain in Dwell-2 is not displayed clearly as a
Fig. 11. Monitored and simulated strain changes after 125 min with respect to the respective reference strain.
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result of the frequent strain undulation, as described above, but it takes effect during the first cooling process. 5. Conclusions (1) The monitored temperature by the FBG sensor can reflect the actual temperature evolution of the CFRP laminate, and can be used as the temperature condition of the numerical analysis on the thermocuring process, which can significantly simplify the FE analysis on the whole thermocuring process. (2) The three-dimensional differential viscoelastic model combining the effects of cure degree, thermal expansion, chemical shrinkage and stress relaxation is established and well verified, and then the evolution of cure degree, strain and stress of the CFRP laminate during the entire cure cycle is analyzed. The simulated strain can serve as the reference to evaluate the monitored strain by FBG sensor. (3) The monitored strain by the FBG sensor cannot accurately characterize the actual strain evolution of the CFRP laminate at the early stage of cure as a result of low resin viscosity, movement of air and vapor bubbles as well as temperature undulation. However, when the resin/grating interfacial bond strength increases enough to transfer resin strain effectively, the changes in the monitored strain achieve good agreement with the actual strain changes of composite laminates. Acknowledgements This work was supported by the National Natural Science Foundation of China (51373090), the China-EU Co-funded Project (MJ2015-HG-103, Horizon 2020-690638), the National Key Basic Research Program of China (JCKY2016205B007), and the Natural Science Foundation of Shandong Province (ZR2014EL013). References [1] Y.K. Kim, S.R. White, Viscoelastic analysis of processing-induced residual stresses in thick composite laminates, Mech. Compos. Mater. Struct. 4 (1997) 361e387. [2] Y. Miao, J. Li, Z. Gong, J. Xu, K. He, J. Peng, Y. Cui, Study on the effect of cure cycle on the process induced deformation of cap shaped stiffened composite panels, Appl. Compos. Mater. 20 (2013) 709e718. [3] R. Joven, B. Tavakol, A. Rodriguez, M. Guzman, B. Minaie, Characterization of shear stress at the tool-part interface during autoclave processing of prepreg composites, J. Appl. Polym. Sci. 129 (2013) 2017e2028. [4] Y. Nawab, S. Shahid, N. Boyard, F. Jacquemin, Chemical shrinkage characterization techniques for thermoset resins and associated composites, J. Mater. Sci. 48 (2013) 5387e5409. [5] J. Sun, Y. Gu, Y. Li, M. Li, Z. Zhang, Role of tool-part interaction in consolidation of L-shaped laminates during autoclave process, Appl. Compos. Mater. 19 (2012) 583e597. [6] O.G. Kravchenko, C. Li, A. Strachan, S.G. Kravchenko, R.B. Pipes, Prediction of the chemical and thermal shrinkage in a thermoset polymer, Compos. Part A Appl. Sci. Manuf. 66 (2014) 35e43. [7] A.S.D. Wang, F.W. Crossman, Edge effects on thermally induced stresses in composite laminates, J. Compos. Mater. 11 (1977) 300e312. [8] K.S. Kim, H.T. Hahn, Residual stress development during processing of graphite/epoxy composites, Compos. Sci. Technol. 36 (1989) 121e132. [9] A.A. Johnston, An Integrated Model of the Development of Process-induced Deformation in Autoclave Processing of Composites Structures, The University of British Columbia, Vancouver, 1997. [10] J. Li, X. Yao, Y. Liu, Z. Cen, Z. Kou, X. Hu, D. Dai, Thermo-viscoelastic analysis of the integrated T-shaped composite structures, Compos. Sci. Technol. 70 (2010) 1497e1503. [11] S. Clifford, N. Jansson, W. Yu, V. Michaud, J.A. Månson, Thermoviscoelastic anisotropic analysis of process induced residual stresses and dimensional stability in real polymer matrix composite components, Compos. Part A Appl. Sci. Manuf. 37 (2006) 538e545. [12] J. Magnus Svanberg, J. Anders Holmberg, Prediction of shape distortions Part I. FE-implementation of a path dependent constitutive model, Compos. Part A Appl. Sci. Manuf. 35 (2004) 711e721.
294
Q. Wang et al. / Polymer Testing 62 (2017) 287e294
[13] S.R. White, Y.K. Kim, Process-induced residual stress analysis of AS4/3501-6 composite material, Mech. Compos. Mater. Struct. 5 (1998) 153e186. [14] A. Ding, S. Li, J. Wang, L. Zu, A three-dimensional thermo-viscoelastic analysis of process-induced residual stress in composite laminates, Compos. Struct. 129 (2015) 60e69. [15] N. Zobeiry, R. Vaziri, A. Poursartip, Differential implementation of the viscoelastic response of a curing thermoset matrix for composites processing, J. Eng. Mater. Technol. 128 (2006) 90e95. [16] K.T. Lau, Structural health monitoring for smart composites using embedded FBG sensor technology, Mater. Sci. Technol. 30 (2014) 1642e1654. [17] G. Lubineau, Estimation of residual stresses in laminated composites using field measurements on a cracked sample, Compos. Sci. Technol. 68 (2008) 2761e2769. [18] R. de Oliveira, C.A. Ramos, A.T. Marques, Health monitoring of composite rot sensors, Comstructures by embedded FBG and interferometric Fabry-Pe put. Struct. 86 (2008) 340e346. [19] K.S.C. Kuang, R. Kenny, M.P. Whelan, W.J. Cantwell, P.R. Chalker, Embedded fibre Bragg grating sensors in advanced composite materials, Compos. Sci. Technol. 61 (2001) 1379e1387. [20] K.T. Lau, L.M. Zhou, The mechanical behaviour of composite-wrapped concrete cylinders subjected to uniaxial compression load, Compos. Struct. 52 (2001) 189e198. [21] A. Lamberti, G. Chiesura, G. Luyckx, J. Degrieck, M. Kaufmann, S. Vanlanduit, Dynamic strain measurements on automotive and aeronautic composite components by means of embedded fiber Bragg grating sensors, Sensors 15 (2015) 27174e27200. [22] C. Yilmaz, C. Akalin, E.S. Kocaman, A. Suleman, M. Yildiz, Monitoring Poisson's ratio of glass fiber reinforced composites as damage index using biaxial fiber Bragg grating sensors, Polym. Test. 53 (2016) 98e107. [23] K.S.C. Kuang, R. Kenny, M.P. Whelan, W.J. Cantwell, P.R. Chalker, Residual
[24]
[25]
[26] [27]
[28]
[29] [30]
[31]
[32]
[33]
strain measurement and impact response of optical fibre Bragg grating sensors in fibre metal laminates, Smart Mater. Struct. 10 (2001) 338e346. A. Riccio, F. Di Caprio, F. Camerlingo, F. Scaramuzzino, B. Gambino, Positioning of embedded optical fibres sensors for the monitoring of buckling in stiffened composite panels, Appl. Compos. Mater. 20 (2013) 73e86. G. Pereira, M. McGugan, L.P. Mikkelsen, Method for independent strain and temperature measurement in polymeric tensile test specimen using embedded FBG sensors, Polym. Test. 50 (2016) 125e134. T.A. Bogetti, J.W. Gillespie, Process-induced stress and deformation in thicksection thermoset composite laminates, J. Compos. Mater. 26 (1992) 626e660. S.R. White, H.T. Hahn, Process modeling of composite materials: residual stress development during cure. Part I. Model formulation, J. Compos. Mater. 26 (1992) 2402e2422. D. Roylance, Engineering Viscoelasticity, 2139, Department of Materials Science and Engineering-Massachusetts Institute of Technology, Cambridge MA, 2001, pp. 1e37. Y.K. Kim, S.R. White, Stress relaxation behavior of 3501-6 epoxy resin during cure, Polym. Eng. Sci. 36 (1996) 2852e2862. E. Marin, L. Robert, S. Triollet, Y. Ouerdane, Liquid resin infusion process monitoring with superimposed fibre Bragg grating sensor, Polym. Test. 31 (2012) 1045e1052. S.N. Economidou, D. Karalekas, Optical sensor-based measurements of thermal expansion coefficient in additive manufacturing, Polym. Test. 51 (2016) 117e121. M. Mulle, H. Wafai, A. Yudhanto, G. Lubineau, R. Yaldiz, W. Schijve, N. Verghese, Process monitoring of glass reinforced polypropylene laminates using fiber Bragg gratings, Compos. Sci. Technol. 123 (2016) 143e150. L. Zeng, L. Zhan, Cure kinetics of YPH-23 carbon fiber/epoxy prepreg by isothermal method, New Chem. Mater. 44 (2016) 193e195 (in Chinese).