Cure strain monitoring in composite laminates with distributed optical sensor

Composites Part A 125 (2019) 105503

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Composites Part A journal homepage: www.elsevier.com/locate/compositesa

Cure strain monitoring in composite laminates with distributed optical sensor

T

Jung-Ting Tsaia, Joshua S. Dustind, , Jan-Anders Manssona,b,c,d ⁎

a

School of Materials Engineering, Purdue University, 701 West Stadium Avenue, West Lafayette, IN 47907, United States School of Aeronautics and Astronautics, Purdue University, 701 West Stadium Avenue, West Lafayette, IN 47907, United States c School of Chemical Engineering, Purdue University, 701 West Stadium Avenue, West Lafayette, IN 47907, United States d Composites Manufacturing & Simulation Center (CMSC), Purdue University, 1105 Challenger Av., Suite 100, West Lafayette, IN 47901, United States b

ARTICLE INFO

ABSTRACT

Keywords: A. Laminate A. Smart materials B. Cure behavior D. Non-destructive testing

Measuring the strain history in pre-impregnated thermoset composites during the curing process provides valuable data for manufacturing specification development, quality control, diagnostics of dimensional stability, and validation of cure models. Distributed Optical Sensors (DOS) provide information along the entire optical path length of the sensor embedded in the laminate and present a promising high-resolution sensing option for in-situ strain measurement. This study’s contribution to the field is the coupling of the optical sensor monitoring of composite cure strain with models of the cure kinetics, viscosity, and glass transition temperature of the thermoset matrix. A unidirectional (UD) laminate and a structural laminate (SL) were manufacture embedded with an optical sensor. The internal residual strain developed during each stage of the thermal cure cycle is examined for both laminate types, including after cooling, and the models of the resin’s physical property development were used to facilitate interpretation of the strain measurement data from the DOS.

1. Introduction Optical fiber sensors for structural monitoring are found in the aerospace, automotive, infrastructure, pressure vessels, sports and wind turbine industries [1,2]. A natural use of these sensors in laminated composite structures involves embedding optical fibers in structural composite materials during processing and cure, which provides a straightforward method to monitor the curing process and quantify effects such as cure shrinkage and thermal residual deformation. Several review papers have previously discussed the application of optical sensors in structural materials monitoring [3,4] where most studies have focused on Fiber Brag Grating (FBG) to monitor the curing shrinkage and stiffness change in the composite plies [5,6]. For example, Minakuchi [7] monitored the curing process of both a unidirectional, symmetric cross-ply laminate, and fabric laminate with FBG sensors embedded in parallel and perpendicular directions to the fiber direction in the plies. Kang, Kang [8], developed a process to monitor the direction-dependent cure shrinkage of a unidirectional laminate in an autoclave. Yoo, Han [9], simulated the curing process of a carbon/ epoxy composite using embedded FBG and further validated with a finite element model. Sorensen, Gmür [10] utilized FBG to measure the residual strain developed in the process of hot-pressing thermoplastic

⁎

composite materials. In FBG, strain measurement is limited to only the grating location in the optical sensor, so the spatial resolution of these sensors is quite restricted. There can be multiple gratings in an optical sensor, but the process for adding these gratings is expensive, thus limiting the use in many industrial applications [3,11]. A detailed research of fabricating FBG can be found in Cusano, Paladino [12]. Most of the studies of process monitoring involving FBG sensors lack the theoretical analysis of cure history dependent strains to validate strain measurements during cure so it is difficult to isolate measurement artifacts from actual experimentally observed phenomena [8,9,13,14]. The detailed high-resolution data obtained experimentally from a Distributed Optical Sensor (DOS) requires the complementary theoretical analysis to interpret/understand the local variability of sensor readings, as the coherent interpretation of sensor readings is imperative to improve the strain measurements. Without recognizing the epoxy curing mechanism producing the strain, many experimental factors may be erroneously neglected without recognition by the end uses. Other factors such as the strain transfer from the laminate to the embedded FBG are also widely studied [15–21]. Based on the shear lag model, the mechanical properties of the fiber core, the coating layer, and the host materials dictate the strain transfer and resulting strain measurement of the FBG sensor. While the effect of shear lag is well

Corresponding author. E-mail address: [email protected] (J.S. Dustin).

https://doi.org/10.1016/j.compositesa.2019.105503 Received 13 February 2019; Received in revised form 6 May 2019; Accepted 26 June 2019 Available online 27 June 2019 1359-835X/ © 2019 Published by Elsevier Ltd.

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Fig. 1. (a) The DOS cross-section (b) The DOS stretched mechanism. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

understood for its effect on the final magnitude of the measured strain, the main focus of this study is to investigate the feasibility of applying DOS in-situ to evaluate the evolution of strain during composite laminate cure. Compensating measurements for any potential shear lag effects near laminate free edges during the curing process could be a promising area for future research. Previously, Montanini and D’Acquisto [22] used an FBG system to observe the temperature and strain changes in a glass fiber/epoxy system. They showed by using an optical sensor that the reflection of a wave varies under different temperatures and the temperature can be different between the layers. Sanchez et al. [23] used a DOS to monitor resin infusion, the in-situ strain development, and changes in resin viscosity, but the curing mechanisms were not explained extensively from the DOS readings. In discussing the residual strain, the authors have not explained the fluctuation of the local strain reported by the optical sensor. Arhant et al. [24] monitored the curing mechanism during a hot press cycle. Meadows et al. [25] monitored the strains in an adhesive layer in composite joint specimens with DOS. Notwithstanding, the use of DOS to monitor the curing mechanisms has not been thoroughly studied. DOS sensors are classified by the techniques used to analyze and reduce the optical data, including Rayleigh scattering, Raman scattering, and Brillouin scattering. Rayleigh scattering corresponds to the strongest intensity range among all three and unlike the inelastic Raman and Brillouin scattering, is an elastic scattering that statically fluctuates along the distance. Elastic scattering produces a linear output from a proportional input power, giving the advantage of detecting the deformation of heterogeneous materials since the proportional response is easier to interpret [4]. Traditionally, Optical Time Domain Reflectometry (OTDR) has been employed to acquire and analyze the data from the scattering mechanisms in the telecom field. OTDR technology is limited by a spatial resolution of 0.1–1 m, which produces the corresponding attenuation of the output wavelengths. The uncertainty of measurements and low resolution inherent to OTDR does not make it a suitable choice for the health monitoring of composite structures. Optical Frequency Domain Reflectometry (OFDR) was developed to overcome these spatial resolution limitations of OTDR. OFDR’s high spatial resolution of 1 µm allows the sensor to be more accurate during monitoring. Distributed optical sensing relies on the detection of the Rayleigh scattering using OFDR, which allows a more efficient and accurate measurement for strain and temperature. Through the use of Rayleigh scattering and OFDR, DOS provides exciting advantages in the area of stain measurement for composite structures including high spatial resolution, easy integration into composite structure, low-cost sensors made of commercially available glass fiber, high measurement

sensitivity, and simultaneous strain measurement along the entire sensor length [26–30]. The fundamentals of the physics of the DOS sensors is outlined in the following. An input wavelength, which is introduced by the tunable laser is separated into a measurement and reference path [4]. The input wavelength travels into the measurement path which later receives the reflection of the wavelength from the sensor. The wavelength is then again combined with the reference path at the coupler. The combined signal then goes through the beam splitter which split the light into orthogonal states, which are recorded in S and P detectors. To calculate the magnitude of the strain or temperature, a comparison of the measured and reference states is performed. The amplitudes of the reference and measurement paths are plotted using a complex Fourier transformation. However, an inverse of the Fourier transformation must be calculated to give the distinct location of the signal along the distance. The position of a defect (e.g. a local gage length) in the optical sensor is then cross-correlated using a calibration coefficient to obtain the local strain and temperature values. This process is continued throughout the entire path of the optical sensor. Thus, the final strain distribution can vary with the thermal history or the deformation along the path of the DOS. The DOS fiber sensors are small, lightweight, resistant to electromagnetic interference, and can be embedded inside or attached to the surface of any material. Fig. 1(a) shows a cross section of an optical fiber sensor, which consists of an inner-core, cladding, and protective coating. The inner-core and cladding have different optical reflection coefficients to prevent wave refraction which causes signal attenuation. The coating increases the flexibility of the sensor, allowing it to conform to complex curvatures. Distributed Optical Sensors (DOS) have no grating, instead they use the internal flaws in the sensor material formed during production to create measuring reference points along the continuous distance of the fiber. Fig. 1(b) schematically shows the distribution of defects along the length of the optical fiber in undeformed and deformed configurations [26]. The defects act as distributed strain gauges which can experience different local deformations, such as ( 1 0 ) shown in Fig. 1(b). A local deformation leads to a shift in an optical frequency spectrum registered by OFDR. A novel application using a DOS embedded in a UD and SL (structural laminate) for measuring chemical and thermal residual strain is explored in this research. The strain results from the DOS were mapped along the path of the DOS to provide an understanding of the local variability. The DOS readings were superimposed with the thermal history, degree of cure (DoC) and glass transition temperature (Tg) to better understand the underlying mechanism of resin cure on strain field development. A micromechanical model was implemented to 2

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Note: Yellow line is the DOS and orange line is the thermal couple

(a)

(b)

Fig. 2. Schematics of embedment of the DOS into (a) Unidirectional (UD) laminate (b) Structural laminate (SL). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

further understand the experimental trend. Lastly, residual strain was measured by the DOS and validated with composite laminate plate theory (CLPT).

ingress/egress region of the laminate material for later mechanical testing. Consider point A and point B shown in Fig. 3. Both the laminate and the DOS expand or contract during temperature changes. Accurate measurement of the laminate strain requires accounting for the DOS sensor thermal expansion. Because the CTE of the DOS and the laminate are in general different, the total strain reported by the DOS has both thermal and mechanical components. Thermal effects can be separated from the total strain acquired by the DOS using the following equation:

2. Manufacturing of composite material specimens with Distributed optical sensor Fig. 2(a) and (b) shows the placement of the DOS sensor in the UD laminate and SL. In the UD laminate, the sections of the sensor were aligned with both the 0- and 90-degree directions, while in the SL the sensor was embedded between [90°/45°], [0°/0], and [45°/0°] plies and oriented parallel to the 0-degree direction. A small opening was slit in each ply parallel to the fibers so that that the DOS could be routed to the adjacent layers. The dimensions of the SL [45°/0°/0°/−45°/90°/ 45°/0°/0°/−45°/0°]s were 305 mm × 51 mm and the dimensions of UD laminate [0]20 were 127 mm × 127 mm. The composite laminate was placed onto a 356 mm × 356 mm × 3.18 mm tool shown in Fig. 3. To ensure stability, the DOS was secured with tape to the aluminum plate. The laminates were then placed into the vacuum bag and sealed. After layup and insertion of the DOS sensor, the laminates were debulked for 30 min to ensure that no air was trapped within the laminate. Also, two k-type thermocouples were installed: one attached close with the DOS in the oven chamber and the other embedded within the laminate. The ingress and egress regions of the optical sensor were protected with composite tape. The optical sensor, thermal couple, and vacuum line were routed through an open hole in the oven chamber designed to accommodate pass-through items. Strain data was recorded using the OFDR via an interrogator and the distributed strain data was acquired throughout the optical sensor location. The acquisition rate was set to 23.8 Hz with gage length of 1.3 mm. This system can monitor the strain within the range of ± 10,000 micro-strains with a sensitivity of ± 25 micro-strains. The thermal couple was linked to the strain acquisition system to interpret the temperature analysis. The optical sensor signal was set to baseline before the vacuum was initiated so that no other factors would influence the measurements. When vacuum reached equilibrium, the thermal cycle recommended by the manufacturer was started. After cooling, the sample was removed from the chamber. The vacuum bag, silicon rubber, release film, and peel plies were disassembled. Extra tape was applied to protect the optical fiber at the

Laminate

=

DOS

(

DOS

T)

(1)

where Laminate is the laminate strain, DOS is the reading from the DOS, T is the DOS is the thermal expansion coefficient of the DOS, and temperature measurement from the thermocouple embedded in the laminate. The DOS is manufactured with a polyimide coating for sensor protection. The polyimide CTE is temperature dependent, and the overall thermal coefficient of the DOS was measured between the range of 7.3 9.9 µ / C over the temperature range of the cure cycle with some small but expected batch to batch variability. In this study, calculations and data reduction were performed assuming an average constant thermal coefficient of8 µ / C. In the local regions of the laminate, T varies from ply to ply. However, the distance between the DOS in the AB section and the CD section is 0.9 mm (6 plies of thickness) in the UD laminate. While the heating rate is 1 °C/min, it was assumed that given the slow heating rate and small thickness that any effect of temperature gradient was negligible. For thicker parts and faster heating rates, the variability of heat conduction between the tool and the laminate could result in strain variation during the temperature ramp depending on the sensor location through the thickness of the laminate. 3. Modeling of a cure-induced deformation in a composite laminate 3.1. Constitutive modeling of laminate during the cure cycle During the manufacturing thermal cycle, a laminate undergoes deformations caused by the cure and thermal shrinkage of the resin. To observe the cure-induced strains, the 22 strain within a UD laminate is tracked and the cure shrinkage and thermal expansion components are isolated through analysis. The analysis of the transverse strain due to 3

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Fig. 3. Preparation of experiment assembly for UD and SL (structural laminate). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

cure shrinkage, 22 ( ) , and thermal expansion, 22 ( T ) , resulting from the advancement of the degree of cure, , and the temperature change, T , is outlined in the following. Unconstrained cure and thermal shrinkage strain changes in a UD laminate are calculated using Eq. (2) 11 22

=

33

11

T

11

22

T

22

33

T

33

The chemical shrinkage equations were derived using the same methods from Eq. (3) and Eq. (7) which are expressed as (6) in the longitudinal direction to the fiber and (7) for the transverse direction:

(2)

=

22

=

1f

E1f f f +

33

=(

2f

+ v12f

) f f + (1 + Vm)

m fm

V12

11

(4)

6.58·T ( C) + 3701

33

d = K1 dt

where the subscript f and m denote fiber and matrix; f f and fm are the fiber and the matrix volume fractions; E1f and Em are the longitudinal direction of the fiber’s modulus and the modulus of the epoxy; and v12 is the fiber’s Poisson ratio. The epoxy modulus Em (T ) changes as a function of temperature T [32], as given by Eq. (5):

Em (T ) =

=

= (1 + Vm )

(6) m fm

V12

(7)

11

The degree of cure from the cure kinetic model are superimposed onto the DOS reading. This aids in understanding the epoxy behavior throughout the thermal history. The Cole, Hechler [34] model and the Kamal and Sourour [35] model were combined to form the cure kinetic model, as given in Eq. (8):

(3) 1f

22

m Em fm

E1f f f + Em fm

3.2. Models for cure-kinetic, viscosity, and glass transition temperature

m Em fm

E1f f f + Em fm

=

where 11 and 22 is the homogenized chemical shrinkage coefficients, and the m is the epoxy chemical shrinkage coefficient. The values for the material properties are provided in the Appendix. In addition, the epoxy chemical shrinkage coefficient is 0.022 [33].

with 23 = 13 = 12 = 0 and where 11, 22, 33 are the lamina effective coefficients of thermal expansion (CTE) and 11, 22, 33 are the lamina effective coefficients of chemical (cure) shrinkage. Schapery’s theory [31] was used to obtain the homogenized (effective) CTE and chemical shrinkage coefficients of a lamina from the fiber and resin properties. The equations for the CTE in the longitudinal direction, 11 and the transverse direction 22, and 33 are shown in Eqs. (3) and (4). 11

11

0

m1

(1

0)

n1

+

K2

0

m2

1 + exp (D (

(1 0

0)

(

c0

n2

+

cT )))

(8)

where is the degree of conversion, t is the time, m1, m2, n1, and n2 are the first and second exponential constants, c0 is the critical degree of cure at absolute zero, cT is the degree of cure with increasing temperature, and D is the diffusion constant. K1 and K2 are material dependents. In addition, the Arrhenius temperature dependency is provided

(5) 4

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K = Aexp(

EA ) RT

the glass transition temperature of cured resin, a is constant, and is the degree of cure. Fig. 4 also presents the glass transition temperature plotted along with the time-temperature history. The glass transition temperature increases as a function of the degree of cure. The epoxy vitrified once passing the glass transition temperature, approximately 329 min into the cure cycle at a temperature of 175.6 ℃.

(9)

where EA is the activation energy, A is a constant number, R is the universal gas constant, and T is the absolute temperature. It is assumed the degree of cure at 0 starts at 0.001. Therefore, using Eq. (8) with the increase of time, thusly acquires the degree of cure with the following thermal cycle time:

=

+

0

(t

(10)

t 0)

3.3. Modeling of a residual strain deformation in a composite laminate

Modeling the viscosity of the thermoset material provides insight when the DOS might be bonded in the composite laminate due to the ability of the sensor to bond to the matrix. Higher viscosity means the DOS has a higher chance of attaching to the laminate while lower viscosity means the DOS may be unattached in the laminate. The Castro and Macosko [36] resin viscosity model, as given in Eq. (11) was used in this work to simulate the thermoset viscosity:

=

1

+

2(

gel

2 ) A +B +C

E i

i

= A iexp( RT ) , i = 1, 2

{ }=

gel i

Tg

Tg 0 Tg 0

=

1

(1

)

1

N + NT M + MT

(14) n i=1

Qi ( e)i ti ) T and MT = ( Qi ( e )i ti Z¯i ) T . Where where NT = ( is strain is curvature, A is the extension stiffness matrix, B is the extension-bending coupling stiffness matrix, and D is the bending stiffness matrix. Furthermore ti is the thickness of each ply, Z¯i is the thickness coordinate from the laminate midplane to center of each ply, and Qi is the plane-stress reduced stiffness matrix. In this case, B = 0 because the laminate is symmetric. There is no coupling between extension and bending. The thermoelastic constitutive relations need to be considered if there are temperature changes. (In this case, MT will be zero, there are no thermomechanical moments due to a temperature changes) Therefore, we have (15):

is the is the (12)

where E i is the activation energy, A i is the pre-exponential cure rate coefficient, R is the universal gas constant, and T is the absolute temperature. Although the model is used for isothermal temperature evolution, it gives an idea of how the viscosity develops at the beginning of the thermal cycle. The viscosity evolution is detailed in Fig. 4. Initially, the viscosity decreases once the temperature rises. The viscosity reaches a minimum 275 min into the cure cycle, this is when the degree of cure begins to exponentially increase. Thus, it can be assumed before 275 min of the cure cycles, the DOS does not respond to any laminate strain because of the low resin viscosity. Once the degree of cure passes 0.55 (the gelation point), the viscosity is sufficiently high so that the sensor is completely bonded to the laminate matrix. The glass transition temperature (Tg) model is developed by DiBenedetto [37], shown in Eq. (13):

Tg

A B B D

n i=1

(11)

gel

where is the viscosity, is the degree of cure from Eq. (10), degree of cure at gelation, A,B,C are constant numbers, and Arrhenius temperature dependency, as given in Eq. (12).

After homogenizing the material properties, the CLPT [38] was implemented to calculate the axial and the transverse strain in the laminate. In this case, the strain is calculate using Eq. (14):

= A 1 (N + NT )

= D 1M

(15)

Thus, the in-plane 3D strains for each layer can be computed as (16): e

=

+ x3

(16)

4. Distributed sensing of cure-induced strains in a composite laminate 4.1. Cure monitoring in a UD laminate Fig. 5(a) reports the distribution of the DOS measured axial strain along the segment A-B, shown in Fig. 2(a), over the entire time-temperature history. The DOS measured axial strain, , along the segment A-B corresponds to the axial strain, 11, of the UD laminate, as this segment of the sensor is aligned with the laminate fiber direction. It can

(13)

where Tg0 is the glass transition temperature of the uncured resin, Tg is

Fig. 4. The viscosity data, DoC, Tg and thermal history. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 5

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Fig. 5. (a) Strain mapping at section A-B (b) Comparison of Tg, ε11, DoC, and thermal history at UD Laminate. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

be observed that strain does not vary substantially along the sensor length, providing a consistent measurement. Fig. 5(b) shows the correlation between the strain and the degree of cure, glass transition temperature, and temperature-time history at a single point (location of the point shown in Fig. 2(a)). The temperature profile was input into the cure kinetic Eq. (10) and glass transition temperature Eq. (13) to obtain the corresponding curves. The UD laminate has a near zero CTE and high modulus in the axial direction, as these properties are governed by the carbon fiber. Therefore, when the DOS is laid parallel to the fiber direction of the unidirectional plies, the axial strain reading shows very little strain variation. Although there are some variations of strain at the three regions of heat ramp, due to non-uniform temperature distribution through the laminate thickness during those times. After passing the gelation and vitrification points, the strain readings remain consistent. During the cool down stage, an increase in strain occurs which is attributable to the slightly-negative axial CTE of the carbon fiber. Fig. 6(a) shows the DOS microscopy image at the cross-section. A resin pocket is formed around the DOS at the C-D section in the UD laminate. Fig. 6(b) represents the DOS axial strain along the segment CD, shown in Fig. 2(a), over the entire time-temperature history. The DOS measured axial strain, ε, along the segment C-D corresponds to the transverse strain, ε22, of the UD laminate, as this segment of the sensor is perpendicular to the laminate fiber direction. It can be observed that the strain varies substantially during the thermal history. Fig. 6(c) shows the correlation between the UD laminate transverse strain (ε22) and the degree of cure, glass transition temperature, and temperaturetime history.

The thermal history consists of seven stages and the strain evolution is analyzed in every stage (Fig. 6(b)). During the first and second stages (first ramp and hold stages), the sensor reports effectively zero strain, because of the low viscosity of epoxy resulting in essentially no attachment between the DOS and the laminate material (shown in Fig. 4). At the third stage (second ramp), a small increase in strain was observed because of the thermal expansion of the laminate in the transverse direction. There are two strain spikes at stage one and stage three. As mentioned above, this is due to the temperature variation between the laminate and the DOS. At the fourth stage (second hold), the gel point is achieved when the degree of cure reaches approximately 0.55, after that point, the epoxy begins to cross-link to develop significant stiffness. However, the DOS at this stage may not be fully attached to the laminate. Therefore, the strain reading does not change. At the fifth stage (final ramp), the thermal expansion of epoxy and carbon fiber produce the increased strain which dominates the chemical shrinkage (compression) reported by the sensor. Moving on to the sixth stage (the final hold stage); the temperature at this stage passes the vitrification point, and the ongoing chemical shrinkage is captured by the DOS (DoC:0.78). Hence, at the peak temperature, the strain decreases asymptotically, approximately −2500 µ from the peak value. At the final stage, the stain fluctuates at the beginning of cooling. Researchers have observed similar results during cooling [23,39]. Some mechanisms which may contribute to the observed strain oscillation during cooling that could be related to the increase in epoxy modulus with reduced temperature or tool-part interactions during cooling due to CTE mismatch. The exact cause of the oscillation is still unknown and will be the subject of future study. However, after cooling to room

6

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Fig. 6. (a) The microscopy of the UD laminate interface at C-D section (b) Strain mapping at section C-D (c) Comparison of Tg, ε22, DoC, and thermal history at UD Laminate. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

temperature, the residual strain is consistent (approximately −5000 µ ). Fig. 7 shows the strain developed at the isothermal stage (stage six in Fig. 6) which is denoted as εch and compares with the change in DoC from the cure kinetic model. The range of DoC in this model was from 0.78 to 0.94, based on the prediction from the cure kinetics model for this cure cycle. This reflects the measurement from the DOS at the sixth stage of the cure cycle where a dramatic decrease in strain is observed in Fig. 6. As the experimental result show, the rate of DoC advancement slows down after passing the vitrification point, which is due to diffusion controlling the cure kinetics of the epoxy. Thus, the slope no longer linearly increases at approximately DoC 0.92. Nevertheless, a homogenized chemical shrinkage coefficient does capture the trend in the △DoC range of 0.27 to 0.39. For this material, we found the homogenized chemical coefficient is 0.0189. According to previous research, the epoxy chemical shrinkage follows a linear behavior [33]. This constant value is homogenized in Eq. (6) which is calculated as 0.0136, a difference of 3.8% was observed between the predicted and the experimentally measured homogenized chemical coefficient. This is

ch

ε = 0.0189△ξ - 0.0049

Fig. 7. Homogenized coefficient of chemical shrinkage in UD laminate. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

7

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Fig. 8. Comparison of Tg, ε22, DoC, and thermal history. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 9. The microscopy of the laminate interface.

Fig. 10. Mapping the three selected paths at [0°/45°], [0°/0°], and [90°/45°] ply interfaces in the SL. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

8

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Fig. 11. (a) Mapping residual strain at section C-D in UD; (b) Image of XRD scanning at UD Laminate. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

because Eq. (6) does not fully considered defects in the laminate such as voids, fiber orientation, and volume fraction inhomogeneity in the plies. Fig. 8 shows the theoretical transverse strain, ε22, of the UD laminate, along with the cure kinetic, and glass transition models plotted along with the temperature history. The theoretical value was calculated from Eq. (2) with the input values from Eqs. (4) and (7). The theoretical strain value was calculated when the DoC is above 0.78. As discussed in 4.1, the DOS reading was dominated by the thermal expansion in the transverse direction of the laminate. The calculated chemical shrinkage is approximately 2700 µ which agrees closely with the experimental result of approximately 2500 µ . During cooling, the epoxy modulus was considered as a function of temperature, as given by Eq. (5), for calculating the residual strain in Eq. (2). The theoretical value of the residual strain follows the trend of the experimental value. The final theoretical value for the residual strain is −4500 µ and the experimental value is in the range of −4800 to −5200 µ (Fig. 11(a)). This theoretical validation provides confidence that the DOS sensor measurements are in-line with expected results.

4.2. Cure monitoring in a structural laminate A cross sectional view in Fig. 9 shows the embedded sensor positioned along the [0°/45°], [0°/0°], and [90°/45°] interfaces of a structural laminate. Resin pockets are developed around the sensor, and the shape of a pocket and position of a sensor relative to the interface depend on the local stacking sequence of the laminate. The DOS embeds into the 0-degree ply in the [0°/45°]-interface but stays in-between the 0-degree plies in the [0°/0°]-interface due to the fibers oriented perpendicular to the sensor. A large elliptical shaped resin pocket is developed around the DOS in the [45°/90°] interface while the sensor itself remains in-between the adjacent plies. In the [0°/0°]-interface, the DOS experiences the most contact with the fibers, thus it is expected that the DOS provides a more constant strain signal from the carbon fiber expansion and contraction. Fig. 10(a) shows the DOS axial strain along the three selected paths (l,ll, and lll), shown in Fig. 2(b), over the entire time-temperature history. The DOS axial strain, ε, along the three selected paths corresponds to the axial strain, εxx, of the SL, as this segment of the sensor is parallel to the laminate global x-direction. The strain fluctuations along the

9

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Fig. 12. Mapping residual strain along the [0°/45°], [0°/0°], and [90°/45°] ply interfaces in the SL. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

sensor length are caused by the locally variable laminate microstructure, such as fiber volume fraction variation, voids, and resin pockets (shown in Fig. 9). Overall, the strain level in the SL is in the range of −300 ∼ 200 µ and is low compared to the transverse strains in a UD laminate. This is a result of the high percentage of plies with the fiber direction aligned with the sensor, and the individual plies with different orientations constraining each other’s deformation, from both chemical and thermal shrinkage during the cure cycle. Fig. 10(b) shows the three inspection points (the red, green, and blue stars in Fig. 2(b)) which are at the [90°/45°], [0°/0°], and [0°/45°] ply interfaces separately plotted with the degree of cure, glass transition temperature, and temperature-time history. The thermal history consists of seven stages (1–7) and the strain evolution is analyzed in every stage. In stage 1, the three different configurations start with the same uniform strain and behave similar to what was observed in the UD laminate where the DOS is embedded parallel to the direction of the carbon fiber. In stage 2, reaching the first temperature plateau, the strain at the [90°/45°] and [0°/0°] interfaces do not completely overlap with the [0°/45°] interface. This is because the epoxy viscosity is sufficiently lowered to allow the resin to flow and the positions of the carbon fibers and DOS sensor to shift in plies where the two are oriented parallel to each other, registering a variation in strain between different ply interfaces. In stage 3, all three configurations have a different strain because of the second temperature ramp. The [0°/0°] interface shows constant uniform strain but the strain varies along the [0°/45°] and [90°/45°] interfaces [40]. At this stage, the compressive strain not only comes from the carbon fiber’s thermal expansion, but also the expansion of the epoxy and the bonding pf plies with dissimilar orientations. In stage 4, the temperature reaches the second isothermal plateau. The DOS in the [90°/45°], [0°/0°] and [0°/45°] ply interfaces shows a uniform strain and the DoC reaches 0.55 which is the gelation point. In stage 5, a decreasing strain at the third ramp is observed. After the compensation of heat transfer, a dramatic

drop of strain occurs. After the epoxy passes the gelation point, the epoxy continues to cross-link and shrinks. However, it is difficult to isolate whether the difference in strain at the [90°/45°], [0°/0°] and [0°/45°] ply interfaces at this stage are affected by either the chemical shrinkage or the temperature gradient. The compression strain is approximately 100 με which is relatively low compared with ε22 in the UD laminate. In stage 6, the strain at all three ply interfaces uniformly decreases as the resin passes the vitrification point. It is expected that the DOS reading may change because of the cure of the epoxy. In stage 7, strain oscillates between 420 min and 620 min, possibly a result of the development of epoxy modulus in this range. After 620 min, at the [90°45°] interface, the strain increases upon cooling and reaches 80 με. For the [0°/0°] and [0°/45°] ply interface, the optical sensor is not evenly distributed at the interface with the carbon fiber and epoxy (microscopy pictures in Fig. 9), thus strain fluctuates. around 0 to-200 με after reaching 1000 min. 5. Distributed sensing of residual strain in a composite laminate 5.1. Residual strain monitoring in a UD laminate Fig. 11(a) shows the DOS measured axial strain along the segment C-D in the UD laminate, which is perpendicular to the fiber direction as shown in Fig. 2(a), during the thermal-history. The DOS strain readings correspond to the laminate transverse thermal-residual strain, ε22. The strain fluctuates substantially along the segment C-D length. Three arbitrary lines in Fig. 11(a) (A-B, C-D, and E-F) were to be examined corresponding to stage four, stage six, and stage seven from the thermal history at a given time instance (Fig. 6). During the final cooling, the residual strain measured in the segment C-D is in the range of −5200 to −4700 µ as shown in Fig. 11(a). One of the sources of local strain variability along the sensor length is the inevitable inaccuracy of sensor

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alignment with the lamina principal directions. To highlight this effect, an XRD probe was used to scan the DOS embedded in the laminate and determine the DOS orientation in relation to the principal fiber direction. As Fig. 11(b) shows, the DOS is not exactly parallel to the fiber direction after processing. More investigation is needed to proceed on calculating the strain at different DOS local orientations from the experimental measurements.

shrinkage and thermal residual strain in a UD laminate and a SL. The strain measurements provided insight into strain evolution within the laminate at global and local level during cure. The cure induced strain was measured in a UD laminate with the DOS, while the analysis of cure kinetics and glass transition temperature evolution allowed for a more accurate interpretation of the experimental measurements. As expected, the axial strain in the UD laminate was small while the transverse strains were much larger due to the low fiber-direction CTE. The cureinduced strains in the SL were small in all directions as they were constrained by the plies with 0° orientation parallel to the sensor orientation. Due to the small strain and the sensitivity of the measurement system, it is concluded that cure shrinkage cannot accurately be measured by the DOS in a laminate where the ply 0° direction is aligned with the sensor. Also, it is found that the DOS does not adequately capture the cure shrinkage in a UD laminate where the ply 90° direction is aligned with the sensor, because the sensor bonds to the epoxy only when a certain degree of cure is achieved (the sensor cannot measure the material strain before it adheres to the epoxy). In this study, once passing the gelation point (DoC: 0.55), the strain measurements from the DOS were dominated by the thermal expansion of the laminate in the transverse direction. After passing a DoC of 0.78, the DOS measures a drastic decrease of strain (approximately −2500 µ ) signifying the cure shrinkage is partially measured. Lastly, the thermal residual strain was measured by the DOS system. A basic micromechanics approach was applied to simulate the experimental measurement of the UD laminate and validate the measurement technique. CLPT was used to calculate the theoretical thermal residual strain, which was further compared to the experimental results for the SL. The chemical shrinkage and the residual strain from the theoretical calculations showed good agreement with the experimental results (partially captured at the ply 90° direction aligned with the sensor) providing confidence in using the DOS system for future studies involving strain measurement in composite laminates, with the understanding of the limitations described in this study.

5.2. Residual strain monitoring in a structural laminate Fig. 12(a) shows the DOS measured axial strain along regions l, ll, and lll, which are parallel to the global laminate direction as shown in Fig. 2(b) in the SL during the cool-down stage. The level of residual strain is in the range of 10 to −200 µ . Three inspection lines show the distributed strain measured at a chosen time instance in three interfaces, [0°/45°], [0°/0°], and [90°/ 45°] (Fig. 12(b)). A symmetric and balanced laminate should theoretically have no thermal residual bending deformation, i.e. the in-plane laminate strain is expected to be uniform throughout the laminate thickness. The DOS in different interfaces reports somewhat different strain readings, which are caused by the locally variable microstructure of the laminate itself and the resin pockets around the sensor. We do no suspect these differences in strain measurement to be the result of bending from thermal residual stress development after cure because the laminate was symmetric and balanced and remained completely flat after cure. To obtain the analytical results of the thermal residual strain, the material properties were homogenized using self-consistent model with the epoxy modulus varying as a function of the temperature. The ply properties were then applied to Eq. (16) to calculate the laminate strain. The thermal residual strain was calculated which is −176 µ . The experimental values, ε11, in the interface of [0°/0°] and [0°/45°] are in the trend with the theoretical results. However, for the [90°/45°] the residual strain is higher than the calculated results. This difference might be because the DOS measures the local strain variation while is influenced by multiple factors including microstructure variation, and the theory only considers the homogenized lamina properties.

Acknowledgements The authors would like to thank LUNA Innovations for providing the fiber optical sensors used in this study and the technical support from Dr. Rahim.

6. Conclusions The present research utilized the DOS to measure the chemical Appendix A

An input wavelength, which is introduced by the tunable laser is separated into a measurement and reference path [4]. The input wavelength travels into the measurement path which later receives the reflection of the wavelength from the sensor. The wavelength is then again combined with the reference path at the coupler. The combined signal then goes through the beam splitter which split the light into orthogonal states, which are recorded in S and P detectors. To calculate the magnitude of the strain or temperature, a comparison of the measured and reference states is performed. The amplitudes of the reference and measurement paths are plotted using a complex Fourier transformation. However, an inverse of the Fourier transformation must be calculated to give the distinct location of the signal along the distance. The position of a defect (e.g. a local gage length) in the optical sensor is then cross-correlated using a calibration coefficient to obtain the local strain and temperature values. This process is continued throughout the entire path of the optical sensor. Thus, the final strain distribution can vary with the thermal history or the deformation along the path of the DOS. Appendix B The prepreg material is composed of Cytec epoxy 5320-1 [36] and Hexcel carbon fiber IM7 [37]. The carbon fiber properties, the value for cure kinetic model, the glass transition temperature model and the laminar properties are listed in Table 1 [38]. This is assuming 60% fiber volume fraction and each ply thickness is average 1.1 mm.

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Table 1 Material properties. Cure kinetic constants Material constants

value 2.54 × 8104

A1 (S 1) EA1(J/mol) m1 n1

60,628 0.55 21.11 4.84 × 104

A2 (S 1) EA2 (J/mol) m2 n2 D

61,752 0.8 1.18 44.3 −1.4

c0 cT (K

5.33 × 10-3

1)

Laminar engineering properties

value

E11Avg (GPa) E22Avg (GPa) ν12 G12 (GPa)

132.5 9.5 0.33 4.95 0.5

α11 (10 6 /℃)

25

α22 (10 6 /℃) Glass transition temperature constants Material constants

Value

Tg0 (℃)

−8.4

Tg (℃)

212

0.66

Carbon fiber properties Material constants

value

E11f (GPa) E22f (GPa) G12f (GPa) ν12f ν23f α11 (10−6/℃) α22 (10−6/℃)

275 15 26 0.26 0.26 −1.5 5

Appendix C The interrogator used in this research can either be operated in the 23.8 Hz or 100 Hz mode (Table 2). The 23.8 Hz interrogator can acquire strain data at a higher resolution along the sensor length compared to the 100 Hz interrogator. Generally, the choice of the interrogator type depends on the material volume, which must be monitored. For instance, if the material volume is large (e.g. in the large-scale structures), the 100 HZ interrogator would be the best option to avoid too much data acquisition. On the other hand, if the material volume is a small (e.g. plates and tools), the 23.8 Hz interrogator could provide a more extensive data acquisition. In this case, the 23.8 Hz type mode interrogator was used as recommended by the manufacturer. The DOS spec and the interrogate apparatus [4] are listed in Table 3. Table 2 The Equipment for the interrogator’s technical data and the DOS system. Parameter

Specification

Mode of Operation Sensor Configurations Maximum Sensor Length Gage Length Measurement Performance-Strain Range Resolution Accuracy Measurement Performance- Temperature Data Acquisition/Processing rate Data Acquisition Rate Data Processing Rate

23.8

100

Hz

10 1.3

10 5.2

m mm

10,000 <1 30 −40 ∼ 220

10,000 <1 25 −40 ∼ 220

με με με ℃

23.8 1.25

100 5

Hz Hz

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UNITS

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Table 3 The Distributed Optical Sensor (DOS) operating details. Parameter

Specification

Sensor Material

High-Definition (HD) Sensor Polyimide coated High Temperature LC/APC 304 Stainless steel

Fiber Connector Termination Dimensions Sensing Length-SL Termination Length Sensor Diameter Minimum Bend Radius Performance Maximum Operating Temperature Sensing Region Minimum Operating Temperature Sensing Region Maximum Operating Temperature Connector Minimum Operating Temperature Connector

Units

2 1 155 10

m cm um mm

220

℃

−40

℃

150

℃

−60

℃

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