INVESTIGATION OF RESIDUAL STRESSES DEVELOPMENT IN A SINGLE FIBRE COMPOSITE WITH FBG SENSOR

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Letitia Peters
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1 INVESTIGATION OF RESIDUAL STRESSES DEVELOPMENT IN A SINGLE FIBRE COMPOSITE WITH FBG SENSOR F. Colpo, D. Karalekas 1, J. Botsis Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-115, Switzerland fabiano.colpo@epfl.ch, dkara@unipi.gr, john.botsis@epfl.ch ABSTRACT A combined experimental and numerical study was undertaken to improve understanding of the development of residual strains in a model thermoset polymer matrix composite due to subsequent thermal post-curing treatment. In the present work, an embedded long fiber Bragg grating (FBG) sensor was used to measure the complete strain distribution built-up in a partially cured epoxy cylinder which was then post-cured at two different temperature profiles. The optical glass fibre was centrally located within the epoxy, thus acting as reinforcement and as a sensor providing relatively non-invasive strain measurements. Such residual strains are due to volume shrinkage of the epoxy resin during curing and post-curing treatment and by the mismatch between the elastic and thermal properties of the two constituents. The local Bragg wavelength shift due to the residual strains along the FBG and changes in temperature were obtained using a technique based on optical low coherence refletometry and inverse scattering. These strains are in good agreement with numerical simulations in which the residual strains in the matrix were treated as an equivalent thermoelastic problem. 1. Introduction One of the most critical reliability issues in polymer-based composites is the magnitude of residual stresses generated during the consolidation process. These process-induced residual stresses and strains lead to significant problems such as shape distortion, warpage, matrix cracks and delaminations, and can have significant effects on the mechanical properties of a composite product. They are mainly caused by volumetric change of the epoxy resin, due to thermal expansion and chemical shrinkage, during curing and post-curing treatment and by the mismatch between the elastic and thermal properties of the composite constituents. Therefore, the capability to predict and measure the processing residual stresses and strains is of great importance in improving the performance of composite structures. During the cure cycle of a polymer composite the matrix changes from a liquid-like uncrosslinked material in the early stages of cure to a viscoelastic solid at the end of curing. The residual stresses that arise during cure are influenced by this complex constitutive behaviour. Several studies have investigated and reported on the optimization of cure conditions (cure rate, cure cycle, pressure and cooling rate) to reduce the process-induced interfacial residual stresses and matrix residual stresses [1-6]. Additionally, numerous works have been performed to predict both analytically and numerically the residual stresses by using elastic and viscoelastic approaches [7-9]. A number of real time cure monitoring techniques have been used in the past, including dielectric analysis, ultrasonic scanning and nuclear magnetic resonance [1-12]. Recently, various investigators have been using fiber optic sensors for curing of composite materials and monitor the induced residual stresses [13]. Some of the main advantages of these sensors are that they are small in size and lightweight, and can be embedded in composite materials in a minimally invasive manner, without significant detrimental effects on their mechanical properties. For instance, extrinsic Fabry Perot interferometric (EFPI) and Bragg fiber optic sensors have been implemented to get local strain fields during the whole cure stage [14]. Further, fiber Bragg sensors (FBG) have been used for simultaneous monitoring of the fabrication strain and the cure temperature [15]. A single embedded FBG sensor within an epoxy resin, placed into a rectangular mold, was implemented to detect on-line the resin gelification onset [16] and the strain build evolution during the whole non-isothermal cure cycle [17]. Nevertheless, it is important to point out that in these FBG-based investigations the information regarding the build-up of process induced strains was extracted by recording the change of FBG wavelength (shift of the Bragg wavelength peak), to obtain the maximum value of the deformation induced to the grating. However, during curing and post-curing, the strain distribution along the FBG is non-uniform and the recorded FBG spectra either broaden and/or consist of several peaks. Thus, it is difficult to extract the actual strain distribution along the embedded fiber. Consequently, the use of FBG is limited to giving some qualitative trends in material processing and residual stress. In this work, a technique based on Optical Low coherence Reflectometry (OLCR) and inverse scattering [18, 19] was implemented to interrogate the FBG in real time measurements of the generated residual strains distribution, along the entire length of an optical fiber embedded into an epoxy cylinder, at the end of two consecutive post-curing cycles. The experimental work was accompanied by numerical analysis in which the optical fiber-host system was considered and modeled as a two 1 On sabbatical leave from the University of Piraeus, Greece

2 phase, single fiber composite to obtain the process-induced residual stresses when the specimen was brought to room temperature. The results demonstrate that the used fiber optic sensor system can provide the complete strain profiles inside the model composite during subsequent post curing processes. 2. FBG principles A Bragg grating is a permanent periodic change of the refractive index in the fibre core, whose fundamental purpose is to reflect a narrow spectral component of a broadband light source. The reflected light is centred on the Bragg wavelength λ B, which is directly related to the grating period Λ, and the mean effective refractive index condition [2] n eff, through the resonance or Bragg λ = 2n Λ (1) B eff When the FBG is homogeneous, its parameters are constant along the grating length (z axis) and the Bragg condition (1) is independent of the position along z. When uniform changes in strain and/or temperature occur, along the FBG, its spectral response exhibits a simple shift of the Bragg peak without modification of its shape. This is the simplest loading case on an FBG and has been used extensively as a measure of applied strain in conventional sensing applications with FBGs. In most cases, the loading conditions result in non-homogeneous strains along the fibre. In such cases, the grating parameters are position dependent. The coupled-mode formalism then provides a direct mathematical tool to describe the interaction of light propagating in the grating. This analysis uses a complex coupling coefficient whose amplitude and phase along the FBG s length need to be determined [18]. The Bragg wavelength becomes a function of z and a local Bragg condition λ ( z) = 2 n Λ ( z) replaces (1). Certain experimental configurations (as in the present case) preserve cylindrical symmetry B eff eff and the transversal strains εx, ε y (or r θ ) applied to the fibre are such that ε =ε = ν ε ( ν f is the Poisson s ratio of the fibre and ε z the applied axial strain) [21]. Thus, assuming constant temperature, the local Bragg wavelength shift Δλ ( z) = λ ( z) λ ( z) is then related to ( z) B B B The photoelastic coefficient Δλ λ B qz ( ) ε, ε x y f z B ( z) ( z) method and the strains along the fiber from (2). ε z by [19] ( 1 p ) ( z) = ε 2 neff p e is given by e ( 1 f ) e ( z p = ν p12 ν f p11 which can be experimentally measured and 2 p, p are the strain-optic constants for the optical fibre. In a typical experiment, λ ( z ) is deduced from the OLCR-based ) B (2) 3. Materials, sample preparation and experimental procedure The epoxy system used in this work was a 7:3:1 per weight mixture of DER33, DER 732 Dow Epoxy resins and of a DEH 26 hardener. Cylindrical epoxy specimens having an outer diameter of 8 mm and length of 4mm were fabricated. The cylindrical configuration was selected because it is simpler to manufacture and to use in numerical simulations due to symmetry conditions. Further, it allows the results to be compared with existing analytical models since such a configuration minimizes free surface effects and can lead to a sufficient level of residual stresses on the fibre, independent of the z- coordinate in a large portion of the fibre. Each specimen contained a standard embedded fiber of.125 mm diameter, centrally located along the cylinders axial direction. The optical fiber-host epoxy system is considered as a two phase composite with a very small fiber volume ratio. The room temperature elastic properties considered for the matrix epoxy are, Young s modulus E m = 2.35 GPa and Poisson s ratio ν m =.38, as obtained by testing of dog-bone epoxy specimens. The corresponding ones for the embedded E-glass fibre were, E f = 7 GPa and ν f =.19. The optical fiber used in this thermal study was equipped with a FBG of 24mm in length having a wavelength of 13 nm. The FBG grating was positioned in such a way that 17mm of its grating length was located within the cylindrical specimen while the rest 7mm outside. As a result, the embedded part of the Bragg grating would respond to both temperature changes and curing induced strain built-up while the part which is outside the cylindrical specimen would be sensitive only to thermal effects due to temperature increase during post-curing.

3 After pouring the mixture into the mould, the system was left to cure at room temperature for 24 hours. When the specimen fabrication was completed, a precise measurement of both the length and the position of the grating carried out using the OLCR apparatus. Then, the cylindrical specimen with the embedded FBG sensor was removed from the mould and placed in an air conventional oven where it was thermally treated following a pre-selected temperature cycle. Each followed post-curing process was consisted of three stages. In the first stage, the ramp-up, the temperature was increased to the desired one within two hours. The second stage which was the cure post-cured phase, where the specimens was left for 9 hours. After postcuring the composite specimen was cooled down to room temperature after opening the oven door at the end of the postcuring plateau. Two separate, but consecutive, post-curing cycles were applied to the same specimen. In the first one the post-curing temperature remained the same, namely at 7 C, while in the second one it was raised to 11 C. During the post-curing process a J-type thermocouple was placed in the oven to record the applied temperature cycle using a data acquisition system. Figure 1 shows the applied temperature profiles as measured by the thermocouple inside the oven during the 7 C and 11 C thermal cycles. The small recorded temperature drifts at the curing plateau are due to the oven operation to maintain the set cure temperature. Symbols 1, 2, 3A, 3B, 3C, 3D and 4 designate the points were Bragg response was measured Temperature ( C) A 3B 3C 3D 7 C Thermal Cycle 11 C Thermal Cycle 2 1 After demolding End of thermal Time (hours) Figure 1. Post-curing temperature profiles at 7 C and 11 o C, respectively. Insert indicates the specimen geometry (not on scale) the FBG and the coordinate system. 4. Numerical modeling The specimen is considered as a cylindrical fibre-reinforced composite with two concentric material sub-domains described by the cylindrical coordinate system (r, θ, z) (Figure 1). The fibre is considered as a central cylinder of radius r f =.625 mm and the surrounding matrix domain corresponds to the annulus of inner r f and outer radii r m = 4 mm. The glass and epoxy are assumed to be linear elastic and isotropic materials with perfect interface conditions between them. To model the matrix shrinkage effect, the problem is considered analogous to a thermo-elastic one. We also consider the elastic properties of the materials to be independent of temperature and not to change as the degree of cure advances during post-curing. As a consequence, the only residual stresses are those associated with curing shrinkage of the epoxy when the system returns to room temperature. To simulate the residual strains at room temperature, a matrix shrinkage function S m (r, z) is introduced in the general strain-stress relations as described in detail in refs. [19, 22]. The form of the S m function is obtained from the strain measurements along the FBG. Due to the cylindrical symmetry of the specimen, an axisymmetric FE model is used to determine the residual stress state in the specimen. Numerical simulations are performed with the commercial ABAQUS TM code by meshing only one half of the rz-plane. Along the longitudinal and transverse directions, the matrix domain is discretized into 3 3 elements and for the fibre, 3 3 elements are used. The mesh is constructed with 8-node biquadratic axisymmetric quadrilateral elements and is refined towards the ends and at the fibre matrix interface to accommodate strong variations of the field quantities. 5. Results and discussion From the obtained measurements, the cylindrical specimen experienced substantial non-uniform compressive strains due to epoxy s consolidation during curing and further thermal post-curing treatment. It has been seen that a maximum strain of 2 micro-strains is recorded close to the central region of the specimen right after curing at room temperature [19]. However, the

4 magnitude of the obtained strains increases considerably when the specimen is thermally post-cured at higher temperatures, at 7 and 11 C respectively. A 3-D representation of the FBG spectra recorded by the same FBG during the first thermal cycle is shown in Figure 2, leading to a more evident picture of the complete spectra evolution with temperature change at different stages of the heating up/hold/cooling down cycle. It is seen that the obtained peaks, that relate to different reflected spectra recorded from the freeend of FBG and correspond to the same temperature of interest (e.g. room temperature, cure temperature), have the same wavelength peak value (nm). However, such spectra are of limited value since they do not give any details on the local wavelength evolution and correspondingly on the strains on the embedded fibre. In Figure 3 the corresponding local Bragg wavelength evolutions along the embedded fiber are plotted. The ones corresponding to the applied post-curing plateau (namely 3A, 3B, 3C and 3D) reflect the material changes due to further cure reactions that take place and the thermal expansion mismatch between the fibre sensor and the host-matrix. In addition, they account for temperature gradients inside the epoxy specimen, especially at the beginning of the heating plateau (point 3A), where the epoxy material around the fibre is exposed to a lower temperature compared to the ones recorded by the oven thermocouple or experienced by the outer surfaces of the cylindrical specimen. These thermal differences are expected to be more pronounced during cooling stage since the outside surfaces of the cylindrical specimen would contract first. The corresponding plots for the second post-curing cycle are presented in Figures 4-5. As can been seen from the local Bragg wavelength evolution, a lower applied temperature profile leads to less residual strains since they are induced by the thermal expansion mismatch between the reinforcing fibre sensor and the epoxy matrix and the matrix shrinkage during the cool-down period. Figure 2. 3-D representation of the FBG spectra measured during the entire first thermal cycle at 7 o C. Figure 3. Local Bragg evolution, reconstructed with the OLCR technique, during the entire first thermal cycle at 7 o C.

5 Figure 4. 3-D representation of the FBG spectra measured during the entire third thermal cycle at 11 o C. Figure 5. Local Bragg evolution, reconstructed with the OLCR technique, during the entire third thermal cycle at 11 o C. In Figure 6 the strain evolutions, experimental and simulated, along the embedded fibre at the end of the thermal cycles at 7 and 11 o C are presented, as obtained by using Eq. 2 where p e = It is seen that the resulted strain profiles at 7 and 11 o C have maximum compressive values of 59 με, and 66 με in the central region, respectively. The corresponding simulated strain distributions along the fibre, correctly follows the experimental measurements. It is evident from the shape of the graphs that the strain profile is of parabolic shape, with the maximum strain value occurring at the center of the specimen. It is noted that in Figure 6 the measured and calculated residual strains do not reach a zero value at the FBG entry point to the

6 specimen. This is due to the fact that there are compressive strains sensed by the free end of the FBG which has been covered by a small quantity of resin material that extends beyond the specimen main body εz (r=, z) [με] -3-4 Experimental Numerical -5-6 T = 7 C T = 11 C -7 Embedded part of the FBG [mm] Figure 6. Comparison between measured and simulated strain distributions along the grating length at the end of the 7 and 11 o C cycles, respectively. In Figures 7a and 7b the axial and radial stresses evolution in the plane z= and at the end of the thermal cycles at 7 and 11 o C are presented. As expected,, σ r, σ θ are significantly compressive at the reinforcing optical fibre while σ r, and σ θ in the matrix retain their maximum values at the fibre/matrix interface (note that the shear stress is zero at z=). Interestingly, the influence of the embedded fibre on the residual stresses expends up to eight fibre radii σr(r, z=) & σ θ (r,z=) [MPa] -5 σ θ σ r (r,z=) [MPa] -1 σ r & σ θ ,5 1 1,5 2 2,5 3 3,5 4 r [mm] Figure 7a. Axial and transversal stresses evolution along the plane z=, at the end of the second thermal treatment cycle at 7 o C.

7 1 1 5 σr(r, z=) & σ θ (r,z=) [MPa] -5 σ θ σ r (r,z=) [MPa] -1 σ r & σ θ ,5 1 1,5 2 2,5 3 3,5 4 r [mm] Figure 7b. Axial and transversal stresses evolution along the plane z=, at the end of the third thermal treatment cycle at 11 o C. 6. Conclusions In this work, a single FBG fibre centrally located inside an epoxy cylinder has been used to monitor the complete strain build up and evolution that occur, along its sensing grating, when a partially cured test sample undergoes successive thermal cycles of post-curing. The reconstructed local Bragg results, using the OLCR technique, do provide significant information regarding strain evolution at different time intervals during the heating plateaus and as well as at the end of their corresponding cooling down stage. An axisymmetric finite element (FE) model, based on an equivalent thermo-elastic approach, was used to determine the residual stresses in the thermally treated cylindrical specimens. In the performed analysis the specimen was modelled as a cylindrical fibre-reinforced composite consisted of two concentric cylinders. The numerical results were in good agreement with the ones obtained experimentally. References 1. Daniel IM, Wang T-M, Karalekas D, Gotro JT. Determination of chemical cure shrinkage on composite laminates. Journal of Composites Technology & Research, 12(3), 172-6, Bogetti TA, Gillespi JW. Process-induced stress and deformation in thick-section composite laminates. Journal of Composite Materials, 26(5), 627-6, Rusell JD. Cure shrinkage of thermoset composites. SAMPE quarterly, 24(2), 28-33, White SR, Hahn HT. Cure cycle optimization fro the reduction of processing-induced residual stresses in composite materials. Journal of Composite Materials, 27, , Rusell JD, et. al. A new method to reduce cure-induced stresses in thermoset polymer composites: part III. Correlating stress history to viscosity, degree of cure, and shrinkage. Journal of Composite Materials, 34, , Merzlyakov M, McKenna GB, Simon SL. Cure-induced and thermal stresses in a constrained epoxy resin. Composites Part A: Applied Science and Manufacturing, 37, , Berman JB, White SR. Theoretical modeling of residual and transformational stresses in SMA composites. Smart Materials and Structures, 5(6), , Prasatya P, Mckenna GB, Simon SL. A viscoelatic model for predicting isotropic residual stresses in thermosetting materials: effect of processing parameters. Journal of Composite Materials, 35(1), , Kim YK, White SR. Cure-dependent viscoelastic residual stress analysis of filament-wound composite cylinders, 5: , Snow AW, Armistead P. Simple dilatometer for thermoset cure shrinkage and thermal expansions measurements. Journal of Applied Polymer Science, 52(3), 41-11, 1994

8 11. O Dwyer, et. al. Relating the state of cure to the real time internal strain development in a curing composite using infiber Bragg gratings and dielectric sensors. Measurement Science and Technology, 9, , Lo Y-L, Chuang H-S. Measurement of thermal expansion coefficients using an in-fibre Bragg-grating sensor. Measurement Science and Technology, 9, , Lawrence CM, et al. An embedded fiber optic sensor method for determining residual stresses in fiber-reinforced composite materials Journal of Intelligent Material Systems and Structures, 9, , Leng J, Asundi A. Real time cure monitoring of smart composite materials using extrinsic Fabry-Perot interferometer and fiber Bragg grating sensors. Smart Materials and Structures, 11, , Kang H-K, Kang D-H, Hong C-S, Kim C-G. Simultaneous monitoring of strain and temperature during and after cure of unsymmetric composite lamninate using fibre-optic sensors. Smart Materials and Structures, 12, 29-35, Antonucci V, et. al. Real time monitoring of cure and gelification of a thermoset matrix. Composites Science and Technology, 66, , Antonucci V, et. al. Cure-induced residual strain build up in a thermoset resin. Composites Part A: Applied Science and Manufacturing, 37, , Giaccari P, Dunkel GR, Humbert L, Botsis J, Limberger HG, Salathe RP. On a direct determination of non-uniform internal strain fields using fibre Bragg gratings. Smart Materials and Structures, vol. 14, , Colpo F, Humbert L, Giaccari P, Botsis J. Characterization of residual stresses in an epoxy block using an embedded FBG sensor and the OLCR technique. Composites Part A: Applied Science and Manufacturing, vol. 37, , Measures RM. Structural Health Monitoring with Fiber Optic Technology, Academic Press, Butter CD, Hocker GB. Fibre optics and strain gauge. Applied Optics, 17(18), , Colpo F, Humbert L, Botsis J, Characterisation of residual stresses in a single fibre composite with FBG sensor, Composites Science and Technology, in press.

Identification of interface properties using Fibre Bragg Grating sensors in a fibre pull-out test Gabriel Dunkel, Laurent Humbert and John Botsis

Identification of interface properties using Fibre Bragg Grating sensors in a fibre pull-out test Gabriel Dunkel, Laurent Humbert and John Botsis Laboratory of Applied Mechanics and Reliability Analysis