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experimental study on the induction heating of adhesives for composite materials bonding
Accepted Manuscript Title: A Numerical/Experimental Study on the Induction Heating of Adhesives for Composite Materials Bonding Authors: A. Riccio, A. Russo, A. Raimondo, P. Cirillo, A. Caraviello PII: DOI: Reference:
S2352-4928(17)30332-X https://doi.org/10.1016/j.mtcomm.2018.03.008 MTCOMM 319
To appear in: Received date: Revised date: Accepted date:
24-11-2017 9-3-2018 14-3-2018
Please cite this article as: A.Riccio, A.Russo, A.Raimondo, P.Cirillo, A.Caraviello, A Numerical/Experimental Study on the Induction Heating of Adhesives for Composite Materials Bonding, Materials Today Communications https://doi.org/10.1016/j.mtcomm.2018.03.008 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A Numerical/Experimental Study on the Induction Heating of Adhesives for Composite Materials Bonding
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Department of Industrial and Informatics Engineering, Università degli studi della
Sòphia High Tech S.r.l. Zona industriale di Marcianise, Marcianise (CE), Italy
Corresponding Author
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Campania “Luigi Vanvitelli”, via Roma 29, Aversa (CE), Italy 2
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A. Riccio1*, A. Russo1, A. Raimondo1, P. Cirillo2, A. Caraviello2
Tel +39 081 5010407; Fax +39 081 5010204
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e-mail: [email protected]
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Graphical Abstract
ABSTRACT In this paper, the bonding of carbon fiber reinforced polymer (CFRP) components by induction heating has been numerically simulated. Being the induction heating bonding phenomenon characterised by an intrinsic multi-physical nature, three different numerical models taking into account, respectively, electromagnetic, thermic and structural aspects, have been introduced and applied to a stiffened composite panel to predict the stringer/skin interface characteristics. The electromagnetic model evaluates
the energy loss due to the Joule effect while the thermal model is used to calculate the temperature distribution within the adhesive layer between skin and stringer. Then the structural model predicts the ultimate failure load of the stiffened panel taking into account the degree of cure of the adhesive depending on the temperature distribution at interface between skin and stringers by means of an experimentally determined degradation law. The overall developed numerical methodology has been preliminary validated by comparisons with experimental data in terms of adhesive temperature as a function of time on rectangular composite coupons. Finally, a sensitivity analysis has been performed to evaluate the effects of the geometrical parameters of the stiffened composite panel and process
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parameters on the degree of cure and then on the mechanical properties of the adhesive at interface between skin and stringers.
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Keywords: Composites Bonding; Induction heating; Finite Element Analysis (FEA).
1. Introduction
The use of adhesive for the bonding of composite structures offers several advantages
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with respect to the bolted joints in terms of lower assembly weight, uniform stress
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distribution and fatigue resistance. However, the main drawbacks of current adhesive
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bonding technology relays in the long times required for the complete cure of the adhesive, usually obtained by autoclave and resulting in long processing times and
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wasted energy. Several techniques have been developed, such as heating blankets and lamps, to accelerate the cure process and to obtain a local heating without the use of
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oven or autoclave, however these methodologies have demonstrated to be inefficient in terms of heat lost by the surrounding structure and environment [1]. The induction
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heating represents a promising technique allowing to reach the cure temperature within fraction of seconds leading to a reduction of energy consumption and time [2-9]. The
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induction heating phenomenon appears when electrically conducting objects are exposed to an alternating electromagnetic field which generates eddy currents that heat the material due to the Joule effect. In ferromagnetic materials heat could also be generated by means of magnetic hysteresis. Early approaches taken to model induction
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heating were focused on the analytical modelling of the phenomenon [10-14]. Only recently, thanks to the computational improvement of FE software the simulation of the 3D electromagnetic model fully coupled with thermal and structural analysis has become possible [15-23]. The aim of these multidisciplinary analyses is to verify the capability of the bonded structure to not develop damages induced by impact or by manufacturing which can be very critical for load carrying capability of composite structures [24,25]. This paper presents a numerical study on the use of induction
heating for bonding composite structures by curing a commercial adhesive at room temperature. Composite stiffened panels have been used as benchmark by adopting the numerical Finite Element Analysis based platform ABAQUS [26] and combining a time-harmonic electromagnetic analysis (to calculate the energy loss due to the Joule effect), a transient heat transfer analysis ( to calculate of the spatial and temporal distribution of temperatures) and, finally, a structural analysis (to evaluate the mechanical behaviour). As added value of the presented investigation and a step
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forward with respect to other research works in the field, an attempt to propose an
analytical formulation, allowing to take into account the variation of the mechanical
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properties with the cure temperature, has been made. Mechanical tests have been
performed on induction heated coupon obtained with different process parameters to provide an experimental reference for the determination of the shape functions adopted to take into account the variation of mechanical properties with the degree of cure/
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temperature. The influence of composite stiffened panel geometrical parameters such as
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the number of stiffeners, the size of the panel together with process parameters such as the inductor current frequency has been assessed by a sensitivity analysis on a number
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of selected stiffened panels geometrical configurations. In section 2 the theoretical
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background is introduced while in section 3 the experimental and numerical activities on coupon are presented. Finally in section 4 the numerical application on composite
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stiffened panel is introduced and discussed.
2. Theoretical background Electromagnetic Field
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2.1.
The induction heating takes place when a conductive material is exposed to an electromagnetic field generated by an alternating current. In particular, the magnetic
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field induces eddy currents on the surface of the material which causes resistive heating due to Joule losses. Different heating mechanisms during induction processing of electrically non conductive materials, having an internal electrical resistance of infinity, are possible. Therefore, it is necessary to introduce the so called “susceptors” in order to convert a magnetic field into heat [17]. In the case of carbon fiber reinforced materials (CFRP) the carbon fibers have an internal electrical resistance different from infinity and when the eddy currents pass through them the electrical energy is transformed into
heat [7]. In the next subsections, the theoretical aspects of the developed electromagnetic and thermal models will be introduced Electrical and magnetic fields are governed by the Maxwell’s equations, describing the electromagnetic phenomena under the low-frequency assumption. It is convenient to express the magnetic flux density vector as a function of a vector potential as in equation (1). 𝑩 = 𝛁×𝑨
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(1)
Where A is the magnetic vector potential. When the system is subjected to a time-
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harmonic excitation, in the case of sinusoidal current J 0 exp(it ) , the analysis seeks a time-harmonic electromagnetic response in the form of A0 exp(it ) . The vectors A0
and J0 represent the amplitude, respectively, of the magnetic potential vector and of the
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volume density current vector. Under these assumptions, the Maxwell’s equations are
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reduced to the equation (2).
(2)
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𝛁 × (𝜇 −1 𝛁 × 𝑨𝟎 ) + 𝑖𝜔𝝈𝑬 ∙ 𝑨𝟎 = 𝑱𝟎
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Where is the magnetic permeability tensor and σE is the electrical conductivity tensor. The relation between the magnetic flux density (B) and the magnetic field (H), is
𝑩 = 𝜇𝑯
(3)
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defined in equation (3).
The electrical conductivity is related to the current density (J) and the electric field (E)
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by the Ohm’s law expressed in equation (4). 𝑱 = 𝝈𝑬 ∙ 𝑬
(4)
The FEM software solves the variational form of the equation (2) for the components of
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the magnetic vector potential, considering a variation of the magnetic potential vector (
A0 ). 2.2.
Heat Transfer formulation
The heat generated by Joule effect due the eddy currents is simulated within the FEM software by a transient analysis, applying the thermodynamic law for heat exchange.
The first law of the thermodynamic states that the energy of an isolated system is conserved. The thermal equilibrium of the system can be expressed by the equation (5).
C p
dT (kT ) Qe dt
(5)
Where is the density, C p is the specific heat capacity, k is the thermal conductivity
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and Qe is the heat generated by the magnetic field. The boundary conditions considered in the present model representing the interaction with the surrounding air, are the convection and radiation expressed respectively by the equation (6) and (7).
(6)
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n (kT ) hc (T T0 ) n (kT ) (T04 T 4 )
(7)
Structural effects
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2.3.
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emissivity and is the Stefan-Boltzmann constant.
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Where hc is the convection coefficient, T0 is the ambient temperature, is the material
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The temperature at interfaces is used as an input to determine the degree of cure of the adhesive and then the mechanical properties distribution within the adhesive self. The increase of materials mechanical properties as a function of the temperature up to the
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cure temperature has been accounted by means of a suitable shape function, derived by the experimental testing activity on coupons, described in the following sections. In the
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range 300 K to 500 K the mass variation due to high temperature can be considered negligible and the material properties are degraded according to the empirical equation
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(8).
𝐸(𝑇) = 𝐸𝑢
𝐸𝑢 −𝐸𝑟 2
(1 − tanh(𝑘(𝑇𝑔 − 𝑇)))
(8)
Where Eu is the modulus at low temperature (300 K), Er is the modulus at high temperature (500 K), Tg is the transition temperature and k is an empirical constant. In Figure 1 an example of the adopted shape function is shown. More in detail, when the induced temperature reaches the cure temperature the normalized material property
is set to 1 which corresponds to the material property of the completely cured adhesive. As the induced temperature decreases, the normalized material property tends to 0.
A structural geometrically non-linear analysis is then performed by applying whatever loading condition. The equilibrium equation states that the external applied loads are
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equal to the internal loads. This condition ca be expressed by the equation (9). 𝑲(𝒖) ∙ 𝒖 = 𝑭𝒆
(9)
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Where K is the global stiffness matrix , u is the displacement and Fe are the external loads. This equation, which is a non linear equation being K a function of u, can be
solved by an iterative procedure. It is clear that different process parameters in induction will lead to a differently generated heating which will in turn generate a different
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temperature distribution influencing the spatial distribution of mechanical properties in
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and then the solution of the structural analysis.
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the adhesive. Mechanical properties of the adhesive will influence the stiffness matrix
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An elasto-plastic material model with isotropic hardening behavior has been considered for the adhesive. In this model, the yield surface changes size uniformly in all directions such that the yield stress increase in all stress direction[26]. In order to simulate the
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debonding of the stringer from the skin, for the adhesive layer a progressive degradation of the material stiffness has been assumed by degradation of the elasticity and softening
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of the yield stress as shown in Figure 2 where the stress-strain response is reported.
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3. Validation of the proposed model In order to validate the proposed numerical procedure, the induction heating on rectangular coupons have been simulated and the obtained numerical results have been
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compared with experimental data. 3.1.
Experimental methods
The experimental set-up consists of a plain coil inductor made of electrolytic copper with an operating frequency of 145 kHz, a support plate made of polyamide material and a CFRP coupon. The main parameters considered for the tests are:
Voltage across the coil;
maximum temperature;
dwell time;
initial (minimum) temperature of 20°C;
induction frequency of 145 kHz.
An Egma 30R induction generator has been adopted for the experimental tests. The generator is totally static, i.e. there are no motors or other moving devices, and the
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magnetic field is generated by an electronic circuit called inverter. Maximum and
minimum temperature values have been fixed in order to allow the coupons temperature reading during the heating phase by means of an optical pyrometer. Experiments have
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been conducted on composite specimens, manufacture in autoclave, dimensioned
according to the Standard Test Method for Short-Beam Strength of Polymer Matrix Composite Materials ASTM D2344.
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The specimen is composed of two 0° unidirectional laminates, with a 2 mm thickness,
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manufactured in autoclave, bonded with a 0.2 mm adhesive. The coil-plate distance is
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10 mm, while the specimen is leans on the support plate. The material system adopted for the plates production is Tepex® dynalite 202-C200(9)/50% (PA6 50% carbon
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fibers), while the adhesive adopted for bonding the plates is Prodas 1400.
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The experimental temperatures have been measured in the warmest point of the adhesive regardless of the location along the thickness. The maximum temperature has been fixed at 200°C, corresponding to the cure temperature of the Prodas. A
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temperature control system has been used to guarantee a constant temperature value once the cure temperature has been reached. The maximum heating power values,
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depending on the voltage across the inductor, considered for the tests are: P.H.=26% for 250 V;
P.H.=51.5% for 350 V.
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The considered values of the dwell time are 10, 20 and 30 s. The 0.8 emissivity value, used for the tests, has been obtained through bibliographic research. Moreover, an optimal value of joining pressure should be considered in order to achieve high quality bonding process and prevent voids, cracks and folds. After the realization of the bonded specimens by means of electromagnetic induction, mechanical tests, according to the standard ASTM D5868 (Standard Test Method for
Lap Shear Adhesion for Fiber Reinforced Plastic (FRP) Bonding), have been performed in order to determine the influence of the induction parameters on the strength of the adhesive. The results of the tests have been summarized in Table 1. The ultimate stresses values in table 1 are value coming from set of specimens with specific parameters Table 1 shows a general increase in ultimate stress with temperature and with induction
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time. This trend is confirmed for each voltage. It can be also noticed that, increasing the voltage, an increase in the ultimate stress is obtained, probably due to the faster approach
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to the target temperature.
The obtained experimental data allow to calibrate the shape function previously introduced in Figure 1 and evaluate the influence of the temperature reached during the induction on the strength of the adhesive layer. All the points in Table 1 have been marked
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in figure 3 and the temperature below 400°C has been extrapolated from the shape
Electromagnetic analysis, thermal analysis and experimental
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3.2.
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function. Hence, this shape function can be applied for each voltage and application time.
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verification
The numerical model adopted for the electro-magnetic analysis is presented in Figure 4,
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where the geometrical dimensions are described.
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The electro-magnetic, thermal and structural material properties, adopted in the FE analysis, for the different components have been summarized in Table 2 and Table 3.
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These properties have been provided by the manufacturer and integrated by a specific characterization test campaign performed preliminarily to the research activity presented in this paper.
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In order to simulate the passage of the electromagnetic field it is necessary to model also the volume of air surrounding the components. All the volume of the geometrical model has been discretized by using 4-node electromagnetic elements EMC3D4. The approximate size of the element is 2.5 mm. No contact elements between plates and adhesive have been used. Nodes at interfaces have been merged to allow the themal conduction between adjacent parts. This solution have also contributed to decrease the computational cost related to the analyses.
The passage of the current through the coil has been simulated by assign a current density as boundary condition. The joining pressure has been neglected in the numerical analyses. Several simulations have been made at different value of the current through the coil. In Figure 5a, as an example, the distribution of magnetic flux density induced by the coil on the support plate and specimen is introduced, while in Figure 5b, the magnetic field within the air volume can be appreciated.
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The magnetic field induces eddy currents on the surface of the material, which due to the Joule effect heats the composite laminate. The FE model for the thermal analyses
consist only of the support plate and the specimen. It has been discretized by using 8-
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node hexahedral thermal element DC3D8. The results of the thermal analysis are shown in Figure 6a and Figure 6b where the temperature distributions are shown, respectively, on the composite specimen and inside the adhesive layer after 55s.
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In Figure 7 the numerical results in terms of adhesive temperature as a function of time
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is compared to experimental results for two different value of the applied potential
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difference across the coil.
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From figure 7, as expected, the increase in the potential difference from 250V to 350V causes the reduction of the time needed to reach the cure temperature. The excellent
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agreement between numerical results and the experimental data in figure 7 proves the effectiveness of the developed numerical model in predicting the temperature evolution as a function of the induction time. Experimental data in figure 7 are the maximum
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temperatures evaluated in the adhesive when applying the induction. Indeed 9 experimental tests were performed for each potential different with a maximum standard
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deviation (evaluated at each induction control time step of about 5% with respect to maximum temperature.
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4. Numerical application
As numerical application of the proposed numerical model for the simulation of the induction heating bonding, a sensitivity study on the effects of the induction heating processing parameters has been performed on some stiffened composite panels geometrical configurations. The analyses have been preliminary carried out on a plate without stiffeners to study the thermal field on the structure. However, these results have not been presented for the sake of brevity. As already remarked, the induction heating phenomenon has been simulated by using three different numerical models: an
electromagnetic model, a thermal model and a structural model. In the frame of the electromagnetic analysis, all the components of the stiffened panel, plane coil inductor, support plate made of polyamide material and the surrounding volume of air have been modeled to simulate the induction phenomenon. The results of this analysis in terms of Joule losses are converted into a concentrated heat flux and used as boundary condition for the subsequent transient heat transfer analysis. In the frame of the transient heat transfer analysis only the specimen and the support plate have been modeled in order to
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estimate the temperature distribution inside the adhesive layer between skin and
stringers. From the temperature distributions, using appropriate degradation functions,
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as shown in the previous sections, it has been possible to obtain the spatial distribution of the elasto-plastic properties of the adhesive depending on the degree of cure. This
information have been passed to the structural analysis and the compressive behavior of the stiffened panel has been numerically investigated. The entire process allows to
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evaluate the influence of different parameters on the degree of cure of the adhesive and,
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hence, on the damage behavior and on the ultimate load of the structure. The flowchart
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of the analyses is presented in Figure 8.
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In the next subsections, the electromagnetic, the thermal and structural numerical models developed for the analysed stiffened panels will be described in detail. Electromagnetic FEM model
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4.1.
The geometrical model adopted for the electro-magnetic analysis, consisting of a plane
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coil inductor, a support plate made of polyamide material and the composite stiffened panel, is presented in Figure 9. All the volumes of the geometrical model have been
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discretized by using 4-node tetrahedral electromagnetic elements EMC3D4 with approximate size of 2.5 mm. The material properties adopted for the analyses are reported in the previous section in Table 2 and Table 3.
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The passage of the current through the coil has been simulated by assign a current density as boundary condition. The frequency of the current represents a key parameter being the characteristics of the magnetic field and of the eddy currents induced into the material strongly dependent on it. Furthermore, the frequency has an effect on the penetration depth which is a measure of how deep the electromagnetic radiation can penetrate into the material. According to the Maxwell’s equations, the penetration depth con be expressed as reported in Equation 10 [27].
f
(10)
Where, is the material resistivity, is the magnetic permeability and
f
is the
current frequency. In the present work a frequency of 145 kHz has been adopted for the experimental and numerical activities. For the numerical activities on the stiffened panel
4.2.
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a voltage of 250 V has been set. Thermal FEM model
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The thermal model allows to evaluate the temporal and spatial distribution of the
temperature inside the adhesive layer given the thermal flux from the electro-magnetic analysis. The geometrical model involves only the support plate and the specimen as shown in Figure 10. The FE model has been realized using the 8-node hexahedral
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thermal element DC3D8 with approximate size of 2 mm.
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The heat generated by the induction model is converted into concentrated heat flux and
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applied as initial condition of transient thermal analysis. In order to accurately predict
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the heat transfer, boundary conditions of natural convection and radiation with the surrounding air have been considered.
Structural FEM model
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4.3.
By starting from the temperature distribution obtained from the heat transfer analysis, it
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has been possible to evaluate the degree of cure of the adhesive layer, as shown in the previous sections.
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The structural analysis considers only the stiffened panel and the adhesive layers between the stiffeners and the skin (Figure 11). The volumes have been discretized by hexahedral elements C3D8R with approximate size of 2 mm with layered solid option
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to take into account the layers’ orientation. A ductile damage model has been adopted to simulate the elasto-plastic behavior of the adhesive. For connecting the stringers to adhesive and to the skin, multi-points-constraints have been adopted. The stiffened panel has been subjected to a compressive load through a displacement-controlled analysis and the failure load has been predicted. The thermal expansion of the composite has been neglected in the structural analysis. In the next subsection, the proposed numerical procedure will be applied to a sensitivity study on stiffened composite panels.
4.4.
Sensitivity Analysis – Stiffened Panel
A sensitivity analysis has been performed in order to evaluate the influence of the different geometrical and physical parameters on the degree of cure of the adhesive layer. The analyzed configurations are summarized in Table 4. The first variable parameter is the number of stiffeners on the panel, then the global
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dimensions of the stiffened panel has been reduced in order to investigate the effect of a bigger coil with respect to the panel size. Finally, a smaller radius for the coil and a
variable current frequency have been considered. The geometrical dimensions of the
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analyzed configurations are shown in Figure 12, while the properties of the used
materials are listed in Tables 2 and 3. The coil-plate distance is 10 mm, while the specimen is leans on the support plate.
The rate of Joule dissipation on the stiffened panel for the configuration SS#1, SS#2 and
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SS#3 obtained from the electromagnetic analysis is shown in Figure 13a.
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As it can be seen from the Figure a, the distribution of Joule losses is influenced by the presence of the stiffeners due to the increase in the thickness in the stringer foot area.
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Only for the configuration with one stiffener (SS#1) the heat flux covers the entire bonding area, while, especially for the configuration SS#3, the lateral stiffeners are,
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substantially, not interested by the eddy currents distribution. The same phenomena can
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be appreciate observing the results of the heat transfer analysis in Figure 13b.
The temperature distributions show, as expected from the electromagnetic analysis, that
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the heating is localized around the center of the stiffened panel. Finally, in Figure 13c, the temperature distributions inside the adhesive layers are displayed. A maximum
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temperature of 200°C have been considered for the adhesive.
Observing the results in Figure 13c, once again, it is possible to appreciate how the most uniform heating of the adhesive is obtained only in the central stiffeners, for the configurations SS#1 and SS#3, while for the configuration SS#2 the heat flux is not sufficient to heat the lateral stiffeners. In order to obtain a more uniform temperature distribution, the global dimension of the panel have been halved (configurations SS#4, SS#5 and SS#6). The rate of Joule dissipation for the configurations SS#4, SS#5 and SS#6 is presented in Figure 14a.
Comparing the results in Figure 14a with those shown in Figure 13a, it is possible to notice how the most heated areas have moved towards the external edges of the panel, allowing to heat also the lateral stiffeners. The nodal temperature distributions, in Figure 14b, are, as expected, in agreement with the electromagnetic analysis.
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Finally, the temperature distributions within the adhesive layers are shown in Figure 14c. Comparing the temperature distributions in Figure c with the results obtained for
configurations SS#1, SS#2 and SS#3, it is possible to notice the increase of uniformity
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in temperature distributions, resulting in a more homogeneous degree of cure of the adhesive.
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The results in Figure 14c show how the choice of the correct ratio between the
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dimensions of the panel and the size of the coil is critical to obtain a uniform degree of
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cure of the adhesive.
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Starting from the reduced model with three stiffeners, the current frequency has been changed in order to investigate its influence on the Joule energy dissipation
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(configuration SS#7).
The results shown in Figure 15, highlight the relevant effects of the current frequency
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changes on the distribution of the Joule loss. Indeed, lower values of the current frequency ensure a more uniform distribution of the energy, but, at the same time, cause a reduction of the heat flux modulus. Hence, lower current frequencies needs to be
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associated to higher value of the current intensity. A final configuration named SS#8, characterized by a smaller inductor, has been introduced. Geometry and results for this configuration are shown in Figure 16a.
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From the results of this last electromagnetic analysis, shown in Figure 16b, it is possible to appreciate how the energy moves toward the center of the panel. However, due to the reduced size of the coil, it is necessary to increase the value of the current density. In order to evaluate how the differences in the degree of cure of the adhesive can influence the mechanical behavior of the stiffened composite panel under compression, structural analyses have been performed on the configuration SS#6 and SS#7. The two
analyzed configurations have identical dimensions, but have been obtained with different values of the current frequency. The structural models have been generated using the data in terms of adhesive failure stress as a function of the temperature presented in Figure 3. The deformed shapes with out-of-plane displacements contour plots, evaluated for the configuration SS#6 at four different levels of applied displacements (0.115 mm; 0.24 mm; 1.26 mm; 1.81 mm), have been reported in Figure
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17.
Finally, the results of the structural analyses for the SS#6 and SS#7 configurations in
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terms of adhesive status variable (a numerical value of 1 for the adhesive status variable corresponds to completely separated components) have been compared in Figure 18. From Figure 18, it is possible to appreciate how different values of the current
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frequency can lead to different a failure development at the interface between skin and
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stringers in terms of damage initiation location and damage propagation as a function of
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the applied load. For the configuration SS#6 the skin-stringer debonding initiation takes place in the middle of the central stiffener for an applied displacement of 1,4 mm, while
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for the configuration SS#7, the damage initiation involves the lateral stiffeners and takes place later in the loading process (1,6 mm of applied displacements). Two snapshot in
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Figure 18, taken at different levels of applied displacements (2 mm and 4 mm) confirms that the damage development is slower for configuration SS#7.
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5. Conclusions
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This paper deals with the numerical simulations of the curing process of an adhesive layer used to bond CFRP stiffened composite panels by induction heating. Three different FE models have been introduced able to simulate the induction heating on composite laminates and their mechanical behavior. The introduced numerical
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procedure has been validate at coupon level by using data from experimental campaign on rectangular composite specimens. Then, a sensitivity analysis on stiffened composite panels has been carried out, showing the influence of the geometrical and processing parameters on the degree of cure of the adhesive and consequently on the compressive mechanical behavior of stiffened composite panels with varying geometry. The results of this sensitivity study have shown that the size of the inductor can have a relevant influence on the energy dissipated by Joule effect. Furthermore, the current frequency
has been found to be a key parameter to optimize the uniformity of the temperature distribution, resulting in a more uniform degree of cure of the adhesive layers and more uniform and improved strength properties. Indeed, for the panel configuration with increased current frequency, a relevant retardation in the damage onset and propagation with a consequent more effective use of bonded composite structures has been found. These results provide relevant input to future investigations on alternative approaches for bonding composites. However, limitations in the proposed approach, which is purely
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numeric at component level, suggest to improve the experimental validation in order to assess the robustness of the proposed numerical model, in particular when different
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boundary conditions and different loading conditions are considered. Finally, future
research should be addressed to the definition of an improved shape function to take
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into account the effect of temperatures on the degree of cure of the adhesive.
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[12] Balzano A, De Rosa IM, Sarasini F, Sarto MS. Effective properties of carbon fibre composites: EM modelling versus experimental testing. In: Proceedings of IEEE international symposium on electromagnetic compatibility, Honolulu, 2007. [13] Knauf BJ, Webb DP, Liu CC, Conway PP. Polymer bonding by induction heating for microfluidic applications. In: Proceedings of the 3rd IEEE international conference on electronics systems and integration technologies (ESTC), Berlin, 2010.
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[14] Knauf BJ, Webb DP, Liu CC, Conway PP. Low frequency induction heating for the sealing of plastic microfluidic systems. Microfluid Nanofluid 2010;9(2–3):243–52.
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[15] Bayerl T, Duhovic M, Mitschang P, Bhattacharyya D. The heating of polymer composites by electromagnetic induction – A review. Composites Part A 2014;57:27-40.
[16] Cebria´n AS, Klunker F, Zogg M. Simulation of the cure of paste adhesives by
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induction heating. Journal of Composite Materials 2014;48(12):1459–1474.
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[17] Ahmed TJ, Stavrov D, Bersee HEN, Beukers A. Induction welding of thermoplastic composites – an overview. Composites Part A 2006;37:1638–51.
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[18] Caldichoury I, L’Eplattenier P, Duhovic M. LS-DYNA R7: coupled Multiphysics
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analysis involving electromagnetism (EM), incompressible CFD (ICFD) and solid mechanics thermal solver for conjugate heat transfer problem solving. In:
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Proceedings of the 9th European LS-DYNA users conference, Manchester, 2013. [19] Duhovic M, Moser L, Mitschang P, Maier M, Caldichoury I, L’Eplattenier P.
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Simulating the joining of composite materials by electromagnetic induction. In: Proceedings of the 12th international LS-DYNA users conference, Detroit, 2012. [20] Duhovic M, Caldichoury I, L’Eplattenier P, Mitschang P, Maier M. Advances in
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simulating the joining of composite materials by electromagnetic induction. In: Proceedings of the 9th European LS-DYNA users conference, Manchester, 2013.
[21] Lopresto V, Caprino G. Damage mechanisms and energy absorption in composite
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laminates under low velocity impact loads. Solid Mechanics and its Applications 2013;192:209-289
[22] Sepe R, Armentani E, Caputo F, Lamanna G. Numerical Evaluation and Experimental Comparison of Elasto-plastic Stress-strain Distribution Around the Corner Cracks of a Notched Specimen. Procedia Engineering 2015;109:285-295
[23] Zarrelli M, Skordos AA, Partridge IK. Toward a constitutive model for curedependent modulus of a high temperature epoxy during the cure. European Polymer Journal 2010;46(8):1705-1712. [24] Caputo, F., De Luca, A., Lamanna, G., Lopresto, V., Riccio, A. Numerical investigation of onset and evolution of LVI damages in Carbon-Epoxy plates. Composites Part B: Engineering 2015; 68:385-391 [25] Perugini, P., Riccio, A., Scaramuzzino, F. Influence of delamination growth and
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contact phenomena on the compressive behaviour of composite panels. Journal of Composite Materials. 1999; 33(15):1433-1456
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[26] ABAQUS Analysis User’s Manual 6.11, 2011.
[27] Rudnev V, Loveless D, Cook R, Black M. Handbook of induction heating. Basel:
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Marcel Dekker AG; 2003.
Figures 1
0,8 0,7 0,6 0,5
0,4
0,2 0,1 0
300
350
400
450
Induced temperature [K]
500
Figure 1: Degradation of material properties with temperature
σ
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σ
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(D=0)
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A
σ
Progressive Damage Degradation
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E
ε
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Figure 2: Stress-Strain curve with progressive damage degradation [21].
Normalised material property
A
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1
0,9 0,8
0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 250
300
350
400
450
500
Induced temperature [K] Normalized Experimental Data
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0,3
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Normalised material property
0,9
Shape function
Figure 3: Calculated Shape Function
a.
b.
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Figure 4: CAE Model – Electromagnetic model.
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4,5 mm
MAGNETIC FLUX DENSITY
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A
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MAGNETIC FLUX DENSITY
Figure 5: a. Magnetic flux density distribution (T); b. a)
NODAL TEMPERATURE
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NODAL TEMPERATURE
Magnetic flux density within the air volume
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Figure 6: Temperature Distribution (°C) after 55s: a) Composite specimen; b) Adhesive Layer.
b)
250
150
EXPERIMENTAL DATA 350 V
100
NUMERICAL RESULTS 350 V 50
NUMERICAL RESULTS 250 V EXPERIMENTAL DATA 250 V
0 0
10
20
30
40
50
60
70
80
90
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Time [s]
Figure 7: Adhesive Temperature as a function of time Electrical Current applied to the coil
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Frequency of the Electrical Current applied to the coil
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Electromagnetic Time-Harmonic Temperature Distribution in the Adhesive Layer
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Transient Heat transfer
Joule Loss
Concentrated Heat Flux
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Elasto-Plastic properties of the adhesive layer
Structural
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Temperature [°C]
200
ULTIMATE LOAD
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Figure 8: Schematic representation of the numerical analysis.
Figure 9: Electromagnetic CAE model.
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Figure 11: Structural CAE Model.
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Figure 10: Thermal CAE model.
Th_Web [mm]
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Length [mm]
L_Foot [mm]
Parameters
SS#1
SS#2
SS#3
SS#4
SS#5
SS#6
Width [mm]
200
200
200
100
100
100
Length [mm]
150
150
150
75
75
75
W_Dist [mm]
90
40
20
45
20
10
W_Bay [mm]
-
80
50
-
40
25
L_Foot [mm]
20
20
20
10
10
10
H_Web [mm]
20
20
20
10
10
10
Th_Web [mm]
1,52
1,52
1,52
0,76
0,76
0,76
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Th_Foot [mm]
W_Bay [mm]
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W_Dist [mm]
H_Web [mm]
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Width [mm]
Th_foot [mm]
1,52
1,52
1,52
0,76
0,76
0,76
Th_ply [mm]
0,190
0,190
0,190
0,190
0,190
0,190
Stacking Sequence skin, foot stringer, web stringer
[0 90 90 0]s
[0 90 90 0]s
[0 90 90 0]s
[0 90 90 0]
[0 90 90 0]
[0 90 90 0]4
Figure 12: Geometrical dimensions of the analyzed configurations.
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Figure 13: Configurations SS#1, SS#2, SS#3: a) Rate of Joule dissipation (W/m3); b) Nodal Temperature
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A
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(°C); c) Nodal Temperature (°C) within the adhesive layer
Figure 14: Configurations SS#4, SS#5, SS#6: a) Rate of Joule dissipation (W/m3); b) Nodal Temperature (°C); c) Nodal Temperature (°C) within the adhesive layer
CONFIGURAZIONE SS#7 RATE OF JOULE DISSIPATION
RATE OF JOULE DISSIPATION
20 kHz
40 kHz
RATE OF JOULE DISSIPATION
RATE OF JOULE DISSIPATION
80 kHz
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RATE OF JOULE DISSIPATION
RATE OF JOULE DISSIPATION
160 kHz
120 kHz
200 kHz
b)
RATE OF JOULE DISSIPATION
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A
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a)
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Figure 15: Rate of Joule dissipation (W/m3) at different current frequency (Configuration SS#7).
Figure 16: a) FE Model; b) Rate of Joule dissipation (W/m3) - Configuration SS#8.
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OUT-OF-PLANE DISPLACEMENT
c)
OUT-OF-PLANE DISPLACEMENT
OUT-OF-PLANE DISPLACEMENT
b)
d)
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OUT-OF-PLANE DISPLACEMENT
a)
Figure 17: Out-of-plane displacement at different applied displacement levels: a) 0.115 mm; b) 0.24 mm; c) 1.26 mm; d) 1.81 mm
SS#6
STATUS VARIABLE
2 mm
4 mm
1.6 mm
2 mm
4 mm
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SS#7
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1.4 mm
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A
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Figure 18: Damage status in the adhesive layer.
Tables T [°C]
t [s]
σult [MPa]
175 175 175 185 185 185 195 195 195 175 175 175 185 185 185 195 195 195 185 185 185 175 175 175 185 185 185 195 195 195
10 20 30 10 20 30 10 20 30 10 20 30 10 20 30 10 20 30 10 20 30 10 20 30 10 20 30 10 20 30
0.451 0.876 0.844 1.156 1.435 1.323 1.198 1.206 1.203 0.740 1.058 0.887 0.892 1.506 1.505 1.471 1.486 1.496 1.504 1.387 1.321 1.029 0.876 0.930 2.086 1.435 1.323 1.743 1.765 1.789
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A
N
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V 150 150 150 150 150 150 150 150 150 250 250 250 250 250 250 250 250 250 300 300 300 350 350 350 350 350 350 350 350 350
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Table 1: Ultimate stress ASTM D5868.
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Table 2: Thermal and Electro-magnetic material properties.
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HEAT CAPACITY AT COSTANT PRESSURE [J/kgK] RELATIVE PERMITTIVITY THERMAL CONDUCTIVITY [W/mK] RELATIVE MAGNETIC PERMEABILITY ELECTRICAL CONDUCTIVITY [S/m] DENSITY [kg/m3]
COIL
PLATE
CFRP
ADEHESIVE
385
1460
1000
1460
1
1
1
1
400
0.20
3.5
0.19
1
1
1
1
6∙107
10-6
2∙104
10-6
8700
1200
1430
980
Table 3: Mechanical material properties.
Properties Value
CFRP
E11 = 147000 MPa; E22 = E33 = 11800 MPa G12 = G13 = 6000 MPa; G23 = 4000 MPa ν12 = ν13 =0.3; ν23 = 0.4
Adhesive Layer
E = 2290 MPa; ν = 0.3 σy = 327 MPa
Table 4: Analyzed configurations – Sensitivity analysis. CURRENT FREQUENCY 145 kHz 145 kHz 145 kHz 145 kHz 145 kHz 145 kHz Variable 145 kHz
A M ED PT CC E A
COIL DIMENSION Normal Normal Normal Normal Normal Normal Normal Reduced
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GLOBAL DIMENSION Normal Normal Normal Reduced Reduced Reduced Reduced Reduced
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SS#1 SS#2 SS#3 SS#4 SS#5 SS#6 SS#7 SS#8
NUMBER STRINGER 1 2 3 1 2 3 3 3
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CONF. ID
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Material
S2352-4928(17)30332-X https://doi.org/10.1016/j.mtcomm.2018.03.008 MTCOMM 319
To appear in: Received date: Revised date: Accepted date:
24-11-2017 9-3-2018 14-3-2018
Please cite this article as: A.Riccio, A.Russo, A.Raimondo, P.Cirillo, A.Caraviello, A Numerical/Experimental Study on the Induction Heating of Adhesives for Composite Materials Bonding, Materials Today Communications https://doi.org/10.1016/j.mtcomm.2018.03.008 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A Numerical/Experimental Study on the Induction Heating of Adhesives for Composite Materials Bonding
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Department of Industrial and Informatics Engineering, Università degli studi della
Sòphia High Tech S.r.l. Zona industriale di Marcianise, Marcianise (CE), Italy
Corresponding Author
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Campania “Luigi Vanvitelli”, via Roma 29, Aversa (CE), Italy 2
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A. Riccio1*, A. Russo1, A. Raimondo1, P. Cirillo2, A. Caraviello2
Tel +39 081 5010407; Fax +39 081 5010204
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e-mail: [email protected]
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Graphical Abstract
ABSTRACT In this paper, the bonding of carbon fiber reinforced polymer (CFRP) components by induction heating has been numerically simulated. Being the induction heating bonding phenomenon characterised by an intrinsic multi-physical nature, three different numerical models taking into account, respectively, electromagnetic, thermic and structural aspects, have been introduced and applied to a stiffened composite panel to predict the stringer/skin interface characteristics. The electromagnetic model evaluates
the energy loss due to the Joule effect while the thermal model is used to calculate the temperature distribution within the adhesive layer between skin and stringer. Then the structural model predicts the ultimate failure load of the stiffened panel taking into account the degree of cure of the adhesive depending on the temperature distribution at interface between skin and stringers by means of an experimentally determined degradation law. The overall developed numerical methodology has been preliminary validated by comparisons with experimental data in terms of adhesive temperature as a function of time on rectangular composite coupons. Finally, a sensitivity analysis has been performed to evaluate the effects of the geometrical parameters of the stiffened composite panel and process
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parameters on the degree of cure and then on the mechanical properties of the adhesive at interface between skin and stringers.
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Keywords: Composites Bonding; Induction heating; Finite Element Analysis (FEA).
1. Introduction
The use of adhesive for the bonding of composite structures offers several advantages
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with respect to the bolted joints in terms of lower assembly weight, uniform stress
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distribution and fatigue resistance. However, the main drawbacks of current adhesive
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bonding technology relays in the long times required for the complete cure of the adhesive, usually obtained by autoclave and resulting in long processing times and
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wasted energy. Several techniques have been developed, such as heating blankets and lamps, to accelerate the cure process and to obtain a local heating without the use of
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oven or autoclave, however these methodologies have demonstrated to be inefficient in terms of heat lost by the surrounding structure and environment [1]. The induction
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heating represents a promising technique allowing to reach the cure temperature within fraction of seconds leading to a reduction of energy consumption and time [2-9]. The
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induction heating phenomenon appears when electrically conducting objects are exposed to an alternating electromagnetic field which generates eddy currents that heat the material due to the Joule effect. In ferromagnetic materials heat could also be generated by means of magnetic hysteresis. Early approaches taken to model induction
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heating were focused on the analytical modelling of the phenomenon [10-14]. Only recently, thanks to the computational improvement of FE software the simulation of the 3D electromagnetic model fully coupled with thermal and structural analysis has become possible [15-23]. The aim of these multidisciplinary analyses is to verify the capability of the bonded structure to not develop damages induced by impact or by manufacturing which can be very critical for load carrying capability of composite structures [24,25]. This paper presents a numerical study on the use of induction
heating for bonding composite structures by curing a commercial adhesive at room temperature. Composite stiffened panels have been used as benchmark by adopting the numerical Finite Element Analysis based platform ABAQUS [26] and combining a time-harmonic electromagnetic analysis (to calculate the energy loss due to the Joule effect), a transient heat transfer analysis ( to calculate of the spatial and temporal distribution of temperatures) and, finally, a structural analysis (to evaluate the mechanical behaviour). As added value of the presented investigation and a step
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forward with respect to other research works in the field, an attempt to propose an
analytical formulation, allowing to take into account the variation of the mechanical
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properties with the cure temperature, has been made. Mechanical tests have been
performed on induction heated coupon obtained with different process parameters to provide an experimental reference for the determination of the shape functions adopted to take into account the variation of mechanical properties with the degree of cure/
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temperature. The influence of composite stiffened panel geometrical parameters such as
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the number of stiffeners, the size of the panel together with process parameters such as the inductor current frequency has been assessed by a sensitivity analysis on a number
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of selected stiffened panels geometrical configurations. In section 2 the theoretical
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background is introduced while in section 3 the experimental and numerical activities on coupon are presented. Finally in section 4 the numerical application on composite
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stiffened panel is introduced and discussed.
2. Theoretical background Electromagnetic Field
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2.1.
The induction heating takes place when a conductive material is exposed to an electromagnetic field generated by an alternating current. In particular, the magnetic
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field induces eddy currents on the surface of the material which causes resistive heating due to Joule losses. Different heating mechanisms during induction processing of electrically non conductive materials, having an internal electrical resistance of infinity, are possible. Therefore, it is necessary to introduce the so called “susceptors” in order to convert a magnetic field into heat [17]. In the case of carbon fiber reinforced materials (CFRP) the carbon fibers have an internal electrical resistance different from infinity and when the eddy currents pass through them the electrical energy is transformed into
heat [7]. In the next subsections, the theoretical aspects of the developed electromagnetic and thermal models will be introduced Electrical and magnetic fields are governed by the Maxwell’s equations, describing the electromagnetic phenomena under the low-frequency assumption. It is convenient to express the magnetic flux density vector as a function of a vector potential as in equation (1). 𝑩 = 𝛁×𝑨
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(1)
Where A is the magnetic vector potential. When the system is subjected to a time-
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harmonic excitation, in the case of sinusoidal current J 0 exp(it ) , the analysis seeks a time-harmonic electromagnetic response in the form of A0 exp(it ) . The vectors A0
and J0 represent the amplitude, respectively, of the magnetic potential vector and of the
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volume density current vector. Under these assumptions, the Maxwell’s equations are
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reduced to the equation (2).
(2)
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𝛁 × (𝜇 −1 𝛁 × 𝑨𝟎 ) + 𝑖𝜔𝝈𝑬 ∙ 𝑨𝟎 = 𝑱𝟎
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Where is the magnetic permeability tensor and σE is the electrical conductivity tensor. The relation between the magnetic flux density (B) and the magnetic field (H), is
𝑩 = 𝜇𝑯
(3)
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defined in equation (3).
The electrical conductivity is related to the current density (J) and the electric field (E)
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by the Ohm’s law expressed in equation (4). 𝑱 = 𝝈𝑬 ∙ 𝑬
(4)
The FEM software solves the variational form of the equation (2) for the components of
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the magnetic vector potential, considering a variation of the magnetic potential vector (
A0 ). 2.2.
Heat Transfer formulation
The heat generated by Joule effect due the eddy currents is simulated within the FEM software by a transient analysis, applying the thermodynamic law for heat exchange.
The first law of the thermodynamic states that the energy of an isolated system is conserved. The thermal equilibrium of the system can be expressed by the equation (5).
C p
dT (kT ) Qe dt
(5)
Where is the density, C p is the specific heat capacity, k is the thermal conductivity
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and Qe is the heat generated by the magnetic field. The boundary conditions considered in the present model representing the interaction with the surrounding air, are the convection and radiation expressed respectively by the equation (6) and (7).
(6)
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n (kT ) hc (T T0 ) n (kT ) (T04 T 4 )
(7)
Structural effects
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2.3.
A
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emissivity and is the Stefan-Boltzmann constant.
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Where hc is the convection coefficient, T0 is the ambient temperature, is the material
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The temperature at interfaces is used as an input to determine the degree of cure of the adhesive and then the mechanical properties distribution within the adhesive self. The increase of materials mechanical properties as a function of the temperature up to the
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cure temperature has been accounted by means of a suitable shape function, derived by the experimental testing activity on coupons, described in the following sections. In the
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range 300 K to 500 K the mass variation due to high temperature can be considered negligible and the material properties are degraded according to the empirical equation
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(8).
𝐸(𝑇) = 𝐸𝑢
𝐸𝑢 −𝐸𝑟 2
(1 − tanh(𝑘(𝑇𝑔 − 𝑇)))
(8)
Where Eu is the modulus at low temperature (300 K), Er is the modulus at high temperature (500 K), Tg is the transition temperature and k is an empirical constant. In Figure 1 an example of the adopted shape function is shown. More in detail, when the induced temperature reaches the cure temperature the normalized material property
is set to 1 which corresponds to the material property of the completely cured adhesive. As the induced temperature decreases, the normalized material property tends to 0.
A structural geometrically non-linear analysis is then performed by applying whatever loading condition. The equilibrium equation states that the external applied loads are
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equal to the internal loads. This condition ca be expressed by the equation (9). 𝑲(𝒖) ∙ 𝒖 = 𝑭𝒆
(9)
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Where K is the global stiffness matrix , u is the displacement and Fe are the external loads. This equation, which is a non linear equation being K a function of u, can be
solved by an iterative procedure. It is clear that different process parameters in induction will lead to a differently generated heating which will in turn generate a different
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temperature distribution influencing the spatial distribution of mechanical properties in
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and then the solution of the structural analysis.
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the adhesive. Mechanical properties of the adhesive will influence the stiffness matrix
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An elasto-plastic material model with isotropic hardening behavior has been considered for the adhesive. In this model, the yield surface changes size uniformly in all directions such that the yield stress increase in all stress direction[26]. In order to simulate the
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debonding of the stringer from the skin, for the adhesive layer a progressive degradation of the material stiffness has been assumed by degradation of the elasticity and softening
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of the yield stress as shown in Figure 2 where the stress-strain response is reported.
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3. Validation of the proposed model In order to validate the proposed numerical procedure, the induction heating on rectangular coupons have been simulated and the obtained numerical results have been
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compared with experimental data. 3.1.
Experimental methods
The experimental set-up consists of a plain coil inductor made of electrolytic copper with an operating frequency of 145 kHz, a support plate made of polyamide material and a CFRP coupon. The main parameters considered for the tests are:
Voltage across the coil;
maximum temperature;
dwell time;
initial (minimum) temperature of 20°C;
induction frequency of 145 kHz.
An Egma 30R induction generator has been adopted for the experimental tests. The generator is totally static, i.e. there are no motors or other moving devices, and the
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magnetic field is generated by an electronic circuit called inverter. Maximum and
minimum temperature values have been fixed in order to allow the coupons temperature reading during the heating phase by means of an optical pyrometer. Experiments have
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been conducted on composite specimens, manufacture in autoclave, dimensioned
according to the Standard Test Method for Short-Beam Strength of Polymer Matrix Composite Materials ASTM D2344.
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The specimen is composed of two 0° unidirectional laminates, with a 2 mm thickness,
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manufactured in autoclave, bonded with a 0.2 mm adhesive. The coil-plate distance is
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10 mm, while the specimen is leans on the support plate. The material system adopted for the plates production is Tepex® dynalite 202-C200(9)/50% (PA6 50% carbon
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fibers), while the adhesive adopted for bonding the plates is Prodas 1400.
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The experimental temperatures have been measured in the warmest point of the adhesive regardless of the location along the thickness. The maximum temperature has been fixed at 200°C, corresponding to the cure temperature of the Prodas. A
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temperature control system has been used to guarantee a constant temperature value once the cure temperature has been reached. The maximum heating power values,
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depending on the voltage across the inductor, considered for the tests are: P.H.=26% for 250 V;
P.H.=51.5% for 350 V.
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The considered values of the dwell time are 10, 20 and 30 s. The 0.8 emissivity value, used for the tests, has been obtained through bibliographic research. Moreover, an optimal value of joining pressure should be considered in order to achieve high quality bonding process and prevent voids, cracks and folds. After the realization of the bonded specimens by means of electromagnetic induction, mechanical tests, according to the standard ASTM D5868 (Standard Test Method for
Lap Shear Adhesion for Fiber Reinforced Plastic (FRP) Bonding), have been performed in order to determine the influence of the induction parameters on the strength of the adhesive. The results of the tests have been summarized in Table 1. The ultimate stresses values in table 1 are value coming from set of specimens with specific parameters Table 1 shows a general increase in ultimate stress with temperature and with induction
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time. This trend is confirmed for each voltage. It can be also noticed that, increasing the voltage, an increase in the ultimate stress is obtained, probably due to the faster approach
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to the target temperature.
The obtained experimental data allow to calibrate the shape function previously introduced in Figure 1 and evaluate the influence of the temperature reached during the induction on the strength of the adhesive layer. All the points in Table 1 have been marked
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in figure 3 and the temperature below 400°C has been extrapolated from the shape
Electromagnetic analysis, thermal analysis and experimental
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3.2.
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function. Hence, this shape function can be applied for each voltage and application time.
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verification
The numerical model adopted for the electro-magnetic analysis is presented in Figure 4,
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where the geometrical dimensions are described.
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The electro-magnetic, thermal and structural material properties, adopted in the FE analysis, for the different components have been summarized in Table 2 and Table 3.
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These properties have been provided by the manufacturer and integrated by a specific characterization test campaign performed preliminarily to the research activity presented in this paper.
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In order to simulate the passage of the electromagnetic field it is necessary to model also the volume of air surrounding the components. All the volume of the geometrical model has been discretized by using 4-node electromagnetic elements EMC3D4. The approximate size of the element is 2.5 mm. No contact elements between plates and adhesive have been used. Nodes at interfaces have been merged to allow the themal conduction between adjacent parts. This solution have also contributed to decrease the computational cost related to the analyses.
The passage of the current through the coil has been simulated by assign a current density as boundary condition. The joining pressure has been neglected in the numerical analyses. Several simulations have been made at different value of the current through the coil. In Figure 5a, as an example, the distribution of magnetic flux density induced by the coil on the support plate and specimen is introduced, while in Figure 5b, the magnetic field within the air volume can be appreciated.
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The magnetic field induces eddy currents on the surface of the material, which due to the Joule effect heats the composite laminate. The FE model for the thermal analyses
consist only of the support plate and the specimen. It has been discretized by using 8-
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node hexahedral thermal element DC3D8. The results of the thermal analysis are shown in Figure 6a and Figure 6b where the temperature distributions are shown, respectively, on the composite specimen and inside the adhesive layer after 55s.
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In Figure 7 the numerical results in terms of adhesive temperature as a function of time
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is compared to experimental results for two different value of the applied potential
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difference across the coil.
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From figure 7, as expected, the increase in the potential difference from 250V to 350V causes the reduction of the time needed to reach the cure temperature. The excellent
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agreement between numerical results and the experimental data in figure 7 proves the effectiveness of the developed numerical model in predicting the temperature evolution as a function of the induction time. Experimental data in figure 7 are the maximum
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temperatures evaluated in the adhesive when applying the induction. Indeed 9 experimental tests were performed for each potential different with a maximum standard
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deviation (evaluated at each induction control time step of about 5% with respect to maximum temperature.
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4. Numerical application
As numerical application of the proposed numerical model for the simulation of the induction heating bonding, a sensitivity study on the effects of the induction heating processing parameters has been performed on some stiffened composite panels geometrical configurations. The analyses have been preliminary carried out on a plate without stiffeners to study the thermal field on the structure. However, these results have not been presented for the sake of brevity. As already remarked, the induction heating phenomenon has been simulated by using three different numerical models: an
electromagnetic model, a thermal model and a structural model. In the frame of the electromagnetic analysis, all the components of the stiffened panel, plane coil inductor, support plate made of polyamide material and the surrounding volume of air have been modeled to simulate the induction phenomenon. The results of this analysis in terms of Joule losses are converted into a concentrated heat flux and used as boundary condition for the subsequent transient heat transfer analysis. In the frame of the transient heat transfer analysis only the specimen and the support plate have been modeled in order to
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estimate the temperature distribution inside the adhesive layer between skin and
stringers. From the temperature distributions, using appropriate degradation functions,
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as shown in the previous sections, it has been possible to obtain the spatial distribution of the elasto-plastic properties of the adhesive depending on the degree of cure. This
information have been passed to the structural analysis and the compressive behavior of the stiffened panel has been numerically investigated. The entire process allows to
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evaluate the influence of different parameters on the degree of cure of the adhesive and,
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hence, on the damage behavior and on the ultimate load of the structure. The flowchart
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of the analyses is presented in Figure 8.
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In the next subsections, the electromagnetic, the thermal and structural numerical models developed for the analysed stiffened panels will be described in detail. Electromagnetic FEM model
ED
4.1.
The geometrical model adopted for the electro-magnetic analysis, consisting of a plane
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coil inductor, a support plate made of polyamide material and the composite stiffened panel, is presented in Figure 9. All the volumes of the geometrical model have been
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discretized by using 4-node tetrahedral electromagnetic elements EMC3D4 with approximate size of 2.5 mm. The material properties adopted for the analyses are reported in the previous section in Table 2 and Table 3.
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The passage of the current through the coil has been simulated by assign a current density as boundary condition. The frequency of the current represents a key parameter being the characteristics of the magnetic field and of the eddy currents induced into the material strongly dependent on it. Furthermore, the frequency has an effect on the penetration depth which is a measure of how deep the electromagnetic radiation can penetrate into the material. According to the Maxwell’s equations, the penetration depth con be expressed as reported in Equation 10 [27].
f
(10)
Where, is the material resistivity, is the magnetic permeability and
f
is the
current frequency. In the present work a frequency of 145 kHz has been adopted for the experimental and numerical activities. For the numerical activities on the stiffened panel
4.2.
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a voltage of 250 V has been set. Thermal FEM model
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The thermal model allows to evaluate the temporal and spatial distribution of the
temperature inside the adhesive layer given the thermal flux from the electro-magnetic analysis. The geometrical model involves only the support plate and the specimen as shown in Figure 10. The FE model has been realized using the 8-node hexahedral
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thermal element DC3D8 with approximate size of 2 mm.
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The heat generated by the induction model is converted into concentrated heat flux and
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applied as initial condition of transient thermal analysis. In order to accurately predict
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the heat transfer, boundary conditions of natural convection and radiation with the surrounding air have been considered.
Structural FEM model
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4.3.
By starting from the temperature distribution obtained from the heat transfer analysis, it
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has been possible to evaluate the degree of cure of the adhesive layer, as shown in the previous sections.
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The structural analysis considers only the stiffened panel and the adhesive layers between the stiffeners and the skin (Figure 11). The volumes have been discretized by hexahedral elements C3D8R with approximate size of 2 mm with layered solid option
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to take into account the layers’ orientation. A ductile damage model has been adopted to simulate the elasto-plastic behavior of the adhesive. For connecting the stringers to adhesive and to the skin, multi-points-constraints have been adopted. The stiffened panel has been subjected to a compressive load through a displacement-controlled analysis and the failure load has been predicted. The thermal expansion of the composite has been neglected in the structural analysis. In the next subsection, the proposed numerical procedure will be applied to a sensitivity study on stiffened composite panels.
4.4.
Sensitivity Analysis – Stiffened Panel
A sensitivity analysis has been performed in order to evaluate the influence of the different geometrical and physical parameters on the degree of cure of the adhesive layer. The analyzed configurations are summarized in Table 4. The first variable parameter is the number of stiffeners on the panel, then the global
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dimensions of the stiffened panel has been reduced in order to investigate the effect of a bigger coil with respect to the panel size. Finally, a smaller radius for the coil and a
variable current frequency have been considered. The geometrical dimensions of the
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analyzed configurations are shown in Figure 12, while the properties of the used
materials are listed in Tables 2 and 3. The coil-plate distance is 10 mm, while the specimen is leans on the support plate.
The rate of Joule dissipation on the stiffened panel for the configuration SS#1, SS#2 and
N
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SS#3 obtained from the electromagnetic analysis is shown in Figure 13a.
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As it can be seen from the Figure a, the distribution of Joule losses is influenced by the presence of the stiffeners due to the increase in the thickness in the stringer foot area.
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Only for the configuration with one stiffener (SS#1) the heat flux covers the entire bonding area, while, especially for the configuration SS#3, the lateral stiffeners are,
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substantially, not interested by the eddy currents distribution. The same phenomena can
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be appreciate observing the results of the heat transfer analysis in Figure 13b.
The temperature distributions show, as expected from the electromagnetic analysis, that
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the heating is localized around the center of the stiffened panel. Finally, in Figure 13c, the temperature distributions inside the adhesive layers are displayed. A maximum
A
temperature of 200°C have been considered for the adhesive.
Observing the results in Figure 13c, once again, it is possible to appreciate how the most uniform heating of the adhesive is obtained only in the central stiffeners, for the configurations SS#1 and SS#3, while for the configuration SS#2 the heat flux is not sufficient to heat the lateral stiffeners. In order to obtain a more uniform temperature distribution, the global dimension of the panel have been halved (configurations SS#4, SS#5 and SS#6). The rate of Joule dissipation for the configurations SS#4, SS#5 and SS#6 is presented in Figure 14a.
Comparing the results in Figure 14a with those shown in Figure 13a, it is possible to notice how the most heated areas have moved towards the external edges of the panel, allowing to heat also the lateral stiffeners. The nodal temperature distributions, in Figure 14b, are, as expected, in agreement with the electromagnetic analysis.
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Finally, the temperature distributions within the adhesive layers are shown in Figure 14c. Comparing the temperature distributions in Figure c with the results obtained for
configurations SS#1, SS#2 and SS#3, it is possible to notice the increase of uniformity
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in temperature distributions, resulting in a more homogeneous degree of cure of the adhesive.
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The results in Figure 14c show how the choice of the correct ratio between the
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dimensions of the panel and the size of the coil is critical to obtain a uniform degree of
A
cure of the adhesive.
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Starting from the reduced model with three stiffeners, the current frequency has been changed in order to investigate its influence on the Joule energy dissipation
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(configuration SS#7).
The results shown in Figure 15, highlight the relevant effects of the current frequency
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changes on the distribution of the Joule loss. Indeed, lower values of the current frequency ensure a more uniform distribution of the energy, but, at the same time, cause a reduction of the heat flux modulus. Hence, lower current frequencies needs to be
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associated to higher value of the current intensity. A final configuration named SS#8, characterized by a smaller inductor, has been introduced. Geometry and results for this configuration are shown in Figure 16a.
A
From the results of this last electromagnetic analysis, shown in Figure 16b, it is possible to appreciate how the energy moves toward the center of the panel. However, due to the reduced size of the coil, it is necessary to increase the value of the current density. In order to evaluate how the differences in the degree of cure of the adhesive can influence the mechanical behavior of the stiffened composite panel under compression, structural analyses have been performed on the configuration SS#6 and SS#7. The two
analyzed configurations have identical dimensions, but have been obtained with different values of the current frequency. The structural models have been generated using the data in terms of adhesive failure stress as a function of the temperature presented in Figure 3. The deformed shapes with out-of-plane displacements contour plots, evaluated for the configuration SS#6 at four different levels of applied displacements (0.115 mm; 0.24 mm; 1.26 mm; 1.81 mm), have been reported in Figure
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17.
Finally, the results of the structural analyses for the SS#6 and SS#7 configurations in
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terms of adhesive status variable (a numerical value of 1 for the adhesive status variable corresponds to completely separated components) have been compared in Figure 18. From Figure 18, it is possible to appreciate how different values of the current
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frequency can lead to different a failure development at the interface between skin and
N
stringers in terms of damage initiation location and damage propagation as a function of
A
the applied load. For the configuration SS#6 the skin-stringer debonding initiation takes place in the middle of the central stiffener for an applied displacement of 1,4 mm, while
M
for the configuration SS#7, the damage initiation involves the lateral stiffeners and takes place later in the loading process (1,6 mm of applied displacements). Two snapshot in
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Figure 18, taken at different levels of applied displacements (2 mm and 4 mm) confirms that the damage development is slower for configuration SS#7.
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5. Conclusions
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This paper deals with the numerical simulations of the curing process of an adhesive layer used to bond CFRP stiffened composite panels by induction heating. Three different FE models have been introduced able to simulate the induction heating on composite laminates and their mechanical behavior. The introduced numerical
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procedure has been validate at coupon level by using data from experimental campaign on rectangular composite specimens. Then, a sensitivity analysis on stiffened composite panels has been carried out, showing the influence of the geometrical and processing parameters on the degree of cure of the adhesive and consequently on the compressive mechanical behavior of stiffened composite panels with varying geometry. The results of this sensitivity study have shown that the size of the inductor can have a relevant influence on the energy dissipated by Joule effect. Furthermore, the current frequency
has been found to be a key parameter to optimize the uniformity of the temperature distribution, resulting in a more uniform degree of cure of the adhesive layers and more uniform and improved strength properties. Indeed, for the panel configuration with increased current frequency, a relevant retardation in the damage onset and propagation with a consequent more effective use of bonded composite structures has been found. These results provide relevant input to future investigations on alternative approaches for bonding composites. However, limitations in the proposed approach, which is purely
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numeric at component level, suggest to improve the experimental validation in order to assess the robustness of the proposed numerical model, in particular when different
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boundary conditions and different loading conditions are considered. Finally, future
research should be addressed to the definition of an improved shape function to take
A
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ED
M
A
N
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into account the effect of temperatures on the degree of cure of the adhesive.
References [1] Tay TE, Fink BK, McKnight SH, Yarlagadda S, Gillespie JW Jr. Accelerated curing of adhesives in bonded joints by induction heating. J Compos Mater 1999;33(17):1643-1664. [2] Mahdi S, Kim H, Gama B, et al. A comparison of oven-cured and induction-cured adhesively bonded composite joints. J Compos Mater 2003;37(6):519–542.
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[3] Miller KJ, Collier KN, Soll-Morris HB, Swaminathan R, McHenry ME. Induction
heating of FeCo nanoparticles for rapid rf curing of epoxy composites. J Appl Phys 2009;105.
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[4] Frauenhofer M, Kunz H, Dilger K. Fast curing of adhesives in the field of CFRP. J Adhes 2012;88(4–6):406–417.
[5] Fink BK, McCullough RL, Gillespie JW Jr. Experimental verification of models for
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induction heating of continuous-carbon-fibre composites. Polym Compos
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1996;17(2):198–209.
[6] Kim JH, Yarlagadda S, Shevchenko NB, Fink BK, Gillespie JW Jr. Development of
A
a Numerical Model to Predict In-Plane Heat Generation Patterns During Induction
M
Processing of Carbon Fiber-Reinforced Prepreg Stacks. J Compos Mater 2003;37 (16):1461–1483.
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[7] Yarlagadda S, Kim HJ, Gillespie JW Jr., Shevchenko NB, Fink BK. A Study on the Induction Heating of Conductive Fiber Reinforced Composites. J Compos Mater 2002;36 (4):401–421.
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[8] Suwanwatana W, Yarlagadda S, Gillespie JW Jr. Hysteresis heating based induction bonding of thermoplastic composites. Compos Sci Technol 2006;66 (11-12):1713–
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1723.
[9] Baker AA, Callinan RJ, Davis MJ, Jones R, Williams JG. Repair of Mirage III aircraft using the BFRP crack-patching technique. Theor. Appl. Fract. Mech. 1984,
A
2:1–15.
[10] Candeo A, Dughiero F. Numerical FEM models for the planning of magnetic induction hyperthermia treatments with nanoparticles. IEEE Trans Magn 2009;45(3):1658–61. [11] Dasgupta A, Agarwal RK. Orthotropic thermal conductivity of plain-weave fabric composites using a homogenization technique. J Compos Mater 1992;26:2736– 2758.
[12] Balzano A, De Rosa IM, Sarasini F, Sarto MS. Effective properties of carbon fibre composites: EM modelling versus experimental testing. In: Proceedings of IEEE international symposium on electromagnetic compatibility, Honolulu, 2007. [13] Knauf BJ, Webb DP, Liu CC, Conway PP. Polymer bonding by induction heating for microfluidic applications. In: Proceedings of the 3rd IEEE international conference on electronics systems and integration technologies (ESTC), Berlin, 2010.
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[14] Knauf BJ, Webb DP, Liu CC, Conway PP. Low frequency induction heating for the sealing of plastic microfluidic systems. Microfluid Nanofluid 2010;9(2–3):243–52.
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[15] Bayerl T, Duhovic M, Mitschang P, Bhattacharyya D. The heating of polymer composites by electromagnetic induction – A review. Composites Part A 2014;57:27-40.
[16] Cebria´n AS, Klunker F, Zogg M. Simulation of the cure of paste adhesives by
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induction heating. Journal of Composite Materials 2014;48(12):1459–1474.
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[17] Ahmed TJ, Stavrov D, Bersee HEN, Beukers A. Induction welding of thermoplastic composites – an overview. Composites Part A 2006;37:1638–51.
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[18] Caldichoury I, L’Eplattenier P, Duhovic M. LS-DYNA R7: coupled Multiphysics
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analysis involving electromagnetism (EM), incompressible CFD (ICFD) and solid mechanics thermal solver for conjugate heat transfer problem solving. In:
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Proceedings of the 9th European LS-DYNA users conference, Manchester, 2013. [19] Duhovic M, Moser L, Mitschang P, Maier M, Caldichoury I, L’Eplattenier P.
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Simulating the joining of composite materials by electromagnetic induction. In: Proceedings of the 12th international LS-DYNA users conference, Detroit, 2012. [20] Duhovic M, Caldichoury I, L’Eplattenier P, Mitschang P, Maier M. Advances in
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simulating the joining of composite materials by electromagnetic induction. In: Proceedings of the 9th European LS-DYNA users conference, Manchester, 2013.
[21] Lopresto V, Caprino G. Damage mechanisms and energy absorption in composite
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laminates under low velocity impact loads. Solid Mechanics and its Applications 2013;192:209-289
[22] Sepe R, Armentani E, Caputo F, Lamanna G. Numerical Evaluation and Experimental Comparison of Elasto-plastic Stress-strain Distribution Around the Corner Cracks of a Notched Specimen. Procedia Engineering 2015;109:285-295
[23] Zarrelli M, Skordos AA, Partridge IK. Toward a constitutive model for curedependent modulus of a high temperature epoxy during the cure. European Polymer Journal 2010;46(8):1705-1712. [24] Caputo, F., De Luca, A., Lamanna, G., Lopresto, V., Riccio, A. Numerical investigation of onset and evolution of LVI damages in Carbon-Epoxy plates. Composites Part B: Engineering 2015; 68:385-391 [25] Perugini, P., Riccio, A., Scaramuzzino, F. Influence of delamination growth and
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contact phenomena on the compressive behaviour of composite panels. Journal of Composite Materials. 1999; 33(15):1433-1456
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[26] ABAQUS Analysis User’s Manual 6.11, 2011.
[27] Rudnev V, Loveless D, Cook R, Black M. Handbook of induction heating. Basel:
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Marcel Dekker AG; 2003.
Figures 1
0,8 0,7 0,6 0,5
0,4
0,2 0,1 0
300
350
400
450
Induced temperature [K]
500
Figure 1: Degradation of material properties with temperature
σ
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σ
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(D=0)
M
A
σ
Progressive Damage Degradation
ED
E
ε
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Figure 2: Stress-Strain curve with progressive damage degradation [21].
Normalised material property
A
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1
0,9 0,8
0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 250
300
350
400
450
500
Induced temperature [K] Normalized Experimental Data
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0,3
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Normalised material property
0,9
Shape function
Figure 3: Calculated Shape Function
a.
b.
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Figure 4: CAE Model – Electromagnetic model.
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4,5 mm
MAGNETIC FLUX DENSITY
M
A
N
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MAGNETIC FLUX DENSITY
Figure 5: a. Magnetic flux density distribution (T); b. a)
NODAL TEMPERATURE
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PT
ED
NODAL TEMPERATURE
Magnetic flux density within the air volume
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Figure 6: Temperature Distribution (°C) after 55s: a) Composite specimen; b) Adhesive Layer.
b)
250
150
EXPERIMENTAL DATA 350 V
100
NUMERICAL RESULTS 350 V 50
NUMERICAL RESULTS 250 V EXPERIMENTAL DATA 250 V
0 0
10
20
30
40
50
60
70
80
90
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Time [s]
Figure 7: Adhesive Temperature as a function of time Electrical Current applied to the coil
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Frequency of the Electrical Current applied to the coil
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Electromagnetic Time-Harmonic Temperature Distribution in the Adhesive Layer
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Transient Heat transfer
Joule Loss
Concentrated Heat Flux
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Elasto-Plastic properties of the adhesive layer
Structural
ED
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Temperature [°C]
200
ULTIMATE LOAD
A
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Figure 8: Schematic representation of the numerical analysis.
Figure 9: Electromagnetic CAE model.
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Figure 11: Structural CAE Model.
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Figure 10: Thermal CAE model.
Th_Web [mm]
A ED
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Length [mm]
L_Foot [mm]
Parameters
SS#1
SS#2
SS#3
SS#4
SS#5
SS#6
Width [mm]
200
200
200
100
100
100
Length [mm]
150
150
150
75
75
75
W_Dist [mm]
90
40
20
45
20
10
W_Bay [mm]
-
80
50
-
40
25
L_Foot [mm]
20
20
20
10
10
10
H_Web [mm]
20
20
20
10
10
10
Th_Web [mm]
1,52
1,52
1,52
0,76
0,76
0,76
CC E A
Th_Foot [mm]
W_Bay [mm]
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W_Dist [mm]
H_Web [mm]
N
Width [mm]
Th_foot [mm]
1,52
1,52
1,52
0,76
0,76
0,76
Th_ply [mm]
0,190
0,190
0,190
0,190
0,190
0,190
Stacking Sequence skin, foot stringer, web stringer
[0 90 90 0]s
[0 90 90 0]s
[0 90 90 0]s
[0 90 90 0]
[0 90 90 0]
[0 90 90 0]4
Figure 12: Geometrical dimensions of the analyzed configurations.
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Figure 13: Configurations SS#1, SS#2, SS#3: a) Rate of Joule dissipation (W/m3); b) Nodal Temperature
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ED
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A
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(°C); c) Nodal Temperature (°C) within the adhesive layer
Figure 14: Configurations SS#4, SS#5, SS#6: a) Rate of Joule dissipation (W/m3); b) Nodal Temperature (°C); c) Nodal Temperature (°C) within the adhesive layer
CONFIGURAZIONE SS#7 RATE OF JOULE DISSIPATION
RATE OF JOULE DISSIPATION
20 kHz
40 kHz
RATE OF JOULE DISSIPATION
RATE OF JOULE DISSIPATION
80 kHz
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RATE OF JOULE DISSIPATION
RATE OF JOULE DISSIPATION
160 kHz
120 kHz
200 kHz
b)
RATE OF JOULE DISSIPATION
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A
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a)
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Figure 15: Rate of Joule dissipation (W/m3) at different current frequency (Configuration SS#7).
Figure 16: a) FE Model; b) Rate of Joule dissipation (W/m3) - Configuration SS#8.
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OUT-OF-PLANE DISPLACEMENT
c)
OUT-OF-PLANE DISPLACEMENT
OUT-OF-PLANE DISPLACEMENT
b)
d)
A
OUT-OF-PLANE DISPLACEMENT
a)
Figure 17: Out-of-plane displacement at different applied displacement levels: a) 0.115 mm; b) 0.24 mm; c) 1.26 mm; d) 1.81 mm
SS#6
STATUS VARIABLE
2 mm
4 mm
1.6 mm
2 mm
4 mm
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SS#7
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1.4 mm
A
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ED
M
A
N
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Figure 18: Damage status in the adhesive layer.
Tables T [°C]
t [s]
σult [MPa]
175 175 175 185 185 185 195 195 195 175 175 175 185 185 185 195 195 195 185 185 185 175 175 175 185 185 185 195 195 195
10 20 30 10 20 30 10 20 30 10 20 30 10 20 30 10 20 30 10 20 30 10 20 30 10 20 30 10 20 30
0.451 0.876 0.844 1.156 1.435 1.323 1.198 1.206 1.203 0.740 1.058 0.887 0.892 1.506 1.505 1.471 1.486 1.496 1.504 1.387 1.321 1.029 0.876 0.930 2.086 1.435 1.323 1.743 1.765 1.789
ED
M
A
N
U
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V 150 150 150 150 150 150 150 150 150 250 250 250 250 250 250 250 250 250 300 300 300 350 350 350 350 350 350 350 350 350
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Table 1: Ultimate stress ASTM D5868.
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Table 2: Thermal and Electro-magnetic material properties.
A
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HEAT CAPACITY AT COSTANT PRESSURE [J/kgK] RELATIVE PERMITTIVITY THERMAL CONDUCTIVITY [W/mK] RELATIVE MAGNETIC PERMEABILITY ELECTRICAL CONDUCTIVITY [S/m] DENSITY [kg/m3]
COIL
PLATE
CFRP
ADEHESIVE
385
1460
1000
1460
1
1
1
1
400
0.20
3.5
0.19
1
1
1
1
6∙107
10-6
2∙104
10-6
8700
1200
1430
980
Table 3: Mechanical material properties.
Properties Value
CFRP
E11 = 147000 MPa; E22 = E33 = 11800 MPa G12 = G13 = 6000 MPa; G23 = 4000 MPa ν12 = ν13 =0.3; ν23 = 0.4
Adhesive Layer
E = 2290 MPa; ν = 0.3 σy = 327 MPa
Table 4: Analyzed configurations – Sensitivity analysis. CURRENT FREQUENCY 145 kHz 145 kHz 145 kHz 145 kHz 145 kHz 145 kHz Variable 145 kHz
A M ED PT CC E A
COIL DIMENSION Normal Normal Normal Normal Normal Normal Normal Reduced
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GLOBAL DIMENSION Normal Normal Normal Reduced Reduced Reduced Reduced Reduced
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SS#1 SS#2 SS#3 SS#4 SS#5 SS#6 SS#7 SS#8
NUMBER STRINGER 1 2 3 1 2 3 3 3
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CONF. ID
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Material