Composite Mould Design with Multiphysics FEM Computations Guidance
Abstract
This work was developed under the European Seventh Framework Program, Theme 4, NMP—Nanosciences, Nanotechnologies, Materials and new Production Technologies, Project COEUS-TITAN [Grant Agreement no. CP-TP 246256-2].
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Citation: Garmendia, I.; Vallejo, H.; Osés, U. Composite Mould Design with Multiphysics FEM Computations Guidance. Computation 2023,11, 41. https://doi.org/10.3390/ computation11020041 Academic Editors: Martynas Patašius and Rimantas Barauskas Received: 3 January 2023 Revised: 6 February 2023 Accepted: 13 February 2023 Published: 17 February 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). computation Article Composite Mould Design with Multiphysics FEM Computations Guidance Iñaki Garmendia 1,* , Haritz Vallejo 2and Usue Osés1 1Mechanical Engineering Department, Engineering School of Gipuzkoa, University of the Basque Country UPV/EHU, Plaza de Europa, 1, E-20018 Donostia-San Sebastián, Spain 2TECNALIA, Basque Research and Technology Alliance (BRTA), Mikeletegi Pasealekua, 7, E-20009 Donostia-San Sebastián, Spain *Correspondence: [email protected]; Tel.: +34-43-018-630 Abstract: Composite moulds constitute an attractive alternative to classical metallic moulds when used for components fabricated by processes such as Resin Transfer Moulding (RTM). However, there are many factors that have to be accounted for if a correct design of the moulds is sought after. In this paper, the Finite Element Method (FEM) is used to help in the design of the mould. To do so, a thermo-electrical simulation has been performed through MSC-Marc in the preheating phase in order to ensure that the mould is able to be heated, through the Joule’s effect, according to the thermal cycle specified under operating conditions. Mean temperatures of 120 ◦ C and 100 ◦ C are predicted for the lower and upper semi-mould parts, respectively. Additionally, a thermo-electrical-mechanical calculation has been completed with MSC-Marc to calculate the tensile state along the system during the preheating stage. For the filling phase, the filling process itself has been simulated through RTM-Worx. Both the uniformand non-uniform temperature distribution approaches have been used to assess the resulting effect. It has been found that this piece of software cannot model the temperature dependency of the resin and a numerical trick must have been applied in the second case to overcome it. Results have been found to be very dependent on the approach, the filling time being 73% greater when modelling a non-uniform temperature distribution. The correct behaviour of the mould during the filling stage, as a consequence of the filling pressure, has been also proved with a specific mechanical analysis conducted with MSC-Marc. Finally, the thermo-elastic response of the mould during the curing stage has been numerically assessed. This analysis has been made through MSC-Marc, paying special attention to the curing of the resin and the exothermic reaction that takes place. For the sake of accuracy, a user subroutine to include specific curing laws has been used. Material properties employed are also described in detail following a modified version of the Scott model, with curing properties extracted from experiments. All these detailed calculations have been the cornerstone to designing the composite mould and have also unveiled some capabilities that were missed in the commercial codes employed. Future versions of these commercial codes will have to deal with these weak points but, as a whole, the Finite Element Method is shown to be an appropriate tool for helping in the design of composite moulds. Keywords: composite moulds; curing simulation; filling simulation; finite element method; thermoelectrical simulation 1. Introduction To this day, metals (mainly steel and aluminium alloys) are the most reasonable option for the fabrication of tools and moulds, as they meet the basic requirements of mass production processes [ 1 ]. However, metals as tooling materials present a number of serious disadvantages such as much higher coefficients of thermal expansion (CTE) than the materials of the produced parts, raw material consumption, and high costs for machining [2]. Computation 2023,11, 41. https://doi.org/10.3390/computation11020041 https://www.mdpi.com/journal/computation
Computation 2023,11, 41 2 of 16 Despite of having a much shorter useful life than metal tools and entailing more problems related to micro-cracking and porosity, composite tooling offers many advantages as it is a lightweight, less costly solution that has lower thermal inertia and is relatively easy to produce. They offer potentially decreased fabrication time, easy repair/maintenance, lower CTE mismatches, tailored thermal and structural properties, and reduced health and safety risks as well. Consequently, it seems appropriate to develop innovative, robust and easy to heat composite moulds (both closed and open), through addressing all those issues that currently prevent composite tooling from being a viable alternative for the industrial production of plastic and composite parts across a wide range of manufacturing routes. Resin Transfer Moulding (RTM) is one of the manufacturing processes that can be studied through the Finite Element Method (FEM) [ 3 – 8 ]. It involves not only the RTM process itself, but also the design of the mould and its behaviour from a thermal, electrical, mechanical, filling, and curing point of view. During a typical RTM process (see Figure 1), four steps can be distinguished: (1) Preheating of the mould until it reaches an adequate temperature, (2) Filling through resin injection, (3) Curing of the resin, and (4) Cooling of the mould. Computation 2023, 11, x 2 of 16 Despite of having a much shorter useful life than metal tools and entailing more problems related to micro-cracking and porosity, composite tooling offers many advantages as it is a lightweight, less costly solution that has lower thermal inertia and is relatively easy to produce. They offer potentially decreased fabrication time, easy repair/maintenance, lower CTE mismatches, tailored thermal and structural properties, and reduced health and safety risks as well. Consequently, it seems appropriate to develop innovative, robust and easy to heat composite moulds (both closed and open), through addressing all those issues that currently prevent composite tooling from being a viable alternative for the industrial production of plastic and composite parts across a wide range of manufacturing routes. Resin Transfer Moulding (RTM) is one of the manufacturing processes that can be studied through the Finite Element Method (FEM) [3–8]. It involves not only the RTM process itself, but also the design of the mould and its behaviour from a thermal, electrical, mechanical, filling, and curing point of view. During a typical RTM process (see Figure 1), four steps can be distinguished: (1) Preheating of the mould until it reaches an adequate temperature, (2) Filling through resin injection, (3) Curing of the resin, and (4) Cooling of the mould. (a) (b) (c) (d) Figure 1. Different stages of a typical RTM process: (a) preheating of the mould, (b) resin filling, (c) curing stage, and (d) cooling down phase. In reference [3], Zade et al. simulated the RTM and cure process of a wing flap composite part through the commercial FEM code ANSYS. They paid special attention to the material properties of the resin, obtained through Differential Scanning Calorimetry (DSC). They also simulated the filling process with different number of injection and vent points. However, they did not simulate the preheating phase of the process and assumed a uniform initial temperature of 120 °C in the mould, which heavily conditioned their filling results. In reference [4], Joo et al. concentrated their simulation efforts on the mechanical strength obtained for an automotive composite front bumper assemble. The composite part was obtained by High Pressure Resin Transfer Moulding Process and shows good agreement when comparing FEM results obtained with LS-DYNA and the experimental results. Reference [5] shows the work performed by Simacek et al. They used the LIMS FEM software to simulate a Compression RTM process. Their geometry was a real 3-D B-pillar, but they recognized that some simplifications had to be accepted if an affordable numerical calculation was to be performed. Once again, preheating was not Figure 1. Different stages of a typical RTM process: ( a ) preheating of the mould, ( b ) resin filling, (c) curing stage, and (d) cooling down phase. In reference [ 3 ], Zade et al. simulated the RTM and cure process of a wing flap composite part through the commercial FEM code ANSYS. They paid special attention to the material properties of the resin, obtained through Differential Scanning Calorimetry (DSC). They also simulated the filling process with different number of injection and vent points. However, they did not simulate the preheating phase of the process and assumed a uniform initial temperature of 120 ◦ C in the mould, which heavily conditioned their filling results. In reference [ 4 ], Joo et al. concentrated their simulation efforts on the mechanical strength obtained for an automotive composite front bumper assemble. The composite part was obtained by High Pressure Resin Transfer Moulding Process and shows good agreement when comparing FEM results obtained with LS-DYNA and the experimental results. Reference [ 5 ] shows the work performed by Simacek et al. They used the LIMS FEM software to simulate a Compression RTM process. Their geometry was a real 3-D B-pillar, but they recognized that some simplifications had to be accepted if an affordable numerical calculation was to be performed. Once again, preheating was not simulated and initial
Computation 2023,11, 41 3 of 16 temperatures for the process were taken based on previous experience. Reference [ 6 ] shows the RTM process simulation of another car component, a cab front, performed with the commercial software PAM-RTM by Kuppusamy et al. They simulated the air entrapment that can happen in such a process and simulated the filling for different mould temperatures. In reference [ 7 ], Xiong et al. incorporated the idea of multiobjective optimization for the design of lightweight car components. Finally, in reference [ 8 ], Mal et al. investigated the RTM process of thin components and the effect of mechanical dispersion on the general heat transfer. These references show the importance of simulation by FEM in the context of industrial processes, such as RTM and others. In fact, computational simulation via the Finite Element Method brings advantages compared to experimental and/or analytical studies, such as faster results and lower cost. The objective of this paper is to show that the Finite Element Method is an adequate tool to ensure an appropriate design of a composite mould and to shorten development costs and times. Consequently, many design decisions can be taken now based on simulation results, which will be confirmed afterwards by appropriate experimentation. 2. Methodology FEM calculations can be a guide and a suitability check of a mould design in the context of an RTM process [ 9 ]. In this paper, different aspects that were taken into account to ensure a proper mould design will be shown. As the mould was expected to be heated by means of the direct resistance method, the preheating was modelled through a thermo-electric analysis to determine the temperature distribution of the mould due to the Joule’s effect. After that, a mechanical analysis was planned to account for the thermal stresses generated by the heating. However, a thermoelectrical-mechanical analysis was carried out to obtain the mechanical response of the mould because of the thermal expansion: the entire coupled analysis could be easily performed with the simulation code used, MSC-Marc [10]. Based on the theoretical thermal cycle, the filling of the mould was modelled assuming isothermal conditions with a commercial software, RTM-Worx [ 11 ]. Additionally, using the temperature contour on the cavity determined in the preheating stage, the filling process simulation was repeated assuming a non-isothermal temperature distribution. In both cases, the pressure profile and the filling time were obtained to compare the effect of the approach selected. Following, a structural analysis was conducted to assess the mechanical behaviour of the mould due to the internal pressure. Regarding the curing of the resin [ 12 – 15 ], a thermal analysis was completed considering the exothermal reaction that took place. Finally, a thermo-mechanical analysis was conducted to determine the dimensional stability of the mould and the stress state due to the resulting transient temperature profile. The cooling down of the mould was not studied. As it can be deduced from this short description, several FEM analyses have been performed in a certain order, making some simplifications. Some other possibilities and coupled analyses have been disregarded and considered not needed, as the complexity would have been excessive and the software employed presented some limitations, which will be explained later in the paper. Figure 2summarizes the FEM calculations performed.
Computation 2023,11, 41 4 of 16 Computation 2023, 11, x 4 of 16 Figure 2. Software framework for the mould design. 3. Mould Design A composite mould with a resistive heater system was developed to be used in the simulation and fabrication activities. As shown in Figure 3, the mould was made up of two mica layers, two semi-moulds of composite, a gasket and the resistive heater system. Mica layers were used for thermal insulation purposes. Figure 3. Components of the mould and views of the resulting assembly. Regarding the heater system concept, a resistive material with needed electrical connections inside and an external housing of fibreglass (to avoid electrical leaks) was considered. Main dimensions of the mould analysed are presented in Figure 4. Figure 2. Software framework for the mould design. 3. Mould Design A composite mould with a resistive heater system was developed to be used in the simulation and fabrication activities. As shown in Figure 3, the mould was made up of two mica layers, two semi-moulds of composite, a gasket and the resistive heater system. Mica layers were used for thermal insulation purposes. Computation 2023, 11, x 4 of 16 Figure 2. Software framework for the mould design. 3. Mould Design A composite mould with a resistive heater system was developed to be used in the simulation and fabrication activities. As shown in Figure 3, the mould was made up of two mica layers, two semi-moulds of composite, a gasket and the resistive heater system. Mica layers were used for thermal insulation purposes. Figure 3. Components of the mould and views of the resulting assembly. Regarding the heater system concept, a resistive material with needed electrical connections inside and an external housing of fibreglass (to avoid electrical leaks) was considered. Main dimensions of the mould analysed are presented in Figure 4. Figure 3. Components of the mould and views of the resulting assembly. Regarding the heater system concept, a resistive material with needed electrical connections inside and an external housing of fibreglass (to avoid electrical leaks) was considered. Main dimensions of the mould analysed are presented in Figure 4.
Computation 2023,11, 41 5 of 16 Computation 2023, 11, x 5 of 16 Figure 4. Main dimensions of the mould. Table 1 collects the physical, electrical, thermal, mechanical, and viscosity properties of the materials involved in the RTM process. A composite made of high conductivity fibres was used for both semi-moulds. For the composite to be manufactured, properties from the AS43K fibres and the RTM6 resin were considered. Rubber, mica, and fibreglass were also used. Table 1 also shows that several properties of the sample have not been considered (NC) as its mechanical influence (which is small) can be neglected. Table 1. Material properties. Property Composite Rubber Mica Fiberglass Dry Fibre Resin Composite Part Density (kg/m3) 1700 1150 2850 1800 1790 1150 1500 Electrical resistivity (ohm·m) xx 5.88 × 10−6 5.88 × 10−6 yy 5.88 × 10−6 1 × 1014 2 × 1013 1 × 1014 5.88 × 10−6 NC NC zz 5.88 × 10−4 5.88 × 10−5 Thermal conductivity W/(m·K) xx 164 6.83 7 yy 164 0.15 0.35 0.58 6.83 0.3 7 zz 1 0.683 1 Specific heat J/(kg·K) 500 2000 880 795 1130 1500 1300 CTE (1/C), × 10−6 xx 1 × 10−3 yy 1 × 10−3 80 10 8 NC NC NC zz 50 Emissivity 0.9 - 0.75 - - - - Young’s modulus (GPa) xx 150 yy 150 7 × 10−3 172 18 NC NC NC zz 4 Figure 4. Main dimensions of the mould (in mm). Table 1collects the physical, electrical, thermal, mechanical, and viscosity properties of the materials involved in the RTM process. A composite made of high conductivity fibres was used for both semi-moulds. For the composite to be manufactured, properties from the AS43K fibres and the RTM6 resin were considered. Rubber, mica, and fibreglass were also used. Table 1also shows that several properties of the sample have not been considered (NC) as its mechanical influence (which is small) can be neglected. Table 1. Material properties. Property Composite Rubber Mica Fiberglass Dry Fibre Resin Composite Part Density (kg/m3) 1700 1150 2850 1800 1790 1150 1500 Electrical resistivity (ohm·m) xx 5.88 ×10−65.88 ×10−6 yy 5.88 ×10−61×1014 2×1013 1×1014 5.88 ×10−6NC NC zz 5.88 ×10−45.88 ×10−5 Thermal conductivity W/(m·K) xx 164 6.83 7 yy 164 0.15 0.35 0.58 6.83 0.3 7 zz 1 0.683 1 Specific heat J/(kg·K) 500 2000 880 795 1130 1500 1300 CTE (1/C), ×10−6 xx 1 ×10−3 yy 1 ×10−380 10 8 NC NC NC zz 50 Emissivity 0.9 - 0.75 - - - - Young’s modulus (GPa) xx 150 yy 150 7 ×10−3172 18 NC NC NC zz 4
Computation 2023,11, 41 6 of 16 Table 1. Cont. Property Composite Rubber Mica Fiberglass Dry Fibre Resin Composite Part Poisson’s ratio xy 0.2 yz 0.015 0.495 0.3 0.3 NC NC NC xz 0.015 Transv. elasticity modulus (GPa) xy 62 yz 2.75 - - - - - - xz 2.75 Viscosity (mPa·s) at 120 ◦C - - - - - 33 - Permeability (m2), ×10−11 xx - - - - - 1.05 - yy - - - - - 1.05 - The heat power that is produced during the curing process follows Equation (1): Pc=dα dt ×(1−Vf)×ρr×Hr×VT(1) where P c represents the generated power (W), d α /dt is the curing rate (s −1 ), V f is the fibre volume fraction (no units), ρr is the resin density(kg/m 3 ), H r is the resin cure reaction heat (J/kg), and VTis the total volume (m3). The resin curing degree α, no units, can be calculated according to Equation (2): αt+∆t=αt+∆t×dα dt (2) Finally, the curing rate follows a modified version of the Scott model [16]: dα dt =K1+K2×αm×(B−α)n(3) where K1=A1×e −∆E1 RT (4) K2=A2×e −∆E2 RT (5) m=m1+m2×T+m3×T2(6) B=b1+b2×T+b3×T2(7) n=n1+n2×T+n3×T2(8) Values of the coefficients and Hr are collected in Table 2. These values come from previous experiments performed in a previous project, not reported in the open literature.
Computation 2023,11, 41 7 of 16 Table 2. Coefficients values of the curing rate equation. Coefficient Value Coefficient Value A11451.873 s−1Hr480,000 J/kg A216,797.24 s−1b11.04578 ∆E17739.757 J/mol b2−7.9×10−4K−1 ∆E27725.694 J/mol b31.4708 ×10−6K−2 m10.75079 n1−1.44997 m22.4 ×10−4K−1n20.0606 K−1 m34.4432 ×10−7K−2n3−7.6515 ×10−7K−2 4. Results and Discussion 4.1. Preheating In an RTM process, the temperature of the cavity is the control variable that must be imposed. This thermal cycle depends on the resin and is the key parameter that defines the evolution of the filling and the curing of the resin and, consequently, the resulting part quality. The thermal cycle considered in this case is presented in Figure 5. Computation 2023, 11, x 7 of 16 Table 2. Coefficients values of the curing rate equation. Coefficient Value Coefficient Value A1 1451.873 s−1 Hr 480,000 J/kg A2 16,797.24 s−1 b1 1.04578 ΔE1 7739.757 J/mol b2 −7.9·10−4 K−1 ΔE2 7725.694 J/mol b3 1.4708 × 10−6 K−2 m1 0.75079 n1 −1.44997 m2 2.4 × 10−4 K−1 n2 0.0606 K−1 m3 4.4432 × 10−7 K−2 n3 −7.6515 × 10−7 K−2 4. Results and Discussion 4.1. Preheating In an RTM process, the temperature of the cavity is the control variable that must be imposed. This thermal cycle depends on the resin and is the key parameter that defines the evolution of the filling and the curing of the resin and, consequently, the resulting part quality. The thermal cycle considered in this case is presented in Figure 5. Figure 5. Thermal cycle considered for RTM6. In the real RTM process considered here, in which the mould was heated by Joule’s effect, the set temperatures depended on the electric potential applied. In this context, it was necessary to calculate the electric potential time evolution that produced a cavity temperature evolution as close as possible to the one shown in Figure 5. To do so, temperatures were applied as thermal loads in the heater plates in a preliminary heat transfer calculation. As a result, the heat power (W) was obtained and the electric potential needed to produce this electric power was also calculated. The electric potential calculation was obtained from the electric power, considering the electrical resistance of the heaters. Figure 6 shows the evolution of the electric power and the electric potential needed to obtain the temperature evolution of Figure 5. 0 25 50 75 100 125 150 175 200 0 30 60 90 120 150 180 210 240 270 300 Time (min) Temperature (ºC) PREHEATING (2ºC/min) PREHEATING (2ºC/min) FILLINGFILLING CURING (1st phase) CURING (1st phase) CURING (2nd phase) CURING (2nd phase) Figure 5. Thermal cycle considered for RTM6. In the real RTM process considered here, in which the mould was heated by Joule’s effect, the set temperatures depended on the electric potential applied. In this context, it was necessary to calculate the electric potential time evolution that produced a cavity temperature evolution as close as possible to the one shown in Figure 5. To do so, temperatures were applied as thermal loads in the heater plates in a preliminary heat transfer calculation. As a result, the heat power (W) was obtained and the electric potential needed to produce this electric power was also calculated. The electric potential calculation was obtained from the electric power, considering the electrical resistance of the heaters. Figure 6shows the evolution of the electric power and the electric potential needed to obtain the temperature evolution of Figure 5.
Computation 2023,11, 41 8 of 16 Computation 2023, 11, x 8 of 16 Figure 6. Evolutions of electric power and voltage difference needed to reach the required temperatures. Once the electrical voltages were determined, a thermo-electric analysis was carried out to numerically confirm that the thermal cycle was actually followed. After that, the structural response caused by the thermal dilatations was studied through a thermoelectrical-mechanical analysis. A finite element mesh (Figure 7) formed by 39,280 hexahedral element and 44,384 nodes was built. Marc Element number 7 (8 nodes linear hexahedral element) was used for mechanical calculations, while Marc Element number 43 (8 nodes linear hexahedral element) was used for thermal, thermal–mechanical, thermal–electric, and cure thermal– mechanical calculations. Due to the existing symmetry on the geometry, materials, and loads, just half of the entire mould was modelled. Figure 7. Finite element mesh used (half model). The electric voltage load applied was already obtained from the preliminary calculation, shown in Figure 6. Regarding thermal boundary conditions, a natural convection of 5 W/(m2K) and a radiation to environment condition were defined in the outer surfaces. An ambient temperature of 20 °C was considered and a value of 20 °C was defined as initial thermal condition. 0 50 100 150 200 250 300 350 400 0 30 60 90 120 150 180 210 240 270 300 Time (min) Electric power (W) 0 1 2 3 4 5 6 7 8 Electric potential difference (V) Electric power Electric potential Figure 6. Evolutions of electric power and voltage difference needed to reach the required temperatures. Once the electrical voltages were determined, a thermo-electric analysis was carried out to numerically confirm that the thermal cycle was actually followed. After that, the structural response caused by the thermal dilatations was studied through a thermoelectrical-mechanical analysis. A finite element mesh (Figure 7) formed by 39,280 hexahedral element and 44,384 nodes was built. Marc Element number 7 (8 nodes linear hexahedral element) was used for mechanical calculations, while Marc Element number 43 (8 nodes linear hexahedral element) was used for thermal, thermal–mechanical, thermal–electric, and cure thermal–mechanical calculations. Due to the existing symmetry on the geometry, materials, and loads, just half of the entire mould was modelled. Computation 2023, 11, x 8 of 16 Figure 6. Evolutions of electric power and voltage difference needed to reach the required temperatures. Once the electrical voltages were determined, a thermo-electric analysis was carried out to numerically confirm that the thermal cycle was actually followed. After that, the structural response caused by the thermal dilatations was studied through a thermoelectrical-mechanical analysis. A finite element mesh (Figure 7) formed by 39,280 hexahedral element and 44,384 nodes was built. Marc Element number 7 (8 nodes linear hexahedral element) was used for mechanical calculations, while Marc Element number 43 (8 nodes linear hexahedral element) was used for thermal, thermal–mechanical, thermal–electric, and cure thermal– mechanical calculations. Due to the existing symmetry on the geometry, materials, and loads, just half of the entire mould was modelled. Figure 7. Finite element mesh used (half model). The electric voltage load applied was already obtained from the preliminary calculation, shown in Figure 6. Regarding thermal boundary conditions, a natural convection of 5 W/(m2K) and a radiation to environment condition were defined in the outer surfaces. An ambient temperature of 20 °C was considered and a value of 20 °C was defined as initial thermal condition. 0 50 100 150 200 250 300 350 400 0 30 60 90 120 150 180 210 240 270 300 Time (min) Electric power (W) 0 1 2 3 4 5 6 7 8 Electric potential difference (V) Electric power Electric potential Figure 7. Finite element mesh used (half model). The electric voltage load applied was already obtained from the preliminary calculation, shown in Figure 6. Regarding thermal boundary conditions, a natural convection of 5 W/(m 2 K) and a radiation to environment condition were defined in the outer surfaces. An ambient temperature of 20 ◦ C was considered and a value of 20 ◦ C was defined as initial thermal condition. Additionally, some mechanical constraints were applied for the thermo-electrical– mechanical analysis. That way, null displacements were defined in the X direction at the symmetry plane, in the Y direction at the centre of the mould, and in the Z direction at the mould base.
Computation 2023,11, 41 9 of 16 Results show that a time-dependent electric current was produced due to the imposed voltage difference. At the end of the preheating process (time = 50 min), the value of the current density was about 1.3 × 10 6 A/m 2 and it was nearly uniform in the whole heater. It was observed also that the electric current was almost zero at the outer surfaces, which indicates that the fibreglass insulates the heater well enough and, consequently, there will be no risk of electrocution. The temperature distribution obtained after the preheating can be seen in Figure 8, and it shows that the maximum temperatures were reached in the resistive heater. The heat generated here was then transferred to the adjoining components. Due to the thermal insulations of mica, the temperature of the outer surfaces was not so high and the temperature in the centre was higher. Computation 2023, 11, x 9 of 16 Additionally, some mechanical constraints were applied for the thermo-electrical– mechanical analysis. That way, null displacements were defined in the X direction at the symmetry plane, in the Y direction at the centre of the mould, and in the Z direction at the mould base. Results show that a time-dependent electric current was produced due to the imposed voltage difference. At the end of the preheating process (time = 50 min), the value of the current density was about 1.3 × 106 A/m2 and it was nearly uniform in the whole heater. It was observed also that the electric current was almost zero at the outer surfaces, which indicates that the fibreglass insulates the heater well enough and, consequently, there will be no risk of electrocution. The temperature distribution obtained after the preheating can be seen in Figure 8, and it shows that the maximum temperatures were reached in the resistive heater. The heat generated here was then transferred to the adjoining components. Due to the thermal insulations of mica, the temperature of the outer surfaces was not so high and the temperature in the centre was higher. Figure 8. Temperatures (°C) distribution at the end of the preheating. The temperature of the cavity was close to the target temperature 120 °C. In fact, average cavity temperature was 120 °C in the lower part and 100 °C in the upper part. However, the distribution was not uniform and higher (up to 134 °C in the lower semimould and 106 °C in the upper one) and lower values (up to 92 °C in the lower semimould and 91 °C in the upper one) could be found. This temperature distribution has influence in the filling phase of the RTM process. Evolutions of the maximum and minimum temperatures of the cavity were close to the set temperature and indicated that the heating rate was nearly linear. This evolution can be seen in Figure 9. Figure 8. Temperatures (◦C) distribution at the end of the preheating. The temperature of the cavity was close to the target temperature 120 ◦ C. In fact, average cavity temperature was 120 ◦ C in the lower part and 100 ◦ C in the upper part. However, the distribution was not uniform and higher (up to 134 ◦ C in the lower semimould and 106 ◦ C in the upper one) and lower values (up to 92 ◦ C in the lower semimould and 91 ◦ C in the upper one) could be found. This temperature distribution has influence in the filling phase of the RTM process. Evolutions of the maximum and minimum temperatures of the cavity were close to the set temperature and indicated that the heating rate was nearly linear. This evolution can be seen in Figure 9. Looking at the mechanical behaviour predicted by this preheating calculation, Table 3 summarizes the most significant results. Table 3. Maximum von Mises stresses and displacements. Location Max. Von Mises Stress (MPa) Max. Displacement (mm) Upper mica cover 125 0.20 Upper composite mould 110 0.19 Sample 0 0.14 Gasket 0 0.10 Heater system 70 0.09 Lower composite mould 110 0.10 Lower mica cover 120 0.10
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