Thermomechanical analysis of composite plates curing process using ANSYS composite cure simulation

Journal Pre-proofs Thermomechanical Analysis of Composite Plates Curing Process Using ANSYS Composite Cure Simulation Ameya S. Patil, Reza Moheimani, Hamid Dalir PII: DOI: Reference:

S2451-9049(19)30229-X https://doi.org/10.1016/j.tsep.2019.100419 TSEP 100419

To appear in:

Thermal Science and Engineering Progress

Received Date: Revised Date: Accepted Date:

3 June 2019 11 August 2019 16 September 2019

Please cite this article as: A.S. Patil, R. Moheimani, H. Dalir, Thermomechanical Analysis of Composite Plates Curing Process Using ANSYS Composite Cure Simulation, Thermal Science and Engineering Progress (2019), doi: https://doi.org/10.1016/j.tsep.2019.100419

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Thermomechanical Analysis of Composite Plates Curing Process Using ANSYS Composite Cure Simulation Ameya S. Patil 2, Reza Moheimani 1,*, Hamid Dalir 2,* 1School

of Mechanical Engineering, Purdue University, West Lafayette, IN, USA. of Mechanical and Energy Engineering, Purdue School of Engineering and Technology, Indianapolis, IN, USA.

2Department

*Corresponding

author: [email protected], [email protected]

ABSTRACT: Process-induced dimensional changes in composite parts has been of great interest for many researchers. The induced residual stresses during curing process while the laminate is in contact with the process tool often lead to shape deformation. This paper focuses on predicting these dimensional changes using software simulation of curing process. Various factors including resin shrinkage, degree of cure, different directional coefficient of thermal expansion (CTE) of the composite laminate are simultaneously taken into the consideration. A cure kinetic model has been employed by the software which illustrates the matrix behavior during cure. The results obtained by ANSYS Composite Cure Simulation (ACCS) were then compared with the previous experimental values of spring-in. The accuracy of ACCS package also was validated in this study. With the support of this validated simulation, users are able to reduce the error of spring-in prediction from 15% of analytical calculation to almost 4% of numerical computation in respect to actual manufacturing.

KEYWORDS: Residual Stresses, Process induced Shape Deformations, Resin Shrinkage

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1. BACKGROUND The necessity of lightweight design in aerospace and motorsports industry has increased the demand of carbon fiber reinforced plastics composite materials. Over the years composite material manufacturing has been growing progressively. Currently, process induced residual stresses and shape deformations of are still a big challenge for the manufacturers, as those unwanted distortions from original shape lead to bigger scrap rates and/or further difficulties during the assembly process. An assembly of deformed parts can cause a massive increase of the part’s internal residual stress level which weaken the part’s performance. Thermomechanical loading behavior of composite or nanocomposite laminated parts, particularly beams, plates and sandwiches have become on the verge of recent computational and analytical works of. [1-4] They didn’t consider shape distortion effects while curing in fabrication yet. Processe-induced distortions of small composite parts are not as critical as those of larger and complex parts. Nowadays, tool designers technically rely on their own experience to deal with the problem, often applying a trial-and-error approach to estimate process-induced deformations. While this gives reasonably decent results for parts with comparatively modest geometry, composite parts with sophisticated profiles require well-designed models to capture the interactions between different geometrical features. The most common problem found, using a standard factor of approximation, is that the spring-in varies due to various parameters. Therefore, standard approximation may not be an effective technique every time. The need of having a reliable approach for predicting these process induced shape distortions has driven researchers to develop new methods. As composite materials are anisotropic in nature, the study of directional properties becomes important while predicting the final material properties. The fiber and matrix behavior during the manufacturing needs a comprehensive study for 2

predicting the final shape of any composite laminate. Curing process analysis is the buidling block of obtaining the accurate results for predicting the final shape of the composite part. Using Classical Laminate Theory (CLT), through thickness coefficient of thermal expansion can be obtained. Different analytical expressions have been proposed previously to estimate the dimensional changes in the laminate [5-10]. However, using the same expressions may not work every time as those expressions are developed based on a generalized approximation of the various factors affecting the shape distortions [11, 12]. Simulating the entire curing process can be an effective method for expecting the final shape of the composite part. Residual stresses that are unavoidably generated in composites while manufacturing, subsequently resluts in distortion of the final cured parts. These stresses get built up on fiber-matrix, laminalaminate, and structural levels. Generation of residual stresses can be attributed to several thermal mechanisms [13-18]. Inherent anisotropy of composite materials is the prominent one. The coefficient of thermal expansion (CTE) changes in different directions for composite materials. Previous experimental studies show that CTE of resin-dominated directions is much higher than that of fiber-dominated directions [14, 17]. The dimensional instability, caused due to the very difference, results in generation of residual stresses. When the composite part is cooled, the residual stresses generated are compensated by the tool when the part is in contact with the tool. The part gets distorted to its equilibrium state to balance the internal residual stresses when the tool is removed. Khan et al. [19] determined and optimized the cured characteristic of a panel processed by means of processing parameters. They investigated on the curing cycle and didn’t study on spring-

in though. Resin cure shrinkage is also significant in generation of residual stresses [15]. For polymeric composites, the resin shrinks when polymerization and cross-linking reactions take place, causing 3

a volume drop and consequently material density increses. Shrinkage is more evident in resin dominated directions of the material [11,14,20]. The induced stresses which grow throughout cure due to CTE mismatch and resin shrinkage are capable of causing distortion and premature cracking of the composite laminates. Effect of moisture is also an important aspect for analyzing the internal stresses induced by cyclical hygrothermal conditions [21]. Another factor that is responsible for generation of residual stresses is tool-part interaction. Owing to the difference in CTE of tool and that of ply in proximity with tool, the tool and the ply expand at different rate upon heating. This mismatch in expansion is responsible for the residual stresses induced in outer plies of the composite laminate. The frictional forces on the ply in contact with tool cause uneven distribution of thermal strains across the laminate. Upon tool removal this effect can be observed as a distortion in the final part [22-24]. Reduction in strength and shape distortions are the prime effects of residual stress. Strength of the component is affected by stresses at the fiber-matrix, lamina-laminate, and structural levels all affect whereas dimensional fidelity is affected by only lamina-laminate and structural level stresses to any significant step [11]. Therefore, predicting residual stresses generated in the composite part is essential. Hörberg et al [25] investigated how shape distortion can be afftected by laminate bending stiffness and thickness of L-shape. They showed spring-in angle is more dependent on specimens’ bending stiffness than to the thickness, but they couldn’t show clearly the dependancy by FE approach. Table 1 shows the classification of parameters responsible for generation of residual stresses. This sorting offers sources of residual stresses associated to material selection and part design to be separated from sources that are inspected by processing.

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Table 1. Classification of the parameters responsible for dimensional changes in composite part Intrinsic Parameters

Extrinsic Parameters

Part Angles

Tool material

Thickness

Curing Pressure and Temperature

Lay-up

Curing Time

Flange Length

Tool-part interaction

Tool dimensions are required to be modified to compensate for process induced distortions. Simulating the composite curing process can help to predict spring-in for composite parts before the first physical prototype is produced, reducing process development costs and increasing product quality. Using simulation, it becomes easier and more reliable to foresee the tooling geometry needed to steadily produce high-quality structures within fitted dimensional tolerances. Simulation can also help predicting the shape deformations in complex and large shaped composite parts, accurately. The thermo-mechanical simulation of the curing process can provide the accurate final part shape. This paper aims to present a reliable approach to estimate accurate final shape of the composite part which can be used later as an input to compensate during tool design. While few methods presented structural finite element methods for prediction of residual stresses [1-9], the other methods [10,12,18] put emphasis on thermal analysis to analyze the stress generation. The presented method takes both thermal and structural aspects of curing process into account. The ability to obtain the thermo-mechanical results makes the methodology unique from the other previous methods. This research not only successfully covers various aspects of the factors which are responsible for spring-in; altogether, but it also has opened new possibilities for optimization of geometric, process related parameters for better final manufacturing in minimum time and cost. 2. SIMULATION PROCESS 5

ANSYS Composite Cure Simulation (ACCS) was used to analyze the residual stresses and spring in composite parts. The ACCS is completely combined into the Workbench setting. The required composite material data for the cure simulation is fed in the engineering data unit. The connectivity of ACCS to ANSYS Composite PrepPost, similar to other ANSYS products, enables continuous exchange of simulation and process design data. The connection with ANSYS DesignXplorer allows progressive design optimization of material and manufacturing process constraints [26].

Fig. 1 ACCS Simulation Workflow

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The ACCS chemical solver is being applied within the transient thermal module and simulation for development of polymerization and glass transition temperature, similarly internal heat generation related to exothermic cross-linking reactions has been conducted. The thermal and cure data then is fed into the structural data unit where the ACCS cure material model studies progress of residual stresses and process-induced distortions. ACCS utilizes a fast three-step simulation approach, for comparatively thin laminates (<5 mm thick), where an even temperature distribution is assumed. This quick solution can be applied in the early design stages for fast assessment of the process parameters. Upon completion of simulation procedure, the distorted geometry of FE model is able to generate compensated tooling geometry [26]. ACCS simulation workflow has been elaborated in figure. 1. 3. PROCESS MODELLING 3.1 Composite Solid Model To obtain a through thickness cure properties the analysis must be done on a solid composite model. A 3-D finite element solid model was used for this analysis. A shell model was first extracted from the CAD file created using Autodesk FUSION 360. The L-shaped plate (Fig. 2 (a)) was then imported to ANSYS Space-claim platform for creating the shell model. ANSYS Composite Prep-post module was then used to create a composite solid model.

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a)

b)

Fig. 2. (a) Composite lay-up sequences (b) Composite Solid model of L-shaped plate

Mesh generation is a significant step in any FE simulation. In FE stress analysis knowing whether key stresses converge and checking if they have converged to a rational level of precision is important. A suitable mesh must be used with respect to the shape and size of the elements to obtain results that are consistent when using FEM. The solution accuracy is usually linked with mesh quality and mesh density [27]. FEA convergence defines the connection between the number of elements or degree of freedom and the analysis accuracy. Meshing was performed (Fig. 2 (b)) on the geometry to get accurate results. 3.2 Material Properties Hexcel AS4-8552 was the selected curable material used inside ANSYS. Hexcel AS4-8552 is a unidirectional prepreg with a high-performance tough epoxy matrix. This material is widely used in aerospace structures. It shows good impact resistance and damage tolerance for a widespread range of applications. Hexcel AS4-8552 shows good translation of fiber properties. For simulating the entire curing process, it is necessary to have the all the orthotropic properties available during the analysis. The cure kinetic equations are then used to obtain the results such as Degree of Cure (DOC), material state, glass transition temperature and heat of reaction. Table 2. illustrates all the

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material properties associated with Hexcel AS4-8552. The material properties presented in table are pre-defined inside ANSYS. It is possible to input material data inside ANSYS for different materials having different properties in X, Y and Z directions. Table 2. Material Properties for Hexcel AS4-8552 [28] Material Property Density Orthotropic Instantaneous Coefficient of Thermal Expansion: (i)X-Direction (ii)Y-Direction (iii)Z-Direction Orthotropic Elasticity: (i)Young’s Modulus X direction (ii)Young’s Modulus Y direction (iii) Young’s Modulus Z direction Poisson’s Ratio (i) XY (ii) XY (iii) XY Shear Modulus: (i) XY (ii) XY (iii) XY Orthotropic Thermal Conductivity: (i) X-direction (ii) Y-direction (iii) Z-direction Specific Heat, Cp Resin Properties: Fiber volume fraction Initial Degree of Cure Maximum Degree of Cure Gelation Degree of Cure Total Heat of Reaction Glass Transition Temperature: Initial Value Final Value λ Orthotropic Cure Shrinkage: (i)X direction (ii)Y direction (iii) Z direction Orthotropic Liquid Pseudo Elasticity: (i) X-direction (ii) Y-direction (iii) Z-direction Poisson’s Ratio (i) XY (ii) XY (iii) XY

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Value 1580

Unit Kg m-3

1E-20 3.26E-05 3.26E-05

°C-1 °C-1 °C-1

1.35E+11 9.5E+09 9.5E+09

Pa Pa Pa

0.3 0.45 0.3 4.9E+09 3.27E+09 4.9E+09

Pa Pa Pa

5.5 0.489 0.658 1300

Wm-1°C-1 Wm-1°C-1 Wm-1°C-1 Jkg-1 C-1

0.5742 0.0001 0.9999 0.33 5.4E+05

J

2.67 218.27 0.4708

°C °C °C

1E-20 0.0073 0.0073

mm-1 mm-1 mm-1

1.322E+11 1.65E+08 1.65E+08

Pa Pa Pa

0.346 0.982 0.346

Shear Modulus: (i) XY (ii) XY (iii) XY

4.43E+05 4.16E+05 4.43E+05

Pa Pa Pa

3.3 Cure Kinetic Model The resin characterization is an important factor in the manufacturing of composite materials. Resin processing properties and their associated constitutive models are necessary as to describe and optimize the processing parameters and predict the final properties of a composite structure. The simulation results are based on cure kinetic model presented by researchers where the case study on CYCOM 890RTM Epoxy Resin was conducted to investigate thermomechanical behavior of the resin [29]. The total heat of reaction released during the cure dynamic was measured using modulated differential scanning calorimeter (MDSC), whereas isothermal scans were used to monitor the heat flow during a series of isothermal cures. The measured heat created by the resin was then converted into cure rate by the assumption that the rate of reaction, d𝛼/dt, is proportional to the rate of the heat flow, dH/dt: 𝑑𝛼 1 𝑑𝐻 = 𝑑𝑡 𝐻𝑇 𝑑𝑡

(1)

where HT is the overall exothermic heat of reaction. The degree-of-cure of the resin can be gained by taking integral of the area under the curve of cure rate vs time [29].

𝛼=

1 𝐻𝑇

1

∫( 0

)

𝑑𝐻 𝑑𝑡 𝑑𝑡

10

(2)

Thus, the cure rate can be stated as a function of the degree-of-cure and compared to existing cure kinetics models. The autocatalytic cure model with a diffusion factor developed by Khoun et al. [29], is by the following equation: 𝛼𝑚(1 ― 𝛼)𝑛 𝑑𝛼 =𝐾 𝑑𝑡 1 + 𝑒𝑥𝑝 [𝐶(𝛼 ― (𝛼𝐶0 + 𝛼𝐶𝑇𝑇))]

(3)

where K is a rate constant resulting an Arrhenius temperature dependency [29]. ―𝐸𝐴

( )

𝐾 = 𝐴 𝑒𝑥𝑝

(4)

𝑅𝑇

The autocatalytic model (Equation (4)) with the following constant values, A=58528 s-1, Ea=68976 J/mol, n=0.6, m=0.63, C=15.66, 𝛼C0=-0.90 and 𝛼CT =0.0039 K-1 accurately offers the resin cure evolution for the different dynamic and isothermal cases addressed. The glass transition temperature (Tg) knowingly affects the resin mechanical properties , changing from its rubbery to glassy state. An increase in the CTE is noticed when the resin progresses from its glassy state to its rubbery state with a temperature ramp. The evolution of the Tg with the degree-of-cure was modeled with the DiBenedetto equation. 𝑇𝑔 ― 𝑇𝑔0 𝑇𝑔∞ ― 𝑇𝑔0

=

𝜆𝛼 1 ― (1 ― 𝜆)𝛼

(5)

where Tg is the glass transition temperature, 𝑇𝑔0 and 𝑇𝑔∞ are the glass transition temperatures of uncured and fully cured resin, respectively, 𝛼 is the degree-of-cure and l is a constant used as a fitting parameter valued between 0 and 1. 3.4 Design of Experiments:

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The spring-in for following parameters was analyzed: Laminate Thickness, Part width, Flange Length, and Cure Cycle .The plate dimensions were varied per the parameters. For the analysis of studying the effect of laminate thickness on spring-in, the plate dimensions were kept constant. Number of layers were changed to change the laminate thickness. For analyzing the effects of part width and flange length, the part thickness was kept constant as 1mm. The layup sequence was also kept same. Only the width and flange lengths were varied. For the analysis of effects of cure cycle on spring-in the part dimensions were same as the dimensions for the analysis of laminate thickness. Different cure cycles were applied to the part. Table 3 illustrates the details about solid models used for different analyses. Table 3.: Parameters for software analysis

Parameter Laminate Thickness Part Width Flange Length

Cure Cycle

Part Dimensions (mm) 300×300×300 (i) 300×300×300 (ii) 300×300×1500 (iii) 300×300×3000 (i) 300×300×75 (ii) 300×300×150 (iii) 300×300×225 (iv) 300×300×300 300×300×300

Laminate Thickness 1 mm 2 mm 4 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm

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Number of Layers 8 16 32 8 8 8 8 8 8 8 8

Layup Sequence [0/90]2S [0/90]4S [0/90]8S [0/90]2S [0/90]2S [0/90]2S [0/90]2S [0/90]2S [0/90]2S [0/90]2S [0/90]2S

3.5 Transient Thermal Analysis A 3-step non-linear thermal analysis was performed to obtain the thermal model for the structural analysis later. Newton-Raphson was used to solve the non-linear analysis. The thermal properties such as degree of cure, glass transition temperature and heat of reaction can be obtained here. A convection condition was given to the composite plate as a thermal input load. The convective load resembles the heating process of the composite part. The stepped convection condition characterizes the cure cycle for the composite. Thermal load calculation for the entire cure cycle is carried out and details about material curing, material phase are obtained. It is possible to obtain the DOC results for each individual ply using the simulation which is helpful in predicting the thermal behavior of the composites having layers of two or more different material. This ability makes this methodology unique from other methods presented previously. In the section 4.3, results of curing cycle will be discussed.

Figure 3. Thermal load condition for composite plate

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Figure 3. shows the convective load applied to the composite plate which represents the heating of the composite plate during the curing process. Figure 4 (a) and (b) represent the application of thermal cure cycle.

(a)

(b) Figure 4. Applied temperature vs time a) Single-hold cure cycle (b) Two-hold cure cycle

3.6 Static Structural Analysis

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Like the thermal analysis a 3-step non-linear structural analysis was performed to obtain the results for process induced residual stresses and shape distortions. The parts were constrained to observe only spring-in and not warpage. A frictionless support and remote displacements were the applied load conditions. A fully cured thermal model was used as the initial boundary condition for the structural analysis. The results of the thermal loads that get applied on the composite part are obtained from the transient thermal module. A support removal action was simulated which imitates the tool removing process for the final step of composite manufacturing.

Figure 5. Applied load conditions for structural analysis

4. SIMULATION RESULTS 4.1 Transient Thermal Results 4.1.1 Degree of Cure The thermal non-linear simulation results were obtained using a semi-empirical model. Figures 3 and figure 4 shows the results for transient thermal solution of the composite curing simulation. 15

Thermal analysis gives the results for Degree of Cure (DOC), Glass Transition Temperature and material state. Effect of cure shrinkage during the polymerization process is also considered during the thermal analysis.

Fig. 6 Degree of Cure Contour Results

Fig. 7 Ply-wise Degree of Cure Results

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Degree of cure at any point of the curing process can be obtained using this simulation. Figure 5 subsequently represents the table of degree of cure at each time step during the simulation. The degree of cure numbers is obtained directly from the software which is the advantage of this method over previous methods. Earlier for obtaining DOC values it was necessary to use Differential Scanning Calorimeter (DSC) while conducting the experiments. A plot is then plotted (figure 6) to present the data of DOC vs Time.

Fig. 8 Plot of degree of cure vs time

Figure 6 presents the cure cycle applied to the composite part inside the software. A two-hold cure cycle where the part was heated from room temperature to 120°C, held for half hour and then again heated to 180°C and again held at the same temperature for half hour and then was cooled down to the room temperature.

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200

Temperature (°C)

160

120

80

40

0 0

1800

3600

5400

7200

10800

Time (s)

Fig. 9 Schematic of the Two-hold cure cycle, Temperature vs. time

4.1.2 Glass Transition Temperature Figure 10 displays the progression of glass transition temperature (Tg) throughout the cure cycle (two-hold). From these results the phase change of the resin can be analyzed. The resin converts from liquid phase to a rubbery phase when gelation occurs. The resin then converts to a glassy solid state. The glass transition temperatures at both these phase changes can be obtained from these results which help in predicting the material phase at any specific point during the cure cycle.

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Fig. 10 Tg vs time plot for two-hold cure cycle 4.2 Static Structural The thermal model is then exported to the static structural module to obtain the results for process induced shape deformations and residual stresses. The thermal loads obtained act as initial boundary conditions for the analysis. Additional structural boundary conditions are applied to the part as well. The constraint (frictionless support) at the outer surface acts a tool for the composite part. The support remover tool simulates the tool removal process.

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Fig. 11 Spring-in for composite L-Shaped plate

The deformed L-shaped composite plate post curing is shown in figure 11. The change in angle can clearly be observed. The values of the spring-in angle are obtained from the simulation results.

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Fig. 12 Residual Stresses generated in L-Shaped composite plate

Since analytical calculation of process induced residual stresses is a time consuming and difficult process, obtaining the results for residual stresses through simulation is a comprehensive technique. The residual stresses induced owing to thermo-mechanical curing process are obtained in the form of contour plot of the composite part. Similar to the thermal module, structural module also provides the stresses induced in each individual ply. This pre-loading stresses over the composite parts can make the part weaker upon loading. Figure 12 is the contour of the residual stresses present in the composite part post deformation. The results for residual stresses are the stresses present in the part post deformation. Even if the part is deformed to get rid of stresses generated during the curing process, there are stresses present in the part post deformation. It is practically impossible to get rid of all the residual stresses as the stresses are trapped in the composite laminate during phase change of the resin. These stresses can be predicted and can be used as the initial

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stress condition for the part while the part is further analyzed for practical load conditions such as crash, impact and torsion or bending. 4.3 Variation in spring-in as per varying parameters Table 4 provides the results for the variation in spring-in for varying parameters. It is evident that with increase in laminate thickness the spring-in decreases. Most of the previous studies had demonstrated this relation between laminate thickness and spring-in angle. Although few studies presented that with increase in laminate thickness the spring in angle is increased, there are adequate experimental results which support the trend obtained in simulation results.

Table 4. Variation in spring-in as per varying parameters

Parameter Laminate thickness Part width Flange Length

Cure cycle

Variation in Parameter 1 mm 2 mm 4 mm 300 mm (1 ft ) 1500 mm (5 ft) 3000 mm (10 ft) 75 mm 150 mm 225 mm 300 mm One-hold Two-hold

Laminate Thickness 1 mm 2 mm 4 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm

Number of Layers 8 16 32 8 8 8 8 8 8 8 8 8

Spring-in Angle 1.15° 0.98° 0.83° 1.15° 0.95° 0.89° 0.98° 1.06° 1.10° 1.15° 1.03° 1.15°

Also, when the width of the part is increased the spring-in angle seems to be declining. The warpage effect is more observable in wider part than the spring-in effect. However, as the parts were constrained in a way to only observe spring-in effects warpage effects can be assumed to be negligible in wide parts. Although, accuracy of the results for wide parts may get hindered due to this.

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Reducing the flange length can effectively reduce the spring-in effects in composite angular parts. However, it cannot be an effective solution as the part geometries are dependent on the assembly of the structures. The simulation results showed that with Increase in flange length the spring-in angle also increases. Thermal model simulation results showed that in single-hold cure cycle cured the composite part quicker than a two-hold cure cycle. Similar trend was observed for the spring-in angles as well. It is seen that spring-in angle for single-hold cycle was less than that for a two-hold cure cycle. Quicker curing may decline the development of residual stresses which ultimately results in springin angle being less for a single-hold cure cycle. 4.4 Mesh independency Mesh generation is an important step in any finite element simulation. In finite-element stress analysis knowing whether key stresses converge and checking if they have converged to a reasonable level of accuracy is important. An acceptable mesh must be used with respect to the shape and size of the elements to achieve results that are reliable when using the finite element method. The solution accuracy is usually linked with mesh quality and mesh density [27]. Finite element analysis convergence defines the relationship between the number of elements or degree of freedom and the analysis accuracy. Meshing was performed on all the geometries to get accurate results. Mesh size was 5 mm per element and total number of nodes was 3088. It was made sure that each element is an equisized cube to obtain the most accurate results. To verify grid independence different simulations were performed on a L plate having dimensions 300 × 300 × 300 (mm). The number of elements were varied by varying the mesh size from 5 mm to 10 mm. Number of nodes are dropped to 2251 then. It was observed that change in the mesh size had a small impact on the final spring-in angle, and it was just varied from 1.15° to 1.143° 23

4.5 Comparison with Experimental Results The methodology presented here was validated by comparing the spring-in results obtained by simulation with the experimental results that were presented by various researchers whose work was reviewed [30]. The simulation results showed a similar trend as the experimental results as simulation was carried out for various parameters. In some cases, the spring-in values achieved from simulation results were found to be more accurate than the analytically calculated spring-in values. LMAT [30] conducted experiments to verify effect of laminate thickness on spring-in angle. The trend in the LMAT results was similar to the simulation results obtained using the methodology presented here.

Fig. 13 Plot of Spring-in vs Laminate Thickness

Figure 13. demonstrations the comparison between the simulation spring-in values and experimental spring-in values for deferent laminate thickness. It is evident that as the laminate thickness increases the spring-in decreases. The difference between the simulation values and experimental values is due to the difference between the lay-up pattern used. Also effect of warpage and effect of tool-part interaction were neglected in this case while simulating the curing 24

process and applying the structural loads. However, the pattern is similar which validates the accuracy of simulation results. The tests were conducted by LMAT to study the effect of cure shrinkage and CTE on the composite L-shaped plates. Albert and Fernlund [2] presented a model where an analytical model were developed to calculate the spring-in for C-shaped composite parts. The simulation results provided results closer to experimental results presented in this particular study than the analytically obtained spring-in values. The comparison between analytical, Numerical (simulation) and experimental values of the spring in are presented in the table 5. The simulation spring in value is closer to the experimental spring-in value than the analytical value. Figure 14 displays the simulation results of spring-in for a C shaped composite part. Table 5. Comparison of results with analytical and experimental Analytical Value of Spring-in

Numerical Value of Spring-in

Experimental Value of Spring-in [30]

0.90°

0.81°

0.78°

25

Fig. 14 Simulation results of spring-in for composite C-Shaped plate

4.6 Three Dimensional Deformations Effect of warpage/bending in wider parts can also be analyzed using the method presented in this thesis. Wider parts show more warpage or bending of the flat surfaces. ACCS can be effective tool to analyze the warpage in wider commercial parts such as gurney flaps or wider composite panels, ribs, roofs etc.

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Figure 15 Warpage effect in wider L-shaped composite plate

Figure 15 shows the bending in the L-shaped composite plate which is 10 feet wider. Warpage in both vertical and horizontal surface can be observed here. Usually tool-part interaction is responsible for the warpage effect occurring. It is possible to model the effects of using different tool on the warpage and bending of composite plate. ACCS assists to analyze the 3-directional dimensional changes in composite parts. This ability is unique as most of previous methods were good for obtaining the results for 2-directional dimensional changes. With this ability analyzing the development of residual stresses in commercial composite parts with complex geometries is feasible.

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Figure 16 (a) Shape Deformations in composite front fender of an automobile

Figure 16 (b) Development of residual stresses in composite front fender of an automobile

Figure 16 (a) and figure 16 (b) show the capability of the methodology to be a ground-breaking technique in commercial composite manufacturing for predicting the final shape of the composite part.

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5. CONCLUSION: This paper has provided a comprehensive methodology to predict the process induced shape distortions accurately and in less time. The ability to predict the final shape of the part before tool design is helpful in reducing the manufacturing cost. Although quite a few previous studies have emphasized using FEA for predicting the shape distortions, all the methods had several limitations. This study has proposed an approach to predict the final shape of the composite part not only for simple flat panels but also for complex composite parts using (ACCS). Furthermore, the paper presented the thermal results for composite parts during cure. This helped in obtaining the results for all the thermal properties. While previous studies provided the structural results for spring-in this study presented both thermal and structural results. When compared with experimental results previously presented, the simulation results obtained here were observed to be more accurate than analytically calculated results. AACS package can exhibit more accurate results up to 11% better than analytical one. The methodology developed here was found to be accurate, less time consuming and effective for further analysis of the composite parts for various practical purposes. This technique may open a new window in composite manufacturing with its higher accuracy. Also, the ability of using the deformed model for further mechanical analysis including static, cyclic and crash analysis. ACCS is a powerful tool which can be used to estimate the dimensional changes in the composite parts which are induced in the curing process. By simulating the entire curing process, it is possible to obtain the values of dimensional changes for different curing temperatures and curing cycles. Spring-in for different parameters can now also be analyzed easily with lower time and cost.

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ACKNOWLEDGMENT Authors would like to thank Mr. Talal Shakfeh from Simutech for his valuable support with the software tutorial and license. We would like to thank all the members of ACSEL team for their assistance in this project. Finally, we would like to thank Department of Mechanical Engineering and Department of Motorsports Engineering at Purdue for the financial assistance for this research. Conflict of interest The authors declare that they have no conflict of interest.

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Highlights   

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A presented cure kinetic model illustrates the matrix behavior during cure Structural and thermal Results are validated with experimental spring-in values A comprehensive methodology to predict the process-induced shape distortions accurately Resin shrinkage, degree of cure, different directional coefficient of thermal expansion (CTE) of the composite laminate are simultaneously taken into the consideration

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Conflicts of Interest Statement The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Manuscript title: Thermomechanical Analysis of Composite Plates Curing

Process Using ANSYS Composite Cure Simulation Authors: Ameya S. Patil, Reza Moheimani, Hamid Dalir Principal/corresponding Authors Name: Reza Moheimani, Hamid Dalir Affiliation: School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA Tell: +15095921008 Email: [email protected] [email protected]

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