Modeling and Simulation of Compression Molding Process for Sheet Molding Compound (SMC) of Chopped Carbon Fiber Composites.
Recent development of lightweight vehicle favors materials with high stiffness-to-mass ratio, among which carbon fiber composites are one of the intuitive options. While polymer reinforced with continuous carbon fiber shows great performance as has been reported widely, significant material cost and limited formability hesitates their application in automobile industry. Alternatively, chopped carbon fiber composites produced via SMC compression molding approach present a more balanced solution with lower cost and better formability and thusly gain increasing focus in recent years. However, due to the random fiber distribution in the SMC chopped carbon fiber composites, remarkable in homogeneity and anisotropy are commonly observed which pose challenges to the design of parts using such type of material. Moreover, these material behaviors are closely related to the processing conditions during compression molding process and thus also sensitive to variations during molding, which amplifies the difficulty in predicting the material properties in the molded parts. Traditional trial-and-error practices during part design are therefore inevitably accompanied with large testing matrix to consider all the factors that can lead to the various part performance, which is obviously cost inefficient. ICME approaches, aiming at replacing unnecessary tests with simulations to reach an optimal design, are therefore favored during the development of the SMC chopped carbon fiber composites.
As an essential part of the ICME approach, modeling and simulation of the manufacturing process are utilized to provide microstructure information which is required to determine the local material properties in the macroscopic performance simulations. Although the application of chopped carbon fiber composites are relatively new in automobile industry, studies of the SMC compression molding can actually date back to several decades ago. [1, 2, 3, 4, 5] Among one of the pioneering efforts, Barone and Caulk [1, 2] conducted the compression molding tests on SMC made with resin as matrix and chopped glass fiber and calcium carbonate as filler phase. Deformation of the initial charge was also modeled by considering the resistance of the material against extensional deformation during the compression molding which was determined by temperature distribution in the cavity. To simulate the flow pattern during SMC compression molding process, different models based on finite element method were developed by a number of researchers, including Lee and Tucker , Osswald and Tucker , Lee et al. , Liang and Tucker , Lin and Weng , Youn and Lee , Dumont et al. , to name a few. Apart from filling simulation, prediction of press force during SMC compression molding was also discussed by Kau and Hagerman , Castro and Tomlinson , Abrams and Castro  and Dumont et al. . As the material properties of the molded SMC parts were significantly influenced by the fiber orientation distribution throughout the parts, fiber orientation models were also developed and coupled with flow field predictions, as seen in Jackson et al.. Later on Advani and Tucker [16, 17] proposed orientation tensor based formulation to describe the distribution of fiber directions within the composites, which bridged the random nature of the fiber directions and the deterministic flow field prediction. Soon enough, this formulation was widely accepted as one of the most popular methods to describe the fiber orientations. Researches were conducted to further improve the numerical details of the orientation tensor formulation [18, 19] as well as the governing equations in the proposed orientation model. [20, 21, 22] Despite the fact most of these works were performed in the scenario of injection molding problems, they usually remained applicable in the compression molding simulations with reasonable accuracy. Commercial software packages have also been developed to provide integrated solution to simulate the compression molding process for SMC composites, for example, Autodesk Moldflow and Moldex3D, which are greatly helpful for the manufacturing engineers to design the process in details without the need of running through trial-and-error approaches.
In the traditional SMC material, however, usually is the case that glass fiber or glass fiber bundles are selected as the filler phase. Carbon fiber in the form of thin chips chopped from continuous fiber tows is rarely seen as the reinforcing material in the composites in the previous studies. To the best knowledge of the authors, as for the SMC made with chopped carbon fiber chips, the validation on the major outputs from the compression modeling and simulation, i.e., filling pattern, press force/displacement of the molding machine and the fiber orientation in the composites, has not been adequately discussed in the literature. With the decreased fiber diameters and stronger anisotropic material behavior brought by the carbon fiber fillers, whether or not the previous models can directly fit into the scheme remains to be examined. As a preliminary study to understand the SMC molding process and examine the validity of models used in simulation of SMC compression molding, the authors performed trial molding experiments to produce plaques parts for testing use. The press force data collected from the molding machine is then compared with the predictions via a model built in Autodesk Moldflow. Furthermore, to evaluate the anisotropy of the elastic properties of the material, tensile tests were performed on the coupons cut from selected locations of the plaques along different directions. A procedure to combine the fiber orientation prediction with a structural finite element analysis (FEA) was developed to perform virtual DIC tensile test on the parts, similar to the methodology we present previously for injection molded parts.  Comparison between results of the DIC tensile test and the simulated test in FEA was then used as an indirect measure of the effectiveness of fiber orientation prediction.
In the following sections, the experimental information of was first introduced, followed by the configuration of SMC compression molding simulation in our Moldflow models. The results from the experiments and simulations are then compared to evaluate the capability and limitation of the current models. Discussion on the results and future works are then summarized.
SMC initial charges were made with uncured resin, curing agent and chopped carbon fiber chips, all provided by Dow Chemical Company. The average cross section of the chips in the initial charge is approximately 3mm x 0.1mm and the average length of the chips is 1.0in. To form the initial charge, chips were chopped from carbon fiber tows with resin and cured agent already dipped on, and then randomly spread to the uncured resin mat and compressed to plaques with planar dimension of 12in x12 in and thickness of roughly 2mm covered with plastic film. The initial charges were stored in refrigerator to prevent curing before molding.
Compression Molding of SMC Plaques
The compression molding of the SMC plaques was carried out in lab scale molding facility at Ford Motor Company. The maximum press force of the machine is 2500kN. Press speed profiles, press force, in-mold temperature and switch criteria from speed to force control can all be programmed in the user interface of the molding machine. Different press speed and force conditions were tested while molding temperature was kept as 150[degrees]C for all the samples. Zero point of molding time, t, was defined as the moment when press contacts the initial charge. The processing parameters are listed in Table 1 while the press speed profiles used in the experiments are listed in Table 2. Force values were set in the machine for t = 0s and t > 1s. During each experiment, press speed increased continuously with press position, following the preset values interpolated from Table 2. Once the force required for maintaining the press speed went beyond the force curve interpolated from Table 1, the machine automatically switched from speed control to force control till the end of curing stage. The plaques were then taken out of the cavity and cooled on a steel plate. The actual press force history was recorded in the molding machine, and later extracted to compare with prediction results.
The setup of the initial charges in the cavity is shown in Figure 1. The initial charges were cut from 12in x 12in plaques into 6 in x 6 in quadrants. 4 pieces of such quadrants were piled up together and placed at the center location of the 12in x 18in cavity. If fully filled, the expected plaque thickness is 1.2mm. To ensure the fiber orientations in the initial charge piles were as close to 2D random as possible, the 4 quadrants were cut from the same larger plaque and rotated by 0/90/180/270[degrees] when placed into the mold.
With the mold temperature set as 150[degrees]C, the crosslinking of the resin happened quickly during the compression molding. Consequently the viscosity built up which provided resistance for the initial charge to fill in the cavity. If the press speed profile was not fast enough or the press force was not high enough, the initial charge could not fill in the whole cavity and produced the unfilled pattern when curing stage was over. For experiments #1~5, we observed the unfilled plaques, while for experiments #6~12, the plaques were all fully filled. The unfilled patterns and an example of fully filled plaque are shown in Figure 2.
DIC Tensile Test
In order to examine the mechanical properties of the SMC composites and check the fiber orientation distribution, the tensile tests were performed on the fully filled plaques. As the processing conditions could largely vary the material properties, plaques molded in experiment #10~12were selected to provide tensile test coupons as they shared the same processing conditions. The schematic of coupons cut from the plaques is shown in Figure 3. The in-plane dimension of the tensile test coupons was chosen as 8in x 1in following an ASTM-D3039 testing standard. 5 locations, A~E, as shown in Figure 3, were chosen as the center locations of the coupons. On each of the selected center locations, coupons aligning along 0[degrees], 45[degrees] and 90[degrees]directions were cut. Due to the limited plaque dimension, only the coupons aligned in the same direction could be obtained from the same plaque and 2 of the coupons, i.e. C-0 and B-0, were with decreased length (6 in). The 0[degrees], 45[degrees] and 90[degrees]coupons were on plaque #10, #12 and #11, respectively. The tensile tests of the coupons were done on MTS tensile test frames, with the strain captured by DIC (Digital Image Correlation) system from GOM. The tests were conducted under displacement control with the loading speed as 5mm/min.
Compression molding simulation models were built in Autodesk Moldflow using the reactive compression molding module. The CAD geometry shown in Figure 1 was imported into Moldflow. Tetrahedron elements with 14 layers along thickness direction and estimated in-plane edge length of 5mm were used to mesh the initial charge and the cavity. Advancing front meshing algorithm built in Moldflow was utilized to generate the mesh. The initial fiber orientations were set as 2D random in XY plane in initial charge elements. The SMC material properties, i.e., the curing kinetics model, thermal properties and the viscosity data fit using a Hershcel-Bulkley-WLF model, were provided by Dow Chemical Company. The mold temperature was set as 150[degrees]C according to the value set for the molding machine. The movement of the press was using displacement control defined with the recorded press position data in the compression molding machine before speed/force switch point in Moldflow and force control thereafter. Two processing conditions, experiment #6 and experiment #10 was modeled.
As mentioned above, the fiber orientation distribution throughout the part was expressed in the form of fiber orientation tensor as described in ref , which could be regarded as the series expansion terms of a probability density function defined in spherical coordinates system. The fiber orientation was predicted using Folgar-Tucker model implemented in Moldflow with interaction coefficient set as 0.01.
RESULTS AND COMPARISON
The press force data recorded by compression molding machine were extracted. The initial contact time between press and initial charge was determined with help of plug-in pressure sensor at the center of the cavity. A sharp increase in the reading indicated the press reached the initial charge. In the Moldflow simulation, the press was automatically adjusted to the contact position when the simulation began. Press speed profile was adjusted when input into Moldflow as tabulated data to make sure the initial press speed and position were consistent in experiment and simulation.
The comparison of the press force from experiment and Moldflow simulation was shown in Figure 4. Only the comparison with the first 10s of the molding process was shown since the press force remained constant at preset peak force value for both simulations and experiments. For both processing conditions applied in the Moldflow simulation, i.e., experiment #6 (Figure 4a) and experiment #10 (Figure 4b), the Molflow prediction of press force was generally well matched with experimental results. Nevertheless, at the beginning of the process, the experimentally measured press force by the molding machine ramped up more quickly than in Moldflow prediction, root cause of which requires further study.
Fill time distribution within mold cavity was closely associated with the press force and press displacement profile. It was also a good measure of the accuracy of the simulation. However, capturing this piece of information in the cavity was very challenging and required special visualization setup  which was beyond the capability of the experimental device in this study. Therefore we only showed the comparison between simulated fill time for experiment #6 (Figure 5a) and experiment #10 (Figure 5b) hereafter. As shown in Figure 5, clearly higher press force peak value yielded shorter fill time during SMC compression molding. It should be noted that experiment #6 was the processing condition with the lowest press force among those conditions which were capable of filling the whole cavity. Possibly this processing condition was close to a threshold value to obtain a fully filled plaque, if other factors remained unchanged. Therefore, strong resistance against flow was expected, which were also indicated in Figure 5a. Majority of the cavity was filled within ~6s, yet it took 27s for the material to fill the corner of the cavity. As the viscosity quickly increased with higher curing degree and slower flow velocity which was commonly seen for shear thinning fluid, the fill time ramped up quickly.
Microstructure and Fiber Orientation
There are some similarities between the injection molding and SMC compression molding, for example, microstructure of the parts from both processes were randomly oriented and dominated by the material flow. However, the fibers in the chopped carbon fiber SMC are usually in the form of bundle chips, which clearly distinguish from the microstructure of the injection molded composites with randomly oriented individual fibers. An example of microscopic images of the molded SMC is shown in Figure 6. The 1in x 1in sample was cut from the plaque #10 and polished to approximately the center along thickness direction of the composites. The image was taken and automatically stitched using Keyence VHX2000 optical microscope. As observed in Figure 6, the microstructure of chopped carbon fiber SMC was filled mostly with closely packed fiber chips, while area rich with resin was seen between the boundaries of the chips. The fibers within the same chip were with basically the same direction.
Previous studies on the fiber orientation models usually started with the replacing the probability density function of directions of individual fibers with the fiber orientation tensor, in order to combine with flow field calculation. However, in the case of SMC composites, the direction of the individual fibers was usually aligned with the bundled chips. The fiber orientation distribution should be considered as the distribution of directions of chips, or bundled fibers, instead of individual ones. In this scenario, whether or not the traditional fiber orientation models are still valid remains to be examined.
Despite these intrinsic differences, to date the fiber orientation models in most compression molding simulation software packages still implement the traditional formulations without considering the effect of bundled fibers within chips. In order to consider such effect in our material system in this preliminary study, we adapted the aspect ratio of the fillers in Moldflow. Rather than using the aspect ratio calculated for individual fibers, we used the estimated aspect ratio of fiber chips, 10, during the simulation. We chose Folgar-Tucker model with fiber-fiber interaction coefficient Ci = 0.01 as the fiber orientation model for this preliminary study, which may not be the best option. It should be noted that the selection of the fiber orientation model for the chopped carbon fiber SMC need extensive further studies, which is future work for the authors of this paper.
The fiber orientation prediction of the models simulating processing conditions in experiment #6 and experiment #10 are shown in Figure 7. Cutting-plane contours of on the top surface plane and the center plane of the plaque parts was plotted in Moldflow. The fiber orientation tensor component being visualized is [a.sub.11], which describes the probability of finding fibers along x direction.  It was observed that the fiber orientations predicted using the selected fiber orientation model showed significant difference at top surface and center of the composites in both models. Additionally, at the same part locations, the models configured with different processing conditions could obtain different fiber orientation distributions. Most regions of the plaque part are with [a.sub.11] much greater or less than 0.5, indicating that the material properties would be highly anisotropic even in the 2D flow plane. The fiber orientation results in Figure 7 again emphasizes that in the material card of SMC composites in structural FEA analysis, anisotropy and inhomogeneity should be included into consideration to better capture the behavior of this type of material.
Deriving the anisotropic elastic properties of fiber reinforced composites including SMC is usually known as "modulus mapping", which has already been implemented in multiple commercial software packages like MSC Digimat and Autodesk Helius, and proved to be effective in our previous studies. However, as material models for the chopped carbon fiber SMC are still being developed and different numerical procedures need to be tested in order to improve the prediction, the authors developed homemade Matlab script so that different models to translate the fiber orientation into elastic properties can be flexibly tested and tuned. The algorithm of the script is briefly described below.
Following the approach in ref , the 4th order stiffness tensor [C.sub.ijkl] can be calculated as a function of fiber orientation tensors for different locations in the molded parts via a tensor averaging procedure as followed:
[C.sub.ijkl] = [B.sub.1]([a.sub.ijkl]) + [B.sub.2]([a.sub.ij][[delta].sub.kl] + [a.sub.kl][[delta].sub.ij]) + [B.sub.3]([a.sub.ik][[delta].sub.jl] + [a.sub.il][[delta].sub.jk] + [a.sub.jl][[delta].sub.ik] + [a.sub.jk][[delta].sub.il]) + [B.sub.4]([[delta].sub.ij][[delta].sub.kl]) + [B.sub.5]([[delta].sub.ik][delta.sub.jl] + [[delta].sub.il][[delta].sub.jk]) (1)
where [a.sub.ij] is the second orientation tensor predicted by Moldflow, [a.sub.ijkl] the 4th order fiber orientation tensor obtain through closure approximation, [[delta].sub.ij] the Kronecker delta [B.sub.1~5] the 5 invariants of a transversely isotropic stiffness matrix, [C.sup.0.sub.ij]. This transversely isotropic stiffness matrix represents the effective elastic properties of a conceptual composite cell with equivalent fiber volume fraction as the SMC composites where all the fibers are aligning along the same direction. [C.sup.0.sub.ij] can be generally expressed as:
[C.sup.0.sub.ij] = f ([C.sup.Fiber.sub.ij], [C.sup.Matrix.sub.ij], [V.sub.f], [lambda]) (2)
where [C.sup.Fiber.sub.ij] and [C.sup.Matrix.sub.ij] are the constituent elastic properties of fiber and matrix, respectively. [V.sub.f] is the volume fraction of the fibers in the SMC and [lambda] is the aspect ratio of the fibers. The function f is determined by the choice of micromechanical models being used. However, as we regard the chips of SMC as the fiber phase in the composites, [C.sup.Fiber.sub.ij], [V.sub.f] and [lambda] were computed for the chopped carbon fiber chips instead of individual carbon fiber. The homogenized constituent properties of the chips were obtained through RVE representing the composites with uni-directional continuous fibers and the same resin matrix, which is demonstrated elsewhere.  The volume fraction is adjusted to the volume fraction of the chips in the composites. This quantity is calculated by total carbon fiber volume fraction in the SMC divided by the volume fraction of individual fibers in uni-directional RVE. The aspect ratio is also adjusted to the aspect ratio of the chips in the SMC. For the micromechanical model, Mori-Tanaka method is used while the closure approximation utilizes IBOF (Invariant-Based Optimal Fitting) as in ref.
After the [C.sub.ijkl] is calculated with [a.sub.ij] extracted from Moldflow, they need to be projected from the mesh in Moldflow to the mesh for structural FEA simulation. The meshes in these two types of simulations are usually significantly different in terms of element type and mesh density. To convert between different meshes, we applied Reproducing Kernel Particle Methods (RKPM) which was previously developed for similar applications in mesh-free FEA. 
With help of this script, the DIC tensile test can be simulated in the structural FEA analysis. According to the geometry of the tensile coupons as shown in Figure 3, Moldflow elements within the coupon region was selected from the mesh along with the predicted fiber orientation tensor. The 4th order stiffness tensor [C.sub.ijkl] was then calculated and mapped to the structural FEA elements to define the anisotropic elastic properties. Rotation of the coordinates system was considered during the calculation of [C.sub.ijkl]. Similar to real DIC tensile test, displacement control boundary conditions were applied. After the simulation of the tensile test, resultant force in the grip nodes were extracted, from which stress can be calculated. Measurement of the tensile strain was done following the same procedure in DIC by calculating the longitudinal strain in the strain gauge. The strain gauge area was chosen as the area selected in the real test to calculate the elongation and the local strain. With stress and strain known, the Young's modulus from the tensile test is then obtained.
The comparison between the Young's modulus from virtual DIC test and the real test is shown in Figure 8. For the virtual DIC tensile test, the structural FEA model was generated by performing modulus mapping on Moldflow model simulating experiment #10 built with the same processing condition as in the real tensile test samples. Generally, comparison between the real test and virtual DIC test shows good match, which indicates that the fiber orientation was well predicted by Moldflow. Discrepancies are found at E location where the 90[degrees]sample showed larger modulus than 0[degrees] sample in the prediction, which was contradict to the experiments. Also for the samples at location B, the modulus of the 90[degrees] sample was overestimated. Due to the limit of molding material in this preliminary study, there were not enough replicates of samples to generate deviation of the results for tensile test experiments. The authors plan to mold more plaques and provide repeats for the tensile test in the future work.
As an essential part of the ICME modeling suite, the processing modeling and simulation provides key information for the microstructure of the materials in the parts. Such procedure is applied to chopped carbon fiber SMC in the present study as an example. Instead of compromising with assumption that such material is homogeneous and isotropic when defining the properties, engineers can obtain local material information of the composites parts by performing processing simulations and link mechanical properties with fiber orientation tensor predictions, which is of great value to the optimal design.
From the simulated compression molding process via Moldflow, different processing conditions can be tested without running into massive number of trial tests. Though chopped carbon fiber SMC are relatively novel composites material systems, the existing models showed generally good performance when predicting the press force. Further detailed comparison, including the evolution of filling patterns, local compression pressure and temperature variation during the curing stage will be examined in the future work to provide complete validation of the filling stage of the compression molding simulation.
Fiber orientation predictions in Moldflow led to reasonably good results when compared with experimental DIC tensile test results. In addition to the match in the prediction of Young's modulus, it was also found in several of the samples that the strain field captured by the DIC tensile test showed similar distribution as in the simulated DIC test performed as described in the previous sections. One example of the comparison between DIC and the FEA simulated DIC was shown in Figure 9. The tensile strain [[epsilon].sub.11]was plotted for real DIC and the DIC simulated in FEA. The spots with higher tensile strain, i.e., weaker elastic modulus, appeared at similar locations in the two strain fields captured by DIC and calculated in FEA. Such match is expected as the mechanical properties of the SMC are dominated by fiber orientation tensor distributions. In ideal cases, one can forecast the locations of such weak spot under certain loading condition utilizing the fiber orientation prediction. Although an encouraging indication of the effectiveness of the modeling approach, it is noted by the authors that more replicates of the tests should be performed to check the consistency of such match. Besides, the uncertainty factors including variations in process and unpredictable defects could also influence the local material properties, yet they are still difficult to be quantified in the developed modeling framework. Nevertheless, the approach, when fully validated, will provide much more information of the parts than calculating a homogenized elastic modulus in the range of strain gauge only.
As mentioned above, selection of the fiber orientation models needs extensive further studies. The flow dynamics of when highly concentrated fiber bundles are present in the initial charge may deviate a lot from the assumptions in the previous studies of fiber orientation predictions. Direct measurement of fiber orientation tensor is still the best way to evaluate if the fiber orientation predictions are consistently accurate or not. Yet it remains a challenging task for chopped carbon fiber SMC. The carbon fibers are usually hard to distinguish from the matrix polymers for industry-level X-Ray CT scan instruments. State-of-art X-Ray resources that can lead to satisfactory resolution are extremely expensive and with limited access. On the other hand, fiber orientation measurement based on the optical microscope images taken along thickness plane of the parts can also be an option, which was used previously by Velez-Garciaet al.  for injection molded composites. But whether or not its effectiveness is affected by the appearance of massive bundled chips in chopped carbon fiber SMC still remains a question. Both of the X-Ray and optical imaging approaches for fiber orientation measurement will be tested in our future work.
Compression molding process for chopped carbon fiber SMC composites is modeled in Moldflow. Molding experiments are also performed, from which process information and tensile testing samples are collected. Press force and tensile modulus data are used to compare the simulations and the experimental results. The prediction of the tensile modulus is done following a virtual DIC procedure which is based on the fiber orientation tensor prediction in Moldflow and modulus mapping program developed by the authors. Both of press force and tensile modulus prediction show reasonably well match in the preliminary study. Future studies will focus on providing replicates of samples for processing data and DIC tensile testing. Fiber orientation models will also be studied in details with improved technique of direct measurement of the direction of fiber chips in the molded SMC parts.
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The authors sincerely acknowledge the funding support by Department of Energy (DE-EE0006867) and the insightful discussion with Dr. Franco Costa at Autodesk and Dr. Shin-Po Lin at Ford Motor Company.
Ford Motor Company
Hongyi Xu, Jeffrey Dahl, and Danielle Zeng
Ford Motor Company
Dow Chemical Company
Ford Motor Company
Table 1. Processing parameters tested in the compression molding experiments. t is the molding time which is defined as 0s when press contacted the top surface of the initial charge. Experiment # Press Speed Press Force at Press Force at Profile t=0s (kN) t>1s (kN) 1 I 0 0 2 II 0 0 3 II 0 0 4 II 0 250 5 II 0 125 6 II 0 500 7 II 0 1000 8 II 250 1000 9 II 250 500 10 II 0 1500 11 II 0 1500 12 II 0 1500 Table 2. Press displacement profile I and II used in the compression molding test. Step Press Speed Profile I Press Speed Profile II Press-Cavity Press Speed Press-Cavity Press Speed distance (mm/s) distance (mm/s) (mm) (mm) 1 200 75 100 50 2 50 25 50 25 3 25 15 10 10 4 15 5 5 5 5 0 1 0 1