**3. Results**

#### *3.1. Compression Molded Ribbed Structure*

Typically, long fiber reinforced plastics (LFRP) are predestined to interlock and accumulate for instance at the entrance of ribs causing FMS. This e ffect is even more pronounced for SMC that consist of ROS since the UD strands are sti ffer than single long fibers, which impedes the flow into narrow structures such as ribs. Filling the complex ribbed part with 50 mm long UD strands is therefore challenging as FMS is highly likely. Simple charge patterns and non-optimal compression molding parameters led to incomplete part filling, as depicted on the left hand side in Figure 12. Simulating several di fferent charge configurations in 3D TIMON CompositePRESS showed uneven pressure distributions and finally helped to develop a complex charge pattern with a more even pressure distribution. The virtually developed final charge pattern (see Figure 5) allows a balanced flow to all cavity areas for an even part filling without visible FMS. The cut strands at the edges and the size and position of each charge package help to fully fill the part. Lowering the material viscosity by the previously described pre-heating procedure increases the flowability when the material is compression molded, which further prevents FMS. Moreover, the charge pattern ensures a good venting, so that no air traps occur. The incompletely filled part in Figure 12 is juxtaposed with a fully filled ribbed part after applying the pre-heating technique and using the final process simulation optimized charge configuration.

**Figure 12.** Ribbed structure compression molded with a simple quadratic HexMC charge pattern and unsuited molding parameters showing extensive fiber matrix separation (FMS) (left) compared to a part molded with a pre-heated and optimized charge pattern developed by means of filling simulation studies using 3D TIMON CompositePRESS (right) (plate areas are removed from the ribbed hat profiles).

Figure 13 shows a picture of three randomly picked ribbed hat profiles that were pre-heated and then compression molded with the optimized charge pattern. These three parts are CT scanned for a comparison with the DFS results of 3D TIMON CompositePRESS. The detailed view on the right hand side shows the middle section of sample #19 in bottom view. In the plate brim of the hat profile just slightly deformed strands can be seen. In contrast, the strands are exposed to complex flow conditions and undergo high shear forces when they flow from the initial charge edge in the hat to the end of the cavity in the end brim. The flow path length is approximately 100 mm. Therefore, the end brim is characterized by highly deformed strands split into fiber bundles. At the flow path end these bundles align along the cavity wall.

**Figure 13.** Three compression molded ribbed structures made of HexMC (plate areas are removed from the ribbed hat profiles) picked for CT scanning and a detailed view on the right hand side showing the middle section of sample #19 in bottom view.

#### *3.2. Filling Simulation Results Compared to Short Shot Experiments*

In velocity-based DFSs good fiber orientation predictions depend on the accuracy of the filling simulation. In order to check and evaluate the flow prediction accuracy in 3D TIMON CompositePRESS short shots were conducted and are used as first quality indicator in direct comparison with the simulation results. Figure 14 shows the predicted mold filling in 3D TIMON CompositePRESS and qualitatively compares it with the real flow front advancement in the corresponding short shot. When the mold closing is interrupted at a cavity gap of 8.65 mm the ribs have begun to fill (dark grey colored) and the numerical filling status is in very good agreemen<sup>t</sup> with the experiment. Due to its higher thickness the charge material in the ribbed area is pressed first, whereas the base layer material in the plate area has no contact to the upper mold half ye<sup>t</sup> (light grey colored). Moreover, at a remaining cavity gap of 4.00 mm the proceeding flow front in the end brim of the hat profile is almost identical in experiment and simulation (see Figure 15). In the plate area the numerical flow front is slightly faster than in reality. In both, in reality and in the simulation the last unfilled rib is the left outer flank, whereas the right outer flank is already filled. Since these numerical filling results are in such a good agreemen<sup>t</sup> with the experimentally observed flow front advancement in the short shots, especially in the complex geometry of the hat area, it is assumed to have an accurate flow field prediction as basis for the subsequent DFS. In total, the flow simulation takes only 21 min (wall clock time) using four cores of a standard tower PC (Intel® Xeon® E-2246G CPU @ 3.60 GHz, 32 GB RAM).

**Figure 14.** 3D TIMON CompositePRESS fill simulation status compared to a real HexMC short shot using 8.65 mm shims.

**Figure 15.** 3D TIMON CompositePRESS fill simulation status compared to a real HexMC short shot using 4.00 mm shims (numerical and real short shot are shown from different viewing angles).

#### *3.3. Direct Fiber Simulation (DFS) Results*

For the DFS of the ribbed part 1,193,306 fibers are generated in the initial charge corresponding to approximately 62,800 strands. The DFS simulation for this number of fibers, the amount of tetra elements and the number of output steps takes 112.41 h or 4.68 days (wall clock time, corresponding to 202.96 h or 8.46 days in CPU time), respectively, using four cores of a standard tower PC (Intel® Xeon® E-2246G CPU @ 3.60 GHz, 32 GB RAM). Since fiber attrition is insignificant during compression molding of CF-SMC materials, fiber breakage is not simulated in this work.

Figure 16 shows the initial charge with the generated UD strands at the start of the DFS and the flowing strands close to the end of the press process. At the end of the end brim the fiber bundles orient parallel to the cavity wall and the material flow stops. The proceeding flow front in the plate area is characterized by blurriness due to the deformed fibers. This effect can also be observed in Figure 17, where the movement and deformation of one highlighted UD strand in the lower right corner of the plate is depicted. The images clearly show how the UD strand flows and slightly rotates. From the images it can be seen that the fibers building one strand (cf. the purple colored fibers of one individual strand) are following the flow field as a grouping, although there is no cohesive force between the fibers of one strand. The initially straight fibers deform into a zigzag shape causing the blurriness. This behavior corresponds to the observations made in reality, where the UD strands stay intact and flow together in the plate area. For a one-to-one comparison, images of the initial strand configuration in the real HexMC charge and of flown strands in a molded part are given in Figure 18. Under more complex flow conditions, like in the ribbed structure, a strand splitting can be seen (cf. Figure 19). The DFS shows how the fiber bundles of one blue highlighted strand flow into and through a rib. After exiting the rib the fibers separate. This effect is also visually notable on the surface of molded parts (for example in the end brim area in Figure 13) and in CT scans of the same area (see Figure 21).

Figure 20 shows the predicted fiber orientations in the entire ribbed hat profile displayed as vectors. After flowing through the ribs the fibers align in flow direction. Between the rib exits a more random orientation is visible. Highly oriented and random orientation area alternate. At the end brim it comes to a distinct alignment with the cavity wall. Following the melt flow direction, the fibers point into the left and right end brim corners, which are the last filled areas of the ribbed structure. Due to the more even flow conditions in the plate brim a uniform fiber orientation distribution can be discerned there. The two connecting rib bridges at the left hand side and the right hand side of the ribbed structure exhibit a complex fiber orientation, whereas the three smaller connecting rib bridges, shown in the cross section in Figure 20b, are characterized by almost homogeneous horizontal fiber alignment.

**Figure 16.** (**a**) Progressing flow front and deformed UD strands during the direct fiber simulation (DFS) with 3D TIMON CompositePRESS at an intermediate time step; (**b**) DFS result close to the end of compression.

**Figure 17.** (**a**) Initial virtual charge configuration with randomly oriented UD strands consisting of 15 fibers each; (**b**) highlighted UD strand (purple colored) at the plate surface before molding; (**c**) same UD strand near to the end of its flow path; (**d**) detailed view showing the 15 slightly deformed single fibers of the flown UD strand (for visualization purposes all other strands are colored in light gray).

**Figure 18.** (**a**) Photo of the initial HexMC charge configuration with randomly oriented UD strands in several charge packages on a metal preform; (**b**) detailed view of the UD strands in the lower right corner of the base charge; (**c**) compression molded part; (**d**) detailed view of the lower right corner of the plate showing the flown and slightly deformed UD strands.

**Figure 19.** Virtual UD strand (colored in blue; initial position blue dotted) in the hat profile area deforming and splitting after flowing into and through a rib shown at two different time steps (all other fibers are colored in light gray).

**Figure 20.** (**a**) Predicted fiber orientation vectors displayed at the part surface of the hat profile; (**b**) detailed view of a cross section (front view) showing the fiber orientation vectors in the three middle ribs.

(**b**)

#### *3.4. Fiber Orientation Measurements (VGSTUDIO MAX 3.3)*

For this study a working combination of CT scan hardware and scanning parameters is found that allows for full-sized analyses of fiber orientations in carbon fiber composite parts. Three randomly picked samples of a series of ribbed HexMC parts are CT scanned. A first example of the achieved scan quality is given in Figure 21. The detailed view of the right end brim section of sample #20 shows a flow-induced mesostructure, where individual fiber bundles can be clearly discerned. This determined mesostructure also resembles the observed strand splitting in the end brim predicted in 3D TIMON CompositePRESS. In the grayscale image the denser carbon fiber bundles are defined by white voxels, whereas the pure low-density epoxy is represented by black voxels. Consequently, gray pixels indicate the homogenized mesoscale density variations. These variations span a range from the density at maximal fiber volume fraction (nominal 57 vol.%) in tightly compacted strands (bright voxels) to the epoxy density occurring at strand boundaries, strand intersections, and in pure resin areas (dark voxels) due to FMS.

The CT images of all three scanned samples in Figure 22a allow a visual analysis of the fiber bundle orientations in the middle section of the hat profile and also a comparison among the scans. The plate brims show less deformed and more randomly oriented UD strands, whereas in the end brims clear alignments of split fiber bundles can be seen. In some areas slight indications of FMS are visible. In the head area of the hat profiles the ribs stand out. This is due to the material flow into the ribs leading to highly oriented areas underneath and within each rib.

For the fiber orientation analysis with the FCMA tool in VG, fiber bundles and matrix material are distinguished by appropriate thresholding in each of the three merged scan volumes. Although the applied scan resolution of 59.6 μm is not fine enough to see discrete carbon fibers or to exactly differentiate between individual strands in thickness direction (~150 μm strand thickness), it is sufficient to determine strand orientations, proven in Figure 22b. This is possible due to the large strand scale and since the direction of least density change within a strand stack is aligned with the strand's longitudinal axis. Instead of identifying single fibers for the orientation analysis, the FCMA algorithm detects inter- and intra-strand density gradients and uses them as indicators for the local fiber bundle orientation. The local relative density gradients in the recorded voxel data can thus be used to determine the mean orientations for each element volume of the integration mesh without even capturing all strand boundaries. In Figure 22b the determined fiber orientations in the brim areas are displayed as ellipsoids in the end brim area and as compass needles representing the 1s<sup>t</sup> eigenvectors in the plate brim area, which is a typical second method to visualize fiber orientations in composite parts. The rounder and flatter the green ellipsoids get, the more random in-plane are the determined bundle orientations. This is especially visible in the middle section of the end brim, whereas the outer sections of the end brim are characterized by more distinct bundle alignments, shown as red elongated ellipsoids. The measured orientations indicate reasonable bundle orientations proving that the local mesoscale density variations in the scanned parts can be used to analyze the fiber orientations by VG.

**Figure 21.** CT scan of sample #20 showing fiber bundles of split UD strands on the surface of the hat profile's end brim after a flow length of approximately 100 mm.

In Figure 23a a detailed 3D view of the hat profile middle section of sample #20 shows fiber bundle orientations at the part surface and inside the slightly removed brim areas. The FOTs visible as ellipsoids in Figure 23b are determined using the process simulation tetra mesh also used for the fill simulation and DFS in 3D TIMON CompositePRESS. For better visibility the CT scan data are set to 100% transparency so that only the ellipsoids are visible. Highly oriented fiber bundles, displayed as red elongated ellipsoids, characterize the ribs and also some areas in the head and in the end brims. Especially the rib exits shows high bundle alignments in flow direction. At the flow path end at the outer edge of the end brim it comes to a clearly visible alignment with the cavity wall. The plate brim shows a more random orientation status. Overall, the image color is more green than red, which indicates that most of the hat profile has a random in-plane fiber bundle orientation, displayed as green flattened ellipsoids. Only in areas with strong material flow the initially random strand orientation of the raw material changes into a process-induced mesostructure with areas of distinct bundle orientations (red elongated ellipsoids). Since the process simulation mesh has only one element across the part thickness, it averages the bundle orientations over the thickness for each element volume. However, it still delivers reasonable FOTs when visually compared with the CT scan grayscale image. Therefore, an easy one-to-one comparison with the DFS results on the same mesh in order to evaluate the simulation accuracy is possible.

**Figure 22.** (**a**) CT images of the hat profile middle sections of all three scanned parts (top view; 1 mm of the each part surface is removed to see the inner strand bundle orientations); (**b**) fiber bundle orientations determined by VGSTUDIO MAX 3.3 on a 5 × 5 mm integration mesh in a wider section of sample #20 displayed as ellipsoids in the end brim and as vectors (1st eigenvector) in the plate brim.

**Figure 23.** (**a**) Detailed 3D view of the CT scanned ribbed structure #20 (displayed are density gradients at the part surface; the surface of the hat brims is slightly removed to show the carbon fiber bundle orientations inside the brims); (**b**) determined FOTs of the same part displayed as ellipsoids in VGSTUDIO MAX 3.3 (analysis based on the process simulation tetra mesh; CT scan data are set to 100% transparency) (red elongated ellipsoids: fibers highly oriented in one direction, green flattened ellipsoids: planar fiber orientation, blue spherical ellipsoids: 3D random fiber orientation).

#### *3.5. Comparison of Predicted and Measured Fiber Orientations*

All three CF-SMC hat profiles show visually similar fiber bundle orientations. This observation can be proved by comparing determined FOTs, eigenvectors, and eigenvalues of all three completely scanned parts. In order to eliminate the expectable local fiber orientation differences between the scanned parts, certain areas in the hat profile are used for the analysis. The determined orientation values for all tetra elements within these analysis zones are averaged to give a representative orientation status in that area. The analysis areas with their designations are given in Figure 24. The analysis boxes are superimposed with the tetra mesh and the box transparency makes it possible to discern which elements are used for the analysis.

**Figure 24.** CAD image of the ribbed structure's middle section (3D view, superimposed tetra mesh) with all analysis areas used for the comparison of the averaged fiber orientations of all three CT scans with the fiber orientations predicted with 3D TIMON CompositePRESS.

The orientation angles for the rib analysis areas are determined by calculating angle θ (see Figure 25). The conversion equation for spherical coordinates given in Equation (29) is applied on the 1st eigenvectors in x-, y-, and z-direction and subsequently the calculated angle is projected onto the yz-plane. For the brims and head analysis areas in the xy-plane Equation (30) is used to calculate angle ϕ (see Figure 25) based on the 1st eigenvectors in x and y-direction.

$$\theta = \arccos{\frac{z}{\sqrt{x^2 + y^2 + z^2}}}.\tag{29}$$

$$\varphi = \arctan2(\mathbf{x}, y) = \begin{cases} \arctan\left(\frac{y}{x}\right), & \text{if } x > 0, \\\arctan\left(\frac{y}{x}\right) + \pi, & \text{if } x < 0 \land y \ge 0, \\\arctan\left(\frac{y}{x}\right) - \pi, & \text{if } x < 0 \land y < 0. \end{cases} \tag{30}$$

**Figure 25.** 1st eigenvector (displayed as arrow) of a fiber orientation in 3D space described by the polar angle θ and the azimuthal angle ϕ (Eulerian angles) in a Cartesian coordinate system.

\*

The CT scan results with the determined average values and standard deviations (SD) for the seven rib analysis areas are given in Table 6. The average fiber orientation components Axx, Ayy, and Azz have mean standard deviation between all three scans of just 0.03, 0.04, and 0.03. Furthermore, the measured average orientation angles show a very low mean standard deviation of 4.1◦. All measured angle SDs are below 4◦, the only higher SD has the left rib center analysis area. Since there is a distinct uniform material flow in the rib areas, these low differences between the three CT scans are expectable.


**Table 6.** Averaged fiber orientation measurement results for the rib analysis areas of three CT scanned ribbed hat profiles.

 normalized to a positive angle between 0◦ and 180◦ related to the z-axis in the yz-plane.

In the brim analysis areas the mean standard deviation for the main FOT components Axx, Ayy, and Azz are comparable low (Table 7). The mean SD for the tensor component Azz is even lower than in the rib areas as in the brim and head areas a low fiber orientation component in z-direction is apparent. The mean SD for the measured orientation angles is at 18.6◦. This deviation is reasonably small considering the initially random in-plane orientation of the UD strands and shows that there is a measurable flow-induced mesostructure.

The consistency between the three scans, ascertainable by the low standard deviations, is justifying to average the fiber orientation results of all three samples in the hat profile section in order to ge<sup>t</sup> a representative depiction of the average mesostructure. Furthermore, the averaged FOTs can subsequently be used to compare the CT scan measurements with the process simulation results. This comparison is a direct method to validate the predicted fiber orientations.

In Table 8 the predicted fiber orientation results coming from the DFS in 3D TIMON CompositePRESS are given for the rib analysis areas. Here the absolute errors with the averaged CT scans in the respective analysis areas are given in order to quantify deviations. To indicate the overall degree of error for all regions of interest, the mean absolute errors (MAEs) are given. The MAE for the FOT components is 0.06 for Axx, 0.15 for Ayy, and 0.16 for Azz. The highest FOT and orientation angle deviation between CT measurement and prediction are observable in the right rib's bottom analysis area. This could be linked to the rib's base wall thickness, which is thicker than at the other two ribs. Here, the narrow gap assumption of the Hele-Shaw simplification method applied in 3D TIMON CompositePRESS might have reached its limits. The 1st and 2nd eigenvalues have a MAE of 0.12 and 0.10, respectively. These MAE values show that the DFS results are not perfect but certainly realistic. The predicted orientation angles have a comparably low MAE versus the measured bundle orientation angles in the CT scans of only 11.6◦, which explicitly shows that the orientation behavior is correctly captured by the DFS.

In order to make the comparison between the measured and the predicted fiber orientations in the respective analysis areas easier, the orientations are visually superimposed as 2D ellipses in Figure 26. Fiber orientations in space can be easily visually represented by ellipsoids. However, in stationary 2D images it is easier to demonstrate FOTs as ellipses, neglecting the extension in the third room direction. For the visualization of the mean bundle orientations in those analysis areas the determined average values for the 1st and 2nd eigenvalues are used to define the length of the ellipses principal axes (outer dimensions) and the averaged orientation angle is used for the rotation of the ellipses (cf. [134]). For the rib analysis areas the angle θ is related to the z-axis and rotates the ellipses in the yz-plane. Since the 1st and 2nd eigenvalues already consider the ignored 3rd eigenvalue (representing the ellipsoid's spatial extent in the third room direction), there is no error between the 3D ellipsoid and the 2D ellipse presentation of the orientation when using a 2D front view without any viewing angle. This method enables to easily visually compare the measured and the predicted orientation values in one figure independently from the software they are coming from.

In Figure 26 the 2D ellipses calculated from the CT measurements in green are compared with the 3D TIMON CompositePRESS results in pink ellipses. There are analysis boxes with pretty good and some with less good but overall reasonable agreements between orientation measurement and prediction. The eigenvalues do not agree perfectly in all cases, ye<sup>t</sup> the orientation angles capture the right orientation trends. According to Table 8 the highest absolute errors exit in the left rib top and the right rib bottom analysis areas, which can be quickly visually checked in Figure 26.


**Table 7.** Averaged fiber orientation measurement results for the brim and head analysis areas of three CT scanned ribbed hat profiles.

*\** normalized to a positive angle between 0◦ and 180◦ related to the x-axis in the xy-plane.

Table 9 gives the predicted fiber orientation results for the brim and head analysis areas. The results from 3D TIMON CompositePRESS exhibit lower MAEs for the FOTs and the eigenvalues than compared to the rib analysis areas. The maximal FOT error is 0.09 for Axx and 0.07 for the eigenvalues, respectively. These lower MAEs could arise out of the fact that here, in all analysis areas, the maximal part thickness is just 2 mm and the orientation component in the thickness direction (Azz) is very low, so that it has a low significance. The mean absolute error (MAE) is in a still reasonable area around the true orientations measured in the CT scans. The tensor components Axx and Ayy are always bigger than Azz similar to the CT scan measurements. So the overall orientation tendencies are correctly captured. The predicted orientation angles' MAE is only 2.9◦ higher than the SD of the measured bundle orientation angles in the CT scans. This is a good indication that on average the orientation trends can be reasonably predicted. This deduction can also be visually proven in Figure 27. Here, the angle ϕ is related to the x-axis and rotates the ellipses in the xy-plane.

In comparison to the ribs, the brims and head analysis areas have lower MAEs for the FOT components and the eigenvalues. This manifests in better agreemen<sup>t</sup> of the ellipses outer dimensions, which in most areas fit well. Additionally, in some areas the deviation between the measured and the predicted orientation angles is very small, so that visually a very good agreemen<sup>t</sup> can be quickly found, for example, in the right end and plate brim section (cf. Figure 27).


**Table 8.** Predicted fiber orientation results for the rib analysis areas of the ribbed hat profile using 3D TIMON CompositePRESS.

*\** normalized to a positive angle between 0◦ and 180◦ related to the z-axis in the yz-plane.

**Figure 26.** CAD image of the ribbed structure's middle section (front view) with the rib analysis areas (white boxes) showing the determined averaged fiber orientations of all three CT scans in green superimposed with the fiber orientations predicted with 3D TIMON CompositePRESS in pink (both displayed as 2D ellipses on the used tetra mesh).


**Table 9.** Predicted fiber orientation results for the brim and head analysis areas of the ribbed hat profile using 3D TIMON CompositePRESS.

\* normalized to a positive angle between 0◦ and 180◦ related to the x-axis in the xy-plane. \*\* since the calculated normalized angle is over 90◦, the smaller supplementary angle (adjacent angle) is taken for the deviation calculation.

**Figure 27.** CAD image of the ribbed structure's middle section (bottom view) with the brims and head analysis areas (white boxes) showing the determined averaged fiber orientations of all three CT scans in green superimposed with the fiber orientations predicted with 3D TIMON CompositePRESS in pink (both displayed as 2D ellipses on the tetra mesh).
