3.2. Simulation Case Studies
Two different forming simulations have been performed in this research, both to demonstrate the capabilities of the simulations, and as validation tools to check the correctness of the material characterizations.
The first case-study is an automotive part. Specifically it is the cover for the rear differential of a pickup truck. The geometry used was derived from measurements of an existing metal part, and direct composite replacements were thermoformed using 3D printed tooling (
Figure 10). The original steel part and thermoformed composite part are seen in
Figure 11.
The forming of this part was simulated with 17 layers using a 10 mm target element size. Initial simulations were run using a set of generic-composite properties modified from an example file from PAM-Form. These were later replaced with those measured experimentally as discussed in
Section 3.1. Before analyzing the numerical results, qualitative inspection of results reveals some useful information. First, several of the defects exhibited by the real differential cover were also exhibited by the model. For example, the separation between tapes within a layer that was visible in early iterations of the process was also visible in the model (see
Figure 12). The figure shows a PAM-Form model result in which the different plies are rendered in different colors. The top layer (blue) is a partial ply that was added to help mitigate the ply separation. Next, we see the first full layer (pink), which has developed gaps that reveal the underlying layer (gray).
Second, stress concentrations appear in an area found to be one critical for ply splitting/tearing (
Figure 13). It is unclear what mechanism causes the longitudinal stress banding to translate to transverse splitting, however, the simulation clearly shows that these regions are important in terms of stress concentration. Further investigation of thermoforming failure modes may be of value in furthering the predictive value of the simulation.
Lastly, the general trend of thickness variation at critical pinching locations is exhibited in both model and formed-part.
These qualitative observations appear even in models run using the generic material properties, thus indicating that some useful approximations, and critical-locations can be predicted without full material characterization, and also that certain behaviors are heavily geometry dependent, rather than material dependent. For smaller defects, such as wrinkles, it is assumed that accurate material data is necessary.
In order to validate the models, a numerical comparison was needed for relating the simulated results with experimental ones. The comparison chosen was to use full-field non-contact digital image correlation (DIC) to measure the displacement field in an experimental part (full-size) from before and after forming. This is then converted to a strain field from which shear angle is taken for comparison to simulations [
52]. Note that shear angle is simply the shear strain (typically presented in radians) converted to degrees for better readability.
The locations chosen for inspection were known critical locations for wrinkling, also being the regions in which the highest shear-angles are observed. In addition to this, the shear angle in the patch (along the crest) was also inspected. See
Figure 14 for the locations of these inspection-points.
Using a DIC system, the peak shear-angle magnitude from each of the critical regions was taken. Measurements were averaged from two formed parts. The number of specimens was limited by the amount of available material for forming. These measured values were then compared with those taken from the surface layers of PAM-Form models, thus determining which material model best simulates the actual material. As discussed in
Section 2, the data necessitated there be 3 different material models in which the shear modulus (
) is defined using the experimental results of samples from the three different panels (labeled 3, 4, and 5).
Table 3 shows the results of this comparison. Note that panel-4 material is omitted due to numerical instability in the corresponding model, which prevented its completion.
From the table, the differences between the different measured properties’ model and the generic properties’ model can be seen.
The first thing to note is that all the models overestimate the shear in the top point of the part. This can be explained in that the peak of the part contacts the mold first, thus facilitating a more rapid cooldown and limiting the shear deformation at this point. Since the simulations treated the process as isothermal, this phenomenon was not captured. For this reason, this point will not be included in the average error measure.
Additionally, with the exception of the top point, the measured material models tend to underestimate the shear, where the generic-material overestimates it. This would suggest that the actual shear modulus in the part is below that found in the measured models, but above that in the generic-material model.
Finally, an average was taken over the magnitudes of the errors from each material model, in order to have a single quantity on which to judge each model’s merit. The results are as follows:
Generic Material had an average error of 60%;
Panel-5 Material had an average error of 51%;
Panel-3 Material had an average error of 43%.
From this, it is clear that the panel-3 material is the best of the models here tested. In addition, since there is an assortment of under- and overpredictions of angle, the error average (rather than average magnitude) shows that holistically, the predictions are slightly better (58%, 48%, and 30%, respectively).
The next case study is a hemisphere, which is a relatively simple shape that also exhibits double-curvature ( where the part curves in multiple directions) as most real-world parts do. Simplicity combined with double-curvature has made the hemisphere a common forming case-study [
41]. Our hemisphere was 76.2 mm (3″) diameter, a size which balanced material usage and deformation visibility. By trial and error, the layup and processing parameters were optimized to achieve good consolidation and shape. For this study, a simplified manual process was utilized whereby a preconsolidated blank with a layup of
was placed in a convection oven set at 200
C for 5 min. The softened blank was then carefully transferred to a 10-ton pneumatic press, and stamped between a set of hemispherical aluminum molds. The forming of this part was simulated with 10 layers using a 5 mm target element size.
Due to the mold shape, the material is not restrained at the region of transition between the hemispherical and flat portions of the mold. As a result, the material in the transition region is quite wrinkled (
Figure 15). This issue means that the comparisons from model to forming will be restricted to the hemisphere itself, and the adjacent regions will be ignored.
As with the differential cover, hemispherical parts were formed from PP/glass, and shear measurements taken using DIC (
Figure 16). These measurements were then compared to simulated results using the several material models (with the exception of M5, which failed by unstable wrinkling behavior). Unlike the differential cover, however, the symmetric nature of this part means that there are no distinct locations to compare. Instead, the peak magnitude of shears in the bias directions (the
directions as shown in
Figure 17) were averaged to generate a comparison criterion. The results of the comparison can be found in
Table 4.
Here, notice that panel-3 properties no longer produce the best results, but performs slightly worse than both other materials. Additionally, the relative predictions of the different models can give a bit more insight into the other models. Since panel-3 properties cause underprediction of shear, and panel-4 properties cause overprediction of shear, these two models were combined to infer a shear modulus that falls between them. Using weighted average of these two produces an average error of only 29% in the differential cover and 12% in the hemisphere, thus proving that the true shear modulus does, in fact, lie between those measured. As discussed in
Section 2, the material variations have been hypothesized to be due to differences in crystallinity due to the rate of cooling during the forming process.
It should be noted here that the errors measured here are larger than those expected for a predictive tool. These predictions, however, would typically not be used as quantitative predictions, but rather as a qualitative indicator of potential problem areas in a given manufacturing process. For this reason it is possible to gain valuable insights even from the generic materials, but any improvement on this can greatly benefit the model’s usefulness. There are a number of possible ways in which this disagreement could arise, which are potentially valuable topics of further research. The first possible source of error is the sliding friction between individual layers, as well as between the blank and tool. Since this was beyond the scope of this research, an approximate friction value was used (as discussed in
Section 2). It may be that a better contact model could produce a more accurate simulation. The second possible source of error is in the isothermal nature of the simulations [
53]. It is possible, as discussed regarding the differential-cover’s measurements on ‘point-T’, that the cooling as the part interacts with the mold has a significant effect on the shearing behavior. Third, the discrepancies in the shear modulus between different sample panels is likely another source of error. Each of these sources could be investigated, along with possible simple methods of characterization, to further improve the models. Finally, it is possible that some error arose from the limited sample size (two samples for each case-study) of the DIC experiments.