**3. Results**

To determine the accuracy of the extended picture frame test stand, the reference geometry was measured after calibrating. The deviations between measured and nominal height were mostly less than 5%, Table 2. Only at peak 4 (nominal height = 15 mm) the deviation was marginally higher than 5%. This could be caused by the averaging over relevant data points of this plateau of peak. Defining those relevant data points is quite challenging, because from the gained data, it is not clear whether a data point belongs to the plateau of the peak or to the very beginning of the inclined flank. In the visualization of data set points the inclined flanks can be seen (Figure 10b). Minor deviations

in horizontal direction result from the limited number of data set points, which are only linearly connected for visualization. This effect is less relevant for plain and sheared textiles compared to the smooth surfaces without any hard transitions.


**Table 2.** Evaluation of reference geometry within the extended picture frame test stand.

The selected materials were investigated (Figure 11), the force/displacement diagram was obtained and the respective deflection of the laser beam was measured optically over time. Due to its fabric construction, the ± 45◦ CF biaxial non-crimp fabric was tested in two directions to investigate the influence of the sewing thread (in test direction/90◦ relative to test direction) on shear behavior. In order to avoid errors in the optical detection due to reflections of the tested reinforcing textiles (glass/carbon), the samples were treated with a digitizing spray in the area of the laser beam. This had no effect on the shear result. Subsequently, the shear force, the shear angle (Figure 12), and the geometrical data of shear deformation in the area of the laser beam (Figure 13) were calculated.

**Figure 11.** Extended picture frame test stand with CF biaxial non-crimp ± 45◦, ST 0◦ at maximum deflection.

**Figure 12.** Shear force/shear angle diagram of investigated materials (average curve from nine samples for each material).

**Figure 13.** Measured height profiles of the laser beam as a function of time (one sample per material is shown); x-axis: time; y-axis: width; z-axis: height (also see Figure 6).

To evaluate the reproducibility of the results, nine samples were tested for each material and material direction. Figures 14 and 15 show the shear force/shear angle curves as well as the recorded surface deformations for the ± 45◦ biaxial non-crimp fabric with the sewing thread in the tensile direction. The deviations of about 20% in the shear force/shear angle curve result from the properties of the semi-finished product caused by fabric construction. For non-crimp fabric the yarn systems are not crossed but held by a sewing thread to ensure good drapeability. The missing crossing lead to a nearly perfectly stretched out situation of the reinforcing fiber. Thus, high mechanical characteristics in the reinforced directions (e.g., mono-, bi- tri- or quadriaxial) can be realized in FRP products. But its low resistance to displacement, restricts its handleability, making it almost impossible to achieve exactly reproducible sample preparation in the shear test.

**Figure 15.** *Cont.*

**Figure 15.** Measured height profiles of the laser beam as a function of time—CF biaxial non-crimp fabric ± 45◦, ST 0◦; x-axis: time; y-axis: width; z-axis: height (also see Figure 6)

The recorded surface deformations show generally similar results (Figure 15). Minor differences in the characteristics are the result of the above-mentioned issues in sample preparation. Moreover, it is obvious that similar shear force/shear angle curves do not lead to similar deformation behavior. To determine the exact beginning of fold formation and the geometric fold characteristics under shear stress, further analysis of the measured surface deformation is needed.

### *3.1. Additional Options for the Analysis of Optically Measured Shear Deformation*

The geometry data of the time-dependent shear deformation can be imported into a software environment for statistical calculations and graphical output. The software used in this application case was "R" [41]. As described in Section 3.1, all data of a test cycle are leveled based on a first time step (initial state of the shear test), in order to eliminate the intrinsic error of the measurement system. The cleansed data can be used in a further process to visualize the deflection of the laser beam over time as a 3D area. Figure 16 shows the characteristics of the folds including their minima and maxima over a constant sample width. A color gradation allows the assignment of numerical values to different fold heights. Moreover, the amplitude maxima and minima of each time step can be illustrated both in a separate diagram (Figure 17a) and as a sum of their amount (i.e., as peak-to-peak value, Figure 17b) as a function of time and the shear angle.

**Figure 16.** Deflection of the laser beam over time of CF biaxial non-crimp fabric ± 45◦, ST 0◦.

**Figure 17.** Amplitudes of maxima and minima (**a**). Peak-to-peak value (**b**). CF biaxial non-crimp fabric ± 45◦, ST 0◦, nine samples.

The amplitudes of maxima and minima revealed qualitatively different curve progressions. As an example, a maximum is initially formed in the case of sample 6, which decreased after about 12 s, as the minimum increased from this point forward. In contrast, the amplitude progression of sample 4 shows a continuous maximum, whereas the minimum remained relatively low. The analysis of the amplitude curve explains the differences of samples of a material variant in shear behavior (cf. Figure 15). The evaluation of the peak-to-peak value, however, clearly indicates qualitatively comparable curve progressions and thus the reproducibility of the developed shear deformation. The deviations that occur (Figure 17b) result from inaccuracies in sample preparation as described above and cannot be avoided even if the test is performed with grea<sup>t</sup> accuracy. Figure 18 shows the averaged results of the peak-to-peak values and the standard deviations over time for each material and material direction. Besides the absolute measured heights, which strongly differ, a closer view on reproducibility is possible. It is obvious that, for the CF-based woven and biaxial non-crimp fabrics, the standard deviations at the beginning of picture frame testing were lower than at higher deflections. Furthermore, the increase in standard deviation seems to be correlated with the beginning of folding. For the CF-based monoaxial non-crimp fabric and the GF/PA-based woven fabric, the standard deviations were nearly constant over time, but significantly higher than for the other materials. Especially for the GF/PA-based woven fabric, reflections occurred during testing, influencing the base data set and leading to the obtained high standard deviations. Furthermore, the observed results for CF monoaxial non-crimp fabric need to be considered critically as earlier investigations [26] revealed that shearing is not an intrinsic behavior of monoaxial non-crimp fabrics. Additionally, sample preparation is much more challenging, given by the loose construction. Overall, the high standard deviations are caused by material-specific behavior, not by the accuracy of the extended picture frame test. Hence, the additional optical evaluation of fold height is more reliable than an objective evaluation of folding.

**Figure 18.** *Cont.*

**Figure 18.** Averaged peak-to-peak value with standard deviations of each material over time.

This provides the user with a tool for automatically detecting the exact point of time of fold formation in a reproducible manner and for relating it to a critical shear angle. Depending on the geometry of the construction part to be produced and on the specific requirements, a limit value can be defined for a critical fold height. If this limit value is exceeded, the critical shear angle can be assigned, based on the time step. Consequently, the shear angle serves as a reliable decision criterion in kinematic draping simulations.
