1.1.2. Picture Frame Test

In the picture frame test (PFT) [12,21,29,30], pure and constant shear is achieved by fixing the edges of a square sample (initial state α = 90◦) in a hinged frame. Tensile loading at two of its opposite corners causes the sample to deform into a rhomboid shape depending on transversal displacement h (Figure 1b). In contrast to BET, the induced shear is uniform. The force and displacement are recorded

analogously to BET. The sample shear angle *ϕ* can be calculated with the use of the transversal displacement h and the picture frame edge length a, as in Equation (1):

$$\varphi = 90^\circ - 2 \times \cos^{-1}\left(\frac{1}{\sqrt{2}} + \frac{h}{2 \times a}\right) \tag{1}$$

The shear force *Fsh* can be calculated directly for standard hinged picture frames depending on the shear angle, with Equations (2) and (3) [30,31]:

$$F\_{\rm sl} = \frac{F}{2 \times \cos a} \tag{2}$$

$$
\alpha = \theta 0^{\circ} - \varphi \tag{3}
$$

A group of academic and industrial researchers conducting suitable picture frame test methods as well as BET methods was set up for benchmarking. Five picture frame devices were investigated and compared [12]. All presented picture frames were based on rigid clamps, but the dimensions differed and consequently lead to different sample sizes. Three normalization methods were compared. Finally, a normalization method with an energy approach considering both the side length of the fabric and of the picture frame [30] was recommended [12]. Besides different dimensions, two picture frames use a lever mechanism, for which the amplification needs to be considered in the calculation of shear force. A main disadvantage of all presented picture frames were the induced in-plane tensions due to rigid clamping as they significantly influence the beginning of folding [25,32]. Additionally, the frame itself and each sample require elaborate preparation. In particular, precise alignment of the sample while being clamped on the frame is essential, or else additional tensions are generated, which also cause folding to begin earlier.

The applicability of the PFT has been investigated for several textiles, mainly for woven fabrics, but also for UD-NCF [26] and pre-consolidated textiles [33]. Furthermore, BET and PFT have been compared extensively [20–22,34]. Cao et al. [12] investigated balanced twill and plain woven fabrics, as well as unbalanced twill woven fabrics with both tests. It was shown that the PFT is feasible for balanced woven fabrics, but not for unbalanced woven fabrics. The obtained shear force/shear angle diagrams were comparable to the results of BET after normalization. Additionally, different preparation methods have also been investigated, leading to the conclusion that mechanical conditioning (e.g., shearing the sample a few times by hand) increases reproducibility. However, it was considered that such a procedure is not feasible in industry. Another conclusion was that it is necessary to remove transverse yarns from the clamping arms to prevent the initiation of folding in these zones, due to the rigid clamps [35]. A comparison of woven fabrics and UD-NCFs with adapted clamping revealed that shear tests are not suitable for UD-NCFs, as shearing is not an intrinsic behavior either in PFT or BET [26]. For pre-consolidated textiles, alternative sample preparation was needed to allow PFT, otherwise clamping would have prevented shearing due to the consolidated state of the material. The authors mentioned that the locking angle cannot be determined by PFT for pre-consolidated textiles. Furthermore, the definition of locking angle needs to be reconsidered. In [36], the theoretical determination of the locking angle based on textile parameters for one specific woven fabric is described and experimentally investigated by PFT and BET. Due to the test procedure of PFT, where intra-plane yarn shear was induced, it was found that locking theoretically occurs at higher angles than in BET. This was confirmed with the experiments for PFT and BET. Additionally, the authors assumed that folding would appear after locking. Even if this was confirmed by their experiments, other investigations showed diverging tendencies, i.e., this observation cannot be generalized.

Other investigations of the last decade have mainly focused on FE-based simulation methods. Therefore, the relationship between tension and shear behavior was examined extensively to improve simulation models and results of forming simulations. In addition, there are several studies dealing with the purposeful generation of pretensions in shear testing and in manufacturing to prevent folding or delay the onset of folding. These studies are necessary for FE-based simulations and contribute to a better understanding of textile deformation behavior in general. However, they are less essential for kinematic draping simulations as they do not determine the critical shear angle or consider the global phenomenon of folding.

Nevertheless, the achieved shear force/shear angle data can be used for determining the critical shear angle by further data analysis. Souter [37] introduced a method to identify the critical shear angle by intersecting two fitting linear regressions in the first and last five degrees of the shear force/shear angle data (Figure 2a). Another method is described in [38,39], where a linear regression is fitted in the shearing phase at the very beginning of the shear force/shear angle data. Once the measured data exceed a deviation of 5% or more as compared to linear regression, the critical shear angle is obtained (Figure 2b).

However, both methods are questionable for several reasons. First of all, these shear force/shear angle diagrams correspond to ideal shear behavior. For realistic data sets, it is more challenging to define different linear zones (Figure 2c). Also, the subjective definition of linear zones leads to minor deviations. Additionally, in Souter's method, the definition of the posterior linear zone is strongly dependent on the procedure parameter of maximum transverse distance, and consequently, influences the intersection point. As can be seen, the post-determination of critical shear angle from shear force/shear angle data is not reliable and prone to error.

**Figure 2.** Evaluation of a shear force/shear angle diagram. Determination of the critical shear angle (**a**) according to [37] and (**b**), according to [38,39], (**c**) shear force/shear angle diagram, biaxial non-crimp fabric ±45◦, sewing thread (ST) 0◦.

Of course, this fact is known and has led to several approaches to determine the critical shear angle in a shear test. Non-destructive optical measurements are suitable for this purpose as the critical shear angle depends on folding. A widely used optical method is DIC (Digital Image Correlation), which can be used to capture local elongations. The distribution of elongations over the sheared samples is examined and evaluated in the matter to determine the critical shear angle. This procedure is very elaborate in regards to data processing. In [39], the distribution of elongation on a PFT sample was averaged at each transversal distance step. As folding occurred, the mean value of elongation rose significantly and was visible in the overall diagram. However, no information of the folding dimensions was obtained.

Another approach is to identify folding by means of a gray-scale image. However, subsequent image analysis is extremely time-consuming and the results are often inaccurate. Commercial 3D deformation detection systems are provided by GOM. However, this technique is quite costly and laborious in terms of sample preparation (PONTOS system) and the evaluation of the recorded data (ARAMIS system). Our own experience has shown that both solutions are prone to error as data points were missing during the progressive test process.

The lack of reproducibility and traceability as well as the discontinuity and high effort of existing solutions (for both PFT and BET) for determining the critical shear angle by means of fold dimensions were the main drivers for the developed test stand presented in this study. This initial situation motivated the joint research project of the Institute of Textile Machinery and High Performance Material Technology of TU Dresden, and the Department of Polymer Engineering of TU Budapest. The objective was to exploit the detection and quantification of folds during the picture frame test and, subsequently, to achieve a cost-efficient solution. Therefore, we investigated image processing methods in terms of suitability and added necessary equipment to the picture frame test stand.
