Analysis of the wrinkle geometry of the woven fabrics during uniaxial bias extension test using Ricker wavelet algorithm
Introduction
Press forming of the engineering fabrics can contribute to the creation of complex geometry characteristics of some composite parts. Such complex geometries are suitable for subsequent liquid composite molding and cure processes. This process can be conducted to reduce errors induced by process, such as wrinkling, as well as controlling the uniform orientation of the yarn in the entire production [1], [2], [3]. In-plane load can be applied to the material perimeter in this kind of process by employing a blank-holder [4], [5], [6], [7].
Studies have shown that the shear compliance of woven engineering fabrics is related to the in-plane stress acting along the warp and weft yarns within the fabric. This can be explained by the increased normal forces acting between yarns cross-overs, which can enhance the internal sliding friction during the deformation of the fabric [2]. Further, it should be noted that conditions related to blank-holder can modify the shear compliance of the fabric as well as its forming response, like its wrinkle tendency [2], [8], [9].
Prediction of the wrinkling of engineering fabrics during the press-forming is very difficult. In contrast to woven engineering fabrics, the stiffness related to out-of-plane deformation in the currently used fabrics can be considerably lower. So, as can be seen from finite element simulations previously published, the assumption is that out-of plane stiffness is zero [10]. Despite this, it has been revealed by numerical as well as experimental evaluations that we need a minimal of the out-of-plane stiffness for accurate prediction of wrinkle [2], [10]. In this regard, the experimental studies have been concerned with the characterization of the wrinkling related to the fabrics by applying the picture frame and uniaxial bias extension tests [8], [9], [11]. Wrinkle is obviously related to the structure of the fabric and the applied stress in the composite production process.
Some researchers have tried to characterize the wrinkle and fiber paths from ideal trajectories in the composite materials by applying nondestructive testing (NDT) methods [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]. These methods are such as the eddy current at 2D and 3D [12], [14], [15], [16], X-ray computed tomography (CT) [13], ultrasonic techniques [17], [18], and image processing method [19], [20], [21], [22], [23], [24], [25], [26]. In this regard, one of the most accessible and economic methods is image processing method. This method can be applied to characterize the wrinkles [19]. For example, the shear–tension coupling and wrinkling of the woven engineering fabrics were investigated by Harrison et al. [20] and Nosrat-Nezami et al [21]. Further, Alsayednoor et al. [22] addressed the impact of two testing errors sources, namely, the pre-tension and wrinkle, on the accuracy of the results obtained by the uniaxial bias extension test. They used three manual, 2D and 3D digital image correlation methods to measure the shear angle and compare it to the calculated one. In one other study, a new setup was devised by Harrison et al. to improve the uniaxial bias extension test accuracy by applying an anti-wrinkle apparatus [23]. They also used the image processing technique to characterize the new set-up results. Based on this set-up, the out of plane wrinkles was found to be decreased during the tests. This could be regarded as a reason for such errors. Then, the obtained results were compared with their analytical counterparts [23]. Rashidi and Milani proposed a new method for decreasing the out of plane effects in wrinkling and de-wrinkling characterization of the woven fabrics. It was so called as the multi-step biaxial bias extension test. The method enables forming and flattening wrinkles with different sizes and proving insight on de-wrinkling mechanisms. They showed a positive effect on decreasing the wrinkle behavior of the woven engineering fabrics during the test [24]. Moezzi et al. [25], [26] also focused on the characterization of the woven engineering fabrics wrinkling behavior with local non-uniformity by employing the image processing method. It was shown that local non-uniformity could be regarded as one of the most important parameters in the wrinkle onset and intensity.
Despite the above researches, the emergence of these non-destructive methods makes it necessary to develop guidance for manufacturing imperfections. These results are, however, no easily transferable into commercial software applications. So, some analytical methods are currently popular among researchers from a wrinkle topology point of view. Hsiao and Daniel [27], for instance, made use of amplitude and wavelength for the characterization of wrinkles, based on the assumption of some sinusoidal wrinkle shape. They delivered some indicative volume that was truncated at one single period of the wrinkle, with the linear reduction of amplitude from the mid-plane to the sample surfaces. Otherwise, Caiazzo et al. [28] employed a polynomial for the description of the wrinkle shape, with amplitude being reduced linearly to the sample surfaces. They considered the peak height as well as the wrinkle extent in the load direction to serve as the ‘gross’ measures of the defect size. El-Hajjar and Petersen [29] have also recently suggested a Gaussian function in order to characterize the ‘bell-curve’ wrinkles. According to their results, ‘waviness height’ was chosen in order to describe the wrinkle severity or extent. Xie et al. [30] have also applied the Gaussian functions in order to describe the wrinkle distribution. However, it was shown that the investigated wrinkle metrics range was remarkably greater than that in the study by El-Hajjar and Petersen.
In all previous studies, wrinkle geometry has been considered for the samples subjected to the compression loading. However, there is no previous work addressing the geometry of the engineering fabrics throughout the implementation of the uniaxial bias extension test, where the sample center is subjected to shear loading. So, this study focusses on the analysis of the woven fabrics wrinkle geometry by using Ricker Wavelet (RW) function during the uniaxial bias extension test. As the very first stage, the measurement of the geometrical parameters of the wrinkle at different crosshead displacements (n) was done by applying the image processing technique. Then, the RW function was selected based on the wrinkle topology and function parameter was accordingly estimated by utilizing the image processing, obtaining values in various crosshead displacements. Correlation of the wrinkle parameters with the crosshead displacement values was estimated using the regression analysis. The effect of the wrinkle parameter on Poisson’s ratio was simultaneously addressed. Eventually, the obtained function was used to predict the wrinkle geometry in the new crosshead displacement.
Section snippets
Wrinkle topology definition in the uniaxial bias extension test
For the explanation and analysis of the topology of wrinkle, in the present research, we are concerned with RW families [31]. Therefore, we gather some basic information about RW. Wavelet theory (or wavelet analysis) is regarded as an interesting method which could be useful in solving difficult problems in such varied fields as mathematics, engineering and physics. The modern applications are covering a wide variety of things including wave propagation, compression of data, processing of
Materials and sample preparation
The material used in the study consisted of a nylon 66 woven engineering plain fabric with 0.021 in. fabric thickness. This fabric is applied in the industry related to the production of vehicle safety belts and other technical textiles. The weft and warp yarn count was 1250 denier with 240 monofilaments (see Table 1).
Uniaxial bias extension test kinematics
The uniaxial bias extension test was carried out by clamping a rectangular piece of woven fabric in which the warp and weft directions of the tows were orientated initially at 45°
Wrinkle parameters results
The measured wrinkle parameters of the fabric geometry in different crosshead displacements and the estimated Wn by method described in Section 3.3 are presented in Table 2. Also, all of the plotted curves by the RW equation are shown in Fig. 7. The results revealed that Mn values had a direct relationship with the Dn and shear angle values. It means that with increasing the deflection in the fabric width and shear angle (as an in plane deformation), the wrinkle depth (as an out of plane
Conclusions
It was revealed in this research that the uniaxial bias extension test could be an appropriate method to characterize the woven engineering fabrics wrinkling behavior. A novel methodology combining NDT characterization and numerical analysis were implemented to achieve the wrinkle parameters and wrinkle geometries. As a general conclusion, the RW equation was determined to be an appropriate model for analyzing the wrinkle geometry due to wrinkle topology. Furthermore, it conducted that wrinkle
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
The research conducted by the corresponding author has been supported by a grant from University of Bonab (9813).
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