Energies 2021 , 14 , 1095
2of 14
In the packing industry, the strength of corrugated cardboard boxes can be examined by carrying out some leading physical tests. The most important, from a practical point of view, are the compressive, tensile, or bursting strength tests. The most common tests of packaging are the box compression test (BCT) and the edge crush test (ECT) for corrugated cardboard. Performing physical experiments is always time- and cost-consuming. Thus, recently, there have been some alternatives for the examination of corrugated cardboard boxes to determine their strength only by physical testing. The first one is the prediction of compressive strength based on the formulas published in the literature. One advantage of such an approach is its simplicity, which makes it very easy and fast to apply in the real world, without the need of performing any additional experiments. Three groups of parameters used in these formulas proposed in the literature over the years can be distinguished. They include parameters of paper, board and box, respectively [2]. The most common formula in the packaging industry is the approach presented by McKee, Gander, and Wachuta in 1963 [3]. The authors formulated a relation- ship between the box perimeter and two corrugated board parameters, which are ECT and flexural stiffness. Two earlier approaches also took into account parameters of the paper- board [4,5]. However, one can notice that the formula proposed by McKee et al. is accurate only for some relatively simple containers. In the literature, there were some attempts for improving accuracy and extending the applicability of the analytical formulas for pre- diction of compressive box strength. Allerby et al. proposed a modification of constants and exponents in the original McKee’s relationship [6]. Schrampfer et al. modified the McKee’s approach, allowing to extend the applicability of the formula for a wide range of cutting methods and equipment [7]. Batelka et al. also took into account dimensions of the box [8], while Urbanik et al. included the Poisson’s ratio [9]. The constants in the original McKee’s formula was later analyzed for more complicated cases and was recently modified by Aviles et al. [10] and later by Garbowski et al. [11,12]. The compression strength of boxes made of corrugated paperboard [13] can be affected by many factors, including the moisture content of the box [14,15], the existence of openings [12,16], storage time, stacking conditions [17], and many others. The other alternative is a purely numerical method, which may be applied to in- vestigate box compression strength. The most popular method in engineering is the finite element method (FEM). It was applied in many problems related to the strength of corrugated boxes. They include research on transverse shear stiffness of corrugated cardboards [18–21] or buckling and post-buckling phenomena [22]. One important step in the numerical analysis of corrugated cardboards is homoge- nization [23–26]. It allows simplifying the analyzed models, saving time on calculations by ensuring adequate accuracy of the results. As a consequence of the homogenization process of layered materials, one can obtain a single layer described by effective properties of the composite instead of the structure of layers made of different materials. Hohe proposed a method of homogenization based on strain energy [27]. It is suitable for sandwich panels. In his approach, there is an assumption of equivalence of a representative element of the homogenized and heterogeneous elements. Buannic et al. proposed a periodic homogeniza- tion method. In this approach, an equivalent membrane and pure bending characteristic of period plates are obtained [28]. They also modified their approach for the analysis of sandwich panels to take into consideration the transfer shear effect. Biancolini obtained the stiffness properties of the sandwich panel using the energy equivalency between the considered model and the plate, and applying the FEM in the analysis of a micromechanical part of the plate [29]. In the approach presented by Abb è s and Guo, the considered plate is decomposed into two beams in directions of the plate [30]. It allows calculating the torsion rigidity of the orthotropic sandwich plates. Another approach to a homogenization of composite materials may be the measurement of the effective properties based on a correctly designed or a selected set of laboratory experiments performed directly on the composite. Such a technique is applied in this study.
Made with FlippingBook Online newsletter maker