Energies 2021 , 14 , 3203
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deteriorated properties (due to decreasing of elastic properties for two regions by scaling factor) were subjected to Garbowski and Gajewski homogenization method [25], see Figure 6d,e. The method based on the stiffness matrix of the RVE enables computing A k matrix, which is the overall stiffness matrix for the laminate shell element. The great advantage of the method is that it captures also the effective transvers shear stiffnesses in CD and MD of the input RVE structure, i.e., A 44 and A 55 , respectively. To summarize, the overall algorithm presented in this subsection enables to compute the representative transvers shear stiffnesses for corrugated cardboard samples with dif- ferent intensity of its crushing included. Results section will prove that the torsion test may be used to effectively validate this algorithm to determine the local deterioration of a corrugated board sample with particular intensity of the crushing.
3. Results 3.1. Experimental Study
In the experimental part of our study, four corrugated boards of different grammage were selected and tested, namely, two B flutes: 285 g/m 2 , (B-285), 410 g/m 2 (B-410) and two C flutes: 340 g/m 2 (C-340), 440 g/m 2 (C-440). Those corrugated boards were subjected to a series of measurements and laboratory tests to check: (a) sample thickness before and after crushing—THK and THK2; (b) sample resistance to edge crushing–ECT; (c) bending stiffness in machine direction (BNT–MD) and in cross-direction (BNT–CD); (d) shear stiffness in machine direction (SST–MD) and in cross-direction (SST–CD); and (e) torsion stiffness in machine direction (TST–MD) and in cross-direction (TST–CD). In most cases, each type of corrugated board was subjected to three to four series of tests at the same crushing level. Each corrugated board was crushed in the range of 10% to 70% of its original thickness with 10% increments. Due to the elastic relaxation of the corrugated cardboard, the measurement of the crushed sample thickness was performed a few minutes after crushing, which guaranteed initial stabilization of the relaxation of the material. In Figures 10–13, the results of the measured parameters for the four analysed corru- gated boards are presented. Based on the data, the regression lines for each test, according to Equation (2) and (3), were determined. The BNT, SST and TST values were presented in a normalized manner, the values demonstrated are the ratio of the value obtained for crushed sample to the value obtained from an intact corrugated cardboard (i.e., for CRS = 0%).
( a )
( b )
( c )
( d ) ( e ) Figure 10. The decreases in measured values for B-285 corrugated cardboard in: ( a ) BNT; ( b ) SST; ( c ) TST; ( d ) ECTand ( e ) THK2.
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