Energies 2021 , 14 , 3203
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The results obtained show that the SST parameters best catch the amount of intentional crushing, the TST parameters are slightly worse and the BNT parameters are the least accurate. Mean coefficients of determination for all four corrugated board types were: SST— 0.977; TST—0.874, BNT—0.865. The correlation of crush amount with the results of the SST tests at the level of 97.7% means that if there is a need to check a posteriori the amount of the unknown damage caused by the converting machines, it is sufficient to measure the SST parameter before and after the converting process and its ratio will indicate the crushing level. This is because the amount of decrease of the SST parameter precisely reflects the degree of corrugated board crushing. The decrease in the parameter measured in SST does not depend on the residual thickness of the crushed corrugated cardboard, which often returns to its original value due to relaxation. Therefore, organoleptic inspection (e.g., measuring thickness) often does not reveal the problem hidden inside the delaminated cardboard fibers. Therefore, the new insight from this part of study is the following: one may use shearing test (SST) for determining the crushing level of the single wall cardboard, other tests such as bending or torsion are less indicative. This conclusion opens new possibilities to design similar test/machines in other types of materials in which crushing is observed and unwanted, for instance in civil engineering or automotive industry. On the other hand, the drop in ECT parameter and the residual thickness, THK2 correlate well with each other. The measured thickness after crushing decreases almost by the same value as the measured ECT value (again after crushing). The amount of deterioration of measured ECT and the permanent thickness reduction is approximately 50% of the actual crush amount of the corrugated board. Thus, thickness/ECT reduction may be used to roughly estimate the amount of crushing in a single wall corrugated boards but is not recommended for cases in which high accuracy is expected. In the numerical part of the study, the results show that the numerical procedure presented can reproduce the deterioration of the samples stiffnesses due to crushing by decreasing the elastic parameters of the RVE, see Table 6. The regions for which the deterioration must be included were identified as the contacting area of liners and fluting (region A) and in the span area (region B), see Figure 9, also the deterioration factors were acquired, i.e., 0.5 for region A and 0.9 for region B. This property seems to be significantly important if one would like to compute the deteriorated properties of the cardboard, basing only on its crushed shape and knowing intact properties of the corrugated cardboard ( A k matrix). As shown, by introducing the analytical formulation, Equation (4), with adequate parameters, see Table 2, to determine the crushed shape one does not have to perform costly FE analysis [37,38], nor have to use advanced (plastic) material constitutive models, see Figure 6. The analytical formulation may be therefore adopted in optimization or inverse problem frameworks, in which computational cost should be limited. It should be underlined that the numerical study presented enables obtaining the transversal shear stiffness properties of the sample by using the torsion test for different levels of crushing, see Table 6. This is extremely important since the crushing of the cardboard is often suspected to cause the biggest amount of unintended decrease of the load capacity of corrugated cardboard boxes. However, up to this point, there are no systematic and implemented in the industry methods that would be able to determine how the crushing influences the deterioration of the transversal shear stiffnesses. Thus, if this phenomenon may be modelled easily, by the procedure proposed (without using FE computations, nor advanced material models, but adopting an analytical/algebraic rapid and versatile approach), we are one step closer to deliver the scientific-based methodology for dealing with the crushing issue for the corrugated board packaging industry. 5. Conclusions The article presents extended laboratory tests of single-walled corrugated cardboard, consisting in checking the impact of crushing on its mechanical properties. The intentional crushing of the cross-section from 10 to 70% of the original height was fully controlled and initiated with high precision. During the tests, a number of parameters of the corrugated
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