Simulation results and validation for the strength of the corrugated

The edge compression resistance and flat crush resistance obtained from the experimental study for both B and C flutes corrugated paperboard are shown Table 4.5. The edge compression resistance measures the ability of a vertically placed corrugated paperboard to sustain top-to-bottom load and helps to evaluate the in- plane compression strength of the corrugated paperboard. The strength of a corrugated paperboard package can also be predicted using the edge compression resistance value, the package geometry and the paperboard properties (Fadiji et al., 2017). As shown in Table 4.5, the ECT value for corrugated paperboard with C flute medium was higher than corrugated paperboard with B flute medium with a percentage difference of about 39%, although not statistically different (p<0.05). The same trend was observed for the FCT values for both corrugated paperboard types except for the statistical difference observed (p<0.05) with a percentage difference of about 43%. Our findings were similar to the study by Urbanik (2001) who studied the influence of flute geometry on the strength and stiffness of corrugated paperboard. The author reported the possibility of balancing cost, strength and stiffness of a corrugated paperboard with an optimum flute profile. A crucial structural performance of a package is its stacking strength and it is a function of the edgewise compression resistance and bending stiffness of the corrugated paperboard (Navaranjan et al., 2013; Urbanik, 2001) and according to

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Ahmed and Bhoomkar (2013), ECT in combination with the bending stiffness of a corrugated paperboard have a direct correlation with BCT. Furthermore, certain manufacturing effects of the corrugation, as well as the strength of the paper material, can be reflected by the edge compression resistance, hence it is a realistic measure of the corrugated paperboard quality (Jinkarn et al., 2006).

Corrugated paperboard with a low flat crush resistance could lead to a reduction in package performance. From our study, a percentage reduction in the flat crush resistance of about 36% was observed in B flute corrugated paperboard when compared to the paperboard with C flute medium. Low flat crush resistance may be an indication of some paperboard conditions such as low medium strength, poorly formed flutes, crushed flutes or leaning flutes. Corrugated paperboard with leaning flutes may not result in low flat-crush resistance and adverse package performance, as lateral movement between liners must occur for leaning flute to result in low flat crush resistance. The lateral movement between liners can be restricted by the geometry of the package when a package is manufactured from corrugated paperboard with low flat crush resistance.

For the simulation of the edge compression resistance of the C flute corrugated paperboard, fringe plots of the first and second buckling mode for the large strain and the small strain model procedures are shown in Figure 4.12 and Figure 4.13, respectively. The small strain procedure for the buckling analysis assumes that the changes after displacement is significantly small so that the geometry remains unchanged, while the large strain procedure was used to capture the geometric nonlinearity of the corrugated paperboard. The edge compressive resistance for the large strain and small strain were 6.24 kN m−1 and 6.32 kN m−1 for C flute corrugated paperboard, with a percentage difference of 2.5% and 1.3%, respectively when compared with the experimental results shown in Table 4.5. For B-flute corrugated paperboard, the large strain and small strain buckling procedure resulted in edge compressive resistance of 3.89 kN m−1 and 3.99 kN m−1, respectively. When the numerical results from large and small strains are compared with the experimental results for the B flute corrugated paperboard (Table 4.5), the percentage difference was about 11% and 8%, respectively.

4.4.3 Simulation results and validation for the strength of the corrugated paperboard package

To model the corrugated paperboard package, the numerical model must be able to represent the physical process accurately. In this study, the influence of the boundary conditions to obtain satisfactory finite element model results was checked. Two boundary conditions similar to the physical phenomenon were used (section 4.3.2.3). Figures 4.14a – h show the fringe plot of the displacement and the first buckling mode for the control package without vent holes and the package with a standard vent configuration using Cases A and B boundary conditions. The results presented are for packages with C flute medium. As shown in the plots, the package width exhibited resistance to buckling while the centre of the package length was

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observed to be the origin of the buckling. An outward buckling occurred on the package length (long side of the package) while the package width (short side of the package) was observed to buckle slightly inward. According to Panyarjun and Burgess (2001), localised crushing of the package liners could lead to package failure. From the simulation, buckling of the vertical edges induced the collapse failure.

Figure 4.15 shows a typical force versus deformation response curve obtained by compressing the cartons (control and standard vent packages). An approximately linear initial response was observed which was followed by a nonlinear behaviour that eventually leads to a maximum load. This may be due to a large deformation in the out-of-plane of the package and local buckling exhibited by the liners (Åslund et al., 2014). The buckling of the package that occurs during compression loading is often produced by the greatest bending moment located around the face of the package as shown in Figures 4.14a – h. Centrally locating the vent or hand holes, will result in a significant reduction in compression strength of the package (Han & Park, 2007; Jinkarn et al., 2006; Biancolini & Brutti, 2003). Table 4.6 shows the buckling loads obtained from the finite element simulation for the packages for both Cases A and B boundary conditions, in comparison with the experimental results. Comparing the buckling loads from the finite element model and the experiment of the control package for Case A boundary condition resulted in a percentage difference of about 13%, while for Case B boundary condition, a percentage difference of about 10% was observed. For the standard vent package, when the buckling loads from the finite element model and the experiment were compared, a percentage difference of about 10% and 5% were observed for Case A and Case B boundary conditions, respectively. For both simulation and experimental results, compared to the control package, the standard vent package had lower buckling loads. In the Case A boundary condition, compared to the control package, the buckling load for the standard vent package decreased by about 9%, while a decrease of about 20% was observed for Case B boundary conditions.

From the experimental results, mean value and standard error of buckling loads obtained for the control and standard vent package were 7268 ± 158 N and 6797 ± 151 N, with a percentage difference of about 7% and a significant difference was observed between the buckling loads (p<0.05) according to Duncan's multiple range tests. The reduction in compression strength of the standard vent package can be attributed to the presence of the vent hole. Although vent holes decrease the mechanical strength of the package (Pathare et al., 2012b), they consequently help to reduce materials wastage as the removed materials can be recycled (Pathare & Opara, 2014; Chen et al., 2011a). They are also a crucial factor affecting the efficiency of cooling the packed produce (Pathare et al., 2012b; Thompson et al., 2002). The design of ventilated corrugated packages should be such that it provides adequate cooling to the packed produce while maintaining its structural integrity.

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Typically, unvented corrugated packages are stronger than ventilated corrugated packages. Vigneault et al. (2009) and Kader (2002) suggested that locating vent holes away from the vertical corners of the package minimises the reduction in the maximum strength in ventilated corrugated packages. In addition, the area of the ventilation openings should not account for more than 5% of the total package area, as most corrugated paperboard packages can have up to 5% ventilation area without minimising the stacking or compression strength (Thompson et al., 2002; Kader, 2002). Packages with more than 5% ventilation area must be carefully designed to provide sufficient structural strength (Pathare et al., 2012b; Thompson et al., 2002). In addition, packed produce depends on the package walls to avoid damage. It is therefore crucial to maintain and retain the strength of package walls to improve minimise produce damage during postharvest handling.