Advances in Materials Science and Engineering
3
R 0.25
r
R 0.55
h
+
𝛿
H
0.30
𝜃
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+
+
60 ∘
60 ∘
h
2L
Figure 2: Model of UV-shaped corrugated board.
Figure 4: Model of corrugated board with two flutes.
From Figure 8, we can see that, with the flute height 𝐻 increased, the maximum stress in the models decreased and the maximum displacement increased. Therefore, with the flute height 𝐻 increased, the flat compression strength of corrugated board decreased and cushioning properties of corrugated board increased. As is well known, the cushioning properties of different shapes of corrugated cardboard have the sequence A > C > B > E, and the flat compression strength of corrugated board has the sequence A < C < B < E. Our simulation results are consistent with these conclusions. 3.3. Arc Radius 𝑟 . Effects of arc radius 𝑟 on the mechanical properties of corrugated cardboard model were investigated in this section. A series of models with different arc radius of flute were built and shown in Figure 9. The arc radius 𝑟 in models are 0, 0.1, 0.2, 0.25, 0.3, 0.35, and 0.4 mm. Fixing the bottom of models and then a static pressure test were made with a pressure of 150 Pa on the top floor. Then the maximum displacement and maximum stress of the models with different arc radius were obtained and the results are shown in Figure 10. From Figure 10, we can see that, with the arc radius of flute increased, the maximum stress in the models decreased and the maximum displacement increased. It means that when the arc radius 𝑟 increases the flat compression properties get worse and the cushioning properties get better. In fact, the smaller the arc radius, the closer the model to the V-shaped flute; the larger the arc radius, the closer the model to U- shaped flute. The simulation result also verified that the flat compression properties of V-shaped flute corrugated board are better than that of the U-shaped flute corrugated board and its cushioning properties are worse than that of the U- shaped flute. Actually, the triangle is the most stable structure. It is difficult to deform when a force was applied at the vertex of a triangle. But this structure is not suitable for the cushioning design. As the arc radius 𝑟 increases, the maximum displace- ments of the structure increase. So the stress can be dispersed to other parts rather than concentrating on one point. In this situation the cushioning properties of corrugated board get better to protect goods. In order to meet the needs of
Figure 3: Improved model of UV-shaped corrugated board with rigid plate.
of models with different number of flutes were built and shown in Figure 4. The numbers of flutes in models are 2, 3, 4, and 5. Fixing the bottom of models and then a static pressure test were made with a pressure of 150 Pa on the top floor. Then the stress and displacement contours of models of corrugated board were obtained as shown in Figure 5 (model with three flutes as example). From above calculation, the maximum displacement and maximum stress of the models with different number of flutes were obtained and the results are shown in Figure 6. From Figure 6, we can see that, with the number of flutes increased, the maximum stress in the models increased and the maximum displacement decreased. While the number of flutes increased to 3 or more, the maximum stress and displacement changed slightly. Therefore, the model of cor- rugated board with three or more flutes is reliable for stress and displacement measurement. In the coming simulation, the numbers of flutes in the models are all greater than 2. 3.2. Flute Height 𝐻 . Effects of flute height 𝐻 on the mechan- ical properties of corrugated cardboard model were investi- gated. A series of models with different flute height 𝐻 were built and shown in Figure 7. The flute heights 𝐻 inmodels are 2, 3, 4, and 5 mm. These models can be roughly classified as A flute (5 mm), C flute (4 mm), B flute (3 mm), and E flute (2 mm). Fixing the bottom of models and then a static pres- sure test were made with a pressure of 150 Pa on the top floor. Then the maximum displacement and maximum stress of the models with different flute height 𝐻 were obtained and the results are shown in Figure 8.
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