14
LINDBERG AND KULACHENKO
advantage of keeping the friction low in the corner. The shape closest to reality is given by the simulation using zero friction in the corner, shown in Figure 18C, which is also the model used for the above presented results. In Figure 19, the effect of the friction in the corner on the Tsai – Wu stress σ TW is shown. Here it is seen that the area where σ TW > 1 is very large for the cases with a friction coefficient of 0.3 and 0.1. In Figure 19C the friction coefficient is zero, and this is the same results as shown in Figure 15A. The results strongly support means of lowering the friction, such as the use of lubricants or increased die tool temperature, in the forming operation to aid problems with failure and bad shapes. In Figure 20 the influence of the creases is shown. The model has zero friction in the corner area and can be compared with the results
parameters, and the drying constraints during the manufacturing of paperboard will further contribute to a variation, as numerically proved in Alzweighi et al. 39 To include a variation of constitutive parameters requires further testing but, if acquired, is then straightfor- ward to include in the analysis. The approach may also be more exact if testing of the materials size dependency is performed. As mentioned earlier, the failure stresses and strains for paperboard have been shown 36 to have a size dependency, that is, locally allowing for higher stresses and strains than seen in standard tensile tests. Data for material size dependency was not accessible for this study and is hence not included, and in that sense the approach is conservative. The effect of the polymer extruded on the paperboard blank before the tray forming operation could also be investigated. This coating may affect the upper ply allowing for higher failure strain. 40 Finally, the use of shell elements leaves the contribution of the out-of-plane (ZD) stress outside of the analysis. The ZD stress will influence the stress-based failure surfaces, locally allowing for both lower and higher stress levels.
3.5
Effect of friction and creases
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In the following the numerical model is used for investigating the influence of friction and the importance of including the creases in the geometry. We used only Board A for this evaluation as the results are similar to Board B. The effect on the shape of changing the friction coefficient in the corner (the area shown in Figure 10) is shown in Figure 18, where the friction coefficient in (a) is 0.3, in (b) 0.1 and in (c) 0. It is obvious that the friction makes the forming operation harder, and that it is an
FIGURE 20
The shape of the formed tray without the use of
creases
FIGURE 18
Effect of friction coefficient in the corner on the shape. (A) Friction coefficient 0.3, (B) 0.1 and (C) 0
FIGURE 19
Effect of friction coefficient in the corner on the Tsai – Wu stress. (A) Friction coefficient 0.3, (B) 0.1 and (C) 0
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