9
LINDBERG AND KULACHENKO
FIGURE 9
The geometry and mesh of the blank. (A) the geometry, (B) the mesh and (C) close-up of the creases
FIGURE 10
Area used for investigating the
effect of changing the friction coefficient
extent agreeing with the shape of the real tray. At position ‘ A ’ in Figure 11, the material is buckling slightly inwards, which is seen in both the real and simulated tray. The same thing is seen at position ‘ C ’ . At position ‘ D ’ , a small outgoing ‘ buckle ’ is seen in both the real and simulated tray. At position ‘ B ’ , some difference is seen. Here the material in the simulated tray has not folded enough to form the fully correct corner, but it is only a small difference. Further, some more wrinkles on the edges can be seen in the simulated tray. The appear- ance of the wrinkles along the edge is undesired as it hinders sealing the tray. The quantification of the wrinkles may be yet another verifi- cation possibility. 31
model uses homogenous material properties, whereas in reality, the paperboard consists of several plies through the thickness with vari- ous stiffness and the possibility to delaminate in the folding process. The interplay delamination and subsequent relaxation of stresses are not resolved with the current model. However, for these specific trays, the failure is seen in the lower corner and the current model outside the creased area, and therefore the limitation of not modelling delamination should affect the stresses in this area. In the MD, the maximum stress outside the region of the creases occurs in the lower corner, see Figure 12A,B. For Board A, the MD stress here is 85 MPa, and for Board B about 65 MPa. For CD, the stress in the corner becomes about 50 MPa for Board A and 35 for Board B, see Figure 12C,D. The maximum stress in CD and MD does not occur in the exact same location.
3.1
Normal stresses
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In Figure 12 the normal stresses in MD and CD are displayed. The stresses are sampled from the mid-plane of the shell elements. For both boards, the highest tensile and compressive stress levels, in both MD and CD, arise between the creases. Although high stresses can occur over these areas, the numerical model used in this study possi- bly overestimates the stresses in that region. The reason is that the
3.2
Total normal strains
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The total normal strains in the MD and CD, sampled from the mid- plane, are shown in Figure 13. At the observed failure location, that is, the lower corner, the strain in MD is about 2% and 1.3% for Board A
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