10
LINDBERG AND KULACHENKO
FIGURE 11 Virtual twin of the tray. To the left the actual tray after a successful forming operation. To the right, the simulated tray
FIGURE 12
Normal stress distribution sampled from the midplane. In (A) Board A MD stress, (B) Board B MD stress, (C) Board A CD stress
and (D) Board B CD stress
would allow for higher strain levels before failure. Hence the Maxi- mum Strain Theory is a conservative approach, something seen in the results in Figure 14. In both models, there are many locations where the strain state is outside of the failure surface, that is, ε F > 1, also in the lower corner for Board B where failure is not seen in production. In Figure 15 the results using the Tsai – Wu Theory for failure eval- uation are shown, see Equation 7. Here it can be seen that Board A experiences a stress state outside of the failure surface ( σ TW >1) in the lower corner, and Board B stays below σ TW ¼ 1 in the lower cor- ner, which is in line with what has been observed in production. For both Board A and Board B, the area over the creases has several loca- tions with high values of σ TW . Although failure can occur over these areas as well, the use of homogenous material properties and ignoring delamination leads to an overestimation of the stresses in these regions.
and Board B respectively. For the CD, the strain for Board A is high, almost 12% close the lower part of the creases, and 8% in the same location for Board B. The strain levels may seem high but, as shown in for instance Hagman et al., 36 can be considerably higher under com- plex loading states than seen in a standard tensile test.
3.3
Failure results
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The stress and strain levels for the analyses are used to study failure of the trays. In Figure 14 the failure evaluation using Maximum Strain Theory is shown. The expression is shown in Equation 10 and, as seen there, only one component at a time of the in-plane strain compo- nents is evaluated. In other words, the contribution from the total strain state is not considered which in most locations (but not all)
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