**6.1. Comparison of numerical and plastomechanical calculations**

Numerical die-bending results of side length L = 40 mm are shown in Figure 10. Now, the strain distribution of the upper and lower fiber of both layers are shown and compared with the plastomechanical preliminary design. Computation according to [25] offer a k-factor of k��� � ��, which fits quite good for the maximum strain, calculated with a numerical method in the midst of the bending. The real positions of the neutral axis are shown schematically.

Inaccuracies of preliminary design are ascribed to the [25]:


## **6.2. Forming tendencies of multilayer sandwich sheets**

Thee founded results to influence the forming behavior, are further tested with simulation of v-die-bending. With a punch radius of r = 8,5 mm, a side length of L = 40 mm and a constant thickness of the sandwich s = 1,4 mm, the five typical constellations for different layer thicknesses (Figure 20) are calculated. The same material as in chapter 3 and 6.1 is used. For this calculation, the adhesive thickness is neglected.

**Figure 20.** Numerical results of die-bending for five multilayer sandwich sheet

For this great side length, the displacement after forming is very small and no failure mode occurs for all five constellations. The symmetrical sandwich (ݏଵ ൌ ݏଶ ൌ Ͳǡ݉݉) sheet no. 1 shows less spring back than all of the other constellations with 4 metal layers. The highest value for spring back shows no. 4 with increasing layer thickness. The remaining stress which can cause failure (chapter 1.2) decreases by using unsymmetrical thicknesses (no. 2, 3 and 4). As proposed in chapter 4.2, the number of layers influences the strain distribution. Minimal elongation shows specimen no. 3 and compression no. 5. Because of the minor stiffness no. 5 tends to buckling. This is an initial point for inner failures. The different spring back of each layer can be absorbed by the adhesive.

The normal plastic strain component in bending direction depends on the thickness of the metal layers. The thinner the inner cover sheet is, the minor is the plastic strain and the displacement of the edges (see no. 2-4). But a thin inner layer tends to buckling. To get the lowest normal stress in bending direction, the thickness should be increased as seen in configuration no. 4. Also the spring-back of the undamaged sandwich depends on the layerconfiguration.

An example for an application of a commercial three-layer sandwich sheet in the automotive industry is shown in [25]. For this profile, formed by rolling the failures displacement, delamination and buckling could be predicted and verified with experimental tests.
