4 Penetration resistance of stiffened steel panels
4.3 Numerical model
The frame is assumed stiff enough to assume fixed ends around the plate and is not modelled. The model is also modelled with one symmetry plane across the middle of the plate. The stiffeners and plate are connected with a tie constraint since they have different materials.
4.3.1 Mesh
These tests are also modelled with S4R elements in Abaqus 2016. The mesh sizes that are used are: 5 mm (le/te= 1), 20 mm (le/te= 4) and 50 mm (le/te= 10). The 5 mm mesh for the test with two flat bar stiffeners is shown in the figure below.
(a)
(b)
Figure 4.2: 5 mm mesh for 2 flat bar stiffeners
The welds are modelled in a similar way to what was done by alsos [3] and the method is also described by Wang et al. [15]. The welds vary between 5 and 7 mm in height and width, so 6 mm wide elements with increased thicknesses are used in the simulations. The increased thicknesses are 2 mm for the plate side, and 4 mm for the stiffener side. This is shown in Figure 4.3. The different thicknesses are modelled with a composite layup in Abaqus with a conventional shell element type.
Figure 4.3: Cross section of the weld elements
4.3.2 Contact
The contact is modelled pretty similar to what is done for the Broekhuijsen tests described in section 3.2.3. The indenter is initially placed 0.001 mm above the plate and the velocity is ramped up the first 10% of the simulation which are also set to 0.05 seconds for these tests. The only difference is the friction coefficient that is set to 0.3 and is normal for coated steel to steel contact.
General contact is also used here. The setup for two bulb stiffeners is shown in the figure below with 20 mm elements.
Figure 4.4: Setup for 2-HP 20 mm elements
4.4 Results
The results for the different configurations are shown in the next pages. The circles indicate where the first element fails. As can be seen on the figures, the results without BWH (the dashed lines in the plots) also shows some necking behavior at for these tests.
4.4.1 Unstiffened plate
(a) First integration point without mesh scaling (b) First integration point with mesh scaling
(c) Middle integration point without mesh scaling (d) Middle integration point with mesh scaling Figure 4.5: Results - Unstiffened plate
We see from the figure that it is not much difference between using the middle integration point and the first integration point. The first integration point is, as expected, more conservative, but the difference is barely noticeable. It is also observed that the mesh scaling for this case is a little too strong.
4.4.2 One flat bar stiffener (1-FB)
(a) First integration point without mesh scaling (b) First integration point with mesh scaling
(c) Middle integration point without mesh scaling (d) Middle integration point with mesh scaling Figure 4.6: Results - 1-FB stiffener
The same observations are observed here, as in the unstiffened plate. Only a little more conser-vative using the first integration point and the mesh scaling is a bit too strong.
4.4.3 Two flat bar stiffeners (2-FB)
(a) First integration point without mesh scaling (b) First integration point with mesh scaling
(c) Middle integration point without mesh scaling (d) Middle integration point with mesh scaling Figure 4.7: Results - 2-FB stiffeners
The same goes for these tests, as for the two previous ones, when looking at the difference between the integration points. However, here is the mesh scaling pretty good.
The evolution of the fracture is shown in Figure 4.8 for this configuration.
(a) 2-FB right before fracture (b) 2-FB right after fracture
(c) 2-FB at the end of the simulation
Figure 4.8: Fracture evolution for two flat bar stiffeners
It is seen that the fracture occurs in the middle of the plate close to the weld, and develops out-wards. This is pretty similar to what happened in the experiments. An image of the experiment after fracture is shown in Figure 4.9.
Figure 4.8c shows that a strain concentration occurs prior to fracture. The stiffener has large resistance and friction effects in the impact zone leads to large deformations in the plate section close to the stiffener. Also, the plate experience a change in geometry close to the weld, which implies larger strain concentration here. This leads to fracture occurring here first.
Figure 4.9: Experiment 2-FB after fracture [14]
4.4.4 One bulb stiffener (1-HP)
(a) First integration point without mesh scaling (b) First integration point with mesh scaling
(c) Middle integration point without mesh scaling (d) Middle integration point with mesh scaling Figure 4.10: Results - 1-HP stiffener
The plots here show pretty similar results as for the 1-FB and unstiffened test, where the mesh scaling is a bit too strong, especially for the middle integration point here, and pretty similar results compared to using the first integration point. Figure 4.10a and 4.10b shows that fracture occurs a bit before we get a bigger drop in force. The reason for this is that the tip of the stiffener fractures first in that case. The bigger drop is when the test fractures in the plate. This can show that the stiffener is carrying small load compared to the plate.
4.4.5 Two bulb stiffeners (2-HP)
(a) First integration point without mesh scaling (b) First integration point with mesh scaling
(c) Middle integration point without mesh scaling (d) Middle integration point with mesh scaling Figure 4.11: Results - 2-HP stiffeners
This is the only test that shows less conservative results for using the first integration point com-pared to the middle. It is observed from Figure 4.11a that the 50 mm mesh does not predict fracture and the 12 mm mesh predict instability too late. The weld is getting large strain concen-tration (see Figure 4.12 and is not working as originally intended by easing the transition between the stiffener and the plate. However, comparing the results to what Alsos got [3], and to the experiments, the results for the middle integration point is pretty good. For the larger mesh sizes, the weld elements get pretty thin and long, and therefore takes up the plastic equivalent strain in the model. So, the reason for the first integration point with 30 mm mesh does not capture the fracture, could be because of this large stress concentration happening in the weld.
Figure 4.12: Plastic equivalent strain concentration in weld elements 2-HP 30 mm mesh size - middle integration point