Simulations of the experiments

This section presents the simulations of four of the experiments in the shock tube with the use of the last improved model from Section 8.2.4. The experiments related to the third plate were not simulated as the perforation alone would require its own study. To evaluate the numerical simulations, they were compared with the corresponding physical experiments.

Two factors were considered, i.e. the crack formation and a collapse of the plate. In terms of the cracks, it was only possible to compare the numerical results with the visible cracks on the surface. Here, the amount of node splitting was used as basis for comparison.

Concrete plate number one

The load subjected to the first concrete plate was modelled with the Friedlander curve fit with a 7.4 bar peak load generated in Section 7.2.

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(a) Numerical (front) (b) Experiment (front)

(c) Numerical (back) (d) Experiment (back)

Figure 8.24: Experiment and numerical simulation for plate number one.

Figure 8.24 present the numerical results compared to the experiments. As shown in Figure 8.24a and 8.24c, the numerical models accumulated damage, but not enough to generate node splitting. The maximum damageDwas approximately 45.6% and was located near the load area on the front of the plate. In the experiment, no damage was visible.

Concrete plate number two

The load subjected to the second concrete plate was modelled with the Friedlander curve fit with a 11.99 bar peak load generated in Section 7.3.

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(a) Numerical (front) (b) Experiment (front)

Figure 8.25: Experiment and numerical simulation for plate number two (front).

(a) Numerical (back) (b) Experiment (back)

Figure 8.26: Experiment and numerical simulation for plate number two (back).

Figures 8.25 and 8.26 shows the numerical results compared to the experiments. In the sim-ulation of the second concrete plate, node splitting appeared along the edges of the clamped area in the front of the plate. A corresponding amount of damage was not visible in the physical experiment.

CHAPTER 8. NUMERICAL STUDIES Concrete plate number four

(a) Numerical (front) (b) Numerical (back)

Figure 8.27: Numerical simulation for plate number four.

For the physical experiment on the fourth concrete plate, total collapse occurred. To recreate the collapse, the measurements in sensor 409 was used to describe the pressure (see Figure 8.29). The IMPETUS keywords for this simulation are included in Appendix D.4.

(a) Experiment (back) (b) Without clamping plate (back)

Figure 8.28: Experiment on plate number four.

As seen in Figures 8.27 and 8.28, the numerical model did not collapse as the plate did in the experiment. The improved model failed in the previous tests for pressures equal to or

CHAPTER 8. NUMERICAL STUDIES higher than 32.5 bar, and the maximum load registered in the physical experiment was 29.4 bar. It was expected that the plate would show some signs of collapse, and it was surprising that this was not the case. Because of this, scaled versions of the 409 pressure readings were applied (see Figure 8.29).

It appeared that an increase of 40% of the load was necessary to collapse the plate. The response of the plate is shown in Figure 8.30 for the scaled load, where the time of the dis-played images corresponds to the red dots in Figure 8.29. As seen in Figure 8.29, the plate required a maximum load of 41.2 bar to collapse, which is almost 30% higher than for a load described by a Friedlander equation (see Section 8.2.4). This showed again that the response of the model was dependent on the shape of the load. The Friedlander equation provided an instantaneously increase to the maximum load, which was not the case for the pressure history in the sensor.

Figure 8.29: Load for simulation of collapsed plate

Figures 8.30a-c show how the cracks developed in the numerical model as the first peak load was applied to the plate. No further damage was accumulated until the load was increased again (see Figure 8.30d). This behaviour corresponded well with the experiment. However, further cracks in the numerical model did not propagate until the load reached its absolute

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maximum. It is shown in Figure 8.30e-f that the model reached its absolute capacity at the maximum load and collapsed shortly after. It should be noted that the pressure history from the physical experiment could imply that the total collapse occurred at the maximum pressure, but that the plate reached its capacity even earlier. In other words, the plate needed time to be accelerated and pushed out of the frame. This could mean that the deviation from the experiment was even higher than first assumed.

(a) t=0.15 ms (b) t=0.45 ms (c) t=0.60 ms

(d) t=6.08 ms (e) t=11.18 ms (f) t=12.56 ms

Figure 8.30: Collapse of the plate with scaled pressure.

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Concrete plate number five

The load subjected to the fifth concrete plate was modelled with the Friedlander curve with a 18.50 bar peak load generated in Section 7.6.

(a) Numerical (front) (b) Numerical (back)

(c) Experiment (front) (d) Experiment (back)

Figure 8.31: Comparison of experiment and numerical simulation for plate number five.

As seen in Figure 8.31, the numerical simulation corresponded well with the experiment.

Both the front and the back developed almost the same crack patterns. There were however some deviations from the physical experiments. First off, the concrete plate was especially damaged in the upper right corner (see Figure 8.31d) and secondly, the crack formations followed the circular holes in the plate. As the reinforcement and the bolt holes were not

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modelled, this was not surprising. The reinforcement was not continuous in the upper right corner, which resulted in less support at this point. Additionally, the circular holes would provide a weakness in the plate and the cracks would therefore propagate from them. Figure 8.32 shows the total amount of cracks developed in the numerical model and Figure 8.33 shows the crack propagation in the plate compared with the experiments.

Figure 8.32: Crack formation of 18.5 bar simulation.

It can be seen in both Figures 8.32 and 8.33 that the numerical model failed to recreate the through-thickness cracks formed in the experiment. Figure 8.33f clearly shows pressure escaping through the backside of the plate, which indicated that through-thickness cracks existed in the experiment. Figure 8.32 shows that the cracks did not occur through the entire thickness in the numerical model. These results indicated that the capacity of the numerical model was too large.

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(a) Numerical (back) (b) Experiment (back)

(c) Numerical (front) (d) Experiment (back)

(e) Numerical (back) (f) Experiment (back) Figure 8.33: Comparison of crack propagation for the fifth plate.

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