Dissipated cohesive energy [J]
Time [s]
Figure 5.14: History of dissipated cohesive energy.
PP PP
PP PP
PP PP
P P
Energies
Analysis
A B
Elastic energy [J] 8000 14000 Dissipated cohesive energy [J] 3985 2304
Table 5.6: Final elastic energy and dissipated cohesive energy computed in the analyses A and B.
5.3 Capability of different hull cross sections to con-
different sandwich panels normalized with respect to the panel weight. The characteristics of three different plates used in the analyses are summarized in Table (5.7).
Fiber composite and foam
Aluminum and foam
Fiber composite only
Total thickness [mm] 100.0 88.7 34.0
Face sheet thickness [mm] 15.0 8.9 -
Core thickness [mm] 70.0 70.9 -
Specific weight [kg/m2] 55.3 55.3 54.7
Table 5.7: Plate sandwich material configurations.
The mesh used in the analyses is the same as the one represented in Figure (5.5(a)) and consists of 2,048 shell elements. The elements are pre-fractured at the beginning to allow for fracture and fragmentation. The material properties for the epoxy resin and the carbon fibers are the same as the ones reported in Tables (5.2) and (5.3). The employed material models have been discussed in Sections (2.1) and (2.2). The material behavior of aluminum is described by a J2 plasticity model with power law hardening and rate dependency. The aluminum material properties are taken from Cirak et al. (2005) and are reported in Table (5.8).
Mass density 2719 kg
Young’s modulus 69000 Mpa
Yield stress 90 MPa
Poisson ratio 0.33
Reference plastic strain 0.001 Hardening exponent (1/n) 4.0 Reference plastic strain rate 0.0001 Rate sensitivity exponent (1/m) 0.01
Cohesive strength 180 MPa Table 5.8: Material properties for aluminum Al2024-0.
The sandwich panels are simply supported on the boundaries and are subjected to the pressure load corresponding to the detonation of an underwater 0.2 kg TNT charge placed at 0.4 m vertically under the center of the plate. The maximum pressure generated by the underwater explosion is equal to 89.9 MPa.
If fiber reinforced face sheets are used as opposed to aluminum face sheets:
1. the kinetic energy of the plate is lower indicating a lower structural damage. More- over, as visible in Figure (5.15) the kinetic energy of the sandwich plate with fiber
composite face sheets reaches a maximum and then markedly decreases, meaning that the plate has contained the pressure due to the explosion and is slowing its motion. On the contrary, the kinetic energy of the aluminum sandwich shells does not decrease markedly after reaching its maximum. This is due to the presence both of fragments detached from the main plate and of cracks in the sandwich panel which reduce the structural stiffness of the sandwich plate.
2. The elastic energy stored in the sandwich core is higher, indicating that a greater part of the explosion energy has been absorbed in the core (Figure 5.16).
3. The fractured cross section area is lower (Figure5.17). The surface of the fractured cross section is computed by dividing the dissipated cohesive energy by the mean fracture energy of the sandwich cross section which is computed averaging the frac- ture energy of the external face sheets and of the internal foam core based on their relative thickness. The average fracture energy for the sandwich cross section with fiber composite and aluminum face sheets is equal to 10708 N/m and 1850 N/m respectively.
3.0E+5
2.5E+5 3.0E+5
2.0E+5 2.5E+5 3.0E+5
y [J]
1.5E+5 2.0E+5 2.5E+5 3.0E+5
c energy [J] Fiber composite and PVC foam
1.0E+5 1.5E+5 2.0E+5 2.5E+5 3.0E+5
Kinetic energy [J]
Fiber composite and PVC foam Aluminum and PVC foam
5.0E+4 1.0E+5 1.5E+5 2.0E+5 2.5E+5 3.0E+5
Kinetic energy [J]
Fiber composite and PVC foam Aluminum and PVC foam
0 0E+0 5 0E 4 1 0E 3 1 5E 3 2 0E 3 0.0E+0
5.0E+4 1.0E+5 1.5E+5 2.0E+5 2.5E+5 3.0E+5
Kinetic energy [J]
Fiber composite and PVC foam Aluminum and PVC foam
0.0E+0 5.0E-4 1.0E-3 1.5E-3 2.0E-3 0.0E+0
5.0E+4 1.0E+5 1.5E+5 2.0E+5 2.5E+5 3.0E+5
Time [s]
Kinetic energy [J]
Fiber composite and PVC foam Aluminum and PVC foam
Figure 5.15: History of the kinetic energy of simply supported 4 m×4 m sandwich plates with different face sheet materials subjected to an underwater explosion.
3 0E+3 4.0E+3 5.0E+3 6.0E+3 7.0E+3
core energy [J]
Fiber composite and PVC foam Aluminum and PVC foam
0.0E+0 5.0E-4 1.0E-3 1.5E-3 2.0E-3 0.0E+0
1.0E+3 2.0E+3 3.0E+3 4.0E+3 5.0E+3 6.0E+3 7.0E+3
Time [s]
Elastic core energy [J]
Fiber composite and PVC foam Aluminum and PVC foam
Figure 5.16: Evolution of the elastic energy stored in the foam core of simply supported 4 m× 4 m sandwich plates with different face sheet materials subjected to an underwater explosion.
6 8 10 12 14
oss section area [m2]
Fiber composite and PVC foam Aluminum and PVC foam Fiber composite only
0.0E+0 5.0E-4 1.0E-3 1.5E-3 2.0E-3
0 2 4 6 8 10 12 14
Time [s]
Fractured cross section area [m2]
Fiber composite and PVC foam Aluminum and PVC foam Fiber composite only
Figure 5.17: Fracture propagation history for simply supported 4 m × 4 m sandwich plates with different face sheet materials subjected to an underwater explosion.
The analyses just described have been repeated using a smaller square sandwich panel with sides of length equal to 2.0 m and thickness equal to 70 mm. In this second set of analyses the applied pressure profile corresponds to a TNT charge equal to 0.15 kg placed at 0.25 m below the plate center. The maximum pressure applied to the plate is equal to 126.9 MPa, and larger structural damage is inflicted. Figures (5.18), (5.19), and (5.20) confirm the observations relative to the first set of analyses.
3.0E+5
2.5E+5 3.0E+5
2.0E+5 2.5E+5 3.0E+5
gy [J]
1.5E+5 2.0E+5 2.5E+5 3.0E+5
etic energy [J]
1.0E+5 1.5E+5 2.0E+5 2.5E+5 3.0E+5
Kinetic energy [J]
Fiber composite and PVC foam
5.0E+4 1.0E+5 1.5E+5 2.0E+5 2.5E+5 3.0E+5
Kinetic energy [J]
Fiber composite and PVC foam Aluminum and PVC foam
0 E+00 2 E-04 4 E-04 6 E-04 8 E-04 0.0E+0
5.0E+4 1.0E+5 1.5E+5 2.0E+5 2.5E+5 3.0E+5
Kinetic energy [J]
Fiber composite and PVC foam Aluminum and PVC foam
0.E+00 2.E-04 4.E-04 6.E-04 8.E-04 0.0E+0
5.0E+4 1.0E+5 1.5E+5 2.0E+5 2.5E+5 3.0E+5
Time [s]
Kinetic energy [J]
Fiber composite and PVC foam Aluminum and PVC foam
Figure 5.18: History of the kinetic energy of simply supported 2 m×2 m sandwich plates with different face sheet materials subjected to an underwater explosion.
6 E+03 7.E+03
5 E+03 6.E+03 7.E+03
J]
Fiber composite and PVC foam Aluminum and PVC foam
4 E+03 5.E+03 6.E+03 7.E+03
nergy [J]
Fiber composite and PVC foam Aluminum and PVC foam
3.E+03 4.E+03 5.E+03 6.E+03 7.E+03
c core energy [J]
Fiber composite and PVC foam Aluminum and PVC foam
2.E+03 3.E+03 4.E+03 5.E+03 6.E+03 7.E+03
Elastic core energy [J]
Fiber composite and PVC foam Aluminum and PVC foam
1.E+03 2.E+03 3.E+03 4.E+03 5.E+03 6.E+03 7.E+03
Elastic core energy [J]
Fiber composite and PVC foam Aluminum and PVC foam
0.E+00 2.E-04 4.E-04 6.E-04 8.E-04
0.E+00 1.E+03 2.E+03 3.E+03 4.E+03 5.E+03 6.E+03 7.E+03
Elastic core energy [J]
Fiber composite and PVC foam Aluminum and PVC foam
0.E+00 2.E-04 4.E-04 6.E-04 8.E-04
0.E+00 1.E+03 2.E+03 3.E+03 4.E+03 5.E+03 6.E+03 7.E+03
Time [s]
Elastic core energy [J]
Fiber composite and PVC foam Aluminum and PVC foam
Figure 5.19: Evolution of the elastic energy stored in the foam core of simply supported 2 m× 2 m sandwich plates with different face sheet materials subjected to an underwater explosion.
8 9
Fiber composite and PVC foam Aluminum and PVC foam 7
8 9
ea [m2]
Fiber composite and PVC foam Aluminum and PVC foam Fiber composite only
5 6 7 8 9
tion area [m2]
Fiber composite and PVC foam Aluminum and PVC foam Fiber composite only
4 5 6 7 8 9
cross section area [m2]
Fiber composite and PVC foam Aluminum and PVC foam Fiber composite only
3 4 5 6 7 8 9
tured cross section area [m2]
Fiber composite and PVC foam Aluminum and PVC foam Fiber composite only
1 2 3 4 5 6 7 8 9
Fractured cross section area [m2]
Fiber composite and PVC foam Aluminum and PVC foam Fiber composite only
0 E+00 2 E-04 4 E-04 6 E-04 8 E-04
0 1 2 3 4 5 6 7 8 9
Fractured cross section area [m2]
Fiber composite and PVC foam Aluminum and PVC foam Fiber composite only
0.E+00 2.E-04 4.E-04 6.E-04 8.E-04
0 1 2 3 4 5 6 7 8 9
Time [s]
Fractured cross section area [m2]
Fiber composite and PVC foam Aluminum and PVC foam Fiber composite only
Figure 5.20: Fracture propagation history for simply supported 2 m × 2 m sandwich plates with different face sheet materials subjected to an underwater explosion.
Although interlayer delamination between the foam core and the external face sheets is not simulated and addressed in the present work, it is worth mentioning that fiber reinforced sandwich panels are expected to offer also a greater resistance to delamination in comparison to sandwich panels with aluminum external layers. Indeed, it is expected that the inner surface in contact with the foam core is, in general, more rough in the case of fiber reinforced external layers, therefore offering a greater interlocking between the foam core and the external face sheets and consequently a higher interlayer cohesive strength.
As it is possible to see from Figures (5.17) and (5.20), a plate made exclusively of fiber composite material sustains the load as well as a sandwich plate with fiber composite face sheets and of equal weight. However, as it appears from Figure (5.21), the plate made of only fiber composite material undergoes a larger deflection if subjected to the same pressure load than a sandwich plate of equal weight (the pressure load used in this last set of analyses is due to a small TNT charge equal to 0.1 kg placed 1.0 m below the plate center and does not cause structural damage). Usual structural applications require the maximum deformation to be limited. Therefore, even if both the sandwich fiber composite plate and the fiber-only composite plate sustain an explosive load equally well, the first is preferred in structural applications.
0 1 2 3 4 5 6 7 8 x 10−3
−0.1
−0.08
−0.06
−0.04
−0.02 0 0.02 0.04
Time [s]
Central displacement [m]
Aluminum and Foam Fiber composite and Foam Only Fiber composite
Figure 5.21: Simply supported 4 m× 4 m square plates subjected to a small underwater explosion: deflection history.