Figure 1: Dimensions, loading, boundary conditions and mesh generation for typical 3/2 FML panel.
Figure 2: Back and front face displacements versus time for panels A3T24-8 and A4T34-5.
Figure 3: Comparison between the experiments and numerical simulations for five FML panel s.
Figure 4: Back and front face displacements versus time for the A4T32-4 panel based on the four aluminium alloys.
Figure 5: Deformed shapes of the A4T32-4 panel based on the four aluminium alloys.
Figure 6: Residual front and back face displacements of the A4T32-4 panel based on the four aluminium alloys versus yield strength.
Figure 7: Debonding energy of the
A4T32-4 panel based on the four aluminium alloys versus yield strength.
Figure 8: The time history of total internal energy and kinetic energy of the A4T32-4 panel based on the four aluminium alloys.
Figure 9: External work and total internal energy components (PD, SE, ED and AE) of the A 4T32-4 panel based on the four aluminium alloys.
Figure 10: Graph of dimensionless permanent displacement of back face versus dimensionless impulse.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
Figure 1: Dimensions, loading, boundary conditions and mesh generation for typical 3/2 FML panel.
Z-symmetric BC
Loading surface Fixed
X-symmetric BC Fixed
150 mm
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
Figure 2: Back and front face displacements versus time for panels A3T24-8 and A4T34-5.
0 5 10 15 20 25 30
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Displcaement of front and back face (mm)
Time (ms)
Front face, A3T24-8 Back face, A3T24-8 Front face, A4T34-5 Back face, A4T34-5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
a. A3T28-5, I=10.34 Ns
b. A4T32-4, I=7.23 Ns
c. A4T34-5, I=7.01 Ns
d. A4T36-2, I=11.61 Ns
e. A4T38-2, I=11.13 Ns
Figure 3: Comparison between the experiments and numerical simulations for five FML panels.
dB= 22.79 mm dF= 3.88 mm
dB= 19.4 mm dF= 1.79 mm dB= 22.6 mm
dF= 5.4 mm
dB= 20.7 mm dF= 4.3 mm
dB= 27.21 mm dF= 1.55 mm dB= 20.90 mm
dF= 2.20 mm
dB= 21.73 mm dF= 9.72 mm dB=17.20 mm
dF=13.80 mm
dB= 24.59 mm dF= 1.29 mm dB= 14.0 mm
dF= 7.6 mm
dB= 17.48 mm dF= 4.57 mm dB= 22.59 mm dF= 3.23 mm
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
a. Back displacement
b. Front displacement
Figure 4: Back and front face displacements versus time for the A4T32-4 panel based on the four aluminium alloys.
0 5 10 15 20 25 30
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Displacement of back face (mm)
Time (ms)
Al 2024-O Al 2024-T3 Al 6061-T6 Al 7075-T6
-5.0 -2.5 0.0 2.5 5.0 7.5 10.0 12.5 15.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Displacement of front face (mm)
Time (ms)
Al 2024-O Al 2024-T3 Al 6061-T6 Al 7075-T6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
a. Al 2024-O
b. Al 2024-T3
c. Al 6061-T6
d. Al 7075-T6
Figure 5: Deformed shapes of the A4T32-4 panel based on the four aluminium alloys.
dB= 24.29 mm dF= 9.48 mm
dB= 16.42 mm dF= 8.52 mm
dB= 19.12 mm dF= 8.04 mm
dB= 12.57 mm dF= 4.91 mm
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
Figure 6: Residual front and back face displacements of the A4T32-4 panel based on the four aluminium alloys versus yield strength.
0 5 10 15 20 25
0 100 200 300 400 500 600
Displacement (mm)
Yield strength (MPa)
Front face Back face
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
Figure 7: Debonding energy of the A4T32-4 panel based on the four aluminium alloys versus yield strength.
0 10 20 30 40 50
0 100 200 300 400 500 600
Debonding energy (J)
Yield strength (MPa)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
a. Total internal energy (IEALL ) and ETOTAL
b. Kinetic energy (KEALL).
Figure 8: The time history of total internal energy and kinetic energy of the A4T32-4 panel based on the four aluminium alloys.
0 50 100 150 200 250
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Energy (J)
Time (ms)
IE - Al 2024O IE - Al 2024T3 IE - Al 6061T6 IE - Al 7075T6 E
0 50 100 150 200 250
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Energy (J)
Time (ms)
KE - Al 2024O KE - Al 2024T3 KE - Al 6061T6 KE - Al 7075T6
ALL ALL ALL ALL TOTAL
ALL ALL ALL ALL
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
Figure 9: External work and total internal energy components (PD, SE, ED and AE) of the A4T32-4 panel based on the four aluminium alloys.
82%
70% 74%
61%
9% 14% 12%
22%
0 50 100 150 200 250
Al 2024-O Al 2024-T3 Al 6061-T6 Al 7075-T6
WK PD SE ED AE Energy (J)
: external work : plastic energy : strain energy : debonding energy : artificial strain energy
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
Figure 10: Graph of dimensionless permanent displacement of back face versus dimensionless impulse.
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Dimensionless displacement
Dimensionless impulse q
Al 2024-O Al 2024-T3 Al 6061-T6 Al 7075-T6 Linear (Al 2024-O) Linear (Al 2024-T3) Linear (Al 6061-T6) Linear (Al 7075-T6)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
List of Tables
Table 1: Details of the lay-ups and impulses for verification.
Table 2: Johnson-Cook constants and static tensile strength for aluminium alloys.
Table 3: Properties of the GFPP layers.
Table 4: Properties of the cohesive layers.
Table 5: Comparison of experimental data from Ref.[9] and numerical simulation results of transient and permanent displacements of front and back faces for verification.
Table 6: Summary of permanent front and back face displacements of FMLs based on the four aluminium alloys.
Table 7: Effective strength values for FMLs of varying composition, based on rule of mixtures approximation.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
Table 1: Details of the lay-ups and impulses for verification.
Lay-ups No. of layers
Thickness (mm)
Impulse (Ns)
A2T18-4 10 5.60 7.94
A3T24-8 11 6.06 7.85
A3T26-3 15 8.10 9.54
A3T28-5 19 9.82 10.34
A4T32-4 10 5.85 7.23
A4T34-5 16 8.73 7.01
A4T36-2 22 11.48 11.61
A4T38-2 28 13.90 11.13
A5T42-4 13 7.46 8.87
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
Table 2: Johnson-Cook constants and static tensile strength for aluminium alloys.
Aluminium type A (MPa)
B (MPa)
n C D1 D2 D3 D4 Ultimate tensile
strength (MPa) Al 2024-O [16] 85 325 0.40 0.0083 0.130* 0.130* -1.500* 0.011* 186
Al 2024-T3 [27] 369 684 0.73 0.0083 0.130 0.130 -1.500 0.011 483 Al 6061-T6 [28] 324 114 0.42 0.0020 -0.770 1.450 -0.470 0.000 310 Al 7075-T6 [29] 546 678 0.71 0.0240 -0.068 0.451 -0.952 0.036 572
* Damage constants for Al 2024-T3 were used due to the lack of available data.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
Table 3: Properties of the GFPP layers.
Elastic properties Values Progressive failure Values
(kg/m3) 1800 X1t(MPa) 300
E1 (GPa) 13.0 X1c(MPa) 200
E2 (GPa) 13.0 X2t(MPa) 300
E3 (GPa) 2.40 X2c(MPa) 200
G12 (GPa) 1.72 S (MPa) 12 140
G13 (GPa) 1.72 S13 (MPa) 140
G23 (GPa) 1.69 S23 (MPa) 140
12 0.1
13 0.3
23 0.3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
Table 4: Properties of the cohesive layers.
Elastic properties Damage initiation Damage evolution
Thickness tc (m)
c
(kg/m3) En
(GPa) Es
(GPa) Et
(GPa)
0
tn
(MPa)
0
ts
(MPa)
(MPa)
c
Gn
(J/m2)
c
Gs
(J/m2)
c
Gt
(J/m2)
104 920 2.05 0.72 0.72 140 300 300 2000 3000 3000
c s c
n G
G , and Gtcare the critical fracture energies in the normal, the first, and the second shear directions.
0 0, s
n t
t and tt0are the critical nominal normal stress, the first and the second shear stresses.
0
tt
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
Table 5: Comparison of experimental data from Ref. [9] and numerical simulation results of transient and permanent displacements of front and back faces for verification.
Panel Impulse (Ns)
Numerical Experiment
Transient displ. (mm) Permanent displ. (mm) Permanent displ. (mm)
Front Back Front Back Front Back
A2T18-4 7.94 12.86 28.09 4.95 22.19 9.10 16.30
A3T24-8 7.85 13.06 25.65 6.06 20.34 10.10 19.30
A3T26-3 9.54 12.07 26.91 4.32 20.35 7.20 23.70
A3T28-5 10.34 10.56 28.47 3.23 22.59 2.20 20.90
A4T32-4 7.23 13.91 25.79 9.72 21.73 13.80 17.20
A4T34-5 7.01 10.19 22.19 4.57 17.48 7.60 14.00
A4T36-2 11.61 9.30 32.70 1.55 27.21 5.40 22.60
A4T38-2 11.13 6.82 30.43 1.29 24.59 4.30 20.70
A5T42-4 8.87 13.28 30.32 7.95 25.31 11.50 19.90
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
Table 6: Summary of permanent front and back face displacements of FMLs based on the four aluminium alloys.
Panel Aluminium types
Dimensional parameters Dimensionless parameters Impulse
(Ns)
Displacement (mm)
Impulse Front Back Front Back
A2T18-4 Al 2024-O 8.00 5.53 22.92 3.81 0.99 4.09 Al 2024-T3 8.00 5.17 18.19 3.41 0.92 3.25 Al 6061-T6 8.00 5.71 20.84 3.63 1.02 3.72 Al 7075-T6 8.00 4.50 15.20 3.32 0.80 2.71 A3T24-8 Al 2024-O 8.00 6.63 18.77 3.16 1.09 3.10 Al 2024-T3 8.00 7.10 16.29 2.72 1.17 2.69 Al 6061-T6 8.00 7.20 18.10 2.95 1.19 2.99 Al 7075-T6 8.00 5.56 12.07 2.62 0.92 1.99 A3T26-3 Al 2024-O 8.00 4.58 16.21 1.81 0.56 2.00 Al 2024-T3 8.00 4.42 13.15 1.62 0.55 1.62 Al 6061-T6 8.00 4.21 15.13 1.72 0.52 1.87 Al 7075-T6 8.00 2.91 9.30 1.57 0.36 1.15 A3T28-5 Al 2024-O 8.00 3.28 17.99 1.18 0.33 1.83 Al 2024-T3 8.00 2.41 12.09 1.07 0.24 1.23 Al 6061-T6 8.00 2.81 14.80 1.13 0.29 1.50 Al 7075-T6 8.00 1.20 9.74 1.05 0.12 0.99 A4T32-4 Al 2024-O 8.00 9.48 24.29 3.35 1.62 4.15 Al 2024-T3 8.00 8.52 16.42 2.72 1.46 2.81 Al 6061-T6 8.00 8.04 19.12 3.04 1.37 3.27 Al 7075-T6 8.00 4.91 12.57 2.60 0.84 2.15
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
A4T34-5 Al 2024-O 8.00 4.95 20.42 1.48 0.57 2.34 Al 2024-T3 8.00 3.02 13.75 1.29 0.35 1.58 Al 6061-T6 8.00 3.43 15.87 1.39 0.39 1.82 Al 7075-T6 8.00 1.88 10.82 1.24 0.22 1.24 A4T36-2 Al 2024-O 8.00 2.36 18.41 0.82 0.21 1.60 Al 2024-T3 8.00 1.21 13.49 0.74 0.11 1.18 Al 6061-T6 8.00 1.45 15.64 0.78 0.13 1.36 Al 7075-T6 8.00 0.47 10.44 0.72 0.04 0.91 A4T38-2 Al 2024-O 8.00 1.18 17.88 0.59 0.09 1.29 Al 2024-T3 8.00 0.68 12.92 0.54 0.05 0.93 Al 6061-T6 8.00 0.71 14.12 0.57 0.05 1.02 Al 7075-T6 8.00 0.28 10.30 0.53 0.02 0.74 A5T42-4 Al 2024-O 8.00 7.62 23.63 3.40 1.02 3.17 Al 2024-T3 8.00 5.26 16.30 2.77 0.71 2.19 Al 6061-T6 8.00 5.51 18.67 3.09 0.74 2.50 Al 7075-T6 8.00 2.92 12.53 2.64 0.39 1.68
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
Table 7: Effective strength values for FMLs of varying composition, based on rule of mixtures approximation.
Lay-ups Total thickness (mm)
Thickness of aluminium (mm)
Thickness of GFPP (mm)
Aluminium type
Estimated static tensile strength (MPa)
GFPP N/A N/A N/A N/A 300
A2T18-4 5.60 1.27 4.33 Al 2024-O 274
Al 2024-T3 342
Al 6061-T6 302
Al 7075-T6 362
A3T24-8
6.06 1.91 4.16 Al 2024-O 264
Al 2024-T3 358
Al 6061-T6 303
Al 7075-T6 386
A3T26-3 8.10 1.91 6.20 Al 2024-O 273
Al 2024-T3 343
Al 6061-T6 302
Al 7075-T6 364
A3T28-5 9.82 1.91 7.94 Al 2024-O 278
Al 2024-T3 335
Al 6061-T6 302
Al 7075-T6 353
A4T32-4 5.85 2.54 3.31 Al 2024-O 251
Al 2024-T3 379
Al 6061-T6 304
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
Al 7075-T6 418
A4T34-5 8.73 2.54 6.19 Al 2024-O 267
Al 2024-T3 353
Al 6061-T6 303
Al 7075-T6 379
A4T36-2 11.48 2.54 8.94 Al 2024-O 275
Al 2024-T3 340
Al 6061-T6 302
Al 7075-T6 360
A4T38-2 13.90 2.54 11.36 Al 2024-O 279
Al 2024-T3 333
Al 6061-T6 302
Al 7075-T6 350
A5T42-4 7.46 3.18 4.29 Al 2024-O 251
Al 2024-T3 378
Al 6061-T6 304
Al 7075-T6 416