2. Air-blast experiments

#### 2.1. Experimental procedure

#### 2.1.1. Specimens

Single-curvature sandwich panel specimens, 310 mm long, with an arc length also of 310 mm, were fabricated from two thin LY-12 aluminum alloy face-sheets bonded to an aluminum foam Single-Curvature Sandwich Panels with Aluminum Foam Cores under Impulsive Loading http://dx.doi.org/10.5772/intechopen.70531 121

Figure 2. Photograph of specimens with the two radii of curvature.

sandwich structures to enhance the blast/shock resistance performance. The sandwich structure typically consists of two thinner but stiffer face-sheets and a softer crushable core, which is a special topology form comprising a combination of different materials that are bonded to each other so as to utilize the properties of each component for the structural advantage of the whole assembly. The face-sheets resist nearly all of the applied in-plane loads and bending moments, while the core sustains the transverse and shear loads mainly. The employment of flatted sandwich structures (i.e., the beam and panel) to resist blast/shock loadings still remains academic and engineering interests, and the responses of these sandwich structures to various loading cases have been widely investigated [4–12]. Some representative failure modes (e.g., face-sheet yielding and core compression or shear) have been experimentally observed [5, 7, 9– 11], while the load-carrying capability and mechanisms of plastic failure and energy absorption

Figure 1. Stress versus strain response curve of the aluminum foam with 11% relative density.

Curved sandwich panels, which better combine the advantages of shell and sandwich structures, are envisaged to possess good potential in withstanding blast or impact [13–15]. However, studies on curved metallic sandwich structures appear quite limited to date. Consequently, a comprehensive study on blast-loaded single-curvature sandwich panels with

Single-curvature sandwich panel specimens, 310 mm long, with an arc length also of 310 mm, were fabricated from two thin LY-12 aluminum alloy face-sheets bonded to an aluminum foam

have been predicted in theory and simulation [4, 6, 8, 12].

2. Air-blast experiments

120 Contact and Fracture Mechanics

2.1. Experimental procedure

2.1.1. Specimens

aluminum foam cores is conducted in experiment and simulation.

core using commercially available adhesive. Figure 2 shows the picture of single-curvature sandwich panels with two radii of curvature, that is, 250 and 500 mm. Three face-sheet thicknesses (i.e., 0.5, 0.8, and 1.0 mm) and three core relative densities (i.e., 11, 15, and 18%) were examined. The quasi-static mechanical properties of LY-12 aluminum alloy face-sheets with the density r = 2780 kg/m3 are Young's modulus E = 68 GPa, Poisson's ratio ν = 0.33, yield stress σfY = 310 MPa, and shear modulus G = 28 GPa.

The core material was closed-cell aluminum foam, and the typical quasi-static uniaxial compressive stress-strain responses for three different relative foam densities are shown in Figure 3. Here, an energy efficiency-based approach is proposed to calculate the plateau stress and densification strain. Energy absorption efficiency η (εa) is defined as the energy absorbed up to a given nominal strain ε<sup>a</sup> normalized by the corresponding stress value σ<sup>c</sup> (ε) [16]:

$$\eta(\varepsilon\_a) = \frac{\int\_{\ell\_{\mathcal{C}}}^{\ell\_a} \sigma(\varepsilon) d\varepsilon}{\sigma(\varepsilon)\_{\ell = \ell\_a}} \tag{1}$$

where εcr is the strain at the yield point corresponding to commencement of the plateau regime. The densification strain ε<sup>D</sup> is the strain value corresponding to the stationary point in the efficiency-strain curve, that is, where the efficiency is a global maximum:

$$\left. \frac{d\eta(\varepsilon)}{d\varepsilon} \right|\_{\varepsilon=\varepsilon\_D} = 0 \tag{2}$$

The energy absorption efficiency curves of the aluminum foams are also depicted in Figure 3, and the plateau stress is obtained from

σpl ¼

18% relative density), respectively.

parameters on the structural response.

by changing the diameter and height of the charges.

2.1.2. TNT charge

density of 1.55 g/cm<sup>3</sup>

2.1.3. Ballistic pendulum system

Figure 4. Picture of cylindrical TNT charge.

Ð <sup>ε</sup><sup>D</sup> <sup>ε</sup>cr σcð Þε dε ε<sup>D</sup> � εcr

Single-Curvature Sandwich Panels with Aluminum Foam Cores under Impulsive Loading

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By calculating, the plateau stress σpl and densification strain ε<sup>D</sup> of aluminum foams with three various relative densities are σpl = 5.30 MPa and ε<sup>D</sup> = 0.62 (for 11% relative density), σpl = 5.49 MPa and ε<sup>D</sup> = 0.55 (for 15% relative density), and σpl = 7.11 MPa and ε<sup>D</sup> = 0.54 (for

A total of 48 specimens were fabricated, and for each blast condition, two nominally identical specimens were tested. All specimens were uniquely labeled—the label R500-H0.5-C10-r15% f1 represents the specimen with a 500 mm radius of curvature, 0.5 mm face-sheet thickness, 10 mm core thickness, and 15% core relative density, which is the first specimen used for exploring the influence of face-sheet thickness on the dynamic response. The specimens were arranged into four groups; each group was designated for examining the effect of one or two

Blast loading was applied to the specimens by detonating a cylindrical TNT charge with a

15, 20, 25, 30, 35, and 40 g) with an approximate height-to-diameter ratio of 1 were fabricated

The specimen-frame assembly was attached to a four-cable ballistic pendulum system, which was employed to measure the impulse imparted to the front face of the specimen, as shown in Figure 5. The charges were mounted in front of the center of specimens, at various standoff

; a photograph is shown in Figure 4. Seven various mass charges (i.e., 10,

(3)

123

Figure 3. Stress versus strain response and energy absorption efficiency versus strain curves of aluminum foam cores.

Single-Curvature Sandwich Panels with Aluminum Foam Cores under Impulsive Loading http://dx.doi.org/10.5772/intechopen.70531 123

$$
\sigma\_{pl} = \frac{\int\_{\ell\_{cr}}^{\varepsilon\_D} \sigma\_c(\varepsilon) d\varepsilon}{\varepsilon\_D - \varepsilon\_{cr}} \tag{3}
$$

By calculating, the plateau stress σpl and densification strain ε<sup>D</sup> of aluminum foams with three various relative densities are σpl = 5.30 MPa and ε<sup>D</sup> = 0.62 (for 11% relative density), σpl = 5.49 MPa and ε<sup>D</sup> = 0.55 (for 15% relative density), and σpl = 7.11 MPa and ε<sup>D</sup> = 0.54 (for 18% relative density), respectively.

A total of 48 specimens were fabricated, and for each blast condition, two nominally identical specimens were tested. All specimens were uniquely labeled—the label R500-H0.5-C10-r15% f1 represents the specimen with a 500 mm radius of curvature, 0.5 mm face-sheet thickness, 10 mm core thickness, and 15% core relative density, which is the first specimen used for exploring the influence of face-sheet thickness on the dynamic response. The specimens were arranged into four groups; each group was designated for examining the effect of one or two parameters on the structural response.

#### 2.1.2. TNT charge

Blast loading was applied to the specimens by detonating a cylindrical TNT charge with a density of 1.55 g/cm<sup>3</sup> ; a photograph is shown in Figure 4. Seven various mass charges (i.e., 10, 15, 20, 25, 30, 35, and 40 g) with an approximate height-to-diameter ratio of 1 were fabricated by changing the diameter and height of the charges.

## 2.1.3. Ballistic pendulum system

The specimen-frame assembly was attached to a four-cable ballistic pendulum system, which was employed to measure the impulse imparted to the front face of the specimen, as shown in Figure 5. The charges were mounted in front of the center of specimens, at various standoff

Figure 4. Picture of cylindrical TNT charge.

Figure 3. Stress versus strain response and energy absorption efficiency versus strain curves of aluminum foam cores.

122 Contact and Fracture Mechanics

Figure 5. Photograph of the overall experimental setup.

distances. The movement of the pendulum was measured by a laser displacement transducer. Each single-curvature sandwich panel was clamped peripherally by steel frames, leaving an effective exposed curved area of 250 � 250 mm.

When the TNT charge is detonated, the impulsive load produced causes the pendulum to move, and its motion corresponds to that of a simple pendulum, described by the following equation:

$$M\frac{d^2\mathbf{x}}{dt^2} + \mathbf{C}\frac{d\mathbf{x}}{dt} + \frac{M\mathbf{g}}{R}\mathbf{x} = \mathbf{0} \tag{4}$$

<sup>x</sup><sup>2</sup> <sup>¼</sup> <sup>T</sup> 2π e �3β<sup>T</sup>

<sup>β</sup> <sup>¼</sup> 2ln ð Þ <sup>x</sup>1=x<sup>2</sup>

If the values of β, x1, and x<sup>2</sup> are known, then the initial velocity of the pendulum is given by

<sup>x</sup>\_ <sup>0</sup> <sup>¼</sup> <sup>2</sup><sup>π</sup> T e βT

where M is the total mass of the pendulum. By introducing (11) into Eq. (12), given by

I ¼ Mx1

In the present tests, β = 0.031, M = 151.3 kg, T = 3.12 s, and R = 2.69 m. Generally, the rotation angle (θ) should be less than 5�; in this study, θ is approximately 2.1�, which is acceptable.

The blast impulse is calculated by Eq. (13), according to the ballistic pendulum movement measured by the laser displacement transducer, as shown in Figure 6. The permanent deflection of the center of the back face-sheet was also examined by the posttest measurements. Here, the experimental results are classified and presented in the following subsections, in terms of typical deformation/failure modes and influences of some key parameters on the final permanent deflection (since the resistance to blast loading is quantified by the permanent

The deformation and failure modes of the single-curvature sandwich panels can be classified into that of the front face-sheet, core, and back face-sheet, respectively, although all the sand-

The front face-sheet of single-curvature sandwich panels subjected to blast loading mainly fails in the local indentation, transverse tearing, and petal-like tearing, as shown in Figure 7. Indentation failure shown in Figure 7(a) is the localized severe deformation without rupture, and the indentation depth is related with the load magnitude. When deformation of the facesheet exceeds its ductility at larger loads, failure is dominated by tearing. The transverse tearing may occur for a certain range of blast loads, as shown in Figure 7(b). With the increase

wich panels present the evident global deformation with the various local failures.

of blast loading, the petal-like tearing mode shown in Figure 7(c) will be caused.

2π T e βT

The impulse imparted into the pendulum is generally given by

2.2. Experimental results and discussion

2.2.1. Deformation modes

deflection of the central point of the back face-sheet).

<sup>4</sup> x\_ <sup>0</sup> (9)

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125

Single-Curvature Sandwich Panels with Aluminum Foam Cores under Impulsive Loading

<sup>T</sup> (10)

<sup>4</sup> x<sup>1</sup> (11)

<sup>4</sup> (13)

I ¼ M � x\_ <sup>0</sup> (12)

where M is the total mass, x the horizontal displacement, C the damping coefficient, and R is the cable length. Suppose 2<sup>β</sup> <sup>¼</sup> <sup>C</sup>=<sup>M</sup> and <sup>ω</sup><sup>2</sup> <sup>n</sup> ¼ g=R, then Eq. (4) is simplified by

$$
\ddot{\mathbf{x}} + 2\beta \dot{\mathbf{x}} + \omega\_n^2 \mathbf{x} = \mathbf{0} \tag{5}
$$

Introducing the damping ratio ξ ¼ β=ωn, the solution of Eq. (5) is given by

$$\propto = A e^{-\beta t} \sin \left( \omega t + \varphi \right) \tag{6}$$

.

where ω ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ω2 <sup>n</sup> � <sup>β</sup><sup>2</sup> q , A ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 <sup>0</sup> <sup>þ</sup> <sup>x</sup>\_0þβx<sup>2</sup> ð Þ<sup>0</sup> ω2 q , and tan<sup>φ</sup> <sup>¼</sup> <sup>x</sup>0<sup>ω</sup> x\_0þβx<sup>0</sup>

With the initial condition x<sup>0</sup> ¼ 0, Eq. (5) can be written as

$$
\dot{\omega} = \frac{\dot{\bar{x}}\_0}{\omega} e^{-\beta t} \sin \omega t \tag{7}
$$

The period of the oscillation of the pendulum T ¼ 2π=ω; if x<sup>1</sup> is the displacement of the pendulum for a period of t = T/4 and x<sup>2</sup> for a period of t = 3 T/4, then

$$\mathbf{x}\_1 = \frac{T}{2\pi} e^{-\frac{\beta T}{4}} \dot{\mathbf{x}}\_0 \tag{8}$$

Single-Curvature Sandwich Panels with Aluminum Foam Cores under Impulsive Loading http://dx.doi.org/10.5772/intechopen.70531 125

$$\mathbf{x}\_2 = \frac{T}{2\pi} e^{-\frac{3\ell T}{4}} \dot{\mathbf{x}}\_0 \tag{9}$$

$$\beta = \frac{2\ln\left(\mathbf{x}\_1/\mathbf{x}\_2\right)}{T} \tag{10}$$

If the values of β, x1, and x<sup>2</sup> are known, then the initial velocity of the pendulum is given by

$$
\dot{\mathbf{x}}\_0 = \frac{2\pi}{T} e^{\frac{\rho T}{T}} \mathbf{x}\_1 \tag{11}
$$

The impulse imparted into the pendulum is generally given by

$$I = M \cdot \dot{\mathbf{x}}\_0 \tag{12}$$

where M is the total mass of the pendulum. By introducing (11) into Eq. (12), given by

$$I = M\mathbf{x}\_1 \frac{2\pi}{T} e^{\frac{\beta T}{4}} \tag{13}$$

In the present tests, β = 0.031, M = 151.3 kg, T = 3.12 s, and R = 2.69 m. Generally, the rotation angle (θ) should be less than 5�; in this study, θ is approximately 2.1�, which is acceptable.

#### 2.2. Experimental results and discussion

The blast impulse is calculated by Eq. (13), according to the ballistic pendulum movement measured by the laser displacement transducer, as shown in Figure 6. The permanent deflection of the center of the back face-sheet was also examined by the posttest measurements. Here, the experimental results are classified and presented in the following subsections, in terms of typical deformation/failure modes and influences of some key parameters on the final permanent deflection (since the resistance to blast loading is quantified by the permanent deflection of the central point of the back face-sheet).

#### 2.2.1. Deformation modes

distances. The movement of the pendulum was measured by a laser displacement transducer. Each single-curvature sandwich panel was clamped peripherally by steel frames, leaving an

When the TNT charge is detonated, the impulsive load produced causes the pendulum to move, and its motion corresponds to that of a simple pendulum, described by the following equation:

where M is the total mass, x the horizontal displacement, C the damping coefficient, and R is

<sup>x</sup>€ <sup>þ</sup> <sup>2</sup>βx\_ <sup>þ</sup> <sup>ω</sup><sup>2</sup>

dt <sup>þ</sup> Mg

, and tan<sup>φ</sup> <sup>¼</sup> <sup>x</sup>0<sup>ω</sup>

x\_0þβx<sup>0</sup> .

<sup>R</sup> <sup>x</sup> <sup>¼</sup> <sup>0</sup> (4)

<sup>n</sup>x ¼ 0 (5)

sin ð Þ ωt þ φ (6)

�β<sup>t</sup> sin ωt (7)

<sup>4</sup> x\_ <sup>0</sup> (8)

<sup>n</sup> ¼ g=R, then Eq. (4) is simplified by

<sup>M</sup> <sup>d</sup><sup>2</sup> x dt<sup>2</sup> <sup>þ</sup> <sup>C</sup>dx

Introducing the damping ratio ξ ¼ β=ωn, the solution of Eq. (5) is given by

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

pendulum for a period of t = T/4 and x<sup>2</sup> for a period of t = 3 T/4, then

<sup>0</sup> <sup>þ</sup> <sup>x</sup>\_0þβx<sup>2</sup> ð Þ<sup>0</sup> ω2

x2

q

With the initial condition x<sup>0</sup> ¼ 0, Eq. (5) can be written as

<sup>x</sup> <sup>¼</sup> Ae�β<sup>t</sup>

<sup>x</sup> <sup>¼</sup> <sup>x</sup>\_ <sup>0</sup> ω e

> <sup>x</sup><sup>1</sup> <sup>¼</sup> <sup>T</sup> 2π e �βT

The period of the oscillation of the pendulum T ¼ 2π=ω; if x<sup>1</sup> is the displacement of the

effective exposed curved area of 250 � 250 mm.

Figure 5. Photograph of the overall experimental setup.

124 Contact and Fracture Mechanics

the cable length. Suppose 2<sup>β</sup> <sup>¼</sup> <sup>C</sup>=<sup>M</sup> and <sup>ω</sup><sup>2</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ω2 <sup>n</sup> � <sup>β</sup><sup>2</sup>

, A ¼

q

where ω ¼

The deformation and failure modes of the single-curvature sandwich panels can be classified into that of the front face-sheet, core, and back face-sheet, respectively, although all the sandwich panels present the evident global deformation with the various local failures.

The front face-sheet of single-curvature sandwich panels subjected to blast loading mainly fails in the local indentation, transverse tearing, and petal-like tearing, as shown in Figure 7. Indentation failure shown in Figure 7(a) is the localized severe deformation without rupture, and the indentation depth is related with the load magnitude. When deformation of the facesheet exceeds its ductility at larger loads, failure is dominated by tearing. The transverse tearing may occur for a certain range of blast loads, as shown in Figure 7(b). With the increase of blast loading, the petal-like tearing mode shown in Figure 7(c) will be caused.

dome, as shown in Figure 9(a). Figure 9(b) shows significant inelastic deformation with tensile tearing at the clamped edges of the curved sandwich panel. For the thinner specimen subjected to a larger impulse, tearing of the back face-sheet was observed, as shown in Figure 9(c).

Figure 8. Collapse patterns of the foam core: (a) progressive compression with shear failure in central area and (b)

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The maximum center-point deflection of curved sandwich panels (H = 0.8 mm, C = 10 mm, relative density = 15%) and curved monolithic plates of equivalent mass (H = 3.0 mm) are plotted in Figure 10, as a function of impulse for different blast distances and six charge masses (10, 15, 20, 25, 30, and 35 g). As expected, the central deflection increases with impulse for all test configurations. By applying a linear fit to the data, the relationship between the

where W and I are, respectively, the central deflection in mm and impulse in Ns; k and b are the two constants with the values of 1.22 mm/Ns and �9.03 mm for R = 500 mm curved sandwich panels and 1.85 mm/Ns and �10.66 mm for R = 250 mm sandwich specimens, respectively.

Figure 9. The deformation/failure of the back face-sheet: (a) Mode I (gross inelastic deformation), (b) Mode II (gross

W ¼ kI þ b (14)

2.2.2. Influence of blast impulse on the shock resistance

fracture of central core.

central deflection and the blast impulse can be written as

inelastic deformation with tensile tearing), and (c) tearing failure.

Figure 6. Typical displacement-time response of ballistic pendulum in a blast test.

Figure 7. Three deformation and failure patterns in front face-sheets: (a) indentation failure, (b) transverse tearing, and (c) petal-like tearing.

Figure 8 illustrates the typical cross-sectional profiles of blast-loaded sandwich specimens with two radii of curvature. Each specimen can be split into three regions (i.e., core crushing region, shear failure region, and an uncompressed region) from the mid-span to the clamped end, according to the deformation degree of the core. Core crushing is considered as the generation of a hole in the specimen central zone, as shown in Figure 8(a). The fracture of core in the central zone may be observed for some specimens as shown in Figure 8(b). The core also can be failed by core shear under the transverse shear force. Moreover, the delamination between the crushed core and face-sheets can be found in the core shear region. In those regions far away from the loading area, the cores are generally uncompressed.

The deformation/failure of the back face-sheet corresponds to Mode I (gross inelastic deformation), Mode II (gross inelastic deformation with tensile tearing at the edges), and tearing. The deformation profile of the back face-sheet for the typical Mode I response is dome-shaped at the center, and with obvious plastic hinges extending from the plate corner to the base of the Single-Curvature Sandwich Panels with Aluminum Foam Cores under Impulsive Loading http://dx.doi.org/10.5772/intechopen.70531 127

Figure 8. Collapse patterns of the foam core: (a) progressive compression with shear failure in central area and (b) fracture of central core.

dome, as shown in Figure 9(a). Figure 9(b) shows significant inelastic deformation with tensile tearing at the clamped edges of the curved sandwich panel. For the thinner specimen subjected to a larger impulse, tearing of the back face-sheet was observed, as shown in Figure 9(c).

#### 2.2.2. Influence of blast impulse on the shock resistance

Figure 8 illustrates the typical cross-sectional profiles of blast-loaded sandwich specimens with two radii of curvature. Each specimen can be split into three regions (i.e., core crushing region, shear failure region, and an uncompressed region) from the mid-span to the clamped end, according to the deformation degree of the core. Core crushing is considered as the generation of a hole in the specimen central zone, as shown in Figure 8(a). The fracture of core in the central zone may be observed for some specimens as shown in Figure 8(b). The core also can be failed by core shear under the transverse shear force. Moreover, the delamination between the crushed core and face-sheets can be found in the core shear region. In those regions far

Figure 7. Three deformation and failure patterns in front face-sheets: (a) indentation failure, (b) transverse tearing, and (c)

The deformation/failure of the back face-sheet corresponds to Mode I (gross inelastic deformation), Mode II (gross inelastic deformation with tensile tearing at the edges), and tearing. The deformation profile of the back face-sheet for the typical Mode I response is dome-shaped at the center, and with obvious plastic hinges extending from the plate corner to the base of the

away from the loading area, the cores are generally uncompressed.

petal-like tearing.

126 Contact and Fracture Mechanics

Figure 6. Typical displacement-time response of ballistic pendulum in a blast test.

The maximum center-point deflection of curved sandwich panels (H = 0.8 mm, C = 10 mm, relative density = 15%) and curved monolithic plates of equivalent mass (H = 3.0 mm) are plotted in Figure 10, as a function of impulse for different blast distances and six charge masses (10, 15, 20, 25, 30, and 35 g). As expected, the central deflection increases with impulse for all test configurations. By applying a linear fit to the data, the relationship between the central deflection and the blast impulse can be written as

$$W = kI + b \tag{14}$$

where W and I are, respectively, the central deflection in mm and impulse in Ns; k and b are the two constants with the values of 1.22 mm/Ns and �9.03 mm for R = 500 mm curved sandwich panels and 1.85 mm/Ns and �10.66 mm for R = 250 mm sandwich specimens, respectively.

Figure 9. The deformation/failure of the back face-sheet: (a) Mode I (gross inelastic deformation), (b) Mode II (gross inelastic deformation with tensile tearing), and (c) tearing failure.

Figure 10. Relationship between central deflection and blast impulse.

A comparison of the blast resistance between curved sandwich panels and monolithic plates of equivalent mass is also shown in Figure 10. Those R = 500 mm sandwich panel specimens show the better resistance to blast loading compared to the solid shells with the equivalent mass. However, the central deflection of R = 250 mm curved sandwich panels were larger than that of solid counterparts. This may be explained that the deformation of the smaller radius of curvature specimens is governed by the local failure, which may decrease the energy absorption capability of the foam cores; however, the deformation of the solid shell counterparts is dominated by the global bending.

Figure 11. Effect of face-sheet thickness on central deflection of curved sandwich panels.

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Figure 12. Effect of core relative density on central deflection of curved sandwich panels.

#### 2.2.3. Influence of face-sheet thickness on the shock resistance

The dependence of the central deflection of the back face-sheet on face-sheet thickness is shown in Figure 11, where additional data corresponding to the same conditions are included to show the possible general trend. The central point deflection decreases with the increased face-sheet thickness, as expected. For R = 250 mm curved sandwich panels, those specimens with 0.8-mm- and 1.0-mm-thick face-sheets show the smaller deflections than curved panels with the 0.5 mm face-sheets, by 28.3 and 56.3%, respectively. This is also the case for the R = 500 mm specimens, whereby the deflections are, respectively, 48.5 and 68.8% smaller.

#### 2.2.4. Influence of core relative density on the shock resistance

The central point deflection of specimens is plotted in Figure 12 as a function of core relative density. For both curvatures, the specimens with the larger core relative density results in the smaller deflections. Taking the core relative density of 11% as a reference, R = 250 mm Single-Curvature Sandwich Panels with Aluminum Foam Cores under Impulsive Loading http://dx.doi.org/10.5772/intechopen.70531 129

Figure 11. Effect of face-sheet thickness on central deflection of curved sandwich panels.

A comparison of the blast resistance between curved sandwich panels and monolithic plates of equivalent mass is also shown in Figure 10. Those R = 500 mm sandwich panel specimens show the better resistance to blast loading compared to the solid shells with the equivalent mass. However, the central deflection of R = 250 mm curved sandwich panels were larger than that of solid counterparts. This may be explained that the deformation of the smaller radius of curvature specimens is governed by the local failure, which may decrease the energy absorption capability of the foam cores; however, the deformation of the solid shell counterparts is

The dependence of the central deflection of the back face-sheet on face-sheet thickness is shown in Figure 11, where additional data corresponding to the same conditions are included to show the possible general trend. The central point deflection decreases with the increased face-sheet thickness, as expected. For R = 250 mm curved sandwich panels, those specimens with 0.8-mm- and 1.0-mm-thick face-sheets show the smaller deflections than curved panels with the 0.5 mm face-sheets, by 28.3 and 56.3%, respectively. This is also the case for the R = 500 mm specimens, whereby the deflections are, respectively, 48.5 and 68.8% smaller.

The central point deflection of specimens is plotted in Figure 12 as a function of core relative density. For both curvatures, the specimens with the larger core relative density results in the smaller deflections. Taking the core relative density of 11% as a reference, R = 250 mm

dominated by the global bending.

128 Contact and Fracture Mechanics

2.2.3. Influence of face-sheet thickness on the shock resistance

Figure 10. Relationship between central deflection and blast impulse.

2.2.4. Influence of core relative density on the shock resistance

Figure 12. Effect of core relative density on central deflection of curved sandwich panels.

sandwich panels with higher relative densities (15 and 18%) can decrease the average deflection, by 46.6 and 55.9%, respectively. However, for R = 500 mm sandwich panels, it is difficult to quantify the effect of core relative density on the structural response of specimens, due to the large variability in both impulse and deflection.

while the foam core was modeled by the default brick element. Similarly, one quarter of the charge was modeled shown in Figure 13, and eight-node brick elements with arbitrary

The mechanical behavior of face-sheets were represented by material model 3 of LS-DYNA (\*MAT\_PLASTIC\_KINEMATIC), while the aluminum foam core was modeled by material model 63 of LS-DYNA (\*MAT\_CRUSHALBE\_FOAM). A high-explosive material model (\*MAT\_HIGH\_ EXPLOSIVE\_BURN) incorporating the JWL equation of state (EOS\_JWL) was used to describe the

�R1<sup>V</sup> <sup>þ</sup> <sup>B</sup> <sup>1</sup> � <sup>ω</sup>

where p is the blast pressure, E is the internal energy per initial volume, V is the initial relative volume, and ω, A, B, R1, and R<sup>2</sup> are the material constants, respectively. The material parameters of the curved sandwich panel and TNT charge are kept the same as experimental ones. The bolts used in the tests to clamp the curved panels to the fixture were represented by nodal constraints in the numerical model. Symmetric boundary conditions about x-z and y-z planes were imposed. The blast load imparted on the front face-sheet of curved sandwich panel was defined with algorithm of \*CONTACT\_ERODING\_SURFACE\_TO\_SURFACE. Automatic,

The whole response can be divided into three stages: Stage I (expansion of the explosive), Stage II (explosive product interacts with the curved sandwich panel), and Stage III (plastic defor-

The expansion of the explosive starts at the point of detonation (central point of the top surface of charge), as shown in Figure 14. The detonation of a high-performance explosive is achieved by compressing and heating of its constituents, resulting that a chemical reaction is triggered and then it is supersonically propagated through the explosive at the Chapman-Jouguet velocity. Whereafter, a strong shock wave, generated by the violent expansion of the gaseous products, propagates into the ambient medium. Since the sound speed increases with the increased temperature in the compressible flow, shock waves are generated. The detonation wave generated by the cylindrical charge presents an obvious directionality and a cross distribution shape. The axial propagation speed is larger than the radial propagation speed, so the axial pressure is also greater than that of radial direction due to the proportional

surface-to-surface contact options were generally used for curved sandwich panels.

R2V <sup>e</sup>

Single-Curvature Sandwich Panels with Aluminum Foam Cores under Impulsive Loading

�R2<sup>V</sup> <sup>þ</sup>

ωE

http://dx.doi.org/10.5772/intechopen.70531

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<sup>V</sup> (15)

Lagrange-Eulerian (ALE) formulation were adopted.

<sup>p</sup> <sup>¼</sup> <sup>A</sup> <sup>1</sup> � <sup>ω</sup>

R1V <sup>e</sup>

material property of the TNT charge:

3.2. Simulation results and discussion

3.2.1.1. Stage I: expansion of the explosive

3.2.1. Explosion and structural response process

mation of the curved sandwich panel under the inertia).

relationship between the wave speed and intensity in air medium.
