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TECHNICAL PAPERS

The Response of Metallic Sandwich Panels to Water Blast

[+] Author and Article Information
Yueming Liang, Alexander V. Spuskanyuk, Shane E. Flores, Robert M. McMeeking, Anthony G. Evans

Mechanical Engineering Department, Materials Department, University of California, Santa Barbara, CA 93106

David R. Hayhurst

School of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Manchester, M60 1QD, UK

John W. Hutchinson

Division of Engineering and Applied Sciences, Harvard University, Pierce Hall, Cambridge, MA 02138

J. Appl. Mech 74(1), 81-99 (Dec 02, 2005) (19 pages) doi:10.1115/1.2178837 History: Received June 09, 2005; Revised December 02, 2005

Metallic sandwich panels subject to underwater blast respond in a manner dependent on the relative time scales for core crushing and water cavitation. This article examines the response at impulses representative of an (especially relevant) domain: wherein the water cavitates before the core crushes. Three core topologies (square honeycomb, I-core, and corrugated) have been used to address fundamental issues affecting panel design. Their ranking is based on three performance metrics: the back-face deflection, the tearing susceptibility of the faces, and the loads transmitted to the supports. The results are interpreted by comparing with analytic solutions based on a three-stage response model. In stage I, the wet face acquires its maximum velocity with some water attached. In stage II, the core crushes and all of the constituents (wet and dry face and core) converge onto a common velocity. In stage III, the panel deflects and deforms, dissipating its kinetic energy by plastic bending, stretching, shearing, and indentation. The results provide insight about three aspects of the response. (i) Two inherently different regimes have been elucidated, designated strong (STC) and soft (SOC), differentiated by a stage II/III time scale parameter. The best overall performance has been found for soft-core designs. (ii) The foregoing analytic models are found to underestimate the kinetic energy and, consequently, exaggerate the performance benefits. The discrepancy has been resolved by a more complete model for the fluid/structure interaction. (iii) The kinetic energy acquired at the end of the second stage accounts fully for the plastic dissipation occurring in the third stage, indicating that the additional momentum acquired after the end of the second stage does not affect panel performance.

Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

A schematic showing the three temporally distinct stages that accompany a panel subject to air blast (3)

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Figure 2

The trends in pressure and velocity in the water at times tc and 2tc (with tc designating the instant when cavitation commences). The plots compare the analytic solution with a calculation conducted using ABAQUS/Explicit. After tc, cavitation fronts propagate through the water (towards and away from the panel) leaving a zone of cavitated water in their wakes. Note that, at the cavitation front, the water has positive velocity in the direction of motion of the panel. The equivalent thickness of the sandwich panel is 20mm. The core has a relative density of 0.03 and yield strength of σYDc∕p0=0.18. The thickness of the front face is 6mm so that β=3.125 and that of the back face is 8mm.

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Figure 3

Fluid structure interaction map (I¯=0.5, m¯=1.0) with axes of core dynamic strength and the Taylor fluid structure interaction parameter β. The four impulse domains are marked on the map. Contours of the impulse transmitted into the sandwich plate at first cavitation are also included (4).

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Figure 4

The geometries of the three core topologies used in the analysis

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Figure 5

Dynamic stress/strain curves for 304 stainless steel used in the simulations (8)

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Figure 6

A schematic of the numerical model used in ABAQUS/Explicit

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Figure 7

The predictions of the transmitted impulse conducted for a solid plate using ABAQUS/Explicit and the comparison with the analytic solution given by Taylor (17)

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Figure 8

The deformations predicted using the numerical model for the three cores shown in Fig. 4. Results for the I-cores and the corrugated cores are shown for both strong and soft responses.

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Figure 9

The constituent velocities and kinetic energies obtained for corrugated cores: (a) and (b) refer to a strong core with relative density, ρ¯=0.05, Δ=4, and β=9.375 while (c) and (d) refer to a soft core with ρ¯=0.02, Δ=5.5, and β=8.70.

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Figure 10

The kinetic energies and velocities for a square honeycomb core with ρ¯=0.03, Δ=1, and β=2.68

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Figure 11

The durations of stages I, II, and III normalized by the expressions derived using the analytic model (Sec. 1): tc∕t0lnβ∕(1−β), tII∕(IT∕2σYDc), and tIII∕Lρ∕σY

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Figure 12

A deformation sequence for a soft I-core showing the dynamic elastic buckling of the core near the back face at instant tb (Hc=0.3L, ρ¯=0.013, Δ=3, and β=4.69).

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Figure 13

A synopsis of back face displacement ascertained for a wide range of strong and soft cores. The coordinates are the ratio of back to front face thickness, Δ, and the relative density of the cores, ρ¯.

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Figure 14

A synopsis of trends in the maximum plastic strain in the front and back faces, ascertained for a range of strong and soft cores. The coordinates are the ratio of back to front face thickness, Δ, and the relative density of the cores, ρ¯.

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Figure 15

(a) The reaction forces at the supports typifying the difference between strong and soft cores (results for I-cores are shown). (b) The corresponding values of the impulse transmitted to the structure determined from the reaction forces.

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Figure 16

A synopsis of trends in the peak reaction force with relative density and ratio of back to front face thickness

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Figure 17

Trends in the momentum acquired at the end of stage II (structure plus attached water), designated MT, with ratio of back to front face thickness for a range of strong cores. The total impulse Itotal transmitted to the system is also plotted. Comparisons with the predicted IT from the existing analytic model, Eq. 11, are included.

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Figure 18

Trends in the kinetic energies acquired at the end of stage II with ratio of back to front face thickness for a range of strong cores. Results for KEII (structure plus attached water) are plotted. A comparison with the existing analytic model (Eq. 12) is included.

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Figure 19

Trends of the transition parameter Π for I-core design

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Figure 20

Location and rate of translation of the cavitation boundary as a function of time for the case shown in Fig. 2

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Figure 21

Characteristic velocity of cavitated fluid for the case shown in Fig. 2

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Figure 22

The velocity distributions at the end of stage II for a foam-core panel ascertained from the new analytic model compared with the result obtained using ABAQUS/Explicit. The core has relative density of ρ¯c=0.03, strength of σYDc∕p0=0.18, and height of Hc=0.2m. The thickness of the front face is hf=6mm so that β=3.125 and that of the back face is hb=8mm.

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Figure 23

Comparisons of transmitted momentum calculated using the present model and that obtained numerically by Deshpande and Fleck (4). The freestanding panel unit has face thickness hf=hb=10mm so that β=1.875, core height Hc=0.1m, the density of the parent metal is 8000kg∕m3, and the relative density of the core is ρ¯c=0.1.

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Figure 24

The momentum at the end of stage II (structure plus attached water) determined numerically and the comparison with the new analytic model (using Eq. 24)

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Figure 25

The kinetic energy at the end of stage II (structure plus attached water) determined with the new analytic model and comparison with numerical calculations for STC design

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Figure 26

Comparison of KEII determined using the new analytic model with the total plastic dissipation in stage III calculated numerically. The height of the core is Hc=0.2L and the relative density of the core is ρ¯=0.03.

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Figure 27

Deformed shape of the square I-core plate (top picture, 14 of the plate shown) and the I-core beam (bottom picture, 12 of the beam shown)

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