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TECHNICAL PAPERS

# The Underwater Blast Resistance of Metallic Sandwich Beams With Prismatic Lattice Cores

[+] Author and Article Information
G. J. McShane, V. S. Deshpande

Department of Engineering,  University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, UK

N. A. Fleck1

Department of Engineering,  University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, UK

Royal Schelde, P.O. Box 16 4380 AA Vlissingen, The Netherlands.

Jos. L. Meyer GmbH, I-Core panels, Industriegebiet Süd, D-26871 Papenburg, Germany.

More accurate calculations are reported by Radford et al. (12) but these involve numerical quadratures rather than explicit formulae.

The interested reader is referred to Figs.  1414 of Deshpande and Fleck (4).

Here the durations $T1$, $T2$, and $T3$ are obtained from the fully decoupled analysis $I∕II∕III$.

1

Author to whom correspondence should be addressed.

J. Appl. Mech 74(2), 352-364 (Feb 16, 2006) (13 pages) doi:10.1115/1.2198549 History: Received October 20, 2005; Revised February 16, 2006

## Abstract

The finite element method is used to evaluate the underwater blast resistance of monolithic beams and sandwich beams containing prismatic lattice cores (Y-frame and corrugated core) and an ideal foam core. Calculations are performed on both free-standing and end-clamped beams, and fluid-structure interaction effects are accounted for. It is found that the degree of core compression in the free-standing sandwich beam is sensitive to core strength, yet the transmitted impulse is only mildly sensitive to the type of sandwich core. Clamped sandwich beams significantly outperform clamped monolithic beams of equal mass, particularly for stubby beams. The Fleck and Deshpande analytical model for the blast response of sandwich beams is critically assessed by determining the significance of cross-coupling between the three stages of response: in stage I the front face is accelerated by the fluid up to the point of first cavitation, stage II involves compression of the core until the front and back faces have an equal velocity, and in stage III the sandwich beam arrests by a combination of beam bending and stretching. The sensitivity of the response to the relative magnitude of these time scales is assessed by appropriately chosen numerical simulations. Coupling between stages I and II increases the level of transmitted impulse by the fluid by 20–30% for a wide range of core strengths, for both the free-standing and clamped beams. Consequently, the back face deflection of the clamped sandwich beam exceeds that of the fully decoupled model. For stubby beams with a Y-frame and corrugated core, strong coupling exists between the core compression phase (stage II) and the beam bending/stretching phase (stage III); this coupling is beneficial as it results in a reduced deflection of the back (distal) face. In contrast, the phases of core compression (stage II) and beam bending/stretching (stage III) are decoupled for slender beams. The significance of the relative time scales for the three stages of response of the clamped beams are summarized on a performance map that takes as axes the ratios of the time scales.

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## Figures

Figure 1

Figure 2

Schematic of the deformation mechanism map for the underwater blast loading of a sandwich beam. Four regimes of behavior are expected depending on the ratios of the durations of the stages: T1∕T2 and T2∕T3. The anticipated values of w¯p (peak deflection of the beams normalized by the prediction of the decoupled analysis) are included in the sketch.

Figure 3

Sketches of the (a) Y-frame (b) corrugated core sandwich beams, comprising a large number of repeating units. The prismatic axes of these cores are along the length of the beams. The cross-sectional beam dimensions employed in the FE calculations for the shell reference planes are given in the figure. All dimensions are in millimeters.

Figure 4

The uniaxial tensile stress versus strain response of 304 stainless steel as measured by Côté (7-8) and employed in all the calculations reported here

Figure 5

Boundary value problems analyzed for the underwater blast loading of (a) the free-standing and (b) the clamped sandwich beam. Only the Y-frame core beams are shown in this figure.

Figure 6

The time variations of the momenta of the free-standing sandwich and monolithic plates for blast pressures (a) p0=100MPa and (b) p0=180MPa. The Taylor prediction of the final transmitted momentum into the sandwich plate based on a free-standing front face-sheet is also included.

Figure 7

The time evolution of core compression εfs in the free-standing sandwich beams for blast pressures (a) p0=100MPa and (b) p0=180MPa

Figure 8

Finite element predictions of the (a) normalized transmitted momentum It∕I0, (b) normalized duration of core compression T2∕θ and (c) peak core compression εfsmax as a function of the blast impulse for free-standing monolithic and sandwich beams

Figure 9

The time variation of (a) normalized deflections of the midspan of the back face w∕L and (b) midspan core compression of the L=1m clamped beams subject to a p0=100MPa blast. Both the back face deflections and core compressions are obtained by spatially averaging the deflections over the width B at the midspans.

Figure 10

Finite element predictions of the deformation modes of the L=1m. (a) Y-frame, (b) corrugated core, and (c) ideal strength foam core clamped sandwich beams at t¯≈0.1 and 0.8 for p0=100MPa.

Figure 11

Finite element predictions of the (a) peak normalized back face deflections wp∕L, (b) normalized peak core compression εcmax∕εfsmax, and (c) normalized time required to attain the maximum deflection T3∕T2 as a function of blast impulse for the L=1m clamped monolithic and sandwich beams

Figure 12

Finite element predictions of the (a) peak normalized back face deflections wp∕L, (b) normalized peak core compression εcmax∕εfsmax and (c) normalized time required to attain the maximum deflection T3∕T2 as a function of blast impulse for the L=3m clamped monolithic and sandwich beams

Figure 13

Comparisons between the fully coupled (I+II+III) and decoupled finite element predictions of the peak normalized back face deflections wp∕L of the L=1m (a) Y-frame and (b) corrugated core clamped sandwich beams. The decoupled calculations for the sandwich beams are the (i) fully decoupled (I∕II∕III), (ii) the decoupled stage I (I∕II+III), and (iii) the decoupled stage III (I+II∕III) calculations. The fully coupled and decoupled stage I predictions for the L=1m monolithic beams are included.

Figure 14

Comparisons between the fully coupled (I+II+III) and decoupled finite element predictions of the peak normalized back face deflections wp∕L of the L=3m (a) Y-frame and (b) corrugated core clamped sandwich beams. The decoupled calculations for the sandwich beams are the (i) fully decoupled (I∕II∕III), (ii) the decoupled stage I (I∕II+III), and (iii) the decoupled stage III (I+II∕III) calculations. The fully coupled and decoupled stage I predictions for the L=1m monolithic beams are included.

Figure 15

Comparisons between the fully coupled (I+II+III) and decoupled finite element predictions of the peak normalized back face deflections wp∕L of the (a) L=1m and (b) L=3m ideal strength core clamped sandwich beams. The decoupled calculations for the sandwich beams are the (i) fully decoupled (I∕II∕III), (ii) the decoupled stage I (I∕II+III), and (iii) the decoupled stage III (I+II∕III) calculations. The fully coupled and decoupled stage I predictions for the L=1m and L=3m monolithic beams are included.

Figure 16

Time variation of the normalized transmitted momentum I∕Io for the L=1m clamped monolithic and sandwich beams subject to the po=100MPa blast. Predictions for the final transmitted impulse in the free-standing cases are shown (for the sandwich beams an average value is given).

Figure 17

A synopsis of the normalized peak deflections w¯p of the Y-frame and ideal strength core sandwich beams. The axes employed are the ratios T1∕T2 and T2∕T3 of the durations of stages I and II and II and III, respectively, as predicted from a fully decoupled analysis. (w¯p is defined as the ratio of the peak deflection as predicted from the fully coupled analysis to that predicted by a fully decoupled analysis.)

Figure 18

The variation of w¯p (a) with T1∕T2 (ratio of the duration of stages I and II) for the ideal strength core beams and (b) with T2∕T3 (ratio of the durations of stages II and III) for the Y-frame core beams. (w¯p is defined as the ratio of the peak deflection as predicted from the fully coupled analysis to that predicted by a fully decoupled analysis.)

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