Application of a Dynamic Constitutive Law to Multilayer Metallic Sandwich Panels Subject to Impulsive Loads

[+] Author and Article Information
Z. Wei1

Materials Department, University of California, Santa Barbara, CA 93106zhensong@engineering.ucsb.edu

M. Y. He, A. G. Evans

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


Corresponding author.

J. Appl. Mech 74(4), 636-644 (Apr 19, 2006) (9 pages) doi:10.1115/1.2424471 History: Received December 10, 2005; Revised April 19, 2006

The present paper describes an investigation that implements and assesses a dynamic continuum constitutive law for all-metallic sandwich panels. It also demonstrates its application to multilayer panels subject to water blast. Finite element calculations of unit cells are used to calibrate the model, especially the hardening curves at different strain rates. Once calibrated, the law is assessed by comparison with two sets of experiments. The dynamic response of panels impacted by Al foam projectiles at impulses comparable to those expected in water blast. The response of a multilayer core to an impulse caused by an explosion occurring in a cylindrical water column. The comparisons reveal that the overall deformation, average core strain, peak transmitted pressure, and velocities of the front and back faces are adequately predicted, inclusive of fluid/structure interactions. The inherent limitations of the approach are the underprediction of the plastic strains in the faces and incomplete assessment of stress oscillations beyond the peak. The former deficiency would pertain for any continuum representation for the core and would lead to problems in the prediction of face tearing. The latter may adversely affect the predictions of the impulse.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

A mechanism map indicating three possible responses of sandwich panels subject to impulsive loads. A fourth possibility, zero back face deflection, is small and not shown. The coordinates Ĩ, H̃, and σ̃ are the normalized impulse, core height, and strength, respectively (2-3). They are defined as, Ĩ=(I∕M)ρ∕σY, H̃-H∕L, and σ̃=σYDc∕ρ¯σY, where M is the mass per unit area of the sandwich panel, L its half span, ρ the density of the solid material, σY its yield strength, and ρ¯ the relative density of the core. The best response to water blast is found in the soft domain close to the transition to slapping.

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Figure 2

Images of the seven-layer truss panel taken before and after testing. Also shown is the numerical model with homogenized cores before and after testing.

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Figure 3

(a) Images of the stainless steel sandwich panels with square honeycomb cores after impact by foam projectiles performed at various values of the nominal impulse (6). (b) The corresponding simulations conducted using the dynamic constitutive law for the core. (c) The deformation of the core near the center of the panel shown in (a), impacted at the highest impulse. A comparison is made between the measured shape and that obtained using the dynamic continuum law using mesh scheme (iii).

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Figure 4

(a) A schematic of the Dynocrusher test arrangement (4). (b) The axisymmetric continuum finite element model built up for the test. Also shown are representative meshes.

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Figure 5

(a) The unit cell for the pyramidal truss core with the relative density, ρ¯=0.04, including the top and bottom faces to capture the truss/face contact. (b) The first buckling mode used to incorporate imperfections.

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Figure 6

A representative dynamic stress/strain plot for the truss core and the associated deformations at six different times after imposing the velocity on the front face (effective strain rate, ε̇eff=1000∕s). The temporal variations of stress are shown for both the back and front faces. Note that, at location e, the front face contacts the core, causing a stress elevation.

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Figure 7

(a) The dynamic stress/strain curves used to characterize truss cores. The curves are for core thickness, Hc=10cm and relative density, ρ¯=0.04. (b) The dynamic stress/strain curves used to characterize square honeycomb cores. The curves are for core thickness, Hc=8.3mm and relative density, ρ¯=0.04. (c) Relationship between the strain at which the core members begin to buckle and the effective strain rate, ascertained from (a),(b).

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Figure 8

Two examples of stress/strain variations on the back face comparing 3D results with the predictions obtained using the dynamic stress/strain curves from Fig. 7 in conjunction with the dynamic constitutive law.

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Figure 9

Crushing sequences for the 3D one-unit column of the seven-layer core and the associated stresses induced on the back face. The solid curve is for a calculation with 1% imperfections in all layers. The corresponding deformation patterns are shown in the sequence a→d. The dotted curve is for the case where the two layers adjoined to the faces have 2% imperfections, with 1% imperfections elsewhere. Deformation patterns at two strain levels, x and y, are also shown. Note that, now, the bottom layer starts to crush before the adjacent layers and that there is a large stress pulse (at y) when contact occurs between the core and the face in this layer.

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Figure 10

Comparisons between measurements, full 3D simulations, and simulations conducted using the continuum law with two different mesh schemes, all corresponding to the tests summarized in Fig. 3: (a) center point displacements; and (b) core crushing strains.

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Figure 11

Comparisons between fully meshed 3D calculations and continuum calculations for a Dynocrusher test with the bottom face rigidly fixed: (a) transmitted pressure and (b) transmitted impulse. Note the close correspondence for both metrics. (c) The pressures transmitted to the gauge columns: a comparison between measurements and values calculated using the constitutive law.

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Figure 12

Comparisons between full 3D calculations and simulations conducted using the continuum model conducted for panels with square honeycomb cores subjected to water blast (1): (a) maximum back face deflection; (b) average core strain; and (c) back face deflection.

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Figure 13

Velocities of the wet and dry faces for the simulations presented in Fig. 1: (a) Simulations conducted using the continuum model; (b) full 3D simulations.

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Figure 14

The deformed shapes of two typical four-layer pyramidal core panels under water blast: (a) a soft core with ρ¯=0.5%; and (b) a strong core with ρ¯=4%.

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Figure 15

The velocities of the front and back faces for the two panels from Fig. 1: (a) a soft core with ρ¯=0.5% and (b) a strong core with ρ¯=4%.



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