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Research Papers

# The Dynamic Strength of a Representative Double Layer Prismatic Core: A Combined Experimental, Numerical, and Analytical Assessment

[+] Author and Article Information
Enrico Ferri, V. S. Deshpande

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

A. G. Evans

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

J. Appl. Mech 77(6), 061011 (Sep 01, 2010) (7 pages) doi:10.1115/1.4000905 History: Received August 01, 2008; Revised October 09, 2009; Published September 01, 2010; Online September 01, 2010

## Abstract

Dynamic out-of-plane compressive testing was used to characterize the dynamic strength of stainless steel prismatic cores with representative double layer topology to be employed in sandwich panels for blast protection. Laboratory-scaled samples of the representative core unit cell were manufactured (relative density of 5.4%) and tested at constant axial impact velocities (ranging from quasi-static to $140 ms−1$). The dynamic strength was evaluated by measuring the stresses transmitted to a direct impact Hopkinson bar. Two-dimensional, plane strain, finite element calculations (with a stationary back face) were used to replicate the experimental results upon incorporating imperfections calibrated using the observed dynamic buckling modes. To infer the response of cores when included in a sandwich plate subject to blast loading, the finite element model was modified to an unsupported (free-standing) back face boundary condition. The transmitted stress is found to be modulated by the momentum acquired by the back face mass and, as the mass becomes larger, the core strength approaches that measured and simulated for stationary conditions. This finding justifies the use of a simple dynamic compression test for calibration of the dynamic strength of the core. An analytical model that accounts for the shock effects in a homogenized core and embodies a simple dual-level dynamic strength is presented and shown to capture the experimental observations and simulated results with acceptable fidelity. This model provides the basis for a constitutive model that can be used to understand the response of sandwich plates subject to impulsive loads.

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## Figures

Figure 1

X-core panel dimensions and unit cell: Hc=50 mm, θ=60 deg, tc=0.76 mm, tf=0.76 mm, C=38 mm, and d=5 mm

Figure 2

Temporal characteristics of stress transmitted through a prismatic core. The dotted line is a simplified two-step representation model (5). The first step has stress equal to ψupper and duration equal to ϕupper. In the second step, the stress drops to a buckled state equal to ψss, which lasts until high densification of the core with value of nominal strain ε¯=εD.

Figure 3

Quasi-static deformation: a comparison of measurements with finite element simulation. Simulation was terminated at 15% strain due to computational time limits.

Figure 4

A comparison of the observed and simulated deformation patterns at 20% strain for three different impact speeds

Figure 5

The temporal evolution of the deformation pattern for an impact at 100 m/s: comparison between observations and simulations. The small discrepancy before the peak stress is attributed to the limited bandwidth of the data acquisition system and the misalignment of the projectile during impact (8). The color code represents the equivalent plastic strain and can be interpreted as follows: dark is the elastic yield and gray is the plastic strain >10%.

Figure 6

The plane strain model (left) and the four eigenmodes grouped by the number of buckles along its web members: n=1 (upper right), n=2 (lower right), and so on

Figure 7

Influence of imperfections on the stress transmitted to a stationary back face vimpact=140 m/s

Figure 8

Influence of the impact velocity on the stress transmitted to a stationary back face

Figure 9

Influence of the impact velocity on the core push back stress on the front face

Figure 10

Comparison of the deformation patterns induced for both the stationary and free standing back face boundary conditions (mb=6 kg m−2) plotted with contours of plastic strain. Dark regions are elastic and gray corresponds to >10% plasticity (vimpact=100 m/s).

Figure 11

The dynamic strength model for the X-core tested is calibrated to the transmitted stress from (a) the stationary back face condition and compared with (b) the free-standing condition for both the FE simulations and (c) the continuum model as a function of varying values of back face mass. The average value for (d) the upper section of the transmitted stress is plotted in MPa against the back face mass mb as a direct comparison between the model and the simulations (vimpact=200 m/s).

Figure 12

Back face acceleration as a function of the average crushing strain for (a) varying back face mass mb and (b) vimpact for both FE simulations and continuum model predictions

Figure 13

Continuum model for a homogenized core. It calculates the back face velocity Vback, front face stress σu, and back face stress σb, given the impact velocity Vimpact, height of the core Hc, dynamic strength of the core σD and its relative density ρc, density of the material ρ, densification strain εD, and back face mass mb

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