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TECHNICAL PAPERS

# Modeling of Elastic Waves in Dynamically Loaded $NiAl$ Bicrystals

[+] Author and Article Information
Eric Loomis

Los Alamos National Laboratory, P.O. Box 1663, MS E526, Los Alamos, NM 87545loomis@lanl.gov

Pedro Peralta

Department of Mechanical and Aerospace Engineering,  Arizona State University, P.O. Box 876106, Tempe, AZ 85287-6106pperalta@asu.edu

Damian C. Swift

Material Science and Technology Division,  Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94551dswift@llnl.gov

J. Eng. Mater. Technol 129(4), 513-522 (May 03, 2007) (10 pages) doi:10.1115/1.2772328 History: Received August 30, 2006; Revised May 03, 2007

## Abstract

Two methods have been used to simulate 2D elastic wave scattering in nickel aluminide $(NiAl)$ bicrystals to study effects of grain boundaries and material anisotropy on elastic wave propagation. Scattering angles and amplitude ratios of the reflected and refracted waves produced at the grain boundary were calculated via slowness curves for both grains, which were plotted in the plane of incidence containing the grain boundary normal. From these curves, scattering angles were measured graphically and amplitude ratios were calculated based on the continuity of tractions and displacements at the boundary. To support these calculations, finite element simulations were performed with ABAQUS /EXPLICIT to obtain time- and space-dependent stresses. The results of each method correlated well with each other for four bicrystals. It was found that for bicrystals where the transmitted quasi-longitudinal (TQL) wave amplitude decreased across the boundary, diminished stresses were found in the finite element models for the same bicrystal. Conversely, where an increase in amplitude of the TQL wave was found, the finite element simulations showed that stress under the boundary increased. In general, the amplitude of the TQL wave was found to have a strong connection to the ratio of incident and TQL sound speeds. However, other directions in each grain are believed to contribute strongly to the overall scattering process since the pairs of bicrystals in this investigation had somewhat similar sound speeds. These findings correlated well with free surface cracking observed in a previous paper (Loomis, E., Peralta, P., Swift, D., and McClellan, K., 2005, Mater. Sci. Eng., Ser. A., 404(1-2), pp. 291–300), where cracks nucleated and propagated due to the focusing of scattered waves at the boundary. Specifically, in bicrystals oriented for shielding, the grain boundary was protected forcing cracks to grow outside of the shielded region.

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Copyright © 2007 by American Society of Mechanical Engineers
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## Figures

Figure 1

(a) Free surface of the ⟨227⟩∕⟨001⟩, (b)⟨335⟩∕⟨123⟩ bicrystals prior to shock compression, and (c) model plane of incidence used in slowness and finite element analyses

Figure 2

Pressure history used in the finite element simulations

Figure 3

Slowness curves for the (a)⟨227⟩ to ⟨001⟩ transition and the (b)⟨001⟩ to ⟨227⟩ transition across the grain boundary

Figure 4

Regions affected by scattered waves in the (a)⟨227⟩ to ⟨001⟩ transition and the (b)⟨001⟩ to ⟨227⟩ bicrystals

Figure 5

Pressure contour plots for the ⟨227⟩∕⟨001⟩ bicrystal

Figure 6

Pressure plots for the ⟨001⟩∕⟨227⟩ bicrystal

Figure 7

Slowness curves for (a)⟨123⟩∕⟨335⟩ and (b)⟨335⟩∕⟨123⟩

Figure 8

Regions affected by scattered waves in the (a)⟨123⟩∕⟨335⟩ and (b)⟨335⟩∕⟨123⟩ bicrystals

Figure 9

Contour plots of pressure for the ⟨123⟩∕⟨335⟩ bicrystal following reflection at the top (free) surface

Figure 10

Optical micrograph of observed fracture in recovered ⟨123⟩∕⟨335⟩ shock loaded bicrystal

Figure 11

Contour plots of pressure for the ⟨335⟩∕⟨123⟩ bicrystal following reflection at the bottom (free) surface

Figure 12

Intergranular fracture of shocked bicrystal ⟨335⟩∕⟨123⟩

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