Modeling of Elastic Waves in Dynamically Loaded $NiAl$ Bicrystals

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.