TY - JOUR
T1 - Effective wave velocity and attenuation in a material with distributed penny-shaped cracks
AU - Ch., Zhang
AU - Achenbach, J. D.
N1 - Funding Information:
Acknowledgements-This work was carried out in the course of research for Contract DEFG02-86-ER13484 with the Department of Energy, Office of Basic Energy Sciences, Engineering Research Program. Support from the Florida State University Supercomputer Computations Research Institute, which is partially funded by the U.S. Department of Energy through Contract No. DE-FC05-85ER250000, is also acknowledged.
PY - 1991
Y1 - 1991
N2 - Wave propagation in a material containing distributed penny-shaped cracks was investigated. An improved approach was developed for calculating the phase velocity and the attenuation of ultrasonic waves. In this approach, the effects of neighboring cracks on a reference crack are approximated by the effects of triads of double forces of strengths proportional to the crack opening volumes, and located at the geometrical centers of the cracks. The averaged crack opening displacements and crack opening volumes of the reference crack are split into two terms. The first term corresponds to the quantities induced by the interaction of the single reference crack with an incident wave, while the second term represents the interaction between this reference crack and neighboring cracks. The averaged crack opening displacements are used in calculating the forward scattering amplitude, from which the phase velocity and the coefficient of attenuation are subsequently computed. The present analysis was limited to parallel cracks and to low frequencies, but the principle can be used for more general cases. Since crack interactions have been taken into account, the analysis provides a better approximation than the standard approach proposed by Foldy (1945, Phys. Rev. 67, 107-119), especially for intermediate and large crack densities.
AB - Wave propagation in a material containing distributed penny-shaped cracks was investigated. An improved approach was developed for calculating the phase velocity and the attenuation of ultrasonic waves. In this approach, the effects of neighboring cracks on a reference crack are approximated by the effects of triads of double forces of strengths proportional to the crack opening volumes, and located at the geometrical centers of the cracks. The averaged crack opening displacements and crack opening volumes of the reference crack are split into two terms. The first term corresponds to the quantities induced by the interaction of the single reference crack with an incident wave, while the second term represents the interaction between this reference crack and neighboring cracks. The averaged crack opening displacements are used in calculating the forward scattering amplitude, from which the phase velocity and the coefficient of attenuation are subsequently computed. The present analysis was limited to parallel cracks and to low frequencies, but the principle can be used for more general cases. Since crack interactions have been taken into account, the analysis provides a better approximation than the standard approach proposed by Foldy (1945, Phys. Rev. 67, 107-119), especially for intermediate and large crack densities.
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U2 - 10.1016/0020-7683(91)90032-B
DO - 10.1016/0020-7683(91)90032-B
M3 - Article
AN - SCOPUS:0025840807
SN - 0020-7683
VL - 27
SP - 751
EP - 767
JO - International Journal of Solids and Structures
JF - International Journal of Solids and Structures
IS - 6
ER -