Wave propagation in microcrack-damaged media under prestress

Ganpat, Sahane Dattatraya
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University of Delaware
Direct computational simulations of wave propagation through prestressed, microcrack-damaged media are conducted to study the interaction between the prestress and stress wave parameters. Tensile and compressive waves, tensile and compressive prestresses and various orientation distributions of microcrack damage are analyzed. The relationships among the input wave amplitude, wavelength and prestress magnitude and the output wave speed and wave attenuation are studied. The results show that wave speed and attenuation depend on the prestress and the wavelength in a complex way. In the cases of compressive waves traveling through tensile prestress and tensile waves passing through compressive prestress, the wave response depends on the ratio of the amplitude of the applied stress pulse to the magnitude of the prestress (defined as R). In direct simulations of unidirectional waves through uniaxially prestressed microcrack-damaged media, the simulations show that the compressive wave speed through tensile prestressed media increases gradually with an increase in R, while the tensile wave speed in media under compressive prestress, decreases with increase in R, but the change is abrupt at a particular R value. In the cases of sufficiently small R, the wave speeds match the results of Su et al. (2007) where the cracks are always open or always closed. However, above a certain wavelength (a cut-off wavelength), the wave speed is a constant function of wavelength and, furthermore, this cut-off wavelength varies with R. The wavelength above which the wave is relatively unattenuated also varies with R. We observed significantly increased attenuation for R values 1 ≤ R≤ 5 for both the case of compressive waves travelling through tensile prestress and tensile waves passing through compressive prestress. In a 2D cylindrical wave propagation study, the reduction in group velocity of a compressive wave in bi-axial tension prestressed damaged media is significant as prestress is introduced (R is decreased), on the other hand, the group velocity of a tensile wave in bi-axial compression prestressed damaged media rises with decrease in R, but the rise is sudden at a particular R value. In both the cases, at small R (R≤10) the group velocity asymptotically approaches the effective media results of Su et al. (2007) where the cracks are always open or always closed. Bi-axial tension prestressed media is highly attenuative for compressive waves and the attenuation depends on R and the microcrack orientation distribution. The generalized self-consistent method (GSCM) with elastic averaging is used to determine the effective properties of microcrack-damaged media under general uniaxial prestress. It predicted the properties fairly well for R≥2.5 for uniaxial tension prestressed media and above R≥10 for uniaxial compression prestressed media. It predicts the highest wave speeds when compared with the wave speeds determined by the direct numerical simulations for uniaxial tension prestressed media. A simple and quick time averaging method is devised to predict the approximate effective properties of the prestressed damaged media.