Ultrasound waves are a powerful tool to evaluate material properties and to characterize microstructures like distributions of microcracks in solids. For example most ceramics contain microcracks, as a result of the way they are manufactured. Ceramics that contain localized residual stresses are known to be capable of microcracking. The residual stresses arise in ceramics as a result of phase transformations, thermal expansion anisotropy in single-phase materials and thermal expansion or elastic mismatch in multiphase materials. Regions of low toughness, such as grain boundaries, would also be expected to be attractive sites for such cracks. Microcracks can form spontaneously during the fabrication process if the grain or particle size is above a critical value. Ceramics containing microcracks after fabrication have been associated with good thermal shock resistance but such materials are expected to have low strengths, as the microcracks are likely failure origins. Therefore, the analysis of microcracking influence on the dynamic response of a solid to propagating waves is important for the material characterization. In the present study, the time-harmonic response of an elastic solid with a microcracked region is analysed. The region is permeated by a random distribution of aligned penny-shaped cracks and the solid is uncracked outside this region. Crack faces are supposed to be traction free. The problem is formulated in terms of the mean values of displacement, strain and stress fields and a nonlocal effective constitutive relation is adopted for the cracked region, assuming a dilute concentration of cracks. Longitudinal waves propagating along the direction normal to the crack surfaces are considered. In the case of waves with half-wavelength greater than the crack diameter, explicit expressions are given for the attenuation and phase velocity of the mean wave in the cracked region, and for the amplitudes of the reflected and transmitted waves in the uncracked parts of the solid.
Dynamic characterization of a solid with microcracking zones
CAPUANI, Domenico
2009
Abstract
Ultrasound waves are a powerful tool to evaluate material properties and to characterize microstructures like distributions of microcracks in solids. For example most ceramics contain microcracks, as a result of the way they are manufactured. Ceramics that contain localized residual stresses are known to be capable of microcracking. The residual stresses arise in ceramics as a result of phase transformations, thermal expansion anisotropy in single-phase materials and thermal expansion or elastic mismatch in multiphase materials. Regions of low toughness, such as grain boundaries, would also be expected to be attractive sites for such cracks. Microcracks can form spontaneously during the fabrication process if the grain or particle size is above a critical value. Ceramics containing microcracks after fabrication have been associated with good thermal shock resistance but such materials are expected to have low strengths, as the microcracks are likely failure origins. Therefore, the analysis of microcracking influence on the dynamic response of a solid to propagating waves is important for the material characterization. In the present study, the time-harmonic response of an elastic solid with a microcracked region is analysed. The region is permeated by a random distribution of aligned penny-shaped cracks and the solid is uncracked outside this region. Crack faces are supposed to be traction free. The problem is formulated in terms of the mean values of displacement, strain and stress fields and a nonlocal effective constitutive relation is adopted for the cracked region, assuming a dilute concentration of cracks. Longitudinal waves propagating along the direction normal to the crack surfaces are considered. In the case of waves with half-wavelength greater than the crack diameter, explicit expressions are given for the attenuation and phase velocity of the mean wave in the cracked region, and for the amplitudes of the reflected and transmitted waves in the uncracked parts of the solid.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
