Monitoring crack-induced changes in elasticity with resonant spectroscopy

The presence and nature of fractures can have a profound impact on the elastic and mechanical properties of materials. Whether it is a fracture-induced loss of strength or the creation of a long-wavelength anisotropy, being able to infer the presence and properties of fractures in a material has many applications. Detecting changes in the spectra of mechanical resonances due to the presence of fractures is not difficult. A more interesting issue is which elastic moduli are sensitive to the presence of these fractures and how are these moduli related to the stiffness of the material? Resonant ultrasound spectroscopy was performed on acrylic cylinders with internal cracks. Inversions were performed for both isotropic and anisotropic moduli. Good agreement was obtained between isotropic moduli and projected (optimal isotropic moduli obtained from anisotropic moduli) for nonverlapping cracks. The same projections yielded poorer agreement for the sample with overlapping cracks. The results also show that the degree of anisotropy depends upon the amount of crack overlap, and that the isotropic shear modulus is a reliable measure of decreasing stiffness.