Acousto-elastic measurement of stress and stress intensity factors around crack tips

Acousto-elasticity predicts that the phase velocity of sound waves in a material will be changed slightly by stress. For a slightly orthotropic plate in a state of plane stress, the shear stress σ_xy can be calculated from $\text{σ}{}_{\mathrm{xy}}\text{=}\text{(B}\text{sin}\text{2 φ)}\text{2m}$ once measurements of the acoustic birefringence B and the angle φ have been made. The birefringence is the difference in phase velocity between SH waves polarized along the ‘fast’ and ‘slow’ acoustic axes, φ is the angle between the acoustic axes in stressed and unstressed state, and m is an acousto-elastic constant for the material.For symmetrical, two-dimensional crack-opening problems, σ_xy can be expressed as a series expansion of stress functions, each of which satisfies the equilibrium equation. The coefficients in the expansion allow the appropriate boundary conditions to be satisfied. The stress intensity factor K₁ is the coefficient of the leading term in the series.Values of σ_xy and K₁ for an ASTM standard test specimen made of 2024 aluminium were acousto-elastically determined. These were compared with those obtained from a similar photoelastic specimen. Good agreement was obtained for both σ_xy and K₁.