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

Abstract 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 σ xy = (B sin 2 φ) 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 K 1 is the coefficient of the leading term in the series. Values of σ xy and K 1 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 K 1 .

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