The Use of Acoustoelastic Measurements to Characterize the Stress States in Cracked Solids

The theory of acoustoelasticity predicts that a plane longitudinal acoustic wave passing through a solid which is already in a deformed state will propagate with a velocity (v) which is different from the (v0) of the same wave propagating through the undeformed medium. It may be shown that b.v/vo = (v-vo)/vo = B(o1+o2l where o1 and o2 are the principal stress in the plane normal to the wave propagation direct1on and B is the acoustoelastic constant. Wave transit time measurements allow the relative velocity change b.v/Vo to be determined, so that contours of constant principal stress sum (o1+o2) may be mapped by acoustically scanning a stressed solid. We have used the technique described above to characterize the states of stress in cracked and notched aluminum panels. A method for extracting crack stress intensity factors from the acoustic data is proposed and illustrated for center-cracked panel specimens. The results indicate that the technique may offer a promising method for nondestructive testing and evaluation. Scanning experiments involving both shear and longitudinal acoustic wave probes may, in principle, be used to nondestructively determine the complete state of plane deformation in a stressed solid. We shall point out how one may use such acoustic information to determine the J integral and theM integral associated with cracked specimens. The integrands of these elastostatic conservation integrals contain terms involving elastic rotations which are not directly obtainable from the acoustic data, but it is possible to use forward integration of the compatibility equations to obtain the requisite information. An illustration example in which J and Mare determined using this technique will be presented. This technique rna) find practical applications in the continuous nondestructive monitoring of critical structural elements.