On the use of acoustic birefringence to determine components of plane stress

To assess the integrity of a structure containing a (known) flaw, it is necessary to know the stresses acting on the flaw. Many common structural elements (e.g. beams and plates) are subjected to either true plane stress or generalized plane stress. For either of these cases, there are three in-plane stresses (one shear stress and two normal stresses) to be determined in general.In this paper, we consider the application of the acoustic birefringence method to generalized plane stress states, where the thickness-averaged values of the shear and normal stresses are sought. It is shown that the times-of-flight are thickness-averaged effects, whereas the polarization directions depend upon local values of stress. Consequently, when the symmetric (axial) component of the stresses dominates the antisymmetric (bending) component, the acoustic birefringence method can be used to determine all three stresses, if the boundary conditions are known. For unknown boundary conditions, the normal stresses can be determined to within arbitrary functions.Problems arise in using the normal incidence technique when either the shear stress vanishes, or the symmetric (membrane) components of generalized plane stress do not dominate the bending components. In the former case, the thickness-averaged difference in normal stresses can be obtained, provided that the birefringence in the unstressed state is known. In the latter case, the (averaged) difference in normal stresses can be obtained by measuring time-of-flight differences of off-axis SH-waves propagating in the planes of material symmetry of the plate.