Explicit Formulae Showing the Effects of Texture on Acoustoelastic Coefficients

Hartig's law and linear elasticity with initial stress

“…As far as I am aware, while there are later studies on cubic and hexagonal (single) crystals, Sayre's experiments may well be the last static measurements with a sufficiently accurate strain resolution that would shed light on the validity of Hartig's law or the approximate validity of equation ( 11) for polycrystalline metals. In this regard much can be learnt by reinterpreting, in the context of linear elasticity with initial stress, the results of modern experiments on ultrasonic measurements of acoustoelastic constants (cf the recent review by Thompson et al [16] and references therein; see also [10,15]). Almost all such measurements corroborate equation ( 3), with L given by ( 6), as a generalization of Hartig's law in the sense that ultrasonic velocities are found empirically to be affine functions of the initial stress, which would follow from ( 3) and ( 6) if the components of…”