Ultrasonic measurement of through-thickness stress gradients in textured sheet metals

Man, Chi-Sing; Li, Jianbo; Lu, Wei-Yang; Fan, Xingyan
May 2000
AIP Conference Proceedings;2000, Vol. 509 Issue 1, p1613
Academic Journal
The objective of this investigation is to explore the possibility of using the dispersion of high-frequency Rayleigh waves for the evaluation of through-thickness stress gradients at the surface of metal sheets. We consider an orthorhombic sheet of cubic metal with through-thickness inhomogeneities in stress and texture, and adopt a coordinate system under which the rolling (RD), transverse (TD), and normal direction (ND) of the sheet are taken as the 1-, 2-, and 3-direction, respectively. We restrict our attention to the special case where only the stress components T[sub 11](x[sub 3]) and T[sub 22](x[sub 3]) in the sheet are nonzero, and consider only Rayleigh waves of sufficiently high frequency for which the sheet can be taken as the half-space x[sub 3]>=0. For Rayleigh waves of two different frequencies (with wave numbers k[sub 1] and k k[sub 2] respectively) propagating on the same wave path along either RD or TD, we appeal to an analysis of J. Li and Man to obtain a high-frequency asymptotic formula which gives the relative change in time-of-flight Δt/t[sub 0] as (1/k[sub 1]-1/k[sub 2]) times a linear combination of the derivatives T[sub 11][sup ′](0), T[sub 22][sup ′](0), W[sub 4m0][sup ′](0)(m=0,2,4) and W[sub 6m0](0)(m=0,2,4,6) at the surface are ascertained and the material constants in the acoustoelastic consitutive equation of this polycrystal are known. An experiment was performed on an AA7075-T651 aluminum alloy beam, in which Δt/t[sub 0] was measured for various values of T[sub 11](0) and T[sub 11][sup ′](0) produced by beam bending (with (T[sub 22]≡0). The relevant texture coefficients of the beam were measured by X-ray diffraction. To obtain specific predictions from the aforementioned symptotic formula, we replace the material constants of the sample by their counterparts predicted for polycrystalline (pure) aluminum by the Man-Paroni model. The predictions and Δt/t[sub 0] are then compar...


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