Inversion of residual stress profiles from ultrasonic Rayleigh wave dispersion data

We investigate theoretically and with synthetic data the performance of several inversion methods to infer a residual stress state from ultrasonic surface wave dispersion data. We show that this particular problem may reveal in relevant materials undesired behaviors for some methods that could be reliably applied to infer other properties. We focus on two methods, one based on a Taylor-expansion, and another one based on a piecewise linear expansion regularized by a singular value decomposition. We explain the instabilities of the Taylor-based method by highlighting singularities in the series of coefficients. At the same time, we show that the other method can successfully provide performances which only weakly depend on the material.

[1]  J. Ditri,et al.  Stress distribution determination in isotropic materials via inversion of ultrasonic Rayleigh wave dispersion data , 1996 .

[2]  John J. Ditri,et al.  Determination of nonuniform stresses in an isotropic elastic half space from measurements of the dispersion of surface waves , 1997 .

[3]  T. Szabo.  Obtaining subsurface profiles from surface−acoustic−wave velocity dispersion , 1975 .

[4]  Marc Duquennoy,et al.  Ultrasonic characterization of residual stresses in steel rods using a laser line source and piezoelectric transducers , 2001 .

[5]  M. Hirao,et al.  Acoustoelastic Effect of Rayleigh Surface Wave in Isotropic Material , 1981 .

[6]  Francis D. Murnaghan,et al.  Finite Deformation of an Elastic Solid , 1967 .

[7]  C. Lee,et al.  Conductivity profile determination by eddy current for shot-peened superalloy surfaces toward residual stress assessment , 2007 .

[8]  Marc Duquennoy,et al.  Characterization of micrometric and superficial residual stresses using high frequency surface acoustic waves generated by interdigital transducers. , 2013, The Journal of the Acoustical Society of America.

[9]  P. Nagy,et al.  Simple analytical approximations for eddy current profiling of the near-surface residual stress in shot-peened metals , 2004 .

[10]  D. S. Hughes,et al.  Second-Order Elastic Deformation of Solids , 1953 .

[11]  Dario Albarello,et al.  Application of Surface-Wave Methods for Seismic Site Characterization , 2011 .

[12]  Dispersion of Rayleigh waves in weakly anisotropic media with vertically-inhomogeneous initial stress , 2015 .

[13]  D. Husson,et al.  A perturbation theory for the acoustoelastic effect of surface waves , 1985 .

[14]  M. Spies,et al.  On the validity of several previously published perturbation formulas for the acoustoelastic effect on Rayleigh waves , 2019, Ultrasonics.

[15]  J. Richardson,et al.  Determination of Physical Property Gradients from Measured Surface Wave Dispersion , 1987, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[16]  Christ Glorieux,et al.  Surface acoustic wave depth profiling of elastically inhomogeneous materials , 2000 .

[17]  Jennifer E. Michaels,et al.  ACOUSTOELASTIC LAMB WAVE PROPAGATION IN A HOMOGENEOUS, ISOTROPIC ALUMINUM PLATE , 2011 .

[18]  Sebastiano Foti,et al.  Surface-wave analysis for building near-surface velocity models — Established approaches and new perspectives , 2010 .

[19]  Christ Glorieux,et al.  Photothermal depth profiling: Analysis of reconstruction errors , 1999 .

[20]  Nils Ryden,et al.  Fast simulated annealing inversion of surface waves on pavement using phase-velocity spectra , 2006 .

[21]  M. Ouaftouh,et al.  Ultrasonic evaluation of stresses in orthotropic materials using Rayleigh waves , 1999 .