Experimental Mechanics

, Volume 36, Issue 4, pp 325–332 | Cite as

Acoustoelasticity: Ultrasonic stress field reconstruction

  • H. R. Dorfi
  • H. R. Busby
  • M. Janssen


Based on the theory of acoustoelasticity, a new ultrasonic stress reconstruction method—the generalized acoustic ratio (GAR) technique—is developed for locally plane structures and orthotropic materials. For given transit times of the three wave modes and the shear wave polarization angle, the local plane stress tensor is uniquely determined. The GAR technique yields accurate stress estimates with relatively small temperature sensitivity. Based on calibration constants from three uniaxial specimens, the entire stress field in a compact tension specimen is reconstructed. The results are in very good agreement with stress predictions from an elastoplastic finite element analysis. To further improve the measurements, a numerical technique, the stress field approximation (SFA) technique, is developed. The SFA technique uses a smooth local bicubic spline approximation and aims at improving the overall stress field estimate by enforcing the equilibrium equations, the stress boundary conditions and symmetry conditions. Numerical results show that both the average error and its spread are indeed reduced.


Shear Wave Orthotropic Material Compact Tension Compact Tension Specimen Spline Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Hughes, D.S. andKelly, J.L., “Second-order Deformation of Solids,”Physical Review,92 (5),1145–1149 (1953).Google Scholar
  2. 2.
    Toupin, R.A. andBernstein, B., “Sound Waves in Deformed Perfectly Elastic Materials. Acoustoelastic Effect,”J. Acoustical Society of America,33,216 (1961).MathSciNetGoogle Scholar
  3. 3.
    Benson, R.W. andRaelson, V.J., “Acoustoelasticity,”Product Engineering,30,56–59 (July 20,1959).Google Scholar
  4. 4.
    Bergman, R.H. andShahbender, R.A., “Effect of Statically Applied Stresses on the Velocity of Propagation of Ultrasonic Waves,”J. Appl. Physics,29 (12),1736–1738 (1958).CrossRefGoogle Scholar
  5. 5.
    Tokuoka, T. andIwashimizu, Y., “Acoustical Birefringence of Ultrasonic Waves in Deformed Isotropic Elastic Materials,”Int. J. Solids and Struct.,4,383–389 (1968).Google Scholar
  6. 6.
    Tokuoka, T. andSaito, M., “Elastic Wave Propagation and Acoustical Birefringence in Stressed Crystals,”J. Acoustical Society of America,45,1241–1246 (1969).Google Scholar
  7. 7.
    Iwashimizu, Y., “Ultrasonic Wave Propagation in Deformed Isotropic Elastic Materials,”Int. J. Solids and Struct.,7,419–429 (1971).CrossRefMATHGoogle Scholar
  8. 8.
    Iwashimizu, Y. andKubomura, K., “Stress-induced Rotation of Polarization Directions of Elastic Waves in Slightly Anisotropic Materials,”Int. J. Solids and Struct.,9,99 (1973).CrossRefGoogle Scholar
  9. 9.
    King, R.B. andFortunko, C.M., “Determination of In-plane Residual Stress States in Plates Using Horizontally Polarized Shear Waves,”J. Appl. Physics,54,3027–3035 (1983).Google Scholar
  10. 10.
    Pao, Y.H. andGamer, U., “Acoustoelastic Waves in Orthotropic Media,”J. Acoustical Society of America,77,806–812 (1985).Google Scholar
  11. 11.
    Crecraft, D.I., “The Measurement of Applied and Residual Stresses in Metals Using Ultrasonic Waves,”J. Sound and Vibration,5,173–192 (1967).CrossRefGoogle Scholar
  12. 12.
    Man, C.S. andLu, W.Y., “Towards an Acoustoelastic Theory for Measurement of Residual Stress,”J. Elasticity,17,159–182 (1987).CrossRefGoogle Scholar
  13. 13.
    Hoger, A., “On the Determination of Residual Stress in an Elastic Body,”J. Elasticity,16,303–324 (1986).CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Biot, M.A., Mechanics of Incremental Deformations, Wiley, New York (1965).Google Scholar
  15. 15.
    Lu, W.Y. andMan, C.S., “Measurement of Stress Based upon Universal Relations in Acoustoelasticity,”Experimental Mechanics,29,109–114 (1989).Google Scholar
  16. 16.
    Dorfi, H., Busby, H. andJanssen, M., “Ultrasonic Stress Measurements Based on the Generalized Acoustic Ratio Technique,”Int. J. Solids and Struct,33 (8),1157–1175 (1996).CrossRefGoogle Scholar
  17. 17.
    Pao, Y.-H., Sachse, W. andFukuoka, H., “Acoustoelasticity and Ultrasonic Measurements of Residual Stresses,”Physical Acoustics XVII, ed. W. Mason andR. Thurston, Academic Press, New York, 61–143 (1984).Google Scholar
  18. 18.
    Dorfi, H., “Acoustoelasticity: Stress Identification Based on Ultrasonic Measurements,”PhD diss., Department of Mechanical Engineering, The Ohio State University, Columbus, OH (1994).Google Scholar
  19. 19.
    Janssen, M. andZuidema, J., “An Acoustoelastic Determination of the Stress Tensor in Textured Metal Sheets Using the Birefringency of Ultrasonic Shear Waves,”J. Nondestructive Evaluation,5 (1),45–52 (1985).Google Scholar
  20. 20.
    Janssen, M., “Evaluation of an Applied Plane-stress Tensor Distribution Using Ultrasonic Shear Waves,”Experimental Mechanics,28,226–231 (1988).CrossRefGoogle Scholar

Copyright information

© Society for Experimental Mechanics, Inc. 1996

Authors and Affiliations

  • H. R. Dorfi
    • 1
  • H. R. Busby
    • 1
  • M. Janssen
    • 2
  1. 1.Department of Mechanical EngineeringThe Ohio State UniversityColumbus
  2. 2.Department of Materials ScienceDelft University of TechnologyDelftThe Netherlands

Personalised recommendations