Experimental Mechanics

, Volume 19, Issue 2, pp 69–75 | Cite as

General stress-velocity expressions in acoustoelasticity

General expressions for the stress-velocity dependence in acoustoelasticity are derived, showing that the principal-stress difference is proportional to the relative velocity difference in tri- and biaxial-stress fields. This has been verified experimentally for biaxial-stress fields
  • F. Bach
  • V. Askegaard


The velocity of a transverse wave propagating in an elastic body depends on the stress field of the body. If transverse waves are sent through a body with a uniaxial stress field, there will be proportionality between the principal-stress difference and the relative velocity difference between the waves polarized in accordance with the two main directions. This technique is used for determining uniaxial residual-stress fields.

The main object of the investigation described in this paper has been to investigate the usefulness of the method in the case of biaxial residual-stress fields. Both theoretically and experimentally, the investigation has shown that there is also proportionality between principal-stress difference and relative-velocity difference for a biaxial field. However, the tests have also shown that inaccuracies with this method, on account for example of preferred orientation in steel materials, are of such an order of magnitude that the method cannot, at the present stage of development, compete with the more traditional methods, such as the drilling method and the X-ray diffraction method.


Drilling Transverse Wave Fluid Dynamics Stress Field Prefer Orientation 
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.

List of Symbols


natural frequency of the crystal


thickness of the specimen

m, n

second-order elasticity constants (Hughes and Kelly)


echo numbers


number of the minimum echo


hydrostatic pressure


uniaxial pressure in the 1-, and 2-directions, respectively


acoustic axes


modulus of elasticity


principal strains


bulk modulus


maximum tensile load in the arms of the specimen


loads in horizontal and vertical arms, respectively


stress-acoustic constant


velocity of transverse waves in a homogenous, isotropic body


velocity of transverse waves propagating along the 1-direction and polarized along the 2- and 3-directions, respectively


velocity difference=U13U12


velocity difference from structure in an unstreassed body


the distance travelled by the pulse when the phase difference is 180 deg


second-order elasticity constants (Truesdell)


principal extensions


principal stretches


principal stresses


density in the undeformed and deformed state, respectively

λ, μ

Lamé constants


Poisson's ratio


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Copyright information

© Society for Experimental Mechanics, Inc. 1979

Authors and Affiliations

  • F. Bach
    • 1
  • V. Askegaard
    • 1
  1. 1.Structural Research LaboratoryTechnical UniversityLyngbyDenmark

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