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
Article

Abstract

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.

Keywords

Drilling Transverse Wave Fluid Dynamics Stress Field Prefer Orientation 

List of Symbols

f

natural frequency of the crystal

h

thickness of the specimen

m, n

second-order elasticity constants (Hughes and Kelly)

k,s

echo numbers

p

number of the minimum echo

p0

hydrostatic pressure

p1,p2

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

x1,x2,x3

acoustic axes

E

modulus of elasticity

Ei

principal strains

K0

bulk modulus

Pmax

maximum tensile load in the arms of the specimen

P2,P3

loads in horizontal and vertical arms, respectively

S

stress-acoustic constant

U0

velocity of transverse waves in a homogenous, isotropic body

U12,U13

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

ΔU

velocity difference=U13U12

ΔUs

velocity difference from structure in an unstreassed body

Xπ

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

α56

second-order elasticity constants (Truesdell)

δi

principal extensions

θi

principal stretches

θi

principal stresses

ϱo

density in the undeformed and deformed state, respectively

λ, μ

Lamé constants

ν

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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