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A new technique for ultrasonic nondestructive evaluation of adhesive joints: Part I. Theory

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Abstract

In this paper we proposed a new technique for ultrasonic nondestructive evaluation (UNDE) of adhesively bonded joints. We report an exact solution to the problem of reflection and tarnsmission of a plane, time-harmonic, longitudinal wave through anN-layered medium. The solution is valid for perfectly elastic as well as linear-viscoelastic materials, and for isotropic as well as anisotropic materials (for example, fiber-reinforced composite) so long as the wavepropagation vector coincids with one of the material coordinates. The transfer function,H *(ω) is defined as the trans-mitted (or reflected) field normalized with respect to the incident field. A closed-form solution forH *(ω) for the case of an adhesive joint (consisting of two adherends joined by an adhesive layer) immersed in an elastic fluid is derived. A detailed analysis of the sensitivity ofH *(ω) to the wave speed and thickness of the adherends and the adhesive is carried out. An experimental verification of the analysis is the subject of Part II of this paper.

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Abbreviations

c :

longitudinal phase velocityin specimen, mm/μs

e r :

error in a measured property

e H :

error in the magnitude of the transfer function

f :

frequency, MHz

F *(ω):

Fourier transform of reference sinnal

G *(ω):

Fourier transform of specimen signal

h, h T :

thickness of the adhesive layer and the joint, respectively, mm

H(ω):

magnitude of the transfer function

H * T (ω):

experimentally acquired transfer function,H *=G */F *

H * R (ω):

theoretical transfer function of the reflected field

H * T (ω):

theoretical transfer function of the transmitte field

k :

complex wave number,k=k′+iα=ω/c, nepers/mm

L :

thickness of the adherends

m :

integer

R ij :

reflection coefficient in mediumi from mediumj

s :

slowness, inverse of wave speed,s=1/c, μs/mm

S H *, th ,S H *, c :

sensitivity ofH * to thickness and wave speed, respectively

S H, h ,S H, c :

sensitivity of the magnitude ofH * to thickness, wave speed

S ϕ, th ,S ϕ, c :

sensitivity of phase ofH * to thickness, wave speed

T ij :

transmission coefficient into mediumj from mediumi

Z :

acoustic impedance, ϱc

α:

the attenuation in the adhesive, nepers/mm

β:

dimensionaless attenuation constant, β=αλ

ϕ:

phase of the transfer funciton, radians

x 0 :

bulk modulus of water

λ:

wavelength, mm; Lamé constant

μ:

Lamé constant; (shear modulus)

ϱ:

density, kg/m3

Ω:

normalized frequency, Ω=k 1 h T =ωh T /c

ω:

circular frequency, rad/μs

ζ:

normalized spatial coordinate, ζ=x/h

()0 :

property of the immersion medium

()1, ()2 :

property of the adherend and adhesive layer, respectively

References

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Authors and Affiliations

  1. Department of Aerospace Engineering, Texas A&M University, 77843, College Station, TX

    S. E. Hanneman (Graduate Research Assistant)

  2. Center for Mechanics of Composites, Texas A&M University, 77843, College Station, TX

    V. K. Kinra (Professor of Aerospace Engineering and Associate Director)

Authors
  1. S. E. Hanneman
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  2. V. K. Kinra
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Hanneman, S.E., Kinra, V.K. A new technique for ultrasonic nondestructive evaluation of adhesive joints: Part I. Theory. Experimental Mechanics 32, 323–331 (1992). https://doi.org/10.1007/BF02325585

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  • DOI: https://doi.org/10.1007/BF02325585

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