AE02.pdf

This value can be determined by simple geometry to be

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This value can be determined by simple geometry to be: (86) The power incident on or reflected from the free surface is equal to the intensity times the area and thus can be written for the three waves as follows: (87) (88) (89) Proceeding in a similar manner, the intensities and powers associated with the P c A rt rt rt i = ( ) ( ) ( ) 1 2 2 2 ρ θ θ cos cos P c A rl rl = ( ) 1 2 1 2 ρ P c il = 1 2 1 ρ w t rt i = ( ) ( ) cos cos θ θ I c A rt rt = ( ) 1 2 2 2 ρ I c A rl rl = ( ) 1 2 1 2 ρ I c il = ( ) 1 2 1 1 2 ρ I c A = ( ) 1 2 2 ρ 86 Acoustic Emission Testing F IGURE 38. Change in area for mode converted wave. Free surface Legend w t = area between rays of transverse wavefront θ i = angle of incidence θ rt = angle of reflected transverse wave θ i θ rt 1 1 w t F IGURE 37. Reflection coefficients for an incident longitudinal wave with Poisson’s ratio of 0.3: (a) amplitude of reflected longitudinal wave for incident longitudinal wave; (b) amplitude of reflected transverse wave for incident longitudinal wave. Amplitude of reflected longitudinal wave (relative unit) 0.5 0 –0.5 –1 0.87 1.57 (50) (90) Angle of incident longitudinal wave, rad (deg) Amplitude of reflected transverse wave (relative unit) 1.5 1.0 0.5 –0 0.87 1.57 (50) (90) Angle of incident longitudinal wave, rad (deg) (a) (b)
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incident and reflected waves for a transverse wave incident on a free surface can be calculated: (90) (91) (92) The value for θ rl is computed using Snell’s law (Eq. 67) and A rt and A rl are given by Eqs. 69 and 70. For both of the cases presented above, the principle of the conservation of energy demands the following relationship: (93) Equation 93 is satisfied by substituting Eqs. 90 through 92 or Eqs. 87 through 89. Graphs showing the partition of power for an incident longitudinal wave and for several values of Poisson’s ratio ν are given in Fig. 39. The figure shows the ratios P rl · P il –1 on the left hand scale and P rt · P il –1 on the right hand scale. Likewise the ratios P rt · P it –1 and P rl · P it –1 are shown in Fig. 40 for the same values of ν . Reflection and Transmission at Interface between Two Solids Another common interface that appears in many practical solids is an interface formed by joining two different materials as shown in Fig. 41. Considered here is the problem of reflection and transmission of a wave normally incident on the interface (a wave whose direction of propagation is normal to the plane interface). If an incident wave of unit amplitude in medium 1 is longitudinal and if the interface between the solids is the plane x 2 = 0, then the solution may be written as below: (94) and when x 2 0: (95) or when x 2 0: (96) u A e j k x t 2 12 2 = ( ) t ω u e A e j k x t j k x t 2 11 2 11 2 = + ( ) ( ) ω ω r u u 1 3 0 = = P P P i rl rt = + = ( ) ( ) ( ) P c A rl rl rl i 1 2 1 2 ρ θ θ cos cos = ( ) P c A rt rt 1 2 2 2 ρ P c it = 1 2 2 ρ 87 Fundamentals of Acoustic Emission Testing F IGURE 39. Energy reflection coefficients for incident longitudinal wave.
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  • Fall '19
  • Nondestructive testing, Acoustic Emission, Acoustic Emission Testing

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