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On the basis of elastodynamics and dislocation theory

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On the basis of elastodynamics and dislocation theory, 1 the acoustic emission wave u ( x , t ) is defined as surface motion at observation point x ; the surface motion is caused by a displacement discontinuity given by crack vector b ( y , t ) on crack surface F : m b n pq pqkl k l C = 392 Acoustic Emission Testing P ART 1. Acoustic Emission Testing Using Moment Tensor Analysis
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(2) where G ip,q is the spatial derivative of the Green’s function, S ( t ) is the function of source versus time and represents the convolution integral. A point source and point observation are assumed here. Materials should be isotropic and homogeneous. The equation describes a generalized relationship between seismic sources and elastic waves. The equation’s application is not restricted to a particular structure or frequency. The applicability of Eq. 2 to acoustic emission waveforms has been confirmed by simulation analysis. 16 When simulated waveforms were compared in a half space with detected waveforms, it was realized that the first portion of detected waveforms is in reasonable agreement with theoretical waveforms but the latter portions detected are distorted by the superposition of shear waves, surface waves and reflected waves. It suggests that only the first motions of longitudinal waves (P waves) are discriminative in practical acoustic emission waveform records. In addition, hundreds of acoustic emission waveforms are easily recorded by just one experiment. On the basis of the experimental findings, a moment tensor inversion procedure by the use of only the P wave amplitudes has been developed for practical analysis using a personal computer. To process acoustic emission waveform data promptly, a moment tensor inversion procedure has been developed for only P wave amplitudes. The moment tensor inversion procedure is accomplished using a simplified Green’s function for moment tensor analysis. 6 By selecting the P wave portion from the full-space Green’s function of homogeneous and isotropic material, Eq. 2 is simplified: (3) where F a is the crack area; R is the distance from observation point x to acoustic emission source y; r = ( r 1 , r 2 , r 3 ) is the direction cosine of R; t is the direction of acoustic emission transducer sensitivity; Ref( t,r ) is the reflection coefficient at the observation surface; ρ is density; υ p is the P wave velocity; and the time dependency is omitted. When an acoustic emission waveform caused by crack nucleation at y is recorded at x, the acoustic emission amplitude of the first motion corresponds to displacement A ( x ) in Eq. 3. After the acoustic emission source location procedure, information on distance R and direction cosine r is obtained. Eventually, Eq. 3 leads to a set of linear algebraic equations with six unknowns m pq because the moment tensor is symmetric. Thus, the amplitude observation of the first motions at more than six transducers could result in an overdetermined system with unknowns m pq . Note that P waves are not assumed to have the largest amplitude. Attenuation
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  • Fall '19
  • The Land, Nondestructive testing, Acoustic Emission, Acoustic Emission Testing

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