Reflection and transmission of ultrasound by a region of damaged material

Jan Drewes Achenbach*, Ch Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


Reflection and transmission of ultrasonic waves by a layer-like region of distributed microcracks in a bulk material has been investigated. It has been assumed that for sufficiently low frequencies and far away from the damaged layer, the reflected and transmitted waves are plane waves. By applying the Betti reciprocal theorem to a cell containing N cracks, and by choosing one elastodynamic state as the actual wave state and the other as a suitably chosen auxiliary wave state, the reflection and transmission coefficients have been expressed in terms of integrals over the N cracks. Simple expressions have been obtained for the case that all cracks are identical and parallel to each other. For the case that the cracks do not interact with each other, numerical results for the reflection and transmission coefficients are presented for a distribution of penny-shaped cracks. The variation of these coefficients with frequency, relative layer thickness and angle of incidence has been displayed in graphs.

Original languageEnglish (US)
Pages (from-to)71-79
Number of pages9
JournalJournal of Nondestructive Evaluation
Issue number2-3
StatePublished - Sep 1 1990


  • layer of cracks
  • reflection
  • transmission
  • Ultrasound

ASJC Scopus subject areas

  • Materials Science (miscellaneous)


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