Numerical modeling of the V(z) curve for a thin-layer/substrate configuration

V. S. Ahn*, J. D. Achenbach, Z. L. Li, J. O. Kim

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A numerical model is presented to calculate V(z) curves for a line-focus acoustic microscope and the specimen configuration of a thin isotropic elastic layer deposited on an isotropic elastic substrate. In this model, a Gaussian beam which is tracked through the lens into the coupling fluid, interacts with the thin-layer/substrate system. The numerical approach is based on the solution of singular integral equations by the boundary element method. The system of singular integral equations follows from the conditions at the interface of the coupling fluid and the thin layer and the interface of the thin layer and the substrate. An electrochemical reciprocity relation is used to express the voltage at the terminals of the microscope's transducer in terms of the calculated incident and back-scattered fields. V(z) curves are presented for various layer thicknesses and various combinations of the elastic constants of the layer and the substrate. The oscillations of the V(z) curves are related to the modes of wave propagation in a thin layer in contact with a solid half-space on one side and a fluid half-space on the other side. Calculated V(z) curves have also been compared with experimentally obtained curves, and good agreement is observed.

Original languageEnglish (US)
Pages (from-to)183-200
Number of pages18
JournalResearch in Nondestructive Evaluation
Issue number4
StatePublished - Dec 1991

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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