Characterization of Global And Localized Material Degradation in Plates and Cylinders Via Nonlinear Interaction of Ultrasonic Guided Waves

Open Access
Liu, Yang
Graduate Program:
Engineering Science and Mechanics
Doctor of Philosophy
Document Type:
Date of Defense:
April 15, 2014
Committee Members:
  • Clifford Jesse Lissenden Iii, Dissertation Advisor
  • Joseph Lawrence Rose, Dissertation Advisor
  • Clifford Jesse Lissenden Iii, Committee Chair
  • Joseph Lawrence Rose, Committee Chair
  • Bernhard R Tittmann, Committee Member
  • Victor Ward Sparrow, Committee Member
  • Localized material degradation
  • nonlinear acoustic guided waves
  • mode interaction
  • material characterization.
Among all the applications for nondestructive evaluation (NDE) and structural health monitoring (SHM), failures occur at geometrical or compositional discontinuities. The material microstructural evolution that precedes macroscale damage exhibits a localized behavior due to high stress concentrations. Therefore, the capability to characterize these “localized hot spots” is of significance to ensure the structure integrity. The cumulative second or third harmonics of guided waves resulting from a primary mode self interaction measures the average nonlinearity over the distance between transmitter and receiver, which are shown to be sensitive to “globalized” material degradation, e.g. fatigue generated dislocation and persistent slip band substructures, creep induced precipitate-dislocation interactions, etc. This thesis provides a systematic analysis on the characteristics of higher order harmonic generation due to guided wave mode interactions which provide advantages to characterize global and localized material degradation. This thesis starts with linear guided wave solutions in plates and pipes in terms of normal modes. A plate ray interpretation of the elastic waves propagation in pipes is proposed based on geometric acoustic concepts and a plate approximation. A helical inter-digital transducer is designed to excite pure flexural waves. The linear wave theories provide fundamentals to analyze higher order harmonic generation in waveguides. A generalized mathematical framework is formulated to investigate the nonlinear generations due to the interaction of two guided wave modes in an isotropic, homogeneous, weakly nonlinear waveguide. A total number of (N+1)(N+2)/2-3 nonlinear boundary problems are formulated due to the Nth order mode interactions in a waveguide with Kth order nonlinearity (N≤K). The analysis of a specific order of nonlinear problem can be conducted by adopting the corresponding order of the strain energy function. The quadractic and cubic nonlinear forcing terms that cause the generation of second and third order harmonic genation are derived within general curvilinear coordinates. The characteristics of the internally resonant higher order harmonic generation in plates are explored thoroughly by considering waves with either shear horizontal (SH) or Rayleigh Lamb (RL) types. It is found that waves with either SH or RL type can be generated as internally resonant second or third order harmonics with specific patterns of primary mode interaction. Similiarly, an analysis is performed to identify the generation of internally resonant higher order harmonics in weakly nonlinear circular cylinders due to mode interactions based on the nonlinear forcing terms in curvilinear coordinates. The criteria are formulated by a synchronism condition, the circumferential orders of the primary modes, as well as the nature of the primary and the secondary wave fields, i.e., torsional or longitudinal. A generalized analysis that provides insight into the cumulative nature of the Nth order harmonics by Nth order interaction of two collimated waves is conducted by considering a cylinder with strain energy function written as Murnaghan’s power series. The nature of the cumulative Nth order harmonics can be determined by the parity of the number of times the primary waves interact, and their circumferential orders. Nonlinear finite element simulations have been conducted which confirmed the generation of internally resonant higher order harmonics. The theoretical guidelines enable us to characterize the global and localized material degradations using the nonlinear interaction of guided waves. A full length scanning of the material nonlinear generation has been conducted with two guided waves mode interaction in plates, which successfully identified the localized material degradation. Furthermore, a tomo-scanning algorithm has been proposed that characterizes multiple material degradation zones with nonlinear interactions of flexural waves in a pipe. Laboratory experiments are conducted that demonstrate that the nonlinear generation of guided waves are sensitive to material degradation such as plastic deformation zones and fatigue damage accumulation.