Influence of surface roughness on the measurement of acoustic nonlinearity parameter of solids using contact piezoelectric transducers.

The current article reports on the experimental study of the influence of surface roughness on the measurement of the acoustic nonlinearity parameter. The nonlinearity parameter was measured using contact piezoelectric transducers, which were calibrated using the reciprocity based technique. Aluminum and steel samples were chosen to study the influence of hardness of the sample on the measurement of the nonlinearity parameter. While, lower Ra value (average asperity height) aluminum samples were more susceptible to surface deformation and scratches from coupling the transducer to the sample, the same could not be observed for steel samples. Results demonstrate a large variation in nonlinearity parameter for aluminum (∼35%) compared to steel (∼2%) between two consecutive experiments, suggesting flattening of asperities after the first experiment. Experiments were also performed with 3 different setup configurations; (1) receiver and transmitter on rough sides, (2) receiver on smooth and transmitter on rough side and (3) receiver on rough and transmitter on smooth side. Results show that least variation in the measured nonlinearity parameter was observed when the receiver was placed on the smooth side, and a 10% variation was observed between the three setup configurations. Finally, a comparison of relative nonlinearity parameter calculated using current or voltage ratio and absolute nonlinearity parameter showed large discrepancies. Conclusions were drawn from the experimental observations.

Receiver calibration and the nonlinearity parameter measurement of thick solid samples with diffraction and attenuation corrections.

This paper presents analytical and experimental techniques for accurate determination of the nonlinearity parameter (ß) in thick solid samples. When piezoelectric transducers are used for ß measurements, the receiver calibration is required to determine the transfer function from which the absolute displacement can be calculated. The measured fundamental and second harmonic displacement amplitudes should be modified to account for beam diffraction and material absorption. All these issues are addressed in this study and the proposed technique is validated through the ß measurements of thick solid samples. A simplified self-reciprocity calibration procedure for a broadband receiver is described. The diffraction and attenuation corrections for the fundamental and second harmonics are explicitly derived. Aluminum alloy samples in five different thicknesses (4, 6, 8, 10, 12cm) are prepared and ß measurements are made using the finite amplitude, through-transmission method. The effects of diffraction and attenuation corrections on ß measurements are systematically investigated. When diffraction and attenuation corrections are all properly made, the variation of ß between different thickness samples is found to be less than 3.2%.

Determination of acoustic nonlinearity parameter (ß) using nonlinear resonance ultrasound spectroscopy: Theory and experiment.

The present article investigates the possibility of using nonlinear resonance ultrasound spectroscopy to determine the acoustic nonlinearity parameter (ß) and third order elastic constant by developing an inverse problem. A theoretical framework was developed for nonlinear forced vibration of a cantilever beam using material nonlinearity (stress-strain nonlinearity). The resulting nonlinear equation was solved using method of multiple time scales to obtain the nonlinear frequency shifts. The present works focuses only on classical nonlinearity and, therefore, a diverse group of intact, classic nonlinear materials were chosen. The samples were tested using nonlinear resonance ultrasound spectroscopy, and the developed theory was used to invert the experimental frequency shifts to obtain the nonlinearity parameters. The third order elastic constants and ß were calculated using their analytical relationship with the nonlinearity parameter. The experimentally determined C111 and ß values for all various materials agree well with literature values. In addition to determining ß, determination of the sign, or phase of ß was also explored theoretically and experimentally.

Influence of laminate sequence and fabric type on the inherent acoustic nonlinearity in carbon fiber reinforced composites.

This paper presents the study of influence of laminate sequence and fabric type on the baseline acoustic nonlinearity of fiber-reinforced composites. Nonlinear elastic wave techniques are increasingly becoming popular in detecting damage in composite materials. It was earlier observed by the authors that the non-classical nonlinear response of fiber-reinforced composite is influenced by the fiber orientation [Chakrapani, Barnard, and Dayal, J. Acoust. Soc. Am. 137(2), 617-624 (2015)]. The current study expands this effort to investigate the effect of laminate sequence and fabric type on the non-classical nonlinear response. Two hypotheses were developed using the previous results, and the theory of interlaminar stresses to investigate the influence of laminate sequence and fabric type. Each hypothesis was tested by capturing the nonlinear response by performing nonlinear resonance spectroscopy and measuring frequency shifts, loss factors, and higher harmonics. It was observed that the laminate sequence can either increase or decrease the nonlinear response based on the stacking sequence. Similarly, tests were performed to compare unidirectional fabric and woven fabric and it was observed that woven fabric exhibited a lower nonlinear response compared to the unidirectional fabric. Conjectures based on the matrix properties and interlaminar stresses were used in an attempt to explain the observed nonlinear responses for different configurations.

Finite element simulation of core inspection in helicopter rotor blades using guided waves.

This paper extends the work presented earlier on inspection of helicopter rotor blades using guided Lamb modes by focusing on inspecting the spar-core bond. In particular, this research focuses on structures which employ high stiffness, high density core materials. Wave propagation in such structures deviate from the generic Lamb wave propagation in sandwich panels. To understand the various mode conversions, finite element models of a generalized helicopter rotor blade were created and subjected to transient analysis using a commercial finite element code; ANSYS. Numerical simulations showed that a Lamb wave excited in the spar section of the blade gets converted into Rayleigh wave which travels across the spar-core section and mode converts back into Lamb wave. Dispersion of Rayleigh waves in multi-layered half-space was also explored. Damage was modeled in the form of a notch in the core section to simulate a cracked core, and delamination was modeled between the spar and core material to simulate spar-core disbond. Mode conversions under these damaged conditions were examined numerically. The numerical models help in assessing the difficulty of using nondestructive evaluation for complex structures and also highlight the physics behind the mode conversions which occur at various discontinuities.

Influence of fiber orientation on the inherent acoustic nonlinearity in carbon fiber reinforced composites.

This paper presents the study of non-classical nonlinear response of fiber-reinforced composites. Nonlinear elastic wave methods such as nonlinear resonant ultrasound spectroscopy (NRUS) and nonlinear wave modulation spectroscopy have been used earlier to detect damages in several materials. It was observed that applying these techniques to composites materials becomes difficult due to the significant inherent baseline nonlinearity. Understanding the non-classical nonlinear nature of the composites plays a vital role in implementing nonlinear acoustic techniques for material characterization as well as qualitative nondestructive testing of composites. Since fiber reinforced composites are orthotropic in nature, the baseline response variation with fiber orientation is very important. This work explores the nature of the inherent nonlinearity by performing nonlinear resonant spectroscopy (NRS) in intact unidirectional carbon/epoxy samples with different fiber orientations with respect to major axis of the sample. Factors such as frequency shifts, modal damping ratio, and higher harmonics were analyzed to explore the non-classical nonlinear nature of these materials. Conclusions were drawn based on the experimental observations.

Nondestructive evaluation of helicopter rotor blades using guided Lamb modes.

This paper presents an application for turning and direct modes in a complex composite laminate structure. The propagation and interaction of turning modes and fundamental Lamb modes are investigated in the skin, spar and web sections of a helicopter rotor blade. Finite element models were used to understand the various mode conversions at geometric discontinuities such as web-spar joints. Experimental investigation was carried out with the help of air coupled ultrasonic transducers. The turning and direct modes were confirmed with the help of particle displacements and velocities. Experimental B-Scans were performed on damaged and undamaged samples for qualitative and quantitative assessment of the structure. A strong correlation between the numerical and experimental results was observed and reported.

Fabrication and comparison of PMN-PT single crystal, PZT and PZT-based 1-3 composite ultrasonic transducers for NDE applications.

This paper describes fabrication and comparison of PMN-PT single crystal, PZT, and PZT-based 1-3 composite ultrasonic transducers for NDE applications. As a front matching layer between test material (Austenite stainless steel, SUS316) and piezoelectric materials, alumina ceramics was selected. The appropriate acoustic impedance of the backing materials for each transducer was determined based on the results of KLM model simulation. Prototype ultrasonic transducers with the center frequencies of approximately 2.25 and 5MHz for contact measurement were fabricated and compared to each other. The PMN-PT single crystal ultrasonic transducer shows considerably improved performance in sensitivity over the PZT and PZT-based 1-3 composite ultrasonic transducers.