Vibration modeling for vibrothermography
Vibrothermography is a nondestructive evaluation method for identifying defects such as fatigue cracks and delaminations, primarily in aerospace components. When a specimen with crack is subjected to mechanical vibrations, friction and/or adhesion hysteresis between vibrating crack faces generates heat. An infrared camera can capture this heat and identify the defect. Vibrothermography has at times, proved to be an effective method for detecting tight and short cracks that other methods may fail to detect. However, long standing issues such as lack of repeatability and incomplete understanding of physics behind crack heat generation have so far failed to instill confidence in this method for use in industry. In this research, we address the questions of how to measure and predict specimen vibration. We propose the use of viscoelastic coatings to identify specimen resonant mode shapes and map vibration distribution. We develop a numerical model for specimen vibration in vibrothermography. This is part of a larger physics based hybrid numerical/empirical model we developed at Iowa State University to predict crack heating in vibrothermography. Specimen vibration in vibrothermography is often affected by external factors like mounting and transducer coupling. We show that using compliant couplant and isolators at the contact points on specimen eliminates the effect of mounting and transducer characteristics on specimen resonances and makes the specimen vibration more repeatable. In addition, we show that isolators act as absorptive springs in parallel to the specimen and increase the effective specimen stiffness and in turn, the resonance frequency. We characterize the couplant and isolators with the use of simplified electrical circuits and explain their effect on specimen vibration based on analogous electrical circuit principles. Based on these observations, we develop a linear vibration model for vibrothermography. We also develop a linear inversion process to quantify isolator and couplant damping. Finally, we validate the vibration model against physical and simulation experiments. Our empirical model for vibrothermography describes crack heat intensity as a function of specimen vibration and other crack related parameters. Crack heat intensity is therefore one of the required input parameters to the model. We propose an inversion process to estimate heat intensity from the measured crack surface heating. Normally, direct inversion of measured surface heating is an ill-posed problem because of the diffusion. However, we make certain assumptions with in the scope of which, the inversion process is tractable and is capable of accurately reconstructing the measured heating.