Toward a Viable Strategy for Estimating Vibrothermographic Probability of Detection

Vibrothermography is a technique for finding cracks and delaminations through infrared imaging of vibration-induced heating. While vibrothermography has shown remarkable promise, it has been plagued by persistent questions about its reproducibility and reliability. Fundamentally, the crack heating is caused by the vibration, and therefore to understand the heating process we must first understand the vibration process. We lay out the problem and begin the first steps toward relating detectability to the local motion around a crack as well as the crack size. A particular mode, the third-order free-free flexural resonance, turns out to be particularly insensitive to the presence of clamping and transducer contact. When this mode is excited in a simple bar geometry the motions of the part follow theoretical calculations quite closely, and a single point laser vibrometer measurement is sufficient to evaluate the motion everywhere. Simple calculations estimate stress and strain anywhere in the bar, and these can then be related to observed crack heating.