Relating crack heating to vibration for vibrothermography

Vibrothermography is an inspection technique that detects cracks by observing vibration induced crack heating. Frictional crack heating in a vibrating specimen is directly linked to the resonant vibrational stress on the crack. In simple geometries we can measure the vibrational mode structure and intuit the dynamic vibrational stress field on the crack. This can be used to establish a relationship between crack heating and vibration, which will be critical for vibrothermography to be accepted as a viable inspection technology. We correlate stress to heating by exciting specimens in a well understood and repeatable resonant vibration mode. Through knowledge of the mode shape, a single point surface velocity measurement is sufficient to calculate the deformed shape of the entire specimen. The loads and stresses within the specimen are calculated from the deformed shape and used to identify the relationship between crack heating and vibration. We explore a simplified case of a bar in third order flexural resonance with a surface crack that heats in response to flexure-induced normal load. Specimens are tuned to resonate in third order flexural bending when excited with a single frequency excitation system. We present an observed relationship between dynamic normal stress, crack size, and crack heating