A Dynamics-based Method for Crack Detection and Estimation

Presented is a dynamics-based boundary effect evaluation (BEE) method for pinpointing crack locations and estimating crack sizes using only operational deflection shapes (ODSs) measured by a scanning laser vibrometer. An ODS consists of central and boundary solutions. Central solutions are periodic functions, and boundary solutions are exponentially decaying functions due to boundary constraints. The BEE method uses a sliding-window curve-fitting technique to extract boundary solutions from an experimental ODS. Because cracks introduce localized small boundaries to a structure, boundary solutions exist around cracks as well as structural boundaries. Since crack-induced boundary solutions show characteristics different from those of actual boundaries, cracks can be easily located. A local strain energy method is derived for estimating crack sizes. In the method, the crack-induced strain energy extracted from an ODS is compared with the one calculated using stress intensity factors to determine the crack size. To verify the capability and accuracy of this BEE method, experiments are performed on six 22″ × 1″ × 0:25″ 2024-T4 aluminum beams each having a through-the-width Mode I crack at its midpoint. These cracks are slots having a width of 0:039″ and depths of 0:0625″ (25% of the beam thickness), 0:05″ (20%), 0:0375″ (15%), 0:025″ (10%), 0:0125″(5%), and 0:005″(2%), respectively. Results show that this BEE method is capable of locating and estimating small cracks.