A Study on the Feasibility of Natural Frequency-Based Crack Detection

Owing to the long-standing statement that natural frequency-based crack detection is not sensitive enough to localised damage to identify small cracks, many natural frequency-based crack detection methods are validated by detecting cracks of moderate size. However, a direct comparison between the crack severity causing a measurable natural frequency change and the crack severity reaching the initiation of crack propagation or leading to brittle fracture is constantly ignored. Without this understanding, it is debatable whether the presented crack detection methods are feasible in practical situations. Through natural frequency calculation and linear elastic fracture mechanics, this study is dedicated to filling the above gap in knowledge. To directly utilize the solution of stress intensity factor, common fracture toughness test specimens featuring a single-edge crack are used. These specimens are essentially cracked rectangular plates under uniform uniaxial tension. Considering the stress resultants obtained via the extended finite element method, the natural frequency of the loaded cracked plates is calculated using the Rayleigh–Ritz method incorporating corner functions. In addition, assuming the specimens as structural components under remote uniform tension, the development of critical load versus crack length is derived based on the solution of the stress intensity factor. Thus, critical crack lengths corresponding to a series of safety factors are obtained by equating service load with critical load. After obtaining natural frequencies of the cracked plates with critical crack lengths, the natural frequency drop caused by a critical crack can be computed. Hence, the critical crack length can be compared with the crack length when the frequency drop is measurable. It is found that the brittleness of the employed metals plays a vital role in the feasibility of natural frequency-based crack detection.