# A Study on the Feasibility of Natural Frequency-Based Crack Detection
## 6 Conclusions  
Through natural frequency calculation and fracture mechanics, this study compares the crack severity causing a measurable frequency change and the crack severity reaching the onset of crack propagation or causing brittle fracture. To determine the critical state  
Figure 8: The development of critical crack length ratio as safety factor increases. when crack propagation begins or when brittle fracture occurs, stress intensity factor \(K\) is used. To employ the solution of \(K\) directly, the common fracture toughness test specimen featuring a single-edge crack is taken as the research object. The test specimen is essentially a single-edge cracked rectangular plate with the crack lying along the centreline. The test specimen can be regarded as a cracked structural component with CFCF boundaries. The situation where the test specimen is under uniform tension can be regarded as the situation where the cracked structural component is carrying a service load. The stress distribution of the loaded cracked structural component (i.e., the loaded cracked plate) is determined using the XFEM. The stress results are then substituted into the natural frequency calculation achieved by the RRM incorporating corner functions. The critical crack severity and the resulting natural frequency drop are compared directly, leading to the following findings. Whether crack detection based on natural frequency measurement is feasible depends on the 'chronological order' between the critical crack severity causing premature fracture or crack initiation and the crack severity resulting in a measurable natural frequency drop. This 'chronological order' is closely related to material properties. As the natural frequency shift also depends on the level of in-plane stress, the results were found to depend on the design safety factor as well. For structural components made of common ductile metals, natural frequency-based early crack detection is possible as these components normally possess relatively high crack tolerance. The crack severity leading to a measurable frequency drop tends to happen earlier than the severity causing the onset of crack propagation, which makes natural frequency-based early crack detection possible. The results obtained indicate that a structural component made of a common ductile metal such as 6061-T6 aluminium alloy can accommodate a relatively large crack before reaching a critical state, which makes it possible to obtain measurable natural frequency drops using the first few modes before the crack threatens the serviceability of the structural component. However, this is not the case for high-strength structural components made of brittle metals, because these components are normally designed to stand high loads with low crack tolerance. Brittle fracture may happen immediately after a small crack arises and the natural frequency drop caused by the small crack may be too subtle to measure. This is demonstrated by the numerical examples of cracked plates made of AISI 52100 alloy steel and 2014-T651 aluminium alloy. The natural frequency-based early crack detection may be inapplicable to a high-strength structural component made of metals as brittle as AISI 52100 alloy steel, however, as the brittleness of material weakens, the maximum bearable crack length increases and the possibility of early crack detection based on frequency measurement grows. Although it may not be possible to draw a broadly applicable conclusion in terms of the minimum detectable crack length based on the limited crack scenarios, this study for the first time reveals the potential of natural frequency-based early crack detection in a quantitative way. It is also worth stressing that the above conclusions address the question of whether techniques based on natural frequency measurement can be used to identify cracks in time to prevent premature failure.