# Microcrack Detection Using Spectral Response Data Alone
## 1 Introduction  
Crack-free manufacturing is very difficult to achieve in mechanical industries. In fact, cracks occur inevitably on the surface of processed materials or products during plastic deformation. In particular, several microcracks can be observed during cold-forming because the deformation resistance of raw materials may be considerably higher than that during hot-forming. Inspectors performing quality inspections of the surface of a cold-formed material subjected to plastic deformation must determine the depth of microcracks on the product. The identified microcrack depth and its reliability often depend strongly on the resolution of the applied nondestructive testing method.  
Many nondestructive testing methods are available for crack detection, including acoustic emission sensor [1; 2], fiber optic sensor [3; 4], and Lamb wave excitation [5; 6]. However, only a few methods are available for inspecting microcracks with depths of 100-200 \(\upmu\)m, and most of these require expensive inspection equipment. All detections or measurements were based on a small variation of the target system during the creation of a micro-depth crack [7; 8; 9; 10]. Surface inspections using an eddy current sensor are currently applied widely in mechanical industries because they offer low costs and short inspection times. However, the minimum microcrack depth that can be detected exceeds 200 \(\upmu\)m; microcracks shorter than 200 \(\upmu\)m cannot be detected. Based on a theoretical model for a basic structure such as beam, one study investigated the changes in dynamic characteristics depending on whether or not a microcrack is produced [10], and another investigatedthe frequency response characteristics by analyzing the sideband frequency near the co-vibration point in a cracked structure when applying a Lamb wave signal [6]. The high sensitivity of a frequency response function (FRF) to crack initiation can be used to inspect microcracks in a mechanical system [8]. The FRF has been used frequently to identify the dynamic behavior of a linear system and to extract the modal parameters, eigenvalue, and mode shape in the frequency domain [11; 12]. FRFs can be measured by simply using an impact hammer or a modal exciter with low experimental cost compared to those of other nondestructive microcrack detection methods. A previous study detected microcracks experimentally by using the coherence function from measured FRFs in a mechanical component [13]. However, it could not be applied to practical problems because the signal processing to calculate the FRF between the input force data and the response data for the target mechanical components had to be conducted before judging the microcrack. In the present study, the feasibility of detecting microcracks from the response data alone was determined using a simple mechanical specimen subjected to a controlled input force produced using an impact hammer. The input force was controlled effectively as in Charpy impact tests [14; 15], and both the spectral responses and the FRFs were calculated experimentally for two simple specimens with and without 200 \(\upmu\)m microcracks. By using the coherence function, the dynamic variation near the resonance frequency of a simple specimen could be detected for different response data locations. Microcracks could be detected successfully near the resonance frequency zone using both the spectral responses and the FRF; therefore, the microcrack depth could be predicted if the impact force could be controlled. Because crack detection using spectral response data alone is simpler than that using FRFs, the newly proposed method may be more effective for a practical inspection solution.