ON QUANTIFYING DETECTABLE FATIGUE CRACK SIZE IN ALUMINUM BEAMS USING VIBRATION AND IMPEDANCE-BASED METHODS

摘要

This paper looks at the impedance-based and vibration methods used for the structural health monitoring (SHM) of aluminum beams and attempts to quantify the smallest fatigue crack size that is detectable by these two methods. The vibration-based method presented in this paper, uses the recent model of Aydin [1] which is based on a simple Euler-Bernoulli beam model. This method treats cracks as localized reduction in the beam's stiffness and models them as massless rotational springs at the locations of the cracks. The beam is then considered to be of multiple sections connected by these springs. The beam studied in the present work is assumed to be an aluminum, uniform, Euler-Bernoulli beam having a single fatigue crack and being axially loaded. It is further assumed that frequencies can only be measured to within half a Hertz. This results in formulas that can be used to predict specific detectable sizes of fatigue cracks given specific geometry of the beam. For example for a beam of dimension 240x19.1x4.8 mm, it is found that the fatigue crack must be approximately 12.5% of the beam width in order to induce a frequency shift of 0.5 Hz. In the second part of this paper, different sets of experiments are conducted on aluminum beams. First, saw-cuts are made in the beams and the resultant shift in the beams' natural frequency is examined to find the minimum detectable cut length. In order to improve this minimum detectable damage size, the beat frequency method is applied, which enhances the minimum detectable frequency shift. These results are then compared to those of the electrical impedance measurements through the HP 4194A Impedance analyzer. At the end, the aluminum beams are being fatigued and by measuring their electrical impedance at different numbers of fatigue cycling, their detectable fatigue crack size is investigated.