The effect of crack geometry on stiffness of spring steel cantilever beam

The survival of the crack in structures always keeps the structure away from performing well in applications due to significant changes in its dynamic response. It has been observed that in service the size of the crack in structures increases with time and finally it leads to its catastrophic failure. Hence it is crucial to do the vibration study of cracked beams in regard of free vibration-based crack detection and its crack classification. Until now the vibration-based nondestructive testing methods are applied to many spring steel cracked cantilever beams for its possible crack detection. However, the effect of various kinds of practical cracks, i.e. V-shaped, U-shaped and rectangular-shaped open cracks, on the applicability of these methods has been overlooked. In order to investigate this issue, artificially cracks are made on the cantilever beam. By free vibration analysis, the effect of crack geometry, crack depth, and crack location on the beam stiffness is investigated. In this study, the stiffness of each cracked case is computed by the deflection methods and vibration methods to ensure the strong validation. The stiffness results obtained from V-shaped, U-shaped and rectangular-shaped crack models for the same configuration are compared with each other and it is found that the results of the stiffness are comparatively more sensitive to U-shaped crack models. Through vibration study, it is found that spring steel structures are slightly sensitive to the change in crack geometries as long as the vibration characteristics are concerned. Hence, it is obvious that free vibration-based crack detection method can satisfactorily predict the location and depth of the crack in any spring steel structures irrespective of the crack geometries. Apart from this, it is also found that for the same configurations, EN 8 and EN 47 cracked cantilever beams give the identical structural integrity or structural stability property for all the cracked cases. Lastly, it is also found that as the crack depth increases by keeping the crack location constant, the stiffness of the beam decreases.