Issue 46

M.F.M. Yunoh et alii, Frattura ed Integrità Strutturale, 46 (2018) 84-93; DOI: 10.3221/IGF-ESIS.46.09 86 selection of signals. DWT is derived from discrete CWT, and it is shown as the following expression, Purushotham et al. [8]:   /2 * 0 0 0 ( , ) ( ) , m m W m n x t a a t nb dt          (3) where a and j are the scale factor, both b and k are the position, and Ψ is the mother wavelet. Oh [9] has previously conducted fatigue data analysis using the wavelet transform (WT) for spike removal, denoising, and data editing. Piotrkowski et al. [10] used the Wavelet Transform application in acoustic emissions to detect damage and corrosion. Fatigue Life Assessment The Palmgren-Miner linear cumulative damaging rule is normally associated with the established strain-life fatigue models Sun et al., [11]. The fatigue damage caused by each cycle of repeated loading is calculated by reference to material life curves, such as S N  or N   curves. The fatigue damage caused by multiple cycles is expressed respectively as: 1 f D N          (4) i f N D N            (5) where D is fatigue damage for one cycle and D  is total fatigue damage i N is the number of cycles within a particular stress range and its mean and f N is a number of cycles. The strain-life model commonly used for the prediction of fatigue strain life is the Coffin-Manson relationship model. This model can provide a traditional prediction when there is more compressive load time history and the mean stress is zero. The following equation can define this model:     ' 2 ' 2 b c f a f f N f N E      (6) E is the material modulus of elasticity, a  is the true strain amplitude, 2 f N is the number of reversals to failure, ' f  is the fatigue strength coefficient, b is the fatigue strength exponent, ' f  is the fatigue ductility coefficient, c is the fatigue ductility exponent, m  is the mean stress, and max  is the maximum stress. The inclusion of mean stress effects in the life prediction makes the process more complex. The Morrow mean stress model is given by Dowling [12]:     ' ' ' 1 2 2 b c f m a f f f f N N E                 (7) where is the total strain amplitude, ' f  , b, ' f  and c are considered to be material properties, f N is the number of cycles to failure, and m  is the mean stress. Another strain life model dealing with mean stress effects is known as the Smith- Watson-Topper (SWT) model, and its equation is written as: 2 2 ' (2 ) ' ' (2 ) f b b c a mak f f f f N N E         (8)