PSI - Issue 2_A

Mohamed Sadek et al. / Procedia Structural Integrity 2 (2016) 1164–1172 M. Sadek, J. Bergström, N. Hallbäck and C. Burman/ Structural Integrity Procedia 00 (2016) 000–000

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The results from the “Pull and release” -method confirm the approach where the effective natural frequency is calculated using Eq. (1), Chati et. al. (1997). However, the frequency still drops at a too high rate with respect to the crack length. Finally, including the whole load train (specimen+horn+oscillator) and applying a FEM half symmetry model corrected the rate under which the frequency dropped closer to the experimentally measured frequencies. 3.2. Fatigue crack growth rates The ΔK values achieved from the different approaches are plotted in Fig. 3. The most noticeable is the difference between static and dynamic simulations. The stress intensities obtained by the static simulations are approximately 30% lower than the ones achieved by the dynamic simulations. The use of the crack length specific frequencies and including the whole load train slightly increased the ΔK values at longer crack lengths and smoothened out the curve. Then, the dynamic Δ K vs a results including the whole load train were used to obtain the values of the calculated geometry function for the pre-selected crack lengths and fitted to a 4 th grade polynomial expression. Thus, the geometry function f(a/w) was derived; By using the geometry function and the calibration parameters of the ultrasonic instrument the controlled ΔK testing is performed. The calibrated ΔK values using Eqs. (2) and (4), are presented in Fig. 3 and includes the crack length of the un-cracked specimen (a = 1 mm). The experimental crack growth results from testing the 38MnSi5V-steel are presented in Fig. 4(a). The initial ΔK-decreasing testing produces decreasing crack growth rates towards the turning point where the growth rate reached the threshold level, and when turning into the ΔK-increasing stage the cracks grow at higher rate than in the prior ΔK-decreasing stage. The results were fitted to the crack growth expression in Eq. (3), and the parameters C and n were estimated to 10 -11 m/cycle and 2,86, respectively. In order to underline the differences obtained using the static ΔK computation, conventionally used, and the full dynamic ΔK computation obtained in the present paper, the static and dynamic da/dN vs Δ K evaluation of the experimental results are presented in Fig. 4(b). Obviously, the selection of analysis method will significantly affect the evaluation of crack growth rates and threshold values. The vertical lines indicate the threshold value (  K th ) representing the lowest stress intensity range required for crack growth. 3,0046( / ) 1,3693( / ) 0,034 ( / ) 6,0932( / ) 7,1881( / ) 2 3 4       a w a w a w a w f a w (4)

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Dynamic "a"-depended frequency - incl. oscillator and horn Calibrated ΔK

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Fig. 3. Different methods of calculating the stress intensity factor dependence on the crack length numerically.