PSI - Issue 23

A. Karolczuk et al. / Procedia Structural Integrity 23 (2019) 69–76 A.Karolczuk, J. Papuga/ Structural Integrity Procedia 00 (2019) 000 – 000

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defined as a 20% drop in the stiffness of the specimen under the applied loading. The fatigue characteristics and the experimental data for combined loading along with experimental points and confidence bands are presented in Fig. 1 and Fig. 2, respectively. Basquin line regression analysis was run under the assumption that only the data items following the linear trend in the log-log stress-life space can be included in it. Some of the data points under reversed plane bending (Fig. 1) and under proportional bending-torsion ( ⁄ = 0 . 33 – Fig. 2) were therefore not included in the regression; these data points can be distinguished by other marks. These graphs show that the transition to the fatigue limit region occurs around 300 000 cycles in the bending load case. The use of the same Basquin curve beyond this number of cycles would not be correct. The subsequent analysis of the two different variants of the Matake method described in the next section is therefore performed only on data points with shorter fatigue lives.

Fig. 1. Fatigue characteristics under fully-reversed plane bending and torsion loading for the tested aluminium alloy.

Fig. 2. Fatigue data obtained under proportional bending and under torsion loading for two stress ratios τ a σ a =0.33 ⁄ and τ a σ a =1.00 ⁄ . 4. Results and discussion The damage model based on the Matake criterion was applied: (1) with the constant parameter estimated from the fatigue characteristics at 3 ·10 5 cycles; (2) with the life-dependent ( ) parameter. The experimental and calculated fatigue lives are presented in Fig. 3. The dotted lines in Fig. 3 represent the uniform scatter band of factor 3.0. For an evaluation of the constant and life-dependent parameter concepts while applying the Matake criterion, the factor of the uniform scatter band of fatigue life (0.95) at a confidence level of 95% was calculated for each type of loading (presented in the legends in Fig. 3), and also for all load cases together (see the top left corner of the graphs in Fig. 3). Additionally, the percentages of conservative results ( < ) are presented in Fig. 3. The calculated results obtained with the assumed constant parameter (Fig.3a) coincide with the experimental results within the experimental scatter band only for torsion loading. Since the parameter was determined for 3 ·1 0 5 cycles, the calculated fatigue lives for loading other than pure torsion tend to shift away from the experimental lives for fatigue lives other than 3 ·10 5 cycles. This dispersion is related to the ratio of the S-N curve slopes. For the aluminum alloy that was tested, the following slope values are found: 8.06 under torsion and 4.59 under bending (see