PSI - Issue 23

Krzysztof Kluger et al. / Procedia Structural Integrity 23 (2019) 89–94 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Andrea Carpinteri & Spagnoli (2001) presented a proposition based on the Gough experimental criterion in the form: √ 2 , + 2 2 , ≤ ǡ (4) wherein contrary to the Gough criterion the stress vector components are calculated in the critical plane, i.e. the maximum normal stress , over time and the shear stress amplitude , . The material parameter is calculated from the formula: = Ǥ (5) The critical plane is defined relative to the averaged directions ( 1̂ , 2̂ , 3̂ ) of principal stresses determined by the method of weight functions. The critical plane is the 1̂ − 3̂ plane rotated by the angle regarding the 2̂ axis. The angle value depends on the coefficient in the function: = 3 8 [1 − 1 2 ] Ǥ (6) Substituting the fatigue characteristics into the place of fatigue limits the following function is obtained: √ 2 , + ( ( ) ( ) ) 2 2 , − ( ) = 0 Ǥ (7) The solution of equation (7) determines the computed lifetime = , and the critical plane orientation through the angle value depends also on the number of cycles to failure. 4. Analysis and results of calculations The effectiveness of the presented models with the application of life dependent parameters has been evaluated on the basis of the life scatter band calculated at the level of confidence equal to 0.95, presented by Karolczuk et al. (2016), Krzysztof Kluger & Łagoda (2018) . The calculated value of (0.95) presents the required scatter band which included 95% of data. A lower value of the (0.95) coefficient describes a better conformity of experimental and calculated fatigue lives . However, the (0.95) coefficient value determined for the model being verified should be referred to the value of that coefficient determined for fatigue characteristics that equals to 1.41 for cyclic bending and for 1.99 for cyclic torsion (Fig 2). The number of cycles to failure was calculated with two methods: for constant material parameters (marked on graphs as (a) – classic approach) and for variable ones (marked on graphs as (b) – new approach). In the classic approach, the material constants correspond to the fatigue limit were determined from the fatigue characteristics for the reference number of cycles equal to = 2 . 10 6 . In Figs. 3 – 4 a comparison of the experimental number of cycles with the computed number of cycles is presented. In addition, in each of figures 3 – 4, the fatigue scatter band coefficients (0.95) are shown calculated separately for every type of loading and the global value computed for all types of loading. Dotted lines indicate the fatigue scatter band with value equal to 3. In Figs. 3 – 4 the percentage number of specimen under the condition < (conservative results) is also presented. The analysis of the obtained results for two models in the classic approach shows unambiguously that the application of constant material parameters based on fatigue limits is not correct when calculating the number of cycles to failure within the range beyond the reference number of cycles (2 . 10 6 cycles). Only in a small range around the reference number of cycles the results of the calculation of lifetime in the classic approach are similar to