PSI - Issue 42

Martin Matušů et al. / Procedia Structural Integrity 42 (2022) 102 – 109 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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the output clearer. This bilinear evolution can be explained by the existence of plastic deformations that are not leading to a failure (are non-damaging, see Klesnil and Lukáš (1992) ) below  FL . The existence of microplastic deformation below  FL is also presented by Munier et al. (2017). Although this visual method provides good results in certain cases, it is not unbiased; see the case in Fig. 5b, where it is obvious that several points on the right-hand side of the plot are strongly affecting the position of the detected fatigue limit. A more robust method based on the Gumbel distribution function is proposed by Fernández-Canteli et al. (2012). The issue of the method, which the authors of this paper found when testing it on the data presented here, is that the detected fatigue limit is affected by the selection of the lowest stress levels. The method evaluated in this paper is based on the work of Huang et al. (2017) who proposed three different methods to describe the transition from one regime to the other. The first solution fitted a bilinear model with the largest angle between the two linear segments. The second method was based on the highest difference between two consecutive levels of stress amplitude. The third method which is used in this paper is based on minimizing the curvature radius of  T s -  evolution; see Fig. 5b.

Fig. 5. a) Illustration of bilinear evolution within  FL estimation. b) Scheme for finding the minimal radius of curvature to approximate  FL .

No stable  T s temperature differences occurred in the experiments described in this paper, thus the temperature growth rates were used in the first two phases of the temperature evolution; see Fig. 4. Previously, the parameter R 0 was used to estimate the S-N curve of fully reversed bending of a plate by Khonsari and Amiri (2010). The R s parameter was used for analyzing the behavior of pure copper specimens under cyclic loading by Wang et al. (2017). Huang et al. (2017) conducted their analyses for experiments with ∆ T s measured on a single specimen with a subsequential increase in the amplitude of stress. In this paper, the results of multiple specimens tested till their failure were the input, and the transition from ∆ T s to R 0 or R s was evaluated. In practice, the R 0 parameter would be convenient to use. There would be no need to wait for stabilized temperatures in the testing blocks of a multiple-step experiment. Shortening of each step would lead to lower damage induced at each stress level, and more points to define the S-H curve could be obtained from a single specimen. The trend of the measured data points was approximated with the exponential function:



b r   = =  a FL a e

y

(2)

In the formula, r represents both R 0 and R s in two separate approximations and y represents an amplitude of stress   relative to  FL . The radius of curvature is calculated: ( ) ( ) 3 2 2 1 1 f r y y = + (3)

where y is the exponential function from Eq. (2). The minimal curvature radius was found by setting the derivation