PSI - Issue 42

Matěj Mžourek et al. / Procedia Structural Integrity 42 (2022) 457 – 464 Matěj Mžourek / Structural Integrity Procedia 00 (2019) 000 – 000

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A typical approach towards quantifying the influence of the critical volume is given by the formula: ,1 ,2 = ( 2 1 ) which originates from the Weibull distribution – see Tomaszewski (2014). The value of the m parameter should lie in the <0;1> interval and quantifies the sensitivity of the material to the size effect. The σ FS,i and V i are the fatigue strength and critical volume of specimen i , respectively. If the m parameter should remain constant across the examined fatigue life domain, the model shifts the entire S-N curve vertically without modifying the original slope. A common approach towards determining the values of the critical volumes V i is given by the condition: ≥ · (2) A sub-volume of a specimen is considered critical when stress σ in this sub-volume is not less than a threshold value. This threshold value is equal to n · σ max , where σ max is the largest value of stress present in the loaded specimen, and n is a value in the <0;1> interval. In the presented paper, the axial stress σ y is used as the stress metric for the analysis. The value of n is typically chosen arbitrarily, and typical numbers used in engineering (0.8 – 0.9 – 0.95 – 0.98 – 0.99) can be encountered, see Ai et al. (2019). In this paper, this value is found through regression analysis. The concept is visualized in Fig. 1. a) on an axially-symmetrical hourglass specimen. Specimens in the experimental campaign dealt with in this paper have displayed cracks that initiate near the surface. It could thus be argued that the volume farther from the surface, even if loaded to the same degree as the volume near the surface, should have a lesser impact on the decrease of fatigue strength due to the size effect, see also Murakami et al. (2019). Two other models are thus employed to account for this expectation – a surface area based model, and a second volumetric model utilizing the critical depth h crit parameter. Surface area-based approaches are not uncommon, see Mäde et al. (2018) or Schmitz et al. (2013). The surface area-based model utilizes the stress condition (2), but the surface areas A i of the critically loaded regions are used in Eq. (1) instead of the volumes V i . The second volumetric model introduces the critical depth h crit parameter, which defines a border below the surface outside of which the loaded volume is not considered to be critical. This geometrical and the stress threshold criterion (2) must be both fulfilled for a region to be considered critical. This concept is visualized in Fig. 1. b). Volumes V i obtained this way are used in Eq. (2) to obtain fatigue strengths σ FS,i . Using solely the n parameter and using the n parameter along the h crit parameter to obtain critical volumes will be referred to as the V-model and V*-model , respectively. The surface area model will be further referenced to in this paper as the A-model . (1)

Fig. 1. (a) Critical volume concept based on the n parameter; (b) Critical volume concept with the additional h crit parameter