PSI - Issue 38

Michaela Zeißig et al. / Procedia Structural Integrity 38 (2022) 60–69 Zeißig, Jablonski / Structural Integrity Procedia 00 (2021) 000–000

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impact of such defects, notches or other local changes to the surrounding stress field is often assessed via the relative stress gradient . It is defined as (1) with the maximum stress ��� caused by the disturbance and rate of the stress increase expressed by d /d , see Radaj and Vormwald (2007). The locally increased stress level might lead to local plasticity and thus might consequently be the origin of fatigue failure. In the defect stress gradient approach, another form of gradient is formulated to estimate the influence of defects on the fatigue limit. The DSG is described in detail e.g. in Vincent, Nadot-Martin et al. (2014), Leopold and Nadot (2010) and Nadot et al. (2020). Among the fundamental assumptions of the approach are that crack initiation determines the fatigue limit and that defects do not interact with each other, hence are assessed independently of each other. The DSG allows for the incorporation of defect geometry, size and position via an analytical approach or finite element (FE) calculations to determine the stress level at the defect in combination with the aforementioned specific gradient. This includes volume as well as surface defects. The results may then be used to plot a synthetic Kitagawa Takahashi diagram. The DSG gradient ∇ �� � is defined in Vincent, Nadot-Martin et al. (2014) as eq M eq 0 eq M size       (2) with �� � being the fatigue equivalent stress at a point M on the defect surface. The DSG gradient thus relates the equivalent stress at the defect with the stress unaffected by the defect �� � , meaning at infinity, via the defect size. This also includes the relation between macroscopic and mesoscopic stresses. The assessment of the defect size is done via the Murakami parameter √ , the projected defect size perpendicular to the maximum principal stress, see e.g. Murakami (2002). In Vincent, Nadot-Martin et al. (2014), the fatigue equivalent stress �� � is calculated using the Crossland fatigue criterion, see Crossland (1956), however the DSG is not limited to this criterion. The DSG gradient is then used to determine a modified equivalent stress �� ∇� at the defect surface, see Vincent, Nadot-Martin et al. (2014). (3) Here, ∇ is a material parameter related to the type of defect and it is calculated using a reference defect and the corresponding fatigue limit as described in Vincent, Nadot-Martin et al. (2014). The DSG equivalent stress is assessed against a threshold value, in this case based on a material parameter of the Crossland criterion. In order to set up the DSG model, three different fatigue tests with information about the corresponding defect sizes are required. Besides conducting all three tests on material containing defects, a combination of results for defect-free and defective material may be used. For the latter approach, one test is conducted on defective material to determine a reference fatigue limit in combination with a reference defect size. The other two tests are performed on defect-free material, one under tension and one under torsion loading with R = -1, as stated in Vincent, Nadot-Martin et al. (2014). This approach is applied in the following. max         1 d d x   eq M eq M    eq M a     