PSI - Issue 28

Kaveh Samadian et al. / Procedia Structural Integrity 28 (2020) 1846–1855 K. Samadian & W. De Waele/ Structural Integrity Procedia 00 (2019) 000–000

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2. Extraction of stress concentration factor from surface waviness The effects of surface waviness are often considered in terms of a stress concentration similar to the notch effect. The stress concentration factor is defined as the ratio of the maximum stress at the notch, denoted a ‘valley’ in the case of surface waviness, and the nominal applied stress. To calculate the stress concentration factor, a 2D finite element (FE) model has been employed in this work. To build the geometrical model, first a white light interferometer has been used to measure the surface profile of a WAAM component (see Fig.1-a). The measurement data consists of multiple lines of two dimensional coordinates. The x coordinate is the position along the length of the specimen and the y coordinate quantifies the height of the surface irregularities. The mesh size of the numerical model was set to be 0.01 mm, following a convergence study. To reduce computation time, the model is divided into three regions of which only the top region (surface) has a very fine 0.01 mm mesh size. The other regions gradually reduce in mesh size, as can be seen in Fig.1-b. The following boundary conditions are used: at one vertical edge all nodes are fixed and symmetrical conditions apply at the bottom horizontal edge. Load is introduced as uniform stress at the opposite vertical edge. Using the stress output of the FE model, the stress concentration factor at the valleys is calculated using the “Theory of Critical Distances” developed by Taylor (2008). The stress averaged over a semi-circular area with radius 0.1 mm at the bottom of each valley is used. It is insufficient to only derive the maximum stress at one element at the critical valley, since this single value might be significantly affected by the finite element mesh size. For each valley the stress concentration factor is calculated as the ratio of the averaged stress to the nominal stress and the maximum ratio is defined as which will be used in the analytical framework for fatigue crack growth calculations.

As shown by Suraratchai et al. (2008) an inverse relationship between the stress concentration factor and the plain fatigue limit of the material exists. Therefore, the plain fatigue limit of a wavy surface ( �� ) scales inversely with compared to the plain fatigue limit of a smooth machined surface ( � ). Figure 1: a) Surface profile of a WAAM component measured by white light interferometry, b) FE model of the as-built surface.