PSI - Issue 5

U. Zerbst et al. / Procedia Structural Integrity 5 (2017) 745–752 U. Zerbst et al./ Structural Integrity Procedia 00 (2017) 000 – 000

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Note that the distinction between material and geometry effects at the right-hand side of Fig. 4 is not always straightforward. Defects such as surface roughness, secondary notches, corrosion pits and scratches can be treated in two different ways: as stress concentrators at the crack driving force side and as parts of the initial cracks with the latter way being significantly easier and frequently target-aimed as well. This has, however, not necessarily to be the case, in particular when the stress rising defect they cause is rather small, i.e., the notch is wide and shallow. Two examples of initial crack depths based on the crack arrest criterion, which have been obtained using the approach of Madia et al. (2017) are shown in Fig. 5. As can be seen, the arrest crack depth is significantly smaller for the higher strength compared to the lower strength steel, whilst only minor differences in the size of nonmetallic inclusions are stated (in both cases the average diameters were in the order of 10  m; Schork et al., 2017). As the consequence, it has to be expected that the inclusion size may substitute the arrest crack depth for higher strength steels as the initial crack size, whereas this is not the case for lower strength steels. This is in line with the observation that nonmetallic inclusions control the fatigue life of high strength steels (Murakami, 2002).

Fig. 5: Initial crack sizes and crack sizes at crack arrest of two steels of different strengths; Simulation based on the model of Madia et al. (2017).

Multiple crack propagation Whilst the fatigue limit is characterized by the transition from the arrest of all cracks to the growth of just one crack, multiple crack propagation becomes an issue at higher load levels as long as not a very large initial crack dominates. The effect is caused by a statistically varying local geometry, e.g., along the toe of a weld, and by statistically varying initial crack sizes and other material properties. Its treatment requires a stochastic approach such as illustrated in Fig. 6 (a) for the special case of the fatigue crack propagation at weld toes. Other applications would require some modification but the general principle is universal. The highly stressed region of the component (in the example the weld toe) is subdivided into equidistant sections. To each of this, a local geometry in terms of the parameters illustrated in Fig. 6 (b) is randomly assigned based on the known statistical distributions of these, and this is also realized for the initial crack size. It is assumed that each section contains a crack. Due to the locally different conditions some of the cracks will rapidly propagate whilst others grow slowly or even not at all. When the surface points of two adjacent cracks touch, crack coalescence is assumed such that the new crack length at surface refers to the sum of both individual crack lengths and the crack depth to that of the deeper crack. An example of a crack propagation analysis is provided in Fig. 7. Figs. 7 (a) and (b) show the development of the multiple cracks along the weld toe (original and graphically reproduced). Note that, in the example, small surface cracks have been made visible by annealing (black respectively white areas at the bottom surface of the plate in Figs (a) and (b)) and longer cracks by beach marking. Starting from the small surface cracks revealed by annealing, crack propagation and coalescence was simulated such as shown in Fig. 7 (c). Stochastic determination of finite fatigue life and endurance limits The principle has already been illustrated in Fig. 6 (a). Based on this scheme, a large number of random geometries is generated which forms the basis for simulating fatigue crack propagation. Note that the simulations are performed as short crack analyses until the long crack stage is reached. At this point the calculations are continued based on long crack fracture mechanics, i.e., common da/dN-  K analyses are performed. The final failure criterion can be fracture or loss of functionality. Since crack growth usually speeds up towards the end, a crack depth of half or three quarters the plate thickness might also be a criterion whereby the