PSI - Issue 38

Alexander Raßloff et al. / Procedia Structural Integrity 38 (2022) 4–11 A. Raßlo ff et al. / Structural Integrity Procedia 00 (2021) 000–000

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Fig. 4. (Left) Reconstructed polycrystalline simulation domain with spherical pores (blue); (right) spatial distribution of the highest Fatemi-Socie FIPs (red) in a SVE with 114 pores (blue).

2.3. Microstructure Properties and Ranking

Crystal plasticity simulations to derive fatigue indicator parameters. The Du¨sseldorf Advanced Material Simulation Kit (DAMASK) as presented by Roters et al. (2019) is used to conduct the CP simulations. Taking the crystalline structure of the material into account enables a thorough investigation of the structure-property relationships. The material of the grains is modelled by a phenomenological powerlaw constitutive equation, see Roters et al. (2019) for detailed information, assuming a hexagonal lattice. The material parameters are chosen to depict the behaviour of Ti-6Al-4V lamellae colonies and are motivated from Bridier et al. (2009); Mayeur and McDowell (2007); Zambaldi et al. (2012). The mechanical behaviour of the pores is modelled by an elastic and plastically dilatational material model proposed by Maiti and Eisenlohr (2018). For the derivation of fatigue related properties, FIPs are calculated from results of cyclic simulations. The processed quantities comprise the plastic shear strain tensor γ , the first Piola-Kirchho ff stress tensor P and the plastic velocity gradient tensor L p . Following the definition as introduced by, e.g. McDowell (2007), the local FIP fields are computed as

cyc

max 2

max 2

α

n , max P y

α

and Φ APS =

P α

∆ γ α

∆ γ α

2 3

D p : D p dt .

1 + k

Φ FS = max

Φ MPS = max

(3)

,

The Fatemi-Socie (FS) FIP Φ FS is defined as a function of the maximum range of plastic shear strain of the last cycle ∆ γ max , the maximum stress normal to the slip plane P n , max , the yield stress P y and a mediating parameter k . Φ MPS denotes the maximum plastic shear strain range (MPS) FIP and Φ APS denotes the accumulated plastic shear strain (APS) FIP. For the latter FIP, the plastic rate of the deformation tensor D p = 1 2 L + L T is used. To extract a representative fatigue property for a specific microstructure characterised by a certain statistical de scription from simulations on non-representative SVEs, an adequate data analysis is conducted. Employing an extreme value distribution approach as by, e.g. Muth et al. (2021), all FIPs from a SVE set, i.e. a set of SVEs that share the same statistical descriptors, above a certain threshold are described by a distribution function. This method is illus trated in Figure 5 at the example of structures with varying porosity. For three porosities, the real distribution of the highest FS FIPs is plotted on the left alongside a dashed line, indicating the cumulative distribution function F EVD of the fitted generalised gamma PDF. The function is defined as