PSI - Issue 53

Rainer Wagener et al. / Procedia Structural Integrity 53 (2024) 151–160 Author name / Structural Integrity Procedia 00 (2019) 000–000

158

8

, = , + , = , ′ ∙ (2 ) + ′ ∙ (2 )

with j = 1 to 3

( 4

)

Therefore, some minor modifications must be done to consider the different nature of the unity cells of Representative Structural Elements (RSE) instead of sound material. Dealing with RSE instead of infinitesimally small material volumes leads to integral values according to Wagener and Chiocca (2021). Nevertheless, it is important to correlate these black box values to the manufacturing parameters to enable the properties transfer within a numerical fatigue approach. Keeping the heterogeneous microstructures of additively manufactured parts in mind, RSE which are correlated to the exposure strategy, can be defined. Investigating additively manufactured specimens in the as-built state means investigating the Representative Structural Element’s behavior of the third order, because a decoupling of the different fatigue related features is not possible. Furthermore, it must be noticed that with increasing order of the RSE the cyclic properties are shifted to lower values, which is caused by the increasing number of considered defects and therefore by a growing difference between the true local stress and the more or less technical stress of the RSE. First, the Fatigue Life Curve, eq. 4, maybe with a modification of the Miner rule proposed by Palmgren (1924), Langer (1937) and Miner (1945) in accordance with the Miner-Modifications recommended by Cortan and Dolan (1956) Hück et al. (1988), Haibach (1970) and Zenner and Liu (1992) to optimize the consideration of cycles with smaller amplitudes within a load-time sequence, and the extended Ramberg-Osgood equation, eq. 3, are used to descript the cyclic behavior. How far transfer functions, discussed by Hell et al. (2017), are still required to consider size effects like the microstructural aspect in case of the stress-strain behavior or the statistical influences on the strain-life is still to investigate. Second, the part to investigate must be distinguished into different regions depending on the exposure strategy to consider the influences causes by up- and down-skin conditions and removed support structures. Each region must be assigned with a set of cyclic properties. Third, the load time history must be simulated path-wise that means from reversal point to reversal point to calculate the local stress-strain state with respect to the macroscopic support effect according to Neuber (1985). Fourth, to evaluate the damage contribution, damage parameters are used. Detailed overviews are given by Fatemi and Shamsaei (2011) as well as Nihei et al. (1986). Depending on the material behavior a suitable damage parameter must be chosen. At this point it is recommended, instead of performing damage contribution consideration of closed hysteresis loops, to do it for each stress-strain path, that means half cycle. Fifth, accumulate the local damage sum to modify the stress-strain behavior for the load simulation of the next load path respectively to calculate the fatigue life of the part. By using RSE of different orders, e.g., the numerical instead of unity cells of sound material, the FE-model can be simplified as demonstrated by Melz (2021) and the numerical effort drastically reduces without losing quality, because the real position and sizes of the defects is, at least at the design stage, unknown. Assumptions to consider the worst case are still assumptions and can be replaced by suitable distributions of defects. Furthermore, a part of the reduced numerical effort should be reinvested in order to optimize the simulation results, like it is suggested, with the modification of the stress-strain behavior depending on the progressing damage, to close the gap between the experimental and numerical achieved fatigue lives. 6. Conclusions Additive manufacturing enables an unforeseen freedom of design, which leads to complex component geometries. Due to the requirement of support structures to fix the part to build on the built platform and to realize overhanging regions different local microstructures and defect distributions occur. Therefore, nominal the same notch geometry can have different fatigue strength due to the influences of the manufacturing process on the local microstructure. Representative Structural Elements consider the knowledge at different stages in the design process. Within the conventional fatigue approaches a worst-case scenario is applied to the fatigue estimation. These worst-case scenarios are based on experiences and observations and maybe differ to the real part properties and application. Furthermore, in case of additively manufactured structures the fatigue relevant features are not limited to one or two, but several