PSI - Issue 34

Riccardo Caivano et al. / Procedia Structural Integrity 34 (2021) 221–228 Riccardo Caivano et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction In the last few years, Additive Manufacturing (AM) technologies for metal alloys, such as Selective Laser Melting (SLM) and Electron Beam Melting (EBM), experienced significant improvements in terms of process speed, cost reduction and overall repeatability. As consequence, the use of AM technologies to manufacture structural parts in industrial applications has grown remarkably (Frazier 2014; Gibson, Rosen, and Stucker 2015; Lee et al. 2017; Yakout, Elbestawi, and Veldhuis 2018). AM permits the manufacture of components with much more shape freedom and fewer manufacturing constraints compared to traditional processes (Hällgren, Pejryd, and Ekengren 2016). With AM technologies, it is possible to produce very complex and customized parts, such as lattice structures and metamaterial cells (Benedetti et al. 2021; Wu et al. 2019). Among these possibilities, one of the greatest synergies is composed of AM and Topology Optimisation (TO) algorithms (M. P. Bendsøe and Sigmund 1999; Martin P. Bendsøe and Sigmund 2002; Ole Sigmund and Maute 2013). Indeed, TO provides the optimal but often complex material distribution which maximises the structural stiffness and minimizes mass employment (Caivano, Tridello, Codegone, et al. 2020; Caivano, Tridello, Paolino, et al. 2020; Plocher and Panesar 2019). TO algorithms can include different types of constraints to safely design optimised AM parts, such as constraints on the maximum allowable stress (Holmberg, Torstenfelt, and Klarbring 2013) or the buckling stability (Gao et al. 2020). More recently, the research community focused on developing novel fatigue-driven TO algorithms to reliably design parts in the fatigue regime as well (Chen et al. 2020; Collet, Bruggi, and Duysinx 2017; Holmberg, Torstenfelt, and Klarbring 2014; Jeong, Choi, and Yoon 2015; Oest and Lund 2017; Shyam Suresh et al. 2019, 2020; Zhang et al. 2019; Zhao et al. 2020). In general, these algorithms include the fatigue constraint as a function of the cumulative damage or related variable, based on classical fatigue theories (S. Suresh 1998), which are effective for a large number of industrial applications. However, for AM parts, even with optimized process parameters, detrimental manufacturing defects, like pores, cluster of pores and lack of fusion defects can form affecting the fatigue response and lowering the fatigue limit (Beretta and Romano 2017; Leuders et al. 2014; Romano et al. 2018; Tridello et al. 2020). Models that take into account the influence of defects, such as that proposed by Murakami (Yukitaka Murakami 2002), are therefore necessary to design AM parts. Recently the Authors proposed a defect-driven TO algorithm with proprietary code, named TopFat (Gao et al. 2021), which can reliably design optimised AM parts subjected to fatigue loads. The fatigue constraint is included in the TO formulation based on the estimated defect population according to the Murakami theory. Nevertheless, even if TopFat is a first step in evaluating the final topology including the defect population, it is not immediately extendible to the industrial applications which may require this type of safe design. For this reason, in the present paper, the TopFat procedure is implemented in the HyperWorks commercial software. The optimized topologies for literature traditional benchmarks obtained with the property code are compared with those obtained with the TopFat methodology implemented by using HyperWorks. The differences between the two topologies are highlighted and discussed, with the aim of showing that the TopFat methodology can be reliably used for the design against fatigue failures from defects even with TO algorithms implemented in commercial software. 2. Method According to the Murakami theory (Yukitaka Murakami 2002), the fatigue limit in presence of defects can be expressed as a limit over the alternate first principal stress. Eq.(1) shows the relationship between the limit on the first principal alternate stress ̄ and the material and load properties as stated in (Gao et al. 2021): ̄ = 1 ∙ ( + 120) (√ ) 1 6 ∙ ( 1 − 2 ) 0.226+ ∙10 −4 (1) where 1 is a constant parameter depending on the defect location, is the Vickers hardness of the material, is the stress ratio which is equal to the ratio between the minimum and the maximum stress during the cyclic load history and √ is the square root of the area of the defect measured in a plane perpendicular to the maximum applied stress. In Eq.(1) the limit on the first principal alternate stress ̄ is a function of the defect population, namely √ . However,