PSI - Issue 33

1100 Riccardo Caivano et al. / Procedia Structural Integrity 33 (2021) 1095–1102 Riccardo Caivano et al./ Structural Integrity Procedia 00 (2019) 000–000 Similarly, considering a stress ratio R of -0.5, the Murakami limit is evaluated as 144 MPa. In this case, the minimum force is equal to half - ��� . Again, the final topology results to be structurally safe and all the constraints are satisfied, as shown in Fig. 3b. Considering R equal to 0 and 0.1, the Murakami limits are 196 MPa and 213 MPa respectively. In both conditions, a single load case with ��� downwards is applied. The final topologies, in Fig. 3b and 3c, are almost identical since the stress limits are quite high and the convergence with the minimum compliance with a volume fraction of 30% is achieved. It is worth noting that all the topologies shown in Fig. 3 are obtained with the command ‘Iso’ within the HyperWorks output environment with a value set to 0.35. It discards all the elements whose intermediate density is below this imposed value to obtain a clearer final topology. As an explicative example, the first principal stress � in the final topology obtained with R equal to -1 is reported in Fig. 4. The tensile zones are completely different in the two load cases, stating the need for the two different loading conditions. For more, the maximum first principal stress is below the prescribed limit, ensuring the fatigue structural safety in presence of defects. 6

� [MPa]

a) Load case 1

b) Load case 2

R=-1

Fig. 4 – Frist principal stress � distribution in final topology with stress R = -1 a) Load case 1, ��� downwards; b) Load case 2, ��� � � ��� upwards. 4. Conclusion In the present paper, a methodology that permits to design of components against fatigue failures originating from defects with the topology optimisation (TO) algorithm included in the commercial software HyperWorks has been proposed. First, the analytical definition to derive the defect driven stress to constrain has been detailed. Thereafter, the procedure to considered variable stress ratios is highlighted. Finally, a complete benchmark on the classical corbel structure is carried out. The results show that the final topology is reliably designed both in the static and in fatigue regime including the process-induced defect population. To conclude, the present paper contains the guidelines for a safe design of components with the TO algorithm implemented in commercial software and by taking into account the detrimental influence of manufacturing defects on the fatigue response, thus permitting for reliable employment of AM parts in critical structural applications which are currently not considered.