PSI - Issue 33

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Riccardo Caivano et al. / Procedia Structural Integrity 33 (2021) 1095–1102 Riccardo Caivano et al./ Structural Integrity Procedia 00 (2019) 000–000

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̄ � � � ∙ �� � 12�� � √� � √� ∙ �� ���� ��� �� � �� � � � ��� (3) The term � is the component volume which is needed to properly scale up the inspected volume with respect to � . Overall, once the final volume has been set, together with the material parameters, the fatigue limit can be straightforwardly accessed by means of Eq. (3). This methodology is essentially the same as traditional stress constrained TO, also available to the commercial software HyperWorks. Therefore, the limit over the first principal alternate stress keeps into consideration the largest defect that may appear in the material to reliably design the part. HyperWorks provides the possibility to limit only the maximum first principal stress ̄ ����� and not the alternate one ̄ � as presented in TopFat [31]. Therefore, to adapt the TopFat procedure to the HyperWorks software, Eq.(4) is used to evaluate the limit in place of Eq.(3) [32]. ̄ ����� � 2 ̄ � 1 � (4) 3. Results In this Section, the results obtained adapting the TopFat procedure to HyperWorks commercial software are shown. HyperWorks allows to set the TO with a constraint over the maximum first principal stress, ̄ ����� , that is evaluated according to Eq.(4). Besides, a limit over the maximum admissible volume fraction and von Mises equivalent stress under compliance minimisation are imposed, following TopFat test cases [31]. The corbel geometry as reported in Fig.1 is employed to perform different defect-driven TO [31]. The material is supposed to be AlSi10Mg, indeed it is one of the most employed in AM metal production [33]. In Table 1, all the data related to the material properties and defect distribution, needed for the TO problem setup, are reported. � � ∙ � 1 � 2 � ��������∙�� ��

Table 1 – Values of material, defect population and fatigue modelling parameters Parameter Value AM AlSi10Mg Young modulus � � � �� [34] � � �� AM AlSi10Mg Poisson ratio [34] � ��� AM AlSi10Mg Yield limit ��� � � �� [34] ��� � 2�� AM AlSi10Mg Vickers hardness �� � [34] � � 12� Superficial defect location parameters � [30] � � 1��1 LEVD location parameter √� � � [34] √� � 1����� LEVD scale location parameter √� � � [34] √� � ����� Reference volume � � � � [34] � � ���1 Initial volume � � � � � ������ � 1���� Upper limit volume, � � � ��� ∙ �

The applied force ��� , as shown in Fig. 1, is downward with an amplitude of 600 N. It is applied on the twenty closest nodes to the indicated point in Fig. 1 so that artificial stress concentrations are avoided. This force is considered as the maximum applied force within the fatigue cyclic history load. According to the TopFat procedure [31], in the condition of R equal to zero, i.e. the applied force varies from zero to its maximum, this is the only force that is needed to be considered. The limit over the maximum first principal stress can be straightforwardly accessed by Eq.(4) as twice the limit on the alternate one. If a condition with R greater than 0 is considered, i.e. the applied minimum force ��� is not null but anyway downward, the limit on the maximum first principal stress changes accordingly to Eq. (4) but no other modifications are needed in the TO set up. Indeed, the minimum force ��� , in this case, can be considered as scaled-down from ��� . This means that the stress field would change in magnitude and not in sign. Indeed, the material portions under traction condition would remain identical. In other words, the only effect in the crack