PSI - Issue 28

Fuzuli Ağrı Akçay et al. / Procedia Structural Integrity 28 (2020) 1399– 1406 Author name / Structural Integrity Procedia 00 (2019) 000–000

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Fig. 2. Free body diagram of the analytical model.

3.1. Cubic Vertex Centroid (CVC) Configuration Cubic vertex centroid model is based on 8-beam model. Hence, the balance between virtual work and the absorbed work (at collapse) in the plastic hinge yields � � � � � 4 � �� � (1) where represents total (applied) load, Δ displacement of a beam, � full plastic moment, length of a beam in half-cube model, and � angle between a strut and the horizontal plane. (length of a beam), which equals half the strut length in half-cube model, and cos � can be determined as √3⁄4 and √2⁄√3 , respectively where represents the size of a cell in each direction. Also, full plastic moment of a circular cross section is given as �4⁄3� � � , where � is yield strength and is the radius of a strut. Substituting these expressions into Eq. (1) yields a collapse load of � � ��� � � � ��√� ��� � � (2) The strength can be obtained by dividing the force over area. Substitution of Eq. (2) into Eq. (1) yields the strength of a cubic vertex centroid lattice � � �√� � � � � � � � � � � � � � � (3) Moreover, total area occupied by the struts over the volume provides the relative density of the lattice � � 1�√3 � � � � � (4) The ratio between the lattice strength and the yield strength equals to 1.5 �� power of the relative density, i.e., � � ⁄ � � �.� , which is consistent with the experimental results. Analytical results along with the experimental results are presented in Table 2. Experimental strengths were determined by dividing the compression load-displacement data over the cross-sectional footprint area of the micro lattices and the initial dimension of the specimens (Yu et al., 2019). A yield strength of σ � �4�� MPa is utilized in analytical determinations as this value corresponds to compressive strength of bulk AlSi10Mg alloy. As can be seen from the table, the maximum absolute relative error in analytical results is on the order of 20%, which is reasonable.