PSI - Issue 28

Yifan Li et al. / Procedia Structural Integrity 28 (2020) 1148–1159 Author name / Structural Integrity Procedia 00 (2019) 000–000

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4

�� ∙ � � � �� � � �� ∙ � � ∙ �� � � � �� � � ��

(2)

(3)

The equivalent reversible load-life curve (F ar – N curve) equation can be expressed as: �� � � � ��� � � � (4) where c is the fatigue load exponent and � � is the fatigue load coefficient (the sign of c is negative). If we know the parameters � � and c in the Eq. (4), which are material-dependent, then the fatigue endurance under a specific load amplitude can be calculated using the Eq. (4). The propagation of a macro-crack in a lattice is the result of a sequence of individual strut fatigue failures. Although the individual strut adjacent to the crack tip will bear the most loading, damage accumulation in the struts not adjacent to the crack tip also needs to be accounted for. The fatigue damage accumulation of aluminium alloy can be described by Miner’s rule (Miner 1945; Carvalho et al. 2010), and the formula can be expressed as ∑ � � � �� � � � (5) where i is the order of the specific load applied to the strut, N i is the number of cycles at a certain force and N if is the number of cycles to failure. The numbers of cycles for the struts to fail are summed to predict the lattice’s fatigue lifetime. A strut will break when the accumulation of damage in Eq. (5) is equal to 1. In this research, the fatigue lives of individual struts in lattice plates will be predicted using the fatigue test data from single struts cut from the lattice. This approach can be described in the following steps: (1) Perform fatigue tests on single struts cut from lattice plates to obtain the equivalent reversed load-life curve and the load related Eq. (4) of struts under cyclic load. (2) Using finite element analysis, determine the cross-sectional cyclic force in the strut ahead of the crack tip in lattice and the cyclic forces in struts in the crack path under a specific loading condition. Then, use the load-life curve with Eq. (4) for single struts to calculate the fatigue life of related individual struts. (3) Considering cumulative damage caused by any prior loading and using Miner’s rule, calculate the accumulated damage for the struts ahead of the crack tip. (4) In the finite element analysis, delete the failed strut near crack tip and extend the macro-crack, then repeat steps (2) to (4) until lattice plate failure 3. Materials and experimental procedures 3.1. Sample preparation Waterjet cutting was chosen to manufacture 2D aluminium triangular lattice plates. This method ensures that the temperature of material does not increase during the manufacturing procedure, which would cause distortion of the struts and non-uniformity in their material properties. All plates were cut from a 2 mm thick aluminium alloy 1050A sheet, and its design drawing is shown in Fig. 3. Enough cells are present in all directions to avoid the size effect in lattice structures (Gu et al. 2018), which can also ensure sufficient crack fatigue propagation path. While, because of the influences of particle size and impinging angle, rough surface and inconstant width of struts in lattice plates were caused during the processing. The lattice plates were scanned to measure the real size of single struts. The strut mean effective length is ̅ =8.5mm and mean width is t = 1.1 mm, and it has smooth lattice corners with a fillet radius of about ̅ = 0.45 mm. Fig. 4 shows the details of struts manufactured by waterjet cutting.