PSI - Issue 37

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Yifan Li et al. / Procedia Structural Integrity 37 (2022) 41–48 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Photographs of the failed lattices for different orientations are shown in Fig. 5. Most of the micro-crack in strut initiated at the location near the joint because of the influence of local stress concentration. When the strut near the crack tip failed the macrocrack in lattice can be considered to be extending forward, and a new strut is at the tip of the macrocrack. This struct will subsequently initiate and propagate a microcrack. The macroscopic crack propagates forward to the critical length in such a cyclic process, then the specimen suddenly fractured. The crack paths of orientations X and Z lattices were almost horizontal to the initial crack. While the crack path of orientation-Y lattice was deviated from the initial crack by 30°.

Fig. 5. The fatigue crack paths of octet-truss lattices.

The relationship between stress intensity factor range (∆K) and the crack growth rate can be expressed using the empirical formula known as Paris’ law (Paris and Erdogan 1963) = ∆ (1) ∆ = − (2) where C and m are constants that depend on the material, a is crack length and N is the number of fatigue cycles. In CT specimen, the stress intensity factor range corresponding to the relative crack length can be calculated by following expression (ASTM E647-15 2015) ∆ = ∆ √ (2+ ) (1− ) 3⁄2 (0.886 + 4.64 − 13.32 2 + 14.72 3 − 5.6 4 ) (3) where relative crack length α= a / W and ∆ P is the force range. W is the width of the specimen and B is the specimen thickness. Compliance method suggested by ASTM E647-15 (2015) was used in this research to calculate the relative crack length α during test. = ⁄ = 0 + 1 + 2 2 + 3 3 + 4 4 + 5 5 (4) = {[ ] 1⁄2 + 1} −1 (5) where E is the equivalent elastic modulus of lattice which was calculated based on the relative density, ̅ , using the expression given in the literature (Deshpande et al. 2001b). v is the displacement between the measurement points and C 0 ~C 5 are the constants determined from the measuring location. The measurement location and constants C 0 ~C 5 are shown in Fig. 6 and Table. 1. As the clip gauge was installed at the specimen knife edges (V 0 ), only the constants at point V 0 was shown in the table.