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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same as experiment, and the effective elastic properties of lattice material is related to the parent material and topology. The effective Young’s modulus and Poisson’s ratio of the lattice plate can be calculated using (Lipperman et al. 2007): � � �√3 � ��� �� ��� �� � (12) � � ��� �� ��� �� (13) � � � � (14) where E e and v e are the effective Young’s modulus and Poisson’s ratio of triangular lattice, respectively. E s is the Young’s modulus of base material, which can be obtained from the stress-strain curve. The nominal length l of strut is 10 mm, and nominal width t is 1 mm. Fatigue crack propagation rates in triangular lattice plates are shown in Fig. 13. The predicted crack growth rate agrees very well with the test results. The fit lines of experimental result and prediction can be written as: Experimental propagation rate: � � � � � �� ������� ∗ ∆ ��� ������� (15) Predicting propagation rate: � � � � � �� ������ ∗ ∆ ��� ������� (16)

-1.0

0  lattice plates

Test results Fit line for test data Predicting results Fit line for predictions

-1.5

-2.0

-2.5

-3.0

-3.5

-4.0 log da/dN (mm/cycle)

-4.5

-5.0

1.6

1.8

2.0

2.2

2.4

2.6

1/2 )

log  K eff (MPa  mm

Fig. 13. Predicted and observed fatigue crack propagation rate of in 2D lattice triangular plates of aluminium alloy 1050A.

6. Conclusions A method for predicting the fatigue life of triangular lattices by considering the fatigue life of single struts has been presented. This method is validated by comparing the predictions with measured fatigue life data for wide lattice plates. The observed fatigue crack growth rates also compare well with predictions. This method can predict a lattice’s fatigue endurance very well considering that materials have a degree of scatter in fatigue life and damage will also be introduced during manufacturing and processing. A three-stage behaviour in crack growth rate was observed in the tests, and the crack path of triangular lattice plates develops in the direction 30° to the horizontal axis of introduced edge crack. The fatigue crack growth rate was also studied by regarding the lattice plates as continuous plates with effective mechanical parameters. Our work indicates that the fatigue life of a periodic lattice can be predicted from the properties of single struts using existing fatigue engineering methods.