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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In general, the macroscopic mechanical properties of lattice structures are closely related to node connectivity (Deshpande et al. 2001a). Lattice materials with high nodal connectivity are stretching-dominated structures – the stresses that their struts develop under loading are dominated by axial tension rather than bending. Stretching dominated lattices generally exhibit higher strength to density ratio than the bending-dominated lattices (Deshpande et al. 2001a, b), so stretching-dominated lattices have significant advantages in lightweight structural applications. A two-dimensional triangular lattice, in which has a unit cell with a nodal connectivity of six, is a good representative of stretching-dominated lattices. The stiffness and strength of 2D triangular lattices as well as their fracture properties and damage tolerance have been extensively researched. For instance, Fleck and Qiu (2007) related brittle triangular lattice’s mode I and mode II fracture toughness to the relative density, ̅ , the cell size, l , and material fracture strength, σ f , obtaining analytical formulas. Qiu et al. (2009) investigated the ductile fracture of triangular lattices by using both analytical estimation and finite element simulation, showing that the normalized yield locus is almost independent of the relative density but is highly sensitive to the principal stress directions. Recently, Gu et al. (2018) has compared the mechanical properties of triangular lattices measured using experimental methods with analytical and numerical studies. They found that the lattice modulus is isotropic, while the tensile strength and fracture behaviour depend significantly on the lattice orientation.

Fig. 1. The unit cell of triangular lattice.

Triangular lattices in real applications are frequently subjected to cyclic mechanical or thermal loadings, so it is important to understand the fatigue properties of these lattices. However, little work has been done on the mechanism of lattice fatigue failure, especially theoretical studies on the fatigue mechanism. More work is now focused on experimental research and numerical simulation. Fatigue properties of lattice materials are highly dependent on the type of unit cell as well as on porosity (Yavari et al. 2015; Ahmadi et al. 2018). For 3D lattice structures, higher porosities result in shorter fatigue lives for the same level of applied stress, and the normalized S-N curves for different porosities can be described by a single power law. Different finite element methods, considering irregularities of strut cross-section and pores in struts caused by manufacturing methods, have been used to simulate the fatigue response and damage accumulation of different lattices (Zargarian et al. 2016; Hedayati et al. 2016), and these computational approaches can obtain satisfactory results. However, research to date has not solved the problem of how to predict the fatigue properties of lattice structures. Experimental testing of lattice structures is an extremely costly and time-consuming process. In this paper, a method to predict the fatigue life of 2D triangular lattice plates is proposed. Fatigue testing of single struts and lattice plates has been conducted to validate the proposed method. Furthermore, macro-crack propagation rate of triangular lattice plates can also be attained from the crack length-cycle curve. This method which combines the overall fatigue life of the lattice structure with the fatigue life of single struts test data can not only provide acceptable fatigue life predictions, but also save the time and money needed in the actual measurement process. 2. Assumptions and Methodology In a lattice plate under cyclic loading, fatigue cracking will firstly initiate in a single strut then the microcrack propagates to the critical length for fast fracture. At this time, the strut breaks and the macrocrack can be seemed as advancing by a unit cell shown in Fig. 2. When the crack tip advances by a unit cell, a new strut is at the tip of the