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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macrocrack and eventually this struct will initiate and propagate a microcrack. This means that lattice structures could have a good resistance to fatigue: crack initiation life usually occupies large proportion of whole fatigue life and in a lattice, initiation must occur many times for the macrocrack to propagate. The crack tip in lattice structure is a blunt damage area different from a crack tip in solid materials, which is assumed to be at the center of the cell rather than at the unbroken strut that adjacent the crack (Hedayati et al. 2018). The macrocrack length in this research defined as the horizontal length of the whole crack.

Fig. 2. The mechanism of macrocrack propagation in a lattice plate under fatigue loading. The breaking of a strut at the tip of the macrocrack each time reveals a new and undamaged strut.

Due to the stress concentration, plastic deformation can occur in a small area close to the crack tip in a lattice structure. For a lattice subjected to remote tension in the direction transverse to the crack, compressive residual stress will be introduced into struts immediately ahead of the crack tip due to the plastic extension of structs here. Residual stress results in a non-zero mean stress, hence the effects of mean stress on strut fatigue life should be considered. Performing multiple tests to get the S–N Curve for a material under different mean stress conditions takes time and effort. A process called mean stress correction is used to transform the original rainflow matrix to a new matrix with equivalent fatigue damage, but where every cycle has zero mean stress. Among many equations proposed by researchers considering mean stress effects, the Goodman’s relationship is used here because experimental data from different aluminium alloys fits this relationship well (Figge 1967). The equivalent reversible stress can be calculated using a modified version of the Goodman’s relationship �� � � � �� � � �� (1) where �� is the equivalent reversible stress, � is the stress amplitude, � is the mean stress and � is the ultimate tensile strength of material. A two-dimensional triangular lattice is a stretching-dominated lattice structure. In a triangular lattice under all loading states, the stress state involves predominantly stretching of the struts. Bending stresses in the struts reach only a few percent of the axial stress (Fleck and Qiu 2007). Wang and McDowell (2004) even idealized the strut in a triangular lattice as a pin-jointed bar to derive closed form expressions for mechanical properties including the modulus and initial yield strength. Therefore, individual struts in triangular lattices can be simplified as a normal force applied in the axial direction of strut cross section. For the convenience of engineering prediction, the fatigue life of individual struts can be summarized as dependent on the amplitude of the cross-sectional force. By multiplying Eq. (1) by the strut cross-sectional area S , the equivalent reversible load equation can be obtained: