Analytical solution and experimental study of effective Young’s modulus of SLM-fabricated lattice structure with triangular unit cells

Research on materials, design, processing and manufacturability of parts produced by Additive Manufacturing (AM) has been investigated significantly in the past. However, very limited research on mechanical behaviour of cellular lattice structures by AM was carried out. In this paper, effective tensile Young’s modulus, E*, of triangular lattice structures was determined.Firstly, analytical solution was derived based on Euler-Bernoulli beam theory. Then numerical results of E* were obtained by FEA for lattice structures classified by three shape parameters. The effects of side length, L, beam thickness, t, and height, h, on E* were investigated individually. FEA results revealed that there is a relationship between E* and the relative density and shape parameters. Among them, t has the most significant effect on E*. Numerical results were also compared with the results from modified general function for cellular structures and modified formula for triangular honeycomb. The E* predicted by the proposed analytical solution shows the best agreement with the numerical results. Finally, tensile tests were carried out using AlSi10Mg triangular lattice structures manufactured by Selective Laser Melting (SLM) process. The experimental results show that both analytical and numerical solutions are able to predict E* with good accuracy. In the future, the proposed solution can be used to design structure with triangular unit cells.