Research Papers

Analytical Solution and Experimental Study of Effective Young's Modulus of Selective Laser Melting-Fabricated Lattice Structure With Triangular Unit Cells

[+] Author and Article Information
Jie Niu

Department of Mechanical, Materials
and Manufacturing Engineering,
The University of Nottingham Ningbo China,
Ningbo 315100, China
e-mail: Jie.Niu@nottingham.edu.cn

Hui Leng Choo

Department of Mechanical, Materials
and Manufacturing Engineering,
The University of Nottingham Ningbo China,
Ningbo 315100, China;
School of Engineering,
Taylor's University,
No. 1 Jalan Taylor's,
Subang Jaya 47500,
Selangor Darul Ehsan, Malaysia
e-mails: Huileng.Choo@nottingham.edu.cn;

Wei Sun

Department of Mechanical, Materials
and Manufacturing Engineering,
The University of Nottingham,
Nottingham NG7 2RD, UK
e-mail: W.Sun@nottingham.ac.uk

Sui Him Mok

SLM Solutions Singapore Pte Ltd,
25 International Business Park,
#02-15/17 German Centre,
Singapore 609916
e-mail: Edwin.Mok@slm-solutions.com

Manuscript received January 3, 2018; final manuscript received April 26, 2018; published online June 28, 2018. Assoc. Editor: Zhijian J. Pei.

J. Manuf. Sci. Eng 140(9), 091008 (Jun 28, 2018) (13 pages) Paper No: MANU-18-1005; doi: 10.1115/1.4040159 History: Received January 03, 2018; Revised April 26, 2018

Research on materials, design, processing, and manufacturability of parts produced by additive manufacturing (AM) has been investigated significantly in the past. However, limited research on tensile behavior 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 finite element analysis (FEA) for triangular 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 AlSi10 Mg 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 lightweight structures with triangular unit cells.

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Fig. 1

Geometry of lattice structure with triangular unit cell: (a) Shape of triangular prism unit cell defined by the geometric parameters, L, t and h, (b) symmetric RVE (20 × 20 × 50 mm) tailored from infinite unit cells, and (c) solid ends added to each side to keep the meshed part from being broken by gripper during tensile test. (Units: mm)

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Fig. 2

Diagram of force distribution in (a) out-plane direction of honeycomb and (b) lattice structure

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Fig. 3

Gauge length determined in the workpiece

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Fig. 4

Calculation of relative density of lattice structure: (a) total materials including force-free cutting edges, (b) effective materials contained in the highlighted volume, and (c) effective area AE covered in overall area, Ao, of cross section C-C'

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Fig. 5

Comparison of E* by various methods for lattice structures with L = 4.5 mm, t = 1.0 mm and different layers of unit cells: (a) relation between E*/ES and (ρ*/ρs)2, (b) plots of E* and h to n, and (c) effect of L/h ratio on E*

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Fig. 6

Comparison of E* by various methods for lattice structures with t = 1.0 mm, n = 4 and L varies from 3.0 to 8.0 mm: (a) relation between E*/ES and (ρ*/ρs)2 and (b) plots of E* against L

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Fig. 7

Comparison of E* by various methods for lattice structures with L = 5.5 mm, n = 4 and t varies from 0.5 to 2.0 mm: (a)relation between E*/ES and (ρ*/ρs)2, (b) plots of E* and h to t, and (c) effect of L/t ratio on E*

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Fig. 8

Relation between E*/Es and (ρ*/ρs)2 when all FEA results for all three case are used to determine the coefficient of Eq. (1)

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Fig. 9

Designs of different numbers of unit cells within the same meshed area: (a) 16 unit cells in sample B5, (b) 44 unit cells in sample B2, and (c) 126 unit cells in sample B1

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Fig. 10

Comparison of calculated E* of lattice structures with different number of unit cells for sample B1, B2 and B5

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Fig. 11

Prototypes printed by SLM process for tensile test

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Fig. 12

Dimension check of geometric parameters of unit cell by microscope: (a) t and L in xy-plane and (b) h in z-direction

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Fig. 13

Experimentally measured behaviors: (a) full load–extension curves and (b) stress–strain curves of the elastic region

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Fig. 14

The fracture surfaces of all tensile test samples with a breaking angle of 60 deg

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Fig. 15

(a) Free-body diagram of the lattice structure, (b) symmetrical loadings on the truss members of the extracted unit cell group, (c) loading at joint A, (d) loading at joint B, (e) loading at joint C, (f) loading on the sectioned segment, and (g) deformation of an arbitrary combined strut in the x- and y-directions



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