Compressive properties of functionally graded lattice structures manufactured by selective laser melting

Accepted Manuscript Compressive properties of functionally graded lattice structures manufactured by selective laser melting

Sing Ying Choy, Chen-Nan Sun, Kah Fai Leong, Jun Wei PII: DOI: Reference:

S0264-1275(17)30589-0 doi: 10.1016/j.matdes.2017.06.006 JMADE 3124

To appear in:

Materials & Design

Received date: Revised date: Accepted date:

24 March 2017 13 May 2017 1 June 2017

Please cite this article as: Sing Ying Choy, Chen-Nan Sun, Kah Fai Leong, Jun Wei , Compressive properties of functionally graded lattice structures manufactured by selective laser melting, Materials & Design (2017), doi: 10.1016/j.matdes.2017.06.006

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ACCEPTED MANUSCRIPT Compressive Properties of Functionally Graded Lattice Structures Manufactured by Selective Laser Melting Sing Ying Choy a,b, Chen-Nan Sun a,c, Kah Fai Leong a,b, Jun Wei a,c a

SIMTech-NTU Joint Laboratory (3D Additive Manufacturing), Nanyang Technological

Singapore Centre for 3D Printing, School of Mechanical & Aerospace Engineering, Nanyang

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University, 50 Nanyang Avenue, Singapore 639798

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Singapore Institute of Manufacturing Technology, 73 Nanyang Drive, Singapore 637662

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Technological University, 50 Nanyang Avenue, Singapore 639798

ACCEPTED MANUSCRIPT ABSTRACT Additive manufacturing provides great geometrical freedom for fabricating structures with complex or customized architecture. One of the applications benefiting from this technology is the fabrication of functionally graded materials with high degree of control of internal architecture which can be strategic application in advanced energy absorption. This study aims to explore the mechanical properties of functionally graded lattice structures fabricated by an

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additive manufacturing technique namely, selective laser melting (SLM),with Ti-6Al-4V as the

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building material. Both cubic lattice and honeycomb lattice structures with varied strut diameter

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and density were designed and manufactured, and their physical characteristics, deformation behaviour and compressive properties were investigated. The collapse of structure always started

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from least dense layer to the denser layers. In contrast, samples with uniform density showed abrupt shear failure with diagonal cracking across the whole structure. The plateau stress and

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specific energy absorption of density graded samples were higher than for uniform density samples for three out of four designs by up to 67% and 72%, respectively. In addition, density

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graded lattices showed distinct energy absorption behaviour with cumulative energy absorption increasing as a power of strain function while uniform density lattices showed a near-linear

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relationship.

Keywords:

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Functionally graded material; Additive manufacturing; Selective laser melting; Lattice structure;

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Compression properties

ACCEPTED MANUSCRIPT 1. Introduction Functionally graded material (FGM) is a material in which the composition and/or the structure change gradually over the volume, resulting in corresponding changes in the mechanical properties of the material. Classification of FGM is generally based on the nature of the gradient in material or design. For instance, transition may occur via dispersed to interconnected second

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phase structure, layered graded or continuously graded structure [1], or gradients by volume

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fraction, shape, orientation or size [2]. Conventional methods of fabricating FGM include physical vapor deposition, chemical vapor deposition, plasma spraying, self-propagating high-

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temperature synthesis, powder metallurgy [3], investment casting [4], and layer-by-layer casting with thermal pressure molding [5]. A more state-of-the-art method to fabricate FGM is additive

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manufacturing (AM). AM is defined as a process of joining materials to make objects from 3D model data, usually layer upon layer, as opposed to subtractive manufacturing methodologies

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according to ISO/ASTM standard 52900. Some of the AM techniques include fused deposition modeling (FDM), selective laser sintering (SLS), selective laser melting (SLM), laser-engineered

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net shaping (LENS), and electron beam melting (EBM). This emerging manufacturing technology is giving greater freedom to designers for the final part geometry along with reduced

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manufacturing time.

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FGMs with change in material composition have been successfully fabricated by various AM techniques. Nylon polymer filled with changing volume of silica nanoparticles fabricated by SLS

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has been found by Chung et al. to increase compressive and tensile modulus in favourable direction within in the polymer part [6].To alleviate the problem of residual stress at interfaces of

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dissimilar materials for high temperature application, Mumtaz et al. functionally graded the thermal barrier coating, Zirconia, within the substrate of nickel alloy by SLM [7], and Zhang et al. functionally graded titanium carbide within the substrate of pure titanium by LENS [8]. Durejko et al. fabricated thin wall tubes of Fe3Al/SS316L FGM with composition change perpendicularly to the wall of the tube by LENS, which are suitable for steam power installations [9].With the FGM feature, the performance of the tubes can be precisely adjusted according to respective working conditions. Yang et al. fabricated titanium/molybdenum FGM by EBM and demonstrated a feasible way to produce a composite with high temperature resistance and good integration of materials [10]. For FGM with change in structural design, this can be achieved by

ACCEPTED MANUSCRIPT AM using two approaches. The first approach is by manipulating the process parameters for density change. The second approach is by designing the architecture of the parts in computer aided drawing software for both pore shape/size variation and density variation before transferring the digital information to AM equipment for printing into 3-dimensional objects. Density variation can be achieved by manipulation of process parameters such as laser power, laser speed and hatch spacing [11-13], but this method provides no control of internal

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architecture on the micro-scale such as the pore distribution. The majority of the research

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reported has focused on the control in design rather than the control in process parameters to

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produce FGM. Research of FGM with control in design includes but is not limited to 13 different polyhedral unit lattice structures made of polycaprolactone which were fabricated by SLS [14],

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cubic lattice made of cobalt-chromium-molybdenum alloy which was fabricated by SLM [15], and cubic lattice made of Ti-6AL-4V alloy which was fabricated by EBM [16]. These studies

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only fabricated different densities of uniform samples for testing the properties of each density but did not test samples with density gradients. Kalita et al. studied the development of

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polypropylene polymer and tricalcium phosphate ceramic scaffold with pore shape and pore size changed segment by segment in radial direction toward the center of cylindric samples using

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FDM technique [17]. Maskery et al. studied FGM lattice structures with density changed every layer of the cellular unit for body-centred-cubic (BCC) lattice made of aluminum alloy which

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was fabricated by SLM [18], and BCC lattice made of polylactide and fabricated by SLS [19]. Grunsven et al. also studied FGM lattice structures with density changed every layer of cellular

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unit for diamond lattice made of Ti-6Al-4V, which was fabricated by EBM [20]. Scaffolds with pore size varied in a step-wise manner were also studied with TheriformTM 3D printing process

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and 3D fibre deposition process [21]. If the environmental or mechanical requirements of a specific application are well-known, optimal distribution of density for FGM part can also be designed through topology optimization [22] using simulation software.

In this study, density graded FGMs fabricated by SLM and using Ti-6Al-4V powder material with design of cubic and honeycomb lattice structures were investigated. The FGM samples were designed with the diameter of lattice struts changing linearly and continuously across cell layers to achieve a smooth density change. No previous work was found to report on research that studied density graded FGM with continuous density change. Most papers found reported on

ACCEPTED MANUSCRIPT abrupt density changes such as step change in strut diameter and pore size [18-20]. Two orientations of each lattice design were studied respectively for their mechanical properties under compression loading and compared to samples without density change. The aim of the study was to investigate the mechanical performance of density graded FGM fabricated by AM method and to assess this type of FGM with different lattice designs for their potential use in impact protection. Properties of fabricated lattice structures investigated in this study include surface

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morphology, dimensional accuracy, deformation behaviour, first maximum compressive strength,

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quasi-elastic gradient, elastic gradient, plateau stress, and energy absorption. The influence of

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cell orientation was also characterized. FGM samples were found to have predictable deformation, higher plateau stress and higher specific energy absorption than non-FGM

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counterparts.

2. Materials and Methods

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The structure of FGM samples was designed using 3-matics software and processed in Magics software, both software packages were supported by Materalise NV. Four FGM samples named

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C1 FGM, C2 FGM, H1 FGM, H2 FGM, respectively, were designed which consisted of two different cell orientations of cubic lattice and honeycomb lattice as shown in Fig. 1.The cell

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orientation for the C2 design was rotated by 90ºcompared to the C1 design, but the gradient of diameter remained oriented with the build direction. A similar process was applied for the H1

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and H2 design. The size of the cellular unit in the cubic lattice was 2 mm x 2mm x 2mm, while the length of cellular unit in honeycomb lattice was 1 mm for every strut of the hexagonal face

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and 2 mm in height. Nodal joints of lattice structures were filleted without any sharp ends, and the cross-sections of lattice struts were designed circular in shape. The number of repeating cellular units in each sample was determined by keeping the ratio of length-to-diameter (in this case length-to-averaged width) to be close to 0.8 based on ASTM standard for compression testing[23]and by keeping the complete shape of a cellular unit at the same time. In meeting these two criteria, the resulting porosity or density of the four FGMs were consequently different. The strut diameter of FGM samples was designed to vary linearly and continuously from 0.4 mm to 1.2 mm in a single direction and along the build direction of SLM process. Samples with uniform strut diameter and the same material volume as the FGM samples were also designed as

ACCEPTED MANUSCRIPT baseline and denoted as UNIFORM. The material volume of uniform samples was assured to be same as FGM samples in design by manipulating the strut diameters until the value of part volume indicated in Magics software was same as part volume of FGM samples. The resulting strut diameters of uniform samples were0.995 mm, 0.875 mm, 0.844 mm, and 0.858 mm, respectively, for C1 UNIFORM, C2 UNIFORM, H1 UNIFORM and H2 UNIFORM. The designed porosities were 71.0%, 68.7%, 48.4% and 47.1%, respectively, for C1, C2, H1 and H2.

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The average designed size of all samples was 14.2 mm x 13.0 mm x 11.6 mm (length x width x

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height).

Fig. 1. Designs of lattice unit and density graded lattice structures with build direction in z-axis

The SLM 250 HL (SLM Solutions Group AG) was used for printing FGM and uniform samples with grade 23 Ti-6Al-4V powder (TLS Technik GmbH & Co.). The titanium alloy powder was spherical in shape with particle size of 20 – 63 µm. The process parameters were set at 150 W laser power, 400 mm/s laser speed, 80 μm hatch spacing, and 30 μm layer thickness. Three

ACCEPTED MANUSCRIPT duplicates were printed for each type of design. Wire cutting was used to separate the printed samples from base plate. No heat treatment was applied to the samples.

The diameters of lattice struts were measured using an optical microscope (Olympus Upright Microscope MX51). The density of each lattice structure was calculated by dividing the sample’s weight with overall sample volume. This calculated density was divided by theoretical density of

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bulk Ti-6Al-4V(4.43 g/cm3) to obtain the relative density of the samples. The density of the

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struts of the lattice was calculated from weight of samples in air and in ethanol measured with a

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weighing device (Mettler Toledo XS204) using Archimedes’ principles. Universal mechanical testing machines (Instron 4505, Shimadzu Autograph AG-X Plus) with 100 KN load cell were

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used for compression testing with a strain rate of 0.05 per minute. Displacement was measured using the crosshead movement. Samples were cut to smaller size when exceeding machine force

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limits. Deformations of samples during compression test were video recorded or captured in photograph images by camera for every 5% strain up to 65% strain. Fracture surfaces of samples

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after compression were characterized with a scanning electron microscope (SEM) (JEOL JSM-

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5600LV).

First maximum compressive strength, quasi-elastic gradient, elastic gradient, plateau stress

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between 20% to 40% strain, and energy absorption per unit volume up to 50% strain were calculated according to ISO 13314:2011 standard [24]. The first maximum compressive strength

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was determined from the first local maximum in stress-strain curve. The quasi-elastic gradient was calculated from the gradient of the straight line within the linear deformation region at the

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beginning of stress-strain curve. The elastic gradient, which represents porosity-dependent rigidity, was calculated from the gradient of the elastic straight line determined by elastic loading and unloading between stresses of 70% and 20% of plateau stress. Plateau stress was established as the mean of stresses between 20% and 40% compressive strain. Energy absorption per unit volume was calculated from the area under the stress-strain curve up to 50% strain.

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3. Results and Discussion

3.1 Structural characteristics FGM lattice samples fabricated by SLM techniques were found to have a gradient of strut

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diameter conforming to the design of changing linearly and continuously as shown in Fig. 2.

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Dimensional accuracy of all samples was assessed by measuring strut diameters with an optical

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microscope, and the measurements are tabulated in Table 1. It can be seen that there were dimensional differences between designed strut diameters and printed designs. More than 50% of

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the measurements were found larger than designed values. These deviations were due to

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partially-melted powder particles on lattice strut surfaces as shown by SEM images in Figure 3.

Fig. 2. Images of density graded lattice structures fabricated by SLM technique

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Table 1 Strut measurement and relative density of lattice samples Designed strut Strut diameter Difference Relative density (µm) diameter (µm) (µm) (%) C1 FGM (top strut) 400 350 ± 40 ± 40 -50 35 ± 0.3 C1 FGM (bottom strut) 1200 1139 ± 20 -61 ± 20 C1 UNIFORM 41 ± 0.2 995 968 ± 4 -27 ± 4 C2 FGM (top strut) 400 545 ± 30 145 ± 30 36 ± 0.4 C2 FGM (bottom strut) 1200 1192 ± 20 -8 ± 20 C2 UNIFORM 40 ± 2 875 1021 ± 20 146 ± 20 H1 FGM (top strut) 400 465 ± 20 65 ± 20 55 ± 0.9 H1 FGM (bottom strut) 1200 1062 ± 50 -138 ± 50 H1 UNIFORM 58 ± 0.4 844 858 ± 1 14 ± 1 H2 FGM (top strut) 400 556 ± 7 156 ± 7 61 ± 0.3 H2 FGM (bottom strut) 1200 1249 ± 30 49 ± 30 H2 UNIFORM 62 ± 0.4 858 976 ± 40 118 ± 40 Note 1: negative value means the measured strut is smaller than designed strut Note 2: strut measurement of all FGM samples was done at horizontal strut except for bottom strut of C2 and H2, which was done at diagonal strut and vertical strut respectively.

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Fig. 3. SEM micrograph of FGM lattice struts with H1 design

The densities of struts in 83% of the lattice samples were measured to be 99% or above, while the remainder of the samples had at least 96% strut density. This demonstrated that the SLM

ACCEPTED MANUSCRIPT process parameters used in this study were able to produce lattice structures with struts near to full density. The measured relative densities for C1, C2, H1 and H2 are also shown in Table 1. The difference in density was due to meeting both criteria of dimensional ratio for compression test and assurance of complete cellular unit by omitting overhang struts as mentioned earlier. The main aim in this study was to distinguish the FGM samples from their corresponding counterparts with uniform strut diameter and same material volume. The measured relative

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densities for FGM designs were found to be smaller than for the respective uniform samples,

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especially for C1and C2 designs. The density differences are attributed to smaller than designed

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diameters as shown in Table 1. Since less material will result in lesser resistance to force exerted, the discrepancy in relative density which shall lower the strength of FGM samples was noted for

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the comparison of different compressive properties in discussion later.

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3.2 Deformation behaviour

Compression tests were conducted on three duplicate samples for each design. The deformation

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behavior is illustrated in Fig. 4 and Fig. 5. All designs of FGM samples deformed similarly starting from the thinnest strut layer to the thickest strut layer in a sequential row by row manner.

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In contrast, uniform strut samples exhibited abrupt shear failure with one diagonal shear band forming throughout the whole sample structure for C1 UNIFORM, C2 UNIFORM and H1

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UNIFORM and with V-shape shear band covering half of the sample structure for H2 UNIFORM. The diagonal cracking of uniform strut samples in this study is due to the relatively

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high density of the samples. According to Gibson and Ashby [18, 25], lattice structures with density larger than 30% are better represented as solid structures with holes. Solid Ti-6Al-4V

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cracks diagonally under loading as demonstrated by the studies of Lee et al. [26] and Hammer [27], which showed planes of maximum shear stress oriented diagonally to the axis of compression. The reason of shear band development in dense structure was inferred to be the cooperative plastic deformation of grains [28]. In comparison, the deformation of FGM samples is deemed favourable as it eliminated abrupt and random shear failure as observed in the case of uniform strut samples. The localized failure sequence was predictable leading to consistent test results for all three samples.

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Fig. 4. Deformation of density graded samples at different strains during compression test

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Fig. 5. Deformation of uniform strut samples during compression test (a) C1 UNIFORM at 15%

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strain (b) C2 UNIFORM at 10% strain (c) H1 UNIFORM at 20% strain (d) H2 UNIFORM at 20% strain

Visual observation during compression test indicated that the abrupt shear failure for uniform strut samples corresponded to the first stress peak in the stress-strain curves as shown in Fig. 6(a) and Fig.6(b). The failure started for relatively low strain values with 15% strain for C1 UNIFORM, 13% strain for H1 UNIFORM, and 5% strain for C2 UNIFORM and H2 UNIFORM as indicated in the figure. Following the first stress peak, which also represents the maximum

ACCEPTED MANUSCRIPT strength, there was a large drop in load-carrying capacity with poor recovery for uniform strut samples. C1 UNIFORM showed gradual reduction in strength recovery, H1 UNIFORM showed lower strength recovery in two out of three samples, C2 UNIFORM and H2 UNIFORM showed little recovery in strength. In contrast, the recovery of strength prior to densification was remarkable for FGM samples. The stress-strain curves of all FGM designs started with smaller stress peaks, and the subsequence peaks were increasingly higher indicating increasing load

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resistance to further crush the cells with larger strut diameters. The ratios of maximum peak to

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the minimum peak are indicated in the figures. The maximum peak which was always the last

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stress peak before densification achieved at least two times (C2 FGM) and up to 6 times (C1 FGM) the initial peak or the minimum peak. Densification started later for FGM samples (above

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50% strain) compared to uniform strut samples. The stress values of C1 FGM were significantly higher than C2 FGM although both cell structures had almost identical relative density. This was

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due to the existence of vertical struts in C1 FGM which reinforced the strength of the structure. Similarly, H1 FGM had smaller relative density than H2 FGM but the stress values of H1 FGM

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were higher due to existence of vertical struts. However, the fluctuation of stress in C1 FGM was large while C2 FGM provided more stable strength recovery in plateau region. Combined graphs

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of single representative curves for all designs are shown in Fig. 7 for ease of comparison. The characteristics of progressive deformation from least dense to most dense layer and staircase

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liked stress-strain curve profiles were also observed in Ti-6Al-4V FGM lattice with diamond unit design fabricated by EBM [20], polyamide FGM lattice with BCC unit design fabricated by SLS

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[19], Al-Si10-Mg FGM lattice with BCC unit design fabricated by SLM [18], and aluminum

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FGM lattice with honeycomb unit design tested by simulation [29].

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max

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shear band failure

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≈6

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Fig. 6 (a). Stress-strain curves of cubic lattice (

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max

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shear band failure

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Fig. 6 (b). Stress-strain curves of honeycomb lattice (

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three duplicate samples respectively) (a) H1 FGM, (b) H1 UNIFORM, (c) H2 FGM, and (d) H2 UNIFORM

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Fig. 7. Stress-strain curves of representative samples for all designs. (a) cubic design, (b)

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honeycomb design

Repeat tests of C1 FGM samples were highly reproducible as all duplicate samples had almost

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identical curves. The reproducibility of H1 FGM and H2 FGM samples was not as good after certain strains (after 40% strain for H1 FGM, after 10% for H2 FGM) because they had higher

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density than C1 FGM and C2 FGM. At higher densities, the release of stress after every failure event was so high that the fractured pieces separated, resulting in different remaining material

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volume in partially crushed samples. The samples was further investigated with SEM by observing the fracture surfaces of lattice struts after compression as illustrated in Fig. 8. The

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fracture surface of the thinner strut (0.4 mm) was found to be coarser with deeper ductile dimples while the fracture surface of the thicker strut (1.2 mm) was smoother with shallower ductile dimples in few areas. This observation shows that as the diameter of lattice strut varied, fracture patterns changed as well. This change was considered to be the reason for the fluctuations of repeated tests for some FGM designs after the collapse of few layers. Uniform strut samples (Fig. 8(c)), which failed like solid structures with diagonal cracks, had smooth fracture surface with no noticeable ductile dimples. There was also no significant difference in fracture surface roughness as in the case of FGM samples. This showed that the uniform strut structure was less ductile than FGM structure.

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The failure of lattice structures is affected by three factors, namely material, density and structural design [30]. Variation of material property due to build thickness was found by Tan et al. in Ti-6Al-4V components [31]. Solid blocks with larger thickness comparison (1 mm, 5 mm, 10 mm and 20 mm) was built individually by EBM technique in their work and the hardness of thicker solid block was shown to be lower than thinner solid block due to higher heat

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accumulation in thicker solid block leading to different material grain formation. The

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observation of their work was the opposite of our study as thick struts were found to be less

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ductile than thin struts in our case for lattice strut failure. It is postulated that the variation of thickness in our study was smaller (from 0.4 mm to 1.2 mm), and hence the material effect was

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not as significant. The effects of density and structural design on strut failure were therefore considered more dominant in our case. In terms of density (i.e. strut diameters), studies of Ullah

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et al. [32] explained the reason of property variation upon change of strut diameter in a lattice structure. Based on compression results for Ti-6Al-4V and SLM built lattice structures, the

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triaxial stress state was found to change with increasing strut diameter from bending to shear dominated failure, which in turn influenced the failure strain. The stiffness and strength

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increased by 4.5 times and 7.4 times respectively as the strut diameter increased from 0.5 mm to 1.2 mm [33]. In terms of structural design, their studies also showed that an increased number of

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internal struts contributed to higher load bearing capacity for the structure, and the triaxial stress

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state was also found to vary for different lattice designs.

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Fig. 8. Fracture surface of samples observed under SEM after compression test (a) 0.4 mm strut

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of C1 FGM sample, (b) 1.2 mm strut of C1 FGM sample, (c) C1 UNIFORM sample

3.3 Compressive properties Five compressive properties defined by ISO 13314:2011 standard for all the samples are tabulated in Table 2. The initial maximum compressive strengths of all the FGM samples were smaller than for uniform strut samples, which was understandable as FGM failure started from smallest strut diameter and gradually increased while the uniform strut samples started randomly from uniform strut diameter during deformation. The calculation method of the quasi-elastic gradient was similar to Young’s modulus [20] or compressive modulus [17] based on literature.

ACCEPTED MANUSCRIPT The quasi-elastic gradient can be used to determine the compressive offset stress of the lattice structure which is an alternative to the compressive yield strength of the material. On the other hand, the calculated values of elastic gradient can be used to determine the compressive proof strength of the lattice structure which is a second alternative to the compressive yield strength of the material according to the ISO standard. Both quasi-elastic gradient and elastic gradient are not the modulus of the material, and the elastic gradient represents the porosity-dependent

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rigidity of the material. Results showed that the quasi-elastic gradient and elastic gradient of

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FGM samples were smaller than the respective values of the uniform samples. Plateau

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stress,which is the mean of stresses between 20% and 40% strain, serves as the indicator of strength for porous materials. Both plateau stress and specific energy absorption of FGM

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samples were significantly higher than for uniform samples for all the designs except C1. The plateau stress of FGM sample was higher than uniform sample by 67% for C2 design, by 19%

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for H1 design and by 30% for H2 design. While the specific energy absorption up to 50% strain for FGM samples were higher than uniform samples by 72% for C2 design, by 10% for H1

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design, and by 19% for H2 design. It should be noted that the measured relative densities of all FGM samples were lower than their respective uniform samples especially for C1 FGM with

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about 6% lower density. The discrepancy in relative density would contribute to reduced plateau stress and energy absorption in FGM samples. The design of graded porosity in FGM

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successfully eliminated the large drop in strength observed for uniform strut samples and had significant implications for the energy absorption of the lattice structures. In terms of design,

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C1design had higher first maximum compressive strength, plateau stress and specific energy absorption than C2 design with the same density. These three properties were also higher in H1

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design compared to H2 design although H1 had lower density. The higher property values were due to the existence of vertical struts in both C1 and H1 designs.

ACCEPTED MANUSCRIPT Table 2 Compressive properties of density graded samples and uniform strut samples

5±0 66 ± 1 25 ± 3 38 ± 2 16 ± 2 145 ± 8 9±5 76 ± 20

113 ± 2 172 ± 10 62 ± 2 37 ± 10 504 ± 4 424 ± 100 221 ± 40 169 ± 10

Energy absorption up to 50% strain (MJ/m3)

95 ± 6

55 ± 1 93 ± 4 32 ± 1 19 ± 7 203 ± 2 184 ± 80 92 ± 10 77 ± 2

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43 ± 2 69 ± 1 25 ± 3 41 ± 2 89 ± 8 141 ± 10 63 ± 7 104 ± 30

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71 ± 3 323 ± 4 64 ± 10 144 ± 20 213 ± 7 692 ± 100 112 ± 5 349 ± 30

Energy absorption up to densification strain (MJ/m3)

39 ± 5 305 ± 20 103 ± 10

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C1 FGM C1 UNIFORM C2 FGM C2 UNIFORM H1 FGM H1 UNIFORM H2 FGM H2 UNIFORM

Quasi-elastic Elastic gradient Plateau stress gradient (MPa) (MPa) (MPa)

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First maximum compressive strength (MPa)

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It was of interest to compare the energy absorption in this study with other design of lattice

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structures from literature. However, the research on FGM fabricated by AM technology with reported values of energy absorption was limited. The energy absorption before full densification

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for BCC lattice structures studied by Maskery et al. were about 5.7 MJ/m 3 and 6.3 MJ/m3 for FGM with graded density and uniform strut samples, respectively [18]. The difference in values

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showed an increase of 11% in energy absorption with FGM design. The values of energy absorption were lower compared to our study as softer material (aluminum alloy) and lower

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density were used in their study but the fabrication technique was similar. Although the energy absorption values could not be fairly compared due to different material, the effect of graded

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density versus non-graded structures on the energy absorption in different context was worth discussing. The effect of FGM design on the energy absorption of aluminum BCC lattice

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structures in their study was not as apparent as in this study. Nonetheless, the effect was very significant in another study by them which used SLS fabrication technique with polymeric material. The increase of energy absorption was 80% for BCC design and 114% for BCC with reinforced vertical struts in case of FGM design [19].

ACCEPTED MANUSCRIPT The changes of cumulative energy absorption per unit volume with increase of strain for all designs are plotted in Fig.9. By fitting the curves with the power law, the exponent value in the resulted equation represented the rate of increase in cumulative energy absorption. It can be seen that uniform samples of all designs were in lower rate range (0.84, 0.89, 0.92, and 1.26 for C1 UNIFORM, C2 UNIFORM, H1 UNIFORM and H2 UNIFORM, respectively) and close to a linear relationship with strain values. The rates of increase for FGM samples of all designs were

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in higher value range (1.28, 1.41, 1.72 and 2.68 for C2 FGM, H2 FGM, H1 FGM and C1 FGM

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respectively). The difference in rate was due to unchanged density in uniform samples and

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increasing density in FGM samples throughout the compression process. These results showed the distinct energy absorption behavior of FGM samples. Similar behavior was found in BCC

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lattice structure with density gradient fabricated by SLM with aluminum alloy [18] and by SLS with polymeric material [19].The exponent values of these BCC lattice structures were about 2

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and 3 respectively. H1 FGM samples in this study had the exponent value close to those of the aluminum alloy BCC in former literature. On the other hand, there was a sudden decrease in the

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rate of the cumulative energy absorption for C1 UNIFORM and H1 UNIFORM at around 15% and 20% strains respectively which impaired the linear curves. This was caused by the abrupt

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shear failure of uniform samples with diagonal cracking throughout the whole sample structure. This impairment was not found in FGM samples which failed locally layer by layer. Hence FGM

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lattice structures exhibited more predictable and gradual energy absorption behavior than uniform samples. It should be noted that the cumulative energy absorption values in different

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geometrical cell orientation (C1 vs C2 and H1 vs H2) were significantly different in uniform

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samples but comparably less so in FGM samples.

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Fig. 9. Cumulative energy absorption per unit volume versus strain curves for density graded lattice samples and uniform lattice samples under compression test (a) cubic lattice (b)

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4. Conclusions

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It was demonstrated that SLM technique can produce Ti-6Al-4V FGM with good repeatability. Powder adhesion was observed on lattice struts which resulted in the deviation of strut diameters

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from design values. Compression tests showed that the deformation of the FGM was novel as localized and gradual failure occurred in a predictable manner for all four tested designs. The

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deformation started from the least dense layer to the densest layer, and the stress-strain curves exhibited profiles of increasing stress maxima. In contrast, the lattice with uniform struts of the

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same material and volume exhibited abrupt shear failure with cracking across the whole sample geometry. In three out of four designs, the plateau stress and specific energy absorption of the FGM were higher than the uniform strut samples. The cumulative energy absorption of FGM increased as a power of strain function while uniform samples exhibited a near-linear relationship. The plasticity of the FGM was also investigated, and it was found to vary with density. In terms of design, both cubic and honeycomb lattices exhibited mechanical anisotropy as the first maximum compressive strength, plateau stress and specific energy absorption in one orientation were superior to the other orientations. Cumulative energy absorption also changed

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Comparing among the four FGM designs, the FGM with vertically oriented struts showed higher energy absorption capacity. The honeycomb FGM was more space-efficient than the cubic FGM as it contains more unit cells within the same volume. The novel deformation characteristics and

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energy absorption capability of FGM can be employed in applications such as packaging

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material, personal protection equipment and surgical implants. Further research on more

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sophisticated density profile in FGM design can be explored to obtain deformation profile, peak

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stress, and rate of energy absorption specific to the applications.

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Acknowledgements

This work was financially supported by A*STAR Industrial Additive Manufacturing Program:

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Work Package 2 (Selective Laser Melting) [Grant No. 1325504102].

References

4. 5.

6. 7. 8.

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3.

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2.

Y. Miyamoto, W.A. Kaysser, B.H. Rabin, A. Kawasaki, R.G. Ford, Functionally graded materials: design, processing and applications, (1999). S. Khan, Analysis of tribological applications of functionally graded materials in mobility engineering, International Journal of Scientific & Engineering Research, 6 (3) (2015) 1150. N. Cherradi, A. Kawasaki, M. Gasik, Worldwide trends in functional gradient materials research and development, Composites Engineering, 4 (8) (1994) 883-894. A.H. Brothers, D.C. Dunand, Mechanical properties of a density-graded replicated aluminum foam, Materials Science and Engineering A, 489 (2008) 439–443. P. Yusong, S. Qianqian, C. Yan, Fabrication and characterisation of functional gradient hydroxyapatite reinforced poly (ether ether ketone) biocomposites, Micro & Nano Letters, 8 (7) (2013) 357–361. H. Chung, S. Das, Functionally graded nylon-11/silica nanocomposites produced by selective laser sintering, Materials Science and Engineering: A, 487 (1-2) (2008) 251-257. K.A. Mumtaz, N. Hopkinson, Laser melting functionally graded composition of Waspaloy® and Zirconia powders, Journal of Materials Science, 42 (18) (2007) 7647-7656. Y.Z. Zhang, Z.M. Wei, L. Shi, M.Z. Xi, Characterization of laser powder deposited Ti–TiC composites and functional gradient materials, Journal of Materials Processing Technology, 206 (2008) 438-444.

AC

1.

ACCEPTED MANUSCRIPT

16.

17.

18.

19. 20. 21.

22. 23. 24. 25. 26.

27.

T

IP

CR

US

15.

AN

14.

M

13.

ED

12.

PT

11.

CE

10.

T. Durejko, M. Zietala, W. Polkowski, T. Czujko, Thin wall tubes with Fe3Al/SS316L graded structure obtained by using laser engineered net shaping technology, Materials and Design, 63 (2014) 766-774. S. Yang, X. Xue, S. Lou, F. Lu, Investigation on gradient material fabrication with electron beam melting based on scanning track control, China Welding, 16 (3) (2007) 19-22. M. Erdal, S. Dag, Y. Jande, C.M. Tekin, Manufacturing of functionally graded porous products by selective laser sintering, Materials Science Forum, 631-632 (2010) 253-258. T. Niendorf, S. Leuders, A. , H.A. Richard, D. Schwarze, Functionally graded alloys obtained by additive manufacturing, Advanced Engineering Materials, 16 (7) (2014) 857-861. K.H. Low, C.N. Sun, K.F. Leong, Z.H. Liu, D.Q. Zhang, Selective laser melting of functionally graded Ti6Al4V. 2014, Singapore Centre for 3D Printing. N. Sudarmadji, J.Y. Tan, K.F. Leong, C.K. Chua, Y.T. Loh, Investigation of the mechanical properties and porosity relationships in selective laser-sintered polyhedral for functionally graded scaffolds, Acta Biomaterialia, 7 (2011) 530-537. K.B. Hazlehurst, C.J. Wang, M. Stanford, An investigation into the flexural characteristics of functionally graded cobalt chrome femoral stems manufactured using selective laser melting, Materials and Design, 60 (2014) 177–183. J. Parthasarathy, B. Starly, S. Raman, A design for the additive manufacture of functionally graded porous structures with tailored mechanical properties for biomedical applications, Journal of Manufacturing Processes, 13 (2011) 160-170. S.J. Kalita, S. Bose, H.L. Hosick, A. Bandyopadhyay, Development of controlled porosity polymerceramiccompositescaffolds via fused deposition modeling, Materials Science and Engineering: C, 23 (5) (2003) 611-620. I. Maskery, N.T. Aboulkhair, A.O. Aremu, C.J. Tuck, I.A. Ashcroft, R.D. Wildman, R.J.M. Hague, A mechanical property evaluation of graded density Al-Si10-Mg lattice structures manufactured by selective laser melting, Materials Science & Engineering A, 670 (2016) 264-274. I. Maskery, A. Hussey, A. Panesar, A. Aremu, C. Tuck, I. Ashcroft, R. Hague, An investigation into reinforced and functionally graded lattice structures, Journal of Cellular Plastics, (2016) 1-15. W.v. Grunsven, E. Hernandez-Nava, G.C. Reilly, R. Goodall, Fabrication and mechanical characterisation of titanium lattices with graded porosity, Metals, 4 (2014) 401-409. K.F. Leong, C.K. Chua, N. Sudarmadji, W.Y. Yeong, Engineering functionally graded tissue engineering scaffolds, Journal of the Mechanical Behavior of Biomedical Materials, 1 (2) (2008) 140-152. A. Burblies, M. Busse, Computer based porosity design by multi phase topology optimization, in AIP Conference Proceedings. 2006. p. 285-290. ASTM E9-09, Standard Test Methods of Compression Testing of Metallic Materials at Room Temperature, 2009. British Standards Institution 2012, BS ISO 13314:2011, Mechanical testing of metals — ductility testing — compression test for porous and cellular metals, 2011. L.J. Gibson, M.F. Ashby, Cellular solids: structure and properties. 2nd edition ed. 1997, Cambridge ; New York: Cambridge University Press. W.-S. Lee, C.-F. Lin, Plastic deformation and fracture behaviour of Ti–6Al–4V alloy loaded with high strain rate under various temperatures, Materials Science and Engineering A, 241 (1998) 48-59. J.T. Hammer, Plastic deformation and ductile fracture of Ti-6Al-4V under various loading conditions. The Ohio State University, Degree Master of Science Academic, Department, 2012.

AC

9.

ACCEPTED MANUSCRIPT 28.

29.

30.

CR

US AN M ED PT CE

33.

AC

32.

IP

T

31.

M.A. Meyers, V.F. Nesterenko, J.C. LaSalvia, Q. Xue, Shear localization in dynamic deformation of materials: microstructural evolution and self-organization, Materials Science and Engineering A, 317 (2001) 204-225. X.-c. Zhang, L.-q. An, H.-m. Ding, Dynamic crushing behavior and energy absorption of honeycombs with density gradient, Journal of Sandwich Structures and Materials, 16 (2) (2014) 125–147. M.F. Ashby, The properties of foams and lattices, Philosophical Transactions of the Royal Society A, 364 (2006) 15-30. X. Tan, Y. Kok, Y.J. Tan, G. Vastola, Q.X. Pei, G. Zhang, Y.-W. Zhang, S.B. Tor, K.F. Leong, C.K. Chua, An experimental and simulation study on build thickness dependent microstructure for electron beam melted Ti–6Al–4V, Journal of Alloys and Compounds, 646 (2015) 303–309. I. Ullah, M. Brandt, S.Feih, Failure and energy absorption characteristics of advanced 3D truss core structures, Materials and Design, 92 (2016) 937–948. I. Ullah, J. Elambasseril, M. Brandt, S. Feih, Performance of bio-inspired Kagome truss core structures under compression and shear loading, Composite Structures, 118 (2014) 294–302.

ACCEPTED MANUSCRIPT Figure Captions Fig. 1. Designs of lattice unit and density graded lattice structures with build direction in z-axis Fig. 2. Images of density graded lattice structures fabricated by SLM technique Table 1 Strut measurement and relative density of lattice samples

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Fig. 3. SEM micrograph of FGM lattice struts with H1 design

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Fig. 4. Deformation of density graded samples at different strains during compression test Fig. 5. Deformation of uniform strut samples during compression test (a) C1 UNIFORM at 15%

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strain (b) C2 UNIFORM at 10% strain (c) H1 UNIFORM at 20% strain (d) H2 UNIFORM at 20%

Fig. 6 (a). Stress-strain curves of cubic lattice (

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strain ,

are densification strain of three

duplicate samples respectively) (a) C1 FGM, (b) C1 UNIFORM, (c) C2 FGM, and (d) C2

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are densification strain of

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Fig. 6 (b). Stress-strain curves of honeycomb lattice (

three duplicate samples respectively) (a) H1 FGM, (b) H1 UNIFORM, (c) H2 FGM, and (d) H2

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honeycomb design

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Fig. 7. Stress-strain curves of representative samples for all designs. (a) cubic design, (b)

Fig. 8. Fracture surface of samples observed under SEM after compression test (a) 0.4 mm strut

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of C1 FGM sample, (b) 1.2 mm strut of C1 FGM sample, (c) C1 SAME sample

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Table 2 Compressive properties of density graded samples and uniform strut samples Fig. 9. Cumulative energy absorption per unit volume versus strain curves for density graded lattice samples and uniform lattice samples under compression test (a) cubic lattice (b) honeycomb lattice

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Density graded lattice structures Fracture surfaces Compression test built by selective laser melting after compression Strut diameter 0.4 mm

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Density graded

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Non-density graded

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New designs of functionally graded material with continuous density change were investigated. The designs were opposed to those reported in literature with abrupt change. The designed structures were shown to have novel deformation behavior than homogenous counterparts under compression. The plateau stress and specific energy absorption of the structures were higher than homogenous counterparts for most tested designs.

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