Lattice structures of Cu-Cr-Zr copper alloy by selective laser melting: Microstructures, mechanical properties and energy absorption

Journal Pre-proof Lattice structures of Cu-Cr-Zr copper alloy by selective laser melting: Microstructures, mechanical properties and energy absorption

Zhibo Ma, David Z. Zhang, Fei Liu, Junjie Jiang, Miao Zhao, Tao Zhang PII:

S0264-1275(19)30844-5

DOI:

https://doi.org/10.1016/j.matdes.2019.108406

Reference:

JMADE 108406

To appear in:

Materials & Design

Received date:

15 September 2019

Revised date:

9 November 2019

Accepted date:

3 December 2019

Please cite this article as: Z. Ma, D.Z. Zhang, F. Liu, et al., Lattice structures of Cu-Cr-Zr copper alloy by selective laser melting: Microstructures, mechanical properties and energy absorption, Materials & Design(2018), https://doi.org/10.1016/j.matdes.2019.108406

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© 2018 Published by Elsevier.

Journal Pre-proof Lattice structures of Cu-Cr-Zr copper alloy by selective laser melting: microstructures, mechanical properties and energy absorption Zhibo Maa, David Z. Zhanga,b,*, Fei Liuc, Junjie Jianga, Miao Zhaoa, Tao Zhanga a

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State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400044, China College of Engineering, Mathematics and Physical Sciences, University of Exeter, North Park Road, Exeter EX4 4QF, UK School of Advanced Manufacturing Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China. Correspondence: [email protected]; Tel.: +86-23-6510-2537

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Abstract Characterized by high thermal-electrical conductivity and reasonable specific strength, lattice structures of copper alloy have great potential in industrial applications. However, they have been rarely studied due to their complicated structures and difficulty in fabrication. Based on the ability of selective laser melting to produce near net shape parts with any complex geometry directly, Cu-Cr-Zr copper alloy lattice structures with high density were manufactured and studied for the first time. A series of lattice structures were designed by a mathematical approach named Triply Periodic Minimal Surfaces and their mechanical properties, microstructures and deformation behaviors were systematically studied. The effects of cell size and volume fraction on their mechanical properties and energy absorptions were analyzed and evaluated. The results demonstrate that the mechanical and energy absorption properties of the lattice structures varied dramatically with the changes of cell size and volume fraction. Due to the good plasticity of the copper alloy, stress-strain curves of the lattice structures exhibit a long stress plateau without stress collapses, which is very beneficial for energy absorption. The deformation of the lattice structures occurred uniformly and were caused by the struts bending without cell breaking and struts fracturing. Keywords selective laser melting, copper-based alloy, lattice structure, mechanical property, energy absorption 1. Introduction Compared with solid materials, lattice materials have characteristics of high specific surface area and high specific stiffness/strength resulting in excellent energy absorption, acoustic insulation and thermal management ability, which are widely used in engineering and biomedical applications as energy/sound absorber, heat transfer/shield, lightweight structural component and biological bone graft [1-6]. Copper and its alloys exhibit prominent electrical and thermal conductivities, which are often used as conductor materials with certain functions [7, 8]. Making copper alloys into lattice structures will combine the advantages of copper alloys and lattice structures, and further deepen and optimize the applications of copper alloy, especially in thermal control fields, such as optimizing heat capacitor and heat exchanger [3,

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However, the formation of lattice structures faces high challenges due to the periodic intricate internal structures. Traditionally, lattice structures are manufactured by deformation forming, investment casting and metal wire approaches [10, 11]. Nevertheless, the complex processes of these manufacturing routes are costly and inefficient and fail to form complex net-shape lattice structures required for advanced applications [12]. Fortunately, these issues can be solved practically with the advent and development of metal additive manufacturing (AM), especially the rapidly development of selective laser melting (SLM). SLM is a powder bed fusion process of AM technologies and capable of producing near net shape metal parts directly from any complex geometry models[13]. In recent years, lattice structures of different types of materials made by SLM have been studied for various applications. Ti-6Al-4V has excellent biocompatibility and suitable mechanical properties, therefore its lattice structures with different cells, such as polyhedral [14], point lattice [15] and graded unit [16], have been developed and widely investigated. Meanwhile, the mechanical characters and biological transplantation performances of them were studied and evaluated. For 316L stainless steel lattice structures, the manufacturability and compression properties was evaluated [17, 18] and the results demonstrated that the lattice structures with ‘Gyroid’ type cell have well self-supported feature, which resulting in a wide feasible cell size ranging [18]. Aluminum alloy has been made into lattice structures for various applications, such as lightweight body structures, sound insulations and heat exchangers etc. due to its peculiarity of lightweight, high specific strength and good thermal conductivity. Lattice structures of “Schwartz Diamond” and graded density lattice structures were triumphantly produced via SLM utilizing Al-Si10-Mg material and the morphological characteristics and compression properties of them were characterized and studied [12, 19]. Despite the broad application prospects, copper alloy lattice structures made by SLM have been rarely studied, even for copper-based solid materials. This can be attributed to the low laser absorption rate and high thermal conductivity of copper, which leads to the difficulty in processing Cu-based alloy via SLM [20]. Hence, it is unclear for the formability and mechanical properties of SLMed copper alloy lattice structures. Triply Periodic Minimal Surfaces (TPMS) are formula-driven mathematical methods, through which it is readily to generate lattice structures with smooth surfaces reducing stress concentration during applications [6, 21-23]. Compared with traditional CAD-based or other design methods, TPMS can generate uniform or graded lattice structures more readily and the lattice size, the relative density and the density gradient of the cellular structure can be adjusted for specific requirements [22, 24]. Thus, TPMS-designed cellular structures have wide application prospects, especially in engineering part topology optimization [12] and biological transplant field [16]. Therefore, many SLMed TPMS-designed lattice structures have been studied in recent years, such as TPMS-designed Gyroid structures [25, 26], graded Gyroid structures [21, 27, 28] and graded or uniform Diamond structures [16, 18, 21]. In this work, Cu-Cr-Zr lattice structure samples designed by TPMS were fabricated via SLM to investigate their microstructures, mechanical properties and energy absorptive properties. The lattice structures adopted diamond cell structures that possess isotropic geometry and well self-supporting properties, thereby allowing SLM to produce the lattice structures in a large-scale varied volume fractions and cell sizes without distinct deformation

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Journal Pre-proof [6, 29]. Moreover, when designing the lattice structures, mainly two variates in terms of cell size and volume fraction were took into consideration to assess their effects on compression features and deformation behaviors.

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2. Model design and experimental details 2.1 TPMS design of the diamond lattice structure An important subclass of TPMS are characterized by partitioning space into two domains that are not disjoint but intertwining and continuous [30, 31]. Therefore, the surfaces that include Schwartz primitive (P), the Schwartz diamond (D), and the Schoen Gyroid (G) surfaces are nowadays widely used to design lattice structures. A type of diamond minimal surface (D), whose pore shape and cell size can be adjusted with modifiable parameters, can be described by equation as follows: φ(x,y,z)= sin(αx) ∙ sin(βy) ∙ sin(γz) + sin(αx) cos(βy) cos(γz) + cos(αx) ∙ sin(βy) ∙ cos(γz) +cos(αx)∙cos(βy)∙sin(γz)-0.07[cos(4αx)+cos(4βy)+cos(4γz)]+R=0 (1) In the equation above, α, β and γ are parameters controlling cell size in x, y and z directions and the larger ones lead to smaller cell sizes. R relates to the porosity (p) of the cellular architecture. Through algebraic calculation, it was found that there is a linear relationship between the parameter R and the relative density (ρ∗) (volume fraction) [21]. For Diamond cell, this linear relationship can be given by equation as follows: [21, 32, 33]: 100ρ* = -38.68×R+48.84 (2) According the equations (1) and (2), nine category lattice structures were designed and two variates of cell size (c) and ρ∗ were considered. Details of design parameters were presented in Table 1. For convenience, the lattice structures were named in the way of ρ∗-c. For example, the sample with 20% relative density and 4 mm cell size were named 20-4. The representative 6 mm unite and the generated TPMS 10-6 lattice structure were presented in Fig. 1, and the lattice structures fabricated by SLM will be demonstrated in the following section. Table 1 Details of design parameters of the copper lattice structures.

structures 20-6 20-5 20-4 15-6 15-5 15-4 10-6 10-5 10-4

𝜌∗ (%) 20 20 20 15 15 15 10 10 10

c (mm) 6 5 4 6 5 4 6 5 4

R 0.746 0.746 0.746 0.875 0.875 0.875 1.004 1.004 1.004

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α π/3 2π/5 π/2 π/3 2π/5 π/2 π/3 2π/5 π/2

β π/3 2π/5 π/2 π/3 2π/5 π/2 π/3 2π/5 π/2

γ π/3 2π/5 π/2 π/3 2π/5 π/2 π/3 2π/5 π/2

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Fig. 1 Model of (a) diamond cell structure and (b) the corresponding generated TPMS lattice structure (10-6).

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2.2 Materials Cu-Cr-Zr precipitation hardening alloys have been widely studied and applied for a long time for their unique combination of high thermal and electrical conductivity and high strength. The lattice structures that investigated in this paper were made from this type alloy. The feedstock is a gas-atomized prealloy powder supplied by Changsha New Material Industry Research Institute Co., Ltd. with a nominal composition (wt %): Cr: 0.60, Zr: 0.40, and balance Cu. The SEM morphology of the powders in Fig. 2 (a) shows that most powder particles exhibit nearly spherical shape and smooth surface, which responsible for the good flow-ability. Particle size analyzation via a laser analyzer (the Malvern UK Master sizer 3000) demonstrates that the powder particles exhibit a narrow size distribution with an average size of 31 µm, as shown in Fig. 2 (b).

Fig. 2 (a) SEM morphology and (b) the particle size distribution of the Cu-Cr-Zr powders.

2.3 Fabrication and tests The samples were manufactured on a commercial SLM machine EOS M290 (EOS GmbH, Germany) that equipped with a maximum 400 W single-mode ytterbium fiber laser. The laser spot have a mean diameter of 80 µm with an energy intensity distribution of

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Gaussian profile. Based on our previous work, the process parameters were set as follows, laser power of 370 W, scanning speed of 650 mm/s, hatching space of 0.11 mm and layer thickness of 30 μm. In addition, a raster scanning strategy was employed with a 67° rotation of scanning direction between two layers. It is worthy of pointing out that the parameters were based on the optimized parameters for bulk Cu-Zr-Cr material. During manufacturing process, the oxygen content in the build chamber was maintained at a low level (<0.1 vol. %) by aerating the building chamber with Argon. The temperature of the build platform was maintained at 80℃. After completion of the manufacturing, the samples were cut off from the build platform carefully via a wire Electrical Discharge Machining (wire-EDM). Before morphological and mechanical characterizations, ultrasonic-cleaning was adopted to wash off the powder residues by immersing the samples into alcohol solution (95%). For microstructure analysis, the samples were prepared through a standard metallography methodology and then etched by a mixed solution of 1.5 g FeCl3, 15 ml HCl and 30 ml distilled H2O. A digital inverted metalloscope (MM-4XC-300C, PUDA, China) and a scanning electron microscopy (SEM, JSM-7800F, JEOL, Japan) were employed to characterize the micro morphologies as well as the forming features. A micro-computer tomography (micro-CT) scanner (diondo d2, Germany) was used to scan and reconstruct the SLMed lattice structure at a resolution ratio of 15 μm to evaluate the SLM fabrication accuracy. Room temperature uniaxial compression tests of the lattice structures and the tensile tests of bulk samples were performed using a CMT5105 electronic universal testing machine (MTS, Eden Prairie, MN, USA) equipped with a 100 KN load cell at a rate of 2 mm/min. A video camera was used to record the lattice structure deformation behaviors during the compression. Frames selectively extracted from these videos can be used to provide more information about the deformation modes.

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3. Results and discussion 3.1 Mechanical properties of bulk copper alloy For a better analyzing the properties of the cellular structures, five 8 mm × 8 mm × 8 mm rectangular samples and three 70 mm long rod solid samples with a 9 mm diameter were fabricated to test the density and the mechanical properties of the SLMed Cu-Cr-Zr material. The densities of the five samples were measured via the Archimedes method and the results were averaged 8.8761 g/cm3 with a relative density of 99.2%. Hence, the SLM process parameters are reasonable and the corresponding cellular structures with excellent density could be manufactured. Fig. 3 (a) and (b) show the representative engineering stress-strain curve and the fracture morphology of the as built tensile sample (ISO6892-1:2009), respectively. For clarity, only one of the three samples' stress-strain curves was exhibited in Fig. 3 (a). The inserted images are the as built rod sample and the corresponding machined tensile sample. The tensile strengths and yield strengths of the samples were averaged to be 321 ± 7 MPa and 244 ± 10 MPa, respectively. The elastic moduli were averaged 98.9 ± 3 GPa and the elongations at break were averaged as high as 25 ± 2%. The fracture morphologies (Fig. 3 (b)) are characterized by many large and small dimples evenly distributing on the fracture surface. The high elongation of the tensile parts and the numerous dimples apparently indicate the

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excellent plasticity of the SLMed Cu-Cr-Zr copper alloy. Hence, the mechanical properties and the deformation behaviors of the corresponding lattice structures would differ from these of fragile or low plastic materials, such as Ti-6Al-4V and AlSi10Mg.

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Fig. 3 (a) Representative engineering stress-strain curve of as built tensile samples and (b) its fracture morphology; the inserted figures in (a) are the as built rod sample and the corresponding machined tensile sample, respectively.

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3.2 Structure characterization of the lattice structures Lattice structures with different cell sizes and relative densities exhibit distinctly different morphology features, as typical structures shown in Fig. 4. Structures 10-4 and 20-4 have the same cell size, while Structure 20-4 has smaller pore sizes but more stronger struts, as shown in Fig. 4 (a) and (b). This phenomenon is more significant between structures 10-6 and 20-6, as shown in Fig. 4 (c) and (d). For structures 10-4 and 10-6, the latter exhibits obvious larger nodes, stronger struts and larger pore sizes than those of the former and the same situation is applicable to structures 20-4 and 20-6. Hence, it is concluded that, given the same volume fraction, cellular structures with larger cell size exhibit stronger struts and larger pore sizes, while given the same cell size, cellular structures with larger volume fraction exhibit smaller pore sizes but stronger struts. Therefore, the well-controlled pore sizes and strut shapes were observed from the cellular structures, which indicates a good reproducibility of the SLMed parts from the designed model. The differences in volume fractions and cell sizes will lead to different mechanical properties, which will be discussed in following sections.

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Fig. 4 SLMed lattice structures of (a) 10-4, (b) 20-4, (c) 10-6 and (d) 20-6.

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Fig. 5 (a) and (b) present the SEM images of the cell nodes and the struts of the as built lattice structures. No cracks and strut deformations or breaks are observed, which suggests the good self-supporting and SLM forming properties of the diamond lattice structure of the copper alloy. Besides, many spherical particles that adhered to the surfaces can be seen. The adhered particles originate from partial melting of powders in heat-affected zone (HAZ), which is very common in SLM process no matter what the materials are. However, this phenomenon is worse for copper-based alloys, compared with other materials, such as Ti6Al4V [34], AlSi10Mg [35]. This could be attributed to the excellent thermal conductivity of copper, which readily leads to a larger HAZ.

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Fig. 5 SEM images of (a) cell node and (b) strut of the lattice structures.

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The SLMed sample (10-6) were well reconstructed by means of Micro-CT scanning. The three-dimensional display of the deviations between the Micro-CT reconstructed model and the designed model is demonstrated in Fig. 6 (a). Fig. 6 (b) shows the statistical diagram of the deviation distributions. According to Fig. 6, it can be found that the SLMed sample corresponds well with the designed model, with the deviation limits around ± 300 μm, which confirms the capability of the SLM to accurately fabricate Cu-based alloy cellular structures. The deviations are mainly caused by the adhered particles originating from the partial melting of powders, as shown in Fig. 5.

Fig. 6 Three-dimensional display of deviations between the Micro-CT reconstructed model and the designed model (10-6) (b) and the statistical diagram of the deviation

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The microstructures of the strut section (20-6) and the SLMed bulk material are exhibited in Fig. 7 (a) and (b). No apparent differences between the two samples are found. The samples demonstrate very dense and no defects such as pores or cracks are observed. The grain sizes of the both samples range from 10 μm to 70 μm and the grain shapes intervene each other and demonstrate irregular and random, which is beneficial to the material strength. This phenomenon can be attributed to the complex crystallization environment during SLM, in which the melting and solidification of the powders and the re-melting and re-solidification of the build platform occurred under the conditions of the recoil pressure of the metallic vapor and the Marangoni effects.

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Fig. 7 Microstructures of a strut section of the cellular structure 20-6 (a) and microstructures of SLMed bulk material (b).

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Fig. 8 (a-c) show the elements distribution maps of the strut section (20-6). The elements of Cr and Zr uniformly distribute in Cu matrix. This suggests no element segregations during SLM, namely no local aggregations of Cr and Zr elements in the sample, which demonstrates the homogeneous deposition of the SLM process. Fig. 8 (d) presents the XRD patterns of the powders and the strut section. No diffraction peaks in terms of other phases were detected other than α-Cu phase. This can be attributed to the uniform distribution and the small amount Cr and Zr elements (no more than 1%), which leads to the quantity of the elements exceeding the detection limit of the XRD device. In addition, the intensity distributions of the Bragg peaks of the SLMed struts differ from those of the powders, while the Bragg peaks of the powders are consistent with those of standard PDF card of Cu. This can be ascribed to the grains' priority in their growth direction that were governed by the specific temperature fields. Similar phenomena were observed in the investigation of Cu-10Zn and Al-based alloy via SLM [36, 37].

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Fig. 8 (a), (b), (c) elements distribution maps of the cellular structure strut section by EDS and (d) XRD patterns of the powders and the cellular structure strut section.

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3.3 Mechanical properties and compression deformation behaviors Compression tests were performed to investigate the mechanical properties and the deformation behaviors of the lattice structures. The engineering stress-strain curves of the nine category lattice structures were exhibited in Fig. 9. For clarity, only one (three for each category) representative curve was exhibited for each categories. Each curve demonstrates a similar curve trajectory. Stresses of all the curves increase with the strain increasing in the initial of compression and then pass into a stress plateau that is without stress collapses except for some slight stress fluctuations. At last, the stresses increase dramatically at around 55% strain, reaching densification stage. However, the stresses corresponding to the same strain of all the curves are different distinctly. Structures with the same volume fraction have comparable stress values that slightly decrease with the cell size decreasing from 6 mm to 4 mm. The Stress plateau is an import characterization for lattice structures during compression deformation, which exhibits different features depending on the types of material. Plastic materials exhibit long plateaus without large stress drops, while brittle materials show plateaus with dramatic stress drops [1, 12]. The prominent stress plateaus without stress drops in this paper benefits from the excellent plasticity of the Cu-Cr-Zr copper alloy and significantly differ from those of brittle materials and low plastic materials whose stress plateaus exhibit dramatic stress drops, such as Ti-6Al-4V [14] and Al-Si-10Mg [19] etc.. According to ISO13314-2011, the plateaus stress were given via calculating the arithmetical mean of the stresses between 20% to 40% strain. Due to no apparent first

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maximum compressive strength within the curves, the stress plateau values of the structures were considered to be the compressive strengths in this paper, as horizontal bold lines shown in Fig. 9. The elastic moduli and yield strengths of the lattice structures were also determined and averaged for each category following the standard of ISO13314-2011. All the details and mechanical properties of the lattice structures are listed in Table 2.

Fig. 9 Engineering stress-strain curves of the lattice structures.

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20-6 20-5 20-4 15-6 15-5 15-4 10-6 10-5 10-4

Yield strength (MPa) 6.91 ± 0.25 6.50 ± 0.14 6.19 ± 0.22 4.00 ± 0.16 3.85 ± 0.31 2.98 ± 0.35 1.78 ± 0.23 1.34 ± 0.17 1.21 ± 0.11

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Table 2 Details and mechanical properties of the lattice structures. Elastic modulus (GPa) 0.590 ± 0.020 0.560 ± 0.015 0.534 ± 0.013 0.345 ± 0.019 0.305 ± 0.025 0.273 ± 0.017 0.145 ± 0.012 0.125 ± 0.011 0.110 ± 0.006

compression strength (MPa) 12.83 ± 0.32 12.13 ± 0.20 11.23 ± 0.24 7.20 ± 0.35 6.56 ± 0.29 5.52 ± 0.27 2.78 ± 0.18 2.20 ± 0.11 1.84 ± 0.09

To evaluate the effects of the cell sizes and the volume fractions on the compression stresses and elastic moduli conveniently, relative stress and relative modulus were introduced among the structures with the same volume fraction. In this paper, the relative value was defined as the ratio of the stress (or modulus) to that of the structure with 6 mm cell size. Fig. 10 (a) and (b) show the stresses and the relative stresses of the lattice structures, which clearly exhibits the tendencies of the stresses with the volume fraction and cell size changing. According to Fig. 10 (a), the compression strengths diminish dramatically with the diminishing of volume fraction, while for structures with the same volume fraction, the compression stress values are mutually comparable. Relative stress can express the effect extent of cell sizes on stresses, as shown in Fig. 10 (b). Obviously, the relative stress

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decreases more significantly for structures with low volume fraction. This means that the stress is more sensitive to cell size for copper lattice structures with low volume fraction. Simultaneously, similar conclusions can be obtained for elastic moduli, as shown in Fig. 10 (c) and (d).

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Fig. 10 (a) The stresses, (b) relative stresses, (c) elastic moduli and (d) the relative elastic moduli of the lattice structures. Fig. 11 exhibits the deformation processes of the lattice structures of 20-4, 20-5, 15-5 and 10-5, which can represent the deformation behaviors of all the lattice structures in this paper. Obviously, all the cells within the structures involved the deformation process. For structures with 20% and 15% volume fractions, the deformations occurred uniformly until to the end of compression. The ɑ (shown in 20-4) that signifies the course of the deformation gradually reduces along with the compression process going. While for samples with 10% volume fraction, the initial stage (before 20% compression ratio) of deformation exhibits uniform. However, when the compression ratio reaches to a certain value (around 30%), the deformation focuses on a certain layer of cell nodes and then extends to the upper or lower portion of the structure, as shown in Fig. 11 (the sample of 10-5). The SEM images of 20-4 and 10-6 before and after deformation are presented in Fig. 12 (a), (b) and (c), (d), respectively. The struts of the both samples demonstrate bending deformation without fracturing and the cell nodes maintain intact, which is responsible for the uniform deformation of the samples and the compression stress plateaus free of stress collapses. This benefits from the excellent plasticity of the Cu-Zr-Cr copper alloy. As for the slight stress fluctuations, it can be attribute to the dislocations of the struts and cell nodes after contact and collision with the compression deformation further increasing.

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Fig. 11 Deformation processes of the lattice structures during compression.

Fig. 12 SEM images of the lattice structures of (a-b) 20-4 and (c-d) 10-6 before and after deformation. In general, the mechanical properties of lattice structures are directly related to the relative density (or volume fraction). Gibson and Ashby provided a series of equations of the relations between relative densities and mechanical properties for stochastic foam structures [1]. Two of the Gibson-Ashby equations are as follows,   Ec  C1  c  E0  0 

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  c  C2  c  0  0 

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(2)

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where Ec, ρc and σc are the apparent modulus, density and yield strength of a lattice structure and E0, ρ0 and σ0 are the elastic modulus, density and yield strength of the corresponding fully dense bulk material. Based on the tensile tests of the bulk samples above, the E0, and σ0 of the Cu-Cr-Zr alloy were determined to be 98.9 GPa and 244 MPa. It should be noted that the ρc/ρ0 equals to the corresponding relative volume fraction. Fig. 13 (a) and (b) show the log-log plots of the relative densities against relative moduli (or relative strengths). According to Fig. 13, the date points of the structures with the same cell size are well fitted to straight lines with the R2 above 0.99. The fitted equations in Fig. 13 (a) and (b) explicitly revealed the correlations between the strengths (or moduli) and relative densities of the lattice structures. By comparison, the fitted lines of the lattice structures with different cell size are discrepant. Specifically, a smaller cell size leads to a greater deviation from the Gibson-Ashby line. This can be explained by the fact that the struts are more slender for lattice structures with smaller cell size, which leads to the struts bending more easily during compression deformation. In addition, the fitted exponents and scaling factors differ from those of Gibson–Ashby model. According to Yan et al. [15], the immediate cause is that the ideal Gibson–Ashby model assumptions that the stochastic foam structures possess straight beams and perfectly smooth surfaces differ from the fact of the rough and irregular struts of the lattice structures. Despite the differences, the fitted equations provide important references for designing lattices structures for copper alloy.

Fig. 13 Log-log plots of (a) the relative moduli against relative densities and (b) the relative strengths against relative densities. 3.4 Energy absorption under compressive deformation It is of little significance for copper alloy lattice structures to act as a weight reducing or energy absorbing material due to the higher specific weight and the lower specific strength compared with lightweight materials, such as titanium alloys and aluminum alloys. However, taking into account of the high thermal and electrical conductivities, the energy absorption features of the copper lattice structures are worthy to be evaluated, which would provide a reference for a comprehensive application design. According to ISO13314:2011, the energy absorption per unit volume is calculated via the equation as follows,

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Wv    ( )d 

(3)

0

Where Wv represents the cumulative absorbed energy per unit volume, ε represents the strain and σ(ε) represents the stress relative to ε strain. According to Li et al. [38], the energy efficiency (η) is the ratio of the absorbed energy to a given strain (ε) divided by the corresponding stress (σ(ε)),which can be express as equation, as follows,

 



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 ( )d  (4)

 ( )

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This equation is often used to determine the point (εd) where η reaches to maximum and the point represents the starting of a lattice structure densification during compression deformation [12]. The functions of ε–Wv (left) and ε–η (right) are plotted in Fig. 14. It shows that the Wv of the 9 categories of the lattice structures are definitely different. The Wv of the cellular structure with 20% volume fraction(6 MJ/m3) is nearly larger 6 times than that of cellular structure with 10% volume fraction(1 MJ/m3). While, for structures with the same volume fraction, a larger cell size results in a higher Wv. Therefore, it can be concluded that the volume fraction has greater effect on Wv and that the effect of cell size on Wv cannot be ignored. In addition, the points are marked out where η reaches maximum on the curve of η-ε and the corresponding densification points are marked out on the curve of ε-Wv, as shown in Fig. 14. It should be pointed out that only three representative η-ε curves of the structures with different volume fractions were plotted due to the small effect of the cell size on the location of densification point. As depicted in Fig. 14, the densification points of the structures with smaller volume fraction correspond to a larger strain value. This is because the stronger struts and the smaller void spaces within the higher volume fraction structures lead to the early contact of the struts and nodes. It is well known that the heat transfer rate is proportional to heat transfer area and thermal conductivity. In this respect, copper-based alloys exhibit excellent thermal conductivities, while the lattice structures have high specific surface areas. Therefore, the relations of the energy absorption and the superficial area are worthy to be discussed for a comprehensive designing copper-based alloy lattice structures. The superficial area and the absorbed energy up to density point (Wd) are presented in one figure for convenient contrast, as shown in Fig. 15. It should be pointed out that the superficial areas were obtained through the corresponding CAD models. According to Fig. 15, the superficial area increases much with the decreasing of the cell size and decreases slightly with the decreasing of the volume fraction. While, the Wd dramatically increases with the volume fraction increasing and reduces moderately with the decreasing of the cell size. Consequently, the results provide a reference for designing copper lattice structures. Comprehensive considerations, such as weight losing, energy absorbing (strength) and thermal conducting (superficial area), should be taken when designing a copper alloy lattice structure and how to balance these considerations would depend on practical requirements. For example, when the main concerns are thermal conducting and energy absorption, the copper alloy lattice structures with larger volume fraction and smaller cell size would be the main concerned objects.

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Fig. 14 Energy absorption per unit volume and the energy efficiency of copper alloy lattice structures during compressive deformation.

Fig. 15 Energy absorption per unit volume up to density point (left) and the superficial area of the lattice structures (right). 4. Conclusions In this work, Cu-Cr-Zr lattice structures with TPMS diamond cell were manufactured via SLM and their mechanical properties, microstructures, compression deformation behaviors and energy absorption properties have been systematically studied for the first time. The effects of cell size and volume fraction on the properties of the cellular structures were evaluated and the relations of the energy absorption and the superficial area were discussed. The main findings are as follows. (1) The grain sizes range from 10 μm to 70 μm. The grain shapes intervene each other and demonstrate irregular and random, which is beneficial to the material strength. The main phase of SLMed samples is α-Cu phase and its Bragg peaks' intensity is different from the standard card. The EDS result suggests no segregation of Cr and Zr elements in Cu matrix. (2) Lattice structures with larger cell size and higher volume fraction exhibit distinctly larger cell nodes and stronger struts, which results in higher plateau stresses and elastic

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moduli. In addition, the plateau stress and elastic modulus are more sensitive to cell size for copper lattice structures with low volume fraction. (3) The compression deformation of the lattice structures occurred uniformly and all cells within the lattice structures involved the deformation. The SEM analysis indicates that the struts occurred bending deformation without fracturing and the cell nodes maintain intact. This is the main reason of the long stress plateaus of the stress-strain curves that without stress collapses. (4) The cumulative absorbed energy per unit volume (Wv) is affected by both the volume fraction and cell size and the Wv is mainly governed by the volume fraction. The lattice structures with larger volume fraction and cell size exhibit a higher Wv. (5) Explicit equations are fitted in terms of the relations between the volume fractions and the relative strengths (or moduli). The fitted lines deviated further from the Gibson-Ashby lines for the lattice structures with low volume fraction.

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Author Contributions Zhibo Ma and David Z. Zhang wrote the paper; Zhibo Ma, Fei Liu, and Junjie Jiang designed and performed the experiments; Zhibo Ma, Miao Zhao and Tao Zhang analyzed the data.

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Conflicts of Interest The authors declare no conflict of interest.

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Acknowledgements The authors gratefully acknowledge the funds from National High Technology Research and Development Program of China (863 Program: 2015AA042501).

References

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Data availability The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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Graphical abstract

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Highlights

Cu-Cr-Zr copper alloy lattice structures were well fabricated via selective laser melting for the first time.

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The compression deformations of the lattice structures occurred uniformly without cell breaking and strut fracturing.

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The stress-strain curves exhibit a long and rising stress plateaus without stress collapses.

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Properties of the lattice structures with lower volume fraction are more sensitive to cell size.

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Explicit equations depict the relations of the volume fractions and the mechanical properties.

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