1 Green laser powder bed fusion based fabrication and rate - dependent mechanical properties of copper lattices

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Green laser powder bed fusion based fabrication and rate-

dependent mechanical properties of copper lattices

Sung-Gyu Kang a*, Ramil Gainov b, Daniel Heußen c, Sören Bieler d, Zhongji Sun e, Kerstin

Weinberg d, Gerhard Dehm a, and Rajaprakash Ramachandramoorthy a*

a Max-Planck-Institut für Eisenforschung GmbH, Max-Planck-Straße 1, 40237 Düsseldorf,

Germany

b Institute of Mineral Resources Engineering, RWTH Aachen University, Wüllnerstraße 2,

52062 Aachen, Germany

c Fraunhofer-Institut für Lasertechnik ILT, Steinbachstraße. 15, 52074 Aachen, Germany

d Lehrstuhl für Festkörpermechanik, Universität Siegen, Paul-Bonatz-Straße 9-11, 57068

Siegen, Germany

e Institute of Materials Research and Engineering, Fusionopolis Way 2, 138634 Singapore

*Corresponding author: Dr. Sung-Gyu Kang and Dr. Rajaprakash Ramachandramoorthy

E-mail: s.kang@mpie.de and r.ram@mpie.de

Abstract

Lattice structures composed of periodic solid frames and pores can be utilized in energy

absorption applications due to their high specific strength and large deformation. However,

these structures typically suffer from post-yield softenings originating from the limited

plasticity of available material choices. This study aims to resolve such an issue by fabricating

lattice structures made of ductile pure copper (Cu). For the first time, Cu lattice structures are

fabricated through laser-powder bed fusion (L-PBF) with green laser (λ = 515 nm). Structural

and microstructural analysis confirm that the lattice structures consist of well-defined unit-cells

and show dense microstructure. The deformation behavior is investigated under a wide range

of strain rates from ~0.001 /s to ~1000 /s. The stress-strain curves exhibit a smooth and

continuous deformation without any post-yield softening, which can be attributed to the

intrinsic mechanical properties of Cu. Correlated with post-mortem microscopy examination,

the rate-dependent deformation behavior of pure Cu lattice structures is investigated and

rationalized. The current work suggests that the complex Cu architectures can be fabricated by

L-PBF with green laser and the lattice structures made of ductile metal are suitable for dynamic

loading applications.

1. Introduction

Lattice structures are composed of periodic solid frames and pores. Its periodicity enables

higher specific strength compared to unstructured foams Combined with large deformation

until densification under constant loads arising from the low relative density, the lattice

structures can exhibit a larger absorption capacity compared to solid materials under

compression[1–3]. Recent advances in the additive manufacturing (AM) processes have

enabled several studies on lattice structures with envisioned applications in a variety of sectors

including aerospace [4,5], biomaterials [6–8], mechanical band gap engineering [9–11], and

impact absorption [12–14]. The deformation characteristics of lattice structures strongly

depend on the geometry and the material. From the geometrical point of view, the strength of

the lattices can be tuned by controlling the orientation of load-bearing solid frames, density,

and connectivity. To date, various lattice geometries such as open-cell truss lattices [12,14–16],

closed-cell plate lattices [17–19], triply periodic minimal surface structures [20–22], and shell

structures [23,24], have been investigated both experimentally and computationally. From the

material point of view, previous studies have shown that the intrinsic plasticity of the material

strongly affects the deformation characteristics of lattice structures. The microlattice structures

made of brittle materials such as alumina [24–26] and pyrolytic carbon [17] show high strength

but low plasticity. On the other hand, the macroscale lattice structures made of Ti- [27,28], Al-

[29], and Fe-alloys [30] show continuous deformation with large plastic strains, leading to

superior energy absorption capacity as compared to random foam structures. Interestingly, even

in these lattice structures made of structural load-bearing alloy systems, abrupt softening may

occur during deformation, which degrades their energy absorption capacity [12]. This abrupt

softening behavior originates from the buckling or cracking of the strut structure. Specifically,

the lattice structures with slender geometry or made of less ductile materials possibly exhibit

post-yield softening under compression [31–33]. Accordingly, to develop a robust lattice

structure without post-yield softening, systematic studies on lattice structures made material

with high plasticity are a pre-requisite [12].

Among various possible material choices, pure copper (Cu) is one of the desired

candidates due to its high plasticity under mechanical loading. Combining its excellent thermal

conductivity with the superior specific energy absorption of the lattice structures, this unique

physical property synergy could potentially lead to singular applications in thermal

management and heat exchanger scenarios. To date, most AM-built lattice structures are made

by the laser-powder bed fusion (L-PBF) technique, largely due to the process’s refined surface

finish and design freedom. However, it is currently a challenge to fabricate pure Cu through

the conventional L-PBF route, which typically employs an infra-red laser with a wavelength

>1000 nm. This is because the Cu energy absorptivity drops significantly (<10 %) once the

laser wavelength is above ~800 nm [34]. Together with this material’s high thermal

conductivity (~400 W/m-K), it is difficult to maintain a stable melt pool during fabrication. A

preliminary study on the solid Cu parts built via L-PBF reported a high density of internal

fusion defects agreeing with the previous hypotheses [35]. This problem can be partially

alleviated by increasing the laser power [36,37], decreasing the spot size [38], and decreasing

the powder size [39]. A more direct approach is to employ a laser source with a lower

wavelength. It has been recently reported that the high energy absorptivity of Cu under a blue

[40] or a green laser [41,42] (λ = 450 and 515 nm, respectively) allows fully dense prints of Cu

parts. Correspondingly, conceptual/theoretical studies for Cu-based 3-dimensional lattices,

utilizing their mechanical, electrical, and thermal properties have been previously proposed

[43–45], yet the fabrication and mechanical performance of Cu-based lattice structures remain

unexplored so far.

To evaluate the mechanical performances and the energy absorption capacity of lattice

structures, the deformation behavior needs to be investigated at a wide range of strain rates.

This is because the strength of bulk metallic materials shows a distinctive strain rate

dependency, governed by the dislocation movements [46]. Likewise, lattice structures made of

such materials are also subjected to the influence of different strain ratesduring plastic

deformations. However, due to the experimental complexities and the requirement of different

testing devices, the deformation behavior of previously designed lattice structures was mainly

studied either at quasi-static (0.001 /s) [47,48] or dynamic strain rates (1000 /s) [49,50].

Therefore, this is currently a knowledge gap on mechanical behavior of lattice structures across

the full range of strain rates, i.e., including the quasi-static, the intermediate (0.01 ~ 100 /s),

and the dynamic strain rates (>1000 /s). Such data is critical to thoroughly understand the

deformation behavior of lattice structures and propose future design guidelines for lattice

structure adoptions.

In this study, we systematically investigated the mechanical properties of pure Cu-based

lattice structures fabricated successfully, for the first time, using L-PBF with a green laser beam

source. Two different lattice structures showing different deformation mechanisms were chosen.

The structure and microstructure of each lattice structure were examined using X-ray and

electron microscopy-based methods, respectively. The lattice structures were compressed at a

wide range of strain rates from 0.001 to 1000 /s. Combined with post-mortem structural and

microstructural analysis, the deformation mechanisms and the mechanical performance of Cu

lattice structures were identified. We believe that this study will expand the applicability of

additively manufactured 3-dimensional architectures and will provide a guideline for the

fabrication of near-ideal ductile metallic lattices for dynamic applications.

2. Experimental methods

2.1. Sample preparation

The deformation of strut-based lattice structures is primarily dictated by the nodal

connectivity according to Maxwell’s criteria [51],

𝑀 = 𝑏 − 3𝑗 + 6 (1)

where 𝑏 and 𝑗 are the number of struts and intersections (nodes) in the unit cell. For the

structure with high nodal connectivity (𝑀 ≥ 0), the deformation is dominated by the stretching

of struts. For the structure with low nodal connectivity (𝑀 < 0), the deformation is dominated

by the bending of struts [32]. Accordingly, we selected an octet-truss structure with 𝑀 = 0

(denoted as Oct) and a cuboctahedron structure with 𝑀 = −6 (denoted as Cub) as unit cells of

the lattice structures (Figure 1(a, b)). The unit-cell length and the strut diameter were chosen

as 1.5 mm and 300 μm, respectively. The relative densities of Oct and Cub structures are 0.38

and 0.21, respectively. Each lattice structure was designed to have 80-unit cell repetitions: A 4-

repetition of unit cells along the z-axis, and a 20-repetition of unit cells in a cross-section

perpendicular to the z-axis. In the cross-section perpendicular to the z-axis, we discretized the

unit-cell geometry and arranged them symmetrically, optimizing the lattice geometry for the

mechanical test (Figure S1). Additional plates at the top and the bottom of the lattice structure

were introduced to ensure uniform deformation under loading along the z-axis. Computer-

aided design (CAD) files of the Cub and the Oct structures were designed for the following

fabrication process.

We utilized the L-PBF process with both green laser and infra-red laser beams (λ = 515

and 1064 nm) for the sample fabrication. The pure Cu (electrolytic tough-pitch) powder with a

diameter of 16-63 µm (Nanoval GmbH) was used. Before the lattice fabrication, the L-PBF

parameters, such as laser power, scan speed, layer thickness, and beam diameter were

determined after a sequential process parameter optimization by fabricating the test cuboidal

samples (10 mm × 10 mm × 10 mm) with varying parameters to maximize the density.

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1Greenlaserpowderbedfusionbasedfabricationandrate-dependentmechanicalpropertiesofcopperlatticesSung-GyuKanga*,RamilGainovb,DanielHeußenc,SörenBielerd,ZhongjiSune,KerstinWeinbergd,GerhardDehma,andRajaprakashRamachandramoorthya*aMax-Planck-InstitutfürEisenforschungGmbH,Max-Planck-Straße1,40237Düsseldo...

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