Topology-mechanical property relationship of 3D printed strut, skeletal, and sheet based periodic metallic cellular materials

Abstract

Recent advances in additive manufacturing facilitated the fabrication of parts with great geometrical complexity and relatively small size, and allowed for the fabrication of topologies that could not have been achieved using traditional fabrication techniques. In this work, we explore the topology-property relationship of several classes of periodic cellular materials; the first class is strut-based structures, while the second and third classes are derived from the mathematically created triply periodic minimal surfaces, namely; the skeletal-TPMS and sheet-TPMS cellular structures. Powder bed fusion technology was employed to fabricate the cellular structures of various relative densities out of Maraging steel. Scanning electron microscope (SEM) was also employed to assess the quality of the printed parts. Compressive testing was performed to deduce the mechanical properties of the considered cellular structures. Results showed that the sheet-TPMS based cellular structures exhibited a near stretching-dominated deformation behavior, while skeletal-TPMS showed a bending-dominated behavior. On the other hand, the Kelvin and Gibson-Ashby strut-based topologies exhibited a mixed mode of deformation while the Octet-truss showed a stretching-dominated behavior. Overall the sheet-TPMS based cellular structures showed superior mechanical properties among all the tested structures. The most interesting observation is that sheet-based Diamond TPMS structure showed the best mechanical performance with nearly independence of relative density. It was also observed that at decreased volume fractions the effect of geometry on the mechanical properties is more pronounced.

Introduction

Cellular metals are materials with voids deliberately integrated in their structure [1]. When voids are arranged periodically the material is referred to as architected cellular metals (or lattices). Architected cellular metals can have two-dimensional cell configuration like in the case of honeycombs or three-dimensional configuration (cubic symmetry) like in the case of strut-based lattice structures. Cellular metals offer unique functional characteristics including high stiffness to weight ratio, heat dissipation and heat transfer control, and enhanced mechanical energy absorption among others. Justifiably, they attract a great deal of interest in several engineering disciplines. For example, such metals are used as biomedical implants [2,3], scaffolds for tissue engineering [4], filters [5], electrodes [6], catalysts [7], heat exchangers [[8], [9], [10]], and lightweight structures [[11], [12], [13]].

The mechanical properties of cellular metals are a function of the relative density (defined as the density of the structure relative to the density of the base material), the solid constituent, and the unit cell architecture. When subjected to a macroscopic loading, the structure deforms by a combination of bending, twisting or stretching of the strut members [14]. In a stretching-dominated deformation mode, the stiffness/strength of cellular structures scales linearly as a function of the relative density and is higher than that of a bending-dominated deformation mode that scale quadratically with the relative density. On the other hand, the toughness of a bending-dominated deformation is larger than that in the case of stretching-dominated deformation mode [15].

When both the base material and the relative density are fixed, the mechanical properties of cellular structures depend highly on the architecture of the unit cell. Research efforts were invested to find the most optimum cell topology that can provide the best mechanical properties with the least amount of material invested in order to maximize the stiffness/strength to weight ratio. As a result, several studies focused on the role of cell topology on enhancing the mechanical properties [16]. In tissue engineering specifically, extensive research has been done to identify the best topology that mimics the nature of bone and provides a viable environment to recuperate and regenerate damaged tissue cells [17,18]. For cellular metals with cubic symmetry, strut-based cell topologies such as the Octet-truss and the Kelvin have been vastly investigated [[[25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40]],[19], [20], [21], [22], [23], [24]]. Recently, focus shifted towards cellular structures with mathematically defined architectures such as triply periodic minimal surface (TPMS) based topologies [[25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40]]. TPMS are complex 3D topologies that locally minimize surface area for a given boundary, and can be repeated periodically in three perpendicular directions [38,39,[41], [42], [43]]. These surfaces split the space into two or more interlocked domains, where each domain is a single connected and infinite component with no enfolded voids. Due to their novel topological features, TPMS have been employed in many engineering disciplines, for instance, in tissue engineering [37,44], and structural engineering [27,30,31,45,46], they proved to have optimal thermal and electrical conductivities [47], optimized fluid permeability [35], tunable acoustic attenuation and transmission [48], as well as visible photonic crystal properties [49]. TPMS-based structures can be created either by thickening the minimal surface to create sheet-based cellular structures or by solidifying the volumes enclosed by the minimal surfaces to create skeletal-based cellular structures [37].

Until recently, the fabrication of complex cell geometries was a big challenge, and the challenge increases when the desired size scale gets smaller. The recent advances in additive manufacturing (AM) helped mitigating these challenges. Additive manufacturing or commonly-known as 3D printing refers to the process of fabricating parts layer by layer, adding materials only where it is needed, reducing considerably the amount of wasted material and allowing for much more design freedom. For metals, powder bed fusion techniques such as selective laser sintering (SLS), selective laser melting (SLM), and selective electron beam melting (SEBM) are used. In these techniques, an energy source (laser or electron beam) is utilized to selectively melt or sinter layers of metal powder to form a 3D structure. Using these techniques, several cellular structures with complex architectures were investigated for their mechanical properties using a range of 3D printable materials including aluminum [45,50], titanium [51] and steel alloys [46,52]. For instance, SEBM was employed to fabricate strut-based cellular structures made of titanium alloys with mechanical properties similar to human bone [2]. SLM was also employed to fabricate strut-based cellular structures for bone in-growth applications where their mechanical properties were found to be analogous to those of human bone [21,22]. The compression and blast loading response of stainless steel structures based on the octahedral and pillar-octahedral structures (both of which are strut-based topologies) fabricated using SLM were also investigated [20]. On the other hand, the influence of processing conditions, laser printing parameters, and printing orientation on the mechanical properties of strut-based cellular structures was also a matter of extensive investigation [[53], [54], [55], [56]]. For example, Liu et al. [54] employed X-ray computed tomography to capture process-induced defects and studied their effect on the overall mechanical properties of 3D printed metallic octet and rhombicuboctahedron lattice structures. Their results showed that geometric imperfections can cause failure mode transitions not visible in defect-free lattices. The effect of building orientation and heat treatments on the microstructure and mechanical properties of 3D printed Ti6Al4 V lattice structures were investigated by Wauthle et al. [55]. Their results show a significant decrease in mechanical strength for samples that are built diagonally. Fogagnolo et al. [56] studied the effect of laser energy inputs on the microstructure and the mechanical properties of Ti6Al4 V 3D printed lattices. Their results showed that the use of high-energy input parameters resulted in better mechanical properties. In general, material and geometric imperfections observed in the as-built lattices strongly influence their elastic response and failure mechanism [54].

TPMS-based cellular structures are characterized by a smoother transition at the connection point of the structure’s components than that observed in strut-based cellular structures (see Fig. 1). The skeletal-Gyroid and skeletal-Diamond cellular structures, which are types of TPMS-based structures, have been studied for their printability and mechanical properties using a variety of metals [45,46,51,52]. Also, the relationship between deformation mechanism and mechanical properties of additively manufactured skeletal-TPMS based cellular structures, namely, the IWP and FRD was investigated [57] where the results showed that stretching-dominated mode of deformation is observed when the global orientation of struts were in line with loading direction.

In recent studies, elastic, viscoelastic, thermal and electrical effective properties of sheet-TPMS based cellular structures and interpenetrating phase composite microstructures based on sheet and skeletal TPMS were studied numerically and experimentally by Abu Al-Rub and co-workers [[25], [26], [27], [28],[30], [31], [32],34,[58], [59], [60], [61]]. Also, stiffness and yield strength of metallic architected foams based on the Schwarz Primitive TPMS [[61], [62], [63]], the quasi-static mechanical properties, and energy absorption of other metallic sheet-TPMS based topologies were investigated [33,64]. For quasi-static mechanical properties, the sheet-TPMS based porous biomaterials made of titanium alloy were tested for a range of relatively high relative densities between 42% and 71% [33]. The results showed a favorable but rare combination of relatively low elastic properties in the range of those observed for trabecular bone and high yield strengths exceeding those reported for cortical bone. Also, energy absorption investigations showed that the sheet-Gyroid structure made of aluminum or steel alloys exhibited desirable specific energy absorption values [33,64].

In the previously mentioned studies, the role of geometry in tuning the mechanical properties of cellular structures was investigated. However, the use of different materials, fabrication techniques and range of relative densities restricts a fair and sound comparison between the examined cell topologies. In this work, we design, fabricate, and mechanically test cellular structures based on the classes mentioned earlier (see Fig. 1), namely, the strut-based, skeletal-TPMS based and sheet-TPMS based cellular structures. For that purpose, we consider the commonly-known Kelvin, Octet-truss, and Gibson-Ashby strut-based cellular structures; the IWP, Gyroid, and Diamond skeletal-TPMS based cellular structures; and the IWP, Gyroid, Diamond and Primitive sheet-TPMS based cellular structures.