Additively Manufactured Lattice Structures

Lattice structures (LS) deliberately allow removal of mass from a structure. Using additive manufacturing (AM) techniques to manufacture LS, proceeds by building up the object one layer at a time, allowing considerable freedom in design and enabling construction of fine internal geometries that are difficult or impossible to achieve with traditional manufacturing methods. The AMLS shown in Fig. 1a consists of two distinguishable phases, solid and air. Therefore, in addition to the microscopic hierarchy of the building solid consisting of e.g., grain boundaries (Fig. 1c), macroscopic structural elements themselves have structure (i.e. topology, Fig. 1b). Since both microscopic and macroscopic features are controllable during the manufacturing process (e.g., heat-treatment and CAD model, respectively), one has more freedom to design multifunctional parts or to tailor properties for a specific application.

For instance, open spaces in the lattice can be filled with fluid that enables heat-transfer applications such as cryogenic heat exchangers, compact heat sinks for high-power electronic devices, and heat shielding for aircraft exhaust [1, 2]. It is possible to design topologies in which Poisson's ratio increases and decreases with time [3]. These properties are controlled at unit cell length-scale. In order to fully utilize LS' capacity and enhance their functionality, it is necessary to move down in length-scale and understand the role of the constituent struts' microstructure, in conjunction with the topology, on the overall performance. Understanding the effect of hierarchical micro and macro structure can guide the manufacturing of LS with enhanced properties by leveraging AM characteristics that allow for the building of complex topologies with controlled microstructure. One of the main concerns in the above applications is mechanical behavior and predictability of LS under loading, which is essential for their successful integration in critical structures.

Specific Objectives

The specific objective of this research is to understand the underlying deformation mechanisms that occur at multiple length scale, which control yielding, post-yielding, plateau region, failure mechanism and give rise to widely disparate local responses in metallic AMLS (Fig. 2). The focus is on understanding the specific contribution and interplay between the microstructurally driven mechanisms (e.g., grain structures, orientation, porosity) and geometrically driven events (e.g., unit-cell buckling, node fracturing, macroscopic shear) on the dominant deformation mechanisms, as well as under what condition one mechanism becomes dominant. Once the governing mechanisms that controls strength and failure modes are understood, we will investigate whether they remain the same when the rate of the deformation increases. Doing so will reveal preferred materials' microstructures and topologies for a specific application and exactly what can be done to control unexpected failure.

Ongoing Research

Simultaneous optimization of microstructure and topology of the hierarchical material requires deciphering the direct relationship and interplay between microstructural features and geometrical topology under loading. The technical approach to investigate evolving intrinsic field variables during deformation relies on fusion of heterogeneous information derived from real-time data and post-mortem analysis obtained using emerging experimental methods. The schematic presented in Fig. 3 shows combination of several state-of-the-art techniques that we are using to correlate underlying microscopic phenomena to the materials response and failure mode at different length scales.

Key Findings

Post-processing heat treatment effects on the porosity distribution

A volumetric XCT investigation was conducted only on AMLS with Octet Truss topology (2 mm unit cell sizes) at as-built (AB), stress relieved (SR), and solution aged (SA) heat treatment conditions (Fig. 4).The total number of voids decreased due to each heat treatment step. Similarly, calculated void volume ratio, which represents the volume of the total porosity divided by the total volume of analyzed space, decreased during the SR heat treatment. However, void volume ratio remained constant when further HIP and solution aged heat treatments were applied. This finding stood out because it was expected that a further substantial decrease in voids would be observed in the SA sample. The fact that porosity did not decrease dramatically during HIP.

Post-processing heat treatment effects on the quasi-static behavior

Figure 5 shows the e ect of the post-processing heat treatments on the quasi-static behavior of the 2mm AMLS by comparing the stress-strain relationship for a fixed topology that undergoes SR, HIP, and SA heat treatment processes. It is seen from Figure 5 that the heat treated topologies undergoes a characteristic post- yielding behavior. Yielding proceeds with a distinctive pattern that is a rise in stress until a total engineering strain of 0:1 to 0:2, followed by a drop in stress. The drastic rise in the flow stress is a result of densification and can be explained by collapse and accumulation of the building struts on top of each other.

AMLS Calcification

Figure 6 shows the numerical results for 4 mm unit cell Octet truss, Diamond (D), Rhombic dodecahedron (RD), Dode-medium (DM). From Figure 6a and 6d unexpected softening after 1 mm and 0.5 mm displacement for OT and D respectively can be noticed. The simulation shows damage of the internal struts is the major cause of the drops in force-displacement behavior in all of the topologies studied here. In contrast, Figure 6b and Figure 6c show hardening during compression deformation. In all unit cells, damage tends to initiate from the junctions and propagate into the struts. This is due to the fact that the aspect ratio of the struts are rather large and they are not expected to experience high bending stresses due to their high flexural stiffness. When damage initiates from multiple junction sites, such as OT structure, a more or less steady plateau is observed in the stress-strain curves. That plateau is an indication of homogeneous propagation of damage. Diamond unit cell shows the least number of damage initiation sites as in Figure 6d, so further loading will cause rapid propagation of damage in the junction that effectively cleaves the struts and causes a significant drop in the load. All structures show eventual densification and internal contact but depending on the geometry, the initiation of densification and its extent are may vary. Unit cells with RD and DM topologies, Figure 6b & c, show a secondary hardening region due to self contact as a result of initial damage in Rhombic Dodecahedron and Dode Medium structures. This secondary hardening curve will lead to a secondary softening due to failure of newly contacted struts. Therefore, considering a single unit cell as the structural element, they can be classified as softening-based and hardening-based structures. Generally, the more diffused initial damage sites are, the more uniform load-displacement response is expected.

References

[1] Chang-Lin Tien and Kambiz Vafai. Convective and radiative heat transfer in porous media. In Advances in Applied Mechanics, volume 27, pages 225-281. Elsevier, 1989.[2] TJ Lu, HA Stone, and MF Ashby. Heat transfer in open-cell metal foams. Acta Materialia, 46(10):3619-3635, 1998.[3] Roderic Lakes. Materials with structural hierarchy. Nature, 361(6412):511, 1993.[4] Kavan Hazeli, Behzad Bahrami Babamiri, Joseph Indeck, Andrew Minor, and Hesam Askari. Microstructure-topology relationship effects on the quasi-static and dynamic behavior of additively manufactured lattice structures. Materials & Design, 176:107826, 2019.

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