Mechanical Properties of Bicrystal-Inspired Lattice Structures Fabricated by Additive Manufacturing

Abstract

While crystal-inspired design has become a promising strategy for developing advanced mechanical metamaterials, the specific role of individual grain boundary interfaces on the macroscopic mechanical properties has remained unclear. This study aims to elucidate the importance of this interface by designing, fabricating, and testing bicrystal-inspired lattice structures. Using the Coincident Site Lattice (CSL) theory, we modeled various Σ5 tilt grain boundaries in a bicrystal configuration. These structures were fabricated from SUS316L powder using a powder bed fusion (PBF) additive manufacturing process. Compression tests revealed that the presence and type of the macroscopic “grain boundary” interface are critical determinants of the mechanical response, with symmetric bicrystal structures exhibiting a distinct two-stage collapse. More importantly, by engineering the fine structure of the interface itself, such as the density of connecting struts, the mechanical properties can be precisely tuned, achieving a systematic variation in yield strength from 9.1 MPa to 11.5 MPa. This work clarifies the crucial role of interfacial structure in crystal-inspired metamaterials and provides a clear design principle for creating lightweight, damage-tolerant structures with programmable mechanical responses.

1. Introduction

The pursuit of materials with superior strength-to-weight ratios and damage tolerance has led to the development of architected metamaterials, a class of materials whose properties are determined more by their engineered internal structure than their chemical composition [1,2]. Additive manufacturing (AM), particularly metal powder bed fusion (PBF), has been a key enabler in this field, allowing for the creation of intricate lattice structures with unprecedented design freedom and geometric complexity [3,4,5]. This technological leap has opened the door to applications in aerospace, biomedical implants, and energy absorption systems where lightweighting and performance are paramount [6,7,8].

However, early architected materials, often composed of a single, repeating unit cell, suffered from a critical flaw: a tendency for catastrophic failure. Upon reaching their elastic limit, these monolithic lattices often failed via the formation and rapid propagation of localized shear bands, leading to an abrupt loss of mechanical integrity [4,9]. This behavior is undesirable for most engineering applications, where predictable and gradual failure (i.e., damage tolerance) is essential for safety and reliability.

To overcome this limitation, a paradigm shift in design philosophy was required. A particularly innovative approach emerged from the field of physical metallurgy: “crystal-inspired design,” where macroscopic lattice structures are designed to mimic the atomic arrangements and, more importantly, the microstructural features of crystalline materials [1]. This strategy has proven remarkably successful. Previous research has demonstrated that introducing features analogous to twin boundaries or polycrystalline arrangements into metamaterials can significantly improve properties like toughness and energy absorption [1,10,11]. This is achieved by creating “meta-grain boundaries” that act as engineered obstacles, effectively impeding the propagation of shear bands in a manner analogous to how atomic-scale grain boundaries hinder dislocation motion in metals. This approach effectively mitigates the catastrophic failure seen in single-orientation lattices.

However, as this design paradigm advances, a fundamental knowledge gap has emerged. While the beneficial effects of complex, polycrystalline-like arrangements are well-documented [10,11], the precise mechanical role of a single grain boundary interface—the fundamental building block of a polycrystal—has not been systematically isolated and investigated. Most studies have focused on polycrystalline analogues, where the effects of individual boundaries are convoluted with the complex stress fields arising from multiple grain interactions and triple junctions [2,10]. In the context of this study, the term “interface” refers to the macroscopic, two-dimensional boundary plane engineered between two distinct, oriented lattice regions (termed “meta-grains”), serving as a direct structural analogue to a grain boundary in a conventional polycrystalline material.

To address this gap, this study focuses on the simplest configuration where a boundary’s effect can be isolated: a bicrystal. We hypothesize that the macroscopic interface is a critical design element that governs the deformation, strengthening, and failure initiation of the entire structure. By designing various bicrystal-inspired lattice structures based on the well-defined Coincident Site Lattice (CSL) theory, we aim to systematically investigate the structure–property relationship. This work focuses specifically on the importance of the interface’s fine structure, demonstrating how it can be engineered to achieve a programmable mechanical response. The findings are expected to provide a clear and fundamental understanding of boundary engineering, paving the way for the rational design of next-generation mechanical metamaterials [12,13].

2. Materials and Methods

2.1. Material and Powder Characterization

Gas-atomized SUS316L stainless steel powder (EOS GmbH, Krailling, Germany) was used as the raw material [14]. The quality of the final additively manufactured part is highly dependent on the characteristics of the starting powder [15,16]. Therefore, a thorough characterization was performed. The characteristics specified by the manufacturer (EOS, Krailling, Germany) for this powder typically include a D50 particle size in the range of 20–50 μm and excellent flowability. Our analysis confirmed the powder’s suitability. As shown in Figure 1, SEM analysis revealed that the powder particles possess a generally spherical morphology with a smooth surface. The particle size distribution, measured by laser diffraction, showed a D10 of 23.26 μm, a D50 of 33.74 μm, and a D90 of 45.63 μm, which is well within the manufacturer’s recommended range for PBF processes [17,18].

The flowability of the powder was evaluated using Hall flowmetry and density measurements. The powder exhibited a flow rate of 14.51 ± 0.03 s/50 g. The apparent density and tap density were measured to be 4.21 ± 0.02 g/cm³ and 4.41 ± 0.03 g/cm³, respectively, resulting in a Hausner ratio of approximately 1.05. This indicates excellent flowability, consistent with the manufacturer’s specifications, which is crucial for forming uniform powder layers and minimizing defects [15].

2.2. Design of Bicrystal-Inspired Structures

To investigate the effect of the grain boundary interface, a multi-step computational approach was employed. The design workflow began with the selection of a base lattice topology, following established Design for Additive Manufacturing (DfAM) principles [5,19,20,21,22,23]. A Body-Centered Cubic (BCC) type lattice was chosen due to its inherent self-supporting geometry, which minimizes the need for support structures—a key consideration in topology optimization for AM [24,25,26].

The crystallographic information for the desired grain boundaries was generated using Atomsk [27]. Specifically, the atomic coordinates for a Σ5 CSL tilt grain boundary were generated, as schematically represented in Figure 2a. A custom Python 3.12 script then converted this atomic data into a macroscopic, strut-based lattice structure. This systematic approach allowed for the creation of several distinct structures for comparison, as summarized in

Table 1. Summary of Designed Lattice Structures.

Sample ID	Structure Type	Description
A, Ā	Single-crystal-like	Baseline structures with a single lattice orientation.
ĀA, AĀ	Asymmetric Bicrystal	Two meta-grains joined at an asymmetric interface.
AĀ-1.3×	Tuned Asymmetric Bicrystal	AĀ structure with the lowest interfacial strut density.
AĀ-1.4×	Tuned Asymmetric Bicrystal	AĀ structure with medium interfacial strut density.
AĀ-1.5×	Tuned Asymmetric Bicrystal	AĀ structure with the highest interfacial strut density.

.

2.3. Fabrication and Mechanical Characterization

The designed lattice structures were fabricated from the characterized SUS316L powder using a Concept Laser M2 PBF(GE Additive, Korea Institute of Materials Science, Changwon, Republic of Korea) system, as shown in Figure 3. The key process parameters, such as laser power (370 W), scan speed (1350 mm/s), and hatch distance (90 μm), were kept constant for all samples to ensure consistency [18,28]. The as-built samples shown in Figure 3 exhibit some surface roughness and minor imperfections (e.g., partially melted powder particles adhering to struts), which are characteristic and unavoidable features of the PBF process for such fine-scale lattice (structures. These surface features were observed to be consistent across all fabricated samples.

As shown on the build plate in Figure 3, the three columns correspond to different sample types as detailed in Table 1, while the rows represent identical repetitions fabricated to ensure consistency. For each of the main design types, three identical samples were tested to ensure reproducibility of the mechanical behavior. While a larger sample size would be beneficial for a comprehensive statistical analysis, the results showed high consistency, with representative curves presented in this study to demonstrate the proof-of-concept.

Following fabrication, mechanical properties were evaluated through quasi-static uniaxial compression tests, following the ISO 13314 standard [29]. The tests were performed at a constant strain rate of 10⁻³ s⁻¹. Load and displacement data were converted to engineering stress and strain. While the samples have a heterogeneous cellular structure, engineering stress (load divided by the initial cross-sectional area of the sample’s bounding box) and strain are used to represent the bulk mechanical response. This is a standard practice in the field of mechanical metamaterials [6,29], as it allows for the effective normalization and comparison of the overall performance of different architectures.

3. Results and Discussion

3.1. Role of Symmetry in Bicrystal Deformation

The mechanical behavior of the architected structures is dictated not only by the presence of an engineered boundary but, more critically, by the overall symmetry of the entire bicrystal or tricrystal system. In this study, none of the samples are simple single crystals; they are all designed as multi-grain systems to probe the effect of interfaces. The key design principle was to use symmetry to isolate the mechanical response of a specific type of interface.

The stress–strain curves in Figure 4 and the summary in Figure 5 reveal distinct deformation mechanisms rooted in the symmetry of each configuration. The ‘A’ structure can be considered a baseline tricrystal model (plate/grain A/plate), where the interfaces are between the meta-grain and the rigid compression plates. Lacking a pre-defined weak central plane, its deformation is more distributed and serves as a reference for a system without an engineered internal boundary.

The most insightful comparison comes from the two bicrystal designs. The ‘ĀA’ structure was intentionally designed with mirror symmetry about its central plane. This symmetry is crucial because it forces the initial deformation to occur at the two identical, centrally located grain boundaries, allowing their intrinsic properties to be studied without artifacts from asymmetric loading. As shown in the inset images of Figure 5 (left), deformation begins precisely at this engineered central boundary, corresponding to the first stress plateau. As strain increases, this central region densifies, leading to a rise in stress until a second collapse event is triggered at the secondary interfaces (near the plates). This sequential collapse gives rise to a distinct, two-stage deformation curve.

In stark contrast, the ‘AĀ’ structure, while also a bicrystal, lacks this central symmetry. Consequently, deformation initiates near the top and bottom plates where stress concentrations are highest. The intrinsic properties of the central grain boundary are masked by the premature failure at the plate-sample interfaces, resulting in a less distinct deformation curve, as seen in Figure 4b.

This design philosophy—using symmetry to isolate the properties of an interface—is conceptually analogous to the “2-Grain-Boundary (2GB)” model widely used in first-principles computational studies of grain boundaries. In such atomistic models, a supercell is constructed with two identical but inverted grain boundaries to satisfy periodic boundary conditions and eliminate artificial surface effects, thereby enabling the study of the intrinsic properties of a single, isolated boundary [30]. The ‘ĀA’ structure is a macroscopic physical realization of this 2GB computational model. Its symmetric design successfully isolates the deformation characteristics of the engineered Σ5 boundary, which manifests as the first, well-defined event in the mechanical response curve. The different behavior of the asymmetric ‘AĀ’ model serves as a control case, validating the critical importance of symmetry in designing experiments to probe interfacial properties.

3.2. Tuning Mechanical Properties via Interfacial Bond Engineering

Beyond the type and symmetry of the boundary, this study demonstrates that the fine structure of the interface itself can be engineered to precisely control the mechanical properties. This was investigated by systematically varying the “bond strength” of the ‘AĀ’ grain boundary interface. During the design phase, the connectivity between the two meta-grains was controlled by adjusting the cutoff distance used to create struts across the interface. As shown in Figure 6, three variations were created using cutoff distances of 1.3, 1.4, and 1.5 times the base interatomic distance, respectively. A larger cutoff distance results in a more densely connected, or “stronger,” interface.

The results demonstrate a clear and systematic trend: as the interfacial connectivity decreases (cutoff multiplier reduced from 1.5× to 1.3×), the initial yield stress systematically decreases from 11.5 MPa to 10.0 MPa, and finally to 9.1 MPa. While the absolute differences may seem modest, this represents a significant and predictable 26% variation in yield strength, achieved solely by altering the fine structure of the interface. This is not about achieving spectacular strength but about demonstrating a fundamental principle: the “programmability” of mechanical properties. This finding directly parallels the relationship between atomic bonding and grain boundary energy in real crystals [31], confirming that principles of atomic-scale grain boundary engineering can be effectively translated to the design of mechanical metamaterials.

4. Conclusions

This study investigated the fundamental role of the grain boundary interface in crystal-inspired mechanical metamaterials. Our results confirm that the interface is a critical design feature that governs the macroscopic mechanical properties. We have shown that the symmetry and fine structure of the interface can be engineered to precisely tune the mechanical response. Specifically, we demonstrated a predictable 26% variation in yield strength by modulating the interfacial strut density.

For engineers, this provides a clear design principle: for applications requiring maximum strength and stiffness from a given lattice topology, a design with a higher density of interfacial connections (e.g., the 1.5× cutoff) is recommended. Conversely, for applications where controlled, lower-stress failure initiation or increased compliance is desired, a sparser interface (e.g., the 1.3× cutoff) can be employed. This work clarifies the importance of interfacial engineering and provides a foundational principle for designing future lightweight, high-performance metamaterials with programmable mechanical properties.