Mechanical behaviors regulation of triply periodic minimal surface structures with crystal twinning

Highlights

• Inspired by crystal twinning, deformation programmable TPMS structures were constructed.

• Effects of the number, location and orientation of twin boundaries on TPMS structures were investigated.

• FE simulations reveal that twin boundaries effectively manipulate the direction and path of stress transfer.

• This method can be extended to other type of crystal defects and may yield different phenomena.

Abstract

Triply periodic minimal surface (TPMS) structures have been realized as excellent mechanical materials with high specific strength, energy absorption, and unique layered deformation mechanism due to their saddle shape-surface with non-positive Gaussian curvature. However, the performance of TPMS structures is limited by anisotropic mechanical behavior owing to the oblique shear band with stress concentration when the load beyond the yield stress, resulting in structural catastrophic failure. Herein, a strategy is proposed to manipulating the path of stress transfer by introducing crystal twinning to achieve a designable deformation behavior of the TPMS structures. Various contact reflection twin boundaries for the gyroid (G) and diamond (D) surface structures have been introduced by connecting the ideal structures by mirror-symmetry while maintaining the structural integrity. Compression tests were carried out from various directions of perfect and twinned- G and D surface scaffolds after 3D printing. It was found that the twin boundary can effectively protect the structure from catastrophic failure by deflecting the cracks under compressive loads, and regulate the deformation behavior by various structural design. This study provides new insights in applying the microscopic crystal defects to macroscopic architectural materials, which also contributes to the understanding of these unique microscopic structures.

Introduction

The study of lightweight architectural materials with high load-bearing capacity and controllable deformation mechanism is of great scientific and technological significance in many engineering applications, such as aerospace, automotive, medical device and infrastructure [1], [2], [3], [4]. Lattice or cellular structures have been extensively investigated in the past decades, such as Octet-truss and Kelvin lattice, honeycomb structures, etc. [2], [5], [6], [7], [8]. However, the sharp transformation of structural connections at the node sites brings about critical stress concentration, often leading to structure collapse [9], [10], [11].

The mathematically well-known TPMS structures can effectively avoid the stress concentration owing to their smooth saddle-shape hyperbolic surface without sharp edges or junctions and the highly interpenetrating networks [10]. The TPMS structures are emerging as outstanding mechanical materials with high specific strength and capacity of deformation [10], [12]. The recent development of additive manufacturing, or three-dimensional (3D) printing process, provides a facile solution for the manufacture of TPMS structures and promotes the research on their mechanical properties, such as compressive strength, elastic modulus, energy absorption, etc. [3], [12], [13], [14], [15], [16]. It has been found that the characteristic mechanical curves of the TPMS structures can be tuned by the printing substrate, topological structures, volume occupancy, repeating units, lattice orientation, etc. [17], [18], [19], [20], [21], [22], [23].

Improving the strength is undoubtedly the focus of the architectural materials. While the programming of the deformation mechanism is also significant, which requires rationally designing the path of stress transfer of the structures under load [24]. In previous reports, brittle bulk materials like glass and ceramics can be enhanced by introducing weak interfaces with weaker strength but good toughness to provide non-linear deformation and guide crack direction [25], [26], [27], [28]. Porous materials, such as honeycomb structures, composed of two-dimensional cells, improve energy absorption by restricting deformation through hierarchical construction [7], [29], [30], [31], [32], Lattice structures control the growth of the deformation shear bands by adjusting the direction and type of cell lattices within the structure [33], [34], [35]. For TPMS, the structures as well as their deformation mechanism can be regulated by tuning pore characteristics such as shapes, size, wall thickness and orientations [13], [17], [36], [37], [38], [39], [40] or the combination of different parameters upon changing their mathematical equations, such as gradient porosity and/or cell size [41], [42], [43], [44], [45]. Generally, designs that make TPMS structures to experience more tensile deformation increases its strength, while more flexural deformation increases its toughness [7], [46], [47], [48]. Branched and hierarchical designs could diversify the deformation mechanism and enhance their mechanics [49], [50], [51]. Moreover, fixed-point fracture can be also introduced by designing transition structure of different TPMS structures [41], [43], [52]. However, understanding the shear band activity of TPMS structures during compression and the effective structural regulations to avoid their catastrophic failure is still challenging.

This work proposes a new concept of damage resistant and deformation programmable TPMS structures inspired by crystal twinning, which effectively manipulate the load transfer and prevent the structural catastrophic fracture. Crystal twinning is a common form of crystal defects that consists of two or more adjacent segments of same structure with epitaxial orientations with respect to each other [53], and have been discovered in various biological and synthetic systems [54], [55], [56]. Inspired by the microscopic crystal defects, we constructed G and D TPMS structures and their structural variations associated with single and multiple twinned structures at different positions. The original structure and the path of stress transfer can be changed due to the designed structural model and the curvature fluctuation at the twin boundary, leading to various deformation and load transfer behaviors. The compressive tests were carried out on these structures obtained by 3D printing. We also employed finite element (FE) simulation to reveal the internal mechanism of the interaction between twin boundaries and shear bands.