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Nov 05, 2024

On the crack resistance and damage tolerance of 3D-printed nature-inspired hierarchical composite architecture | Nature Communications

Nature Communications volume 15, Article number: 9532 (2024) Cite this article Metrics details Materials scientists have taken a learn-from-nature approach to study the structure-property

Nature Communications volume 15, Article number: 9532 (2024) Cite this article

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Materials scientists have taken a learn-from-nature approach to study the structure-property relationships of natural materials. Here we introduce a nature-inspired composite architecture showing a hierarchical assembly of granular-like building blocks with specific topological textures. The structural complexity of the resulting architecture is advanced by applying the concept of grain orientation internally to each building block to induce a tailored crack resistance. Hexagonal grain-shaped building blocks are filled with parallel-oriented filament bundles, and these function as stiff-blocks with high anisotropy due to the embedded fiber reinforcements. Process-induced interfacial voids, which provide preferential crack paths, are strategically integrated with cracks to improve fracture toughness at the macroscopic scale. This study discusses the structural effects of the local/global orientations, stacking sequences, feature sizes, and gradient assemblies of granular blocks on crack tolerance behavior. Alternating stacking sequences induce cracks propagating in the arrestor direction, which boost the fracture energy up to 2.4 times higher than the same layup stacking sequence. Gradient arrangements of feature sizes from coarse to fine or fine to coarse result in the coexistence of stiffness and toughness. Our approach to applying crystallographic concepts to complex composite architectures inspires for original models of fracture mechanics.

Nature is a plentiful source of inspiration for overcoming the current challenges facing the science of artificial materials. As the mechanical limitations of existing engineering materials have become apparent, material scientists have turned their attention to natural biological systems to find original models for toughening mechanisms1,2,3. For example, biomineralized materials, such as the brick-and-mortar structure of abalone shell nacres4, the gradient structure of bamboo stem vascular bundles5, and the bouligand structure of crustacean exoskeletons6, have provided abundant structural motifs to inspire the design of damage-tolerant architectures. These structures usually originate from simple elementary building blocks, the hierarchical assembly of which exhibits a synergistic mechanical performance beyond the capabilities of the individual building blocks7,8.

The recent emergence of a bottom-up 3D printing process, which corresponds to the architectural concept of natural evolution, has accelerated the expansion of research on nature-inspired structures by providing design freedom in geometric constructions9,10,11,12,13. For example, the 3D printing of specific topological arrangements using two different materials, stiffer platelets and softer matrix, resulted in tough composites inspired by mineralized natural materials12. The granular microstructure of crystalline materials in metallurgy has also served as an inspiration motif for 3D printing. By mimicking elements of crystal microstructures such as crystal phases, grain boundaries and precipitates, a range of robust and damage-tolerant architectures has been developed13. By expanding our interest to composite materials, we can find further applications14,15. Among many studies, much attention has been focused on the process-induced shear alignment and hierarchical distribution of fibrous or 2D platelet reinforcements16,17,18,19,20. Induced magnetic fields and nozzle rotations have also made significant contributions to the tunable alignments of reinforcements in concentric, stacked, and spiral patterns17,18,19,20.

In terms of fracture mechanics, recent reports demonstrated that fine planar alignment of discontinuous reinforcement, when induced layer by layer, improves fracture toughness accompanied by increased crack resistance and fracture surface21,22. Indeed, a model of nature-inspired fracture mechanics designed by combining bouligand and nacrous staggered structures showed a hybrid-toughening mechanism of crack twisting and crack bridging along the planar fiber orientations gradually rotated by a certain pitch angle21. Moreover, the anisotropic arrangement and heterogeneous distribution of fibers over the micro and macro scales control the crack propagation mode and assign enhanced fracture toughness far beyond monolithic anisotropic structures. The monolithic anisotropic structures have a simple in-plane arrangement, which allows cracks to propagate straight along the lowest toughness direction. In contrast, the anisotropy and heterogeneity of fiber orientation force crack tips to repeatedly deflect and arrest, which increases local crack resistance and causes additional fracture energy dissipation throughout the system23,24.

On the negative side, the spontaneous formation of void defects that are inherent in 3D printing has been identified as a critical issue25,26. However, recent studies have shown that controlled void formation in biomimetic composites may not be detrimental in terms of nature-inspired engineering27,28. The strategic incorporation of voids in printed composites can help realize engineering solutions that imbue effects such as crack blunting and crack deflection6,27. Accordingly, there has been much discussion about the hierarchical organization of subfilament bundles prepared by FDM printing, and it has been clarified that the geometric arrangement and interfacial bonding strength of subfilament bundles can have a significant impact on fracture toughness29. The macroscopic crack planes along weak interfaces, accompanied by multiple crack deflections and branchings, reduced the fracture driving force and induced progressive damage. Since large amounts of filaments and interfaces participated in plastic energy dissipation, the total amount of fracture energy that can be consumed throughout the system increased correspondingly. Rather, contrary to expectations, excessive interfacial bonding strength inhibited crack blunting and led to fatal damage. Interestingly, the strategically integrated void-crack provides detectable warning and a wide margin before final failure, thereby guiding a safe failure mechanism with a high residual load carrying capacity. This synergistic void-crack interaction has been well addressed in simple layup monolithic composites6,27,29,30, but a meaningful attempt in complex hierarchical architectures has so far not been undertaken, and furthermore, experimental evidence has not been presented to verify the basic assumptions. Our efforts on these issues would occupy this blank space in two aspects: the presentation of nature-inspired complex hierarchical structures and the scientific understanding of their failure mechanisms.

We report a concept of nature-inspired architecture, which is hierarchically assembled from grain-like building blocks with specific topological textures. Granular domains have been defined by sequential local printing, filling each sub-region with aligned filament bundles of anisotropic properties. The individual granular domains, which serve as fundamental building blocks, were strategically positioned in a planar layer with varying sizes, orientations, and organizations, and then hierarchically layered in various stacking sequences. The reinforcing fibers embedded in the elementary filaments contributed to the local anisotropy from granular orientation15,31. The macroscopic topological texture was specified by the textural contrast of the interfaces between the subfilament bundles in the building block assembly.

Our study starts with the three-dimensional visualization of a series of nature-inspired architectures, assembled by local/global orientations, stacking sequences, feature sizes, and gradient assemblies of granular blocks, respectively, and then is extended to the observation of the corresponding fracture behaviors. The main objective is to investigate the resulting characteristic granular cracking behaviors, which are inherently induced by the synergistic crack-void interactions and the obstacle effects of aligned fibers. It is well known that crack growth along grain phases or grain boundaries in crystallography determines the embrittlement and damage tolerance of materials, which should be properly compared to our hierarchical artifacts32. The current work focuses specifically on the spatiotemporal capture of three-dimensional fracture geometry along process-induced multiscale arrangements of discontinuous reinforcing fibers and weak void interfaces, aiming to clarify the resulting anisotropic fracture behavior by presenting experimental evidence. In fact, previously presented surface observations have limited usefulness due to the loss of spatial information about the interior of the bulk material, which leads to incomplete understanding or incorrect information about the failure mechanisms of 3D structures33,34. Here the crack geometry was correctly identified in the micro-macroscopic range, and consequently, the understanding of the microstructural effects of hierarchical orientation and void-crack interactions on macroscale crack propagation was improved with definite scientific validation.

Biomimetic and 3D printing is a co-operative and collaborative approach to elucidate the design principles of complex structures of natural mineral materials. Figure 1 shows schematic illustrations of nature-inspired meso- and macro-structures of 3D-printed composite architectures. Representative nature-inspired structures, such as the grain orientations and grain boundaries of polycrystalline materials (e.g., metals or ceramics) and the two-dimensional layered structure of natural nacres, are also presented for comparison (Fig. 1a–c). In order to seek an analogy with these natural structures and their resultant fracture behavior, we have designed the 3D printing of hierarchical granular architectures using fiber-reinforced composites as the base filament material (Fig. 1d). Fiber-reinforced composites are good material candidates to meet the high local anisotropic stiffness requirement, which is a key design factor for mimicking the grain orientation of polycrystalline materials. Fused filament extrusion induces local orientation of the embedded fiber reinforcement along the printed filament’s direction because of the shear flow from the narrow nozzle wall. The resulting fiber orientation serves to improve the anisotropic stiffness of the polymer matrix (Suppl. Fig. 1a)15,25. The inherent nature of 3D printing, which fills the three-dimensional architecture with parallel filament threads, also spontaneously produces voids that weaken and lower the adhesion of the interfaces between filaments (Suppl. Fig. 1b)28. We propose that these two process-induced microstructural features, i.e., a high degree of material alignment (fused filament and embedded fiber) and interfacial void formation, are important functional building elements that induce a tailored crack resistance, and we have strategically used them to fabricate hierarchical architectures with specific topological texture by motif-modeling of natural systems.

a Structural mimics of natural granular systems. b, c Motif modeling of grain microstructure of polycrystalline materials and brick-and-mortar of natural nacres in terms of granular orientation and stacking sequence. In order, CAD model, optical image, and schematic illustration, respectively. d Schematic representations showing strategic functions of two process-induced microstructural features to mimic natural crystalline grain microstructure. e Representative set of images showing the inter- and intra-granular cracking behaviors driven by interfacial voids and aligned fibers.

Each sub-granular filamentary domain, which has the motif of a grain in a polycrystalline natural material, contains bundles of microfilaments that are highly aligned in the same direction. The interfacial voids between adjacent filamentary domains can be defined as a granular domain boundary, i.e., with the motif of a grain boundary in natural polycrystalline materials (Fig. 1d). Within the granular domain, the structural voids that form naturally along the interfaces of aligned filaments have the same motif as cleavage planes or slip planes in a crystal grain. Note that the interfacial filament adhesion within the granular domain is stronger than the adhesion of the granular boundary. This is because the printing of the granular domain is completed with a high packing density and this is sequentially followed by printing of the neighboring granular domains with a small margin, so each granular boundary has a relatively low packing density (Suppl. Fig. 1c). Grain orientation is defined by local adjustment of the printing direction, such that the microfilament bundles within an individual granular domain all have the same printing direction. The printing of each local region creates a two-dimensional representative hexagonal granular building block that is densely packed with filament bundles in a specific printing direction, and the granular size is scaled by controlling the hexagonal feature size. Eventually, the in-plane grain structure is extended into three dimensions by modeling the staggered stacking sequence of natural nacre. The staggered stacking sequence forms a complex network of filaments in overlapped planes, with each layer consisting of different filament arrangements (see Fig. 1c).

Figure 1e presents a representative set of images comparing the inter- and intra-granular cracking behavior of 3D printed nature-inspired architectures with the corresponding mechanisms in polycrystalline materials. Natural polycrystalline materials demonstrate two representative brittle fracture mechanisms depending on the competition between inter- and intra-grain cracking; inter-granular cracks occur along the grain boundaries, and intra-granular cracks follow specific sets of cleavage planes that are defined by the crystallographic structure. The propagating crack in the nature-inspired 3D-printed architecture, on the other hand, preferentially explores the interfacial voids between the aligned filaments of inter- and intra-granular domains. Since the hexagonal granular domains have enhanced stiffness in the specific direction of densely packed filament bundles with aligned reinforcing fibers, the crack preferentially selects the interfacial voids along the granular boundary as the most energetically favorable path. This crack propagation model is representative of the inter-granular cracking behavior of natural polycrystalline materials, although different in detail. Intra-granular crack propagation in the trans-filament direction can occur in certain geometric configurations of the hexagonal blocks. However, once in the granular domain, the crack direction is again guided by energy minimization by the intra-granular voids along the interfaces between aligned filaments. We expect that the propagating crack expands and distorts the fracture path along the guided weak interfaces, which dissipates additional fracture energy and eventually behaves as the macroscopic strengthening mechanism. Nevertheless, this mechanism still corresponds to the two-dimensional crack propagation mode expected for the single-layer structure, and our interest is in the basic question of how the energetically driven three-dimensional crack propagation will be further determined by the stacking sequence design. Cracks have an inherent tendency to propagate toward easy paths guided by energy minimization, but nevertheless, it remains to be examined what mechanisms promote the fracture toughness when crack propagation paths are forced tailoring layer-by-layer.

In composite materials with filament bundles, the reinforcement effects of the embedded fibers, including fiber length, fiber content, length-to-diameter ratio, as well as the interfacial bonding strength between fibers and matrix, are important geometrical/physical parameters. These affect the cracking behavior of the granular architecture. The rational design of fiber length, content, etc., determines the anisotropic stiffness of local granular domains and can also control the stiffness ratios between the local regions of the granular domains and their boundaries. The highly aligned fibers within the granular domain will strongly resist crack propagation in the trans-filament direction and will act to divert the crack path towards the longitudinal fiber direction. This effective obstruction by embedded fibers can be understood in a similar way to oriented hard phases in natural polycrystalline materials35. As the embedded fiber length increases from short to long or continuous fibers, the resistance to trans-filament crack propagation will increase significantly. The interfacial adhesion between fiber and matrix also plays an essential role in crack blunting to resist penetration across the filamentary domain. A more in-depth study of the 3D-printed composite materials is certainly needed, but this is currently beyond the scope of our study, and therefore a brief examination is provided here.

The fracture toughness of three monolithic samples before and after surface treatment is compared in Suppl. Figure 2: unidirectional samples [30°/30°/30°], [90°/90°/90°], and crossply sample [30°/90°/150°]. Here composite filaments have been prepared as a representative material, with a unidirectional alignment of discontinuous basalt fibers in a PLA (poly-lactic acid) matrix. The interfacial bonding strength between fiber and matrix (τ, IFSS) was enhanced by depositing a silane coupling agent. The change in chemical bonding of the fiber surface and the change in interfacial adhesion between fiber and matrix before and after surface treatment are presented in Suppl. Fig. 2a, b, respectively. The appearance of amino groups in the range of 1200–1700 cm−1 depending on the deposition of the silane coupling agent on the fiber surface has been discussed in depth in our previous study36,37 and is therefore briefly mentioned here. The interfacial adhesion was performed by a nano-indentation push-in test. At higher push-in load ranges, a slope change in the modulus curve of the treated fiber was detected, indicating a higher interfacial bonding strength between fiber and matrix. The load-displacement (L-D) curve shows the characteristic mechanical responses of notched samples in monolithic composites (Suppl. Fig. 2c). After reaching the maximum load, a linear decreasing trend was observed in all monolithic composites. The notch fracture toughness behaviors of the three monolithic composites are shown in Suppl. Fig. 2d–f. Crossply sample showed that the cross-arrangement of filaments forms a complex filament network which promotes crack bridging mechanism to resist penetrating transverse cracks. In the crack bridging region, severe plastic deformation of the filament bundles occurred, sometimes accompanied by fiber pull-out stresses. The deformation causes the filament bundles to rearrange parallel to the loading direction, so that the fracture toughness is dependent on the interfacial shear strength as the fibers are pulled from the matrix. Unidirectional samples, however, exhibited smooth crack propagation along weak void interfaces between neighboring filament bundles without dependence on the fiber-matrix interface strength. This behavior was also seen in the L-D curves with the same low-level mechanical response both before and after fiber treatment.

Key information about the composite material, including the geometric/physical parameters of fiber and matrix, stiffness comparison of composite and pure filaments, and interfacial bonding strength between fiber and matrix, is summarized in Suppl. Figure 2g. The high level of fiber length lf (700um), interfacial bonding strength τ (40 MPa), and resulting mechanical properties of the BF/PLA composite filament, compared to current commercial products, are notable. The resulting composite filament has a longitudinal elastic modulus that is 1.8 times higher than the pure PLA filament15.

Three representative hexagonal models of sub-granular domains with specific local orientations of 30°, 90°, and 150° were prepared as fundamental building blocks (Fig. 2a), and three representative nature-inspired architectures were built with these (Fig. 2b).

a Three representative hexagonal building blocks of sub-granular domains with specific orientations of 30°, 90°, and 150°. b Three representative nature-inspired architectures; anisotropic architectures built with ① 90° building blocks and ② 30° building blocks. ③ An isotropic architecture built with 30°, 90°, and 150° building blocks. c Large field tomographic images of the representative architectures providing the full observation of macroscopic crack propagation in a wide region of the sample. d Extended images of regions of interest α, β, and γ showing the crack propagation in the internal microstructure. (red: cracks, blue: voids, yellow: matrix, and gray: fibers) Red arrows indicate local fiber orientation. e, f Load-displacement (L-D) curves showing the fracture toughness of granular domain architectures made with pure and composite filaments. g Comparative plot of crack surface extension (∆S) as a function of crack tip opening displacement in anisotropic and isotropic architectures. h Fracture energy (G) dissipated during the crack propagation, defined as the integrated area under the L-D curve. Fracture energy is presented as mean values ± SD, n = 5 independent samples. Source data are provided as a Source Data file.

X-ray microscopy (XRM) tomographic images (Fig. 2c) confirmed these materials closely mimic the natural polycrystalline structure at macro- and mesoscale levels, with a hierarchical assembly of sub-granular domains of specific orientations. The use of a large field of view XRM imaging (i.e., stitch mode) also allowed three-dimensional observation of macroscopic crack propagation in a wide region of the sample. As shown in Suppl. Fig. 3, successive tomographic images from top to bottom in four partitioned windows create one stitched image with a large field of view and high resolution.

Inspired by the local and global orientation polarizations of polycrystalline materials in nature, this systematic organization of building blocks has accordingly created an artificial orientation polarization of structural properties. In detail, the first anisotropic nature-inspired designed architecture is built only with transverse building blocks of 90° orientation, with tensile loading direction perpendicular to the filaments. The second anisotropic architecture consists only of a building block of 30° (or 150°) orientation, which is inclined to the tensile direction. In these two anisotropic architectures, both the local granular domain and the global system are anisotropic, and the results from geometric image-based simulations of the elastic properties support this well (see a and b in Suppl. Fig. 4). In contrast, the isotropic natural mimetic architecture, which has all three building blocks strategically positioned, shows an impressive topological texture. The local granular domains are anisotropic, whereas the global system is isotropic (see c in Suppl. Fig. 4). Note that all these samples were produced with a stack of 3 layers of the same pattern, thus when viewed orthogonally all 3 layers share the same granular domains and boundaries (Fig. 2b).

An initial interest of our study was to observe intra- and inter-domain cracking behaviors along the interfacial voids at the intra-granular and inter-granular boundaries, respectively, in these simple model architectures. The images in Fig. 2d demonstrate the impressive effect of the microstructure on crack propagation in the pre-notched planar sample. The 3D projection image of the internal microstructure was obtained by image segmentation of X-ray tomographs to identify crack morphology and local fiber orientation, identified by red arrows. In all specimens, the interfacial voids were energetically favorable crack paths, and the synergetic void-crack interactions led to a stable crack propagation. A closer look at the crack propagation paths reveals significant differences based on local and global orientations. The 90° anisotropic architecture exhibited relatively easy crack propagation along the interfacial voids that are perpendicular to the global tensile stress because the propagating direction of the initial crack matched the orientation of the global system (see α in Fig. 2d). Although the inter-granular voids give the domain boundaries a lower strength than fracture through the intra-granular voids, deviations (kinking) of the crack path are not energetically favorable38. All parallel voids were competitive candidates for crack propagation, leading to minimal crack deflection. The 30° (or 150°) anisotropic architecture shows progressive crack propagation accompanied by crack deflection along the granular boundaries, which have low crack resistance (see β in Fig. 2d). This stepped crack profile was attributed to the directional mismatch between propagating crack and local/global orientations. The high-stiffness fibers prevented crack penetration into the granular domain and led to crack deflection to the domain boundary. The expanded fracture surface caused by crack deflection increased the total energy dissipation and delayed final failure even after the initial crack creation, thereby maintaining structural stability until the final failure was reached. Interestingly, the isotropic architecture shows a potential for more tailored adjusting of the crack growth direction using the weak interfaces with voids (see γ in Fig. 2d). Cracks may be encouraged to propagate toward specific directions, guided by interfacial voids, across granular domains or along domain boundaries, thereby increasing the crack surface area and improving fracture toughness. That is, the isotropic sample showed the ability to provide more potential paths for crack propagation, in contrast to the anisotropic 2 sample, where cracks propagate monotonically along the granular boundaries. These crack characteristics between the two samples led to slight differences in mechanical responses and fracture toughness. Overall, the results show that local/global orientations can be used to tailor the crack resistance, even using building blocks of the same contour shape.

In Fig. 2e, f, the L-D curves for tensile loading for the granular architectures printed with both pure PLA filaments and fiber-composite filaments show the effect of the reinforcing fibers. In both types of material, the cracks propagated along the interfacial voids that are intrinsic to the printed architectures. Compared to the pure samples, the composite architectures showed a distinctive mechanical response with more stable crack propagation and more desirable mechanical performance. This is due to the increased stiffness contrast between the neighboring granular domains, which arises from the increased anisotropy due to the fibers. It should also be noted that the granular architectures show stepwise decrease trends after maximum load, which contrasts with the linear decrease trends after maximum load in the monolithic samples. The monolithic isotropic sample has the limitation of having different interlayer modulus, which is a major cause of de-lamination. On the other hand, granular architectures have the potential to have a controlled modulus in all layers (see Suppl. Fig. 5).

Figure 2g, h plot the crack surface extension (∆S) along the crack propagation and the fracture energy (G) obtained by integrating the load-displacement curve, respectively. Due to crack deflection guided by interfacial voids, the crack surface was increased in 30° (or 150°) anisotropic and isotropic structures, up to 1.3 times larger than in 90° anisotropic structures. Crack deflection reduced the fracture driving force and required an increase in the applied stress to allow the fracture to continue along a new, more energetically favorable direction. The increase in stress demands an increase in the total amount of fracture energy that can be dissipated throughout the system, resulting in an increase of overall toughness.

Our results can be explained by comparison with the isotropic herringbone structure as one of the inspired structures of recent interest24. The herringbone structure has two regions of opposing patterns divided by different angular alignments of discontinuous fibers, and the angular contrast at the dividing region forces the crack to keep moving toward the boundary as the propagation path. Since crack propagating along the forced path can be effectively pinned and driven forward against the strong orientation of the reinforcement while preventing the crack tip deflection in an energetically favorable direction, the herringbone structure shows improved fracture toughness compared to monolithic composites with initial crack direction-dependent properties. Compared to our results, there is a significant difference in whether the crack tip is prevented or guided along an energetically favorable direction. In the next chapter, we will further discuss the effect of alternating stacking sequences on suppressing crack propagation in an energetically favorable direction.

Our attention next moved from simple architectures with the same layup stacking configuration to complex composite architectures with alternate layup stacking configurations. Numerous minerals and natural organisms possess different kinds of layered structures, and in particular, the brick and mortar of natural nacres is a mature development of a hierarchical architecture with a distinctive stacking configuration of a stiff laminate that enhances fracture toughness. Nature’s stacking systems can be qualitatively represented by strategically designing stacking sequences of artificial structures, such as is shown in the cross-sectional view (Fig. 3a). The modified architectural models used an αβγ stacking sequence in contrast to an ααα stacking sequence of the initial model material, though both of the models have an isotropic global orientation (compare Fig. 3d and Suppl. Fig. 4c). The front image in Fig. 3a provides information on the granular orientation in the local region of interest with overlapping layers. This alternate stacking sequence makes the propagating intergranular crack tip meet different positions where crack branching may occur, layer by layer.

a Alternate layup stacking configuration of the modified isotropic architecture showing the αβγ stacking sequence with respect to the shift position and specific orientation of the granular domains. b, c Tomographic images of the fracture surfaces. Straight-through failure of the pure filament sample (b). Complex post-fracture surface and extended crack profile images of composite architecture showing damage tolerance and fracture resistance driven by the αβγ stacking sequence effect (c). d Anisotropic approximation graph showing stiffness differences in local and global regions between pure PLA and BF/PLA composite architectures. e Extended tomography images of the region of interest (e) in Fig. 3c showing details of inter- and intra-granular crack propagation in the α top, β middle, and γ bottom layers, respectively. Individual granular domains were identified according to local fiber orientation and then segmented into 30° (yellow), 90° (red), and 150° (blue) hexagonal regions. The schematic images provide detailed descriptions of crack propagation types. f Extended images of the region of interest (f) in Fig. 3c Increased width of the crack arrow indicates increased crack driving force. g L-D curves of pure and composite filaments. SEM shows severe crack bridging and pullout of the transverse fibers. h Step-like rising R-curve showing fracture toughness with accompanying continuous crack arrest and crack propagation. The gray shaded region shows the shape of the R-curve macroscopically. i, j Comprehensive comparison of tensile modulus and fracture energy of pure and composite architectures. Tensile modulus (E) and Fracture energy (G) are presented as mean values ± SD, n = 5 independent samples. Source data are provided as a Source Data file.

Figure 3b, c compare post-fracture surfaces of samples prepared with pure and composite filaments, respectively. Compared to the pure sample, the composite architecture shows impressive fracture behavior for the αβγ stacking sequence. The pure sample shows straight-through failure, whereas the composite sample shows a more complex crack profile with high fracture resistance (Fig. 3c). The pure sample has low stiffness contrast between local structural regions and exhibits brittle failure without resistance from local effects that are due to the geometric topology. The L-D curve of the pure sample also shows a rapid drop after reaching the maximum load, which indicates a catastrophic failure (Fig. 3g). In contrast, the increased local stiffness variations of the sub-granular regions in the composite architecture make the propagating crack turn to arrester direction as potential crack branching positions are encountered. We argue that the local and hierarchical arrangement of individual composite filaments is entirely responsible for this impressive fracture behavior. Note that the characteristic arrangement of the composite filaments provides interfacial voids as energetically preferable crack propagation paths while also making embedded fiber reinforcements act as hard inclusions that inhibit trans-filament crack penetration.

To clarify the corresponding toughening mechanism, the R-curve was measured by the experimental J-integral calculation. The characteristics of the R-curve were originally designed to determine the fracture toughness of homogeneous metallic materials, but have recently been applied to study the fracture toughness of heterogeneous structural materials7,14,39. The initial L-D curve showed significant load retention over an extended displacement range and until the complete failure occurred gracefully (Fig. 3g). Accordingly, the rising R-curve of the composite architecture indicates increased fracture toughness with crack extension (Fig. 3h). According to ASTM standards, the theoretical effective crack length of Δa is limited to 0.25b0 = 6 mm. However, to understand the macroscale crack patterns throughout the system and resulting toughening behavior, observations must be extended to the whole crack length, unlike common applications for homogeneous materials. Here, our interest extends to the whole range beyond the effective crack length, not only the initial slope region but also the further rising R-curve region. The top priority here is to directly establish the correlation between the rising R-curve and the macroscale toughening mechanism.

Figure 3e, f illustrate an expanded region of interest for each layer at two locations and show details of the fiber orientation and crack paths in local granular domains and boundaries. (These are the thinly sliced surface images in each α, β, and γ layer showing fiber orientation/distributions) The top layer shows trans-filament crack penetration in a 30° domain (see α in Fig. 3e). Such transverse cracking is generally not preferred because it requires higher fracture energy than interfacial void-guided crack paths. However, it should be noted that the global crack path is determined by the total fracture energy through the three layers, assuming that the global crack path is shared in all layers due to inter-layer adhesion. The overlap regions of both middle and bottom layers show interfacial void-guided crack paths and, more precisely, intra- and inter-granular cracking behaviors, respectively (see β and γ in Fig. 3e). This global crack across all layers is quite reasonable, given a simple crack path model based on the energy principle. The propagating crack repeatedly searches for a favorable energy path whenever it approaches each granular domain. In particular, when a propagating crack passes from an energetically easy path to a hard path, the crack resistance increases, and inversely, when passing from a hard path to the next easy path, locally rapid crack propagation occurs. The energy released in this process eventually leads to dynamic crack propagation. In fact, the transverse crack across the alternating layers, in the first region of interest, arrested due to severe crack bridging and pull out of the transverse fibers (Fig. 3e). In the next second region of interest, incident cracks in all layers formed a global crack path along parallel aligned filaments with a relatively lower total fracture energy compared to the pre-existing crack path (Fig. 3f). These are partial examples of dynamic crack propagation showing consecutive crack arrest and crack propagation in a slight step-like rising R-curve (Fig. 3h).

Figure 3i and j compare the tensile moduli and fracture energies of the different nature-inspired architectures. The effect of reinforcing fiber on the tensile modulus was pronounced in the anisotropic system, especially in the 30° (or 150°) architecture with a global orientation slightly parallel to the tensile direction. More notably, the two isotropic systems with ααα and αβγ stacking sequences have the same tensile modulus but significantly different fracture energy because of the crack-tolerance of the αβγ stacking sequence. Compared to the pure sample, the composite architecture of the αβγ stacking sequence showed a 5.2 times higher increase in fracture energy, which is 2.4 times higher than that of the ααα stacking sequence. This is because the αβγ stacking sequence has the effect of boosting up the fracture energy by forcing the propagating crack in the arrester direction. To further discuss the practical increase in performance, a comparison with traditional 3D printed patterns (e.g., rectilinear infill 0°, 45°, 90°, 0°/90°, and 45°/135°) is provided in Suppl. Figure 6. Overall, the proposed architectures showed competitive performance in fracture toughness compared to traditional patterns. The transverse 90° pattern (monolithic) showed very vulnerable to crack propagation along the interfacial voids, but the 90° granular pattern in the architecture had crack resistance to rapid propagation. For the isotropic system, the αβγ alternating sequence slightly outperformed other patterns in terms of fracture toughness and showed gradual crack growth behavior along with high fracture energy at crack initiation and growth. We argue that the microstructural complexity and toughness mechanisms of the proposed architecture have significant similarities with those of the traditional chopped sheet or tape-reinforced composites40,41, especially in terms of high local anisotropic stiffness and resulting fracture toughness.

Figure 4 compares crack propagations heading toward the divider and arrester directions in the ααα and αβγ stacking sequences, respectively. The crack extension plot of the αβγ stacking sequence showed slight differences in the crack surface in each layer, broadly indicating the development of multiple cracking modes, accompanied by shear crack opening (see Fig. 4b, d). This is because the progressive cracking faces different propagation paths for each layer, and then each layer is placed in different strain fields. In the ααα stacking sequence, however, it is meaningless to compare crack surfaces for each layer because the overlapped orientations provide the same crack path. All layers showed an energetically favorable single crack path, indicating a dominant crack opening mode (see Fig. 4c, e). Overall, it can be defined that the toughening mechanism of the ααα stacking sequence represents a crack propagation toward the divider direction guided by weak interfaces, whereas the toughening mechanism of the αβγ stacking sequence represents a crack propagation toward the arrester direction affected by crack bridging. The effect of this stacking sequence was more significant in the tensile mode for the non-notched samples. The αβγ stacking sequence showed strong tensile strength comparable to that of monolithic samples (especially for [30°/90°/150°] sample) and contrasted with the low tensile strength of the ααα stacking sequence, which showed catastrophic fracture along intergranular boundaries perpendicular to the tensile direction (see Suppl. Fig. 7).

a 3D tomographic image showing different fracture surfaces for each layer in the αβγ stacking sequence. b, c Crack surface extension (ΔS) as a function of crack tip opening displacement for each layer in the αβγ and ααα stacking sequences. d, e 3D tomographic images showing propagating cracks for each layer in the αβγ and ααα stacking sequences. Representative colors for each layer in all results are as follows: red area: layer 1 (bottom), yellow area: layer 2 (middle), and blue area: layer 3 (top). Source data are provided as a Source Data file.

In natural polycrystalline materials, the grain size determines the relative dimensions of the grain boundary and is an important parameter that affects yield strength and fracture toughness. Due to the immature artificial representations and structural scale differences, nature-inspired architectures and natural crystalline materials may yield different results, but this crystallographic concept provides the inspiration for meaningful scientific findings.

The granular size of nature-inspired architectures can be flexibly tailored by resizing the hexagonal layered features. We here designed three types of grain size-inspired composite architectures assembled with three different granular sizes of building blocks labeled L, M, and S, respectively, as shown in Fig. 5a. Figure 5b, c show the significant contribution of particle size to local area isotropy and local stiffness. This grain size-inspired architecture provides an alternative method for gaining insight into specific grain size effects at the meso- and macro-scale. The thickness, as well as the width of granular domains, were considered as important parameters in terms of grain-size effects. Thus, to maintain constant thickness, the L-, M-, and S- architectures have 1 (αααα), 2 (ααββ), and 4 (αβγα’) layers of alternate stacking sequences, respectively (Fig. 5d). With the homogeneous combination of the anisotropic granular domains, the global orientation of all architectures is isotropic. The interlayer and intralayer voids for grain architectures L, M, and S is compared in Suppl. Fig. 8. The ratio of the granular boundary is a dependent variable of the content of interfacial voids and is inversely related to the size of the granular domain. The quantitative content values for the interfacial voids were computed by image segmentation of the tomographic morphology. The intralayer voids show an increase in the void content in the order S > M > L, verifying the increase of granular boundaries. The interlayer voids, identified as layers 1, 2, 3, and 4 from the top to the bottom region, show a gradual decrease, which is attributed to the thermal gradient formed spontaneously during printing.

a Three different granular sizes of building blocks labeled L, M, and S. b Grain size effects contributing to local region isotropy and local region stiffness. Colors represent the same local region across grain sizes. c Anisotropic approximation graph showing stiffness difference in the same light red region in L, M, and S and the modulus transition from anisotropy (L) to isotropy (S). d Three types of grain size-inspired composite architectures; ① L-, ② M-, and ③ S-inspired architectures. e Large field tomographic images showing complex post-fracture surfaces of grain size-inspired composite architectures. f Characteristic crack profiles in 3D space depending on the granular domain size. g, h L-D curves and R-curves of L-, M-, and S-inspired architectures. The initial slopes of the R-curves show a high steepness in the order of M > S > L, which means that crack bridging contributes more to fracture toughness at crack initiation than crack deflection. i Extended images of the region of interest (i) in Fig. 5e showing the crack bridging at crack branches that guide different crack paths layer by layer. (α: top, and β: bottom layers.) j Extended images of the region of interest (j) in Fig. 5e. Increased grain boundaries suppress crack deflection and guide minimum crack path across small grains. (α: top, β: high-middle, γ: low-middle, and α’: bottom layers.) k 3D tomographic image showing significant crack bridging due to complex filament (and fiber) network. Red: propagating crack, brown: cross-aligned fibers. Source data are provided as a Source Data file.

The crack surface projections in Fig. 5e show characteristic crack profiles in 3D space for the different granular domain sizes. The crack image reveals that the crack surface was markedly expanded along the macrocontour geometry in L- architecture; in contrast, a narrowly diverging crack morphology was observed in the S- architecture (Fig. 5f). The L- architecture also contains a large amount of co-oriented reinforcing fiber in its thickness and width, which means locally higher stiffness and anisotropy, eventually leading to a distinct mechanical response in the L-D curve in Fig. 5g. As the grain size became smaller, in contrast, the stiffness in the local region tended to decrease, resulting in blurring of the grain-to-grain anisotropy and eventually reaching a near-amorphous/homogeneous nature in mechanical performance (compare Fig. 5b, c).

The rising R-curves of grain size-inspired structures suggest that several toughening mechanisms operate as a function of grain size (Fig. 5h). In the following, we discuss in more detail the toughness mechanisms of grain size-inspired architectures. In the L-inspired architecture, significant crack deflection was observed along the large grain boundary, though in some cases of the same crack-void direction, a void-guided crack path inside the grain was also observed. The high local stiffness of the macro-grains forces the crack to follow a longer route along the macro-grain interface, and the resulting crack extension contributes to additional energy dissipation. Since the crack resistance varies depending on the angle of the large hexagonal grain boundary, the main crack path is divided into a straight-through crack path and an oblique shear crack path, each having significantly different crack resistance (see ① in Fig. 5e, f). The steep drops of the L-D curve show the low crack resistance of the straight-through crack path.

In the M-inspired structure, the alternate stacking sequence of 2 layers creates a crack branch that guides different crack paths layer by layer, resulting in a crack bridging mechanism (see α and β in Fig. 5i). A relatively smooth region after the maximum load in the L-D curve essentially arises from crack bridging by transverse filaments. The step-like R-curve also shows the effects of consecutive crack bridgings, especially as the different orientations of the filamentary region are approached, with accompanying crack arrest and re-propagation (Fig. 5g, h).

The S-inspired architecture also resists the crack driving force through the crack bridging mechanism. Indeed, the stacking of 4 layers forms a complex filamentary network, leading to severe crack bridging (Fig. 5k). The increased number of grain boundaries gives the crack tip multiple route options for propagation. This suppresses crack deflection and leads to a narrow crack profile from a minimum crack path across small grains (see α, β, γ, and α’ in Fig. 5j). The resultant L-D curve shows a linearly decreasing region with stable crack propagation (Fig. 5g). The narrowed distance between the small grains in the process zone of the front and rear crack tip contributes to the linear decrease of the load despite the crack bridging effect.

Overall, the initial slopes of the R-curves show a high gradient, ranked in the order of M > S > L, which means that crack bridging contributes more to the initial toughness than crack deflection, and also the high stiffness of the local grains affects the initial toughness. The high initial slope of the M-architecture is a result of both crack bridging and crack deflection in the surrounding grain regions with high stiffness. It is also noteworthy that the prolonged rising curve was observed in the S-architecture, meaning a high contribution of crack bridging to the total toughness after crack initiation (Fig. 5h).

This size effect trend is contrary to that of natural polycrystalline material, and a fair discussion on this is needed. It is well known that the Hall-Petch law dominates the strength-grain size relationship5,32,38, but our results clearly show that smaller grain size leads to lower strength, which is opposite to the Hall-Petch law. In fact, the smaller the grain size in polycrystalline materials, the higher the stiffness and the lower the ductility. Since the composites field tells us otherwise, it is hard not to conclude that the results are overshadowed by other variables beyond the microstructure focused upon here. We suggest several reasons that greatly influenced the results.

1. The stiffness of the grain structure is not high enough. 2. The anisotropy effect of fiber orientation is not significant. 3. As the grain structure becomes smaller, more defects occur due to the less precise process. 4. Immature artificial representations. 5. Structural scale differences.

In particular, the comparison was at two different scales (grain size of metals is in the range of 10 ~ 200 microns) and what happens on the micro-scale is not superimposable to the macro-scale. However, the results do not necessarily comply with the theoretical laws of natural materials and should be understood as independent results presented by the new artificial structure. Our interest is how structural benefits can be realized when nature-inspired structures are scaled to the mesoscale of fiber-reinforced composites. In the conventional top-down process, fiber-reinforced composite materials have been experiencing technical limitations in structural design. But now, bottom-up manufacturing of 3D printing allows a more flexible design of composite materials with desired structures and properties. This expanded research environment leads to the need to report more novel structures and understand the underlying mechanisms. These assignments have been addressed recently with great interest in biomimetic engineering materials. (e.g., a robust and damage-tolerant structural material of nodes and struts inspired by grain boundaries, precipitates, and phases of metallic crystalline materials13, and interpenetrating phase composites (IPCs) mimicking nanocrystalline structures of FCC and BCC14.).

Nature has developed gradient microstructures over a long period of structural evolution to achieve a simultaneous improvement of stiffness and toughness. The attainment of both stiffness and toughness have been regarded as mutually exclusive in existing engineering fields, so interesting attempts to emulate or draw the gradient microstructures of biological systems have attracted massive attention in the past decade5. We understood in the previous section that the crack propagation mechanisms of the coarse and fine grain-inspired architectures, i.e., crack deflection and crack bridging, are different, respectively. Therefore, synergistic combinations between the two crack propagation mechanisms and systematic connections between the coarse and fine grain blocks can be derived through the inspiration of the gradient structures.

Here, granular building blocks prepared in three different sizes were gradient-assembled at the macro scale to ideally mimic the natural gradient structure (Fig. 6). Two assembled architectures were systematically printed, each with a gradient structure from coarse-grained to fine-grained (L → S) and from fine-grained to coarse-grained (S → L). Figure 6a, b show the gradual changes of tensile modulus as a function of grain size for both gradient architectures. Since the decrease of modulus is attributed to the increase of grain boundaries (i.e., with higher void fraction), the tensile modulus increases in the coarse-grained region and decreases in the fine-grained region.

a, b Gradual modulus decreases and increases in the L → S gradient architecture from coarse to fine grains and the S → L gradient architecture from fine to coarse grains, respectively. c, d Large field tomographic images of (i) post-fracture surface, (ii) crack profile, and (iii) fiber orientation/distributions in the L → S and S → L gradient architecture. e L-D curves of the L → S and S → L gradient architectures showing increased fracture toughness compared to the initial case of monotonically assembled architectures. f R-curves of the L → S and S → L gradient architectures showing J-shaped and Γ shaped curves, respectively. Detailed tomographic images of the fracture surface and thickness are presented in Suppl. Fig. 9. Source data are provided as a Source Data file.

The stitched tomographic images in Fig. 6c, d provide all the results for microscale fiber orientation and distribution as well as macroscale crack morphology (Sample size = 30 x 35 mm, Fiber length = 700 μm). The three-dimensional crack profiles of the L → S and S → L gradient composite architectures show contrasting crack propagation as the grain size changes (see (ii) in Fig. 6c, d). The L → S gradient architecture shows crack deflection first along the macro grain boundary in the coarse-grained region, but the crack arrests as it approaches the fine-grained region. The straight-through crack in the coarse-grained region propagates relatively quickly, which is revealed as an instantaneous load drop in the L-D curve. This propagating crack passed through the M region and was eventually suppressed by a complex filamentary network in the S region. This impressive fracture behavior is represented by a J-shaped R-curve where initially fast crack growth becomes more stabilized by the crack arrest in the backward region (Fig. 6e, f). Note that here the observations are extended to the whole crack propagation region to analyze the macroscale crack profile along the gradient of grain size.

On the other hand, the S → L gradient architecture shows crack bridging-dominant behavior in the initial fine-grained region, which is evidenced by a characteristic bell-shaped mechanical response in the L-D curve. Crack bridging is extended even in the M region, prolonging the crack resistance, which is characterized by a stable load plateau in the L-D curve. When the propagating crack reaches the L region, fluctuations are observed in the L-D curve. In broad terms, a Γ-shaped R-curve represents the fracture toughness behavior of the S → L gradient architecture (Fig. 6e, f).

Overall, the fracture toughness results above clearly show that there is a synergetic effect between crack bridging and crack deflection mechanisms. The synergistic combination of the two mechanisms demonstrates the potential ability to simultaneously improve stiffness and toughness compared to the initial case of monotonically assembled grain size-inspired architectures. The characteristic fracture toughness of the two gradient architectures will further extend their commercial application.

The present work has provided a natural inspiration motif for the 3D printing of artificial granular architectures and demonstrated composites’ fracture behaviors correlating with the poly-granular cracking behavior mechanisms found in natural mineralized materials. The process-induced microstructural features, i.e., a high degree of material alignment and weak interfacial void formation, were used to systematically organize hierarchical granular architectures of specific geometric topology in the filamentary phase. Large-field tomographic observation has contributed to the three-dimensional visualization of various structural configurations of granular building blocks (local/global orientation, stacking sequence, feature size, and gradient structure) and provided impressive internal microstructures and crack morphologies for identifying the segmented constituents and understanding the resulting toughness mechanisms.

The significance of this work is that the structural complexity of the resulting architecture was advanced by the systematic organization of granular building blocks consisting of composite filament bundles (compared to the general case using pure materials in the existing literature), and consequently, the resulting hierarchical composite architecture contributed to the exceptionally high crack resistance. Our initial attention focused on the characteristic cracking behaviors, i.e., inter- and intra-granular cracking behaviors, inherently induced by synergistic crack-void interactions and the obstacle effects of aligned fibers. Crack growth along grain phases or grain boundaries tailored the crack driving force with progressive crack patterns. Eventually, the alternating stacking sequence led cracks propagating in the divider direction to cracks propagating in the arrester direction, which caused complex multiple cracking modes, including shear crack opening, resulting in a dramatic increase in fracture toughness. To the best of the author’s knowledge, this is the first thorough observation of the three-dimensional cracking behavior of 3D-printed nature-inspired composite architecture. This challenge means that further studies are needed to understand the mechanical behaviors of more diverse and complex architectures as a function of materials, compositions, and configurations, and such work can provide plenty of research space in the field of structural engineering. This approach using the inherent characteristics of 3D printing will help to break through technical limitations from a nature-inspired engineering perspective and will broaden the scope of 3D printing into a more extensive range of research and engineering applications. In future work, we will investigate the reinforcement effects of embedded fibers, including fiber length, fiber content, length-to-diameter ratio, and interfacial bonding strength between fibers and matrix, which are important physical/geometrical parameters but have been overlooked here due to paper limitations. To clarify these effects, we will explore more suitable structures and develop efficient analytical procedures while maintaining the intention of this study to gain scientific inspiration from the robust and dynamic structural systems of natural materials.

In order to draw nature-inspired architecture with locally diverse orientations, high-strength, printable composite filament was prepared as a base material. In the composite filament, the embedded fibers are assigned the role of reinforcements to compensate for the insufficient stiffness of the filament in the longitudinal direction, imparting anisotropy to the resulting architecture. Here, basalt fiber (BF, Kamenny Vek, Moscow, Russia) in the form of chopped strands with an initial length of 3 mm was used as reinforcements and was added into pure filament PLA (Polylactic acid, HANZENITH Co., China) by melt extrusion. The use of biodegradable PLA material and natural mineral BF reinforcement was intended to be in line with the eco-friendly policy and research trend. (The chemical composition of BF is similar to that of glass fibers, with relatively high Al2O3, Fe 2O3, K2O, MgO, Na2O, and TiO2, but low SiO2 and CaO. Accordingly, BF has a slightly higher density of 2.67 g/cm3 and heat resistance of up to 1,095 °C.) BF/PLA composites were extruded into continuous-filament form with a diameter of 1.75 mm using a Haake twin-extruder (Thermo Fisher Scientific, Waltham, USA) at a barrel temperature of 220° and a rotation speed of 60 rpm. During the filament extrusion, BF was fed into the device via a side feeder at a ratio of 10 vol% and the initial 3 mm length of BF was reduced to a smaller size (~700 μm). To improve the interfacial adhesion between BF and PLA, the surface of BF was treated before the filament process. The silane coupling treatment of BF was performed using the solution dipping method. A 95% ethanol-water solution (EtOH:H2O = 95:5) was first prepared, and the pH of the solution was adjusted to 6-7 by adding a small amount of acetic acid. Then, 0.4 g of a liquid amino-silane coupling agent (N-(2-aminoethyl)−3-aminopropyltrimethoxysilane, Shin-Etsu Co., Japan) was added to the solution. The mixture was stirred for 3 hours to hydrolyze the silane molecule to form silanol groups. When the silanol groups were completely formed, BF was immersed in the coupling agent solution and stirred for 2 hours. After silane treatment, the silane-sized BF was dried in a vacuum oven at 120 °C for 2 hours and then the samples were stored at 50 °C to prevent moisture absorption.

All samples used in the study were designed using the Computer-Aided Design Package (CADian3D, IntelliKorea Co., Korea) and then fabricated by an FDM-type 3D printer (3DISON AEP, Rokit Co., Korea). The representative building blocks constituting the nature-inspired architecture were first designed in the following procedure. The granular building block was defined as a symmetric hexagonal structure where the vectors a and b are equal and the internal angle is 120°. The printing nozzle (nozzle diameter = 0.4 mm) filled the molten filament into the hexagonal structure towards a specific orientation direction. The neighboring bundles of filaments (with 100% packing density) were placed parallel to each other along the three inclined directions of 30°, 90°and 150° of the hexagonal structure. Accordingly, three fundamental building blocks, 30°, 90°, and 150° building blocks, respectively, were created. The length of the inclined plane (vectors a or b) determines the feature size of the granular block. Three grain sizes, namely L, M, and S, were described as symmetric hexagonal structures with a = b = 1.5 mm, a = b = 3 mm, and a = b = 6 mm, respectively. The cross-section of the filament shows an elliptical shape, width = 0.65 mm (including interfacial voids), height = 0.4 mm (single layer height = 0.4 mm), and therefore L, M, and S have 4, 8, and 16 infill filaments, respectively. The thickness of the building blocks also varies depending on the grain size; Grain L = 4 layers, Grain M = 2 layers, and Grain S = 1 layer. (The architecture has a total of 4 layers.) The systematic organization of the three building blocks of 30°, 90°, and 150° orientations determines the global orientation. The global orientation contains the orientation information of all individual building blocks in horizontal and vertical lines and stacking layers. For structural isotropy, the 30°, 90°, and 150° building blocks were sequentially arranged in horizontal rows, and the three neighboring building blocks on the same plane were organized in different orientations. In contrast, anisotropic architectures were monotonically assembled by only single building blocks with the same orientation. The plane-positioned building blocks are then piled up in either a simple ααα stacking sequence or an alternating αβγ stacking sequence. Note that the ααα stacking sequence overlaps the center points of all granular blocks, whereas the αβγ stacking sequence matches the center points of the upper layer granular blocks to the angular points of the lower layer granular blocks. The center points of the granular blocks are shifted layer by layer in a zig-zag form to the right and left lower angular points, along with the accompanying orientation movements. Accordingly, the L-, M-, and S-inspired architectures have 1 (αααα), 2 (ααββ), and 4 (αβγα’) layers of alternate stacking sequences, respectively. (As an exception, the initial models of Figs. 2–4 have a total layup of 3 layers, size of M, and the stacking sequence of 3 layers (αβγ).) For ease of understanding, drawing details showing the stacking sequence of the architectures are provided in Suppl. Fig. 10. The gradient architectures were prepared by the systematic organization of L, M, and S. The vertical samples were divided into three regions, and then L, M, and S grains were placed in the gradient order of L → S and S → L. (Due to sample size limitations, the shape and size of some granular blocks were slightly modified.) In the next step, the above models were sliced into multiple thin layers using a 3D slicer software (Simplify3D, USA), and digital codes were generated. By manually changing the digital code, the 3D printer was programmed to draw a complete building block without any route changes to the next block. Individual granular blocks were locally blocked by boundary lines with 95% packing density of filaments. Eventually, the 3D printer fabricated the nature-inspired architectures using a heated nozzle of 220 °C at a bed temperature of 60 °C according to the programmed procedures. The print times for the architectures were highly dependent on the nozzle speed and extrusion length. During printing, the nozzle speed was 15 mm/s, and the movement speed without extrusion was 60 mm/s. If the infill space is the same, the extrusion length is the same, so the printing time did not differ significantly from that of the monolithic sample with a simple direction pattern. The printing times of L, M, and S are compared in Suppl. Table 1. There was a slight loss in printing time when moving without extrusion, but it was not significant, generally showing printing times of 7–8 min.

Tensile tests (for non-notched samples) were performed at room temperature on a universal tensile testing machine with a 30 kN load cell (Instron 5866, Norwood, MA) at a crosshead speed of 0.5 mm/min. Rectangular specimens with a width of 9 mm and a length of 25 mm were first printed. Then, both ends of the specimens were connected with grip parts made of epoxy resin molds and prepared as dog-bone specimens for the tensile test. Given the single layer thickness of 0.4 mm, the 3-layer layup samples have a total thickness of 1.2 mm. The granular orientation of the 90° building block is perpendicular to the tensile direction, thus constituting a transverse sample. The 30° and 150° samples form a 60° angle to the axis line of the tensile direction. To ensure the reliability of the obtained data, tensile testing was conducted at least five times for each type of sample.

Fracture toughness was tested with single-edge notched tensile samples based on elastic-plastic fracture mechanics. Large-area planar samples with a height H of 30 mm, a length L of 35 mm, and a width W = 30 mm were prepared for the fracture test. Thickness B is 1.2 mm and 1.6 mm for the 3-layer and 4-layer layup samples, respectively. A 5 mm long pre-notch was prepared for all samples parallel to the crack propagation direction. The ligament b0 of the sample, which is the non-cracked area, is 30 mm for all samples. For the reader’s understanding, the experimental test set up is presented in Suppl. Fig. 11. The R-curve was used to evaluate the fracture toughness of the samples and was characterized by a representative R-curve. The J integral was calculated as the sum of Jel for the elastic component and Jpl for the plastic component (J = Jel + Jpl). This method has been applied to evaluate the fracture toughness of heterogeneous materials in many studies7,14,29,42.

The elastic component Jel is obtained by substituting the load Pi (at each measurement point) and the total crack length (ai = a0+da) into the following equation. da is the crack extension length during the test.

and, the linear elastic stress intensity K was estimated from:

where n and E are the material’s Poisson’s Ratio and Young’s modulus, respectively.

The Young’s modulus of a composite material can be obtained as:

where Ef and Em are the Young’s modulus of the fiber and matrix, respectively, and Vf and Vm are the volume fractions of the fiber and matrix, respectively.

f(ai/W) is a polynomial of ai/W given by.

Based on the L-D curve, the plastic component Jpl was also derived as the following equation.

The plastic work energy Apl can be obtained by calculating the integrated area on the L-D curve. The integrated region represents a closed curve fitted with an initial slope line at the load Pi. The fracture test was performed at a constant displacement rate of 0.1 mm/min. Video recorded during the test provided the crack extension length. The work was completed by testing multiple specimens under different loads and displacements, and the crack length of each propagation was obtained.

We obtained large-field tomographic images of the internal microstructure and crack morphology of the nature-inspired architectures using the stitching mode of an X-ray microscope (Xradia 520 Versa, Zeiss, Germany). This X-ray imaging technique provides an extended measurement region with vertical stitching, wide field mode, and wide field mode stitching features. Stitching mode captures multiple images and stitches them together to visualize large samples wider and taller than standard fields of view. A routine X-ray scan is as follows. First, the post-mortem sample was pinned, mounted in a sample holder, and placed on the sample stage of the instrument. The sample aligned between the X-ray source and detector was extended into the region of interest by adjusting the source-to-sample distance and sample-to-detector distance, respectively. Upon entering stitching mode, the total region of interest in the vertical sample can be divided into multiple windows by setting the top and bottom windows. Accordingly, the multiple windows here were created in a vertical row along the vertical cracks and vertical stitches were added in succession with enough overlap region between each window. The region of interest in each window was sequentially scanned by the X-ray beam with 360° stage rotation at set intervals. The operating conditions of X4 objective lens magnification, 50 keV accelerating voltage and 4 W power were shared for all imaging. The total number of projection images was 1601 and each projection image was acquired with an exposure time of 2.5 seconds and a pixel binning of the 2024 ×2048 detector of 2, which have projection images with a voxel size of 4 μm. The collected projection images were reconstructed into 3D geometric images using the Zeiss software package (Oberkochen, Germany). During the reconstruction process, the overlapping regions between each window were stitched and all windows were merged into one image. Dragonfly pro (Object Research Systems, Canada) was used to segment each constituent into different phases according to gray value comparison and visualize the image in three-dimensional space.

3D tomographic image-based simulations were used to analyze the internal microstructure of nature-inspired architectures, such as local/global orientations, stacking sequences, feature sizes, and gradient organizations, as well as crack/void morphologies throughout the system. Fiber length/orientations and void distributions were quantitatively characterized using GeoDict software (Math2Market GmbH, Kaiserslautern, Germany), especially the sub-modules of FiberGuess and PoroDict, respectively. FiberGuess module identified the short diameter and long length of fibers and then determined the longitudinal length of individual fibers. The orientation of embedded fibers was derived in the form of a second-order fiber orientation tensor by analyzing the in-plane orientation angle (ϕf) and out-plane orientation angle (θf), respectively. Local fiber orientation was determined by analyzing a narrow region of individual granular building blocks, whereas global fiber orientation was estimated statistically by extending the region of interest to the building block assembly. The PoreDict module identifies individual voids distributed throughout the system and vertical crack propagation paths and visualizes the results schematically by analyzing their size, shape, and distribution. In addition, the ElastoDict, a sub-module of GeoDict, provides advanced simulation to predict the modulus of the composite system based on the above geometric parameters and physical properties. The modulus (stiffness) of the XY-plane was calculated using the FeelMath Elasticity-VOX Solver. For the modulus simulation, the physical properties were entered as follows; BF was defined as a linear elastic isotropic solid with a density of 2.67 g/cm3. Young’s modulus, shear modulus, and Poisson’s ratio were set to 89 GPa, 37 GPa, and 0.2, respectively. The orientation information was defined based on the second-order fiber orientation tensor values obtained by the FiberGuess module. PLA used as a matrix resin was defined as an isotropic elastic-plastic material with a density of 1.25 g/cm3, Young’s modulus, shear modulus, and Poisson’s ratio were set to 3.5 GPa, 1.31 GPa, and 0.33, respectively.

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

All data supporting the findings of this study are available within this article and Supplementary Information or from the corresponding author upon request. The data generated in this study are provided in the Supplementary Information/Source Data file. Source data are provided with this paper.

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We are grateful for the financial support of the Postdoctoral Fellowship Program (Nurturing Next-generation Researchers) in 2022 granted (2022R1A6A3A03065160) by the National Research Foundation of Korea (NRF) (S.Y.). This work was also supported by the Commercialization Promotion Agency for R&D Outcomes (COMPA) grant funded by the Korean Government (Ministry of Science and ICT,2023-00304729) and Nano & Material Technology Development Program through the National Research Foundation of Korea (NRF) funded by Ministry of Science and ICT (NRF-2022M3H4A3046292) (J.Y.H.).

Department of Materials, University of Oxford, Oxford, OX1 3PH, UK

Siwon Yu & Thomas James Marrow

Department of Material Science and Engineering, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon, 34141, Republic of Korea

Siwon Yu & Soon Hyung Hong

Institute of Advanced Composite Materials, Korea Institute of Science and Technology (KIST), Jeonbuk, 55324, Republic of Korea

Siwon Yu, Seunggyu Park & Jun Yeon Hwang

Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon, 34141, Republic of Korea

Kang Taek Lee

Nanotechnology Research Institute, Jiaxing University, Jiaxing, China

Soon Hyung Hong

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S.H.H., J.Y.H., and S.Y. have analyzed unsolved issues and designed the direction of research. S.Y. fabricated samples and performed testing with assistance from S.G.P., and K.T.L. S.Y. and S.G.P. investigated the fracture toughness models and performed the analytical studies and numerical calculations. S.Y. and T.J.M. analyzed the experimental data and discussed the crack propagation behavior and its mechanisms.

Correspondence to Jun Yeon Hwang, Soon Hyung Hong or Thomas James Marrow.

The authors declare no competing interests.

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Yu, S., Park, S., Lee, K.T. et al. On the crack resistance and damage tolerance of 3D-printed nature-inspired hierarchical composite architecture. Nat Commun 15, 9532 (2024). https://doi.org/10.1038/s41467-024-53850-w

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Received: 21 April 2024

Accepted: 23 October 2024

Published: 04 November 2024

DOI: https://doi.org/10.1038/s41467-024-53850-w

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