Fig. 5: Insight into specific grain size effects on fracture toughness.

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.