Materials become insensitive to flaws at nanoscale: lessons from nature

Abstract

Natural materials such as bone, tooth, and nacre are nanocomposites of proteins and minerals with superior strength. Why is the nanometer scale so important to such materials? Can we learn from this to produce superior nanomaterials in the laboratory? These questions motivate the present study where we show that the nanocomposites in nature exhibit a generic mechanical structure in which the nanometer size of mineral particles is selected to ensure optimum strength and maximum tolerance of flaws (robustness). We further show that the widely used engineering concept of stress concentration at flaws is no longer valid for nanomaterial design.

Figure 1

Many hard biological tissues, such as tooth (a), vertebral bone (b), or shells (c) are made of nanocomposites with hard mineral platelets in a soft (protein) matrix. Enamel (d) is made of long, more or less needle-like crystals ≈15–20 nm thick and 1,000 nm long, with a relatively small volume fraction of a soft protein matrix (8, 13). Dentin and bone (e) are made up of plate-like crystals (2–4 nm thick, up to 100 nm long) embedded in a (collagen-rich) protein matrix (12, 14, 15). The volume ratio of mineral to matrix is on the order of 1:2. Nacre (f) is made of plate-like crystals (200–500 nm thick and a few micrometers long) with a very small amount of soft matrix in between (3). All of the composites share the structural feature of hard platelets with a very large aspect ratio, arranged parallel in a brick-and-mortar-like fashion. An unsolved problem is the question of why these crystals are in the nanometer range.

Figure 2

A model of biocomposites. (a) A schematic diagram of staggered mineral crystals embedded in protein matrix. (b) A simplified model showing the load-carrying structure of the mineral–protein composites. Most of the load is carried by the mineral platelets whereas the protein transfers load via the high shear zones between mineral platelets.

Figure 3

A length scale for optimized fracture strength in mineral platelet. (a) A schematic diagram of mineral platelet with a surface crack. (b) Comparison of the fracture strength of a cracked mineral platelet calculated from the Griffith criterion with the strength of a perfect crystal.

Figure 4

The color map of normal stress σ₂₂ at critical fracture load in a mineral platelet containing a thumbnail crack with depth equal to half of the platelet thickness. The calculation is performed by using a 3D finite element method based on the virtual internal bond model, as the thickness of the mineral platelet decreases toward the critical thickness for optimum fracture strength. At large thicknesses (h/h* = 20,200), the stress concentration at the crack tip significantly reduces the fracture strength σ_f from the theoretical strength σ_th. Near the critical thickness h*, the stress concentration vanishes and the strength approaches the theoretical strength.