keep reading-27

Materials become insensitive to flaws at nanoscale: Lessons from nature, Gao, Ji, Jger, Arzt, Fratzl, PNAS, 2003

Novelty/impact/significance:

It is firstly/ingeniously demonstrated that the biological nanocomposites’ generic structure is mechanically advantageous: the nanometer size of mineral reinforcements is selected to ensure optimum strength and maximum tolerance of flaws. The derivations are simple and effective.

Scientific question:

Why is the nanometer size ubiquitously shown for the mineral reinforcement of biological strong and tough materials (e.g., nacre, bone, and tooth)?

Key of how:

Based on the staggered arrangement of mineral reinforcements embedded in protein matrix structure, (1) a tension-shear chain model is established generating an expression for the composite elastic modulus (matrix shear and mineral platelet tension), (2) using Griffith criterion the platelet approaches theoretical strength without sensitivity to flaws/defects when the length scale below a nanometer size, (3) using force balance of platelet (tension v.s. interfacial shear) the importance of large aspect ratio is shown, which allows large modulus difference between matrix and reinforcement, leads to large composite modulus, and compensate for lower volume fraction.

Major points:

1. Many natural strong and tough materials, i.e., shell nacre, tooth enamel, bone, show generic nanometer reinforcing minerals embedded in protein matrix structure, despite different hierarchical/macrostructures.

Previously research has addressed the structural characterization, mechanical models for the platelet-matrix structure, toughening mechanisms with respect to the hierarchical structure, the effects of constituent protein matrix, etc., but why the elementary structure is universally on nanoscale remains unanswered.

2. Based on the Jäger-Fratzl staggered model, a tension shear chain model for the mineral platelets embedded in protein matrix is established, in which the platelet sustains a major load in tension while the matrix is purely shear deformation (constant shear). A compact expression for the composite elastic modulus shows that a high stiffness is correlated to large aspect ratio, a major load is carried by the mineral platelets, and the proteins transfers tress by shear.

3. The tensile strength of the mineral platelets is the key factor in the load bearing and fracture behavior of the nanocomposites, while in practice any materials contain crack-like flaws. By considering microcracks within the platelet (may be caused by entrapped weak proteins) and using classical Griffith criterion, the fracture strength can be expressed as a function of platelet thickness.

Then a critical length scale can be found, below which the theoretical strength of perfect mineral platelet is maintained irrespective of any preexisting crack-like flaws. This indicates that the nanometer length scale may be a result of fracture strength optimization and flaw tolerance maximization.

A virtual internal bond method showing the stress field of a cracked platelet corroborates the analytical results.

4. Using simple force balance (interfacial shear stress times aspect ratio equals the tensile stress) and the strength equation of the platelet lead to an expression for an optimum aspect ratio, which is correlated to the platelet thickness/length scale. The smaller the platelet, the larger aspect ratio, and the larger stiffening effect (by the composite modulus expression).

5. The analyses present a new, sound, and useful perspective that there may be an overarching driving force, the mechanical strength and flaw tolerance, for the selection of nanometer size for the reinforcement in diversely different biological strong and tough materials. Other important biological/chemical factors may also take effect.

The article is clear, coherent, and concise, a role model research work.

One special caution is that (personally): the nanometer size accounts for the reinforcement, geometrically allowing the reinforcement with maximized fracture strength and flaw tolerance, but not directly equal to maximized strength and flaw tolerance of the composite, although perfect reinforcement always lead to better-performance composites.

Here is the link of the full text: https://www.pnas.org/content/100/10/5597