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On the mechanics of mother of pearl: A key feature in the material hierarchical structure, Barthelat, Tang, Zavattieri, Li, Espinosa, JMPS, 2007

Novelty/impact/significance:

One key structural feature, microscale waviness of the tablets (rather than the high strength of the tablet), is discovered to strengthen and toughen nacre at macroscale through exhibiting strain hardening and withstanding large inelastic strain (uniform) (in addition to the known interface shearing), and the mechanism is tablet sliding on one another accompanied by tablet transverse expansion.

Scientific question:

What aspects in nacre’s structure provide local hardening/macroscale strengthening and meanwhile mechanical stability over large deformation, and how?

Key of how:

Through miniaturized mechanical tests with strain distributions (using digital image correlation) and finite element analysis incorporating detailed nanoscale features, tablet waviness generates progressive tablet interlocking during tablet sliding and the spreading of inelastic deformations over large volumes. This leads to significant strain hardening/strengthening and damage tolerance/toughness.

Major points:

With extensive studies on nacre structure and mechanics/mechanical properties, models including the shear lag theories and finite element analyses and mechanisms, such as the nanoscale size of tablet, the nanoasperities on tablet surface, mineral bridges, viscoplasticity of the organic interface material, the nanostructured tablets, exist.

Shearing of the interface and the sliding of the mineral tablets seem to be main deformation mechanisms, and the combination of small sized hard components with a small amount of organic material provide relatively large inelastic deformations.

However, what structural aspects provide and how these account for the local hardening and strengthening are not well understood, nor clear design guideline for the artificial nacre composites with superior properties.

Nacre structure

Nacre is the inner layer of seashells, and consists of 95% vol. of aragonite CaCO3, as polygonal stacked tablets (~8 µm in diameter and 0.4 µm in thickness) outlined by polymer interface materials (20-30 nm thick) in columns (brick-and-mortar) across the layers.

Columnar nacre shows a Voronoi-like tiling within one layer and partial overlap pattern (overlapping area takes 1/3 tablet surface area) between adjacent columns.

The tablets (and the interface) show a prominent waviness, observed in optical microscopy, SEM, TEM, laser profilometry and AFM. Roughness is 85 nm on average, with peak amplitude exceeding 200 nm (v.s. 450 nm tablet thickness), with its effects on mechanical performance not known.

The surface topology of one tablet to the next is highly conformal. Within tablets are nanograins of aragonite. On tablets nanoasperities and mineral bridges are obersved.

Interface between tablets

Nacre in tension

From the real scenario of mechanical loading (concentrated loads normal to the shell surface), the nacre layer is subjected to tension along the tablets. Tensile strength and toughness are critical properties.

Miniaturized tension tests (width 1.5 mm, thickness 0.6 mm, length 1.5 mm) under an optical microscope and using digital image correlation (DIC, to track the displacement fields and determine strains) show that dry nacre is similar as pure aragonite (linear elastic, E~90 GPa, failure stress 95-135 MPa, failure strain <0.002), while wet nacre is firstly linear then a large region of inelastic strains with hardening and uniform strain distribution in the specimen (E ~70 GPa, 70 MPa, failure strain 0.01).

The relative large deformations accompanied with hardening are from several mechanisms. Interface materials shear and channel tensile stresses to tablets; once reaching the shear strength, tablets start sliding (occurs in the overlap regions); higher stresses are required to slide them further so that initiating new sliding sites is more favorable, thus spreading uniform deformation over large volumes (stable large deformation).   The transverse strains initially decrease, reasonable as Poisson’s effect, but then a slight transverse expansion shows up, and then remained constant (transverse expansion may be generated to counteract the Poisson’s transverse contraction).

Hydrated interfaces can deform and maintain tablets cohesion for tablet sliding, while dry interfaces cannot.

Nacre in shear

Miniaturized shear tests (1 mm x 1 mm x 1 mm) show an initial linear response and a region of large shear strain and hardening. DIC shows uniform strain distribution (no localization). Interface shearing is the prominent deformation mechanism (as stress levels is much lower than the tablet strength). 

With stress increasing, the tablets layers sled on one another, creating a staircase like deformation, and hardening at the interface occurs (more pronounced than in tension in which only overlap interface shears). Shearing is accompanied by a significant transverse expansion (across the layers), suggesting that the layers have to climb some type of obstacles to slide on one another.

Nacre in shear-compression

Off axis compression (layers in 45o from the loading axis) tests, subjecting specimens in shear and in compression with equal magnitude, show significant inelastic deformations, and as sliding starts, the layers show obvious transverse expansion (as additional evidence of climbing mechanism during sliding).

The transverse compression increases shear resistance compared with simple shear; all show that shearing is accompanied by a significant lateral expansion.

For the hardening and the transverse expansion, the effect of the interface biopolymer is ruled out (the organic molecules are extensible without significant hardening nor expansion), the mineral bridges cannot play a role during the large sliding distance, and the nanoasperities may contribute to the very initial stage but their interactions are too limited to produce the observed hardening.

The microscale waviness of tablets with a larger size could produce hardening and transverse expansion over the experimentally observed tablet sliding distance.

Finite element models and simulation results

A representative volume element (RVE) of hydrated nacre with large numbers of tablets using actual images of nacre structure (overlapping, wavy tablets) is adopted (tablets transversely isotropic elastic), and cohesive elements are assigned at the interfaces and vertical junctions (zero thickness), in which the chosen parameters reflect the nanoscale mechanisms of mineral bridges, nanoasperities and biopolymer.  

Interface deformations due to tensile strains on the RVE are modeled, and the predicted stress-strain curves show consistent behavior to the experiments. The wavy interface model shows a large, uniform strain of 0.008-0.01, and is able to spread deformation for larger strains.

The hardening allows relatively large strains to develop and propagate over large volumes.

Hardening features

The waviness of the interface generates tablets that are thicker at their periphery, very similar to a dovetail in two-dimensional shape (the angle is not so high to generate progressive pullout accompanying hardening); in about equal proportion, the overlap regions appeared to be flat, and in rare scenes as inverse dovetail. These are captured by the large RVE.

A RVE model with dovertail geometry in tension shows significant compressive stress tablet locking developed, about 15% of the model volume; considering 30% being overlapping areas, this indicates progressive tablet locking is sufficiently strong to generate macroscale hardening.

Effect of the tablet junctions

The junctions add to the stiffness and strength of the RVE, should not affect the hardening rate.

Perfectly hexagonal tablets

A RVE model of perfectly hexagonal tablets all with same size and overlap (30%), and the waviness modeled as a sinusoidal surface. The sinusoidal surface generates hardening and large deformation like the nacre tablet waviness does, but the hardening rate is much lower, indicating the role of statistical variation/randomness in the strengthening of nacre.

Guidelines suggested for biomimetic nacreous composites

Tablet material with high stiffness, high strength and small size;

Interface material capable of large strains;

Thin interface, material with a high compressive stiffness and strength to allow progressive locking mechanisms;

High aspect ratio for the tablets to maximize the overlap areas and the load transfer;

Wavy interface between tablets to generate geometric hardening through locking;

Some degree of randomness in the arrangement of tablets for strengthening;

Core area (non-overlap), interface tensile strength and waviness amplitude should be finely tuned (balance the climbing force by transverse compression in locking regions) for the locking/hardening to operate.

This classical work is extremely reader-friendly with great clearness and profound findings, do not be frightened by the number of pages.  Here is the link of the fulltext: https://www.sciencedirect.com/science/article/pii/S0022509606001268