## Introduction

Nacre is a hierarchical material with extraordinary strength and toughness1,2,3,4,5,6,7,8,9,10,11,12. Composed of ~95% aragonite and ~5% protein, nacreous structures exhibit orders of magnitude higher toughness than their brittle aragonite constituents primarily due to nano- and microscale brick-and-mortar structures1,4,13,14,15,16,17. Different toughening mechanisms have been proposed to explain the mechanical behavior of nacre. At the nanoscale, the sliding of nacreous tables are resisted by nanopillars (i.e., mineral bridges)18,19,20,21, contacts of nanoasperities20,22,23,24 and the unfolding of protein chains25. At the microscale, interactions of wavy tablets26,27, crack deflections and pulling out of tablets28 provide essential resistance to the nacreous deformation. Despite prior studies, it is still difficult to quantify how various nanoscale toughening mechanisms contribute to the shear resistance in the initial sliding of nacreous tablets. It is also unclear how nacre exhibits brittle behavior under different stress conditions. In this work, we employ pure shear stresses of torsion to investigate the mechanical properties of nacre in red abalone, and to further elucidate the evolution of toughening mechanisms during the deformation of nacre.

We focus on separating adjacent nacreous tablets using pure shear stresses of torsion29,30. We created composite dog-bone shaped specimens using the pure nacreous sections without any growth layers21,31,32,33 from a red abalone shell. The hexagonal surfaces of aragonite tablets are perpendicular to the cylindrical axis (Fig. 1b). For a shaft under torsion, pure shear stresses exist in every two-dimensional cross-sectional planes over the entire gauge section. This feature enables the nanoscale interfaces between nacreous tablets to be tested successfully. The shear stress and strain in torsion are described by

$$\tau =\frac{T\cdot \rho }{J}$$
(1)
$${s}_{max}={\rm{\Delta }}\theta \cdot r={\gamma }_{max}\cdot l$$
(2)

## Results and Discussion

### Pure shear stresses generate complete brittle fracture of nacre

A total of five successful composite dog-bone shaped nacre specimens were created due to the scarce of pure nacre sections in red abalone shells. For each specimen, the torque-rotation curve collected during quasi-static monotonic torsional tests exhibits an increase and a sharp drop (Fig. 2a). The increase segments are almost linear since R2 values of the linear fitting are above 0.99 for all specimens (Fig. 2c). The shear strength is 41.5 ± 14.7 MPa at 2.0 ± 0.8% strain. The variation is due to the specimen locations in the red abalone shell. The post-peak curves are nearly vertical, showing that catastrophic failures happen in a short time (Fig. 2a and b). In comparison, single-crystal aragonite minerals were shaped to the same size and orientation of nacreous specimens. The shear strength of aragonite is 14.5 ± 2.2 MPa at 1.4 ± 0.2% strain. Although the R2 values of aragonite segments are close to unity, the relatively flat drop (Fig. 2b) indicates that crack propagations are affected by the spiral fractural surfaces (Fig. 3d). For the same geometry, cracks travel faster between the nacreous tablets than in aragonite minerals since the dropping periods of nacre specimens last shorter (5.0 ± 2.0 milliseconds) than those of aragonite specimens (20.0 ± 0.6 milliseconds). By discretizing the twisting angle of the gauge section to the rotational angle of two adjacent tablets, the measured sliding distance at the external edge in the initial stage is ~20 nm (20.0 ± 8.4 nm) that agrees with prior estimations22.

### Fractographic characterization proves interfacial fracture in nacre

We observed two flat surfaces over the entire 3 mm-diameter circular cross sections of nacreous specimens after failure (Fig. 3a,c). Under the white light, the flat surface exhibits a combination of green (λ≈510 nm) and yellow (λ≈570 nm) colors, which is different from the iridescence of the inner surface of red abalone shells. The reason is that uniform horizontal tablet (~500-nm thick) layers underneath reinforce lights with specific wavelengths over the entire fracture surface. Elevated tablet sections appear on the left (Fig. 3b and c). This is because pure shear stress condition is no longer maintained once cracks start to propagate after the failure of external tablets. As a result, cracks kink from one interface to another that eventually separate the specimen. Detail SEM image (Fig. 3e) shows that large areas of tablets are exposed and are interlaced with broken edges that transit spirally from one layer to the next20. The broken edges (Fig. 3f) include both the smooth intertablet delamination and brutal transtablet breakage. However, these sharp edges are different from the blunted edges of polished nacre specimens34, demonstrating that tablets and spiral connections are quickly removed during crack propagations. The microCT image (Fig. 3d) clearly shows the different brittle fracture of aragonite specimens. Aragonite specimens exhibit a classical 45-degree helical fracture perpendicular to the principal tensile stress, while nacreous specimens fracture sharply through the interfaces between aragonite tablets.

### Mathematical modeling quantifies nanoscale toughening mechanisms

To detail the nanoscale toughening mechanisms in the initial sliding stage, we created isotropic linear elastic finite element models to quantify the contribution of nanopillars, nanoasperities and protein chains to the shear resistance. A contour of an exposed tablet (Fig. 4a) shows that stresses in nanopillars and nanoasperities (E = 100 GPa) are substantially higher than those of protein chains (E = 20 MPa) due to the significantly different elastic moduli. The lower and upper bounds of shear stress curves (Fig. 4b) correspond to nanopillar densities of 1.4 and 5.6/µm2, respectively. The mean shear strength (~41.5 MPa) curve corresponds to a density of ~2.2/µm2. By decoupling the contribution of each mechanism with respect to various tablet moduli (E = 80 to100 GPa) and pressures (p = −35 to 35 kPa), Fig. 4c shows that nanopillars contribute to more than 95% of the shear resistance, while nanoasperities and protein chains contribute limitedly in the initial sliding stage. High shear stresses in the middle section of nanopillars (~1.0 GPa) enable their breakage at the end of the initial sliding stage. Compared to the shear strength of aragonite mineral specimens (~14.5 MPa), nacreous nanopillars exhibit much higher shear resistance, demonstrating the ‘smaller-is-stronger’ size effect down to the nanoscale.

### The Achilles heel of nacre

If we define the intact nanopillars, nanoasperities and protein chains before sliding as ‘mortar’, the ductile or brittle behavior of nacre is highly dependent on how bricks (tablets) perform after mortar sections fail. The mineral bridges, nanoasperities and protein chains are activated to resist sliding in the beginning. When mineral bridges break after tablets slide about twenty nanometers, vertical distances between tablets decrease (Fig. 5a and b). In most stress conditions, contact areas between tablets increase gradually and substantially as cracks propagate completely or partially parallel to the sliding direction (Fig. 5c). The toughening mechanisms then change to the nanoasperity contact and protein deformation in nanoscale, and to interactions of wavy tablets, tablet pulling-out and crack deflections in microscale1,27,28 (Fig. 5d). For example, when nacre is in tension along the tablets18,24,35, mortar sections fail first (the linear increment), and some tablets start to touch each other (the nonlinear increment). Then, microscale toughening mechanisms are triggered at various locations continuously (the extended stress plateau). Similar behavior exists in nacre under compression36,37, bending24, 45-degree shear24,26 or direct shear26,38. However, when nacre is under torsion normal to aragonite layers, the sliding of tablets (tangential) is perpendicular to the crack propagation (radial), and the large stress gradients enable the specimen to fail quickly (Fig. 1b). Thus, nacre exhibits completely interfacial brittle fracture since there is little chance for brick interactions after the mortar sections fail (Fig. 5e). The Achilles heel of nacre is to avoid triggering microscale toughening mechanisms that can induce the ductile behavior. The discretization nature of torsional loads enable us to study nano- and microscale material behavior using relatively large specimens. Torsion can be particularly advantageous to study interlayer/interfacial mechanical behavior of layered materials.

In summary, by applying pure shear stresses of torsion, we exhibit the linear response in the initial sliding stage of nacreous tablets. Mathematical modeling shows that nanopillars contribute dominantly to the shear resistance, while nanoasperity contact and protein chains contribute limitedly in this stage. Complete brittle fracture observed between tablet interfaces in torsion is convincing proof that microscale toughening mechanisms are not triggered to promote ductile behavior of nacreous structures. These findings open an exciting perspective into studying mechanical properties of natural and artificial layered materials using pure shear stresses of torsion. Future effort could also be extended to study the interactions between nanoparticles that build the nacreous tablets, such as rotations, orders, protein strengthening, and deformation twinning.

## Materials and Methods

### Sample preparation

A red abalone shell with a maximum length of ~210 mm (The Shell shop, CA, US) was obtained to prepare specimens for mechanical tests. The shell was first shaped to 7.6 mm by 7.6 mm cubes, and epoxy ends (Loctite Fixmaster, Rocky Hill, CT) were bonded to increase the gripping area. Using a modified minilathe G8688 (Grizzly Industrial Inc., WA, US) with the high precision control, dry composite dog-bone shaped specimens were created by tuning the cylindrical axis perpendicular to the tablet layers. The gauge sections had diameters of ~3.0 mm and lengths of ~3.0 mm. Then, sample surfaces were smoothed using 400 to 1200 grit sandpapers (3 M Company, Maplewood, Minnesota). A total of five specimens were created using pure nacreous gauge sections that are devoid of growth lines. A similar procedure was followed to create single-crystal aragonite specimens (Gold Nugget Miner online) with diameters of ~3.4 mm and gauge section lengths of ~3.4 mm.