Crack deflection occurs by constrained microcracking in nacre
Jingru Song1, Cuncai Fan1, Hansong Ma1, Lihong Liang1, Yueguang Wei2,*
1. LNM Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
2. College of Engineering, Peking University, Beijing 100871, China
*Corresponding author. Yueguang Wei,Email: weiyg@pku.edu.cn; ywei@LNM.imech.ac.cn
Abstract

Nacre continues for decades to inspire researchers for its sophisticated hierarchical structure and remarkable mechanical properties, especially the extreme fracture toughness compared with its predominant constituent, CaCO3 in the form of aragonite. Crack deflection has been extensively reported and regarded as the principal toughening mechanism for nacre. In this paper, our attention is focused on crack evolution in nacre under quasi-static state. We use the notched three-point bending test of dehydrated nacre in situ in a scanning electron microscope (SEM) to monitor the evolution of damage mechanisms ahead of the crack tip. The observations show that the crack deflection actually occurs by constrained microcracking. On the basis of our findings, a crack propagation model is proposed, which will contribute to uncovering the underlying mechanisms of nacre’s fracture toughness and its damage evolution. These investigations would be of great value to the design and synthesis of novel biomimetic materials.

Key words: Biological mineralized material; Nacre; Toughening mechanism; Three-point bending test; Crack deflection; Microcracking
1 Introduction

Almost all engineering structural materials are required to be both strong and tough (damage tolerant), but these two mechanical properties are mutually exclusive [1]. For some mineralized biological tissues, they resolve this conflict by incorporating hard minerals into soft organic matrices, producing sophisticated composites with certain combinations of stiffness, toughness and strength to meet the physiological demand for structural support and armored protection [2, 3, 4]. Mollusk shell is an extraordinary example that exhibits excellent mechanical properties. In the past decades, it has been of great interest to material scientists and engineers, as it promises to be a model for synthetic ceramic composite [5, 6, 7, 8].

Many mollusk shells consist of two or more discrete layers which can be simply classified into several types according to their microstructural features [9]. Nacre, the inner iridescent layer of mollusk shells, displays inherent mechanical robustness. The earlier research showed that nacre has an extreme high fracture toughness that is roughly an order of magnitude higher than its predominant constituent, CaCO3 (approximately up to 95% by volume in the form of aragonite) [10]. This optimal mechanical performance is achieved through multi-dimensional architectural design: nacre is composed of a fine-scale layered brick wall-like structure comprising of sub-micrometer (0.5-1μ m) layered aragonite platelets bonded by a thin (20-40nm) layer of organic biopolymer [11, 12, 13, 14, 15]. It is from the hierarchical structure that nacre derives its high fracture toughness with a series of toughening mechanisms [16]. To date, some suggested mechanisms include: (1) crack deflection along the inter-platelet biopolymer [17, 18, 19, 20, 21], (2) fiber pullout [22], (3) mineral bridges or organic matrix bridges [23, 24], (4) the interlocking of platelets [25], etc. Among them, crack deflection is the most commonly observed phenomenon, especially when cracking occurs in a direction perpendicular to the aragonite platelet. However, all these investigations bear largely upon the observations and characterizations of fractography and crack path profile after failure. The techniques cannot reveal the concrete specifics of crack initiation and propagation under externally applied stress, so it is necessary to observe the crack deflection process in real time.

In the present study, we use the three-point bending test of dehydrated nacre in situ in a scanning electron microscope (SEM), to discern how crack evolves and forms the consequent deflection outline. Finally, a crack propagation model is proposed based on our experiments, which will help us obtain a comprehensive understanding of the underlying mechanisms for nacre’ s superior fracture toughness.

2 Experimental methods

The hard shells of Hyriopsis cumingii, a kind of limnetic oyster, were obtained from south of China, cut into strips using a low-speed diamond saw, and ground off the outer periostracum and prismatic layers. Then they were rinsed thoroughly in constant irrigation of water. The specimens for SEM observation were mechanical polished and subsequently etched with 10wt% ethylene diamine-tetra-acetic acid disodium salt (EDTA-2Na) solutions for ten minutes. The specimens for bending test were first cut into small beams, carefully polished and finally stored at room temperature for three months to be completely dehydrated. All specimens were coated with a thin film of gold prior to SEM imaging.

Fig.1 Schematic of bending tested specimens (units in millimeter). Red circle denotes the position of SEM imaging.

The shapes and sizes of the specimens used in bending test are shown in Fig.1. The first specimen (see Fig.1a) was experimented as previously reported investigations: controlled bending deflection was gradually applied to the specimen (at the rate of 0.55 μ m/s) until it eventually ruptured, followed by the analysis of macro appearance, loading-displacement curve measurement and failure microstructure. By comparison, the second notched specimen was mounted to a micromechanical tester which was integrated with an SEM to image nacre surface (the area of red circle in Fig.1b) during the experiment. Once the crack initiated on the surface at notch root, the loading was suspended temporarily for SEM imaging. As the crack tip terminated in nacre, additional controlled deflection was applied again and immediately suspended if the crack resumed extending. This method allowed for the control over crack growth rate and the real time monitoring of morphology evolutions during testing. The fracture mechanism for the nacre material will be developed and the fracture process will be modeled.

3 Experimental observation and measurement
3.1 Hierarchical structure

Nacre has a complex hierarchical architecture that spans multiple length scales from nanometers to millimeters. Figure 2a is a schematic illustration of nacre. On the platelet surface it presents to be polygon-shaped (see Fig. 2e), while on the cross-sectional surface it exhibits the so called “ brick-and-mortar” structure (see Fig. 2b). Generally, there are two kinds of nacre: columnar nacre and sheet nacre [12]. The distinction between them lies in the stacking mode of aragonite platelets and the ultrastructural features on their surfaces. Here our used sample from the shell of Hyriopsis cumingii, belongs to the sheet one, whose aragonite platelets are randomly stacked with no nanoapsperites on the surface and no mineral bridges between them, as shown in Fig. 2b and Fig. 2c. Based on these observations, the aragonite platelets were also measured as 4.60± 1.67 μ m in length, and 0.93± 0.17 μ m in thickness.

Fig.2 Hierarchical structure of nacre. (a) A schematic drawing showing how polygonal aragonite platelets are arranged to form a lamellar structure in nacre. Magnified figures of nacre on cross-sectional surface (b-d) and platelet surface (e-g). ICOM: inter-crystalline organic matrix; ILOM: inter-laminar organic matrix.

In addition, the magnified figures revealed the existence of organic biopolymer (about 30 nm in thickness) between platelets. This inter-platelet organic matrix (IPOM) can be subdivided into two types: inter-laminar organic matrix (ILOM, black arrowed in Fig. 2d) and inter-crystalline organic matrix (ICOM, black barrowed in Fig. 2f). According to the “ organic-matrix-mediated” theory of surface-templated growth, ILOM precedes ICOM during biomineralization process, so they might be different both in structure and composition [26, 27, 28, 29]. Also, it is worth noting that the intracrystalline organic biopolymer, embedded inside individual mineral platelets, has recently been detected using different techniques [30, 31, 32, 33, 34]. In our experiment the closer examination in Fig. 2g on the etched platelet surface clearly exposes the nanograins inside aragonite platelets, consistent with the literature description that the aragonite in nacre is constructed with highly oriented nanoparticles and biopolymers [35, 36]. It is believed that these organic inclusions definitely have great effect on mineral platelet’ s mechanical properties [37, 38].

3.2 Three-point bending test

The resulting load-deflection curves are shown in Fig. 3. In the first experiment of the sample without notch (see Fig.1a), the dry nacre behaved like ceramic and failed in a brittle fashion (see Fig. 3).

Fig.3 Load-deflection curves of the specimen without notch and the specimen with a single notch.

Figure 4 shows its surface morphology after failure. The overall failure form seems a joint of two main failure mechanisms from the compressive zone and tensile zone of two sides. The magnified figure in Fig. 4b seems to indicate that the main crack traveled both around and through mineral platelets with broken and intact platelets (white arrowed). However, a branch crack (see Fig. 4c), which developed and accompanied by the main crack come from tensile zone and terminated in the compressive zone, behaves quite differently. Closer examinations along the branch crack exposed the unexpected evolution of crack which maybe is the second joint of two failure mechanisms from compressive region and tensile region, respectively. In the position far behind the crack tip (see Fig. 4d), the fracture path exhibits like that of the main crack; but when the observed view moves toward crack tip (see Fig. 4e), no broken platelets are found, indicating the crack propagated strictly along the biopolymers between aragonite platelets. This assumption is confirmed by the SEM micrograph in the area just ahead of the crack tip (see Fig. 4f). It clearly shows the successive stair-like steps on the surface, and such steps go up and down along the biopolymer interlayer.

To fully investigate how crack deflection occurs in nacre, another three-point bending test with a single-notched sample was performed in situ in the SEM. This technique allows us to monitor the evolution of damage mechanisms ahead of crack tip. In this experiment, the stable fracture from three cycles of loading and unloading (see Fig. 3) was observed.

Fig.4 Crack path profile and damage morphology in nacre under three-point bending test. (a) The fracture path observation of broken sample. (b) A closer examination from the white boxed area in (c) showing the main crack path profile with both broken and intact aragonite platelets (white arrowed). (c) A close-up view from the white boxed area in (a) showing a branch crack that develops from the main crack. (d), (e), (f) Magnified figures of the branch crack toward the crack tip in positions marked as “ d” , “ e” and “ f” in (c).

When the load reached around 40 N, a crack initiated at the notch, shown in the white boxed area in Fig. 5a. After unloading, the crack propagated slowly with a reduction in load from the point of A to B in Fig. 3, and finally ended in nacre. During the second loading from the point of B to C in Fig. 3, the crack resumed propagating. Once unloading the crack propagated further with another comparatively less reduction in load from the point of C to D. Interestingly, the area just ahead of the crack tip began to take the shape of arborization (see Fig. 5b). A closer examination on this area in Fig. 5c clearly demonstrates the formation of multiple microcracks contained within the ICOM. At the beginning of the third loading from the point of D to E in Fig. 3, the crack traveled through these constrained microcracks as shown in Fig. 5d. Simultaneously, some preexisted microcracks (indicated by the dotted ovals in Fig. 5c and Fig. 5d) were preserved beside the main crack, while some new microcracks were produced continually (indicated by the dotted squares). In conclusion, these observations clearly reveal the crack deflection in nacre occurs by constrained microcracking, and this mechanism allowed for a stable growth of crack until the final failure at the point of F in Fig. 3.

Fig.5 In situ SEM micrographs reveal the evolution of damage mechanisms ahead of the crack tip. (a) A crack initiates at the notch. (b) The crack terminates in nacre with a shape of arborization at crack tip (white boxed). (c), (d) Sequential snapshots show crack deflection occurs by constrained microcracking with some microcracks preserved (in dotted ovals) and some newly produced (in dotted squares). The black arrows in (c) and the dotted line with arrow in (d) show the main crack path profile under continued loading; the light areas in (d) indicate electrical charging in the SEM resulting from the deformation of the gold coating during crack propagation.

3.3 Crack propagation process

To better understand the development and morphology of microcracking in nacre, a schematic model is proposed in Fig. 6. The application of deflection results in the initiation of a crack at notch root and the subsequent formation of a microcrack zone ahead the crack tip. These microcracks are confined between aragonite platelets in ICOM (stage I). With continued loading, the main crack propagates through this zone. Meanwhile, some new microcracks are being produced ahead the main crack tip (indicated by the dotted square), while some preexisted microcracks (indicated by dotted ovals) are persevered beside the main crack (stage II). Stage II continues until a local saturation of microcracks in the area ahead the crack tip is achieved. The main crack propagates again to repeat stage I followed by stage II. This pattern of alternating stage I and II is repeated as the main crack continues to propagate stably through the nacre.

Fig.6 Schematic model showing the development of crack deflection through microcracking in nacre.

Over the past decades, the understanding of nacre’ s principal toughening strategy has long stayed at the crack deflection along biopolymer interface, but our findings clearly show that the crack deflection in nacre does not happen directly, but rather it occurs by constrained microcracking ahead the main crack tip. The presence of such microcracks initiated ahead the main growing crack can effectively release the local stress concentration that would otherwise cause the nacre to fracture, thus enhancing the crack extension resistance. Most importantly, akin to other biological mineralized composites, such as bone, the microcracking is advantageous for the development of crack deflection, as fracture is closely associated with the intrinsic (damage) mechanisms ahead of the crack tip that promote cracking [39, 40, 41]. The crack deflection in return enables to provide the most contribution to nacre’ s toughness. Nevertheless, our experiments were conducted upon a quasi-static state. Some recent studies have shown that nacre exhibits much higher fracture strength under high-strain-rate loading, which is attributed to the fracture transition from crack deflection to invasion through the aragonite platelets [42, 43]. Here we can reasonably speculate that the fracture transition might be caused by the suppression of nucleation of microcracks under high-strain-rate state.

In addition, our investigations are also significant in uncovering the evolution of damage morphology in nacre. Consistent with the wide thought that the organic biopolymer layers are so well bonded to the mineral platelets that microcracking is able to be activated and followed by crack deflection. Therefore, the aragonite platelets invariably remain shielded from the propagating crack, resulting in the “ ragged platelets” morphology, but with the increasing displacement some separated platelets are broken off due to the interaction between adjacent ones. This is very important, considering a recently proposed assumption that crack invasion might happen at the crack tip as the intracrystalline organic matrix inside individual platelets serves as the defects leading to cracking [38]. Our research, on the other hand, indicates such organic inclusions actually strengthen the mineral platelet by modifying it into nanoparticle-architecture which becomes insensitive to flaws [6]. This is verified by the direct evidence that the microcracks arise from ICOM instead of from the inside of aragonite platelets, yet more quantitative details are required to further evaluate nacre’ s mechanical design.

4 Modeling of the energy release rate

Referring to the experimental observation in Fig. 5, we present a small-scale damage zone model as shown in Fig. 7, near notch, crack forms and propagates due to bend and interface shear sliding between bricks.

Fig.7 Crack propagation model for nacre under three-point bending due to interface shear sliding.

Energy release rate when damage zone is small is written as follows

$G=-\frac{1}{B}\frac{\partial \Pi }{\partial a}$, (1)

where $\Pi $ is total potential of the system, a is crack length, B is width of beam.

$\Pi =U-P\Delta $, (2)

where U is strain energy of beam, P is load, and ∆ is the deflection of central point of beam (acted point by load). For small deformation case of beam and small scale damage case, U is bend energy

$U=\frac{{{P}^{2}}{{L}^{3}}}{96EI}$ (3)

for three-point bend beam, where L is beam length, E is Young’ s modulus, I is inertial momentum

$I=\frac{B{{h}^{3}}}{12}$ (4)

for rectangular section beam, where h is height of beam. Equation (2) can be rewritten as follows,

$\Pi =\frac{1}{2}P{{\Delta }_{0}}-P\Delta $, (5)

where 0 is the deflection at central point of beam when beam is without notch,

${{\Delta }_{0}}=\frac{P{{L}^{3}}}{48EI}$ or $P=\frac{48EI}{{{L}^{3}}}{{\Delta }_{0}}$. (6)

The load-deflection curves for unnotched beam and notched beam are shown in Fig. 3a, 3b, respectively.

The crack propagation condition can be expressed as follows,

$G={{\Gamma }_{0}}+{{\Gamma }_{D}}$, (7)

where Γ 0 is elastic fracture toughness (or elastic fracture energy density), Γ D is damage dissipation energy density due to sliding between bricks. Based on the model sketched in Fig. 7, we further assume that shear stress within the organic layer can be described as

$\tau =\left\{ \begin{align} {{\tau }_{s}}\text{, }|\Delta u|\le l{{\gamma }_{s}}, \\ & 0, \text{ }|\Delta u|> l{{\gamma }_{s}}\text{, } \\ \end{align} \right.$ (8)

where | ∆ u| is the relative sliding displacement neiboure two bricks, (τ s, γ s) is shear strength and shear strain strength of organic layer, l is sliding zone length between neighbor two bricks. So Γ can be expressed as

${{\Gamma }_{D}}=\rho {{\tau }_{s}}{{\gamma }_{s}}ld$, (9)

where ρ =1/t is density of “ brick” in vertical direction, t is brick thickness, d is width of damage zone.

5 A simple comparison of model result with experimental result about energy release rate

From experimental observation, seen in Fig. 4, specimen failure form of both notched specimen and without notch specimen is cross-section fracture. From load-displacement curve, shown in Fig. 3, one can obtain the average energy release rates through calculating the area under load-displacement curves divided by the cross-section area of specimens: $\bar{G}={{\Gamma }_{0}}\approx 200\text{J}\cdot {{\text{m}}^{\text{-2}}}$ for specimen without notch, and $\bar{G}\approx 303\text{J}\cdot {{\text{m}}^{\text{-2}}}$ for specimen with notch. On the other hand, one can also use the theoretical model given in Sect. 4 (see Eqs. (7)-(9)) to calculate the energy release rate. From Fig. 2b and 2c, t ~ 0.93 μ m, l ~ 4.6 μ m, and from Fig. 5c or 5d, d ~ 18 μ m, in addition τ s37 MPa, and γ s=τ s/μ s0.038 from Refs. [44, 45], one can obtain the energy release rate $\bar{G}={{\Gamma }_{0}}+{{\Gamma }_{D}}\approx 325\text{J}\cdot {{\text{m}}^{\text{-2}}}$, where Γ 0≈ 200J· m-2 is the energy release rate without notch.

6 Conclusions

The nacreous layer from the shell of Hyriopsis cumingii has sophisticated structure with rigid hierarchical design that can generate high fracture toughness primarily by crack deflection. Under quasi static loading state, crack deflection occurs by constrained microcracking. This crack propagation model contributes to our understanding of nacre’ s toughening mechanisms in at least two ways: first, the microcracking just ahead the crack tip can effectively release the local stress concentration, thus enhancing the crack extension resistance; second, the formation of microcracking is advantageous for the main crack to propagate along biopolymer layers and dissipate the most energy, namely becoming tougher. Furthermore, this model also contributes to uncovering the evolution of damage morphology and the distinctive mechanical responses between high-strain-rate and quasi static state. In summary, it is expected that the present experimental findings shall be quite helpful to inspire us in replicating nacre’ s mechanical design.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos. 91216108, 11432014, 11672301, 11372318, and 11502273), and by the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB22040501).

The authors have declared that no competing interests exist.

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