On flaw tolerance of nacre: a theoretical study

As a natural composite, nacre has an elegant staggered ‘brick-and-mortar’ microstructure consisting of mineral platelets glued by organic macromolecules, which endows the material with superior mechanical properties to achieve its biological functions. In this paper, a microstructure-based crack-bridging model is employed to investigate how the strength of nacre is affected by pre-existing structural defects. Our analysis demonstrates that owing to its special microstructure and the toughening effect of platelets, nacre has a superior flaw-tolerance feature. The maximal crack size that does not evidently reduce the tensile strength of nacre is up to tens of micrometres, about three orders higher than that of pure aragonite. Through dimensional analysis, a non-dimensional parameter is proposed to quantify the flaw-tolerance ability of nacreous materials in a wide range of structural parameters. This study provides us some inspirations for optimal design of advanced biomimetic composites.     

The toughening mechanism of nacre and structural materials inspired by nacre

Abstract

The structure and the toughening mechanism of nacre have been the subject of intensive research over the last 30 years. This interest originates from nacre’s excellent combination of strength, stiffness and toughness, despite its high, for a biological material, volume fraction of inorganic phase, typically 95%. Owing to the improvement of nanoscale measurement and observation techniques, significant progress has been made during the last decade in understanding the mechanical properties of nacre. The structure, microscopic deformation behavior and toughening mechanism on the order of nanometers have been investigated, and the importance of hierarchical structure in nacre has been recognized. This research has led to the fabrication of multilayer composites and films inspired by nacre with a layer thickness below 1 μm. Some of these materials reproduce the inorganic/organic interaction and hierarchical structure beyond mere morphology mimicking. In the first part of this review, we focus on the hierarchical architecture, macroscopic and microscopic deformation and fracture behavior, as well as toughening mechanisms in nacre. Then we summarize recent progress in the fabrication of materials inspired by nacre taking into consideration its mechanical properties.     

Nanostructured artificial nacre

Finding a synthetic pathway to artificial analogs of nacre and bones represents a fundamental milestone in the development of composite materials. The ordered brick-and-mortar arrangement of organic and inorganic layers is believed to be the most essential strength- and toughness-determining structural feature of nacre. It has also been found that the ionic crosslinking of tightly folded macromolecules is equally important. Here, we demonstrate that both structural features can be reproduced by sequential deposition of polyelectrolytes and clays. This simple process results in a nanoscale version of nacre with alternating organic and inorganic layers. The macromolecular folding effect reveals itself in the unique saw-tooth pattern of differential stretching curves attributed to the gradual breakage of ionic crosslinks in polyelectrolyte chains. The tensile strength of the prepared multilayers approached that of nacre, whereas their ultimate Young modulus was similar to that of lamellar bones. Structural and functional resemblance makes clay- polyelectrolyte multilayers a close replica of natural biocomposites. Their nanoscale nature enables elucidation of molecular processes occurring under stress.     

On the nature of mirror substrates

The use of reflecting substrates to enhance the Kerr magnetooptic effect has frequently been discussed. The nature of such a realizable high reflectivity mirror is described in a simple way.     

On the statistical nature of fracture

This paper explores the statistical nature of the mechanisms of fracture in structural materials and the loads that initiate them. The result of employing either a weak link or bundle model in the application of statistics to problems of fracture is examined. Experimental data is presented for the fracture of metal chains and the fracture of sheet aluminum containing machined cut-outs and cracks. The scatter in fracture loads for the chains and fracture toughness for the sheet specimens is statistically analyzed utilizing four statistical distributions: normal, lognormal, extreme value, and two-parameter Weibull functions. Based upon this work there appears to be no general a priori justification to utilize either the weak link or the bundle model in the statistical assessment of the fracture of typical engineering structural components.     

On the nature of the fourth sound

The density-density correlation function of He II bounded by solid walls is calculated in the hydrodynamic region. The migration of its poles as a function of the resistance parameter is investigated, and it is found that the fourth-sound pole can only be related to the first-sound pole far enough (_s0/₀>1/9) from the critical temperature. Otherwise, it arises from a mixture of the first- and second-sound poles. The contributions of poles to the sum rules are also discussed.     

The dynamics of nacre self-assembly

We show how nacre and pearl construction in bivalve and gastropod molluscs can be understood in terms of successive processes of controlled self-assembly from the molecular- to the macro-scale. This dynamics involves the physics of the formation of both solid and liquid crystals and of membranes and fluids to produce a nanostructured hierarchically constructed biological composite of polysaccharides, proteins and mineral, whose mechanical properties far surpass those of its component parts.     

On bending stiffness of composite tubes

Theoretical formulations are provided for the determination of stiffness of composite tubes. A three-dimensional laminate theory is used to determine the equivalent flexural stiffness 〈EI〉 for composite tubes. The same theory is also used to determine the load versus axial strain of the tubes. An approximate (more simplified) formulation is also presented. Values of the equivalent bending stiffness 〈EI〉 are compared between the two formulations. Experimental work was carried out on four composite tubes made of different lay-ups. The stiffness represented by the slope of the force-axial strains compares well between theoretical formulation and experimental results.     

Mechanical properties of the elemental nanocomponents of nacre structure

Sheet nacre is a nanocomposite with a multiscale structure displaying a lamellar “bricks and mortar” microarchitecture. In this latter, the brick refer to aragonite platelets and the mortar to a soft organic biopolymer. However, it appears that each brick is also a nanocomposite constituted as CaCO₃ nanoparticles reinforced organic composite material. What is the role of this “intracrystalline” organic phase in the deformation of platelet? How does this nanostructure control the mechanical behaviour of sheet nacre at the macroscale? To answer these questions, the mechanical properties of each nanocomponents are successively investigated and computed using spherical and sharp nanoindentation tests combined with a structural model of the organomineral platelets built from AFM investigations.     

On the electromagnetic nature of the turbulence onset

Based on the new experimentally justified notions about the interrelation and mutual influence of various physical fields and the vortex character of the electromagnetic field, the driving force is explained and a mechanism is proposed of the onset of turbulence, whereby a vortex motion arises “from nothing” in a hydrodynamic flow. Equations describing the vortex formation process are derived, and the possible scenarios of the turbulence development are outlined.     

On the microscopic nature of the Young modulus

On introducing the Van der Waals forces and Kittel mechanism of coupling into consideration, a physical approach to analytical computation of the Young modulus E has been outlined. By using a numerical analysis, a nontrivial behavior of the dependence of E on the atomic mass of an element has been predicted. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 4, pp. 197–199, July–August, 2006.     

Molecular origin of the sawtooth behavior and the toughness of nacre

We present in this paper a method to build a computer model that mimic the mineral–protein composite structure of a nacre tablet. Motivated by the interesting observations in AFM experiments of nacre, protein chains stretching out from grain boundaries are simulated by steered molecular dynamics (SMD) to gain an insight into the effect of protein–aragonite interaction on the mechanical properties of nacre and the molecular mechanisms of the sawtooth behavior. Force-extension curves are obtained and the key characteristics of sawtooth behavior are observed in SMD simulations in agreement with existing AFM experiments of nacre. The effect of water on protein–mineral interaction is investigated through including and excluding water molecules in the grain boundaries of the models. Different from the existing belief that protein unfolding is the origin of the “sawtooth” behavior, we have found that the electrostatic interactions between the protein and aragonite mineral are responsible for the sawtooth behavior and hence the high toughness of nacre.     

Comparison of nacre with other ceramic composites

Mother-of-pearl, the highly filled ceramic composite of mollusc shell, is compared with other, less highly filled, artificial ceramics. Stiffness is fairly simply related to volume fraction of ceramic, but no model seems to be adequate to describe this relationship. Strength, stress-intensity factor and the work of fracture are also dependent on the ceramic content but in a much more complex manner. Nacre has the highest value for all these parameters.     

On the nature of bond bending in water

It is shown that the theory of the Jahn-Teller pseudoeffect provides physical ground for the hydrogen bond bending postulated by Popl (this hypothesis underlies the continuum model of water) and explains the anomalous properties of water.     

On the nature of attractive dislocation crossed states

Attractive non-coplanar dislocations that cannot react to form junctions can, nevertheless, form crossed states, i.e., junctions of null length. Such configurations have recently been described by Wickham and co-workers as an output of numerical simulations. The physical origin of the crossed states is cleared out and their conditions of occurrence are calculated within a simplified elastic frame. The results are further discussed by comparison with mesoscopic simulations of intersecting dislocations in fcc and bcc crystals.     

Micromechanical model of nacre tested in tension

A modified shear lag theory is used to model the tensile behavior of Pinctada nacre. A two-dimensional model is used to analyze the stress transfer between the aragonite platelets of nacre assuming that the ends of the platelet are not bonded with the organic matrix. Elastic-perfectly plastic behavior of the organic matrix is assumed. A model for stress transfer between the platelets when the matrix between the platelets starts behaving plastically is developed. It is assumed that nacre fails when the matrix breaks after the ultimate shear strain in the matrix is exceeded. This theory can be used to model the stress transfer in platelet reinforced composites at high volume fractions.     

Special assembly of laminated nanocomposite that mimics nacre

Assembly of organic–inorganic nanocomposite with nacre-like structure has long been considered a valuable bio-inspired route to design materials with excellent mechanical properties. However, effective control of nanostructure and organic content concurrently is a key problem. In this research, a special assembly method—hydrothermal–electrophoretic assembly was introduced into preparing nanocomposite that mimics nacre, both in structure and composition. The two-step assembly process included intercalation of polymer into interlayer space of montmorillonite by hydrothermal process and the subsequent electrophoretic deposition. X-ray diffraction, Fourier transform infrared spectroscopy, thermal gravimetric analysis and scanning electronic microscopy were employed to characterize the structure and composition of the films. Reduced Young's modulus was determined by nanoindentation. Results showed that by constructing brick-and-mortar nanostructure, reduced Young's modulus of the composite film was effectively enhanced even when organic content was low.