Mineral bridges of nacre and its effects

Nacre, or mother-of-pearl, is a kind of composites of aragonite platelets sandwiched between organic materials. Its excellent mechanical properties are thought to stem from the microarchitecture that is traditionally described as a “brick and mortar” arrangement. In this paper, a new microstructure, referred to as mineral bridge in the biomineralization, is directly observed in the organic matrix layers (mortar) of nacre. This is an indication that the organic matrix layer of nacre should be treated as a three-dimensional interface and the microarchitecture of nacre ought to be considered as a “brick-bridge-mortar” structure rather than the traditional one. Experiments and analyses show that the mineral bridges not only improve the mechanical properties of the organic matrix layers but also play an important role in the pattern of the crack extension in nacre. The project supported by the Natural Science Foundation of Chinese Academy of Sciences (KJ951-1-201) and the National Natural Science Foundation of China (19891180 and 10072067)     

Crack deflection occurs by constrained microcracking in nacre

For decades, nacre has inspired researchers because of its sophisticated hierarchical structure and remarkable mechanical properties, especially its extreme fracture toughness compared with that of its predominant constituent, \(\hbox {CaCO}_{3}\), 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 a 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.     

Understanding the influence of structural hierarchy and its coupling with chemical environment on the strength of idealized tropocollagen–hydroxyapatite biomaterials

Hard biomaterials such as bone, dentin, and nacre have primarily an organic phase (e.g. tropocollagen (TC)) and a mineral phase (e.g. hydroxyapatite (HAP) or aragonite) arranged in a staggered arrangement at the nanoscopic length scale. Interfacial interactions between the organic phase and the mineral phase as well as the structural effects arising due to the staggered arrangement significantly affect the strength of such biomaterials. The effect of such factors is intricately intertwined with the chemical environment of such materials. In the present investigation, an idealized TC–HAP composite system under tensile loading is analyzed using explicit three-dimensional (3-D) molecular dynamics (MD) simulations to develop an understanding of these factors. The material system is analyzed in three different environments: (1) in the absence of water molecules (non-hydrated), (2) in the presence of water molecules (hydrated), and (3) in the presence of water molecules with calcium ions (ionized water). The analyses focus on understanding the correlations among factors such as the structural arrangement, the peak stress during deformation, Young's modulus, the peak interfacial strength, and the length scale of the localization of peak stress during deformation. Analyses show that maximizing the contact area between the TC and HAP phases results in higher interfacial strength as well as higher fracture strength. Due to the staggered arrangement, the orientation of HAP crystals has insignificant effect on the biomaterial strength. Analyses based on strength scaling as a function of structural hierarchy level reveal that while peak strength follows a multiscaling relation, the fracture strength does not. The peak strain for failure was found to be independent of the changes in levels of structural hierarchy. Overall, the analyses, being limited in size due to the computational time constraint, point out important correlations between the mechanical strength and chemically influenced structural hierarchy of biomaterials.     

Discontinuous crack-bridging model for fracture toughness analysis of nacre

Studying the structure–property relation of biological materials can not only provide insight into the physical mechanisms underlying their superior properties and functions but also benefit the design and fabrication of advanced biomimetic materials. In this paper, we present a microstructure-based fracture mechanics model to investigate the toughening effect due to the crack-bridging mechanism of platelets. Our theoretical analysis demonstrates the crucial contribution of this mechanism to the high toughness of nacre. It is found that the fracture toughness of nacre exhibits distinct dependence on the sizes of platelets, and the optimized ranges for the thickness and length of platelets required to achieve higher fracture toughness are given. In addition, the effects of such factors as the mechanical properties of the organic phase (or interfaces), the effective elastic modulus of nacre, and the stacking pattern of platelets are also examined. Finally, some guidelines for the biomimetic design of novel materials are proposed based on our theoretical analysis.     

Optimization design of strong and tough nacreous nanocomposites through tuning characteristic lengths

How nacreous nanocomposites with optimal combinations of stiffness, strength and toughness depend on constituent property and microstructure parameters is studied using a nonlinear shear-lag model. We show that the interfacial elasto-plasticity and the overlapping length between bricks dependent on the brick size and brick staggering mode significantly affect the nonuniformity of the shear stress, the stress-transfer efficiency and thus the failure path. There are two characteristic lengths at which the strength and toughness are optimized respectively. Simultaneous optimization of the strength and toughness is achieved by matching these lengths as close as possible in the nacreous nanocomposite with regularly staggered brick-and-mortar (BM) structure where simultaneous uniform failures of the brick and interface occur. In the randomly staggered BM structure, as the overlapping length is distributed, the nacreous nanocomposite turns the simultaneous uniform failure into progressive interface or brick failure with moderate decrease of the strength and toughness. Specifically there is a parametric range at which the strength and toughness are insensitive to the brick staggering randomness. The obtained results propose a parametric selection guideline based on the length matching for rational design of nacreous nanocomposites. Such guideline explains why nacre is strong and tough while most artificial nacreous nanocomposites aere not.     

Effect of proximity of barrier on lifting force produced by vertical solid jets

The effect of proximity to the ground on the lifting force generated by a vertical solid jet is studied in connection with development of vertical takeoff and landing devices and of air cushion devices. Such a study was made in [1 ] for planar flow by an incompressible ideal fluid. There a generalization of the results obtained on a compressible fluid was made by the approximation method. In the present work the planar problem of streamline flow past a dihedral barrier of a gas jet emerging from a channel with parallel walls was solved by the Chaplygin-Fal'kovich method [2, 3], The results of [1, 4–9] follow as a particular case from the solution obtained. Calculations were carried out clarifying the effect of the proximity of a barrier and the lifting effect of a fluid on flow characteristics at subsonic speeds.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 123–131, September–October, 1971.     

Toughness amplification in natural composites

Natural structural materials such as bone and seashells are made of relatively weak building blocks, yet they exhibit remarkable combinations of stiffness, strength and toughness. This performance can be largely explained by their “staggered microstructure”: stiff inclusions of high aspect ratio are laid parallel to each other with some overlap, and bonded by a softer matrix. While stiffness and strength are now well understood for staggered composites, the mechanisms involved in fracture are still largely unknown. This is a significant lack since the amplification of toughness with respect to their components is by far the most impressive feature in natural staggered composites such as nacre or bone. Here a model capturing the salient mechanisms involved in the cracking of a staggered structure is presented. We show that the pullout of inclusions and large process zones lead to tremendous toughness by far exceeding that of individual components. The model also suggests that a material like nacre cannot reach steady state cracking, with the implication that the toughness increases indefinitely with crack advance. These findings agree well with existing fracture data, and for the first time relate microstructural parameters with overall toughness. These insights will prove useful in the design of biomimetic materials, and provide clues on how bone fractures at the nano and microscales.     

Dispersed phase motion in laminar boundary layer flow over a wedge

The motion of a dispersed phase in the laminar boundary layer on a wedge is considered with allowance for the effect of not only the Stokes force, which coincides in direction with the flow velocity, but also the transverse force (Saffman force) resulting from the transverse nonuniforrnity of the flow over the individual particle [1–3].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 34–42, November–December, 1993.In conclusion, the authors wishes to thank S. V. Manuilovich for assisting with the numerical calculations.     

A constitutive model of nanocomposite hydrogels with nanoparticle crosslinkers

Nanocomposite hydrogels with only nanoparticle crosslinkers exhibit extraordinarily higher stretchability and toughness than the conventional organically crosslinked hydrogels, thus showing great potential in the applications of artificial muscles and cartilages. Despite their potential, the microscopic mechanics details underlying their mechanical performance have remained largely elusive. Here, we develop a constitutive model of the nanoparticle hydrogels to elucidate the microscopic mechanics behaviors, including the microarchitecture and evolution of the nanoparticle crosslinked polymer chains during the mechanical deformation. The constitutive model enables us to understand the Mullins effect of the nanocomposite hydrogels, and the effects of nanoparticle concentrations and sizes on their cyclic stress–strain behaviors. The theory is quantitatively validated by the tensile tests on a nanocomposite hydrogel with nanosilica crosslinkers. The theory can also be extended to explain the mechanical behaviors of existing hydrogels with nanoclay crosslinkers, and the necking instability of the composite hydrogels with both nanoparticle crosslinkers and organic crosslinkers. We expect that this constitutive model can be further exploited to reveal mechanics behaviors of novel particle-polymer chain interactions, and to design unprecedented hydrogels with both high stretchability and toughness.     

The influence of the drag force due to the interstitial gas on granular flows down a chute

Fully-developed steady flow of granular material down an inclined chute has been a subject of much research interest, but the effect of the interstitial gas has usually been ignored. In this paper, new expressions for the drag force and energy dissipation caused by the interstitial gas (ignoring the turbulent fluctuations of the gas phase) are derived and used to modify the governing equations derived from the kinetic theory approach for granular–gas mixture flows, where particles are relatively massive so that velocity fluctuations are caused by collisions rather than the gas flow. This new model is applied to fully-developed, steady mixture flows down an inclined chute and the results are compared with other simulations. Our results show that the effect of the interstitial gas plays a significant role in modifying the characteristics of fully developed flow. Although the effect of the interstitial gas is less pronounced for large particles than small ones, the flowfields with large particles are still very different from granular flows which do not incorporate any interactions with the interstitial gas.     

Motion of a suspension in the laminar boundary layer on a flat plate

The boundary layer motion of a weak suspension is investigated with allowance for the effect on the particles not only of the Stokes force but also of the additional transverse force resulting from the transverse nonuniformity of the flow over the individual particle. As distinct from studies [1–3], in which the limiting values of the transverse force (Saffman force) were used [4], the velocity and density of the dispersed phase have been determined with allowance for the dependence of the Saffman force on the ratio of the Reynolds numbers calculated from the velocity of the flow over the individual particle and the transverse velocity gradient of the undisturbed flow, respectively [5, 6].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 66–73, January–February, 1992.In conclusion the authors wishes to thank M. N. Kogan, N. K. Makashev, and A. Yu. Boris for useful discussions of the results.     

Vortex motion of a disperse mixture

A study is made of the motion of fine spherical particles in a given steady vortex flow of an incompressible fluid. The results are given of an investigation into the Lyapunov stability of a particle trajectory coincident with the vortex axis, and of trajectories from which the distance to the vortex axis is determined by the condition of equality of the radial components of the force of the phase interaction and of the centrifugal force which acts on the particle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 167–169, November–December, 1984.     

On the mechanics of mother-of-pearl: A key feature in the material hierarchical structure

Mother-of-pearl, also known as nacre, is the iridescent material which forms the inner layer of seashells from gastropods and bivalves. It is mostly made of microscopic ceramic tablets densely packed and bonded together by a thin layer of biopolymer. The hierarchical microstructure of this biological material is the result of millions of years of evolution, and it is so well organized that its strength and toughness are far superior to the ceramic it is made of. In this work the structure of nacre is described over several length scales. The tablets were found to have wavy surfaces, which were observed and quantified using various experimental techniques. Tensile and shear tests performed on small samples revealed that nacre can withstand relatively large inelastic strains and exhibits strain hardening. In this article we argue that the inelastic mechanism responsible for this behavior is sliding of the tablets on one another accompanied by transverse expansion in the direction perpendicular to the tablet planes. Three dimensional representative volume elements, based on the identified nacre microstructure and incorporating cohesive elements with a constitutive response consistent with the interface material and nanoscale features were numerically analyzed. The simulations revealed that even in the absence of nanoscale hardening mechanism at the interfaces, the microscale waviness of the tablets could generate strain hardening, thereby spreading the inelastic deformation and suppressing damage localization leading to material instability. The formation of large regions of inelastic deformations around cracks and defects in nacre are believed to be an important contribution to its toughness. In addition, it was shown that the tablet junctions (vertical junctions between tablets) strengthen the microstructure but do not contribute to the overall material hardening. Statistical variations within the microstructure were found to be beneficial to hardening and to the overall mechanical stability of nacre. These results provide new insights into the microstructural features that make nacre tough and damage tolerant. Based on these findings, some design guidelines for composites mimicking nacre are proposed.     

Mechanical properties of nanostructure of biological materials

Natural biological materials such as bone, teeth and nacre are nanocomposites of protein and mineral with superior strength. It is quite a marvel that nature produces hard and tough materials out of protein as soft as human skin and mineral as brittle as classroom chalk. What are the secrets of nature? Can we learn from this to produce bio-inspired materials in the laboratory? These questions have motivated us to investigate the mechanics of protein-mineral nanocomposite structure. Large aspect ratios and a staggered alignment of mineral platelets are found to be the key factors contributing to the large stiffness of biomaterials. A tension-shear chain (TSC) model of biological nanostructure reveals that the strength of biomaterials hinges upon optimizing the tensile strength of the mineral crystals. As the size of the mineral crystals is reduced to nanoscale, they become insensitive to flaws with strength approaching the theoretical strength of atomic bonds. The optimized tensile strength of mineral crystals thus allows a large amount of fracture energy to be dissipated in protein via shear deformation and consequently enhances the fracture toughness of biocomposites. We derive viscoelastic properties of the protein-mineral nanostructure and show that the toughness of biocomposite can be further enhanced by the viscoelastic properties of protein.     

Ductile reinforcements for enhancing fracture resistance in composite materials

Ductile reinforcements can supply fracture toughness to a polymer matrix by pulling out and by plastically deforming. In the case of metal reinforcements that are not in a toughened condition, there may be more toughening to be gained when the fibers remain in the matrix and plastically deform rather than pulling out. These fibers can be said to have an unused plastic potential. When these fibers bridge a crack, their plastic deformation causes a rise in the force which is trying to pull out the fiber. Because of this, the shape of the fiber must be adjusted along its length if it is to remain anchored and contribute its plastic work. The use of anchored, ductile fibers provides a new design axis that brings new possibilities not achievable by the current research focus on the fiber–matrix interface. This paper describes the experimental pullout of aligned ductile fibers from a polymer matrix, and indicates the effect of the shape and embedded length of the fiber on the toughness increase of the composite. Anchored, plastically deforming fibers are shown to provide a major improvement to the toughening. Even for unoptimized ductile fibers, the calculated toughening improvement equals or exceeds the toughening available from current short glass or graphite fibers. In addition, pullout values are obtained for fibers that are embedded at an angle, simulating fiber bridging from fibers not perpendicular to the crack surface. These results further demonstrate the toughening efficiency of ductile fibers.     

Equation of state of static and dynamic compression of barium chalcogenides

The alkali-halide compounds and 16 crystals of chalcogenides of alkaline-earth metals (oxides, sulfides, selenides, tellurides) form a large group of ionic crystals which under normal conditions have a structure of the NaCl type. Analysis of the existing experimental data on the compression of ionic crystals shows that most of them undergo under pressure a first-order phase transition from a structure of the NaCl type (the B1 phase) to a structure of the CsCl type (B2 phase). Many theoretical works on the equations of state and phase transitions of ionic compounds are devoted to alkali-halide crystals. Similar theoretical calculations for chalcogenides have been performed only for oxides [1–3]. It is undoubtedly of interest to further study theoretically the equations of state of the static and dynamic compression of chalcogenides of alkalineearth metals. This would enable establishing the general laws governing the behavior of chaocogenides and analyzing the specific features of their interparticle interactions at high pressure. In this paper the pressures of phase transitions of the type B1–B2, the equations of state of hydrostatic compression, and the shock adiabats of the barium chalcogenides BaS, BaSe, and BaTe in the B1 and B2 phases are calculated based on the binding energy function proposed in [1].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 114–117, May–June, 1986.     

Stationary mode of a nonlinear elastically hereditary oscillator

The steady-state forced oscillations of a single-mass system subject to an external pure harmonic force are considered. The role of restoring force is played by a nonlinear function, which takes account of hereditary effects as a sum of multiple integrals in accordance with the Volterra theory. The problem is solved by the method of equivalent linearization, the discussion being confined to a triple integral of the hereditary type. The influence of the hereditary nonlinearity on the system dynamic characteristics, namely, its amplitude, phase, dynamic rigidity, hysteresis loop area, and Q, is investigated. In particular, the reciprocal of the Q, which can be taken as a measure of the internal friction, is shown to be independent of the amplitude of oscillation and to be the same as that obtained by linear theory. The other dynamic characteristics prove sensitive to the nonlinear properties. The exponential rational fractions proposed by Yu. N. Rabotnov are used as concrete hereditary functions.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 3, pp. 111–116, May–June, 1970.     

An Experimental Investigation of Deformation and Fracture of Nacre–Mother of Pearl

Nacre, also known as mother-of-pearl, is a hard biological composite found in the inside layer of many shells such as oyster or abalone. It is composed of microscopic ceramic tablets arranged in layers and tightly stacked to form a three-dimensional brick wall structure, where the mortar is a thin layer of biopolymers (20–30 nm). Although mostly made of a brittle ceramic, the structure of nacre is so well designed that its toughness is several order of magnitudes larger that the ceramic it is made of. How the microstructure of nacre controls its mechanical performance has been the focus of numerous studies over the past two decades, because such understanding may inspire novel composite designs though biomimetics. This paper presents in detail uniaxial tension experiment performed on miniature nacre specimens. Large inelastic deformations were observed in hydrated condition, which were explained by sliding of the tablets on one another and progressive locking generated by their microscopic waviness. Fracture experiments were also performed, and for the first time the full crack resistance curve was established for nacre. A rising resistance curve is an indication of the robustness and damage tolerance of that material. These measurements are then discussed and correlated with toughening extrinsic mechanisms operating at the microscale. Moreover, specific features of the microstructure and their relevance to associated toughening mechanisms were identified. These features and mechanisms, critical to the robustness of the shell, were finely tuned over millions of years of evolution. Hence, they are expected to serve as a basis to establish guidelines for the design of novel man-made composites.     

End-shaped copper fibers in an epoxy matrix—predicted versus actual fracture toughening

End-shaped copper fibers are placed in a brittle thermoset epoxy matrix at 10 vol% and tested in four-point bending to determine the fracture toughness of the composite. Results from four-point bend tests agree well with the theoretical predictions of the fracture toughness increment ‘ΔG’ of a metal fiber/brittle thermoset matrix composite based on single fiber pullout (SFP) tests. This close agreement demonstrates that SFP testing, along with the theoretical model, can be used as an effective end-shape screening tool for ductile fibers before full scale composite testing. The model predicts that the composite’s fracture toughness will be 46% higher with flat end-impacted fibers and 4% lower with rippled fibers compared to straight fibers at a 0° orientation. Four-point bend results show the actual composite’s fracture toughness is 49% higher with flat end-impacted fibers and 5% lower with rippled fibers compared to straight fibers. Further, four-point bend results show that end-shaped copper fibers improve both the flexural strength and modulus of the composite, demonstrating that end-shaped ductile fibers provide a good stress transfer to the fibers by anchoring the fibers into the matrix. Lastly, experimental validation of the model also indicates that at low fiber volume fractions, fiber–fiber interaction has only a minor influence on the fracture toughness for the tested ductile fiber/brittle matrix composite.     

Tribology and Its Many Facets: From Macroscopic to Microscopic and Nano-scale Phenomena

The key features of tribology – interfacial phenomena of interacting bodies in relative motion – are as origin of friction and wear scientifically interesting and have important applications in technology and engineering. The interfacial interactions have been studied in various theoretical and experimental approaches. Depending on the scope of the investigation and the nature of the tribological solid/fluid/solid or solid/solid system under study, these approaches apply contact mechanics, hydrodynamics, and rheology as well as solid state physics and chemistry. Accordingly, also various experimental techniques have been used, ranging from Coulomb's classical tribometer to the contemporary atomic force microscope.This paper reviews by way of examples some of the basic interfacial facets of tribology – from bulk continuum to atomistic/discrete phenomena – in a macroscopic, microscopic, and nano-scale point of view. For tribo-testing it is important to characterize the tribo-system under study by an appropriate choice of a systems envelope and to consider the hierarchy of interaction levels.