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.     

珍珠母的微结构与力学行为研究进展

珍珠母(nacre或mother-of-pearl)是软体动物贝壳内层的主要结构材料,具有优异的力学性能,已成为当前先进工程材料仿生设计和制备的研究热点.该生物材料具有完善的分级微结构,使其强度与韧性远高于组成这种材料的纯文石相.本文从珍珠母的微结构、实验研究以及力学模型3个方面对珍珠母的研究现状进行了概述,并指出目前研究中一些仍待解决的关键问题.      

<Emphasis Type="Italic">In-situ</Emphasis> AFM Experiments with Discontinuous DIC Applied to Damage Identification in Biomaterials

Natural materials (e.g. nacre, bone, and spider silk) exhibit unique and outstanding mechanical properties. This performance is due to highly evolved hierarchical designs. Building a comprehensive understanding of the multi-scale mechanisms that enable this performance represents a critical step toward realizing strong and tough bio-inspired materials. This paper details a multi-scale experimental investigation into the toughening mechanisms in natural nacre. By applying extended digital image correlation and other image processing techniques, quantitative information is extracted from otherwise prodominantly qualitative experiments. In situ three point bending fracture tests are performed to identify and quantify the toughening mechanisms involved during the fracture of natural nacre across multiple length scales. At the macro and micro scales, fracture tests performed in situ with a macro lens and optical microscope enable observation of spreading of damage outward from the crack tip. This spreading is quantified using an iso-contour technique to assess material toughness. At the nanoscale, fracture tests are performed in situ an atomic force microscope to link the larger-scale damage spreading to sliding within the tablet-based microstructure. To quantify the magnitude of sliding and its distribution, images from the in situ AFM fracture tests are analyzed using new algorithms based on digital image correlation techniques which allow for discontinuous displacement fields. Ultimately, this comprehensive methodology provides a framework for broad experimental investigations into the failure mechanisms of bio- and bio-inspired materials.     

Modeling the effects of material non-linearity using moving window micromechanics

In the analysis of materials with random heterogeneous microstructure the assumption is often made that material behavior can be represented by homogenized or effective properties. While this assumption yields accurate results for the bulk behavior of composite materials, it ignores the effects of the random microstructure. The spatial variations in these microstructures can focus, initiate and propagate localized non-linear behavior, subsequent damage and failure. In previous work a computational method, moving window micromechanics (MW), was used to capture microstructural detail and characterize the variability of the local and global elastic response. Digital images of material microstructure described the microstructure and a local micromechanical analysis was used to generate spatially varying material property fields. The strengths of this approach are that the material property fields can be consistently developed from digital images of real microstructures, they are easy to import into finite element models (FE) using regular grids, and their statistical characterizations can provide the basis for simulations further characterizing stochastic response. In this work, the moving window micromechanics technique was used to generate material property fields characterizing the non-linear behavior of random materials under plastic yielding; specifically yield stress and hardening slope, post yield. The complete set of material property fields were input into FE models of uniaxial loading. Global stress strain curves from the FE–MW model were compared to a more traditional micromechanics model, the generalized method of cells. Local plastic strain and local stress fields were produced which correlate well to the microstructure. The FE–MW method qualitatively captures the inelastic behavior, based on a non-linear flow rule, of the sample continuous fiber composites in transverse uniaxial loading.     

An examination of the competition between bulk behavior and interfacial behavior of ceramics subjected to dynamic pressure-shear loading

A grain level micromechanical analysis of ceramic microstructures subjected to dynamic compression-shear loading conditions is presented. The investigation consists of a combined experimental/numerical approach in which bulk and surface properties are examined by means of pressure-shear impact experiments for a ceramic plate in contact with steel plates. The model for the ceramic microstructure accounts for heterogeneities and randomness in grain orientation and composition. A cohesive zone model is included to capture inter-granular microcrack initiation and evolution as a natural outcome of the calculated material response. Surface roughness is also included in the analysis to capture the time-dependent frictional behavior of the various interfaces. The model for the steel anvil plate accounts for visco-plasticity, thermal softening and strain hardening. Representative volume elements of ceramic microstructure and anvil plates are considered to account for features observed in real experiments. Pressure-shear impact velocity histories are used not only to identify inelasticity, but also to determine dominant failure modes. Bridging between micro- and macroscales is achieved by using the developed model. Simulated velocity histories have been found to be in a good agreement with the experimental observations when bulk and surface features are included in the analysis. However, it is demonstrated that information gathered from these experiments is not sufficient to determine the mechanical behavior of the brittle material. Instead, the velocity histories provide important information on the time-dependent frictional behavior of the specimen-anvil interfaces.     

On the coupling of anisotropic damage and plasticity models for ductile materials

In this contribution various aspects of an anisotropic damage model coupled to plasticity are considered. The model is formulated within the thermodynamic framework and implements a strong coupling between plasticity and damage. The constitutive equations for the damaged material are written according to the principle of strain energy equivalence between the virgin material and the damaged material. The damaged material is modeled using the constitutive laws of the effective undamaged material in which the nominal stresses are replaced by the effective stresses. The model considers different interaction mechanisms between damage and plasticity defects in such a way that two-isotropic and two-kinematic hardening evolution equations are derived, one of each for the plasticity and the other for the damage. An additive decomposition of the total strain into elastic and inelastic parts is adopted in this work. The elastic part is further decomposed into two portions, one is due to the elastic distortion of the material grains and the other is due to the crack closure and void contraction. The inelastic part is also decomposed into two portions, one is due to nucleation and propagation of dislocations and the other is due to the lack of crack closure and void contraction. Uniaxial tension tests with unloadings have been used to investigate the damage growth in high strength steel. A good agreement between the experimental results and the model is obtained.     

Localization of deformation and stress–strain relation for mesoscopic heterogeneous brittle rock materials under unloading

Stress redistribution induced by excavation of underground engineering and slope engineering results in the unloading zone in parts of surrounding rock masses. The mechanical behaviors of crack-weakened rock masses under unloading are different from those of crack-weakened rock masses under loading. A micromechanics-based model has been proposed for brittle rock material undergoing irreversible changes of their microscopic structures due to microcrack growth when axial stress is held constant while lateral confinement is reduced. The basic idea of the present model is to classify the constitution relation of rock material into four stages including some of the stages of linear elasticity, pre-peak nonlinear hardening, rapid stress drop, and strain softening, and to investigate their corresponding micromechanical damage mechanisms individually. Special attention is paid to the transition from structure rearrangements on microscale to the macroscopic inelastic strain, to the transition from distribution damage to localization of damage and the transition from homogeneous deformation to localization of deformation. The closed-form explicit expression for the complete stress–strain relation of rock materials containing cracks under unloading is obtained. The results show that the complete stress–strain relation and the strength of rock materials under unloading depend on the crack spacing, the fracture toughness of rock materials, orientation of the cracks, the crack half-length and the crack density parameter.     

Dynamic toughness in elastic nonlinear viscous solids

This work addresses the interrelationship among dissipative mechanisms—material separation in the fracture process zone (FPZ), nonelastic deformation in the surrounding background material and kinetic energy—and how they affect the macroscopic dynamic fracture toughness as well as the limiting crack speed in strain rate sensitive materials. To this end, a micromechanics-based model for void growth in a nonlinear viscous solid is incorporated into a microporous strip of cell elements that forms the FPZ. The latter is surrounded by background material described by conventional constitutive relations. In the first part of the paper, the background material is assumed to be purely elastic. Here, the computed dynamic fracture toughness is a convex function of crack velocity. In the second part, the background material as well as the FPZ are described by similar rate-sensitivity parameters. Voids grow in the strain rate strengthened FPZ as the crack velocity increases. Consequently, the work of separation increases. By contrast, the inelastic dissipation in the background material appears to be a concave function of crack velocity. At the lower crack velocity regime, where dissipation in the background material is dominant, toughness decreases as crack velocity increases. At high crack velocities, inelastic deformation enhanced by the inertial force can cause a sharp increase in toughness. Here, the computed toughness increases rapidly with crack velocity. There exist regimes where the toughness is a non-monotonic function of the crack velocity. Two length scales—the width of the FPZ and the ratio of the shear wave speed to the reference strain rate—can be shown to strongly affect the dynamic fracture toughness. Our computational simulations can predict experimental data for fracture toughness vs. crack velocity reported in several studies for amorphous polymeric materials.     

GPU-based simulations of fracture in idealized brick and mortar composites

Stiff ceramic platelets (or bricks) that are aligned and bonded to a second ductile phase with low volume fraction (mortar) are a promising pathway to produce stiff, high-toughness composites. For certain ranges of constituent properties, including those of some synthetic analogs to nacre, one can demonstrate that the deformation is dominated by relative brick motions. This paper describes simulations of fracture that explicitly track the motions of individual rigid bricks in an idealized microstructure; cohesive tractions acting between the bricks introduce elastic, plastic and rupture behaviors. Results are presented for the stresses and damage near macroscopic cracks with different brick orientations relative to the loading orientation. The anisotropic macroscopic initiation toughness is computed for small-scale yielding conditions and is shown to be independent of specimen geometry and loading configuration. The results are shown to be in agreement with previously published experiments on synthetic nacre.     

碳纤维/环氧树脂仿贝壳珍珠层结构强韧机制与性能优化的实验研究

材料的轻量化设计在生产实践中具有重大意义,将天然贝壳珍珠层结构应用到现有的高性能人工合成材料上,能够获得性能更加优异的轻质高强结构材料。本文采用碳纤维/环氧树脂复合材料,设计出了多种具有规则"砖-泥"交错叠层结构的仿贝壳珍珠层复合材料,通过力学性能测试实验、微观结构表征及力学原理分析等对不同片层单元长度及不同单元搭接形式的材料在拉伸载荷下的力学行为进行了研究,探索了其微观结构对材料强度和韧性的影响机制。结果表明,"砖-泥"交错叠层结构中"砖块"单元长度是影响材料强度和韧性的关键因素,而在此基础上通过对片层搭接形式的优化设计,可进一步改善其内部的应力分布与载荷传递机制,从而实现其强度和韧性的进一步提升与有效调控。     

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.     

A void nucleation and growth based damage framework to model failure initiation ahead of a sharp notch in irradiated bcc materials

A continuum damage framework is developed and coupled with an existing crystal plasticity framework, to model failure initiation in irradiated bcc polycrystalline materials at intermediate temperatures. Constitutive equations for vacancy generation due to inelastic deformation, void nucleation due to vacancy condensation, and diffusion-assisted void growth are developed. The framework is used to simulate failure initiation at dislocation channel interfaces and grain boundaries ahead of a sharp notch. Evolution of the microstructure is considered in terms of the evolution of inelastic deformation, vacancy concentration, and void number density and radius. Evolution of the damage, i.e., volume fraction of the voids, is studied as a function of applied deformation. Effects of strain rate and temperature on failure initiation are also studied. The framework is used to compute the fracture toughness of irradiated specimens for various loading histories and notch geometries. Crack growth resistance of the irradiated specimens are computed and compared to that of virgin specimens. Results are compared to available experimental data.     

Wave propagation and dispersion in elasto-plastic microstructured materials

A Mindlin continuum model that incorporates both a dependence upon the microstructure and inelastic (nonlinear) behavior is used to study dispersive effects in elasto-plastic microstructured materials. A one-dimensional equation of motion of such material systems is derived based on a combination of the Mindlin microcontinuum model and a hardening model both at the macroscopic and microscopic level. The dispersion relation of propagating waves is established and compared to the classical linear elastic and gradient-dependent solutions. It is shown that the observed wave dispersion is the result of introducing microstructural effects and material inelasticity. The introduction of an internal characteristic length scale regularizes the ill-posedness of the set of partial differential equations governing the wave propagation. The phase speed does not necessarily become imaginary at the onset of plastic softening, as it is the case in classical continuum models and the dispersive character of such models constrains strain softening regions to localize.     

Nonlocal plasticity effects on the tensile properties of a metal matrix composite

For a metal reinforced by aligned short fibres the effect of a material length scale characterising the inelastic deformations of the metal is studied. The elastic-plastic constitutive relations used here to represent the nonlocal effects are formulated so that the instantaneous hardening moduli depend on the gradient of the effective plastic strain. Numerical cell-model analyses are used to obtain a parametric understanding of the influence of different combinations of the main material parameters. The analyses show a strong dependence on the fibre diameter for given values of all other material parameters, and it is shown that this dependence differs somewhat for different values of the fibre aspect ratio.     

Equilibrium Paths of a Hyperelastic Body Under Progressive Damage

This paper deals with equilibrium problems in nonlinear dissipative inelasticity, where inelastic effects are produced by the damage of the material. The inelastic constitutive law is obtained by modifying the classical constitutive law for a hyperelastic isotropic material through a damage function. To define this damage function, which allows to measure the effective stress and the dissipated energy, it is first used the Clausius-Duhem inequality, to have the (rate-independent) flow law of the damaged state and then it has been imposed a damage criterion based on an energy approach. After making the constitutive modeling, the boundary-value problem of the Rivlin’s cube, now composed of damaged material, is formulated. The purpose is to analyze a three-dimensional body that, during the deformation process, experiences a progressively increasing damage. Equilibrium branches of symmetric and asymmetric solutions, together to bifurcation points, are computed. Emphasis is placed in investigating how the damage can alter these equilibrium paths with respect to the virgin undamaged case. In particular, the stress reductions caused by damage can give rise to transitions from hardening type to the softening one of the constitutive behavior. These changes can affect the quality of the equilibrium solutions. Accordingly, the analysis is completed by assessing the stability of the solutions. For this aim, the energetic method is extended to damaged materials.     

高周疲劳的损伤-硬化模型

两级循环加载条件下,材料的剩余寿命强烈地依赖于加载历史。究其原因,不同加载历史将引起材料的微结构发生不同的变化,使得材料的硬化效果和变形行为表现出明显的差异,从而影响了损伤的演化过程。本文引入硬化状态变量来表征加载历史对疲劳损伤演化过程的影响。通过对两级循环加载下损伤演化规律和剩余寿命的研究,认为在两级（或多级）加载条件下,材料的损伤演化和剩余寿命强烈地依赖于加载历史造成的损伤和硬 化状态。     

Experimental investigation of nanomechanics of the mineral-protein interface in nacre

Nacre, the inner layer of molluscan seashells is a model biomimetic nanocomposite system that has been an inspiration for design of novel composites. The organic phase present in nacre is believed to play an important role in enhancing the toughness of nacre. The understanding of the adhesion forces of the organic matrix on to the mineral phase is essential for the fundamental assessment of the toughening properties in nacre. Our prior work using molecular dynamics simulations revealed that a very large force is needed to pull the protein molecules when in close proximity with the aragonite phase. In the current work, we have experimentally described the mechanical response of the organic phase in proximity of aragonite using force mode atomic force microscopy. Our results indicate that a very large force is required (>5–6 nN) to pull the proteins away from the aragonite. Our experiments show that the molecular interactions at the organic–inorganic interface in nacre are substantial and may play a significant role on the overall toughness of nacre. Thus, molecular interactions albeit weak and non-bonded play a significant role on the mechanics of hybrid nanocomposite systems.