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1.
It is natural that, with the recent fast development of fracture mechanics, the meanings of some standard expressions such as brittleness, fracture energy and size effect need to be revised in order to avoid serious misunderstandings and ambiguities. The paper aims at answering such ticklish questions as the following. Can Griffith's criterion for quasi-static crack propagation, which is valid in linear-elastic fracture mechanics, be applied to the non-linear stress softening theory called the fictitious crack model? What is in fact the mutual relationship of the two theories? How can brittleness be distinctly defined? What is a brittle material and what does quasi-brittle mean? Is the fracture toughness a measure of toughness or rather a measure of strength? Is the fracture energy a material parameter and can a material parameter be ‘measured’ directly or must a theory always be used for interpreting results from experiments? What is the fundamental idea of damage mechanics? What does size effect mean? Is a size-effect law the same as a model law derived from dimensional analysis? What is in fact the relation of a model law to the theory (known or unknown) to which the model law is connected? Giving replies to such questions it is essential to distinguish between theory and reality and not to mix two or more theories, unless the mutual relations of the theories involved are taken into account.  相似文献   

2.
Abstract

The room temperature mechanical properties of polycrystalline diamonds, i.e. tensile strength, transverse rupture strength, compressive strength, impact strength, fracture toughness, and elastic constants, have been determined. The applied test techniques are described and the results compared with those obtained by other authors. The fracture mode under the present experimental conditions was primarily transgranular. A grain size dependence, where strength increases with decreasing grain size, has been found. Fracture toughness was found to go through a maximum for grain sizes between 10 to 30 μm. The modulus of elasticity increases with increasing grain size. An influence of cobalt content on strength and modulus of elasticity has been found, while no significant influence on toughness could be determined. Increasing the cobalt content increases strength, but has the inverse effect on the modulus of elasticity. The results of strength, toughness, and elastic constants measurements are discussed in terms of available models and theories of polycrystalline ceramic materials. It can be seen from the results that polycrystalline diamonds behave in a manner similar to that of most engineering ceramics, but have the distinct advantage of a higher fracture toughness.

MST/596  相似文献   

3.
Fracture mechanics concepts are applied to gain some understanding of the hierarchical nanocomposite structures of hard biological tissues such as bone, tooth and shells. At the most elementary level of structural hierarchy, bone and bone-like materials exhibit a generic structure on the nanometer length scale consisting of hard mineral platelets arranged in a parallel staggered pattern in a soft protein matrix. The discussions in this paper are organized around the following questions: (1) The length scale question: why is nanoscale important to biological materials? (2) The stiffness question: how does nature create a stiff composite containing a high volume fraction of a soft material? (3) The toughness question: how does nature build a tough composite containing a high volume fraction of a brittle material? (4) The strength question: how does nature balance the widely different strengths of protein and mineral? (5) The optimization question: Can the generic nanostructure of bone and bone-like materials be understood from a structural optimization point of view? If so, what is being optimized? What is the objective function? (6) The buckling question: how does nature prevent the slender mineral platelets in bone from buckling under compression? (7) The hierarchy question: why does nature always design hierarchical structures? What is the role of structural hierarchy? A complete analysis of these questions taking into account the full biological complexities is far beyond the scope of this paper. The intention here is only to illustrate some of the basic mechanical design principles of bone-like materials using simple analytical and numerical models. With this objective in mind, the length scale question is addressed based on the principle of flaw tolerance which, in analogy with related concepts in fracture mechanics, indicates that the nanometer size makes the normally brittle mineral crystals insensitive to cracks-like flaws. Below a critical size on the nanometer length scale, the mineral crystals fail no longer by propagation of pre-existing cracks, but by uniform rupture near their limiting strength. The robust design of bone-like materials against brittle fracture provides an interesting analogy between Darwinian competition for survivability and engineering design for notch insensitivity. The follow-up analysis with respect to the questions on stiffness, strength, toughness, stability and optimization of the biological nanostructure provides further insights into the basic design principles of bone and bone-like materials. The staggered nanostructure is shown to be an optimized structure with the hard mineral crystals providing structural rigidity and the soft protein matrix dissipating fracture energy. Finally, the question on structural hierarchy is discussed via a model hierarchical material consisting of multiple levels of self-similar composite structures mimicking the nanostructure of bone. We show that the resulting “fractal bone”, a model hierarchical material with different properties at different length scales, can be designed to tolerate crack-like flaws of multiple length scales.  相似文献   

4.
Criteria for predicting initiation of cracks in brittle materials like ceramics are based on two parameters: the material fracture toughness and the tensile strength. Standardized experiments exist to estimate the former. However, the tensile strength is often taken from experiments (mainly uniaxial bending) on specimens with various geometries and surface finish, usually tested under ambient conditions at a given loading rate. The reported strength is commonly the Weibull characteristic strength, which scatters due to the critical defect size distribution on the tested specimen. In this work, we propose a definition of the “inherent” or “intrinsic” tensile strength to be used in numerical models, making a distinction between extrinsic defects due to manufacturing and intrinsic ones relying on the microstructure. Our approach is based on the Finite Fracture Mechanics theory and the Coupled Criterion applied to small surface flaws and its influence on the measured (extrinsic) strength. Numerical results are compared with experiments on alumina reported in the literature. In addition, a model for the Petch law (strength vs. grain size) in polycrystalline materials is proposed using the Coupled Criterion, which predicts an initial crack length of increasing numbers of grains as the grain size decreases.  相似文献   

5.
We present a phase-field model to simulate intergranular and transgranular crack propagation in ferroelectric polycrystals. The proposed model couples three phase-fields describing (1) the polycrystalline structure, (2) the location of the cracks, and (3) the ferroelectric domain microstructure. Different polycrystalline microstructures are obtained from computer simulations of grain growth. Then, a phase-field model for fracture in ferroelectric single-crystals is extended to polycrystals by incorporating the differential fracture toughness of the bulk and the grain boundaries, and the different crystal orientations of the grains. Our simulation results show intergranular crack propagation in fine-grain microstructures, while transgranular crack propagation is observed in coarse grains. Crack deflection is shown as the main toughening mechanism in the fine-grain structure. Due to the ferroelectric domain switching mechanism, noticeable fracture toughness enhancement is also obtained for transgranular crack propagation. These observations agree with experiment.  相似文献   

6.
In situ observation of nanograin rotation and deformation in nacre   总被引:2,自引:0,他引:2  
Li X  Xu ZH  Wang R 《Nano letters》2006,6(10):2301-2304
Nacre is a natural nanocomposite material with superior mechanical strength and toughness. What roles do the nanoscale structures play in the inelasticity and toughening of nacre? Can we learn from this to produce nacre-like nanocomposites? Here we report in situ dynamic atomic force microscope observations of nacre with aragonite nanograins (nanoparticles) of an average grain size of 32 nm, which show that nanograin rotation and deformation are the two prominent mechanisms contributing to energy dissipation in nacre. The biopolymer spacing between the nanograins facilitates the grain rotation process. The aragonite nanograins in nacre are not brittle but deformable.  相似文献   

7.
A review of the fracture energy and toughness data for dense ceramics at 22 °C shows maxima commonly occurring as a function of grain size. Such maxima are most pronounced for non-cubic materials, where they are often associated with microcracking and R-curve effects, especially in oxides, but often also occur at too fine a grain size for association with microcracking. The maxima are usually much more limited, but frequently definitive, for cubic materials. In a few cases only a decrease with increasing grain size at larger grain size, or no dependence on grain size is found, but the extent to which these reflect lack of sufficient data is uncertain. In porous ceramics fracture toughness and especially fracture energy commonly show less porosity dependence than strength and Young's modulus. In some cases little, or no, decrease, or possibly a temporary increase in fracture energy or toughness are seen with increasing porosity at low or intermediate levels of porosity in contrast to continuous decreases for strength and Young's modulus. It is suggested that such (widely neglected) variations reflect bridging in porous bodies. The above maxima as a function of grain size and reduced decreases with increased porosity are less pronounced for fracture toughness as opposed to fracture energy, since the former reflects effects of the latter and Young's modulus, which usually has no dependence on grain size, but substantial dependence on porosity. In general, tests with cracks closer to the natural flaw size give results more consistent with strength behaviour. Implications of these findings are discussed.  相似文献   

8.
The effect of aging treatment on fracture toughness in Mg–6Zn–1Mn (wt-%) was investigated by optical microscopy, scanning electron microscopy, transmission electron microscopy, scanning transmission electron microscopy, uniaxial tensile and fracture toughness tests, respectively. The results showed that the fracture toughness of Mg–6Zn–1Mn alloy can be enhanced by aging treatment. The fracture toughness and strength showed a reverse trend in single aged and double aged alloy. Synergetic effect of fine grains and precipitates improved the fracture toughness more sharply than aging treatment. The precipitate free zones and grain boundary precipitates made the largest contribution to the reduction of toughness. Under as extruded and aged conditions, the main origins of cracks were elastic incompatibility and plastic deformation.  相似文献   

9.
Wei Y  Wu J  Yin H  Shi X  Yang R  Dresselhaus M 《Nature materials》2012,11(9):759-763
The two-dimensional crystalline structures in graphene challenge the applicability of existing theories that have been used for characterizing its three-dimensional counterparts. It is crucial to establish reliable structure-property relationships in the important two-dimensional crystals to fully use their remarkable properties. With the success in synthesizing large-area polycrystalline graphene, understanding how grain boundaries (GBs) in graphene alter its physical properties is of both scientific and technological importance. A recent work showed that more GB defects could counter intuitively give rise to higher strength in tilt GBs (ref. 10). We show here that GB strength can either increase or decrease with the tilt, and the behaviour can be explained well by continuum mechanics. It is not just the density of defects that affects the mechanical properties, but the detailed arrangements of defects are also important. The strengths of tilt GBs increase as the square of the tilt angles if pentagon-heptagon defects are evenly spaced, and the trend breaks down in other cases. We find that mechanical failure always starts from the bond shared by hexagon-heptagon rings. Our present work provides fundamental guidance towards understanding how defects interact in two-dimensional crystals, which is important for using high-strength and stretchable graphene for biological and electronic applications.  相似文献   

10.
Strength and Toughness, Criteria of Safety for Construction of Apparata. In the chemical research technique often high requirements are being set on the materials of apparata due to pressure, temperature and corrosive medias. While the strength necessary to avoid macroscopical deformation can be guaranteed today without difficulties, this does not go similarly for the toughness. The toughness of steel being a condition in the strength calculation is the real safety criterion for welded structures. This is especially applicable in the case of local peak stress due to construction or of micro cracks caused during manufacturing or service. If – as mostly in practice – local inhomogeneities and unknown residual stresses are existing, the linear fracture mechanics can only be applied with empirical factors. The best safety even with unforeseen overloadings can be seen in such a toughness, which avoids brittle fracture at all. The possible test methods will in any case have to reliably consider also the heat affected zones of weldings, since brittle cracks also in tough matrix can only be absorbed under limited stresses.  相似文献   

11.
The microstructural dependence of fracture energy and toughness of ceramics and ceramic particulate, platelet, and whisker composites is compared with the corresponding dependence of their tensile (flexure) strengths at 22 °C. These comparisons show that fracture energy and toughness often do not have the same porosity, or grainor particle-size dependence as strength. This is attributed to the scale of the cracks for measuring fracture energy or toughness often being too large in comparison to the cracks controlling strength. The large cracks reflect crack-microstructure interaction phenomena such as crack-wake bridging and R-curve effects that are not, or are much less, involved in the control of propagation of most strength-controlling cracks. Thus fracture mechanics must account for the scale of the cracks used in measuring fracture mechanics parameters relative to the scale of the cracks controlling the strength behaviour that is to be explained or predicted.  相似文献   

12.
In this investigation, fracture process zone model is used to establish a new relationship to predict the intrinsic fracture toughness from the apparent fracture toughness of a notched-crack specimen. The parameters needed in the proposed model are very rare, such as, the fracture process zone size of materials, the notch radius. Specimens made up of two kinds of polycrystalline alumina and one soda-lime glass with notch radii as small as a few micrometer are used to verify the predictions of this model. Besides, the results also show that fracture toughness of ceramics decreases with the decreasing of notch root radius. Under condition of the radius of crack tip is not greater than the averaged grain size, the apparent toughness can be approximately regarded as the fracture toughness of the materials.  相似文献   

13.
The theory of Clarke for the formation of grain boundary cracks in anisotropic polycrystalline materials, is re-examined in the light of recent experimental data. The theory predicts correctly the conditions for the formation of grain boundary cracks of length similar to a grain dimension. However, the theory cannot be used to explain the experimentally observed strength/grain size and strength/irradiation dose relationships, for example for BeO. The theory supposes that the process controlling catastrophic fracture is the growth of a crack from a grain boundary pore with an energy absorption rate corresponding to the grain boundary surface energy of 103 erg/cm2. In practice, the process controlling catastrophic fracture is the subsequent growth of a crack from a grain dimension, with a higher energy absorption rate corresponding to an effective surface energy of 104 erg/cm2.  相似文献   

14.
The load-carrying capacity of notched timber beams can be predicted using linear elastic fracture mechanics (LEFM). Material properties such as fracture toughness and energy are needed for the analysis. The micro and macroscopic complexity of wood and its anisotropic nature give different fracture properties in the longitudinal, radial and tangential grain directions. This complexity and the infrequent use of LEFM mean there is little data available. While wood is highly anisotropic, fracture analysis can use a subset of the possible material properties because wood normally cracks parallel to its grain due to its low tensile strength perpendicular to grain. This allows a significant reduction in the number of tests required to measure fracture properties, with considerable saving of resources. This paper presents the results of an experimental study investigating the fracture energy and fracture toughness of Radiata Pine laminated veneer lumber in mode I (opening). A more efficient test apparatus is proposed and shown to produce identical results to the test apparatus used by others. Results are presented for the fracture toughness properties in the grain direction, and include fifth percentiles and coefficients of variation. The influence that the specimen size has on the fracture toughness is also presented. Numerical analyses using the ABAQUS software package show good agreement with the experimental test results. The experimental results are within the range of experimental values reported in the literature for solid wood.  相似文献   

15.
The trend toward broader application of high-strength structural alloys has increased the potential for failure by low-cycle fatigue crack propagation. There is a significant probability that complex structures will contain undetected cracks remaining from fabrication or that cracks will readily initiate from less severe fabrication defects. Under the repeated application of high stresses, imposed on high-strength alloys, such cracks will rapidly grow in low-cycle fatigue. To guard against disastrous failures caused by cracks propagating to terminal fracture, high-strength structural alloys which also possess high levels of fracture resistance have been developed in recent years. This paper describes the principal fatigue crack propagation characteristics which are derived from high fracture toughness and discusses the potential benefits available through the use of high-toughness alloys in cyclically-loaded structures.  相似文献   

16.
In this paper, we develop an efficient multiscale molecular dynamics (MD)–finite element (FE) modeling scheme capable of determining the elastic and fracture properties of polycrystalline graphene. The local elastic properties of a grain boundary (GB) connecting two adjacent graphene grains, with different lattice orientations, were first determined using MD simulations. In a two-dimensional medium, randomly distributed grains connected with GBs were then created using the Voronoi tessellation method. The constructed Voronoi diagrams were used to create FE models of the polycrystalline graphene, where the GBs were represented by interphase regions with their local properties determined using MD. The grains were modeled as pristine graphene and the accuracy of the polycrystalline FE model was validated with MD simulations of a geometrically identical polycrystalline graphene. The results reveal good agreement between MD and FE simulations. They further show that the elastic and fracture properties of polycrystalline graphene are greatly influenced by the grain size and the misorientation angle. They also indicate that the predicted elastic properties are in agreement with earlier reported experimental and MD results. We believe that this newly proposed multiscale scheme could be easily integrated into current design software to model graphene based nano- and micro-devices.  相似文献   

17.
Mechanical properties of graphene, e.g., strength, modulus, and fracture toughness are extremely sensitive to flaws. Here the fracture properties of stacked bilayer graphene sheets (SBLG) are reported, obtained via stacking two individually grown graphene sheets. The SBLG is presented here as a building block for flaw-resilient nanomaterials. The fracture properties of freestanding SBLG sheets, suspended on transmission electron microscope (TEM) grids, are characterized by stretching the TEM grid inside an scanning electron microscope (SEM) chamber and monitoring the local displacements in real-time. The fracture toughness is measured and expressed as a function of the critical displacement required to propagate existing cracks in the experiment via computational models. This approach decouples force and displacements measurements, and utilizes the known elastic modulus along with the known displacement boundary conditions at the onset of crack growth to estimate the far field force and stress. This strategy represents a breakthrough in nanoscale fracture mechanics for statistical analysis and high throughput experimens on multiple samples at a time. Results demonstrate that the SBLG is markedly tougher than as-grown single or multilayer graphene, with a mode I fracture toughness of ≈28.06 ± 7.5 MPa m $\sqrt m $ . The mechanisms leading to a higher toughness of SBLG are also analyzed and discussed.  相似文献   

18.
The crack path of polycrystalline ceramics has been theoretically analysed with a stochastic model based on the difference between the released energies in intergranular and transgranular crack propagation. Assuming that the path with the lowest released energy should be realized as the actual crack path, the expected values of the fraction of transgranular fracture on fracture surface and the fracture toughness of polycrystalline ceramics were formulated as functions of grain size and the critical energy release rates of grain and grain boundary. By comparison between the theory and the experimental results it was shown that the stochastic model proposed here expressed the change of the crack path and the fracture toughness of polycrystalline Al2O3, relative to grain size. This revised version was published online in November 2006 with corrections to the Cover Date.  相似文献   

19.
The major objective of this work has been to apply a new compatibility-based fracture theory to the investigation of dynamic failure of polycrystalline metals and alloys. To model the nucleation and propagation of failure surfaces at the microstructural scale, under large deformations and dynamic loading conditions, a general fracture criterion based on the integral law of compatibility is used. This new fracture criterion, was coupled with rate-dependent dislocation-density based crystalline plasticity formulations to elucidate the microstructural mechanisms related to the evolution of intergranular and transgranular failure and to understand how grain sizes and strain-rate sensitivity affect aggregate strength, ductility, and dynamic damage tolerance. It is shown that cracks commonly nucleate at triple junctions and at grain boundaries as intergranular cracks, and that slip bands through grains result in transgranular cracks.  相似文献   

20.
Defects such as pores and non-metallic inclusions have a significant influence on the long-life fatigue strength of high strength steels. The largest of these defects in a critical material volume is in the range of tens of micrometres which is on the same size scale as the grain size. At this scale materials are non-homogeneous since each grain in a polycrystalline material will have a different orientation. Finite element-based mesoscale modelling has been used to model the stress and strain in individual grains in the vicinity of a spherical defect. Microcrack nucleation and propagation models based on shear stress and plastic shear strain have been applied. Especially for low stress amplitudes near the endurance limit, critical grain orientation and defects are both essential for cracks to initiate and propagate.  相似文献   

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