Kinetics of brittle fracture of elastic materials

A phenomenological model is proposed for the evolution of microcavities in materials under load based on a study of the kinetics of brittle fracture in a linearly elastic deformable medium containing a microcavity. The basic principle of the model is that, during deformation of a material containing a micropore, fluctuations of its shape occur. The surface tension at the micropore-medium interface stabilizes these fluctuations but if the load exceeds a critical value, these fluctuations may begin to evolve. In so doing, they distort the shape of the microcavity. These fluctuations are none other than cracks. This concept of crack growth and their nature has a close analogy with the evolution of dendrites formed in supercooled melts as a result of the loss of stable crystal shape. An analysis is made of the laws governing the evolution of a microcavity and local loss of shape stability under steady-state pressure for the case of a sphere containing a quasispherical cavity. Fiz. Tverd. Tela (St. Petersburg) 40, 1259–1263 (July 1998)     

From brittle to ductile fracture in disordered materials

We introduce a lattice model able to describe damage and yielding in heterogeneous materials ranging from brittle to ductile ones. Ductile fracture surfaces, obtained when the system breaks once the strain is completely localized, are shown to correspond to minimum energy surfaces. The similarity of the resulting fracture paths to the limits of brittle fracture or minimum energy surfaces is quantified. The model exhibits a smooth transition from brittleness to ductility. The dynamics of yielding exhibits avalanches with a power-law distribution.     

Mode II brittle fracture assessment using an energy based criterion

In this paper the minimum strain energy density criterion is modified to predict the values of mode II fracture toughness reported in the literature for several brittle and quasi-brittle materials. The experimental results are all related to mode II fracture tests performed on the semicircular bend specimen. The modified mode II fracture criterion takes into account the effect of T-stress (in addition to the singular terms of stresses/strains) when calculating the strain energy density factor at a very small critical distance from the crack tip. It is shown that the proposed criterion provides significantly better predictions for mode II fracture toughness compared with the classical minimum strain energy density criterion.     

The effect of crack interaction on the critical stress for fracture propagation in brittle materials

Summary An analytical solution is found for the stress needed for catastrophic crack propagation, by means of a model of a solid with interacting, uniformly distributed microcracks. From the experimental data for Westerly granite is is shown that the classical single-crack model may be considered a fair approximation for most purposes.

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Riassunto Si trova una soluzione analitica dello sforzo necessario per il verificarsi della propagazione catastrofica di fratture partendo da un modello di solido reale con microfratture uniformemente distribuite ed interagenti. Usando i dati sperimentali per il granito Westerly si mostra che il modello classico a frattura singola può essere considerato una buona approssimazione per molti scopi.

     

Surface energy for brittle fracture of alkali halides from lattice dynamics

A lattice dynamics approach to the surface energy γ for brittle fracture of several ionic crystals is presented, based on recent work on surface dynamics and a reformulation of a model previously worked out for metals. The model requires the knowledge of the crystal structure, the eigenfrequencies and eigenvectors of the normal modes of vibration, as well as an analytical definition of the critical interplanar displacement appropriate to the cleavage mode. Some temperature dependent values of γ are also computed for the (100) and (110) planes. Qualitatively the results indicate the correct cleavage systems for all cases and quantitively are reasonably consistent with the available experimental values.     

Damage and fracture evolution in brittle materials by shape optimization methods

This paper is devoted to a numerical implementation of the Francfort–Marigo model of damage evolution in brittle materials. This quasi-static model is based, at each time step, on the minimization of a total energy which is the sum of an elastic energy and a Griffith-type dissipated energy. Such a minimization is carried over all geometric mixtures of the two, healthy and damaged, elastic phases, respecting an irreversibility constraint. Numerically, we consider a situation where two well-separated phases coexist, and model their interface by a level set function that is transported according to the shape derivative of the minimized total energy. In the context of interface variations (Hadamard method) and using a steepest descent algorithm, we compute local minimizers of this quasi-static damage model. Initially, the damaged zone is nucleated by using the so-called topological derivative. We show that, when the damaged phase is very weak, our numerical method is able to predict crack propagation, including kinking and branching. Several numerical examples in 2d and 3d are discussed.     

Effects of energy dissipation on anisotropic materials

A model and its simulations are presented to describe the effects of energy dissipation on anisotropic systems. When the current electromigration is constant, energy dissipation depends on lattice constants, resistivity, and the angles along the longitudinal and transversal directions. It is shown that an orientation variation of the grain can significantly influence the energy dissipation for some anisotropic materials. Based on calculations for the grain model, the mechanism of grain growth and microstructure evolution under electromigration is explained. Theoretical implications about material selection and reliability are derived.     

The fracture energy of materials under pulse microsecond-scale loading

Based on the results of fracture in polymethyl methacrylate and a spheroplastic using a magnetic-pulse setup, the specific work of the formation of a new surface is estimated, which is similar to Griffith’s surface energy for quasi-static tests. The value obtained is greater than the corresponding value determined from the quasi-static tests by an order of magnitude and tends to increase as the loading time decreases.     

多孔脆性材料对高能量密度脉冲的吸收和抵抗能力

作用在脆性结构材料表面的高能量密度脉冲会以冲击波的形式传播进入材料内部, 导致压缩破坏和功能失效. 通过设计并引入微孔洞, 显著增强了脆性材料冲击下的塑性变形能力, 从而使脆性结构材料可以有效地吸收耗散冲击波能量, 并抑制冲击诱导裂纹的扩展贯通. 建立格点-弹簧模型并用于模拟研究致密和多孔脆性材料在高能量密度脉冲加载下的冲击塑性机理、能量吸收耗散过程和裂纹扩展过程. 冲击波压缩下孔洞塌缩, 导致体积收缩变形和滑移以及转动变形, 使得多孔脆性材料表现出显著的冲击塑性. 对致密样品、气孔率5%和10%的多孔样品吸能能力的计算表明, 多孔脆性材料吸收耗散高能量密度脉冲的能力远优于致密脆性材料. 在短脉冲加载下, 相较于遭受整体破坏的致密脆性材料, 多孔脆性材料以增加局部区域的损伤程度为代价, 阻止了严重的冲击破坏扩展贯通整个样品, 避免了材料的整体功能失效.     

Nanoscale periodic morphologies on the fracture surface of brittle metallic glasses

Out-of-plane, nanoscale periodic corrugations are observed in the dynamic fracture surface of brittle bulk metallic glasses with fracture toughness approaching that of silica glasses. A model based on the meniscus instability and plastic zone theory is used to explain such dynamic crack instability. The results indicate that the local softening mechanism in the fracture is an essential ingredient for controlling the formation of the unique corrugations, and might provide a new insight into the origin of fracture surface roughening in brittle materials.     

脆性金属玻璃断面上的奇妙图案

文章简要介绍了脆性块体金属玻璃(简称BMG)断裂面上几种主要的图案花样:河流花样、"韧窝"结构花样和自组装条纹结构花样,并总结了目前对上述各种形貌形成机理的可能的物理解释.对BMG断裂面上形貌的研究可以揭示材料的断裂机理,有助于更深刻地理解材料的力学性能,开发高性能金属玻璃材料,并为工程选材提供安全标准.     

脆性金属玻璃断面上的奇妙图案

文章简要介绍了脆性块体金属玻璃(简称BMG)断裂面上几种主要的图案花样：河流花样、“韧窝”结构花样和自组装条纹结构花样,并总结了目前对上述各种形貌形成机理的可能的物理解释.对BMG断裂面上形貌的研究可以揭示材料的断裂机理,有助于更深刻地理解材料的力学性能, 开发高性能金属玻璃材料,并为工程选材提供安全标准.     

脆性光学材料的超声磨削实验研究

分别采用超声磨削和普通磨削加工方法加工了几种脆性光学材料,研究了几种主要工艺参数对工件加工表面粗糙度的影响。结果表明,超声频率和振幅、金刚石磨料粒度、切深、工具的横向进给速度和旋转速度等工艺参数对表面粗糙度的影响较大。通过比较发现,超声磨削方法比普通磨削方法具有更好的加工表面粗糙度,更高的材料去除率,以及更低的工具磨损量。     

Molecular dynamics simulation of brittle fracture in silicon

Brittle fracture in silicon is simulated with molecular dynamics utilizing a modified embedded atom method potential. The simulations produce propagating crack speeds that are in agreement with previous experimental results over a large range of fracture energy. The dynamic fracture toughness is found to be equal to the energy consumed by creating surfaces and lattice defects in agreement with theoretical predictions. The dynamic fracture toughness is approximately 1/3 of the static strain energy release rate, which results in a limiting crack speed of 2/3 of the Rayleigh wave speed.     

Acoustical properties of double porosity granular materials

Granular materials have been conventionally used for acoustic treatment due to their sound absorptive and sound insulating properties. An emerging field is the study of the acoustical properties of multiscale porous materials. An example of these is a granular material in which the particles are porous. In this paper, analytical and hybrid analytical-numerical models describing the acoustical properties of these materials are introduced. Image processing techniques have been employed to estimate characteristic dimensions of the materials. The model predictions are compared with measurements on expanded perlite and activated carbon showing satisfactory agreement. It is concluded that a double porosity granular material exhibits greater low-frequency sound absorption at reduced weight compared to a solid-grain granular material with similar mesoscopic characteristics.     

Mathematical model of thermocracking of anisotropic brittle materials

A mathematical model of the process of laser-co ntrolled thermocracking for thin plates of aniso-tropic elastic materials has been constructed. By means of sequential replacement of the variable scale along one of the orthogonal coordinates, the problem of determination of the potential has been reduced to the Poisson equation. A comparison with the experiment by the example of thermocracking of a single-crystal quartz plate in a circumferential direction has been carried out.     

Acoustic emissioin monitoring of strength in brittle materials

It has been established that for porcelain, ferrite and cement-porcelain mortar the tensile strength, σ_F, during subsequent loading is closely related to the stress σ_O at which during the unloading period of the proof test the acoustic emission (AE) response changes from a continuous activity to a discrete one. The coefficients in the equation σ_F = A + Bσ_O in bending were found to be the same as those for radial compression. For a very homogeneous material with no continuous AE during unloading, σ_F correlates well with the relative change, κ, in pulse amplitude when two proof tests are carried out. The relationships σ_F(σ_O) and σ_F(κ) are independent of the mode and direction of abrasive machining.