Similarity Relations for the Impact Penetration of an Elastic Rod into a Brittle Target

Similarity factors for the kinetic parameters of the rod (impact velocity or energy) in case of geometric and energy similarities of target fracture patterns are determined from the analysis of the penetration equation and experimental results. The geometric and energy similarities of the target fracture upon the rod penetration over the investigated range of impact velocities (up to 10 m/s) and penetration depths (h >> d) are shown to be attained on linear variations of longitudinal and transverse rod dimensions, with impact velocities remaining unchanged.     

Loading Rates and the Dynamic Initiation Toughness in Brittle Solids

The experimentally determined marked rise of the stress intensity factor required to initiate crack propagation in brittle solids under variably high loading rates, is analyzed. This problem of fracture initiation at the tip of a crack is considered in terms of activating a flaw at some distance away from the tip. By using a semi-infinite crack in an unbounded two-dimensional solid subjected to spatially uniform but temporally varying crack-face pressure, we consider the evolution of stress at the failure initiation site. Fracture initiation is assumed synonymous with attaining a critical stress at the fracture site. The results conform to typical experimental data of dynamic crack initiation in brittle solids.     

压电元件驱动的功能梯度弹性薄板的屈曲

考虑功能梯度薄板,其上下表面嵌有压电执行元件.根据逆压电效应将电压转换成作用于板上的等效电载荷.假设梯度材料的弹性参数为板厚度方向坐标的幂函数,基于经典板理论,导出了功能梯度弹性薄板小挠度屈曲平衡微分方程.利用双三角级数展开法,得到了四边简支具有压电元件的功能梯度矩形板的临界屈曲载荷,在此基础上通过数值例子讨论了弹性板的几何尺寸、材料梯度指数的变化对临界电压(载荷)的影响.研究结果表明,材料的梯度指数对临界电压有重要影响,并且通过调整作用于执行元件上的电压的大小和方向,可实现对结构稳定性的有效控制.     

Creating Three-Dimensional Models to Investigate Brittle Fracture in Polycrystalline Metals

Three-dimensional models with irregular grain geometries and appropriate physical properties are needed to investigate fracture in polycrystalline metals and alloys. Creating such models is challenging but achievable using a two-stage process, suitable for any polycrystal. The processes described in this paper are illustrated by examples of brittle fracture in ferritic steel, zinc and nickel. The predicted crack path in a model is compared with the grain boundary fracture seen in three point bend specimens of nickel embrittled by sulphur.     

Control of thermally induced elastic displacement of an isotropic structural plate bonded to a piezoelectric ceramic plate

Summary The present paper deals with a thermoelastic problem in an isotropic structural plate to which a piezoelectric ceramic plate of crystal class 6mm is perfectly bonded. It is assumed that the combined plate is subjected to a thermal load and then is deformed. In this case, we try to control the deformation of the isotropic structural plate by applying an electric potential to the piezoelectric ceramic plate. By analyzing the piezothermoelastic problem in the combined plate, we obtain an appropriate applied electric potential which alters the isotropic structural plate to a prescribed deformation. Finally numerical calculations are carried out for an isotropic steel plate to which a cadmium selenide plate is perfectly bonded, and the results are illustrated graphically.     

Mixed Mode Brittle and Ductile Fracture of a High Strength Rotor Steel at Room Temperature

The mixed mode fracture of a high strength rotor steel has been investigated at room temperature using single edge notched specimens. In mode I, and for limited amounts of shear loading, the steel exhibited cleavage fracture. For conditions near mode~II ductile fracture occurred. A transition from brittle to ductile fracture occurred for mixed mode loading. Finite element analysis provided estimates of the extent of near crack tip yielding and elastic-plastic stress intensity factors. Test results agreed with the maximum tensile stress (MTS) criterion for small scale yielding for limited amounts of shear loading. The load for mode II fracture was lower than predicted from the MTS criterion, but higher than predicted from plastic collapse predictions. Observed fracture angles where in broad agreement with the predicted fracture mechanisms. The load for the transition from brittle to ductile fracture was found to agree approximately with the predicted load. This revised version was published online in July 2006 with corrections to the Cover Date.     

Prediction of the Brittle Fracture Toughness of Neutron-Irradiated Reactor Pressure-Vessel Steels. Part 1

The irradiation effect on the temperature dependence of the brittle fracture toughness of reactor pressure-vessel steels is simulated using the probabilistic model for the fracture-toughness prediction, which was proposed by the authors earlier. The paper analyzes the irradiation effect on the parameters controlling the plastic deformation and brittle fracture of reactor pressure-vessel steels. We consider the mechanisms of microcrack nucleation in nonirradiated, irradiated, and post-irradiation-annealed reactor pressure-vessel steels.     

Brittle fracture assessment of engineering components in the presence of notches: a review

Brittle fracture of notched components has been widely investigated in recent decades both experimentally and theoretically. This is because of designers' concern about catastrophic failure in notched engineering components made of brittle or quasi‐brittle materials. Up to now, extensive studies have been performed on brittle fracture analysis of engineering components weakened by notches of various features under mode I, mode II, mode III and mixed mode loading conditions. In the present paper, the attempt is made to review the research articles published in the open literature on brittle fracture assessment of notched components by means of notch fracture mechanics concepts. The main focus of this paper is on the stress‐based fracture criteria, which are the basis of authors' experience in recent years.     

人工神经网络在冷脆断裂诊断中的应用

采用人工神经网络方法研究了晶体结构，强度，应力集中，晶粒尺寸，加速速度和温度与冷脆断裂关系的方法。     

Prediction of the Brittle Fracture Toughness of Neutron-Irradiated Reactor Pressure Vessel Steels. Part 2

We apply the proposed model to study the effect of irradiation on the temperature dependence of brittle fracture toughness of 15Kh2MFA steel. We analyze also the influence of irradiation and the content of phosphorus and copper on the brittle fracture toughness. It is demonstrated that the probabilistic model, which is based on a new formulation of the brittle fracture criterion, allows an adequate prediction of the irradiation effect on the fracture toughness of reactor pressure vessel steels. Alternative models of prediction of fracture toughness are discussed.     

Investigation of the Fracture of Brittle Bodies Due to Their Contact Interaction with Rigid Dies

We propose a theoretical and experimental procedure for determining fracture conditions of brittle bodies subjected to the action of rigid dies of various shapes. Similarly to the fracture mechanics approach, we specify the stress intensity factors K₁ and K₂ in the vicinity of the die base, which determine the conditions of crack initiation, as well as values of the angle between cracks and the specimen base. It is established that upon the specimen compression by the die, the angle of the inclination of the fracture surface to the specimen base plane remains practically unchanged , which agrees fairly well with the theoretical data obtained. Body fragments have been revealed after pressing dies of different types into specimens: in a shape close to a circular cone for a round die, in a shape close to a quadrangular pyramid for a square die, and in a shape close to a triangular prism for a rectangular die.     

Brittle Fracture Analysis Using a Ring-Shape Specimen Containing Two Angled Cracks

A ring shaped specimen is used for studying mixed mode fracture in brittle materials. The ring specimen is subjected to a compressive diametral load and contains two angled central cracks. A series of fracture tests are conducted under various mode mixities using the ring specimen. It is shown that the obtained experimental results are in a very good agreement with theoretical predictions of the modified maximum tangential stress criterion.     

基于细分粒子的刚体破裂动画

为了模拟固体在外力作用下产生的破裂现象,提出一种采用细分粒子的刚体破裂的模拟算法.该算法首先将固体的四面体网格绑定到一系列离散的粒子上;再利用光滑粒子流体动力学（SPH）对线弹性力学方程进行离散求解;并采用粒子细分的算法来进行开裂面的生成和延展.最后实现了多个固体现象的模拟,如砖块碎落、砖墙受力倒塌等.文中算法可适用于刚体脆性破碎的动画应用.     

Propagation of a penny-shaped hydraulic fracture parallel to the free-surface of an elastic half-space

In this paper we analyze the problem of a penny-shaped hydraulic fracture propagating parallel to the free-surface of an elastic half-space. The fracture is driven by an incompressible Newtonian fluid injected at a constant rate at the center of the fracture. The flow of viscous fluid in the fracture is governed by the lubrication equation, while the crack opening and the fluid pressure are related by singular integral equations. We construct two asymptotic solutions based on the assumption that either the solid has no toughness or that the fluid has no viscosity. These asymptotic solutions must be understood as corresponding to limiting cases when the energy expended in the creation of new fracture surfaces is either small or large compared to the energy dissipated in viscous flow. It is shown that the asymptotic solutions, when properly scaled, depend only on the dimensionless parameter cal R cal, the ratio of the fracture radius over the distance from the fracture to the free-surface. The scaled solutions can thus be tabulated once and for all and the dependence of the solution on time can be retrieved for specific parameters, through simple scaling and by solving an implicit equation.     

Simulation of Coupled Processes of Deformation and Cracking in Elastic Brittle Materials

We propose an approximate model of combined deformation and microcracking of elastic brittle materials leading to the formation of a system of stochastically distributed shallow microcracks.     

Experimental Observations and Computational Modeling of Fracturing in an Anisotropic Brittle Crystal (Sapphire)

The commonly used fracture criteria-maximum K_I, zero K_II, maximum hoop-stress, and maximum energy-release rate-predict similar fracture paths in isotropic materials, but not in anisotropic materials. In the general anisotropic case, the fracture path depends on the material-symmetry properties, the nature of the applied loads, and the overall geometry of the specimen. In addition, anisotropy in the material's resistance to fracturing plays a key role in defining crack initiation and its propagation path. Experiments are performed on notched specimens made from sapphire, a microscopically homogeneous and brittle single-crystal solid. The force required for fracture initiation is measured. The experimental measurements/observations are compared with the numerical results of the FEM simulations. A stress-based fracture parameter, is shown to be a good measure of the fracture criterion, where σ and E, respectively, are the tensile stress and Young's modulus in the direction normal to the cleavage plane, with surface energy γ , and R is a characteristic length, e.g., the notch radius. This parameter takes into account the effects of the surface energy of the corresponding cleavage plane, as well as the strength of the atomic bonds in the direction normal to the cleavage plane. More than two-thirds of the notched specimens fractured at the point and along a cleavage plane where A is maximum. The measurements of the applied force made it possible to quantitatively obtain a critical value for parameter A. Finally, experiments show that for the notched sapphire specimens the weakest family of cleavage planes, , are the fracture planes, although a few specimens fractured along non-cleavage planes. This revised version was published online in July 2006 with corrections to the Cover Date.     

A thin cracked layer bonded to an elastic half-space under an antiplane concentrated load

The antiplane elasticity problem for a thin cracked layer bonded to an elastic half-space under an antiplane concentrated load is considered. The fundamental solution is obtained as a rapidly convergent series in terms of the complex potentials via iterations of Möbius transformation. The singular integral equation with a logarithmic singular kernel is derived to model a crack problem that can be solved numerically in a straightforward manner. The dimensionless mode-III stress intensity factors obtained for various crack inclinations and crack lengths are discussed in detail and provided in graphic form. A strip problem with an arbitrarily oriented crack is also considered.     

Prediction of the Warm Prestressing Effect on an Increase in the Brittle Strength of Crack-Containing Heat-Resistant Structural Steels. Part 1. Model and Procedure of Calculating the Warm Prestressing Effect

The physicomechanical model of warm prestressing and the procedure of calculating this effect for heat-resistant steels are proposed. The procedure is based on the analysis of stress-strain state variations in the elementary volume of the material near the crack tip during warm prestressing and further loading. This procedure takes account of such factors as crack tip blunting, residual stresses, and strain hardening of the material near the crack tip, which determine the effect of warm prestressing on the brittle strength of heat-resistant steels.