Quasi-brittle fracture diagram of structured bodies in the presence of edge cracks

The Neuber-Novozhilov approach is used to obtain necessary and sufficient fracture criteria. Using a modified Leonov-Panasyuk-Dugdale model, simple relations for the critical fracture parameters are derived for opening mode edge cracks for the case where the diameter of the prefracture zone coincides with the diameter of the plasticity zone. These relations are suitable for studying fracture where the crack length is negligibly small. A fracture diagram using critical stresses under both criteria is proposed for a wide range of crack length. At a certain level of loading, three regions are identified, in the first of which the crack is stable, in the second, the crack extends but remains stable, and in the third, the crack is unstable. Experimental data on the fracture of specimens with edge cracks are obtained. It is established that the theoretical critical fracture curves are in good agreement with the obtained critical parameters for flat tensile specimens with two collinear edge cracks.     

Construction of quasi-brittle and quasi-ductile fracture diagrams based on necessary and sufficient criteria

Materials with a regular structure characterized by quasi-brittle and quasi-ductile fractures are considered in the case where the characteristic linear dimension of the structural element is known. Necessary and sufficient fracture criteria are constructed using the Neuber-Novozhilov approach. A modified Leonov-Panasyuk-Dugdale model for an opening mode crack is proposed where the width of the prefracture zone coincides with the width of the plasticity zone. For the critical parameters of quasi-brittle fracture (tensile stress, length of prefracture zones, stress intensity factors), relations are obtained that allow material fracture to be considered in the case where the crack length is negligible compared to the characteristic linear dimension of the structural element. A fracture diagram obtained using the critical stresses calculated from the necessary and sufficient criteria is considered in a wide range of crack lengths. The elastoplastic problem of extension of a plate with a central crack is solved using the finite-element method. The dimensions and shape of the plastic zone near the crack tip are determined for different levels of loads corresponding to quasi-brittle and quasi-ductile fracture. The obtained results are analyzed to estimate the width of the prefracture zone and the critical crack opening.     

Electro-mechanical pre-fracture zones for an electrically permeable interface crack in a piezoelectric bimaterial

A plane strain problem for two piezoelectric half-spaces adhered by a very thin isotropic interlayer with a crack under the action of remote mixed mode mechanical loading and electrical flux is considered. The crack is situated either at an interface or in the interlayer. It is assumed that the substrates are much stiffer than the intermediate layer. Therefore, pre-fracture zones (plastic or damage) arise at the crack continuations. Normal and shear stresses are assumed to be constant in this zones and to satisfy some material equation, which can be taken from theory or derived experimentally. Modeling the pre-fracture zones by the crack continuations with unknown cohesive stresses on their faces reduces the problem to elastic interface crack analysis leading to a Hilbert problem. This problem is solved exactly. The pre-fracture zone lengths and stresses in these zones are found from algebraical and transcendental equations. The latter are derived from the conditions of stress finiteness at the ends of pre-fracture zones and the material equations. The electrical displacement at any point of the pre-fracture zones is found in closed form as well. Particular cases of symmetrical loading and of equivalent properties of the upper and lower bimaterial components are considered. Numerical results corresponding to certain material combinations and interlayer material equations are presented and analysed. In the suggested model, any singularities connected with the crack are eliminated, i.e., all mechanical and electrical characteristics are limited in the near-crack tip region.     

Propagation of thin plastic zones in the vicinity of a normally separating crack

A problem of the development of a plastic zone in the vicinity of a physical cut in the plain strain and stress states is posed and solved on the basis of a discrete deformation model under the assumption of an ideal elastoplastic medium. The Tresca yield condition and the ultimate plasticity condition are used in studying the plane stress state. The dependence of the plastic zone length on the external load is compared with a similar dependence obtained on the basis of the Leonov-Panasyuk-Dugdale model. In contrast to the Leonov-Panasyuk-Dugdale model, the distributions of stresses and lengths of plastic zones in the plane strain and stress states are found to be substantially different if elastic compressibility and compressive-tensile stresses along the cut direction are taken into account.     

Generation of cracks in a perforated reinforced plate

A problem of fracture mechanics on crack nucleation in a reinforced plate attenuated by a periodic system of circular holes is considered. Crack nucleation is modeled by a pre-fracture band in the plastic flow state with a constant stress, which is considered as a region of attenuated bonds between material particles. Determining unknown parameters characterizing the emerging crack reduces to solving a singular integral equation. The condition of crack emergence is formulated with allowance for the criterion of the limiting opening of the faces of the material pre-fracture band. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 170–180, November–December, 2008.     

Limited permeable crack in an interlayer between piezoelectric materials with different zones of electrical saturation and mechanical yielding

A plane problem for two identical piezoelectric semi-infinite spaces adhered by means of a thin isotropic interlayer is considered. It is assumed that a crack of a limited electric permeability occurs in the interlayer parallel to its faces. Combined electromechanical loading is prescribed at infinity. It is assumed that the interlayer is softer than the adherent materials. To avoid the singularities, which are typical for the Griffith crack model, two distinct zones – a zone of mechanical yielding and a zone of electrical saturation – of unknown lengths are introduced as crack continuations. These lengths can be essentially different, with the zone of mechanical yielding significantly longer or shorter than the zone of electrical saturation. Assuming that the interlayer thickness tends to zero, a constant normal stress is prescribed in the zone of mechanical yielding and a saturated electrical displacement is prescribed in the zone of electrical saturation. Outside of these zones, the semi-infinite spaces are assumed to be perfectly bonded. This formulation results in a linear fracture mechanics problem with unknown pre-fracture zone lengths. The problem, formulated mathematically by a system of two equations of linear relationship, is solved exactly. The unknown yield and saturated zones lengths are found from the conditions of finiteness of stress and electrical displacement at the ends of these zones for the both cases when the electrical saturated zone is longer and shorter than the zone of mechanical yielding. It is shown that the same equation as for the Griffith crack model can be used for the determination of the electrical displacement in the crack region. The main results of the paper are obtained in the form of simple analytical equations which are convenient for engineering applications. Some numerical illustrations in graphical and tabular form show dependencies of the pre-fracture zone lengths, the energy release rate, the mechanical displacement and electrical potential jumps on the electromechanical loading and the electrical permeability of the crack medium.     

Damage accumulation and fracture initiation in uncracked ductile solids subject to triaxial loading

A damage plasticity model for ductile fracture is proposed. This model is established on the cylindrical coordinate system of principal stress space. Experimental results show that fracture initiation in uncracked ductile solids is sensitive to the hydrostatic pressure and dependent on the Lode angle. The joint effects of pressure and Lode angle define a fracture envelope in principal stress space. Plastic deformation induced damage is calculated by an integral of the damage rate measured at current loading and deformation status with respect to the fracture envelope. A power law damage rule is proposed to characterize the nonlinearity in damage accumulation. A damage-related weakening factor is adopted to describe the material deterioration. The material parameters are calibrated from standard laboratory tests. The proposed model is numerically implemented. Four simulations with emphasis on crack path prediction are presented.     

Modeling of crack nucleation in a variable-thickness band under nonuniform heating

A mathematical model of crack nucleation in a variable-thickness band (rod) under nonuniform heating is constructed. As the band (rod) is thermally loaded, pre-fracture zones are assumed to appear; these zones are modeled as regions with attenuated bonds between material particles. The presence of bonds between the pre-fracture zone faces is modeled by adhesion forces applied to the pre-fracture zone surface. Solving the problem of equilibrium of an isotropic variable-thickness band with a prefracture zone is reduced to solving a nonlinear singular integrodifferential equation with a Cauchy-type kernel, which establishes the relation between the adhesion forces in the crack-nucleation zone and the distance between the crack faces. The condition of crack nucleation in a variable-thickness band is formulated with allowance for the criterion of ultimate tension of bonds in the material.     

Complex variable approach in studying modified polarization saturation model in two-dimensional semipermeable piezoelectric media

A modified polarization saturation model is proposed and addressed mathematically using a complex variable approach in two-dimensional(2 D) semipermeable piezoelectric media. In this model, an existing polarization saturation(PS) model in 2D piezoelectric media is modified by considering a linearly varying saturated normal electric displacement load in place of a constant normal electric displacement load, applied on a saturated electric zone. A centre cracked infinite 2D piezoelectric domain subject to an arbitrary poling direction and in-plane electromechanical loadings is considered for the analytical and numerical studies. Here, the problem is mathematically modeled as a non-homogeneous Riemann-Hilbert problem in terms of unknown complex potential functions representing electric displacement and stress components. Having solved the Hilbert problem, the solutions to the saturated zone length, the crack opening displacement(COD), the crack opening potential(COP), and the local stress intensity factors(SIFs) are obtained in explicit forms. A numerical study is also presented for the proposed modified model, showing the effects of the saturation condition on the applied electrical loading, the saturation zone length, and the COP. The results of fracture parameters obtained from the proposed model are compared with the existing PS model subject to electrical loading, crack face conditions, and polarization angles.     

Law of damage accumulation and fracture criteria in highly filled polymer materials

We present the results of a large series of experiments aimed at the study of laws of damage accumulation and fracture in highly filled polymer materials under loading conditions of various types: monotone, repeated, low- and high-cycle, with varying type of stress state, dynamic (in general, more than 50 programs implemented on specimens from one lot of material). The data obtained in these test allow one to make conclusions about the constitutive role of the attained maximum of strain intensity when estimating the accumulated damage in the process of uniaxial tension by various programs (in particular, an additional cyclic deformation below the preliminary attained strain maximum does not affect the limit values of strain and stress in the subsequent active extension), about the strong influence of the stress state on the deformation and fracture, about the specific features of the nonlinear behavior of the material under the shock loading conditions and its influence on the repeated deformation. All tests are described (with an accuracy acceptable in practical calculations, both with respect to stresses and strains in the process of loading and at the moment of fracture) in the framework of the same model of nonlinear viscoelasticity with the same set of constants. The constants of the proposed model are calculated according to a relatively simple algorithm by using the results of standard uniaxial tension tests with constant values of the strain rate and hydrostatic pressure (each test for 2–3 levels of these parameters chosen from the ranges proposed in applications, each loading lasts until the fracture occurs, and one of the tests contains an intermediate interval of total loading and repeated loading) and one axial shock compression test if there are dynamic problems in the applications. The model is based on the use of the criterion fracture parameter which, in the class of proportional loading processes, is the sum of partial increments of the strain intensity on active segments of the process (where the strain intensity is at its historical maximum) with the form of the stress state and the intensity of strain rates taken into account.     

混凝土黏聚开裂模型若干进展

黏聚模型是用来描述混凝土断裂行为的基本模型, 首先介绍了混凝土的黏聚开裂模型的基本概念,总结了确定黏聚区的本构方程的各种方法,即直接单轴拉伸测试、J积分方法、R曲线法、柔度法和逆推法.然后介绍了黏聚模型在I型和复合型裂纹问题、疲劳断裂问题中的应用以及黏聚模型与混凝土尺寸效应的关系.最后对黏聚开裂模型与桥联模型、带状裂缝模型进行了比较和总结, 指出了该模型存在的问题, 并对其以后的发展方向提出了建议.      

脆性材料在双向应力下的断裂实验与理论分析

研究了脆性材料在双向应力下的断裂特性和失效机理，特别是在平行于裂纹的应力对临界断裂参数的影响方面进行了实验上和理论上的研究．采用玻璃、陶瓷等脆性材料进行了平面双向拉伸和单向拉伸试验，并对实验结果进行比较．观测直通裂纹的启裂和扩展过程，证明了双向应力对裂纹驱动力有明显影响，讨论了裂纹扩展的应变准则．     

Experimental study of D16AT alloy deformation under periodic loading

An experimental procedure and results of an experimental study of the kinetics of the strained state of a material under periodic uniaxial loading are reported. Diagrams of the principal components of the total strain tensor for an asymmetric periodic “soft” regime of tension-compression of the samples are presented. Specific features of deformation revealed under periodic asymmetric loading of the samples can be used to formulate a criterion of fatigue fracture of materials and to identify the mechanism of strain hardening of pre-fracture zones in machine elements.     

Study of a propagating finite crack in functionally graded piezoelectric materials considering dielectric medium effect

This paper provides a study of the problem of a propagating finite crack under in-plane loading in functionally graded piezoelectric materials (FGPMs). The analytical formulations are developed by Fourier transforms and the resulting singular integral equations are solved by using Chebyshev polynomials. By using a dielectric crack model with deformation-dependent electric boundary condition, numerical simulations are made to show the effects of the dielectric medium, the gradient of material properties and the speed of crack propagation on the fracture parameters, such as the stress, electric displacement and crack opening displacement intensity factors. A critical state for the electromechanical loading applied to the FGPMs is observed, which determines whether the traditionally impermeable (or permeable) crack model serves as the upper or lower bound for the dielectric model. The validity of this dielectric crack model is also examined by comparing the results of different existing crack models.     

Review of brittle fracture criteria in case of static and cyclic mixed mode loading

The paper gives in the first part in pressed form a survey of brittle fracture criteria using a reference intensity factor in case of static mixed mode loading. Criteria (expressed in terms of different quantities such as stress, deformation and strain energy) usually refer to a parameter that is characteristic of the material response at fracture. Criteria include information on two basic hypotheses (crack propagation direction and unstable crack growth). In the second part a generalized method is suggested for application of cyclic reference intensity factor in case of cyclic mixed mode loading. Three basic hypotheses describe crack growth direction, stable crack growth steps and unstable crack growth.     

Deformation and fracture of crystalline materials under complex loading-program conditions

In predicting the deformation and conditions of fracture of materials under complex loading program conditions one must consider the entire duration of the deformation process.The problem becomes complicated in cases of a simultaneous operation of various mechanisms of deformation and fracture, e. g., when plastic deformation is superposed (once or repeatedly) on creep.A promising phenomenological approach to this problem may be based on concepts of the mechanical equation of state of materials. A hypothesis of the existence of the equation of state depending on a finite number of structural parameters was formulated by Kröner [1] for the case of the three-dimensional law of plasticity and by Rabotnov [2] for the case of creep and fracture under uniaxial stress state conditions.This article is concerned with the application of the hypothesis of the mechanical equation of state to the problem of deformation and fracture of materials (in the uniaxial case) under complex loading program conditions.     

Crack buckling in soft gels under compression

Recent interest in designing soft gels with high fracture toughness has called for simple and robust methods to test fracture behavior. The conventional method of applying tension to a gel sample suffers from a difficulty of sample gripping. In this paper, we study a possible fracture mechanism of soft gels under uni-axial compression. We show that the surfaces of a pre-existing crack, oriented parallel to the loading axis, can buckle at a critical compressive stress. This buckling instability can open the crack surfaces and create highly concentrated stress fields near the crack tip, which can lead to crack growth. We show that the onset of crack buckling can be deduced by a dimensional argument com- bined with an analysis to determine the critical compression needed to induce surface instabilities of an elastic half space. The critical compression for buckling was verified for a neo-Hookean material model using finite element simulations.     

LC4—M材料复合型韧断主要影响因素的分析

通过分析LC4－M铝合金材料在不同复合比载荷下的断裂试验结果,参照常规断裂现象,修正了一般断裂试验中认定裂纹启裂方向的方法,结合不同复合比下裂尖附近应力三维、主应力方向的计算分析,得到：在裂端的钝化变形区域、应力三维度的极大值处,对应于裂纹的启裂位置,即使在高韧性材料中发生剪切断裂的情况下也是如此;裂纹的启裂方向在拉伸断裂时与启裂点最大拉应力方向有关,在剪切断裂时启裂点最大剪应力方向有关,引起两种形式断裂的主要因数和破坏机理有很大不同。     

Yielding on inclined planes at the tip of a crack loaded in uniform tension

Plane-strain yielding from a crack in an infinite elastic body is represented here by a distribution of edge dislocations on two planes inclined at angles ±ga to the crack plane, and the equilibrium condition is solved numerically. Approximate analytical expressions are obtained for the plastic-zone length, the crack opening displacement, and the J-integral, as functions of the applied stress and α. A comparison with a co-planar model of the plastic zone gives very similar results for α ≈ 65°. It is shown that fracture criteria based either on a critical crack opening displacement (COD) or on a critical value of J are always different, and the use of the former may lead to critical defect-sizes which are twice as large as those given by the latter. Furthermore, COD appears not to be a well-defined material property. The critical J criterion gives a fracture stress which is α-dependent : this may be responsible for deviations towards results of linear elastic fracture mechanics when post-yield fracture mechanics is used to analyse extensive yielding. The changes in the stress field of the crack due to the existence of the plastic zone are also discussed.