Prefracture Zone Research Articles

Crack initiation in a stiffened plate

The fracture mechanics problem of crack initiation in a stiffened plate is considered. The crack nucleus is modeled by a prefracture zone with bonds between the crack faces, which is treated as a region of weakened interparticle bonds of the material. The boundary-value problem of the equilibrium of a stiffened plate with a crack nucleus reduces to a nonlinear singular integrodifferential equation with a Cauchy type kernel. The strains in the crack initiation zone are found by solving this equation. The case of the stress state of the plate with a periodic system of prefracture zones is considered.

Nonlocal criteria for determining a prefracture zone in the process of defect growth for finite strains

Nonlocal criteria for determining a prefracture zone in the process of defect growth for finite strains

Plastic flow localization in h.c.p. Zr alloys on macro- and microscale levels

The regular features exhibited by plastic strain localization on macro- and microscale levels at the parabolic strain hardening stage are examined for commercial Zr alloys used in nuclear power industry. The plastic flow shows instability, which is manifested as oscillatory variation of space-time distributions of local strain patterns as revealed by speckle interferometry. It is shown that the periodic accumulation of deformation in the flow nuclei enhances the evolution of dislocation structure within the nuclei so that one of them becomes a prefracture zone in which necking would finally occur. The data obtained are discussed within the framework of a synergetic approach to plastic deformation evolution at the final flow stage.

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.

Analysis of Pre-Fracture Zones for an Electrically Permeable Crack in an Interlayer Between Piezoelectric Materials

The method of determination of the pre-fracture zone length and the crack opening displacement for a plain strain problem of electrically permeable crack located in a thin interlayer between two identical piezoelectric materials is suggested. This method takes into account certain stress distribution appearing at the crack continuation. This distribution is related to interlayer yielding or damage and it can be found experimentally or theoretically.

Models of plane elements with various singular features

In the present article some problems of fracture mechanics are investigated with the help of polarization-optical methods. Experimental data obtained through static loading of plane models with singularities of various kinds are analyzed. The features and some paradoxes in the distribution of stresses in prefracture zones are revealed, and the control of several theoretical solutions of different authors is carried out. Applications of the research presented here are described.

Splitting a Viscoelastic Orthotropic Body with a Rigid Wedge of Thickness Increasing with Time

A crack model with a constant-length prefracture zone and a critical opening criterion are used to solve the wedging problem for a linear elastic body split by a rigid wedge with thickness increasing with time. Governing equations describing the behavior of the crack during the incubation and transient stages are presented. An algorithm is proposed to solve numerically the governing equation of transient crack growth

Initial Development of the Prefracture Zone Near the Tip of a Crack Reaching the Interface Between Dissimilar Media

The Wiener–Hopf method is used to analyze, within the framework of a plane static problem, the prefracture zone near the tip of a mode I crack reaching the interface separating two isotropic media and containing a corner point

Wedging an Orthotropic Body by a Rectangular Wedge of Finite Length

Galin's method is used to derive equations that relate the basic parameters of the problem on wedging an orthotropic space by a rigid rectangular wedge. To eliminate the stress singularity at the wedging crack tips, a Leonov–Panasyuk–Dugdale prefracture zone is assumed to exist at the crack front. The equations are derived using the COD criterion

Determining Prefracture Zones at a Crack Tip Between Two Elastic Orthotropic Bodies

The model of prefracture zones is generalized to a crack between two anisotropic materials. An exact analytical solution is found on the assumptions that the prefracture zone is localized on the crack continuation and that only the normal displacements undergo discontinuity in the zone. From this solution, equations for determining the prefracture length and crack tip opening are derived

Deformation model of fracture in concrete

We propose a deformation model describing fracture of concrete, where the stressed state in a prefracture zone is assumed to be equivalent to the second and third segments of the complete tension stress–strain diagram (i.e., the segments of plastic deformation and loosening). The model involves the following material characteristics: critical crack-tip opening displacement, model crack opening displacement in the prefracture zone at the boundary between the plastic-deformation and loosening segments, cohesion stress in a model crack, and lengths of the loosening and plastic- deformation segments.

Modeling of Material Deformation Kinetics in the Prefracture Zone

Based on the concept of complete stress–strain diagrams, we propose a new model describing the law of stress distribution in the prefracture zone in plastic materials in view of the type of the stressed state.

Plastic Flow Localization in Commercial Zirconium Alloys

The behavior of plastic flow curves and patterns of plastic strain localization were studied for tension of samples of Zr — 1% Nb (E110 alloy) and Zr — 1% Nb — 1.3% Sn — 0.4% Fe (E635 alloy) were studied. The relationship of the localization kinetics with the strain hardening law in plastic flow and transition to fracture is established. The dislocation microstructure of the alloys in strain localization and prefracture zones is examined.

Effect of Closure of a Crack Caused by the Roughness of Its Surfaces on Fatigue Fracture under the Conditions of Transverse Shear

We develop a model aimed at the prediction of propagation of mode II fatigue cracks with regard for the interaction of their lips caused by the roughness of the fracture surfaces. In this model, the relationship between normal and shear contact stresses is described by the Amonton's law of friction and the plastic yield of the material in the prefracture zone is taken into account with the help of the model of thin plastic strips. The method of singular integral equations is used to solve the corresponding boundary-value problem for a plate with cracks propagating from two semiinfinite collinear notches. The distribution of contact stresses is determined and the stress intensity factors and displacements of the crack lips are evaluated. The proposed example is used to analyze the basic specific features of the influence of contact of the crack lips on fatigue fracture under the action of shear loads. The obtained results are confirmed by the experimental data on the propagation of mode II fatigue cracks in specimens of HY-130 steel.

Wedging an Orthotropic Body

The problem of wedging an orthotropic body with a semi-infinite rigid wedge of constant thickness is solved in the context of the Leonov–Panasyuk model. The lengths of a free crack and prefracture zone are found from the material parameters

Application of the Model of Reverse Yield of a Material in Thin Plastic Strips for the Prediction of Growth of Fatigue Cracks

On the basis of the model of thin plastic strips and the method of singular integral equations, we obtain a closed analytic solution of the problem of stress-strain state of a material near the tip of a fatigue crack taking into account its reverse plasticity in the prefracture zone and the effect of crack closure. This solution is used for the prediction of crack growth under loads with constant and variable amplitudes and the analysis of the behavior of small cracks. It is shown that the obtained results agree with the experimental data.

Dimensions of the Prefracture Zone in the Process of Exfoliation of a Linear Rigid Inclusion

Dimensions of the Prefracture Zone in the Process of Exfoliation of a Linear Rigid Inclusion

Role of the Prefracture Zone in the Evaluation of Stress Concentration in Cyclically Deformed Materials

The processes of initiation and growth of fatigue macrocracks near stress concentrators are regarded as a two-parameter process described by the range of local stresses and the linear (structural) parameter of the material, namely, the size of the prefracture zone d *. We show that the value of d * determines the value of the cyclic stress concentration factor K f and the length of the initial macrocrack a i = d *. We perform the comparative analysis of the experimental and numerical procedures used for the evaluation of the parameter d *. For beam and compact specimens with notches, we compare the results of evaluation of the factor K f obtained on the basis of author's approach and by using the well-known relations of Neuber and Peterson.

Study of the tensile fracture of plates with a rigid linear inclusion

The limit equilibrium of elastoplastic body is studied under the conditions of a plane problem. The body contains a linear inclusion, which is rigid but of finite rupture strength. The plastic or prefracture zones develop near the ends of the inclusion and are modeled by slip cracks along the matrix—inclusion interface. A new interpretation of the boundary conditions is proposed to solve a model problem for such a composition, and its analytical solution is derived. Two possible mechanisms of local fracture are considered: (a) fracture of the inclusion and (b) separation of the inclusion. The critical length of the inclusion is determined. This length together with the elastic and strength parameters of the composition determines the mechanism of local fracture. The limit loads are found for each mechanism of fracture.

Development of a crack with a considerable prefracture zone in a viscoelastic orthotropic plate under variable loads

The study is made of the delayed fracture of a viscoelastic orthotropic plate caused by subcritical advancement of a rectilinear microcrack, which is located along one of the orthotropic axes. The crack develops because of stretching of the plate by uniformly distributed increasing and cyclic external forces perpendicular to the crack line. The investigation is carried out within the framework of the Boltzmann-Volterra theory for resolvent integral operators of difference type, which describe the deformation of a material with time-dependent rheological properties. The analytical form of the kernel of an irrational function of a linear combination of the above integral operators is determined by the method of operator continued fractions. Numerical calculations are conducted for resolvent bounded integral operators with a kernel in the form of Rabotnov's fractional-exponential function. The kinetics of growth of a crack with tip regions commensurable with the crack length is studied. A comparison with the results obtained within the framework of the concept of the thin structure of the crack tip is given.