Prefracture Zone Research Articles

Моделирование упругопластического разрушения компактного образца

The strength of a compact specimen under normal fracture (fracture mode I) is studied within the framework of the Neuber-Novozhilov approach. A model of an ideal elasto-plastic material with limiting relative elongation is chosen as the model of the deformable solid. This class of materials includes low-alloy steels that are used in structures operating at temperatures below the cold brittleness threshold. The crack propagation criterion is formulated using the modified Leonov-Panasyuk-Dugdale model, which uses an additional parameter, i.e., the diameter of the plasticity zone (the width of the prefracture zone). In the case of stress field singularity occurring in the vicinity of the crack tip, a two-parameter (coupled) criterion for quasi-brittle fracture is developed for type I cracks in an elastoplastic material. The coupled fracture criterion includes the deformation criterion attributed to the crack tip and the force criterion attributed to the model crack tip. The lengths of the original and model cracks differ by the length of the prefracture zone. Diagrams of the quasi-brittle fracture of the specimen under plane strain and plane stress conditions are constructed. The constitutive equations of the analytical model are analyzed in terms of the characteristic linear dimension of the material structure. Simple formulas applicable to verification calculations of the critical fracture load and pre-fracture zone length for quasi-brittle and quasi-ductile fractures are obtained. The parameters in the presented model of quasi-brittle fracture are analyzed. It is proposed to select the parameters of the model according to the approximation of the uniaxial tension diagram and the critical stress intensity factor.

SIMULATION OF ELASTOPLASTIC FRACTURE OF A CENTER CRACKED PLATE

The strength of a square plate with a central crack at normal separation was studied within the framework of the Neuber–Novozhilov approach using a modified Leonov–Panasyuk–Dugdale model using an additional parameter, the diameter of the plasticity zone (width of the pre-fracture zone). As a model of a deformable solid body, a model of an ideal elastic-plastic material with a limiting relative elongation was chosen. This class of materials includes, for example, low-alloy steels used in structures operating at temperatures below the cold brittleness threshold. In the presence of a singular feature in the stress field in the vicinity of the crack tip, it is proposed to use a two-parameter discrete integral strength criterion. The deformation fracture criterion is formulated at the tip of a real crack, and the force criterion for normal stresses, taking into account averaging, is formulated at the tip of a model crack. The lengths of real and model cracks differ by the length of the pre-fracture zone. The constitutive equations of the analytical model are analyzed in detail depending on the characteristic linear dimension of the material structure. Simple formulas suitable for verification calculations for the critical breaking load and the length of the pre-fracture zone are obtained. Numerical modeling of the propagation of plasticity zones in square plates under quasi-static loading has been performed. In the numerical model, the updated Lagrangian formulation of the equations of mechanics of a deformable solid body is used, which is most preferable for modeling the deformation of bodies made of an elastic-plastic material at large deformation. The plastic zone in the vicinity of the crack tip is obtained by the finite element method. The results of analytical and numerical prediction of plate fracture under plane deformation are compared. It is shown that the results of numerical experiments are in good agreement with the results of calculations using the analytical model of fracture of materials with a structure under normal separation. Diagrams of quasi-brittle and quasi-ductile fracture of a structured plate are constructed.

Prediction of the durability of a plate with a through crack taking into account biaxial constraints of deformations along the front of a normal rupture crack

A methodology for evaluating the durability of plate elements of structures taking into account biaxial constraints of deformations along the front of a normal rupture crack (Mode I crack) is presented. The absence of the available literature data in which the prediction of the crack growth is carried out using Txx- and Tzz-stresses which are non-singular terms in the Williams expansion for stresses at the crack tip is noted. The calculation of the fatigue crack growth rate is based on the Paris equation in which the range of the effective SIF is used instead of the range of the usual stress intensity factor (SIF). In this case, the expression for the effective SIF includes Txx- and Tzz-stresses in addition to the usual SIF. This approach provides taking into account, for example, the thickness of the plate for predicting the durability, which is impossible when only the SIF and Txx-stresses are used. The formula for the effective SIF is derived proceeding from the assumption that tangential stresses in the pre-fracture zone are equal to the local strength of the material. In this case, the size of the pre-fracture zone and the local strength of the material are determined taking into account Txx- and Tzz-stresses. The numerical simulation is based on the proprietary finite-element program which allows calculating Txx- and Tzz-stresses at the front of a through crack in a plate subjected to cyclic uniaxial and biaxial tension. It is shown that nonsingular Txx-stresses primarily describe the effect of biaxial loading on the survivability, whereas Tzz-stresses describe the effect of the plate thickness on the survivability. It is shown that with increasing thic kness of the plate the value of the effective SIF increases due to the increased constraint along the crack front, thus increasing the crack growth rate and decreasing the survivability. With an increase in the stress ratio R, under the condition of a constant stress range, the maximum effective SIF reaches the critical value equal to the fracture toughness much faster thus reducing the durability. It is shown that for uniaxial cyclic tension, the durability predicted by the proposed methodology is higher than that in the classical approach, when the conventional SIF is used in the Paris equation. For biaxial cyclic tension of a plate, an increase in stresses directed parallel to the crack banks leads to an increase of crack front constraints and therefore to a decrease in the durability compared to the classical approach. In other words, the classical theory does not always provide a conservative estimate of the durability, which indicates the expediency of using the developed method for calculating the durability taking into account biaxial constraints of deformations along the crack front.

Analytical Methods of Modeling the Prefracture Zone near an Interfacial Crack Tip (Review)

Analytical Methods of Modeling the Prefracture Zone near an Interfacial Crack Tip (Review)

A Fracture Criterion with Biaxial Constraints of Deformations along the Front of a Normal Rupture Crack

In this article, a new fracture criterion is formulated for a normal rupture crack, the most common in practice, based on the assumption that the tangential stresses in the prefracture zone are equal to the local strength of the material. In this case, the size of the prefracture area and the local strength are determined taking into account the nonsingular Тхx and Тzz stresses included in the asymptotic stress distribution according to Williams and characterizing the two-dimensional local constraint of deformation along the crack front in three-dimensional bodies. An expression for the effective stress intensity factor is obtained. In addition to the classical stress intensity factor, it includes the ratios of the Тxx and Тzz stresses to the yield strength. This makes it possible to take into account the restriction of deformations in the transverse (due to Тxx stresses) and longitudinal (due to Тzz stresses) directions in the vicinity of the crack front. Verification of the developed software tools and the proposed fracture criterion has been carried out. Examples of the implementation of the developed criterion for assessing crack resistance of a plate stretched in one or two directions with a coaxial transverse crack are given.

Аналитическая модель квазихрупкого разрушения пластины с трещиной

The paper considers a rectangular plate with the edge crack of mode I of normal separation from the elastoplastic material with the ultimate strain. This class of materials includes, for example, the low-alloy steels used in structures operating at temperatures below the cold brittleness threshold. The strength of the plate was studied within the framework of the Neuber --- Novozhilov approach. The crack propagation criterion was formulated using the modified Leonov --- Panasyuk --- Dugdale model using an additional parameter, i.e., the plasticity zone diameter (pre-fracture zone width). Under conditions of small-scale yielding in the presence of the stress field singular feature in the vicinity of the crack tip, the two-parameter (dual) criterion for quasi-brittle fracture was formulated for mode I cracks in the elastoplastic material. The fracture dual criterion included deformation criterion at the crack tip, as well as the force criterion at the fictitious crack tip. The lengths of the original and fictitious cracks were differing by the length of the pre-fracture zone. Diagrams of the plate quasi-brittle fracture under conditions of plane deformation and plane stress were constructed. The parameters included in the proposed quasi-brittle fracture model were analyzed. It was proposed to select model parameters according to the approximation (σ--ε)-diagram of uniaxial tension and the KIc critical stress intensity factor

Detection of prefracture zones in structural materials by magnetic and optical methods

The study of the applicability of magnetic and optical methods to the detection of prefracture zones under fatigue degradation of structural materials is exemplified by the 09G2S steel. The regularities of changes in the signal of an attached fluxgate gradiometer with the increasing number of loading cycles have been revealed; namely, significant changes in the gradiometer readings on individual specimen surface areas prove to result from the formation of fracture zones. The change in the value of the coefficient of correlation among the speckle images is studied at different stages of cyclic testing. Speckle image heterogeneity is shown to appear due to fracture nucleation. Thus, the applicability of magnetic and speckle-interferometric methods to detecting prefracture zones in objects under cyclic loading is substantiated.

Двопараметрична модель зони передруйнування у квазіпружному матеріалі біля вершини міжфазної тріщини

A model of the pre-fracture zone, which under plane strain conditions extends from the tip of the interface crack at an angle to the plane interface of two different homogeneous isotropic materials, has been developed. The pre-fracture zone is represented by the displacement discontinuity line, on which the strength condition of the Mises-Hill type is satisfied. The parameters of the model are the tensile resistance and shear resistance of the material in which the zone develops. The model takes into account brittle and ductile fracture mechanisms and can be used to describe the quasi-brittle fracture of a piece-homogeneous body with an interface crack. The possibility of a transition between brittle and ductile fracture mechanisms is shown when the ratio of tensile and shear resistance of the material changes.

SCIENTIFIC FOUNDATIONS OF THE CREATION OF DIAMOND DRILLING TOOLS OF THE RING TYPE

To solve the mentioned problem of accelerated commissioning of minerals occurring in hard rocks, studies have been carried out to formulate the following recommendations for the creation of high-performance diamond bits: - the crown matrix should contain several (five or more) impregnated diamond-bearing layers in height, separated by diamond-free layers of significantly lower hardness (for example, VK-20 hard alloy); - each diamond impregnated layer of the matrix must have a "comb" profile, representing annular wedge-shaped protrusions and depressions; - the impregnated diamond layers of the matrix during drilling should be equally loaded along the radius of the bit, which makes it possible to increase the wear resistance of the tool and reduce the number of rough diamonds for the manufacture of the latter; - to maintain the diameters of the well and the drilled core, the inner and outer side surfaces of the matrix must be equipped with wear-resistant diamond inserts (for example, from tvesala); - to produce a high-quality wear-resistant matrix, small amounts of various components should be added to the composition of the binder of the 94WC + Co + Cu type diamond grains. Recommendations 1-4 are embodied in the design of diamond impregnated crowns, for which the Republic of Kazakhstan has received patents. Crowns have been introduced into production with a significant effect. A diamond crown has been developed and patented, the impregnated layers placed in a matrix on a three-start helical surface with a slight pitch of 0.8 - 1.2 mm. It is expected that with this design, the pre-fracture zone will be involved in the bottom hole destruction process, which lies under the intrusion zone and represents a hard rock broken and weakened by cracks to a depth ten times greater than the intrusion depth of diamond grains. An experimental batch of multilayer crowns with an equally loaded comb profile and placement of impregnated layers on a three-start helical surface was made using software and CNC (numerical control) machines.

Visualization of fractographic signs of operational degradation of heat-resistant steel for estimating its actual structural-mechanical state

Fracture surfaces of specimens of the steel 15H1M1F long-term (approx. 2·105 h) operated on the main steam pipelines of a thermal power plant have been analysed after their mechanical testing. Fractographic analysis showed some distinctions resulted from different number of shutdowns (501 and 576) of power units during their operation. After impact toughness and fracture toughness tests, as expected, the fracture surfaces of the steel subjected to more shutdowns have less area of ductile (subcritical) fracture in the vicinity of notch or pre-crack, and more intergranular fragments against the background of typical transgranular relief in the zone of spontaneous fracture. These features are concerned with more intensive degradation of the steel after more shutdowns of power units. It can be explained by a larger pre-fracture zone in impact specimens and, accordingly, the possibility of a greater deviation of the crack from its main path, involving the boundaries of dozens of grains with operational damages. In contrast, pre-cracked specimens for fracture toughness evaluation have the narrower pre-fracture zone, therefore, there is significantly less grain boundaries weakened by degradation on the crack path. Some areas of intergranular fracture against the background of a classical, as a whole, transgranular fatigue fracture were also found at the fracture surfaces of the operated steel after fatigue tests, namely, in the near-threshold region of the crack growth. They are associated with grains encountered along the path of fatigue crack propagation, the boundaries of which were damaged as a result of creep during long-term operation of the steel on steam pipelines. Based on fractographic research of the long-term operated steel, the area of intergranular fragments in the unit area of the fracture surfaces is proposed as a quantitative fractographic indicator of changes in its structural and mechanical state due to degradation. The mechanical characteristics of brittle fracture resistance of the steel are consistent with the proposed fractographic indicator of the metal state.

Predicting the state of heat-resistant steel of a steam pipeline at a TPP taking into account changes in its strength due to operational damage

The microstructure of heat-resistant 15Kh1M1F steel is analysed in the initial state and after long-term operation on the main steam pipelines of TPPs. According to the criteria adopted in fracture mechanics, the low volumetric content of fine carbides, which did not exceed 0.5% in the structure of the analysed steel in the initial state, does not significantly affect its strength. However, as a result of long-term high-temperature operation, a redistribution of carbon and alloying elements occurred in its structure with the precipitation and coagulation of carbides along the grain boundaries. Large carbides concentrated along the grain boundaries have a low cohesion with the matrix, which promotes the formation of pores along their interfaces. As a result, the cohesion of adjacent grains decreases, which contributes to the formation of a system of intergranular microcracks. Merging, they form a macrocrack, which has a significant effect on the strength of the material.A mathematical model is proposed for predicting changes in the ultimate strength of steel, based on the well-known solution of the problem with tension of a body with a periodic system of collinear cracks. The relationship between the intensity of tensile forces, the distance between the cracks, their size and the size of the pre-fracture zones in the vicinity of operational defects is found. The beginning of the merging of the pre-fracture zones at the tips of the nearest defects was taken as the condition for material destruction.A dependence has been obtained that makes it possible to make predictive estimates of a decrease in the ultimate strength of long-term operation of steel on steam pipelines of different units, due to its additional damage under the influence of shutdown numbers of TPP units corresponding to this steel. To do this, it is only necessary to calculate the fraction of the steel resource loss according to normalized technological indicators, such as the operation lifetime and the number of shutdowns of the units.

Influence of adhesive bond line thickness on joint strength of composite aircraft structures

Methods for assessing the effect of the thickness of the adhesive layer in the adhesive joint of thin-walled composite structural elements on the strength of the entire joint are considered; a critical analysis of existing theoretical methods for predicting the strength of adhesive joints is given. The contradiction between the theoretical estimates of the effect of the adhesive thickness on the strength and the results of experiments and practical experience in the use of adhesive joints of composite panels is established. It is revealed that the most effective methods for predicting the load-bearing capacity of adhesive joints are energy models of fracture mechanics based on the intensity of the release of fracture energy and the formation of a pre-fracture zone in the adhesive layer. Assuming the determining role of changes in the size and shape of the initial fracture zone depending on the thickness of the adhesive layer, the results of the prediction of the strength of the adhesive joint are compared with experimental data.

Experimental simulation of tensile fractures from a circular cavity

The authors experimentally study initiation of tensile fractures from a circular cavity in a geomedium subjected to nonuniform compression. It is found that diameter of the cavity has a significant influence on the local fracture of the geomaterial. A new criterion is proposed for the quasi-brittle fracture of a material in the tensile stress concentration zone. The new criterion holds an integrated parameter which characterizes the size of the pre-fracture zone, the structure of a material and its plastic properties, the cavity geometry and the conditions of loading. The calculation and experiment result agree well.

Criterion for elastoplastic failure of bimetallic plate with edge crack of transverse shear at the boundary of the materials joint

The initiation of a transverse shear edge crack in elastoplastic materials with the limiting strain is considered. The crack propagation criterion is formulated using a modified Leonov-Panasyuk-Dugdale model using the additional parameter - the width of the plasticity zone. The coupled quasi-brittle fracture criterion for mode II cracks in an elastoplastic material is formulated under conditions of small-scale yield in the presence of a singular feature of the stress field in the vicinity of the crack tip. The coupled fracture criterion includes the deformation criterion, which is formulated at the crack tip, as well as the force criterion, which is formulated at the model crack tip. The lengths of the initial and model cracks differ by the length of the prefracture zone. The sequential analysis of the possibility of applying the proposed fracture criterion in determining the critical loads for solids containing edge cracks of transverse shear at the interface of different media is performed. Quasi-brittle fracture diagrams are constructed for a composite plate with an edge crack under plane strain and plane stress conditions. he analysis of the parameters included in the proposed model of quasi-brittle fracture is carried out. The model parameters are proposed to be selected by approximation of simple shear diagram and critical stress intensity factor. The critical loads were found numerically for the quasi-ductile and ductile fracture types. The finite element method is used to solve the problem of drawing out a reinforcing layer from a metal composite under quasi-static loading. The process of propagation of plastic zones in the vicinity of the crack tip is described consistently. It is shown that the shapes of the constructed plastic zones differ significantly from the well-known classical concepts.

Study of the strength of monolithic concrete lining of mine shaft under variable heat loads

Monolithic concrete lining is the most popular shaft lining because it is able to endure the rock pressure effects and to exclude large deformations of shaft walls. In the case of starting the reverse ventilation mode in the winter season, a significant negative temperature difference may occur between the warm shaft walls and the cold air from the surface. That temperature difference may have adverse impacts on concrete lining, causing high tensile stresses in it. In this paper, the stress-strain state of the concrete lining and rock mass surrounding the mine shaft is investigated to evaluate the strength of the lining during the reverse ventilation mode in the winter season. The object of the study is the ventilation shaft with surrounding concrete lining and rock mass. Solid and concrete are considered to be isotropic and homogeneous, and their thermodynamic properties are independent of temperature. This allows considering a two-dimensional problem. It is assumed that the temperature drop in lining and rock mass is the only significant factor affecting the stress-strain state of the system. When calculating the temperature of the lining and rock mass, the conductive heat transfer in the volume of rocks and lining, the heat exchange of the lining and rocks with atmospheric air and the heat exchange of the lining with the mine air are taken into account. The presence of moisture in rock mass is not considered. Based on the results of numerical simulation, the following was established. The concrete lining mostly undergoes tensile stresses; the maximum tensile stress acts in a vertical direction. The width of the pre-fracture zone of the lining nonlinearly depends on the duration of the reverse ventilation mode. With an increase in the air temperature in the shaft, the width of the pre-failure zone of the lining decreases, and the permissible duration of the reverse mode significantly increases.

An approximate method for solving Wiener-Hopf matrix equations in problems of applied mechanics

Method of successive approximations for the solution of the Wiener---Hopf functional equations system is offered. The method uses the presentation of matrix coefficient of the system as a sum of two matrices, where the first matrix assumes the exact factorization, and the second matrix --- matrix-perturbation --- is much smaller than the first matrix in the domain of system definition. Solution of the system is sought in the form of expansions in powers of the matrix-perturbation. At each step of the approximation the solution of the system is carried out by means of the Wiener---Hopf method using factorization of the main component of the matrix coefficient. The example of the use of method is considered for the solution of the problem about the calculation of the pre-fracture zone parameters in connecting material near the tip of the interfacial crack outcoming from the angular point of the broken interface of two different materials. The zone is modeled by the discontinuity line of displacement, on which the stresses meet the Mises---Hill failure criterion. It is shown that under certain conditions, already in the first approximation, the method allows to obtain solutions with permissible accuracy.

Mutual influence of the faces contact area and the pre-fracture zone near the tip of the interfacial crack

BACKGROUND: Under plane strain conditions, a crack model was developed on a plane interface between two different materials, which assumes the existence near its tip of the faces contact area and a narrow lateral pre-fracture zone in a less crack-resistant material of the composite compound. The pre-fracture zone is modeled by the line of normal displacement rupture, on which the normal stress is equal to the tensile strength of the material. Assuming that the dimensions of the pre-fracture zone and the contact zone have the same order of magnitude and are significantly smaller than the crack length, the problem is reduced to the vector Wiener–Hopf equation. METHODS: An approximate method for solving the vector Wiener–Hopf equation was developed, which was used to obtain the equations for determining the sizes of the pre-fracture zone and the contact faces area. The pre-fracture zone orientation was determined from the condition of the potential energy maximum accumulated in the zone. Numerical calculations of the indicated parameters and analysis of their dependences on the configuration and module of external load are executed. RESULTS: A significant mutual influence of the pre-fracture zone and crack faces contact on their sizes and orientation of the zone was revealed.

Elastic–plastic problem for a circular hole plate with regard to crack initiation in elastic zone

A plane elastic–plastic problem of stress distribution in a circular hole thin plate involving initiation and propagation of cracks in an elastic zone, is considered. It is assumed that the stress level is such that the circular hole is entirely enclosed by the plastic deformations zone. The plate material satisfies the Tresca–Saint Venant plasticity condition. It is supposed that cracks initiation and fracture of the plate material occur in the loading process in the elastic zone. Location and size of prefracture zone in the plate material are unknown in advance and are to be determined. The methods of theory of perturbations and theory of singular integral equations are used. As a crack appearance condition, we use the criterion of critical opening of prefracture zone faces. The interface of elastic and plastic deformations and also the location and sizes of crack initiation zones are found.

ВЛИЯНИЕ ПОВЕРХНОСТНО-АКТИВНЫХ ВЕЩЕСТВ НА ИСКРИВЛЕНИЕ СКВАЖИН ПРИ БУРЕНИИ В АНИЗОТРОПНЫХ ГОРНЫХ ПОРОДАХ

Актуальность. Отклонение от проектной траектории скважин приводит к ошибочным результатам и как следствие к невыполнению поставленной задачи бурения. К важным геологическим условиям, которые влияют на искривление скважины, относятся сланцеватость, трещиноватость, слоистость, перемежаемость слоев пород различной твердости, флюидальность, пористость, зоны дробления пород, разломы, пустоты, твердые включения и т. п. Как показывает опыт проведения буровых работ, значительная часть перебуриваемых горных пород являются анизотропными. Показатель анизотропии горных пород характеризует степень совокупного влияния нескольких факторов на процесс естественного искривления скважин. Тип инструмента и параметры режима бурения являются основными факторами такого рода. Борьба с естественным искривлением зачастую вызывает технические затруднения и связано с большими затратами времени и материальных ресурсов. В связи с этим актуальным является изучение особенностей бурения в условиях анизотропии горных пород и рассмотрение возможностей влияния на искривление скважин при повышенной флюидальности. Цель: определение возможностей влияния на естественное искривление скважин при бурении в анизотропных горных породах. Объект: механизм разрушения анизотропной горной породы. Методы: экспериментальные, аналитические исследования, анализ. Результаты. Применение в процессе бурения скважин жидкостей с добавлением поверхностно-активного вещества и гидродинамическое воздействие на забой способствуют снижению естественного искривления скважин. Активное воздействие очистного агента, содержащего поверхностно-активные вещества, на зону предразрушения породы устраняет неравномерность поражения забоя при движении резцов инструмента в направлении навстречу и вслед плоскостям флюидальности. Промывочный агент с добавками поверхностно-активного вещества снижает значение отношения скорости фрезерования породы в стенке скважины к углублению забоя, при этом особый эффект наблюдается при высокой механической скорости бурения скважины. Данное обстоятельство связано с возможностью проникновения промывочного агента в трещины, образовавшиеся в зоне предразрушения горной породы.

About the cohesive pre-fracture zone at the tip of a crack outcoming from the corner point of the broken interface of materials

About the cohesive pre-fracture zone at the tip of a crack outcoming from the corner point of the broken interface of materials