In this paper, the crack initiation characteristics of compression-shear plane crack with hydraulic pressure were studied by using theoretical analysis and experimental verification methods. The formula derivation pro...In this paper, the crack initiation characteristics of compression-shear plane crack with hydraulic pressure were studied by using theoretical analysis and experimental verification methods. The formula derivation process of stress intensity factor of crack tip and open-type crack initiation angle and initiation strength was expounded in detail. Cement mortar specimens prefabricated with open-type crack were made for biaxial compression test. The results show that the mode I stress intensity factor is inversely proportional to the dip angle of pre-exciting crack, water pressure and crack width. The fracture toughness is most easily achieved when the dip angle of pre-exciting crack is 60°. The mode II stress intensity factor is symmetrically distributed with the dip angle and independent of the water pressure and crack width. For open-type crack, the crack initiation angle decreases with the increase of the dip angle of pre-exciting crack, water pressure and crack width;the crack initiation strength is inversely proportional to the water pressure and proportional to the lateral pressure. The research results can provide ideas for the study of crack initiation under the coupling of ground stress and osmotic pressure in tunnel engineering.展开更多
A series of true triaxial unloading tests are conducted on sandstone specimens with a single structural plane to investigate their mechanical behaviors and failure characteristics under different in situ stress states...A series of true triaxial unloading tests are conducted on sandstone specimens with a single structural plane to investigate their mechanical behaviors and failure characteristics under different in situ stress states.The experimental results indicate that the dip angle of structural plane(θ)and the intermediate principal stress(σ2)have an important influence on the peak strength,cracking mode,and rockburst severity.The peak strength exhibits a first increase and then decrease as a function ofσ2 for a constantθ.However,whenσ2 is constant,the maximum peak strength is obtained atθof 90°,and the minimum peak strength is obtained atθof 30°or 45°.For the case of an inclined structural plane,the crack type at the tips of structural plane transforms from a mix of wing and anti-wing cracks to wing cracks with an increase inσ2,while the crack type around the tips of structural plane is always anti-wing cracks for the vertical structural plane,accompanied by a series of tensile cracks besides.The specimens with structural plane do not undergo slabbing failure regardless ofθ,and always exhibit composite tensile-shear failure whatever theσ2 value is.With an increase inσ2 andθ,the intensity of the rockburst is consistent with the tendency of the peak strength.By analyzing the relationship between the cohesion(c),internal friction angle(φ),andθin sandstone specimens,we incorporateθinto the true triaxial unloading strength criterion,and propose a modified linear Mogi-Coulomb criterion.Moreover,the crack propagation mechanism at the tips of structural plane,and closure degree of the structural plane under true triaxial unloading conditions are also discussed and summarized.This study provides theoretical guidance for stability assessment of surrounding rocks containing geological structures in deep complex stress environments.展开更多
Peridynamics(PD)is an effective method for simulating the spontaneous initiation and propagation of tensile cracks in materials.However,it faces great challenges in simulating compression-shear cracking of geomaterial...Peridynamics(PD)is an effective method for simulating the spontaneous initiation and propagation of tensile cracks in materials.However,it faces great challenges in simulating compression-shear cracking of geomaterials due to the lack of efficient contact-friction models.This paper introduces an original contact-friction model that leverages twin mesh and potential function principles within PD to model rock cracking under tensile and compressive stresses.The contact detection algorithm,based on space segmentation axis-aligned bounding box(AABB)tree data structure,is used to address the significant challenge of highly efficient contact detection in compression and shear problems.In this method,the twin mesh and potential function are utilized to quantify contact detection and contact degree,as well as friction behavior.This is in contrast to the distance and circular contact area model,which lacks physical significance in the classical PD method.As demonstrated by the tests on specimens containing cracks,the proposed model can capture 8 types of secondary fractures,reduce the contact detection error by about 29%e56%,and increase the contact retrieval efficiency by over 1600 times compared to the classic PD models.This significantly enhances the capability of PD to simulate the initiation,expansion,and coalescence of intricate compression-shear cracks.展开更多
To meticulously dissect the cracking issue in the transverse diaphragm concrete,situated at the anchor point of a colossal large-span,single cable plane cable-stayed bridge,this research paper adopts an innovative lay...To meticulously dissect the cracking issue in the transverse diaphragm concrete,situated at the anchor point of a colossal large-span,single cable plane cable-stayed bridge,this research paper adopts an innovative layered modeling analysis methodology for numerical simulations.The approach is structured into three distinct layers,each tailored to address specific aspects of the cracking phenomenon.The foundational first layer model operates under the assumption of linear elasticity,adhering to the Saint Venant principle.It narrows its focus to the crucial zone between the Bp20 transverse diaphragm and the central axis of pier 4’s support,encompassing the critically cracked diaphragm beneath the N1 cable anchor.This layer provides a preliminary estimate of potential cracking zones within the concrete,serving as a baseline for further analysis.The second layer model builds upon this foundation by incorporating material plasticity into its considerations.It pinpoints its investigation to the immediate vicinity of the cracked transverse diaphragm associated with the N1 cable,aiming to capture the intricate material behavior under stress.This layer’s predictions of crack locations and patterns exhibit a remarkable alignment with actual detection results,confirming its precision and reliability.The third and most intricate layer delves deep into the heart of the matter,examining the cracked transverse diaphragm precisely where the cable force attains its maximum intensity.By leveraging advanced extended finite element technology,this layer offers an unprecedented level of detail in tracing the progression of concrete cracks.Its findings reveal a close correlation between predicted and observed crack widths,validating the model’s proficiency in simulating real-world cracking dynamics.Crucially,the boundary conditions for each layer are meticulously aligned with those of the overarching model,ensuring consistency and integrity throughout the analysis.These results not only enrich our understanding of the cracking mechanisms but also underscore the efficacy of reinforcing cracked concrete sections with external steel plates.In conclusion,this study represents a significant contribution to the field of bridge engineering,offering both theoretical insights and practical solutions for addressing similar challenges.展开更多
The fracture network of hydraulic crack is significantly influenced by the bedding plane in coalbed methane extraction.Under mode Ⅱ loading,crack deflection holds a key position in hydraulic cracking,especially in hy...The fracture network of hydraulic crack is significantly influenced by the bedding plane in coalbed methane extraction.Under mode Ⅱ loading,crack deflection holds a key position in hydraulic cracking,especially in hydraulic shearing.This study first analyzed the crack deflection theory of layered rock.The semi-circle bending test under asymmetric loading is performed,and the four-dimensional Lattice Spring Model(4D-LSM)is established to examine how the bedding parameters affect coal crack propagation under mode Ⅱ dominant loads.The 4D-LSM results are comparable to the coal loading test results under quasi-mode Ⅱ and the analytical prediction of crack deflection theory.During mode Ⅱ loading,the coal crack propagation is greatly influenced by the angle,strength,and elastic modulus of the bedding plane,while the effects of thickness and spacing of bedding are insignificant.The crack of coal tends to propagate towards the bedding,following a decrease in bedding angle,a decrease in bedding strength,and an increase in elastic modulus.With higher bedding strength,spacing,and thickness,the peak load on the coal sample is higher.The influences of bedding strength,elastic modulus,spacing,and thickness on the peak load of coal samples and its anisotropy gradually decrease.It is proved that compared with the tangential stress ratio and traditional energy release ratio theories,the corrected energy release ratio criterion can more accurately predict the direction of crack deflection of coal,especially under mode Ⅱ loading.The results can provide assistance in the design of initiation pressure and fracturing direction in coal seam hydraulic fracturing.展开更多
The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so t...The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so the displacement and stress fields, the stress intensity factor and strain energy release rate were determined. The results show that the stress intensity factor is independent of material constants, and the strain energy release rate is dependent on all material constants. These provide important information for studying the deformation and fracture of the new solid material.展开更多
Aim To determine numerically the field characteristics in the vied at the tip of a place crack growing steadily in a power-law hardening material. Meteods. Methods on the Euler mode and small-scale yield assumption, t...Aim To determine numerically the field characteristics in the vied at the tip of a place crack growing steadily in a power-law hardening material. Meteods. Methods on the Euler mode and small-scale yield assumption, the numerical results were given by nonlinear finite element analysis. Results The numerical results of the shape of the active plastic sone, the angular distribution of stresseses and Clack tip opening displacement (CTOD) in the vicinity at the hp of the steadily groWing CraCk are determined. Conclusion The comparison between the numerical results given by the present wort and those given by analytic asymptotic analysis shows that the present work reached a very high accuracy.展开更多
Crack line field analysis method has become an independent method for crack elastic-plastic analysis, which greatly simplifies the complexity of crack elastic-plastic problems and overcomes the corresponding mathemati...Crack line field analysis method has become an independent method for crack elastic-plastic analysis, which greatly simplifies the complexity of crack elastic-plastic problems and overcomes the corresponding mathematical difficulty. With this method, the precise elastic-plastic solutions near crack lines for variety of crack problems can be obtained. But up to now all solutions obtained by this method were for different concrete problems, no general steps and no general form of matching equations near crack line are given out. With crack line analysis method, this paper proposes the general steps of elastic plastic analysis near crack line for mode I crack in elastic-perfectly plastic solids under plane stress condition, and in turn given out the solving process and result for a specific problem.展开更多
This paper presents an exact solution for the transverse interface crack in the plane strain case. The crack is perpendicular to the interface and in one material. The exact complex stress functions are first obtained...This paper presents an exact solution for the transverse interface crack in the plane strain case. The crack is perpendicular to the interface and in one material. The exact complex stress functions are first obtained with some unknown constants. The satisfactions of all boundary conditions are then checked, the condition at infinity is considered and the unknown constants are determined. Further study may focus on the case with different shear moduli and the influence of the large deformation.展开更多
In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method （F2LFEM）. The general solutio...In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method （F2LFEM）. The general solution of an orthotropic crack problem is obtained by assimilating the problem with isotropic crack problem, and is employed as the global interpolation function in F2LFEM. In the neighborhood of crack tip of the crack plate, the fractal geometry concept is introduced to achieve the similar meshes having similarity ratio less than one and generate an infinitesimal mesh so that the relationship between the stiffness matrices of two adjacent layers is equal. A large number of degrees of freedom around the crack tip are transformed to a small set of generalized coordinates. Numerical examples show that this method is efficient and accurate in evaluating the stress intensity factor （SIF）.展开更多
The crack tip stress-strain fields of the elastic-plastic cracked specimens have been analyzed using finite element calculations.The crack initiation and steady propagation behaviours have also been investigated by me...The crack tip stress-strain fields of the elastic-plastic cracked specimens have been analyzed using finite element calculations.The crack initiation and steady propagation behaviours have also been investigated by means of slip line pattern etching technique and mechanical tests. The results show that there are HRR near field and distant field in the crack tip region,and the later depends on the specimen configuration.The crack initiation behaviour is controlled by a single parameter J.In contrast,the steady crack propagation is affected by the distant strain field and can not be described by single parameter only.展开更多
The problem of scattering of SH-wave by a circular cavity and an arbitrary beeline crack in right-angle plane was investigated using the methods of Green's function,complex variables and muti-polar coordinates.Fir...The problem of scattering of SH-wave by a circular cavity and an arbitrary beeline crack in right-angle plane was investigated using the methods of Green's function,complex variables and muti-polar coordinates.Firstly,we constructed a suitable Green's function,which is an essential solution to the displacement field for the elastic right-angle plane possessing a circular cavity while bearing out-of-plane harmonic line source load at arbitrary point.Secondly,based on the method of crack-division,integration for solution was established,then expressions of displacement and stress were obtained while crack and circular cavities were both in existence.Finally,the dynamic stress concentration factor around the circular cavity and the dynamic stress intensity factor at crack tip were discussed to the cases of different parameters in numerical examples.Calculation results show that the crack produces adverse engineering influence on both of the dynamic stress concentration factor and the dynamic stress intensity factor.展开更多
The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress intensity factor at the crack-tip is computed. The scattering problem can be d...The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress intensity factor at the crack-tip is computed. The scattering problem can be decomposed into two problems: one is the reflection and refraction problem of general SH plane waves at perfect interface (with no crack); another is the scattering problem due to the existence of crack. For the first problem, the viscoelastic wave equation, displacement and stress continuity conditions across the interface are used to obtain the shear stress distribution at the interface. For the second problem, the integral transformation method is used to reduce the scattering problem into dual integral equations. Then, the dual integral equations are transformed into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Finally, the singular integral equation is solved by Kurtz's piecewise continuous function method. As a consequence, the crack opening displacement and dynamic stress intensity factor are obtained. At the end of the paper, a numerical example is given. The effects of incident angle, incident frequency and viscoelastic material parameters are analyzed. It is found that there is a frequency region for viscoelastic material within which the viscoelastic effects cannot be ignored.展开更多
The near crack line analysis method has been used in the present paper,The classical small scale yielding conditions have been completely abandoned in the analyses and one inappropriate matching condition used to be u...The near crack line analysis method has been used in the present paper,The classical small scale yielding conditions have been completely abandoned in the analyses and one inappropriate matching condition used to be used at the elasticplastic boundary has been corrected.The reasonable solution of the plastic stresses near the crack line region has been established.By matching the plastic stresses with the exact elastic stresses at the elastic-plastic boundary,the plastic stresses the length of the plastic zone and the unit normal vector of the elastic-plastic boundary near the crock line region have been obtained for a mode I crack under uniaxial tension,as well as a mode I crack under biaxial tension,which shows that for both conditions the plastic stress componentsσy, and σsy.he length of the plastic zone and the unit normal vector of the elastic-plastic boundary are quite the same while the plastic stress σs is different.展开更多
Finite element computations are carried out to simulate plane strain crack growth on a bimaterial interface under the assumption of small scale yielding.The modified Guron constitutive equation and the element vanish ...Finite element computations are carried out to simulate plane strain crack growth on a bimaterial interface under the assumption of small scale yielding.The modified Guron constitutive equation and the element vanish technique introduced by Tvergaard et al.are used to model the final formation of an open crack.It is found from the calculation that the critical fracture toughness for crack growth is much low- er in bimaterials than that in homogeneous material.The critical fracture toughness is strongly dependent on material properties of the bimaterial pair and the mixed mode of remote loads.The interface crack grows in the more compliant(lower hardening)material or in the weaker(lower yield strength)material.In Mode-Ⅰ loading,the crack grows zigzag along the interface.展开更多
The dynamic stress intensity factor history for a half plane crack in an otherwise unbounded elastic body, with the crack faces subjected to a traction distribution consisting of two pairs of suddenly-applied shear li...The dynamic stress intensity factor history for a half plane crack in an otherwise unbounded elastic body, with the crack faces subjected to a traction distribution consisting of two pairs of suddenly-applied shear line loads is consid- ered. The analytic expression for the combined mode stress intensity factors as a function of time is obtained. The method of solution is based on the application of integral transforms and the Wiener-Hopf technique. Some features of the solutions are discussed and graphical numerical results are presented.展开更多
Based on the complex potential method, the Greed’s functions of the plane problem in transversely isotropic piezoelectric media with an elliptic hole are obtained in terms of exact electric boundary conditions at th...Based on the complex potential method, the Greed’s functions of the plane problem in transversely isotropic piezoelectric media with an elliptic hole are obtained in terms of exact electric boundary conditions at the rim of the hole. When foe elliptic hole degenerates into a crack, the fundamental solutions for the field intensity factors arc given. The general solutions for concentrated and distributed loads applied on the surface of the hole or crack are produced through the superposition of fundamental solutions With the aid of these solutions , some erroneous results provided previously in other works are pointed out More important is that these solutions can be used as the fundamental solutions of boundary element method to solve more practical problems in piezoelectric media.展开更多
The mathematical problem of an infinite elastic plane consisting of three different media with an arbitrary number of cracks is considered. It is reduced to singular integral equations along the interfaces and the cra...The mathematical problem of an infinite elastic plane consisting of three different media with an arbitrary number of cracks is considered. It is reduced to singular integral equations along the interfaces and the cracks by a constructive method. Those along the interfaces are further reduced to Fredholm ones.展开更多
Exact solutions in elementary functions are derived for the stress and electric displacement intensity factors of a half-plane crack in a transversely isotropic piezoelectric space interacting with various resultant s...Exact solutions in elementary functions are derived for the stress and electric displacement intensity factors of a half-plane crack in a transversely isotropic piezoelectric space interacting with various resultant sources, including force dipole, electric dipole, moment, force dilatation and rotation. Such force and charge sources may model defects like vacancies, foreign particles and dislocations. The locations and orientations of the stress and charge sources with respect to the crack are arbitrary.展开更多
An exact and complete solution of the problem of a half-planecrack in an infinite transversely isotropic piezoelectric body ispresented. The upper and lower crack faces are assumed to be loadedantisym- metrically by a...An exact and complete solution of the problem of a half-planecrack in an infinite transversely isotropic piezoelectric body ispresented. The upper and lower crack faces are assumed to be loadedantisym- metrically by a couple of tangential point forces inopposite directions. The solution is derived through a lim- itingprocedure from that of a penny-shaped crack. The expressions for theelectroelastic field are given in terms of elementary functions.Finally, the numerical results of the second and third mode stressintensity factors k_2 and k_3 of piezoelectric materials and elasticmaterials are compared in figures.展开更多
文摘In this paper, the crack initiation characteristics of compression-shear plane crack with hydraulic pressure were studied by using theoretical analysis and experimental verification methods. The formula derivation process of stress intensity factor of crack tip and open-type crack initiation angle and initiation strength was expounded in detail. Cement mortar specimens prefabricated with open-type crack were made for biaxial compression test. The results show that the mode I stress intensity factor is inversely proportional to the dip angle of pre-exciting crack, water pressure and crack width. The fracture toughness is most easily achieved when the dip angle of pre-exciting crack is 60°. The mode II stress intensity factor is symmetrically distributed with the dip angle and independent of the water pressure and crack width. For open-type crack, the crack initiation angle decreases with the increase of the dip angle of pre-exciting crack, water pressure and crack width;the crack initiation strength is inversely proportional to the water pressure and proportional to the lateral pressure. The research results can provide ideas for the study of crack initiation under the coupling of ground stress and osmotic pressure in tunnel engineering.
基金supports from the National Natural Science Foundation of China (Grant Nos.52004143 and 52374095)the open fund for the Laboratory of Mining Response and Disaster Prevention and Control in Deep Coal Mines (Grant No.SKLMRDPC21KF06).
文摘A series of true triaxial unloading tests are conducted on sandstone specimens with a single structural plane to investigate their mechanical behaviors and failure characteristics under different in situ stress states.The experimental results indicate that the dip angle of structural plane(θ)and the intermediate principal stress(σ2)have an important influence on the peak strength,cracking mode,and rockburst severity.The peak strength exhibits a first increase and then decrease as a function ofσ2 for a constantθ.However,whenσ2 is constant,the maximum peak strength is obtained atθof 90°,and the minimum peak strength is obtained atθof 30°or 45°.For the case of an inclined structural plane,the crack type at the tips of structural plane transforms from a mix of wing and anti-wing cracks to wing cracks with an increase inσ2,while the crack type around the tips of structural plane is always anti-wing cracks for the vertical structural plane,accompanied by a series of tensile cracks besides.The specimens with structural plane do not undergo slabbing failure regardless ofθ,and always exhibit composite tensile-shear failure whatever theσ2 value is.With an increase inσ2 andθ,the intensity of the rockburst is consistent with the tendency of the peak strength.By analyzing the relationship between the cohesion(c),internal friction angle(φ),andθin sandstone specimens,we incorporateθinto the true triaxial unloading strength criterion,and propose a modified linear Mogi-Coulomb criterion.Moreover,the crack propagation mechanism at the tips of structural plane,and closure degree of the structural plane under true triaxial unloading conditions are also discussed and summarized.This study provides theoretical guidance for stability assessment of surrounding rocks containing geological structures in deep complex stress environments.
基金supported by the National Natural Science Foundation of China(Grant No.52278333)the China Scholarship Council(CSC)and the Science and Technology Department of Liaoning Province(Grant No.2024JH2/102500069).
文摘Peridynamics(PD)is an effective method for simulating the spontaneous initiation and propagation of tensile cracks in materials.However,it faces great challenges in simulating compression-shear cracking of geomaterials due to the lack of efficient contact-friction models.This paper introduces an original contact-friction model that leverages twin mesh and potential function principles within PD to model rock cracking under tensile and compressive stresses.The contact detection algorithm,based on space segmentation axis-aligned bounding box(AABB)tree data structure,is used to address the significant challenge of highly efficient contact detection in compression and shear problems.In this method,the twin mesh and potential function are utilized to quantify contact detection and contact degree,as well as friction behavior.This is in contrast to the distance and circular contact area model,which lacks physical significance in the classical PD method.As demonstrated by the tests on specimens containing cracks,the proposed model can capture 8 types of secondary fractures,reduce the contact detection error by about 29%e56%,and increase the contact retrieval efficiency by over 1600 times compared to the classic PD models.This significantly enhances the capability of PD to simulate the initiation,expansion,and coalescence of intricate compression-shear cracks.
基金financially supported by National Natural Science Foundation of China(Project No.51878156,received by Wenwei Wang).
文摘To meticulously dissect the cracking issue in the transverse diaphragm concrete,situated at the anchor point of a colossal large-span,single cable plane cable-stayed bridge,this research paper adopts an innovative layered modeling analysis methodology for numerical simulations.The approach is structured into three distinct layers,each tailored to address specific aspects of the cracking phenomenon.The foundational first layer model operates under the assumption of linear elasticity,adhering to the Saint Venant principle.It narrows its focus to the crucial zone between the Bp20 transverse diaphragm and the central axis of pier 4’s support,encompassing the critically cracked diaphragm beneath the N1 cable anchor.This layer provides a preliminary estimate of potential cracking zones within the concrete,serving as a baseline for further analysis.The second layer model builds upon this foundation by incorporating material plasticity into its considerations.It pinpoints its investigation to the immediate vicinity of the cracked transverse diaphragm associated with the N1 cable,aiming to capture the intricate material behavior under stress.This layer’s predictions of crack locations and patterns exhibit a remarkable alignment with actual detection results,confirming its precision and reliability.The third and most intricate layer delves deep into the heart of the matter,examining the cracked transverse diaphragm precisely where the cable force attains its maximum intensity.By leveraging advanced extended finite element technology,this layer offers an unprecedented level of detail in tracing the progression of concrete cracks.Its findings reveal a close correlation between predicted and observed crack widths,validating the model’s proficiency in simulating real-world cracking dynamics.Crucially,the boundary conditions for each layer are meticulously aligned with those of the overarching model,ensuring consistency and integrity throughout the analysis.These results not only enrich our understanding of the cracking mechanisms but also underscore the efficacy of reinforcing cracked concrete sections with external steel plates.In conclusion,this study represents a significant contribution to the field of bridge engineering,offering both theoretical insights and practical solutions for addressing similar challenges.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.52225402,U1910206)the National Key Research and Development Project of China(Grant No.2022YFC3004602).
文摘The fracture network of hydraulic crack is significantly influenced by the bedding plane in coalbed methane extraction.Under mode Ⅱ loading,crack deflection holds a key position in hydraulic cracking,especially in hydraulic shearing.This study first analyzed the crack deflection theory of layered rock.The semi-circle bending test under asymmetric loading is performed,and the four-dimensional Lattice Spring Model(4D-LSM)is established to examine how the bedding parameters affect coal crack propagation under mode Ⅱ dominant loads.The 4D-LSM results are comparable to the coal loading test results under quasi-mode Ⅱ and the analytical prediction of crack deflection theory.During mode Ⅱ loading,the coal crack propagation is greatly influenced by the angle,strength,and elastic modulus of the bedding plane,while the effects of thickness and spacing of bedding are insignificant.The crack of coal tends to propagate towards the bedding,following a decrease in bedding angle,a decrease in bedding strength,and an increase in elastic modulus.With higher bedding strength,spacing,and thickness,the peak load on the coal sample is higher.The influences of bedding strength,elastic modulus,spacing,and thickness on the peak load of coal samples and its anisotropy gradually decrease.It is proved that compared with the tangential stress ratio and traditional energy release ratio theories,the corrected energy release ratio criterion can more accurately predict the direction of crack deflection of coal,especially under mode Ⅱ loading.The results can provide assistance in the design of initiation pressure and fracturing direction in coal seam hydraulic fracturing.
文摘The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so the displacement and stress fields, the stress intensity factor and strain energy release rate were determined. The results show that the stress intensity factor is independent of material constants, and the strain energy release rate is dependent on all material constants. These provide important information for studying the deformation and fracture of the new solid material.
文摘Aim To determine numerically the field characteristics in the vied at the tip of a place crack growing steadily in a power-law hardening material. Meteods. Methods on the Euler mode and small-scale yield assumption, the numerical results were given by nonlinear finite element analysis. Results The numerical results of the shape of the active plastic sone, the angular distribution of stresseses and Clack tip opening displacement (CTOD) in the vicinity at the hp of the steadily groWing CraCk are determined. Conclusion The comparison between the numerical results given by the present wort and those given by analytic asymptotic analysis shows that the present work reached a very high accuracy.
文摘Crack line field analysis method has become an independent method for crack elastic-plastic analysis, which greatly simplifies the complexity of crack elastic-plastic problems and overcomes the corresponding mathematical difficulty. With this method, the precise elastic-plastic solutions near crack lines for variety of crack problems can be obtained. But up to now all solutions obtained by this method were for different concrete problems, no general steps and no general form of matching equations near crack line are given out. With crack line analysis method, this paper proposes the general steps of elastic plastic analysis near crack line for mode I crack in elastic-perfectly plastic solids under plane stress condition, and in turn given out the solving process and result for a specific problem.
文摘This paper presents an exact solution for the transverse interface crack in the plane strain case. The crack is perpendicular to the interface and in one material. The exact complex stress functions are first obtained with some unknown constants. The satisfactions of all boundary conditions are then checked, the condition at infinity is considered and the unknown constants are determined. Further study may focus on the case with different shear moduli and the influence of the large deformation.
文摘In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method （F2LFEM）. The general solution of an orthotropic crack problem is obtained by assimilating the problem with isotropic crack problem, and is employed as the global interpolation function in F2LFEM. In the neighborhood of crack tip of the crack plate, the fractal geometry concept is introduced to achieve the similar meshes having similarity ratio less than one and generate an infinitesimal mesh so that the relationship between the stiffness matrices of two adjacent layers is equal. A large number of degrees of freedom around the crack tip are transformed to a small set of generalized coordinates. Numerical examples show that this method is efficient and accurate in evaluating the stress intensity factor （SIF）.
文摘The crack tip stress-strain fields of the elastic-plastic cracked specimens have been analyzed using finite element calculations.The crack initiation and steady propagation behaviours have also been investigated by means of slip line pattern etching technique and mechanical tests. The results show that there are HRR near field and distant field in the crack tip region,and the later depends on the specimen configuration.The crack initiation behaviour is controlled by a single parameter J.In contrast,the steady crack propagation is affected by the distant strain field and can not be described by single parameter only.
文摘The problem of scattering of SH-wave by a circular cavity and an arbitrary beeline crack in right-angle plane was investigated using the methods of Green's function,complex variables and muti-polar coordinates.Firstly,we constructed a suitable Green's function,which is an essential solution to the displacement field for the elastic right-angle plane possessing a circular cavity while bearing out-of-plane harmonic line source load at arbitrary point.Secondly,based on the method of crack-division,integration for solution was established,then expressions of displacement and stress were obtained while crack and circular cavities were both in existence.Finally,the dynamic stress concentration factor around the circular cavity and the dynamic stress intensity factor at crack tip were discussed to the cases of different parameters in numerical examples.Calculation results show that the crack produces adverse engineering influence on both of the dynamic stress concentration factor and the dynamic stress intensity factor.
基金This work was supported by the National Natural Science Foundation of China(No.19772064)by the project of CAS KJ 951-1-20
文摘The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress intensity factor at the crack-tip is computed. The scattering problem can be decomposed into two problems: one is the reflection and refraction problem of general SH plane waves at perfect interface (with no crack); another is the scattering problem due to the existence of crack. For the first problem, the viscoelastic wave equation, displacement and stress continuity conditions across the interface are used to obtain the shear stress distribution at the interface. For the second problem, the integral transformation method is used to reduce the scattering problem into dual integral equations. Then, the dual integral equations are transformed into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Finally, the singular integral equation is solved by Kurtz's piecewise continuous function method. As a consequence, the crack opening displacement and dynamic stress intensity factor are obtained. At the end of the paper, a numerical example is given. The effects of incident angle, incident frequency and viscoelastic material parameters are analyzed. It is found that there is a frequency region for viscoelastic material within which the viscoelastic effects cannot be ignored.
文摘The near crack line analysis method has been used in the present paper,The classical small scale yielding conditions have been completely abandoned in the analyses and one inappropriate matching condition used to be used at the elasticplastic boundary has been corrected.The reasonable solution of the plastic stresses near the crack line region has been established.By matching the plastic stresses with the exact elastic stresses at the elastic-plastic boundary,the plastic stresses the length of the plastic zone and the unit normal vector of the elastic-plastic boundary near the crock line region have been obtained for a mode I crack under uniaxial tension,as well as a mode I crack under biaxial tension,which shows that for both conditions the plastic stress componentsσy, and σsy.he length of the plastic zone and the unit normal vector of the elastic-plastic boundary are quite the same while the plastic stress σs is different.
基金Project supported by Fok Ying-Tung Education Foundation National Natural Science Foundation of China.
文摘Finite element computations are carried out to simulate plane strain crack growth on a bimaterial interface under the assumption of small scale yielding.The modified Guron constitutive equation and the element vanish technique introduced by Tvergaard et al.are used to model the final formation of an open crack.It is found from the calculation that the critical fracture toughness for crack growth is much low- er in bimaterials than that in homogeneous material.The critical fracture toughness is strongly dependent on material properties of the bimaterial pair and the mixed mode of remote loads.The interface crack grows in the more compliant(lower hardening)material or in the weaker(lower yield strength)material.In Mode-Ⅰ loading,the crack grows zigzag along the interface.
基金The project supported by the National Natural Science Foundation of China
文摘The dynamic stress intensity factor history for a half plane crack in an otherwise unbounded elastic body, with the crack faces subjected to a traction distribution consisting of two pairs of suddenly-applied shear line loads is consid- ered. The analytic expression for the combined mode stress intensity factors as a function of time is obtained. The method of solution is based on the application of integral transforms and the Wiener-Hopf technique. Some features of the solutions are discussed and graphical numerical results are presented.
文摘Based on the complex potential method, the Greed’s functions of the plane problem in transversely isotropic piezoelectric media with an elliptic hole are obtained in terms of exact electric boundary conditions at the rim of the hole. When foe elliptic hole degenerates into a crack, the fundamental solutions for the field intensity factors arc given. The general solutions for concentrated and distributed loads applied on the surface of the hole or crack are produced through the superposition of fundamental solutions With the aid of these solutions , some erroneous results provided previously in other works are pointed out More important is that these solutions can be used as the fundamental solutions of boundary element method to solve more practical problems in piezoelectric media.
基金Project supported by the Science Fund of the Chinese Academy of Sciences
文摘The mathematical problem of an infinite elastic plane consisting of three different media with an arbitrary number of cracks is considered. It is reduced to singular integral equations along the interfaces and the cracks by a constructive method. Those along the interfaces are further reduced to Fredholm ones.
基金Project supported by the National Natural Science Foundation of China (No. 10172075)the Yu-Ying Foundation of Hunan University.
文摘Exact solutions in elementary functions are derived for the stress and electric displacement intensity factors of a half-plane crack in a transversely isotropic piezoelectric space interacting with various resultant sources, including force dipole, electric dipole, moment, force dilatation and rotation. Such force and charge sources may model defects like vacancies, foreign particles and dislocations. The locations and orientations of the stress and charge sources with respect to the crack are arbitrary.
基金the National Natural Science Foundation of China(No.19872060 and 69982009)the Postdoctoral Foundation of China
文摘An exact and complete solution of the problem of a half-planecrack in an infinite transversely isotropic piezoelectric body ispresented. The upper and lower crack faces are assumed to be loadedantisym- metrically by a couple of tangential point forces inopposite directions. The solution is derived through a lim- itingprocedure from that of a penny-shaped crack. The expressions for theelectroelastic field are given in terms of elementary functions.Finally, the numerical results of the second and third mode stressintensity factors k_2 and k_3 of piezoelectric materials and elasticmaterials are compared in figures.
