Taylor stochastic finite element method (SFEM) is applied to analyze the uncertainty of plane multiple cracks stress intensity factors (SIFs) considering the uncertainties of material properties, crack length, and loa...Taylor stochastic finite element method (SFEM) is applied to analyze the uncertainty of plane multiple cracks stress intensity factors (SIFs) considering the uncertainties of material properties, crack length, and load. The stochastic finite element model of plane multiple cracks are presented. In this model, crack tips are meshed with six-node triangular quarter-point elements; and other area is meshed with six-node triangular elements. The partial derivatives of displacement and stiffness matrix with resp...展开更多
The maximum Mode Ⅰ and Mode Ⅱ stress intensity factors(SIFs), KI,kmax(θ) and KII,kmax(θ)(0°<θ<360°), of inclined parallel multi-crack varying with relative positions(including horizontal and verti...The maximum Mode Ⅰ and Mode Ⅱ stress intensity factors(SIFs), KI,kmax(θ) and KII,kmax(θ)(0°<θ<360°), of inclined parallel multi-crack varying with relative positions(including horizontal and vertical spacings) are calculated by the complex function and integration method to analyze their interacting mechanism and determine the strengthening and weakening zone of SIFs. The multi-crack initiation criterion is established based on the ratio of maximum tension-shear SIF to predict crack initiation angle, load, and mechanism. The results show that multi-crack always initiates in Mode Ⅰ and the vertical spacing is better not to be times of half crack-length for crack-arrest, which is in good agreement with test results of the red-sandstone cube specimens with three parallel cracks under uniaxial compression. This can prove the validity of the multi-crack initiation criterion.展开更多
Multiple crack identification plays an important role in vibration-based crack identification of structures. Traditional crack detection method of single crack is difficult to be used in multiple crack diagnosis. A th...Multiple crack identification plays an important role in vibration-based crack identification of structures. Traditional crack detection method of single crack is difficult to be used in multiple crack diagnosis. A three-step-meshing method for the multiple cracks identification in structures is presented. Firstly, the changes in natural frequency of a structure with various crack locations and depth are accurately obtained by means of wavelet finite element method, and then the damage coefficient method is used to determine the number and the region of cracks. Secondly, different regions in the cracked structure are divided into meshes with different scales, and then the small unit containing cracks in the damaged area is gradually located by iterative computation. Lastly, by finding the points of intersection of three frequency contour lines in the small unit, the crack location and depth are identified. In order to verify the effectiveness of the presented method, a multiple cracks identification experiment is carried out. The diagnostic tests on a cantilever beam under two working conditions show the accuracy of the proposed method： with a maximum error of crack location identification 2.7% and of depth identification 5.2%. The method is able to detect multiple crack of beam with less subdivision and higher precision, and can be developed as a multiple crack detection approach for complicated structures.展开更多
Partition of unity based numerical manifold method can solve continuous and discontinuous problems in a unified framework with a two-cover system,i.e.,the mathematical cover and physical cover.However,renewal of the t...Partition of unity based numerical manifold method can solve continuous and discontinuous problems in a unified framework with a two-cover system,i.e.,the mathematical cover and physical cover.However,renewal of the topology of the two-cover system poses a challenge for multiple crack propagation problems and there are few references.In this study,a robust and efficient strategy is proposed to update the cover system of the numerical manifold method in simulation of multiple crack propagation problems.The proposed algorithm updates the cover system with a bottom-up process:1)identification of fractured manifold elements according to the previous and latest crack tip position;and 2)local topological update of the manifold elements,physical patches,block boundary loops,and non-persistent joint loops according to the scenario classification of the propagating crack.The proposed crack tracking strategy and classification of the renewal cases promote a robust and efficient cover renewal algorithm for multiple crack propagation analysis.Three crack propagation examples show that the proposed algorithm performs well in updating the cover system.This cover renewal methodology can be extended for numerical manifold method with polygonal mathematical covers.展开更多
How to simulate fracture mode and crack propagation path in a plate with multiple cracks is an attractive but difficult issue in fracture mechanics.Peridynamics is a recently developed nonlocal continuum formulation t...How to simulate fracture mode and crack propagation path in a plate with multiple cracks is an attractive but difficult issue in fracture mechanics.Peridynamics is a recently developed nonlocal continuum formulation that can spontaneously predict the crack nucleation,branch and propagation in materials and structures through a meshfree discrete technique.In this paper,the peridynamic motion equation with boundary traction is improved by simplifying the boundary transfer functions.We calculate the critical cracking load and the fracture angles of the plate with multiple cracks under uniaxial tension.The results are consistent with those predicted by classical fracture mechanics.The fracture mode and crack propagation path are also determined.The calculation shows that the brittle fracture process of the plate with multiple cracks can be conveniently and correctly simulated by the peridynamic motion equation with boundary conditions.展开更多
The concept of eigen crack opening displacement （COD） can be defined as the COD of a crack in infinite plate under the tractions acting on the crack surface. By introducing this concept, the eigen COD formulation of...The concept of eigen crack opening displacement （COD） can be defined as the COD of a crack in infinite plate under the tractions acting on the crack surface. By introducing this concept, the eigen COD formulation of boundary integral equation is proposed in this paper, together with the solution procedures for multiple crack problems in plane elasticity. With the proposed approach, the multiple crack problems can be solved with the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix as that in the numerical Green’s function （NGF） approach but without the trouble to determine the complementary solutions since the standard boundary element discretization on the crack surface is no longer required with the proposed approach. Some numerical examples computing the stress intensity factors are presented and compared with those in literature to show the accuracy and the effectiveness of the proposed approach.展开更多
This paper presents a numerical solution to model multiple cracks in a finite plate of an elastic isotropic material. Both the boundaries and the cracks are modeled by distributed dislocations. This method results in ...This paper presents a numerical solution to model multiple cracks in a finite plate of an elastic isotropic material. Both the boundaries and the cracks are modeled by distributed dislocations. This method results in a system of singular integral equations with Cauchy kernels which can be solved by Gauss-Chebyshev quadrature method. Four examples are provided to assess the capability of this method.展开更多
This article examines the interaction of multiple cracks in an infinite plate by using a numerical method. The numerical method consists of the non-singular displacement discontinuity element presented by Crouch and S...This article examines the interaction of multiple cracks in an infinite plate by using a numerical method. The numerical method consists of the non-singular displacement discontinuity element presented by Crouch and Startled and the crack tip displacement discontinuity elements proposed by the author. In the numerical method implementation, the left or the right crack tip element is placed locally at the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. The numerical method is called a hybrid displacement discontinuity method. The following test examples of crack problems in an infinite plate under tension are included： “ center-inclined cracked plate”, “interaction of two collinear cracks with equal length”, “interaction of three collinear cracks with equal length”, “interaction of two parallel cracks with equal length”, and “interaction of one horizontal crack and one inclined crack”. The present numerical results show that the numerical method is simple yet very accurate for analyzing the interaction of multiple cracks in an infinite plate.展开更多
A newly developed approach without crack surface discretization for modeling 2D solids with large number of cracks in linear elastic fracture mechanics is proposed with the eigen crack opening displacement (COD) bound...A newly developed approach without crack surface discretization for modeling 2D solids with large number of cracks in linear elastic fracture mechanics is proposed with the eigen crack opening displacement (COD) boundary integral equations in this paper. The eigen COD is defined as a crack in an infinite domain under fictitious traction acting on the crack surface. Respect to the computational accuracies and efficiencies, the multiple crack problems in finite and infinite plates are solved and compared numerically using three different kinds of boundary integral equations (BIEs): 1) the dual BIEs require crack surface discretization;2) the BIEs with numerical Green’s functions (NGF) without crack surface discretization, but have to solve a complementary matrix;3) the eigen crack opening displacement (COD) BIEs in the present paper. With the concept of eigen COD, the multiple crack problems can be solved by using a conventional displacement discontinuity boundary integral equation in an iterative fashion with a small size of system matrix as that in the NGF approach, but without troubles to determine the complementary matrix. Solution of the stress intensity factors of multiple crack problems is solved and compared in some numerical examples using the above three computational algorithms. Numerical results clearly demonstrate the numerical models of eigen COD BIEs have much higher efficiency, providing a newly numerical technique for multiple crack problems. Not only the accuracy and efficiency of computation can be guaranteed, but also the overall properties and local details can be obtained. In conclusion, the numerical models of eigen COD BIEs realize the simulations for multiple crack problems with large quantity of cracks.展开更多
This study focused on the buckling characteristics of egg-shaped shells with single crack and double cracks under axial pressure.First,the geometric parameters of the egg-shaped shell were designed,and a numerical mod...This study focused on the buckling characteristics of egg-shaped shells with single crack and double cracks under axial pressure.First,the geometric parameters of the egg-shaped shell were designed,and a numerical model of the egg-shaped shell was established.Then,the initial crack was introduced into the equatorial weld of the egg-shaped shell,and the effects of the crack on the buckling characteristics under different wall thicknesses were explored,as were the effects of the single crack direction,double crack angle and spacing on the buckling characteristics.Finally,crack-free,single crack and double crack egg-shaped shells were fabricated from Q235 steel.The buckling loads and failure modes of the three egg-shaped shells were obtained via axial compression experiments.The numerical critical buckling loads and buckling modes were compared with the experimental results to verify the accuracy of the numerical model.The results of this study are valuable for the design of egg-shaped shells under axial loading.展开更多
Large-grain REBa_(2)Cu_(3)O_(7-δ)(REBCO,RE=rare earth)bulk superconductors offer promising magnetic field trapping capabilities due to their high critical current density,making them ideal for many important applicat...Large-grain REBa_(2)Cu_(3)O_(7-δ)(REBCO,RE=rare earth)bulk superconductors offer promising magnetic field trapping capabilities due to their high critical current density,making them ideal for many important applications such as trapped field magnets.However,for such large-grain superconductor bulks,there are lots of voids and cracks forming during the process of melting preparation,and some of them can be up to hundreds of microns or even millimeters in size.Consequently,these larger size voids/cracks pose a great threat to the strength of the bulks due to the inherent brittleness of superconductor REBCO materials.In order to ensure the operational safety of related superconducting devices with bulk superconductors,it is firstly important to accurately detect these voids/cracks in them.In this paper,we proposed a method for quantitatively evaluating multiple voids/cracks in bulk superconductors through the magnetic field and displacement response signals at superconductor bulk surface.The proposed method utilizes a damage index constructed from the magnetic field signals and displacement responses to identify the number and preliminary location of multiple defects.By dividing the detection area into subdomains and combining the magnetic field signals with displacement responses within each subdomain,a particle swarm algorithm was employed to evaluate the location and size parameters of the defects.In contrast to other evaluation methods using only magnetic field or displacement response signals,the combined evaluation method using both signals can identify the number of cracks effectively.Numerical studies demonstrate that the morphology of voids and cracks reconstructed using the proposed algorithm ideally matches real defects and is applicable to cases where voids and cracks coexist.This study provides a theoretical basis for the quantitative detection of voids/cracks in bulk superconductors.展开更多
Longitudinal cracks on the tunnel lining significantly influence the performance of tunnels in operation.In this study,we propose a semi-analytical method that provides a simple and effective way to calculate the inte...Longitudinal cracks on the tunnel lining significantly influence the performance of tunnels in operation.In this study,we propose a semi-analytical method that provides a simple and effective way to calculate the internal forces of tunnel linings with multiple cracks.The semi-analytical solution is obtained using structural analysis considering the flexural rigidity for the cracked longitudinal section of the tunnel lining.Then the proposed solution is verified numerically.Using the proposed method,the influences of the crack depth and the number of cracks on the bending moment and modified crack tip stress are investigated.With the increase in crack depth,the bending moment of lining scetion adjacent to the crack decreases,while the bending moment of lining scetion far away from the crack increases slightly.The more the number of cracks in a tunnel lining,the easier the new cracks initiated.展开更多
The stress fields are obtained for a functionally graded half-plane containing a Volterra screw dislocation.The elastic shear modulus of the medium is considered to vary ex-ponentially.The dislocation solution is util...The stress fields are obtained for a functionally graded half-plane containing a Volterra screw dislocation.The elastic shear modulus of the medium is considered to vary ex-ponentially.The dislocation solution is utilized to formulate integral equations for the half-plane weakened by multiple smooth cracks under anti-plane deformation.The integral equations are of Cauchy singular type at the location of dislocation which are solved numerically.Several examples are solved and the stress intensity factors are obtained.展开更多
In this paper, the interactions of multiple parallel symmetric and permeable finite length cracks in a piezoelectric/piezomagnetic material plane subjected to anti-plane shear stress loading are studied by the Schmidt...In this paper, the interactions of multiple parallel symmetric and permeable finite length cracks in a piezoelectric/piezomagnetic material plane subjected to anti-plane shear stress loading are studied by the Schmidt method.The problem is formulated through Fourier transform into dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces.To solve the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials.Finally, the relation between the electric field, the magnetic flux field and the stress field near the crack tips is obtained.The results show that the stress, the electric displacement and the magnetic flux intensity factors at the crack tips depend on the length and spacing of the cracks.It is also revealed that the crack shielding effect presents in piezoelectric/piezomagnetic materials.展开更多
The Schmidt method is adopted to investigate the fracture problem of multiple parallel symmetric and permeable finite length mode-III cracks in a functionally graded piezoelectric/piezomagnetic material plane. This pr...The Schmidt method is adopted to investigate the fracture problem of multiple parallel symmetric and permeable finite length mode-III cracks in a functionally graded piezoelectric/piezomagnetic material plane. This problem is formulated into dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. In order to obtain the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. The results show that the stress, the electric displacement, and the magnetic flux intensity factors of cracks depend on the crack length, the functionally graded parameter, and the distance among the multiple parallel cracks. The crack shielding effect is also obviously presented in a functionally graded piezoelectric/piezomagnetic material plane with mul- tiple parallel symmetric mode-III cracks.展开更多
A method of continuous-discontinuous cellular automaton for modeling the growth and coalescence of multiple cracks in brittle material is presented. The method uses the level set to track arbitrary discontinuities, an...A method of continuous-discontinuous cellular automaton for modeling the growth and coalescence of multiple cracks in brittle material is presented. The method uses the level set to track arbitrary discontinuities, and calculation grids are independent of the discontinuities and no remeshing are required with the crack growing. Based on Grif- fith fracture theory and Mohr-Coulumb criterion, a mixed fracture criterion for multiple cracks growth in brittle mate- rial is proposed. The method treats the junction and coales- cence of multiple cracks, and junction criterion and coales- cence criterion for brittle material are given, too. Besides, in order to overcome the tracking error in the level set ap- proximation for crack junction and coalescence, a dichotomy searching algorithm is proposed. Introduced the above the- ories into continuous-discontinuous cellular automaton, the present method can be applied to solving multiple crack growth in brittle material, and only cell stiffness is needed and no assembled global stiffness is needed. Some numerical examples are given to shown that the present method is efficient and accurate for crack junction, coalescence and percolation problems.展开更多
This paper contains a theoretical formulations and solutions of multiple cracks sub- jected to an anti-plane time-harmonic point load in a functionally graded strip. The distributed dislocation technique is used to co...This paper contains a theoretical formulations and solutions of multiple cracks sub- jected to an anti-plane time-harmonic point load in a functionally graded strip. The distributed dislocation technique is used to construct integral equations for a functionally graded material strip weakened by several cracks under anti-plane time-harmonic load. These equations are of Cauchy singular type at the location of dislocation, which are solved numerically to obtain the dislocation density on the faces of the cracks. The dislocation densities are employed to evaluate the stress intensity factor and strain energy density factors （SEDFs） for multiple cracks with differ- ent configurations. Numerical calculations are presented to show the effects of material properties and the crack configuration on the dynamic stress intensity factors and SEDFs of the functionally graded strip with multiple curved cracks.展开更多
The tensile and flexural properties of polyvinyl alcohol （PVA） fiber reinforced ultra high toughness cementitious composite （UHTCC） were investigated. The composite, tested at the age of 14 d, 28 d and 56 d, shows...The tensile and flexural properties of polyvinyl alcohol （PVA） fiber reinforced ultra high toughness cementitious composite （UHTCC） were investigated. The composite, tested at the age of 14 d, 28 d and 56 d, shows extremely remarkable pseudo strain hardening behavior, saturated multiple cracking and ultra high ultimate strain capacity above 4% under uniaxial loading. Also, the corresponding crack widths are controlled under 50 um even at 56 days age. In the third point bending tests on thin plate specimens, the composite shows ultra high flexural ductility and multiple cracking on the tension surface. The high ultimate flexural strength/first tensile strength ratio of about 5 verifies the pseudo strain hardening behavior of UHTCC. SEM observation on fracture surfaces provides indirect evidence of optimal design for the composite.展开更多
Mechanical behaviors of UHTCC after freezing and thawing were investigated,and compared with those of steel fiber reinforced concrete（SFRC）,air-entrained concrete（AEC） and ordinary concrete（OC）.Four point bendin...Mechanical behaviors of UHTCC after freezing and thawing were investigated,and compared with those of steel fiber reinforced concrete（SFRC）,air-entrained concrete（AEC） and ordinary concrete（OC）.Four point bending tests had been applied after different freezing-thawing cycles（0,50,100,150,200 and 300 cycles,respectively）.The results showed that residual flexural strength of UHTCC after 300 freezing-thawing cycles was 10.62 MPa（70% of no freezing thawing ones）,while 1.58 MPa（17% of no freezing thawing ones） for SFRC.Flexural toughness of UHTCC decreased by 17%,while 70% for SFRC comparatively.It has been demonstrated experimentally that UHTCC without any air-entraining agent could resist freezing-thawing and retain its high toughness characteristic in cold environment.Consequently,UHTCC could be put into practice for new-built or retrofit of infrastructures in cold regions.展开更多
The multiple cracking and deflection hardening performance of polyvinyl alcohol fiber reinforced engineered cementitious composites(PVA-ECC)under four-point flexural loading have been investigated.Matrices with differ...The multiple cracking and deflection hardening performance of polyvinyl alcohol fiber reinforced engineered cementitious composites(PVA-ECC)under four-point flexural loading have been investigated.Matrices with different binder combinations and W/B ratios(from 0.44 to 0.78)providing satisfactory PVA fiber dispersion were specially designed.Effect of pre-existing flaw size distribution modification on deflection hardening behavior was comparatively studied by adding 3 mm diameter polyethylene beads into the mixtures(6%by total volume).Natural flaw size distributions of composites without beads were determined by cross sectional analysis.The crack number and crack width distributions of specimens after flexural loading were characterized and the possible causes of changes in multiple cracking and deflection hardening behavior by flaw size distribution modification were discussed.Promising results from the view point of deflection hardening behavior were obtained from metakaolin incorporated and flaw size distribution modified PVA-ECCs prepared with W/B=0.53.The dual roles of W/B ratio and superplasticizer content on flaw size distribution,cracking potential and fiber-matrix bond behavior were evaluated.Flaw size distribution modification is found beneficial in terms of ductility improvement at an optimized W/B ratio.展开更多
基金National Natural Science Foundation of China (10577015)Chinese Aeronautics Foundation (2006ZD53050, 03B53008)
文摘Taylor stochastic finite element method (SFEM) is applied to analyze the uncertainty of plane multiple cracks stress intensity factors (SIFs) considering the uncertainties of material properties, crack length, and load. The stochastic finite element model of plane multiple cracks are presented. In this model, crack tips are meshed with six-node triangular quarter-point elements; and other area is meshed with six-node triangular elements. The partial derivatives of displacement and stiffness matrix with resp...
基金The authors are grateful for the financial supports from the National Natural Science Foundation of China(51874351,51474251)Hunan Provincial Innovation Foundation For Postgraduate,China(CX2018B047)the Open Sharing Fund for the Large-scale Instruments and Equipments of Central South University,China(CSUZC201923).
文摘The maximum Mode Ⅰ and Mode Ⅱ stress intensity factors(SIFs), KI,kmax(θ) and KII,kmax(θ)(0°<θ<360°), of inclined parallel multi-crack varying with relative positions(including horizontal and vertical spacings) are calculated by the complex function and integration method to analyze their interacting mechanism and determine the strengthening and weakening zone of SIFs. The multi-crack initiation criterion is established based on the ratio of maximum tension-shear SIF to predict crack initiation angle, load, and mechanism. The results show that multi-crack always initiates in Mode Ⅰ and the vertical spacing is better not to be times of half crack-length for crack-arrest, which is in good agreement with test results of the red-sandstone cube specimens with three parallel cracks under uniaxial compression. This can prove the validity of the multi-crack initiation criterion.
基金supported by National Natural Science Foundation of China(Grant Nos. 11176024, 51035007)National Basic Research Program of China(973 Program, Grant No. 2011CB706805)Open Research Fund Program of Hunan Provincial Key Laboratory of Health Maintenance for Mechanical Equipment, China
文摘Multiple crack identification plays an important role in vibration-based crack identification of structures. Traditional crack detection method of single crack is difficult to be used in multiple crack diagnosis. A three-step-meshing method for the multiple cracks identification in structures is presented. Firstly, the changes in natural frequency of a structure with various crack locations and depth are accurately obtained by means of wavelet finite element method, and then the damage coefficient method is used to determine the number and the region of cracks. Secondly, different regions in the cracked structure are divided into meshes with different scales, and then the small unit containing cracks in the damaged area is gradually located by iterative computation. Lastly, by finding the points of intersection of three frequency contour lines in the small unit, the crack location and depth are identified. In order to verify the effectiveness of the presented method, a multiple cracks identification experiment is carried out. The diagnostic tests on a cantilever beam under two working conditions show the accuracy of the proposed method： with a maximum error of crack location identification 2.7% and of depth identification 5.2%. The method is able to detect multiple crack of beam with less subdivision and higher precision, and can be developed as a multiple crack detection approach for complicated structures.
基金Project(51321065,51479191,11672360)supported by the National Natural Science Foundation of China。
文摘Partition of unity based numerical manifold method can solve continuous and discontinuous problems in a unified framework with a two-cover system,i.e.,the mathematical cover and physical cover.However,renewal of the topology of the two-cover system poses a challenge for multiple crack propagation problems and there are few references.In this study,a robust and efficient strategy is proposed to update the cover system of the numerical manifold method in simulation of multiple crack propagation problems.The proposed algorithm updates the cover system with a bottom-up process:1)identification of fractured manifold elements according to the previous and latest crack tip position;and 2)local topological update of the manifold elements,physical patches,block boundary loops,and non-persistent joint loops according to the scenario classification of the propagating crack.The proposed crack tracking strategy and classification of the renewal cases promote a robust and efficient cover renewal algorithm for multiple crack propagation analysis.Three crack propagation examples show that the proposed algorithm performs well in updating the cover system.This cover renewal methodology can be extended for numerical manifold method with polygonal mathematical covers.
基金The work was supported by the National Nature Science Foundation of China through the Grant Nos.12072145 and 11672129.
文摘How to simulate fracture mode and crack propagation path in a plate with multiple cracks is an attractive but difficult issue in fracture mechanics.Peridynamics is a recently developed nonlocal continuum formulation that can spontaneously predict the crack nucleation,branch and propagation in materials and structures through a meshfree discrete technique.In this paper,the peridynamic motion equation with boundary traction is improved by simplifying the boundary transfer functions.We calculate the critical cracking load and the fracture angles of the plate with multiple cracks under uniaxial tension.The results are consistent with those predicted by classical fracture mechanics.The fracture mode and crack propagation path are also determined.The calculation shows that the brittle fracture process of the plate with multiple cracks can be conveniently and correctly simulated by the peridynamic motion equation with boundary conditions.
基金supported by the National Natural Science Foundation of China (Grant No.10972131)the Graduate Innovation Foundation of Shanghai University (Grant No.SHUCX102351)
文摘The concept of eigen crack opening displacement （COD） can be defined as the COD of a crack in infinite plate under the tractions acting on the crack surface. By introducing this concept, the eigen COD formulation of boundary integral equation is proposed in this paper, together with the solution procedures for multiple crack problems in plane elasticity. With the proposed approach, the multiple crack problems can be solved with the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix as that in the numerical Green’s function （NGF） approach but without the trouble to determine the complementary solutions since the standard boundary element discretization on the crack surface is no longer required with the proposed approach. Some numerical examples computing the stress intensity factors are presented and compared with those in literature to show the accuracy and the effectiveness of the proposed approach.
基金supported by National Natural Science Foundation of China(No.51174162)
文摘This paper presents a numerical solution to model multiple cracks in a finite plate of an elastic isotropic material. Both the boundaries and the cracks are modeled by distributed dislocations. This method results in a system of singular integral equations with Cauchy kernels which can be solved by Gauss-Chebyshev quadrature method. Four examples are provided to assess the capability of this method.
文摘This article examines the interaction of multiple cracks in an infinite plate by using a numerical method. The numerical method consists of the non-singular displacement discontinuity element presented by Crouch and Startled and the crack tip displacement discontinuity elements proposed by the author. In the numerical method implementation, the left or the right crack tip element is placed locally at the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. The numerical method is called a hybrid displacement discontinuity method. The following test examples of crack problems in an infinite plate under tension are included： “ center-inclined cracked plate”, “interaction of two collinear cracks with equal length”, “interaction of three collinear cracks with equal length”, “interaction of two parallel cracks with equal length”, and “interaction of one horizontal crack and one inclined crack”. The present numerical results show that the numerical method is simple yet very accurate for analyzing the interaction of multiple cracks in an infinite plate.
文摘A newly developed approach without crack surface discretization for modeling 2D solids with large number of cracks in linear elastic fracture mechanics is proposed with the eigen crack opening displacement (COD) boundary integral equations in this paper. The eigen COD is defined as a crack in an infinite domain under fictitious traction acting on the crack surface. Respect to the computational accuracies and efficiencies, the multiple crack problems in finite and infinite plates are solved and compared numerically using three different kinds of boundary integral equations (BIEs): 1) the dual BIEs require crack surface discretization;2) the BIEs with numerical Green’s functions (NGF) without crack surface discretization, but have to solve a complementary matrix;3) the eigen crack opening displacement (COD) BIEs in the present paper. With the concept of eigen COD, the multiple crack problems can be solved by using a conventional displacement discontinuity boundary integral equation in an iterative fashion with a small size of system matrix as that in the NGF approach, but without troubles to determine the complementary matrix. Solution of the stress intensity factors of multiple crack problems is solved and compared in some numerical examples using the above three computational algorithms. Numerical results clearly demonstrate the numerical models of eigen COD BIEs have much higher efficiency, providing a newly numerical technique for multiple crack problems. Not only the accuracy and efficiency of computation can be guaranteed, but also the overall properties and local details can be obtained. In conclusion, the numerical models of eigen COD BIEs realize the simulations for multiple crack problems with large quantity of cracks.
基金supported by the National Natural Science Foundation of China(Grant No.52271277)the Natural Science Foundation of Jiangsu Province(Grant No.BK20211343)the Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grant No.SJCX23_2150).
文摘This study focused on the buckling characteristics of egg-shaped shells with single crack and double cracks under axial pressure.First,the geometric parameters of the egg-shaped shell were designed,and a numerical model of the egg-shaped shell was established.Then,the initial crack was introduced into the equatorial weld of the egg-shaped shell,and the effects of the crack on the buckling characteristics under different wall thicknesses were explored,as were the effects of the single crack direction,double crack angle and spacing on the buckling characteristics.Finally,crack-free,single crack and double crack egg-shaped shells were fabricated from Q235 steel.The buckling loads and failure modes of the three egg-shaped shells were obtained via axial compression experiments.The numerical critical buckling loads and buckling modes were compared with the experimental results to verify the accuracy of the numerical model.The results of this study are valuable for the design of egg-shaped shells under axial loading.
基金supported by the National Natural Science Foundation of China(Grant Nos.12232005 and 12072101).
文摘Large-grain REBa_(2)Cu_(3)O_(7-δ)(REBCO,RE=rare earth)bulk superconductors offer promising magnetic field trapping capabilities due to their high critical current density,making them ideal for many important applications such as trapped field magnets.However,for such large-grain superconductor bulks,there are lots of voids and cracks forming during the process of melting preparation,and some of them can be up to hundreds of microns or even millimeters in size.Consequently,these larger size voids/cracks pose a great threat to the strength of the bulks due to the inherent brittleness of superconductor REBCO materials.In order to ensure the operational safety of related superconducting devices with bulk superconductors,it is firstly important to accurately detect these voids/cracks in them.In this paper,we proposed a method for quantitatively evaluating multiple voids/cracks in bulk superconductors through the magnetic field and displacement response signals at superconductor bulk surface.The proposed method utilizes a damage index constructed from the magnetic field signals and displacement responses to identify the number and preliminary location of multiple defects.By dividing the detection area into subdomains and combining the magnetic field signals with displacement responses within each subdomain,a particle swarm algorithm was employed to evaluate the location and size parameters of the defects.In contrast to other evaluation methods using only magnetic field or displacement response signals,the combined evaluation method using both signals can identify the number of cracks effectively.Numerical studies demonstrate that the morphology of voids and cracks reconstructed using the proposed algorithm ideally matches real defects and is applicable to cases where voids and cracks coexist.This study provides a theoretical basis for the quantitative detection of voids/cracks in bulk superconductors.
基金The authors gratefully acknowledge the financial support by the Key Project of High-speed Rail Joint Fund of National Natural Science Foundation of China(Grant No.U1934210)the Natural Science Foundation of Beijing,China(Grant No.8202037).
文摘Longitudinal cracks on the tunnel lining significantly influence the performance of tunnels in operation.In this study,we propose a semi-analytical method that provides a simple and effective way to calculate the internal forces of tunnel linings with multiple cracks.The semi-analytical solution is obtained using structural analysis considering the flexural rigidity for the cracked longitudinal section of the tunnel lining.Then the proposed solution is verified numerically.Using the proposed method,the influences of the crack depth and the number of cracks on the bending moment and modified crack tip stress are investigated.With the increase in crack depth,the bending moment of lining scetion adjacent to the crack decreases,while the bending moment of lining scetion far away from the crack increases slightly.The more the number of cracks in a tunnel lining,the easier the new cracks initiated.
文摘The stress fields are obtained for a functionally graded half-plane containing a Volterra screw dislocation.The elastic shear modulus of the medium is considered to vary ex-ponentially.The dislocation solution is utilized to formulate integral equations for the half-plane weakened by multiple smooth cracks under anti-plane deformation.The integral equations are of Cauchy singular type at the location of dislocation which are solved numerically.Several examples are solved and the stress intensity factors are obtained.
基金supported by the National Natural Science Foundation of China (Nos.10572043 and 10872057)the Research Fund for the Doctoral Program of Higher Education of China (No.20092302110006)the Natural Science Foundation of Hei Long Jiang Province (No.A2007-05)
文摘In this paper, the interactions of multiple parallel symmetric and permeable finite length cracks in a piezoelectric/piezomagnetic material plane subjected to anti-plane shear stress loading are studied by the Schmidt method.The problem is formulated through Fourier transform into dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces.To solve the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials.Finally, the relation between the electric field, the magnetic flux field and the stress field near the crack tips is obtained.The results show that the stress, the electric displacement and the magnetic flux intensity factors at the crack tips depend on the length and spacing of the cracks.It is also revealed that the crack shielding effect presents in piezoelectric/piezomagnetic materials.
基金Project supported by the National Natural Science Foundation of China(Nos.11002041 and11272105)the Key Laboratory Opening Funding of Advanced Composites in Special Environment(No.HIT.KLOF.2009032)the Research Fund for the Doctoral Program of Higher Education ofChina(No.20092302110006)
文摘The Schmidt method is adopted to investigate the fracture problem of multiple parallel symmetric and permeable finite length mode-III cracks in a functionally graded piezoelectric/piezomagnetic material plane. This problem is formulated into dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. In order to obtain the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. The results show that the stress, the electric displacement, and the magnetic flux intensity factors of cracks depend on the crack length, the functionally graded parameter, and the distance among the multiple parallel cracks. The crack shielding effect is also obviously presented in a functionally graded piezoelectric/piezomagnetic material plane with mul- tiple parallel symmetric mode-III cracks.
基金supported by the National Key Basic Research Program of China(2013CB036405)the National Natural Science Foundation of China(11002154,41272349,and 41372315)the CAS/SAFEA International Partnership Program for Creative Research Teams(KZCX2-YW-T12)
文摘A method of continuous-discontinuous cellular automaton for modeling the growth and coalescence of multiple cracks in brittle material is presented. The method uses the level set to track arbitrary discontinuities, and calculation grids are independent of the discontinuities and no remeshing are required with the crack growing. Based on Grif- fith fracture theory and Mohr-Coulumb criterion, a mixed fracture criterion for multiple cracks growth in brittle mate- rial is proposed. The method treats the junction and coales- cence of multiple cracks, and junction criterion and coales- cence criterion for brittle material are given, too. Besides, in order to overcome the tracking error in the level set ap- proximation for crack junction and coalescence, a dichotomy searching algorithm is proposed. Introduced the above the- ories into continuous-discontinuous cellular automaton, the present method can be applied to solving multiple crack growth in brittle material, and only cell stiffness is needed and no assembled global stiffness is needed. Some numerical examples are given to shown that the present method is efficient and accurate for crack junction, coalescence and percolation problems.
文摘This paper contains a theoretical formulations and solutions of multiple cracks sub- jected to an anti-plane time-harmonic point load in a functionally graded strip. The distributed dislocation technique is used to construct integral equations for a functionally graded material strip weakened by several cracks under anti-plane time-harmonic load. These equations are of Cauchy singular type at the location of dislocation, which are solved numerically to obtain the dislocation density on the faces of the cracks. The dislocation densities are employed to evaluate the stress intensity factor and strain energy density factors （SEDFs） for multiple cracks with differ- ent configurations. Numerical calculations are presented to show the effects of material properties and the crack configuration on the dynamic stress intensity factors and SEDFs of the functionally graded strip with multiple curved cracks.
基金Funded by the Hong Kong Research Grant Council( CERG UST6138/04E)the Key Program of National Natural Science Foundation of China( No.50438010)the Research & Application of Key Technology for the South-North Water Transfer Project Construction in China( JGZXJJ2006-13)
文摘The tensile and flexural properties of polyvinyl alcohol （PVA） fiber reinforced ultra high toughness cementitious composite （UHTCC） were investigated. The composite, tested at the age of 14 d, 28 d and 56 d, shows extremely remarkable pseudo strain hardening behavior, saturated multiple cracking and ultra high ultimate strain capacity above 4% under uniaxial loading. Also, the corresponding crack widths are controlled under 50 um even at 56 days age. In the third point bending tests on thin plate specimens, the composite shows ultra high flexural ductility and multiple cracking on the tension surface. The high ultimate flexural strength/first tensile strength ratio of about 5 verifies the pseudo strain hardening behavior of UHTCC. SEM observation on fracture surfaces provides indirect evidence of optimal design for the composite.
基金Funded by the Key Program of National Natural Science Foundation of China (No.50438010)
文摘Mechanical behaviors of UHTCC after freezing and thawing were investigated,and compared with those of steel fiber reinforced concrete（SFRC）,air-entrained concrete（AEC） and ordinary concrete（OC）.Four point bending tests had been applied after different freezing-thawing cycles（0,50,100,150,200 and 300 cycles,respectively）.The results showed that residual flexural strength of UHTCC after 300 freezing-thawing cycles was 10.62 MPa（70% of no freezing thawing ones）,while 1.58 MPa（17% of no freezing thawing ones） for SFRC.Flexural toughness of UHTCC decreased by 17%,while 70% for SFRC comparatively.It has been demonstrated experimentally that UHTCC without any air-entraining agent could resist freezing-thawing and retain its high toughness characteristic in cold environment.Consequently,UHTCC could be put into practice for new-built or retrofit of infrastructures in cold regions.
基金Project(114M246)supported by the Scientific and Technological Research Council of Turkey
文摘The multiple cracking and deflection hardening performance of polyvinyl alcohol fiber reinforced engineered cementitious composites(PVA-ECC)under four-point flexural loading have been investigated.Matrices with different binder combinations and W/B ratios(from 0.44 to 0.78)providing satisfactory PVA fiber dispersion were specially designed.Effect of pre-existing flaw size distribution modification on deflection hardening behavior was comparatively studied by adding 3 mm diameter polyethylene beads into the mixtures(6%by total volume).Natural flaw size distributions of composites without beads were determined by cross sectional analysis.The crack number and crack width distributions of specimens after flexural loading were characterized and the possible causes of changes in multiple cracking and deflection hardening behavior by flaw size distribution modification were discussed.Promising results from the view point of deflection hardening behavior were obtained from metakaolin incorporated and flaw size distribution modified PVA-ECCs prepared with W/B=0.53.The dual roles of W/B ratio and superplasticizer content on flaw size distribution,cracking potential and fiber-matrix bond behavior were evaluated.Flaw size distribution modification is found beneficial in terms of ductility improvement at an optimized W/B ratio.
