The aim of the present work is to investigate the numerical modeling of interfacial cracks that may appear at the interface between two isotropic elastic materials. The extended finite element method is employed to an...The aim of the present work is to investigate the numerical modeling of interfacial cracks that may appear at the interface between two isotropic elastic materials. The extended finite element method is employed to analyze brittle and bi-material interfacial fatigue crack growth by computing the mixed mode stress intensity factors(SIF). Three different approaches are introduced to compute the SIFs. In the first one, mixed mode SIF is deduced from the computation of the contour integral as per the classical J-integral method,whereas a displacement method is used to evaluate the SIF by using either one or two displacement jumps located along the crack path in the second and third approaches. The displacement jump method is rather classical for mono-materials,but has to our knowledge not been used up to now for a bimaterial. Hence, use of displacement jump for characterizing bi-material cracks constitutes the main contribution of the present study. Several benchmark tests including parametric studies are performed to show the effectiveness of these computational methodologies for SIF considering static and fatigue problems of bi-material structures. It is found that results based on the displacement jump methods are in a very good agreement with those of exact solutions, such as for the J-integral method, but with a larger domain of applicability and a better numerical efficiency(less time consuming and less spurious boundary effect).展开更多
This paper studies the dynamic stress intensity factor (DSIF) at the interface in an adhesive joint under shear loading. Material damage is considered. By introducing the dislocation density function and using the i...This paper studies the dynamic stress intensity factor (DSIF) at the interface in an adhesive joint under shear loading. Material damage is considered. By introducing the dislocation density function and using the integral transform, the problem is reduced to algebraic equations and can be solved with the collocation dots method in the Laplace domain. Time response of DSIF is calculated with the inverse Laplace integral transform. The results show that the mode Ⅱ DSIF increases with the shear relaxation parameter, shear module and Poisson ratio, while decreases with the swell relaxation parameter. Damage shielding only occurs at the initial stage of crack propagation. The singular index of crack tip is -0.5 and independent on the material parameters, damage conditions of materials, and time. The oscillatory index is controlled by viscoelastic material parameters.展开更多
Adopting the complex function approach, the paper studies the stress intensity factor in orthotropic bi-material interface cracks under mixed loads. With con- sideration of the boundary conditions, a new stress functi...Adopting the complex function approach, the paper studies the stress intensity factor in orthotropic bi-material interface cracks under mixed loads. With con- sideration of the boundary conditions, a new stress function is introduced to transform the problem of bi-material interface crack into a boundary value problem of partial dif- ferential equations. Two sets of non-homogeneous linear equations with 16 unknowns are constructed. By solving the equations, the expressions for the real bi-material elastic constant εt and the real stress singularity exponents λt are obtained with the bi-material engineering parameters satisfying certain conditions. By the uniqueness theorem of limit, undetermined coefficients are determined, and thus the bi-material stress intensity factor in mixed cracks is obtained. The bi-material stress intensity factor characterizes features of mixed cracks. When orthotropic bi-materials are of the same material, the degenerate solution to the stress intensity factor in mixed bi-material interface cracks is in complete agreement with the present classic conclusion. The relationship between the bi-material stress intensity factor and the ratio of bi-material shear modulus and the relationship be- tween the bi-material stress intensity factor and the ratio of bi-material Young's modulus are given in the numerical analysis.展开更多
The problems of finite bimaterial plates, hearing uniform tension, compact: tension and three point bending, are studied by using the eigenfunction expansion variation method (EEVM). And interfacial stress intensity f...The problems of finite bimaterial plates, hearing uniform tension, compact: tension and three point bending, are studied by using the eigenfunction expansion variation method (EEVM). And interfacial stress intensity factors (SIFs) are determined. The SIFs varying with shear modulus mu and Poisson's ratios nu of both materials are discussed.展开更多
The stress intensity factors (SIF) considering arbitrarily distributed surface tractions are evaluated based on the sealed boundary finite element method (SBFEM). The semi-analytical solving process for the stress...The stress intensity factors (SIF) considering arbitrarily distributed surface tractions are evaluated based on the sealed boundary finite element method (SBFEM). The semi-analytical solving process for the stress intensity factors including the effects of surface tractions is presented. Provided are the numerical examples for the evaluation of mode I and Ⅱ stress intensity factors with linear and non-linear distributing forces loaded on the crack surfaces. The crack problems of anisotropy and bimaterial interface are also studied and the stress intensity factors of single-edge-cracked orthotropic material and bi-material interface problems with surface tractions are calculated. Comparisons with the analytical solutions show that the proposed approach is effective and possesses high accuracy.展开更多
Semi_weight function method is developed to solve the plane problem of two bonded dissimilar materials containing a crack along the bond. From equilibrium equation, stress and strain relationship, conditions of contin...Semi_weight function method is developed to solve the plane problem of two bonded dissimilar materials containing a crack along the bond. From equilibrium equation, stress and strain relationship, conditions of continuity across interface and free crack surface, the stress and displacement fields were obtained. The eigenvalue of these fields is lambda. Semi_weight functions were obtained as virtual displacement and stress fields with eigenvalue?_lambda. Integral expression of fracture parameters, K Ⅰ and K Ⅱ, were obtained from reciprocal work theorem with semi_weight functions and approximate displacement and stress values on any integral path around crack tip. The calculation results of applications show that the semi_weight function method is a simple, convenient and high precision calculation method.展开更多
The method of complex function and the method of Green's function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an...The method of complex function and the method of Green's function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an elliptical hole, and the solution of dynamic stress intensity factor at the crack tip was given. A Green's function was constructed for the problem, which is a basic solution of displacement field for an elastic half space containing a half elliptical gap impacted by anti-plane harmonic linear source force at any point of its horizontal boundary. With division of a crack technique, a series of integral equations can be established on the conditions of continuity and the solution of dynamic stress intensity factor can be obtained. The influence of an elliptical hole on the dynamic stress intensity factor at the crack tip was discussed.展开更多
By using the hypothesis of the deformation of the straight bar and beam in mechanics of materials,a new engineering calculating model for a linear inclusion in plane is presented.Through the Kelvin's solution of a...By using the hypothesis of the deformation of the straight bar and beam in mechanics of materials,a new engineering calculating model for a linear inclusion in plane is presented.Through the Kelvin's solution of a concentrated force,the inclusion problem is reduced to solving a set of uncoupled singular integral equations which can be solved by the numerical method of singular integral equation.Based on these results,several applicable examples including an inclusion-crack problem are calculated and the results are quite satisfactory.展开更多
A frequency-domain approach based on the semi-analytical scaled boundary finite element method(SBFEM) was developed to calculate dynamic stress intensity factors(DSIFs) at bimaterial interface cracks subjected to tran...A frequency-domain approach based on the semi-analytical scaled boundary finite element method(SBFEM) was developed to calculate dynamic stress intensity factors(DSIFs) at bimaterial interface cracks subjected to transient loading.Be-cause the stress solutions of the SBFEM in the frequency domain are analytical in the radial direction,and the complex stress singularity at the bimaterial interface crack tip is explicitly represented in the stress solutions,the mixed-mode DSIFs were calculated directly by definition.The complex frequency-response functions of DSIFs were then used by the fast Fourier transform(FFT) and the inverse FFT to calculate time histories of DSIFs.A benchmark example was modelled.Good re-sults were obtained by modelling the example with a small number of degrees of freedom due to the semi-analytical nature of the SBFEM.展开更多
In this paper the variation of interface stress intensity factors is considered under arbitrary material combinations for several problems such as central internal interface cracks, periodic interface cracks, and edge...In this paper the variation of interface stress intensity factors is considered under arbitrary material combinations for several problems such as central internal interface cracks, periodic interface cracks, and edge interface cracks. The stress intensity factors for all these problems have been determined in terms of Dundurs' parameters a, b by the application of FEM in the authors' previous papers. In this paper, the variations of the stress intensity factors for all these problems are discussed under arbitrary a, b, then the maximum and minimum values of dimensionless stress intensity factors FI,max, FII,max, FI,min, FII,max are indicated on the map of a, b. As an example, it is found that FI,max always appears when (a, b)= (0.2,0.3), and FI,min always appears when (a, b)= (1,0), for the central internal interface cracks independent of crack length.展开更多
The dynamic fracture behavior of the three-point bending beam with double deformity inclusions under impact loading is studied by using digital high-speed photography in combination with the transmission-type dynamic ...The dynamic fracture behavior of the three-point bending beam with double deformity inclusions under impact loading is studied by using digital high-speed photography in combination with the transmission-type dynamic caustic method. The experimental results indicate that the fluctuation of crack propagation velocity v first increases and then decreases in the crack propagation process. During the process of crack propagating into the inclusion area, the fracture resistance effect of the circular inclusion is the most significant and the effects of triangular and square inclusions are less obvious. The stress intensity factor near the crack tip increases during the propagation process and reaches its maximum value when the crack tip is close to the inclusions. The crack tip’s dynamic stress intensity factor ( DSIF) decreases when the crack exceeds the middle area of the double inclusions. These results provide an experimental basis and scientific foundation to strengthen the evaluation and fracture analysis of the structure containing deformity inclusions.展开更多
The approach combining the dynamic caustics method with high-speed photography technology is used to study the interaction between propagating cracks and three kinds of deformity inclusions( cylinder inclusion, quadr...The approach combining the dynamic caustics method with high-speed photography technology is used to study the interaction between propagating cracks and three kinds of deformity inclusions( cylinder inclusion, quadruple inclusion and triangular inclusion) under lowvelocity impact loading. By recording the caustic spots of crack tips at different moments during the crack propagation, the variation regulations of dynamic stress intensity factors( DSIF) and crack growth velocity with respect to time are obtained. The experimental results showthat the resistance effects to crack growth are varied with different shapes of inclusions in specimens, and the quadruple inclusion's effect is more apparent. The distortion degree of caustic spots is affected by the shapes of inclusions as well, and the situation is more serious for cylinder and quadruple inclusions. The overall values of DSIFs of triangular inclusion specimen are greater than the others, and the crack growth velocities, characteristic sizes and DSIFs showprocesses of fluctuations because of the disturbance of reflection waves in specimens. The results provide an experimental basis for the analysis of strength and impact-resistance ability in structures with deformity inclusions.展开更多
Due to the incompatibility of the interlaminar deformations,the interface debonding or cracking usually happens in a layered magnetoelectric(ME)structure under an applied load.In this paper,the transient responses of ...Due to the incompatibility of the interlaminar deformations,the interface debonding or cracking usually happens in a layered magnetoelectric(ME)structure under an applied load.In this paper,the transient responses of the anti-plane interface cracks in piezoelectric(PE)-piezomagnetic(PM)sandwich structures are studied by the standard methods of the integral transform and singular integral equation.Discussion on the numerical examples indicates that the PE-PM-PE structure under electric impact is more likely to fracture than the PM-PE-PM structure under a magnetic impact.The dynamic stress intensity factors(DSIFs)are more sensitive to the variation of the active layer thickness.The effects of the material constants on the DSIFs are dependent on the roles played by PE and PM media during the deformation process.展开更多
Prediction of mode I fracture toughness(KIC) of rock is of significant importance in rock engineering analyses. In this study, linear multiple regression(LMR) and gene expression programming(GEP)methods were used to p...Prediction of mode I fracture toughness(KIC) of rock is of significant importance in rock engineering analyses. In this study, linear multiple regression(LMR) and gene expression programming(GEP)methods were used to provide a reliable relationship to determine mode I fracture toughness of rock. The presented model was developed based on 60 datasets taken from the previous literature. To predict fracture parameters, three mechanical parameters of rock mass including uniaxial compressive strength(UCS), Brazilian tensile strength(BTS), and elastic modulus(E) have been selected as the input parameters. A cluster of data was collected and divided into two random groups of training and testing datasets.Then, different statistical linear and artificial intelligence based nonlinear analyses were conducted on the training data to provide a reliable prediction model of KIC. These two predictive methods were then evaluated based on the testing data. To evaluate the efficiency of the proposed models for predicting the mode I fracture toughness of rock, various statistical indices including coefficient of determination(R2),root mean square error(RMSE), and mean absolute error(MAE) were utilized herein. In the case of testing datasets, the values of R2, RMSE, and MAE for the GEP model were 0.87, 0.188, and 0.156,respectively, while they were 0.74, 0.473, and 0.223, respectively, for the LMR model. The results indicated that the selected GEP model delivered superior performance with a higher R2value and lower errors.展开更多
The complex stress intensity factor K governing the stress field of an interface crack tip may be split into two parts, i.e.,■ and s^(-iε), so that K = ■ s^(-iε), s is a characteristic length and ε is the osc...The complex stress intensity factor K governing the stress field of an interface crack tip may be split into two parts, i.e.,■ and s^(-iε), so that K = ■ s^(-iε), s is a characteristic length and ε is the oscillatory index. ■ has the same dimension as the classical stress intensity factor and characterizes the interface crack tip field. That means a criterion for interface cracks may be formulated directly with■, as Irwin(ASME J. Appl. Mech. 24:361–364, 1957) did in 1957 for the classical fracture mechanics. Then, for an interface crack,it is demonstrated that the quasi Mode I and Mode II tip fields can be defined and distinguished from the coupled mode tip fields. Built upon SIF-based fracture criteria for quasi Mode I and Mode II, the stress intensity factor(SIF)-based fracture criterion for mixed mode interface cracks is proposed and validated against existing experimental results.展开更多
A new node-pairs contact algorithm is proposed to deal with a composite material or bi-material interface crack face contact and friction problem (e.g., resistant coating and thermal barrier coatings) subjected to c...A new node-pairs contact algorithm is proposed to deal with a composite material or bi-material interface crack face contact and friction problem (e.g., resistant coating and thermal barrier coatings) subjected to complicated load conditions. To decrease the calculation scale and calculation errors, the local Lagrange multipliers are solved only on a pair of contact nodes using the Jacobi iteration method, and the constraint modification of the tangential multipliers are required. After the calculation of the present node-pairs Lagrange multiplier, it is turned to next contact node-pairs until all node-pairs have finished. Compared with an ordinary contact algorithm, the new local node-pairs contact algorithm is allowed a more precise element on the contact face without the stiffness matrix singularity. The stress intensity factors (SIFs) and the contact region of an infinite plate central crack are calculated and show good agreement with those in the literature. The contact zone near the crack tip as well as its influence on singularity of stress fields are studied. Furthermore, the frictional contacts are also considered and found to have a significant influence on the SIFs. The normalized mode-II stress intensity factors KII for the friction coefficient decrease by 16% when f changes from 1 to 0.展开更多
The problem of a mode-II crack interface of two bonded dissimilar materials close to and perpendicular to an imperfect is investigated. The imperfect interface is modelled by a linear spring with the vanishing thickne...The problem of a mode-II crack interface of two bonded dissimilar materials close to and perpendicular to an imperfect is investigated. The imperfect interface is modelled by a linear spring with the vanishing thickness. The Fourier transform is used to solve the boundary-value problem and to derive a singular integral equation with the Cauchy kernel. The stress intensity factors near the left and right crack tips are evaluated by numerically solving the resulting equation. SeverM special cases of the mode-II crack problem with an imperfect interface are studied in detail. The effects of the interfacial imperfection on the stress intensity factors for a bimaterial system of aluminum and steel are shown graphically. The obtained observation reveals that the stress intensity factors are dependent on the interface parameters and vary between those with a fully debonded interface and those with a perfect interface.展开更多
Using dislocation simulation approach, the basic equation for a finite crack perpendicular to and terminating at a bimaterial interface is formulated. A novel expansion method is proposed for solving the problem. The ...Using dislocation simulation approach, the basic equation for a finite crack perpendicular to and terminating at a bimaterial interface is formulated. A novel expansion method is proposed for solving the problem. The complete solution to the problem, including the explicit formulae for theT stresses ahead of the crack tip and the stress intensity factors are presented. The stress field characteristics are analysed in detail. It is found that normal stresses {ie27-1} and {ie27-2} ahead of the crack tip, are characterised byQ fields if the crack is within a stiff material and the parameters |p T | and |q T | are very small, whereQ is a generalised stress intensity factor for a crack normal to and terminating at the interface. If the crack is within a weak material, the normal stresses {ie27-3} and {ie27-4} are dominated by theQ field plusT stress.展开更多
Investigated is the push-in test used to determine the interfacial strength of fiber-reinforced composites via the method of singular integral equation. Singularity analysis shows that stresses near the end for an int...Investigated is the push-in test used to determine the interfacial strength of fiber-reinforced composites via the method of singular integral equation. Singularity analysis shows that stresses near the end for an intact interface have a power singularity, and the singularity index is only dependent on the material constants of the fiber and the matrix. In order to describe the interfacial strength at the initial debonding of the push-in test, critical interfacial shear stress intensity factor and the related singularity index are adopted. This interfacial strength characteristic parameter is applied to analysis of the push-in test results of carbon fiber reinforced epoxy resin composites.展开更多
The fracture problems near the similar orthotropic composite materials are interface crack tip for mode Ⅱ of double disstudied. The mechanical models of interface crack for mode Ⅱ are given. By translating the gover...The fracture problems near the similar orthotropic composite materials are interface crack tip for mode Ⅱ of double disstudied. The mechanical models of interface crack for mode Ⅱ are given. By translating the governing equations into the generalized hi-harmonic equations, the stress functions containing two stress singularity exponents are derived with the help of a complex function method. Based on the boundary conditions, a system of non-homogeneous linear equations is found. Two real stress singularity exponents are determined be solving this system under appropriate conditions about bimaterial engineering parameters. According to the uniqueness theorem of limit, both the formulae of stress intensity factors and theoretical solutions of stress field near the interface crack tip are derived. When the two orthotropic materials are the same, the stress singularity exponents, stress intensity factors and stresses for mode II crack of the orthotropic single material are obtained.展开更多
文摘The aim of the present work is to investigate the numerical modeling of interfacial cracks that may appear at the interface between two isotropic elastic materials. The extended finite element method is employed to analyze brittle and bi-material interfacial fatigue crack growth by computing the mixed mode stress intensity factors(SIF). Three different approaches are introduced to compute the SIFs. In the first one, mixed mode SIF is deduced from the computation of the contour integral as per the classical J-integral method,whereas a displacement method is used to evaluate the SIF by using either one or two displacement jumps located along the crack path in the second and third approaches. The displacement jump method is rather classical for mono-materials,but has to our knowledge not been used up to now for a bimaterial. Hence, use of displacement jump for characterizing bi-material cracks constitutes the main contribution of the present study. Several benchmark tests including parametric studies are performed to show the effectiveness of these computational methodologies for SIF considering static and fatigue problems of bi-material structures. It is found that results based on the displacement jump methods are in a very good agreement with those of exact solutions, such as for the J-integral method, but with a larger domain of applicability and a better numerical efficiency(less time consuming and less spurious boundary effect).
基金the National Natural Science Foundation of China(No.10672027)the National Basic Research Program of China(No.2006CB601205)the National Science Fund for Distin-guished Young Scholars of China(No.50625414)
文摘This paper studies the dynamic stress intensity factor (DSIF) at the interface in an adhesive joint under shear loading. Material damage is considered. By introducing the dislocation density function and using the integral transform, the problem is reduced to algebraic equations and can be solved with the collocation dots method in the Laplace domain. Time response of DSIF is calculated with the inverse Laplace integral transform. The results show that the mode Ⅱ DSIF increases with the shear relaxation parameter, shear module and Poisson ratio, while decreases with the swell relaxation parameter. Damage shielding only occurs at the initial stage of crack propagation. The singular index of crack tip is -0.5 and independent on the material parameters, damage conditions of materials, and time. The oscillatory index is controlled by viscoelastic material parameters.
基金supported by the National Key Basic Research Program of China(973 Program)(No.2009CB724201)the Science and Technology Major Project of the Ministry of Education of China(No.208022)+1 种基金the Postgraduate Scientific and Technological Innovation Project of Taiyuan University of Science and Technology(No.20125027)the Scientific Research Funds for Doctoral Students of Taiyuan University of Science and Technology(No.20122005)
文摘Adopting the complex function approach, the paper studies the stress intensity factor in orthotropic bi-material interface cracks under mixed loads. With con- sideration of the boundary conditions, a new stress function is introduced to transform the problem of bi-material interface crack into a boundary value problem of partial dif- ferential equations. Two sets of non-homogeneous linear equations with 16 unknowns are constructed. By solving the equations, the expressions for the real bi-material elastic constant εt and the real stress singularity exponents λt are obtained with the bi-material engineering parameters satisfying certain conditions. By the uniqueness theorem of limit, undetermined coefficients are determined, and thus the bi-material stress intensity factor in mixed cracks is obtained. The bi-material stress intensity factor characterizes features of mixed cracks. When orthotropic bi-materials are of the same material, the degenerate solution to the stress intensity factor in mixed bi-material interface cracks is in complete agreement with the present classic conclusion. The relationship between the bi-material stress intensity factor and the ratio of bi-material shear modulus and the relationship be- tween the bi-material stress intensity factor and the ratio of bi-material Young's modulus are given in the numerical analysis.
文摘The problems of finite bimaterial plates, hearing uniform tension, compact: tension and three point bending, are studied by using the eigenfunction expansion variation method (EEVM). And interfacial stress intensity factors (SIFs) are determined. The SIFs varying with shear modulus mu and Poisson's ratios nu of both materials are discussed.
基金The present research workis financially supported by the National Natural Science Foundation of China (Grant No90510018)China Postdoctorial Science Foundation (Grant No20060390985)
文摘The stress intensity factors (SIF) considering arbitrarily distributed surface tractions are evaluated based on the sealed boundary finite element method (SBFEM). The semi-analytical solving process for the stress intensity factors including the effects of surface tractions is presented. Provided are the numerical examples for the evaluation of mode I and Ⅱ stress intensity factors with linear and non-linear distributing forces loaded on the crack surfaces. The crack problems of anisotropy and bimaterial interface are also studied and the stress intensity factors of single-edge-cracked orthotropic material and bi-material interface problems with surface tractions are calculated. Comparisons with the analytical solutions show that the proposed approach is effective and possesses high accuracy.
文摘Semi_weight function method is developed to solve the plane problem of two bonded dissimilar materials containing a crack along the bond. From equilibrium equation, stress and strain relationship, conditions of continuity across interface and free crack surface, the stress and displacement fields were obtained. The eigenvalue of these fields is lambda. Semi_weight functions were obtained as virtual displacement and stress fields with eigenvalue?_lambda. Integral expression of fracture parameters, K Ⅰ and K Ⅱ, were obtained from reciprocal work theorem with semi_weight functions and approximate displacement and stress values on any integral path around crack tip. The calculation results of applications show that the semi_weight function method is a simple, convenient and high precision calculation method.
文摘The method of complex function and the method of Green's function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an elliptical hole, and the solution of dynamic stress intensity factor at the crack tip was given. A Green's function was constructed for the problem, which is a basic solution of displacement field for an elastic half space containing a half elliptical gap impacted by anti-plane harmonic linear source force at any point of its horizontal boundary. With division of a crack technique, a series of integral equations can be established on the conditions of continuity and the solution of dynamic stress intensity factor can be obtained. The influence of an elliptical hole on the dynamic stress intensity factor at the crack tip was discussed.
基金The project supported by National Natural Science Foundation of China.
文摘By using the hypothesis of the deformation of the straight bar and beam in mechanics of materials,a new engineering calculating model for a linear inclusion in plane is presented.Through the Kelvin's solution of a concentrated force,the inclusion problem is reduced to solving a set of uncoupled singular integral equations which can be solved by the numerical method of singular integral equation.Based on these results,several applicable examples including an inclusion-crack problem are calculated and the results are quite satisfactory.
基金the Scientific Research Foundation for the Returned Overseas Chinese Scholars,Ministry of Education of China(Grant No.J20050924)the Australian Research Council Discovery Project(Grant No.DP0452681)
文摘A frequency-domain approach based on the semi-analytical scaled boundary finite element method(SBFEM) was developed to calculate dynamic stress intensity factors(DSIFs) at bimaterial interface cracks subjected to transient loading.Be-cause the stress solutions of the SBFEM in the frequency domain are analytical in the radial direction,and the complex stress singularity at the bimaterial interface crack tip is explicitly represented in the stress solutions,the mixed-mode DSIFs were calculated directly by definition.The complex frequency-response functions of DSIFs were then used by the fast Fourier transform(FFT) and the inverse FFT to calculate time histories of DSIFs.A benchmark example was modelled.Good re-sults were obtained by modelling the example with a small number of degrees of freedom due to the semi-analytical nature of the SBFEM.
基金supported by the Japanese Government (Monbukagukusho) Scholarshipthe National Basic Research Program of China (Grant No.2011CB013702)
文摘In this paper the variation of interface stress intensity factors is considered under arbitrary material combinations for several problems such as central internal interface cracks, periodic interface cracks, and edge interface cracks. The stress intensity factors for all these problems have been determined in terms of Dundurs' parameters a, b by the application of FEM in the authors' previous papers. In this paper, the variations of the stress intensity factors for all these problems are discussed under arbitrary a, b, then the maximum and minimum values of dimensionless stress intensity factors FI,max, FII,max, FI,min, FII,max are indicated on the map of a, b. As an example, it is found that FI,max always appears when (a, b)= (0.2,0.3), and FI,min always appears when (a, b)= (1,0), for the central internal interface cracks independent of crack length.
基金The National Basic Research Program of China(973 Program)(No.2011CB606105)the National Natural Science Foundation of China(No.51374210,51134025)
文摘The dynamic fracture behavior of the three-point bending beam with double deformity inclusions under impact loading is studied by using digital high-speed photography in combination with the transmission-type dynamic caustic method. The experimental results indicate that the fluctuation of crack propagation velocity v first increases and then decreases in the crack propagation process. During the process of crack propagating into the inclusion area, the fracture resistance effect of the circular inclusion is the most significant and the effects of triangular and square inclusions are less obvious. The stress intensity factor near the crack tip increases during the propagation process and reaches its maximum value when the crack tip is close to the inclusions. The crack tip’s dynamic stress intensity factor ( DSIF) decreases when the crack exceeds the middle area of the double inclusions. These results provide an experimental basis and scientific foundation to strengthen the evaluation and fracture analysis of the structure containing deformity inclusions.
基金The National Natural Science Foundation of China(No.51374210,51134025)the 111 Project(No.B14006)
文摘The approach combining the dynamic caustics method with high-speed photography technology is used to study the interaction between propagating cracks and three kinds of deformity inclusions( cylinder inclusion, quadruple inclusion and triangular inclusion) under lowvelocity impact loading. By recording the caustic spots of crack tips at different moments during the crack propagation, the variation regulations of dynamic stress intensity factors( DSIF) and crack growth velocity with respect to time are obtained. The experimental results showthat the resistance effects to crack growth are varied with different shapes of inclusions in specimens, and the quadruple inclusion's effect is more apparent. The distortion degree of caustic spots is affected by the shapes of inclusions as well, and the situation is more serious for cylinder and quadruple inclusions. The overall values of DSIFs of triangular inclusion specimen are greater than the others, and the crack growth velocities, characteristic sizes and DSIFs showprocesses of fluctuations because of the disturbance of reflection waves in specimens. The results provide an experimental basis for the analysis of strength and impact-resistance ability in structures with deformity inclusions.
基金Project supported by the National Natural Science Foundation of China(Nos.11272222,11502108,and 11611530686)the Natural Science Foundation for Distinguished Young Scholars of Jiangsu Province of China(No.BK20140037)
文摘Due to the incompatibility of the interlaminar deformations,the interface debonding or cracking usually happens in a layered magnetoelectric(ME)structure under an applied load.In this paper,the transient responses of the anti-plane interface cracks in piezoelectric(PE)-piezomagnetic(PM)sandwich structures are studied by the standard methods of the integral transform and singular integral equation.Discussion on the numerical examples indicates that the PE-PM-PE structure under electric impact is more likely to fracture than the PM-PE-PM structure under a magnetic impact.The dynamic stress intensity factors(DSIFs)are more sensitive to the variation of the active layer thickness.The effects of the material constants on the DSIFs are dependent on the roles played by PE and PM media during the deformation process.
文摘Prediction of mode I fracture toughness(KIC) of rock is of significant importance in rock engineering analyses. In this study, linear multiple regression(LMR) and gene expression programming(GEP)methods were used to provide a reliable relationship to determine mode I fracture toughness of rock. The presented model was developed based on 60 datasets taken from the previous literature. To predict fracture parameters, three mechanical parameters of rock mass including uniaxial compressive strength(UCS), Brazilian tensile strength(BTS), and elastic modulus(E) have been selected as the input parameters. A cluster of data was collected and divided into two random groups of training and testing datasets.Then, different statistical linear and artificial intelligence based nonlinear analyses were conducted on the training data to provide a reliable prediction model of KIC. These two predictive methods were then evaluated based on the testing data. To evaluate the efficiency of the proposed models for predicting the mode I fracture toughness of rock, various statistical indices including coefficient of determination(R2),root mean square error(RMSE), and mean absolute error(MAE) were utilized herein. In the case of testing datasets, the values of R2, RMSE, and MAE for the GEP model were 0.87, 0.188, and 0.156,respectively, while they were 0.74, 0.473, and 0.223, respectively, for the LMR model. The results indicated that the selected GEP model delivered superior performance with a higher R2value and lower errors.
文摘The complex stress intensity factor K governing the stress field of an interface crack tip may be split into two parts, i.e.,■ and s^(-iε), so that K = ■ s^(-iε), s is a characteristic length and ε is the oscillatory index. ■ has the same dimension as the classical stress intensity factor and characterizes the interface crack tip field. That means a criterion for interface cracks may be formulated directly with■, as Irwin(ASME J. Appl. Mech. 24:361–364, 1957) did in 1957 for the classical fracture mechanics. Then, for an interface crack,it is demonstrated that the quasi Mode I and Mode II tip fields can be defined and distinguished from the coupled mode tip fields. Built upon SIF-based fracture criteria for quasi Mode I and Mode II, the stress intensity factor(SIF)-based fracture criterion for mixed mode interface cracks is proposed and validated against existing experimental results.
基金supported by the National Basic Research Program of China(Grant No.2012CB026200)the National Natural Science Foundation of China(Grant No.50878048)
文摘A new node-pairs contact algorithm is proposed to deal with a composite material or bi-material interface crack face contact and friction problem (e.g., resistant coating and thermal barrier coatings) subjected to complicated load conditions. To decrease the calculation scale and calculation errors, the local Lagrange multipliers are solved only on a pair of contact nodes using the Jacobi iteration method, and the constraint modification of the tangential multipliers are required. After the calculation of the present node-pairs Lagrange multiplier, it is turned to next contact node-pairs until all node-pairs have finished. Compared with an ordinary contact algorithm, the new local node-pairs contact algorithm is allowed a more precise element on the contact face without the stiffness matrix singularity. The stress intensity factors (SIFs) and the contact region of an infinite plate central crack are calculated and show good agreement with those in the literature. The contact zone near the crack tip as well as its influence on singularity of stress fields are studied. Furthermore, the frictional contacts are also considered and found to have a significant influence on the SIFs. The normalized mode-II stress intensity factors KII for the friction coefficient decrease by 16% when f changes from 1 to 0.
基金supported by the National Natural Science Foundation of China (No. 90815001)the Natural Science Foundation of Guangxi Province of China (No. 2011GXNSFA018132)the Scientific Research Foundation of Guangxi University (No. XBZ111497)
文摘The problem of a mode-II crack interface of two bonded dissimilar materials close to and perpendicular to an imperfect is investigated. The imperfect interface is modelled by a linear spring with the vanishing thickness. The Fourier transform is used to solve the boundary-value problem and to derive a singular integral equation with the Cauchy kernel. The stress intensity factors near the left and right crack tips are evaluated by numerically solving the resulting equation. SeverM special cases of the mode-II crack problem with an imperfect interface are studied in detail. The effects of the interfacial imperfection on the stress intensity factors for a bimaterial system of aluminum and steel are shown graphically. The obtained observation reveals that the stress intensity factors are dependent on the interface parameters and vary between those with a fully debonded interface and those with a perfect interface.
基金This work was supported by the Swedish Research Council for Engineering Sciences.
文摘Using dislocation simulation approach, the basic equation for a finite crack perpendicular to and terminating at a bimaterial interface is formulated. A novel expansion method is proposed for solving the problem. The complete solution to the problem, including the explicit formulae for theT stresses ahead of the crack tip and the stress intensity factors are presented. The stress field characteristics are analysed in detail. It is found that normal stresses {ie27-1} and {ie27-2} ahead of the crack tip, are characterised byQ fields if the crack is within a stiff material and the parameters |p T | and |q T | are very small, whereQ is a generalised stress intensity factor for a crack normal to and terminating at the interface. If the crack is within a weak material, the normal stresses {ie27-3} and {ie27-4} are dominated by theQ field plusT stress.
文摘Investigated is the push-in test used to determine the interfacial strength of fiber-reinforced composites via the method of singular integral equation. Singularity analysis shows that stresses near the end for an intact interface have a power singularity, and the singularity index is only dependent on the material constants of the fiber and the matrix. In order to describe the interfacial strength at the initial debonding of the push-in test, critical interfacial shear stress intensity factor and the related singularity index are adopted. This interfacial strength characteristic parameter is applied to analysis of the push-in test results of carbon fiber reinforced epoxy resin composites.
基金supported by the Natural Science Foundation of Shaanxi Province (No.2007011008)
文摘The fracture problems near the similar orthotropic composite materials are interface crack tip for mode Ⅱ of double disstudied. The mechanical models of interface crack for mode Ⅱ are given. By translating the governing equations into the generalized hi-harmonic equations, the stress functions containing two stress singularity exponents are derived with the help of a complex function method. Based on the boundary conditions, a system of non-homogeneous linear equations is found. Two real stress singularity exponents are determined be solving this system under appropriate conditions about bimaterial engineering parameters. According to the uniqueness theorem of limit, both the formulae of stress intensity factors and theoretical solutions of stress field near the interface crack tip are derived. When the two orthotropic materials are the same, the stress singularity exponents, stress intensity factors and stresses for mode II crack of the orthotropic single material are obtained.