Using a method of potential functions introduced successively to integrate the field equations of three-dimensional problems for transversely isotropic piezoelectric materials, we obtain the so-called general solution...Using a method of potential functions introduced successively to integrate the field equations of three-dimensional problems for transversely isotropic piezoelectric materials, we obtain the so-called general solution in which the dis- placement components and electric potential functions are represented by a singular function satisfying some special partial differential equations of 6th order. In order to analyse the mechanical-electric coupling behaviour of penny-shaped crack for above materials, another form of the general solution is obtained under cylindrical coordi- nate system by introducing three quasi-harmonic functions into the general equations obtained above. It is shown that both the two forms of the general solutions are complete. Furthermore, the mechanical-electric coupling behaviour of penny-shaped crack in transversely isotropic piezoelectric media is analysed under axisymmetric tensile loading case, and the crack-tip stress field and electric displacement field are obtained. The results show that the stress and the electric displacement components near the crack tip have (r^(-1/2)) singularity.展开更多
This paper analyzes the dynamic magnetoelectroelastic behavior induced by a pennyshaped crack in a magnetoelectroelastic layer. The crack surfaces are subjected to only radial shear impact loading. The Laplace and Han...This paper analyzes the dynamic magnetoelectroelastic behavior induced by a pennyshaped crack in a magnetoelectroelastic layer. The crack surfaces are subjected to only radial shear impact loading. The Laplace and Hankel transform techniques are employed to reduce the problem to solving a Fredholm integral equation. The dynamic stress intensity factor is obtained and numerically calculated for different layer heights. And the corresponding static solution is given by simple analysis. It is seen that the dynamic stress intensity factor for cracks in a magnetoelectroelastic layer has the same expression as that in a purely elastic material. And the influences of layer height on both the dynamic and static stress intensity factors are insignificant as h/a 〉 2.展开更多
An exact analysis of the modes Ⅱ and Ⅲ problems of a penny- shaped crack in a transversely isotropic piezoelectric medium is performed in this paper.The potential theory method is employed based on the general solut...An exact analysis of the modes Ⅱ and Ⅲ problems of a penny- shaped crack in a transversely isotropic piezoelectric medium is performed in this paper.The potential theory method is employed based on the general solution of three-dimensional piezoelasticity and the four harmonics involved are represented by one complex potential.Previous results in potential theory are then utilized to obtain the exact solution that is expressed in terms of elementary functions.Comparison is made between the current results with those published and good agreement is obtained.展开更多
The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is devel- oped i...The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is devel- oped in which the opening and the sliding displacements on each crack surface are taken as the basic unknown functions. The basic unknown functions can be expanded in series of Legendre polynomials with unknown coefficients. Based on superposition technique, a set of governing equations for the unknown coefficients are formulated from the traction free conditions on each crack surface. The boundary collocation procedure and the average method for crack-surface tractions are used for solving the governing equations. The solution can be obtained for quite closely located cracks. Numerical examples are given for several crack problems. By comparing the present results with other existing results, one can conclude that the present method provides a direct and efficient approach to deal with three-dimensional solids containing multiple cracks.展开更多
Exact solutions of three-dimensional(3D)crack problems are much less in number than those of two-dimensional ones,especially for multi-field coupling media exhibiting a certain kind of material anisotropy.An exact3Dth...Exact solutions of three-dimensional(3D)crack problems are much less in number than those of two-dimensional ones,especially for multi-field coupling media exhibiting a certain kind of material anisotropy.An exact3Dthermoelastic solution has been reported for a uniformly heated penny-shaped crack in an infinite magnetoelectric space,with impermeable electromagnetic conditions assumed on the crack faces.Exact 3Dsolutions for the penny-shaped crack subjected to uniform or point temperature load are further presented here when the crack faces are electrically and magnetically permeable.The solutions,obtained by the potential theory method,are exact in the sense that all field variables are explicitly derived and expressed in terms of elementary functions.Along with the previously reported solution,the limits or bounds of the stress intensity factor at the crack-tip for a practical crack can be identified.展开更多
Fractures are widely present in geomaterials of civil engineering and deep underground engineering.Given that geomaterials are usually brittle,the fractures can significantly affect the evaluation of underground engin...Fractures are widely present in geomaterials of civil engineering and deep underground engineering.Given that geomaterials are usually brittle,the fractures can significantly affect the evaluation of underground engineering construction safety and the early warning of rock failure.However,the crack initiation and propagation in brittle materials under composite loading remain unknown so far.In this study,a three-dimensional internal laser-engraved cracking technique was applied to produce internal cracks without causing damage to the surfaces.The uniaxial compression tests were performed on a brittle material with internal cracks to investigate the propagation of these internal cracks at different dip angles under compression and shear.The test results show that the wing crack propagation mainly occurs in the specimen with an inclined internal crack,which is a mixed-ModeⅠ–Ⅱ–Ⅲfracture;in contrast,ModeⅠfracture is present in the specimen with a vertical internal crack.The fractography characteristics of ModeⅢfracture display a lance-like pattern.The fracture mechanism in the brittle material under compression is that the internal wing cracks propagate to the ends of the whole sample and cause the final failure.The initial deflection angle of the wing crack is determined by the participation ratio of stress intensity factors KII to KI at the tip of the internal crack.展开更多
By the theory of complex functions, the dynamic propagation problem on Dugdale model of mode Ⅲ interface crack for nonlinear characters of materials was studied. The general expressions of analytical solutions are ob...By the theory of complex functions, the dynamic propagation problem on Dugdale model of mode Ⅲ interface crack for nonlinear characters of materials was studied. The general expressions of analytical solutions are obtained by the methods of self-similar functions. The problems dealt with can be easily transformed into Riemann-Hilbert problems and their closed solutions are attained rather simply by this approach. After those solutions were utilized by superposition theorem, the solutions of arbitrarily complex problems could be obtained.展开更多
An aim of current study is to analyze the contribution of reflected longitudinal waves to wave-induced fluid flow(WIFF) in the cracked porous solid.Initially,we investigate the time harmonic plane waves in cracked por...An aim of current study is to analyze the contribution of reflected longitudinal waves to wave-induced fluid flow(WIFF) in the cracked porous solid.Initially,we investigate the time harmonic plane waves in cracked porous solid by employing the mathematical model proposed by Zhang et al.(2019).The solution is obtained in form of the Christoffel equations.The solution of the Christoffel equations indicates that there exist four(three dilatational and one shear) waves.These waves are attenuated in nature due to their complex and frequency-dependent velocities.The reflection coefficients are calculated at the sealed pore stress-free surface of cracked porous solid for the incidence of P1 and SV waves.It is found that three longitudinal waves contribute to WIFF and the contribution of these waves to the induced fluid in the cracked porous solid is analyzed using the reflection coefficients of these longitudinal waves.We analytically show that the fluid flow induced by these longitudinal waves is linked directly to their respective reflection coefficients.Finally,a specific numerical example is considered to discuss and to depict the impact of various parameters on the characteristics of propagation like phase velocity/attenuation,reflection coefficients and WIFF of longitudinal waves.展开更多
The torsional impact response of a penny-shaped crack in a nonhomogeneous strip is considered. The shear modulus is assumed to be functionally graded such that the mathematics is tractable. Laplace and Hankel transfor...The torsional impact response of a penny-shaped crack in a nonhomogeneous strip is considered. The shear modulus is assumed to be functionally graded such that the mathematics is tractable. Laplace and Hankel transforms were used to reduce the problem to solving a Fredholm integral equation. The crack tip stress field is obtained by considering the asymptotic behavior of Bessel function. Explicit expressions of both the dynamic stress intensity factor and the energy density factor were derived.And it is shown that, as crack driving force, they are equivalent for the present crack problem. Investigated are the effects of material nonhomogeneity and (strip's) highness on the dynamic fracture behavior. Numerical results reveal that the peak of the dynamic stress intensity factor can be suppressed by increasing the nonhomogeneity parameter of the shear modulus, and that the dynamic behavior varies little with the adjusting of the strip's highness.展开更多
A penny-shaped interfacial crack between dissimilar magnetoelectroelastic layers subjected to magnetoelectromechanical loads is investigated,where the magnetoelectrically impermeable crack surface condition is adopted...A penny-shaped interfacial crack between dissimilar magnetoelectroelastic layers subjected to magnetoelectromechanical loads is investigated,where the magnetoelectrically impermeable crack surface condition is adopted. By using Hankel transform technique,the mixed boundary value problem is firstly reduced to a system of singular integral equations,which are further reduced to a system of algebraic equations. The field intensity factors and energy release rate are finally derived. Numerical results elucidate the eects of crack configuration,electric and/or magnetic loads,and material parameters of the magnetoelectroelastic layers on crack propagation and growth. This work should be useful for the design of magnetoelectroelastic composite structures.展开更多
Similar to hydraulic fracturing(HF), the coalescence and fracture of cracks are induced within a rock under the action of an ultrasonic field, known as ultrasonic fracturing(UF). Investigating UF is important in both ...Similar to hydraulic fracturing(HF), the coalescence and fracture of cracks are induced within a rock under the action of an ultrasonic field, known as ultrasonic fracturing(UF). Investigating UF is important in both hard rock drilling and oil and gas recovery. A three-dimensional internal laser-engraved crack(3D-ILC) method was introduced to prefabricate two parallel internal cracks within the samples without any damage to the surface. The samples were subjected to UF. The mechanism of UF was elucidated by analyzing the characteristics of fracture surfaces. The crack propagation path under different ultrasonic parameters was obtained by numerical simulation based on the Paris fatigue model and compared to the experimental results of UF. The results show that the 3D-ILC method is a powerful tool for UF research.Under the action of an ultrasonic field, the fracture surface shows the characteristics of beach marks and contains powder locally, indicating that the UF mechanism includes high-cycle fatigue fracture, shear and friction, and temperature load. The two internal cracks become close under UF. The numerical result obtained by the Paris fatigue model also shows the attraction of the two cracks, consistent with the test results. The 3D-ILC method provides a new tool for the experimental study of UF. Compared to the conventional numerical methods based on the analysis of stress-strain and plastic zone, numerical simulation can be a good alternative method to obtain the crack path under UF.展开更多
To determine the solutions of the well-known problem of a finite width strip with single edge crack,some results on elasto-plastic fracture analysis for metallic foams are reported.Meanwhile,in order to discuss and pu...To determine the solutions of the well-known problem of a finite width strip with single edge crack,some results on elasto-plastic fracture analysis for metallic foams are reported.Meanwhile,in order to discuss and put an insight into the nonlinear fracture analysis,the Dugdale model for plastic deformation of this configuration for metallic foams is recommended and solved.Combining the asymptotic solution with the Dugdale model and elastic solution,the stress field in the plastic zone and the size of the plastic zone are expressed as analytical forms.Based on Williams expansion method,the estimate of the scale factor is also completed and analyzed.In view of these analytical solutions,the results show the scale factor is a useful parameter for the fracture theory of metallic foams.展开更多
By using Fourier transformation the boundary problem of periodical interfacial cracks in anisotropic elastoplastic bimaterial was transformed into a set of dual integral equations and then it was further reduced by me...By using Fourier transformation the boundary problem of periodical interfacial cracks in anisotropic elastoplastic bimaterial was transformed into a set of dual integral equations and then it was further reduced by means of definite integral transformation into a group of singular equations. Closed form of its solution was obtained and three corresponding problems of isotropic bimaterial, of a single anisotropic material and of a bimaterial of isotropy- anisotropy were treated as the specific cases. The plastic zone length of the crack tip and crack openning displacement ( COD) decline as the smaller yield limit of the two bonded materials rises, and they were also determined by crack length and the space between two neighboring cracks . In addition , COD also relates it with moduli of the materials .展开更多
基金The project supported by the Natural Science Foundation of Shaanxi Province, China
文摘Using a method of potential functions introduced successively to integrate the field equations of three-dimensional problems for transversely isotropic piezoelectric materials, we obtain the so-called general solution in which the dis- placement components and electric potential functions are represented by a singular function satisfying some special partial differential equations of 6th order. In order to analyse the mechanical-electric coupling behaviour of penny-shaped crack for above materials, another form of the general solution is obtained under cylindrical coordi- nate system by introducing three quasi-harmonic functions into the general equations obtained above. It is shown that both the two forms of the general solutions are complete. Furthermore, the mechanical-electric coupling behaviour of penny-shaped crack in transversely isotropic piezoelectric media is analysed under axisymmetric tensile loading case, and the crack-tip stress field and electric displacement field are obtained. The results show that the stress and the electric displacement components near the crack tip have (r^(-1/2)) singularity.
基金Project supported by the National Natural Science Foundation of China(No.10772123)the Natural Science Fund of Hebei Province(No.E2006000398).
文摘This paper analyzes the dynamic magnetoelectroelastic behavior induced by a pennyshaped crack in a magnetoelectroelastic layer. The crack surfaces are subjected to only radial shear impact loading. The Laplace and Hankel transform techniques are employed to reduce the problem to solving a Fredholm integral equation. The dynamic stress intensity factor is obtained and numerically calculated for different layer heights. And the corresponding static solution is given by simple analysis. It is seen that the dynamic stress intensity factor for cracks in a magnetoelectroelastic layer has the same expression as that in a purely elastic material. And the influences of layer height on both the dynamic and static stress intensity factors are insignificant as h/a 〉 2.
基金The project supported by the National Natural Science Foundation of China(No.19872060)
文摘An exact analysis of the modes Ⅱ and Ⅲ problems of a penny- shaped crack in a transversely isotropic piezoelectric medium is performed in this paper.The potential theory method is employed based on the general solution of three-dimensional piezoelasticity and the four harmonics involved are represented by one complex potential.Previous results in potential theory are then utilized to obtain the exact solution that is expressed in terms of elementary functions.Comparison is made between the current results with those published and good agreement is obtained.
文摘The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is devel- oped in which the opening and the sliding displacements on each crack surface are taken as the basic unknown functions. The basic unknown functions can be expanded in series of Legendre polynomials with unknown coefficients. Based on superposition technique, a set of governing equations for the unknown coefficients are formulated from the traction free conditions on each crack surface. The boundary collocation procedure and the average method for crack-surface tractions are used for solving the governing equations. The solution can be obtained for quite closely located cracks. Numerical examples are given for several crack problems. By comparing the present results with other existing results, one can conclude that the present method provides a direct and efficient approach to deal with three-dimensional solids containing multiple cracks.
基金This work was supported by the National Natural Sci- ence Foundation of China （11321202） and the Specialized Research Fund for the Doctoral Program of Higher Educa- tion （2013010 1110120）.
文摘Exact solutions of three-dimensional(3D)crack problems are much less in number than those of two-dimensional ones,especially for multi-field coupling media exhibiting a certain kind of material anisotropy.An exact3Dthermoelastic solution has been reported for a uniformly heated penny-shaped crack in an infinite magnetoelectric space,with impermeable electromagnetic conditions assumed on the crack faces.Exact 3Dsolutions for the penny-shaped crack subjected to uniform or point temperature load are further presented here when the crack faces are electrically and magnetically permeable.The solutions,obtained by the potential theory method,are exact in the sense that all field variables are explicitly derived and expressed in terms of elementary functions.Along with the previously reported solution,the limits or bounds of the stress intensity factor at the crack-tip for a practical crack can be identified.
基金National Natural Science Foundation of China,Grant/Award Numbers:51409170,51739008。
文摘Fractures are widely present in geomaterials of civil engineering and deep underground engineering.Given that geomaterials are usually brittle,the fractures can significantly affect the evaluation of underground engineering construction safety and the early warning of rock failure.However,the crack initiation and propagation in brittle materials under composite loading remain unknown so far.In this study,a three-dimensional internal laser-engraved cracking technique was applied to produce internal cracks without causing damage to the surfaces.The uniaxial compression tests were performed on a brittle material with internal cracks to investigate the propagation of these internal cracks at different dip angles under compression and shear.The test results show that the wing crack propagation mainly occurs in the specimen with an inclined internal crack,which is a mixed-ModeⅠ–Ⅱ–Ⅲfracture;in contrast,ModeⅠfracture is present in the specimen with a vertical internal crack.The fractography characteristics of ModeⅢfracture display a lance-like pattern.The fracture mechanism in the brittle material under compression is that the internal wing cracks propagate to the ends of the whole sample and cause the final failure.The initial deflection angle of the wing crack is determined by the participation ratio of stress intensity factors KII to KI at the tip of the internal crack.
文摘By the theory of complex functions, the dynamic propagation problem on Dugdale model of mode Ⅲ interface crack for nonlinear characters of materials was studied. The general expressions of analytical solutions are obtained by the methods of self-similar functions. The problems dealt with can be easily transformed into Riemann-Hilbert problems and their closed solutions are attained rather simply by this approach. After those solutions were utilized by superposition theorem, the solutions of arbitrarily complex problems could be obtained.
文摘An aim of current study is to analyze the contribution of reflected longitudinal waves to wave-induced fluid flow(WIFF) in the cracked porous solid.Initially,we investigate the time harmonic plane waves in cracked porous solid by employing the mathematical model proposed by Zhang et al.(2019).The solution is obtained in form of the Christoffel equations.The solution of the Christoffel equations indicates that there exist four(three dilatational and one shear) waves.These waves are attenuated in nature due to their complex and frequency-dependent velocities.The reflection coefficients are calculated at the sealed pore stress-free surface of cracked porous solid for the incidence of P1 and SV waves.It is found that three longitudinal waves contribute to WIFF and the contribution of these waves to the induced fluid in the cracked porous solid is analyzed using the reflection coefficients of these longitudinal waves.We analytically show that the fluid flow induced by these longitudinal waves is linked directly to their respective reflection coefficients.Finally,a specific numerical example is considered to discuss and to depict the impact of various parameters on the characteristics of propagation like phase velocity/attenuation,reflection coefficients and WIFF of longitudinal waves.
文摘The torsional impact response of a penny-shaped crack in a nonhomogeneous strip is considered. The shear modulus is assumed to be functionally graded such that the mathematics is tractable. Laplace and Hankel transforms were used to reduce the problem to solving a Fredholm integral equation. The crack tip stress field is obtained by considering the asymptotic behavior of Bessel function. Explicit expressions of both the dynamic stress intensity factor and the energy density factor were derived.And it is shown that, as crack driving force, they are equivalent for the present crack problem. Investigated are the effects of material nonhomogeneity and (strip's) highness on the dynamic fracture behavior. Numerical results reveal that the peak of the dynamic stress intensity factor can be suppressed by increasing the nonhomogeneity parameter of the shear modulus, and that the dynamic behavior varies little with the adjusting of the strip's highness.
基金supported by the National Natural Science Foundation of China (10772123)the Natural Science Fund for Outstanding Younger of Hebei Province of China (A2009001624)
文摘A penny-shaped interfacial crack between dissimilar magnetoelectroelastic layers subjected to magnetoelectromechanical loads is investigated,where the magnetoelectrically impermeable crack surface condition is adopted. By using Hankel transform technique,the mixed boundary value problem is firstly reduced to a system of singular integral equations,which are further reduced to a system of algebraic equations. The field intensity factors and energy release rate are finally derived. Numerical results elucidate the eects of crack configuration,electric and/or magnetic loads,and material parameters of the magnetoelectroelastic layers on crack propagation and growth. This work should be useful for the design of magnetoelectroelastic composite structures.
基金supported by the National Natural Science Foundation of China (Grant Nos. 52104125, U1765204 and 51739008)
文摘Similar to hydraulic fracturing(HF), the coalescence and fracture of cracks are induced within a rock under the action of an ultrasonic field, known as ultrasonic fracturing(UF). Investigating UF is important in both hard rock drilling and oil and gas recovery. A three-dimensional internal laser-engraved crack(3D-ILC) method was introduced to prefabricate two parallel internal cracks within the samples without any damage to the surface. The samples were subjected to UF. The mechanism of UF was elucidated by analyzing the characteristics of fracture surfaces. The crack propagation path under different ultrasonic parameters was obtained by numerical simulation based on the Paris fatigue model and compared to the experimental results of UF. The results show that the 3D-ILC method is a powerful tool for UF research.Under the action of an ultrasonic field, the fracture surface shows the characteristics of beach marks and contains powder locally, indicating that the UF mechanism includes high-cycle fatigue fracture, shear and friction, and temperature load. The two internal cracks become close under UF. The numerical result obtained by the Paris fatigue model also shows the attraction of the two cracks, consistent with the test results. The 3D-ILC method provides a new tool for the experimental study of UF. Compared to the conventional numerical methods based on the analysis of stress-strain and plastic zone, numerical simulation can be a good alternative method to obtain the crack path under UF.
基金Supported by the National Natural Science Foundation of China(10972035)
文摘To determine the solutions of the well-known problem of a finite width strip with single edge crack,some results on elasto-plastic fracture analysis for metallic foams are reported.Meanwhile,in order to discuss and put an insight into the nonlinear fracture analysis,the Dugdale model for plastic deformation of this configuration for metallic foams is recommended and solved.Combining the asymptotic solution with the Dugdale model and elastic solution,the stress field in the plastic zone and the size of the plastic zone are expressed as analytical forms.Based on Williams expansion method,the estimate of the scale factor is also completed and analyzed.In view of these analytical solutions,the results show the scale factor is a useful parameter for the fracture theory of metallic foams.
基金the National Natural Science Foundation of China (19872076) the Postdoctoral Science Foundation of China (00-2001)the National Natural Science Foundation of China for Out-sanding Young Scientists (19925209)
文摘By using Fourier transformation the boundary problem of periodical interfacial cracks in anisotropic elastoplastic bimaterial was transformed into a set of dual integral equations and then it was further reduced by means of definite integral transformation into a group of singular equations. Closed form of its solution was obtained and three corresponding problems of isotropic bimaterial, of a single anisotropic material and of a bimaterial of isotropy- anisotropy were treated as the specific cases. The plastic zone length of the crack tip and crack openning displacement ( COD) decline as the smaller yield limit of the two bonded materials rises, and they were also determined by crack length and the space between two neighboring cracks . In addition , COD also relates it with moduli of the materials .
