The near crack line analysis method has been used in the present paper,The classical small scale yielding conditions have been completely abandoned in the analyses and one inappropriate matching condition used to be u...The near crack line analysis method has been used in the present paper,The classical small scale yielding conditions have been completely abandoned in the analyses and one inappropriate matching condition used to be used at the elasticplastic boundary has been corrected.The reasonable solution of the plastic stresses near the crack line region has been established.By matching the plastic stresses with the exact elastic stresses at the elastic-plastic boundary,the plastic stresses the length of the plastic zone and the unit normal vector of the elastic-plastic boundary near the crock line region have been obtained for a mode I crack under uniaxial tension,as well as a mode I crack under biaxial tension,which shows that for both conditions the plastic stress componentsσy, and σsy.he length of the plastic zone and the unit normal vector of the elastic-plastic boundary are quite the same while the plastic stress σs is different.展开更多
Under the condition that all the stress components at a crack-tip are the functions of 0 only, making use of the equations of steady-state motion. Hill anisotropic yield condition and stress-strain relations, we obtai...Under the condition that all the stress components at a crack-tip are the functions of 0 only, making use of the equations of steady-state motion. Hill anisotropic yield condition and stress-strain relations, we obtain the general solution of anisotropic plastic field at a rapidly propagating plane-stress crack-tip. Applying this general solution to four particular cases of anisotropy, the general solutions of these four particular cases are derived. Finally, we give the anisotropic plastic field at the rapidly propagating plane-stress mode I crack-tip in the case of X=Y=Z展开更多
The crack-tip field under plane stress condition for an incompressible rubbermaterial￣[1] is investigated by. the use of the fully nonlinear equilibrium theory. It isfound thai the crack-tip field is composed of two ...The crack-tip field under plane stress condition for an incompressible rubbermaterial￣[1] is investigated by. the use of the fully nonlinear equilibrium theory. It isfound thai the crack-tip field is composed of two shrink sectors and one expansion se-ctor. At the crack-tip, stress and strain possess the singularity of R￣(-1) and R￣(-1n), respec-tively, (R is the distance to the crack-tip before deformation, n is the material const-ant). When the crack-tip is approached, the thickness of the sheet shrinks to zerowith the order of R￣(1.4n). The results obtained in this paper are consistent with that ob-tained in [8] when s→∞ .展开更多
Under the hypothesis that all the perfectly plastic stress components at a orach tip are the functions of θ only, making use of yield conditions and equilibrium equations. we derive the generally analytical expressio...Under the hypothesis that all the perfectly plastic stress components at a orach tip are the functions of θ only, making use of yield conditions and equilibrium equations. we derive the generally analytical expressions of the perfectly plastic stress field at a crack tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of perfectly plastic stress fields at the tips of Mode Ⅰ Mode Ⅱ, Mode Ⅲ and Mixed Mode Ⅰ-Ⅱ cracks are obtained.展开更多
Under the condition that all the perfectly plastic stress components at a crack tip are the functions of ? only, making use of equilibrium equations and Von-Mises yield condition containing Poisson ratio, in this pape...Under the condition that all the perfectly plastic stress components at a crack tip are the functions of ? only, making use of equilibrium equations and Von-Mises yield condition containing Poisson ratio, in this paper, we derive the generally analytical expressions of perfectly plastic stress field at a stationary plane-strain crack tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of perfectly plastic stress fields at the stationary tips of Mode I, Mode II and Mixed-Mode I-II plane-strain cracks are obtained. These analytical expressions contain Poisson ratio.展开更多
The problem regarding the reflection of plane waves in a transversely isotropic dissipative medium is considered, in which we are studying about the reflection of incidence waves in initially stressed dissipative half...The problem regarding the reflection of plane waves in a transversely isotropic dissipative medium is considered, in which we are studying about the reflection of incidence waves in initially stressed dissipative half space. After solving the governing equations, we find the two complex quasi-P (qP) and quasi-SV (qSV) waves. The occurrence of reflected waves is studied to calculate the reflection coefficient and the energy partition of incidence wave at the plane boundary of the dissipative medium. Numerical example is considered for the reflection coefficient and the partition of incident energy, in which we study about the effect of rotation, initial stresses and magnetic field.展开更多
Through detailed three-dimensional （3D） finite element （FE） calculations, the out-of-plane constraints Tz along embedded center-elliptical cracks in mode I elastic plates are studied. The distributions of Tz are o...Through detailed three-dimensional （3D） finite element （FE） calculations, the out-of-plane constraints Tz along embedded center-elliptical cracks in mode I elastic plates are studied. The distributions of Tz are obtained near the crack front with aspect ratios （a/c） of 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0. Tz decreases from an approximate value of Poisson ratio v at the crack tip to zero with increasing normalized radial distances （r/a） in the normal plane of the crack front line, and increases gradually when the elliptical parameter angle φ changes from 0° to 90°at the same r/a. With a/c rising to 1.0, Tz is getting nearly independent of φ and is only related to r/a. Based on the present FE calculations for Tz, empirical formulas for Tz are obtained to describe the 3D distribution of Tz for embedded center-elliptical cracks using the least squares method in the range of 0.2 ≤ a/c ≤ 1.0. These Tz results together with the corresponding stress intensity factor K are well suitable for the analysis of the 3D embedded centerelliptical crack from field, and a two-parameter K-Tz principle is proposed.展开更多
The strain gradient effect becomes significant when the size of frac- ture process zone around a crack tip is comparable to the intrinsic material length l, typically of the order of microns. Using the new strain grad...The strain gradient effect becomes significant when the size of frac- ture process zone around a crack tip is comparable to the intrinsic material length l, typically of the order of microns. Using the new strain gradient deformation theory given by Chen and Wang, the asymptotic fields near a crack tip in an elastic-plastic material with strain gradient effects are investigated. It is established that the dom- inant strain field is irrotational. For mode Ⅰ plane stress crack tip asymptotic field, the stress asymptotic field and the couple stress asymptotic field can not exist si- multaneously. In the stress dominated asymptotic field, the angular distributions of stresses are consistent with the classical plane stress HRR field; In the couple stress dominated asymptotic field, the angular distributions of couple stresses are consistent with that obtained by Huang et al. For mode Ⅱ plane stress and plane strain crack tip asymptotic fields, only the stress-dominated asymptotic fields exist. The couple stress asymptotic field is less singular than the stress asymptotic fields. The stress asymptotic fields are the same as mode Ⅱ plane stress and plane strain HRR fields, respectively. The increase in stresses is not observed in strain gradient plasticity for mode Ⅰ and mode Ⅱ, because the present theory is based only on the rotational gradi- ent of deformation and the crack tip asymptotic fields are irrotational and dominated by the stretching gradient.展开更多
The Ms6.2 Dayao, Yunnan, earthquake occurred on July 21, 2003, followed by a major Ms6.1 earthquake about 88 days later in the same region. Hypocenters of the two earthquakes are almost in the same place. Based on the...The Ms6.2 Dayao, Yunnan, earthquake occurred on July 21, 2003, followed by a major Ms6.1 earthquake about 88 days later in the same region. Hypocenters of the two earthquakes are almost in the same place. Based on the P wave first motion polarities of the two aftershock sequences recorded by temporary stations, we have studied the stress field in the aftershock zone and obtained the two stress field directions in Dayao region using the new version of PKU_Grid^Test Software provided by Chunquan Yu. Assuming that the rotation of the stress field is caused by the second main shock, we estimated the crustal stress value in the focal region by using the stress value calculation method proposed by Yongge Wan. The estimated maximum, intermediate and minimum principal stresses are 166.3 MPa, 158.7 MPa and 151 MPa, respectively, before the second main shock. The normal and shear stresses projected on the fault plane of the second main shock before it occurred are 157.3 MPa, 7.4 MPa, and are 158.8 MPa, 0.2 MPa after it occurred, respectively. The perturbed input parameters experiments attest the stability of the solution. The result shows that the preseismic shear stress is larger than the post-seismic one, and their difference corresponds to the stress drop approximately. The estimated compressive stress level is very high, but the differential stress is low. The result is helpful for friction coefficient estimation, plate motion simulation and related studies.展开更多
Using complex variable methods in elasticity, this paper deals with the plane problems ot a finite disc containing an internal linear crack at any position under general loads, obtains the general forms of Complex str...Using complex variable methods in elasticity, this paper deals with the plane problems ot a finite disc containing an internal linear crack at any position under general loads, obtains the general forms of Complex stress functions and stress-intensity tactors expressed in terms of series, and to these problems disiusses three sposial cases,i.e.the cases of the crack under a uniform pressure, a uniform shear stress and the use of the dise rotating uniformly. In these cases the approximate formulas calcidating the stress-intensity factors are also presented. The calculated results shun that for the middle and.small orachs situated inside the disc and not near the external boundary,these approximate formulas give good or better approximation.展开更多
This paper presents an exact analysis for high order asymptotic field of theplane stress crack problem.It has been shown that the second order asymptotic field is notan independent eigen field and should be matched wi...This paper presents an exact analysis for high order asymptotic field of theplane stress crack problem.It has been shown that the second order asymptotic field is notan independent eigen field and should be matched with the elastic strain term of the firstorder asymptotic field.The second order stress field ahead of the crack tip is quite smallcompared with the first order stress field.The stress field ahead of crack tip is character-ized by the HRR field.Hence the J integral can be used as a criterion for crack initiation.展开更多
文摘The near crack line analysis method has been used in the present paper,The classical small scale yielding conditions have been completely abandoned in the analyses and one inappropriate matching condition used to be used at the elasticplastic boundary has been corrected.The reasonable solution of the plastic stresses near the crack line region has been established.By matching the plastic stresses with the exact elastic stresses at the elastic-plastic boundary,the plastic stresses the length of the plastic zone and the unit normal vector of the elastic-plastic boundary near the crock line region have been obtained for a mode I crack under uniaxial tension,as well as a mode I crack under biaxial tension,which shows that for both conditions the plastic stress componentsσy, and σsy.he length of the plastic zone and the unit normal vector of the elastic-plastic boundary are quite the same while the plastic stress σs is different.
文摘Under the condition that all the stress components at a crack-tip are the functions of 0 only, making use of the equations of steady-state motion. Hill anisotropic yield condition and stress-strain relations, we obtain the general solution of anisotropic plastic field at a rapidly propagating plane-stress crack-tip. Applying this general solution to four particular cases of anisotropy, the general solutions of these four particular cases are derived. Finally, we give the anisotropic plastic field at the rapidly propagating plane-stress mode I crack-tip in the case of X=Y=Z
文摘The crack-tip field under plane stress condition for an incompressible rubbermaterial￣[1] is investigated by. the use of the fully nonlinear equilibrium theory. It isfound thai the crack-tip field is composed of two shrink sectors and one expansion se-ctor. At the crack-tip, stress and strain possess the singularity of R￣(-1) and R￣(-1n), respec-tively, (R is the distance to the crack-tip before deformation, n is the material const-ant). When the crack-tip is approached, the thickness of the sheet shrinks to zerowith the order of R￣(1.4n). The results obtained in this paper are consistent with that ob-tained in [8] when s→∞ .
文摘Under the hypothesis that all the perfectly plastic stress components at a orach tip are the functions of θ only, making use of yield conditions and equilibrium equations. we derive the generally analytical expressions of the perfectly plastic stress field at a crack tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of perfectly plastic stress fields at the tips of Mode Ⅰ Mode Ⅱ, Mode Ⅲ and Mixed Mode Ⅰ-Ⅱ cracks are obtained.
文摘Under the condition that all the perfectly plastic stress components at a crack tip are the functions of ? only, making use of equilibrium equations and Von-Mises yield condition containing Poisson ratio, in this paper, we derive the generally analytical expressions of perfectly plastic stress field at a stationary plane-strain crack tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of perfectly plastic stress fields at the stationary tips of Mode I, Mode II and Mixed-Mode I-II plane-strain cracks are obtained. These analytical expressions contain Poisson ratio.
文摘The problem regarding the reflection of plane waves in a transversely isotropic dissipative medium is considered, in which we are studying about the reflection of incidence waves in initially stressed dissipative half space. After solving the governing equations, we find the two complex quasi-P (qP) and quasi-SV (qSV) waves. The occurrence of reflected waves is studied to calculate the reflection coefficient and the energy partition of incidence wave at the plane boundary of the dissipative medium. Numerical example is considered for the reflection coefficient and the partition of incident energy, in which we study about the effect of rotation, initial stresses and magnetic field.
基金The project supported by the National Natural Science Foundation of China （50275073）
文摘Through detailed three-dimensional （3D） finite element （FE） calculations, the out-of-plane constraints Tz along embedded center-elliptical cracks in mode I elastic plates are studied. The distributions of Tz are obtained near the crack front with aspect ratios （a/c） of 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0. Tz decreases from an approximate value of Poisson ratio v at the crack tip to zero with increasing normalized radial distances （r/a） in the normal plane of the crack front line, and increases gradually when the elliptical parameter angle φ changes from 0° to 90°at the same r/a. With a/c rising to 1.0, Tz is getting nearly independent of φ and is only related to r/a. Based on the present FE calculations for Tz, empirical formulas for Tz are obtained to describe the 3D distribution of Tz for embedded center-elliptical cracks using the least squares method in the range of 0.2 ≤ a/c ≤ 1.0. These Tz results together with the corresponding stress intensity factor K are well suitable for the analysis of the 3D embedded centerelliptical crack from field, and a two-parameter K-Tz principle is proposed.
文摘The strain gradient effect becomes significant when the size of frac- ture process zone around a crack tip is comparable to the intrinsic material length l, typically of the order of microns. Using the new strain gradient deformation theory given by Chen and Wang, the asymptotic fields near a crack tip in an elastic-plastic material with strain gradient effects are investigated. It is established that the dom- inant strain field is irrotational. For mode Ⅰ plane stress crack tip asymptotic field, the stress asymptotic field and the couple stress asymptotic field can not exist si- multaneously. In the stress dominated asymptotic field, the angular distributions of stresses are consistent with the classical plane stress HRR field; In the couple stress dominated asymptotic field, the angular distributions of couple stresses are consistent with that obtained by Huang et al. For mode Ⅱ plane stress and plane strain crack tip asymptotic fields, only the stress-dominated asymptotic fields exist. The couple stress asymptotic field is less singular than the stress asymptotic fields. The stress asymptotic fields are the same as mode Ⅱ plane stress and plane strain HRR fields, respectively. The increase in stresses is not observed in strain gradient plasticity for mode Ⅰ and mode Ⅱ, because the present theory is based only on the rotational gradi- ent of deformation and the crack tip asymptotic fields are irrotational and dominated by the stretching gradient.
基金supported by the National Natural Science Foundation of China (40874022,41074072)Public Utility Research Project (200808053)973 program (2008CB425703)
文摘The Ms6.2 Dayao, Yunnan, earthquake occurred on July 21, 2003, followed by a major Ms6.1 earthquake about 88 days later in the same region. Hypocenters of the two earthquakes are almost in the same place. Based on the P wave first motion polarities of the two aftershock sequences recorded by temporary stations, we have studied the stress field in the aftershock zone and obtained the two stress field directions in Dayao region using the new version of PKU_Grid^Test Software provided by Chunquan Yu. Assuming that the rotation of the stress field is caused by the second main shock, we estimated the crustal stress value in the focal region by using the stress value calculation method proposed by Yongge Wan. The estimated maximum, intermediate and minimum principal stresses are 166.3 MPa, 158.7 MPa and 151 MPa, respectively, before the second main shock. The normal and shear stresses projected on the fault plane of the second main shock before it occurred are 157.3 MPa, 7.4 MPa, and are 158.8 MPa, 0.2 MPa after it occurred, respectively. The perturbed input parameters experiments attest the stability of the solution. The result shows that the preseismic shear stress is larger than the post-seismic one, and their difference corresponds to the stress drop approximately. The estimated compressive stress level is very high, but the differential stress is low. The result is helpful for friction coefficient estimation, plate motion simulation and related studies.
文摘Using complex variable methods in elasticity, this paper deals with the plane problems ot a finite disc containing an internal linear crack at any position under general loads, obtains the general forms of Complex stress functions and stress-intensity tactors expressed in terms of series, and to these problems disiusses three sposial cases,i.e.the cases of the crack under a uniform pressure, a uniform shear stress and the use of the dise rotating uniformly. In these cases the approximate formulas calcidating the stress-intensity factors are also presented. The calculated results shun that for the middle and.small orachs situated inside the disc and not near the external boundary,these approximate formulas give good or better approximation.
基金Project supported by the National Natural science Foundation of china.
文摘This paper presents an exact analysis for high order asymptotic field of theplane stress crack problem.It has been shown that the second order asymptotic field is notan independent eigen field and should be matched with the elastic strain term of the firstorder asymptotic field.The second order stress field ahead of the crack tip is quite smallcompared with the first order stress field.The stress field ahead of crack tip is character-ized by the HRR field.Hence the J integral can be used as a criterion for crack initiation.
