The analysis of plane strain elastic-plastic bending of a linear strain hardening curved beam with a narrow rectangular cross section subjected to couples at its end is conducted based on a unified yield criterion. Th...The analysis of plane strain elastic-plastic bending of a linear strain hardening curved beam with a narrow rectangular cross section subjected to couples at its end is conducted based on a unified yield criterion. The solutions for the mechanical properties of plane strain bending are derived, which are adapted for various kinds of non-strength differential materials and can be degenerated to those based on the Tresca, von Mises, and twin-shear yield criteria. The dependences of the two critical bending moments, the radii of the interfaces between the elastic and plastic regions and the radial displacements of the points at the symmetrical plane on different yield criteria and Poisson’s ratios are discussed. The results show that the influences of different yield criteria and Poisson’s ratio on the two critical bending moments, the radii of the interfaces between the elastic and plastic regions and the radial displacements of the points at the symmetrical plane of the curved beam are significant. Once the value of bis obtained by experiments, the yield criterion and the corresponding solution for the materials of interest are then determined.展开更多
Many experimental results show that a wide class of ductile materials obey often nonlinear behavior, thus it is important to propose a nonlinear criterion describing nonlinear behavior of ductile material. A new nonli...Many experimental results show that a wide class of ductile materials obey often nonlinear behavior, thus it is important to propose a nonlinear criterion describing nonlinear behavior of ductile material. A new nonlinear yield criterion was proposed which gives a series of new failure criteria, establishes a relationship among various failure criteria, and encompasses previous yield criteria as special cases or approximations. The criterion is capable of being expressed in a simple mathematical expression and through a particular physical concept, it also agree with some experimental data. It may therefore serve as a possible admissible isotropic yield criterion.展开更多
In Haigh Westergaard stress space linear combination of twin shear stress and Tresca yield functions is called the mean yield （MY） criterion. The mathematical relationship of the criterion and its plastic work rate ...In Haigh Westergaard stress space linear combination of twin shear stress and Tresca yield functions is called the mean yield （MY） criterion. The mathematical relationship of the criterion and its plastic work rate done per unit volume were derived. A generalized worked example of slab forging was analyzed by the criterion and its corresponding plastic work rate done per unit volume. Then, the precision of the solution was compared with those by Mises and Twin shear stress yield criterions, respectively. It turned out that the calculated results by MY criterion were in good agreement with those by Mises criterion.展开更多
Using the twin shear stress yield criterion, the surface integral of the co-line vectors, and the integration depending on upper limit, Kobayashi＇s three-dimensional velocity field of rolling was analyzed and an anal...Using the twin shear stress yield criterion, the surface integral of the co-line vectors, and the integration depending on upper limit, Kobayashi＇s three-dimensional velocity field of rolling was analyzed and an analytical expression of rolling torque and single force was obtained. Through redoing the same experiment of rolling pure lead as Sims, the calculated results by the above expression were compared with those of Kobayashi and Sims formulae. The results show that the twin shear stress yield criterion is available for rolling analysis and the calculated results by the new formula are a little higher than those by Kobayashi and Sims ones if the reduction ratio is less than 30%.展开更多
A generalized yield criterion is proposed based on the metai plastic deformation mechanics and the fundamental formula in theory of plasticity. Using the generalized yield criterion, the reason is explained that Mises...A generalized yield criterion is proposed based on the metai plastic deformation mechanics and the fundamental formula in theory of plasticity. Using the generalized yield criterion, the reason is explained that Mises yield criterion and Tresca yield criterion do not completely match with experimental data. It has been shown that the yield criteria of ductile metals depend not only on the quadratic invariant of the deviatoric stress tensor J2, but also on the cubic invariant of the deviatoric stress tensor J3 and the ratio of the yield stress in pure shear to the yield stress in uniaxial tension κ/σs. The reason that Mises yield criterion and Tresca yield criterion are not in good agreement with the experimental data is that the effect of J3 and κ/σs is neglected.展开更多
Currently, for some complex plastic deformations, the analytical solution can not be obtained by using Mises yield criterion, because Mises yield criterion is nine dimensions, the velocity field is complex, and the so...Currently, for some complex plastic deformations, the analytical solution can not be obtained by using Mises yield criterion, because Mises yield criterion is nine dimensions, the velocity field is complex, and the solving methods are not innovative. Corresponding solutions of these problems are that yield criterion is linearized to reduce the variable numbers, and the velocity field and the solving methods are reasonably simplified, respectively. In this paper, a new linear yield criterion--mean yield（MY） criterion and inner-product of strain rate vector are used to analytically solve 3D forging taking into account bugling of sides. The velocity field is expressed as a vector in three dimensions, and rotation and divergence are applied to confirm that the velocity field is kinematically admissible. Then, the corresponding strain rate tensor of the velocity field is transformed into principal one by making the determinant of coefficients of the tensor cubic equation be zero. By using MY criterion, the plastic power is term by term integrated and summed according to inner-product of strain rate vector. An upper bound analytical solution is obtained for the forging, and verified by a pure lead press test. The test result turns out that the total pressure calculated by MY criterion is higher by 2.5%-15% than measuring value. In addition, a measuring formula of bulging parameter （a） is proposed, but the values of a measured by the formula are lower than those optimized by the golden section search. The total pressure calculated by MY criterion is compared with the ones by twin shear, Trasca yield, and Mises yield criterion. The comparing result shows that the total pressure calculated by MY criterion is slightly higher than the mean value of that by twin shear and Trasca yield criterion, and lower than that by Mises yield criterion, but more close to that by Mises yield criterion compared with that by other two. The proposed analytical solving methods can be effectively used to other complex plastic deformation, simplifying the solving process and obtaining the reasonable results.展开更多
A novel yield criterion based on CPB06 considering anisotropic and tension-compression asymmetric behaviors of magnesium alloys was derived and proposed(called M_CPB06).This yield criterion can simultaneously predict ...A novel yield criterion based on CPB06 considering anisotropic and tension-compression asymmetric behaviors of magnesium alloys was derived and proposed(called M_CPB06).This yield criterion can simultaneously predict the yield stresses and the Lankford ratios at different angles(if any)under uniaxial tension,compression,equal-biaxial and equal-compression conditions.Then,in order to further describe the anisotropic strain-hardening characteristics of magnesium alloy,the proposed M_CPB06 criterion was further evolved to the M_CPB06ev model by expressing the parameters of the M_CPB06 model as functions of the plastic strain.As the model was developed,the stresses and Lankford ratios of AZ31B and ZK61M magnesium alloys at different angles under tensile,compressive and through-thickness compressive conditions were used to calibrate the M_CPB06/M_CPB06ev and the existing CPB06ex2 model.Calibration results reveal that compared with the CPB06ex2 yield criterion with equal quantity of coefficients,the M_CPB06 criterion exhibits certain advancement,and meanwhile the M_CPB06ev model can relatively accurately predict the change of the yield locus with increase of the plastic strain.Finally,the M_CPB06ev model was developed through UMAT in LS-DYNA.Finite element simulations using the subroutine were conducted on the specimens of different angles to the rolling direction under tension and compression.Simulation results were highly consistent with the experimental results,demonstrating a good reliability and accuracy of the developed subroutine.展开更多
Spalling of pillar ribs has been a major hazard in the mining industry for decades.In the absence of rib support guidelines,accidents have continued to occur in recent years.Developing effective support guidelines req...Spalling of pillar ribs has been a major hazard in the mining industry for decades.In the absence of rib support guidelines,accidents have continued to occur in recent years.Developing effective support guidelines requires a complete understanding of complex pillar damage mechanisms.Continuum models represent a convenient tool for analyzing this problem,but the behavior of such models is dependent of the choice of the constitutive model.In this study,a recently proposed constitutive model was used to simulate the rib fracturing process in a longwall chain pillar at West Cliff mine.After calibration,the model was able to capture the rib displacement profiles for multiple locations of the longwall face and the stress evolution 4 m into the pillar.The rib bolts in the model were found to be yielding over 60% of their length under the headgate loading condition.The model also predicted a steady damage accumulation in the rib for certain face locations,which is consistent with the description of the rib at the site.Damage was localized along the upper part of the pillar and underscored the role that the dirt band played in controlling rib deterioration at the site.The ability of the numerical model to replicate field measurements provides confidence in the capabilities of the new constitutive model.Finally,the need of using multi-point calibration is highlighted by comparing the results of the calibrated model to an alternative model calibrated to a smaller amount of data.展开更多
Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tenso...Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tensor equation, decouples the spher- ical/deviatoric strain energy density, and lays the foundation for the von Mises yield criterion. Besides, it is verified that under the precondition of energy decoupling and the simplest form, the DSDT is the only possible form of the additive decomposition with physical meanings.展开更多
In this paper a linearized and unified yield crierion of metals is presented, which is in a form of a set of linear functions with two pararneters. The parameters are ex- pressed in terms of tension yield stress and ...In this paper a linearized and unified yield crierion of metals is presented, which is in a form of a set of linear functions with two pararneters. The parameters are ex- pressed in terms of tension yield stress and so-called “shear-stretch ratio” and can bereadily determined from experimental data. It is shown that in stress space the set of yield functions is a set of polygons with twelve edges located between the Tresca’s hexagon and twin-shear-stress hexagon￣[1]. In this paper the present yield function isused to analyse the prestressiap loose running fit cylinders.展开更多
The correction in the derivation of the Gurson yield criterion is reported. Aprerequisite kine-matical condition ignored in Gurson's paper is imposed, and a parameter (C_1) ,which was unreasonably set to zero, is ...The correction in the derivation of the Gurson yield criterion is reported. Aprerequisite kine-matical condition ignored in Gurson's paper is imposed, and a parameter (C_1) ,which was unreasonably set to zero, is restored.展开更多
When the Drucker Prager yield criterion is used, the MSC/NASTRAN program frequently predicts noticeable errors. The relevant part of NASTRAN Handbook was checked and some errors in the elasto plastics theory used in...When the Drucker Prager yield criterion is used, the MSC/NASTRAN program frequently predicts noticeable errors. The relevant part of NASTRAN Handbook was checked and some errors in the elasto plastics theory used in NASTRAN were detected in this paper. The procurement to prove these errors was verified by numerical calculation.展开更多
The study results of the internal friction character of geomaterials conclude that the internal friction exists in mechanical elements all the time having a direction opposite to the shear stress,and the deformation f...The study results of the internal friction character of geomaterials conclude that the internal friction exists in mechanical elements all the time having a direction opposite to the shear stress,and the deformation failure mechanism of geomaterials greatly differs from that of metals. For metals,the failure results from shear stresses make the crystal structure slip; whereas for geomaterials,owing to its attribute of granular structures,their deformation follows the friction law,it is the co-action of shear stresses and perpendicular stresses that makes grains overcome the frictions between them,thus leading to the final failure of relative sliding.Therefore,on the basis of the cognition above,a triple shear energy criterion is proposed. Its corresponding Drucker-Prager criterion for geomaterials is also given. The new criterion can be rewritten to the Mohr-Coulomb criterion by neglecting the effect of the intermediate principal stress,and to the Mises criterion by not taking the internal friction angle into consideration. Then the studies of yield criteria commonly used are conducted systematically from the points of stress,strain and energy of geomaterials. The results show that no matter which expression form of stress,strain or energy is used for the yield criterion,the essence is the same and the triple shear energy yield criterion is the unified criterion of materials. Finally,the experimental verification is conducted in connection with the practical application of the triple shear energy yield criterion in an engineering project,and the calculation result shows that the Mohr-Coulomb criterion which only takes the single shear surface into account is more conservative than the energy criterion that does consider the effect of triple shear surfaces.展开更多
In order to overcome the nonlinearity of Mises criterion, a new linear yield criterion with a dodecagon shape of the same perimeter as Mises criterion was derived by means of geometrical analysis. Its specific plastic...In order to overcome the nonlinearity of Mises criterion, a new linear yield criterion with a dodecagon shape of the same perimeter as Mises criterion was derived by means of geometrical analysis. Its specific plastic work rate expressed as a linear function of the yield stress, the maximum and minimum strains was also deduced and compared with that of Mises criterion. The physical meaning of the proposed yield criterion is that yielding of materials begins when the shear yield stress τs reaches the magnitude of 0.594σs. By introducing the Lode parameter, validation of evolution expressions of the proposed yield criterion with those based on Tresca, Mises and TSS criteria as well as available classical yield experimental results of various metals shows that the present results intersect with Mises results and coincide well with experimental data. Moreover, further application to the limit analysis of circle plate as an example is performed to demonstrate the effectiveness of the proposed yield criterion, and the subsequent comparison of limit loads with the Tresca analytical solutions and Mises numerical results shows that the present results are higher than the Tresca analytical results, and are in good agreement with the Mises numerical results.展开更多
A kinematically admissible continuous velocity field was proposed for the analysis of three-dimensional forging.The linear yield criterion expressed by geometric midline of error triangle between Tresca and Twin shear...A kinematically admissible continuous velocity field was proposed for the analysis of three-dimensional forging.The linear yield criterion expressed by geometric midline of error triangle between Tresca and Twin shear stress yield loci on the π-plane,called GM yield criterion for short,was firstly applied to analysis of the velocity field for the forging.The analytical solution of the forging force with the effects of external zone and bulging parameter is obtained by strain rate inner product.Compression tests of pure lead are performed to compare the calculated results with the measured ones.The results show that the calculated total pressures are higher than the measured ones whilst the relative error is no more than 9.5%.It is implied that the velocity field is reasonable and the geometric midline yield criterion is available.The solution is still an upper-bound one.展开更多
For the sake of solving the problem that it is difficult to be integrated for the Mises specific plastic power due to its nonlinearity,a new linear criterion,named the globally optimal approximation criterion,is const...For the sake of solving the problem that it is difficult to be integrated for the Mises specific plastic power due to its nonlinearity,a new linear criterion,named the globally optimal approximation criterion,is constructed by the polygonal approximation to the Mises circle.The new criterion is proved to be the linear function of the principal stress componentsσ1,σ2 andσ3 and the trajectory of it on theπ-plane is a non-equiangular but equilateral dodecagon intersecting the Mises circle.The theoretical results of the current criterion described by the Lode stress parameters are in excellent accordance with the experimental results.Meanwhile,according to the trend that the metallic flow velocity between rollers aggrandizes gradually from the inlet to the outlet during the hot rolling of a thick plate,a biomimetic velocity field is proposed in which the horizontal velocity component fits the egg-circular curve distribution.The velocity field and its simulated results agree quite well.Subsequently,using the determined linear criterion,energy analysis of the constructed velocity field is utilized to obtain the interior deformation power,while the vector decomposition approach is utilized to obtain the frictional power and shear power.On this basis,the overall power is obtained and the analytical solutions are generated for the rolling torque,rolling force and the coefficient of the stress state under different egg curves by minimizing the neutral angle.Furthermore,the parameter optimization of the characteristic parameterρwhich affects the slope of the egg-circular curve is carried out and the best egg-circular curve which can minimize the energy consumption is determined.The best agreement between the theoretical and observed values of rolling force and rolling torque is under this curve,and the mean relative errors of the rolling torque and rolling force are no more than 2.93%,while the maximum error is no more than 8.35%.展开更多
This paper is devoted to developing a yield criterion that can model the asymmetry and anisotropy in yielding of pressure insensitive metals,in terms of accuracy and simplicity of formulation.First,a new isotropic yie...This paper is devoted to developing a yield criterion that can model the asymmetry and anisotropy in yielding of pressure insensitive metals,in terms of accuracy and simplicity of formulation.First,a new isotropic yield criterion,which can model the asymmetry in yielding of pressure insensitive metals,is proposed.Further,using Cazacu's generalizations to anisotropic conditions of the invariants of the deviatoric stress,the proposed isotropic yield criterion is extended to orthotropy.The proposed anisotropic criterion has a quite simple form,and the number of material constants involved is only half of that of Cazacu's(2004) yield criterion.Compared to Hill's(1948) yield criterion,the proposed anisotropic yield criterion has three additional constants,which are used to model the tension-compression asymmetry of materials.All the material constants involved in the criterion can be determined by simple tests.The proposed criterion reduces to Hill's(1948) yield criterion if the tensile and compressive yield stresses are equal.In other words,the proposed anisotropic yield criterion can be considered as an extension of Hill's(1948) criterion to tension-compression asymmetry materials.The anisotropic yield criterion is used to describe the plastic response of Cu-Al-Be shape memory alloy(data after Laydi and Lexcellent) and Ni3Al based intermetallic alloy IC10 sheets.It is shown that the proposed yield criterion can describe very well the asymmetry and anisotropy observed in those materials.展开更多
On the basis of the analysis of the hexagons inscribed and circumscribed of the Mises yield circle on the π- plane in Haigh Westergaard stress space, a new equation called equal area linear yield criterion or EA crit...On the basis of the analysis of the hexagons inscribed and circumscribed of the Mises yield circle on the π- plane in Haigh Westergaard stress space, a new equation called equal area linear yield criterion or EA criterion was proposed, and its plastic specific work rate was derived. Then, a generalized worked example of plate rolling was analyzed by the criterion and its corresponding plastic specific work rate. Finally, the precision of the solution was compared with measured roll separation force in plate finish rolling process. It indicates that the calculated results by EA criterion are slightly higher than the measured ones.展开更多
A class of plastic-damage models for concrete require an unambiguous definition of cohesion in the yield criteria. For this reason, the Lubliner yield criterion has been adopted by many investigators and the commercia...A class of plastic-damage models for concrete require an unambiguous definition of cohesion in the yield criteria. For this reason, the Lubliner yield criterion has been adopted by many investigators and the commercial FE program Abaqus. As is well known, this criterion has achieved great success especially in plane stress states. In this paper, we are trying to extend it to triaxial compression stress states. First, a major limitation of the Lubliner criterion is analyzed. Then, a revised version of the Lubliner criterion is proposed, which shows appropriate properties over a wide range of stress states often encountered in engineering structures, and the predicted failure envelopes fit well with experimental data. For the concrete damaged plasticity model in Abaqus, a calibration strategy is suggested for uniformly confined concrete.展开更多
In order to analyze the hot tandem roiling force, a new logarithmic velocity field is proposed. Using the field and linear EA （equal area） yield criterion, the plastic deformation power for plate rolling is analyzed...In order to analyze the hot tandem roiling force, a new logarithmic velocity field is proposed. Using the field and linear EA （equal area） yield criterion, the plastic deformation power for plate rolling is analyzed, and the friction power is obtained based on the co-line vector inner product method. Then analytical solution of plate rolling power functional is obtained. Finally, by minimizing the power functional, the rolling torce and torque are received. Compared with those measured ones in hot tandem rolling on-line, the calculated rolling forces are in good agreement with the actual measured ones since the maximum error is less than 12~. Moreover, the effects of various rolling conditions such as thickness reduction, friction factor and shape factor, upon separating force, location of neutral an- gle, and stress state coefficient are discussed systematically.展开更多
基金The Project of the Ministry of Housing and Urban-Rural Development(No.2014-K4-010)
文摘The analysis of plane strain elastic-plastic bending of a linear strain hardening curved beam with a narrow rectangular cross section subjected to couples at its end is conducted based on a unified yield criterion. The solutions for the mechanical properties of plane strain bending are derived, which are adapted for various kinds of non-strength differential materials and can be degenerated to those based on the Tresca, von Mises, and twin-shear yield criteria. The dependences of the two critical bending moments, the radii of the interfaces between the elastic and plastic regions and the radial displacements of the points at the symmetrical plane on different yield criteria and Poisson’s ratios are discussed. The results show that the influences of different yield criteria and Poisson’s ratio on the two critical bending moments, the radii of the interfaces between the elastic and plastic regions and the radial displacements of the points at the symmetrical plane of the curved beam are significant. Once the value of bis obtained by experiments, the yield criterion and the corresponding solution for the materials of interest are then determined.
文摘Many experimental results show that a wide class of ductile materials obey often nonlinear behavior, thus it is important to propose a nonlinear criterion describing nonlinear behavior of ductile material. A new nonlinear yield criterion was proposed which gives a series of new failure criteria, establishes a relationship among various failure criteria, and encompasses previous yield criteria as special cases or approximations. The criterion is capable of being expressed in a simple mathematical expression and through a particular physical concept, it also agree with some experimental data. It may therefore serve as a possible admissible isotropic yield criterion.
基金This research was supported by the National Natural Sci—ence Foundation of China(Grant No.50474015)
文摘In Haigh Westergaard stress space linear combination of twin shear stress and Tresca yield functions is called the mean yield （MY） criterion. The mathematical relationship of the criterion and its plastic work rate done per unit volume were derived. A generalized worked example of slab forging was analyzed by the criterion and its corresponding plastic work rate done per unit volume. Then, the precision of the solution was compared with those by Mises and Twin shear stress yield criterions, respectively. It turned out that the calculated results by MY criterion were in good agreement with those by Mises criterion.
基金ItemSponsored by National Natural Science Foundation of China (50474015)
文摘Using the twin shear stress yield criterion, the surface integral of the co-line vectors, and the integration depending on upper limit, Kobayashi＇s three-dimensional velocity field of rolling was analyzed and an analytical expression of rolling torque and single force was obtained. Through redoing the same experiment of rolling pure lead as Sims, the calculated results by the above expression were compared with those of Kobayashi and Sims formulae. The results show that the twin shear stress yield criterion is available for rolling analysis and the calculated results by the new formula are a little higher than those by Kobayashi and Sims ones if the reduction ratio is less than 30%.
文摘A generalized yield criterion is proposed based on the metai plastic deformation mechanics and the fundamental formula in theory of plasticity. Using the generalized yield criterion, the reason is explained that Mises yield criterion and Tresca yield criterion do not completely match with experimental data. It has been shown that the yield criteria of ductile metals depend not only on the quadratic invariant of the deviatoric stress tensor J2, but also on the cubic invariant of the deviatoric stress tensor J3 and the ratio of the yield stress in pure shear to the yield stress in uniaxial tension κ/σs. The reason that Mises yield criterion and Tresca yield criterion are not in good agreement with the experimental data is that the effect of J3 and κ/σs is neglected.
基金supported by National Natural Science Foundation of China (Grant No. 50474015)State Key Laboratory of Rolling and Automation(RAL) Self-determination Science Foundation of UK (Grant No. RAL_SD_2008_2)
文摘Currently, for some complex plastic deformations, the analytical solution can not be obtained by using Mises yield criterion, because Mises yield criterion is nine dimensions, the velocity field is complex, and the solving methods are not innovative. Corresponding solutions of these problems are that yield criterion is linearized to reduce the variable numbers, and the velocity field and the solving methods are reasonably simplified, respectively. In this paper, a new linear yield criterion--mean yield（MY） criterion and inner-product of strain rate vector are used to analytically solve 3D forging taking into account bugling of sides. The velocity field is expressed as a vector in three dimensions, and rotation and divergence are applied to confirm that the velocity field is kinematically admissible. Then, the corresponding strain rate tensor of the velocity field is transformed into principal one by making the determinant of coefficients of the tensor cubic equation be zero. By using MY criterion, the plastic power is term by term integrated and summed according to inner-product of strain rate vector. An upper bound analytical solution is obtained for the forging, and verified by a pure lead press test. The test result turns out that the total pressure calculated by MY criterion is higher by 2.5%-15% than measuring value. In addition, a measuring formula of bulging parameter （a） is proposed, but the values of a measured by the formula are lower than those optimized by the golden section search. The total pressure calculated by MY criterion is compared with the ones by twin shear, Trasca yield, and Mises yield criterion. The comparing result shows that the total pressure calculated by MY criterion is slightly higher than the mean value of that by twin shear and Trasca yield criterion, and lower than that by Mises yield criterion, but more close to that by Mises yield criterion compared with that by other two. The proposed analytical solving methods can be effectively used to other complex plastic deformation, simplifying the solving process and obtaining the reasonable results.
基金Beijing Natural Science Foundation(No.L201010)the United Fund of Ministry of Education for Equipment Pre-Research(Grant No.6141A02033121)National Natural Science Foundation of China(Grant No.51975041).
文摘A novel yield criterion based on CPB06 considering anisotropic and tension-compression asymmetric behaviors of magnesium alloys was derived and proposed(called M_CPB06).This yield criterion can simultaneously predict the yield stresses and the Lankford ratios at different angles(if any)under uniaxial tension,compression,equal-biaxial and equal-compression conditions.Then,in order to further describe the anisotropic strain-hardening characteristics of magnesium alloy,the proposed M_CPB06 criterion was further evolved to the M_CPB06ev model by expressing the parameters of the M_CPB06 model as functions of the plastic strain.As the model was developed,the stresses and Lankford ratios of AZ31B and ZK61M magnesium alloys at different angles under tensile,compressive and through-thickness compressive conditions were used to calibrate the M_CPB06/M_CPB06ev and the existing CPB06ex2 model.Calibration results reveal that compared with the CPB06ex2 yield criterion with equal quantity of coefficients,the M_CPB06 criterion exhibits certain advancement,and meanwhile the M_CPB06ev model can relatively accurately predict the change of the yield locus with increase of the plastic strain.Finally,the M_CPB06ev model was developed through UMAT in LS-DYNA.Finite element simulations using the subroutine were conducted on the specimens of different angles to the rolling direction under tension and compression.Simulation results were highly consistent with the experimental results,demonstrating a good reliability and accuracy of the developed subroutine.
基金funded by the National Institute for Occupational Safety and Health(NIOSH)(Grant No.200-2016-90154)sponsored by the Alpha Foundation for the Improvement of Mine Safety and Health,Inc.(ALPHA FOUNDATION)。
文摘Spalling of pillar ribs has been a major hazard in the mining industry for decades.In the absence of rib support guidelines,accidents have continued to occur in recent years.Developing effective support guidelines requires a complete understanding of complex pillar damage mechanisms.Continuum models represent a convenient tool for analyzing this problem,but the behavior of such models is dependent of the choice of the constitutive model.In this study,a recently proposed constitutive model was used to simulate the rib fracturing process in a longwall chain pillar at West Cliff mine.After calibration,the model was able to capture the rib displacement profiles for multiple locations of the longwall face and the stress evolution 4 m into the pillar.The rib bolts in the model were found to be yielding over 60% of their length under the headgate loading condition.The model also predicted a steady damage accumulation in the rib for certain face locations,which is consistent with the description of the rib at the site.Damage was localized along the upper part of the pillar and underscored the role that the dirt band played in controlling rib deterioration at the site.The ability of the numerical model to replicate field measurements provides confidence in the capabilities of the new constitutive model.Finally,the need of using multi-point calibration is highlighted by comparing the results of the calibrated model to an alternative model calibrated to a smaller amount of data.
基金supported by the National Natural Science Foundation of China(Nos.11072125 and11272175)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20130002110044)the China Postdoctoral Science Foundation(No.2015M570035)
文摘Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tensor equation, decouples the spher- ical/deviatoric strain energy density, and lays the foundation for the von Mises yield criterion. Besides, it is verified that under the precondition of energy decoupling and the simplest form, the DSDT is the only possible form of the additive decomposition with physical meanings.
文摘In this paper a linearized and unified yield crierion of metals is presented, which is in a form of a set of linear functions with two pararneters. The parameters are ex- pressed in terms of tension yield stress and so-called “shear-stretch ratio” and can bereadily determined from experimental data. It is shown that in stress space the set of yield functions is a set of polygons with twelve edges located between the Tresca’s hexagon and twin-shear-stress hexagon￣[1]. In this paper the present yield function isused to analyse the prestressiap loose running fit cylinders.
文摘The correction in the derivation of the Gurson yield criterion is reported. Aprerequisite kine-matical condition ignored in Gurson's paper is imposed, and a parameter (C_1) ,which was unreasonably set to zero, is restored.
文摘When the Drucker Prager yield criterion is used, the MSC/NASTRAN program frequently predicts noticeable errors. The relevant part of NASTRAN Handbook was checked and some errors in the elasto plastics theory used in NASTRAN were detected in this paper. The procurement to prove these errors was verified by numerical calculation.
基金National Natural Science Foundation of China (No.50609027)
文摘The study results of the internal friction character of geomaterials conclude that the internal friction exists in mechanical elements all the time having a direction opposite to the shear stress,and the deformation failure mechanism of geomaterials greatly differs from that of metals. For metals,the failure results from shear stresses make the crystal structure slip; whereas for geomaterials,owing to its attribute of granular structures,their deformation follows the friction law,it is the co-action of shear stresses and perpendicular stresses that makes grains overcome the frictions between them,thus leading to the final failure of relative sliding.Therefore,on the basis of the cognition above,a triple shear energy criterion is proposed. Its corresponding Drucker-Prager criterion for geomaterials is also given. The new criterion can be rewritten to the Mohr-Coulomb criterion by neglecting the effect of the intermediate principal stress,and to the Mises criterion by not taking the internal friction angle into consideration. Then the studies of yield criteria commonly used are conducted systematically from the points of stress,strain and energy of geomaterials. The results show that no matter which expression form of stress,strain or energy is used for the yield criterion,the essence is the same and the triple shear energy yield criterion is the unified criterion of materials. Finally,the experimental verification is conducted in connection with the practical application of the triple shear energy yield criterion in an engineering project,and the calculation result shows that the Mohr-Coulomb criterion which only takes the single shear surface into account is more conservative than the energy criterion that does consider the effect of triple shear surfaces.
基金Project(51074052)supported by the National Natural Science Foundation of ChinaProject(BK20140334)supported by the Basic Research Program of Jiangsu Province+2 种基金ChinaProject(14KJB460024)supported by the Natural Science Foundation of Jiangsu Higher Education Institutions of ChinaProject(2014M561707)supported by China Postdoctoral Science Foundation
文摘In order to overcome the nonlinearity of Mises criterion, a new linear yield criterion with a dodecagon shape of the same perimeter as Mises criterion was derived by means of geometrical analysis. Its specific plastic work rate expressed as a linear function of the yield stress, the maximum and minimum strains was also deduced and compared with that of Mises criterion. The physical meaning of the proposed yield criterion is that yielding of materials begins when the shear yield stress τs reaches the magnitude of 0.594σs. By introducing the Lode parameter, validation of evolution expressions of the proposed yield criterion with those based on Tresca, Mises and TSS criteria as well as available classical yield experimental results of various metals shows that the present results intersect with Mises results and coincide well with experimental data. Moreover, further application to the limit analysis of circle plate as an example is performed to demonstrate the effectiveness of the proposed yield criterion, and the subsequent comparison of limit loads with the Tresca analytical solutions and Mises numerical results shows that the present results are higher than the Tresca analytical results, and are in good agreement with the Mises numerical results.
基金Project(50474015)supported by the National Natural Science Foundation of China
文摘A kinematically admissible continuous velocity field was proposed for the analysis of three-dimensional forging.The linear yield criterion expressed by geometric midline of error triangle between Tresca and Twin shear stress yield loci on the π-plane,called GM yield criterion for short,was firstly applied to analysis of the velocity field for the forging.The analytical solution of the forging force with the effects of external zone and bulging parameter is obtained by strain rate inner product.Compression tests of pure lead are performed to compare the calculated results with the measured ones.The results show that the calculated total pressures are higher than the measured ones whilst the relative error is no more than 9.5%.It is implied that the velocity field is reasonable and the geometric midline yield criterion is available.The solution is still an upper-bound one.
基金support from the National Natural Science Foundation of China(Grant Nos.52074187,U1960105 and 52274388)the Undergraduate Training Program for Innovation and Entrepreneurship,Soochow University,China(Grant No.202210285158Y).
文摘For the sake of solving the problem that it is difficult to be integrated for the Mises specific plastic power due to its nonlinearity,a new linear criterion,named the globally optimal approximation criterion,is constructed by the polygonal approximation to the Mises circle.The new criterion is proved to be the linear function of the principal stress componentsσ1,σ2 andσ3 and the trajectory of it on theπ-plane is a non-equiangular but equilateral dodecagon intersecting the Mises circle.The theoretical results of the current criterion described by the Lode stress parameters are in excellent accordance with the experimental results.Meanwhile,according to the trend that the metallic flow velocity between rollers aggrandizes gradually from the inlet to the outlet during the hot rolling of a thick plate,a biomimetic velocity field is proposed in which the horizontal velocity component fits the egg-circular curve distribution.The velocity field and its simulated results agree quite well.Subsequently,using the determined linear criterion,energy analysis of the constructed velocity field is utilized to obtain the interior deformation power,while the vector decomposition approach is utilized to obtain the frictional power and shear power.On this basis,the overall power is obtained and the analytical solutions are generated for the rolling torque,rolling force and the coefficient of the stress state under different egg curves by minimizing the neutral angle.Furthermore,the parameter optimization of the characteristic parameterρwhich affects the slope of the egg-circular curve is carried out and the best egg-circular curve which can minimize the energy consumption is determined.The best agreement between the theoretical and observed values of rolling force and rolling torque is under this curve,and the mean relative errors of the rolling torque and rolling force are no more than 2.93%,while the maximum error is no more than 8.35%.
文摘This paper is devoted to developing a yield criterion that can model the asymmetry and anisotropy in yielding of pressure insensitive metals,in terms of accuracy and simplicity of formulation.First,a new isotropic yield criterion,which can model the asymmetry in yielding of pressure insensitive metals,is proposed.Further,using Cazacu's generalizations to anisotropic conditions of the invariants of the deviatoric stress,the proposed isotropic yield criterion is extended to orthotropy.The proposed anisotropic criterion has a quite simple form,and the number of material constants involved is only half of that of Cazacu's(2004) yield criterion.Compared to Hill's(1948) yield criterion,the proposed anisotropic yield criterion has three additional constants,which are used to model the tension-compression asymmetry of materials.All the material constants involved in the criterion can be determined by simple tests.The proposed criterion reduces to Hill's(1948) yield criterion if the tensile and compressive yield stresses are equal.In other words,the proposed anisotropic yield criterion can be considered as an extension of Hill's(1948) criterion to tension-compression asymmetry materials.The anisotropic yield criterion is used to describe the plastic response of Cu-Al-Be shape memory alloy(data after Laydi and Lexcellent) and Ni3Al based intermetallic alloy IC10 sheets.It is shown that the proposed yield criterion can describe very well the asymmetry and anisotropy observed in those materials.
基金Item Sponsored by National Natural Science Foundation of China(50474015)RAL Self-Determination Science Foundation of China(RAL-SD-2008-2)
文摘On the basis of the analysis of the hexagons inscribed and circumscribed of the Mises yield circle on the π- plane in Haigh Westergaard stress space, a new equation called equal area linear yield criterion or EA criterion was proposed, and its plastic specific work rate was derived. Then, a generalized worked example of plate rolling was analyzed by the criterion and its corresponding plastic specific work rate. Finally, the precision of the solution was compared with measured roll separation force in plate finish rolling process. It indicates that the calculated results by EA criterion are slightly higher than the measured ones.
文摘A class of plastic-damage models for concrete require an unambiguous definition of cohesion in the yield criteria. For this reason, the Lubliner yield criterion has been adopted by many investigators and the commercial FE program Abaqus. As is well known, this criterion has achieved great success especially in plane stress states. In this paper, we are trying to extend it to triaxial compression stress states. First, a major limitation of the Lubliner criterion is analyzed. Then, a revised version of the Lubliner criterion is proposed, which shows appropriate properties over a wide range of stress states often encountered in engineering structures, and the predicted failure envelopes fit well with experimental data. For the concrete damaged plasticity model in Abaqus, a calibration strategy is suggested for uniformly confined concrete.
基金Sponsored by National Natural Science Foundation of China(51074052,50734002)
文摘In order to analyze the hot tandem roiling force, a new logarithmic velocity field is proposed. Using the field and linear EA （equal area） yield criterion, the plastic deformation power for plate rolling is analyzed, and the friction power is obtained based on the co-line vector inner product method. Then analytical solution of plate rolling power functional is obtained. Finally, by minimizing the power functional, the rolling torce and torque are received. Compared with those measured ones in hot tandem rolling on-line, the calculated rolling forces are in good agreement with the actual measured ones since the maximum error is less than 12~. Moreover, the effects of various rolling conditions such as thickness reduction, friction factor and shape factor, upon separating force, location of neutral an- gle, and stress state coefficient are discussed systematically.
