Generalization of Hill's yield criterion to tension-compression asymmetry materials

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.

Analysis of plane strain bending of a strain hardening curved beam based on unified yield criterion

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.

Derivation of Plastic Work Rate Done per Unit Volume for Mean Yield Criterion and Its Application

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.

A Generalized Yield Criterion

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.

Three-Dimensional Analysis of Rolling by Twin Shear Stress Yield Criterion

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%.

Equal perimeter yield criterion and its specific plastic work rate: Development, validation and application

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.

New double yield surface model for coarse granular materials incorporating nonlinear unified failure criterion

A new double-yield-sarface （DYS） model was developed to characterize the strength and deformation behaviors of coarse granular materials （CGMs）. Two kinds of deformation mechanisms, including the shear and compressive plastic deformation, were taken into account in this model, These two deformation mechanisms were described by the shear and compressive yield functions, respectively. The Lode angle dependent formulations of proposed model were deduced by incorporating a 3D nonlinear unified failure criterion. Some comparisons were presented between the numerical predictions of proposed model and test data of true triaxial tests on the modeled rockfills. The model predictions are in good agreement with the test data and capture the strain hardening and plastic volumetric dilation of CGMs. These findings verify the reasonability of current DYS model, and indicate that this model is well suited to reproduce the stress-strain-volume change behavior of CGMs in general.

Analytical Solution for Three-dimensional Forging Taking into Account Bulging of Sides by Mean Yield Criterion

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.

Disease Grading Criterion and Assessment of Yield Loss Caused by Maize Rough Dwarf Disease

[Objective] The paper was to study the disease grading criterion and assess the yield loss caused by maize rough dwarf disease. [Method] The ear lengths and yields of each healthy and infected plant of 5 cultivars were measured during 2009 and 2010. The severity grading criterion was deduced according to the ear length ratios. [Result]When the ratios were 0.92-1.00, 0.67-0.91, 0.41-0.66, 0.10-0.40 and 0, its corresponding disease grading criterions were 0, 1, 3, 5 and 7, respectively. The severity grading criterion was closely correlated to the yield loss. By analyzing the data of disease indexes and yield loss rates of 27 cultivars with DPS （Data Processing System）, the regression equations were established respectively. According to the comparison with each other, the Weibull Model was proved to have the highest fitting degree. Validating with the disease indexes of 27 cultivars in 2010, the equation supported the feasibility of the equation to predict the yield loss caused by maize rough dwarf disease. [Conclusion] The paper provided theoretical basis for further study on maize rough dwarf disease.

A New Nonlinear Yield Criterion

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.

An improved yield criterion characterizing the anisotropic and tension-compression asymmetric behavior of magnesium alloy

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.

Modeling behaviors of a coal pillar rib using the progressive S-shaped yield criterion

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.

Application of geometric midline yield criterion to analysis of three-dimensional forging

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.

A Linearized and Unified Yield Criterion of Metals and Its Application

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.

CORRECTION OF THE GURSON YIELD CRITERION

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.

Relations between cubic equation, stress tensor decomposition, and von Mises yield criterion

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.

A unified criterion for yielding behavior of metallic glasses

The yield behavior of metallic glasses was studied. Three yield criteria, including von Mises yield criterion, Mohr-Coulomb yield criterion and the unified yield criterion were used to describe the yield phenomena of the metallic glasses. Two classes of the experimental data were chosen to draw the yield loci using the unified yield criterion. It is shown that the unified yield criterion can be used to describe the yield behavior of the metallic glasses no matter whether the metallic glasses show strength- different effect or non-strength-different effect. Almost all the widely accepted yield criteria are the subsets of the unified yield criterion if the intermediate principle stress and/or the intermediate principle shear stress are not considered at all.

Cause of Errors Associated with Application of Drucker-Prager Yield Criterion in MSC/NASTRAN Program

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.

Optimization of yield criterion and simulation based on QP980 high strength steel

QP980 is an ultra high strength steel.First,uniaxial and biaxial tension tests have been done in different loading paths.Then QP980 basic mechanical properties have been obtained.And the stress and strain graph has been drawn.Second,according to the equal principle of the unit volume plastics work and yield stress,QP980 plastic work contour map has been drawn.Third,through comparing Mises,Hill'48,Hosford and Barlat89 yield criterion theoretical curves with the experimental plastic work contour map,the result shows that the Hill'48 yield criterion is in good conformity with the QP980 material.Fourth,Hill'48 yield criterion is optimized by introducing an equivalent plastic strain parameter.The result shows that average error of optimized Hill'48 theoretical yield trajectory is reduced by 8.4%.Last,finite element model about variable cross-section roll forming is established,then applying the optimized Hill'48 parameter yield criterion to the ABAQUS for finite element simulation.The simulation result shows that the forming quality is good,and in agreement with the actual forming parts.Therefore,the optimized Hill'48 yield criterion can be used to precisely describe QP980 ultra high strength steel.

A study of the energy yield criterion of geomaterials

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.