PREDICTION OF YIELD FUNCTIONS ON BCC POLYCRYSTALS

By the nonlinear optimization theory, we predict the yield function of single BCC crystals in Hill＇s criterion form. Then we give a formula on the macroscopic yield function of a BCC polycrystal Ω under Sachs＇ model, where the volume average of the yield functions of all BCC crystallites in Ω is taken as the macroscopic yield function of the BCC polycrystal. In constructing the formula, we try to find the relationship among the macroscopic yield function, the orientation distribution function （ODF）, and the single BCC crystal＇s plasticity. An expression for the yield stress of a uniaxial tensile problem is derived under Taylor＇s model in order to compare the expression with that of the macroscopic yield function.

Investigation of the Capabilities of Yield Functions on Describing the Deformation Behavior of 5754O Aluminum Alloy Sheet Under Combined Loading Paths

The combined loading tests of 5754 O aluminum alloy sheet are used to verify the yield function. Three yield functions are implemented into the commercial finite element model(FEM) code ABAQUS as a user material subroutine UMAT for the FEM simulation of the combined loading tests. The comparison of the simulating and experimental results shows that the modified Yld2000-2d yield function can describe the mechanical behavior of5754 O aluminum alloy sheet under combined loading paths reasonably while other three yield functions do not.The performance of the modified Yld2000-2d yield function on describing the mechanical behavior under combined loading paths is analyzed in detail. It is concluded that the modified Yld2000-2d yield function can be adopted to describe the deformation behavior of 5754 O aluminum alloy sheet for industrial applications.

Calibration of anisotropic yield function by introducing plane strain test instead of equi-biaxial tensile test

The equi-biaxial tensile test is often required for parameter identification of anisotropic yield function and it demands thespecial testing technique or device. Instead of the equi-biaxial tensile test, the plane strain test carried out with the traditional uniaxialtesting machine is suggested to provide the experimental data for calibration of anisotropic yield function. This simplified method byusing plane strain test was adopted to identify the parameters of Yld2000-2d yield function for 5xxx aluminum alloy and AlMgSialloy sheets. The predicted results of yield stresses, anisotropic coefficients and yield loci by the proposed method were very similarwith the experimental data and those by the equi-biaxial tensile test. It is validated that the plane strain test is effective to provideexperimental data instead of equi-biaxial tensile test for calibration of Yld2000-2d yield function.

NEW NON QUADRATIC ORTHOTROPIC YIELD FUNCTION FOR TRIAXIAL STRESS STATE

A new Don-quadratic orthotropic yield function is developed in the present paper.It does not have those limitatioins which existing non-quadratic anisotropic yield functions have,such as being usable only for the plane stress problems and in-plane isotropic sheet metals,and that the directions of principal stress or the ex ponent in yield function can not be arbitrary,etc.Furthermore all of the material constants involved in this yield function can be determined by performing only uniaxial tension lest.This yield function contains three new parameters,of which each one is present for one principal plane of anisotropy.Their values can be.generally,selected to equal 3.Other methods to determine the value of these parmeters are discussed and given in this paper.From the regression estimate for the yield stress in five directions of several kinds of titanium metal sheet.it is obtained that the suitable value of exponent in yield function for titanium sheets is 6 or 8.This is confirmed from the use for several plastic deformation problems of titanium sheets.

Improvement of the Yield Function of Continuum Mechanics of Textured Polycrystals

The calculation procedure of the continuum mechanics of textured polycrystals (CMTP) method is reviewed to estimate calculating time with various yield functions (YFs). A so called semi quadratic YF is proposed to eliminate time consuming numerical calculation and avoid the decrease of prediction precision. The reasonability of the new YF is proved by making the comparisons between predicted R values and earing behaviour for some materials and the experimental results.

Effect of hydrostatic stress on yield function and plastic constitutive relations

A new yield function taking effect of hydrostatic stress into account is presented through establishing and solving the functional equation satisfied by the yield function, and its characteristic is simple in form and strong in generality. In order to reveal its availability, a comparison is made between the results obtained with it and the experimental results of grey cast iron has be done, both seem to be in good agreement. At the same time, taking the yield function obtained here as a potential function, a new associative plastic constitutive equation taking effect of hydrostatic stress into account is built, and the plastic volume change ratio of plastic deformation is given.

Effect of Plastic Anisotropy on the Formability of Aluminum 6016-T4 Sheet Material

Sheet metal formed of lightweight materials such as aluminum sheeting has received great attention related to the reduction of vehicle emissions. This paper evaluates the anisotropic yield locus using Kuwabara＇s biaxial tensile tester and stretches formability using Hecker＇s hemispheri- cal punch stretching test for aluminum 6016-T4 sheet material. The anisotropic yield locus of the A16016-T4 sheet measured is fitted well by the modified Drucker yield func- tion. Moreover the best fitting to the experimental stress- strain curve from the tensile test was obtained by taking an appropriate hardening model. Analytical study to predict the stretch formability by using Hora＇s Modified Maximum Force Criterion （MMFC） was performed. The predicted forming limit curves （FLC） based on various yield functions were compared with the experiments and discussed.

Numerical implementation of a modified Mohr–Coulomb model and its application in slope stability analysis

The hyperbolic function proposed by Abbo- Sloan was employed not only to approach the Mohr- Coulomb criterion but also to express the plastic potential function. A better approximation to the Mohr-Coulomb yield and potential surfaces was achieved by increasing the transition angle and proven to be highly efficient in numerical convergence. When a Gaussian integral point goes into plastic state, two cases on yield stress adjustments were introduced. They may avoid solving the second derivative of the plastic potential function and the inverse matrix compared with the existing subroutine. Based on the above approaches, a fully implicit backward Euler integral regression algorithm was adopted. The two- and three-di- mensional user subroutines which can consider the asso- ciated or non-associated flow rule were developed on the platform of the finite element program--ABAQUS. To verify the reliability of these two subroutines, firstly, the numerical simulations of the indoor conventional triaxial compression and uniaxial tensile tests were performed, and their results were compared with those of the embedded Mohr-Coulomb model and the analytical approach. Then the main influential factors including the associated or non- associated flow rule, the judgment criteria of slope failure, and the tensile strength of soil were analyzed, and the application of the two-dimensional subroutine in the sta- bility analysis of a typical soil slope was discussed in detail through comparisons with the embedded model and the limit analysis method, which shows that this subroutine is more applicable and reliable than the latter two.

A FINITE ELEMENT ANALYSIS OF THE FLANGE EARRINGS OF STRONG ANISOTROPIC SHEET METALS IN DEEP-DRAWING PROCESSES

Flange earrings of strong anisotropic sheet metals in deep-drawing process are numerically analyzed by the elastic-plastic large deformation finite element formulation based on a discrete Kirchhoff triangle plate shell element model. A Barlat-Lian anisotropic yield function and a quasi-flow corner theory are used in the present formulation. The numerical results are compared with the experimental ones of cylindrical cup drawing process. The focus of the present researches is on the numerical analysis and the constraining scheme of the flange earring of circular sheets with strong anisotropy in square cup drawing process.

FLANGE EARING AND ITS CONTROL ON DEEP-DRAWING OF ANISOTROPY CIRCULAR SHEETS

The Hill's quadric anisotropy yield function and the Barlat-Lian anisotropy yield func- tion describing well anisotropy sheet metal with stronger texture are introduced into a quadric-flow cor- ner constitutive theory of elastic-plastic finite deformation suitable for deformation localization analy- sis.And then,the elastic-plastic large deformation finite element formulation based on the virtual power principle and the discrete Kirchhoff shell element model including the yield functions and the constitutive theory are established.The focus of the present research is on the numerical simulation of the flange earing of the deep-drawing of anisotropy circular sheets,based on the investigated results, the.schemes for controlling the flange earing are proposed.

Effect of Combined Use of Brackish Water and Nitrogen Fertilizer on Biomass and Sugar Yield of Sweet Sorghum

Soil salinization and non-point source pollution are among the most important and widespread environmental problems in European Mediterranean regions. Sweet sorghum （Sorghum bicolor （L.） Moench var. saccharatum） is a moderate to high salinity tolerant crop with low water and nutrient needs, seen as an alternative to grow in the water scarce regions. A three-year multifactorial study was conducted in southern Portugal to evaluate the combined effects of saline water and nitrogen application on the dry biomass （total, stems, and leaves）, sugar content （total reducing sugars and sucrose eontents） and sugar yield （here defined as the product of total reducing sugars and stems dry biomass） functions of sweet sorghum. Sorghum dry biomass and sugar yield showed diminishing returns for each incremental change of nitrogen. The use of saline irrigation waters also led to yield reduction. Exception was sucrose content which increased with increasing levels of sodium in the soil. Nitrogen need decreased as the amount of sodium applied increased. Stem dry biomass, sucrose content, and sugar yield progressively increased with progress in the experiment. The effect could be attributed to the increase of the amount of irrigation applied throughout the years, thus increasing the leaching fraction which promoted salt leaching from the root zone, reduced the salinity stress, increased plant transpiration, nitrogen uptake and biomass yield.

A quadratic yield function with multi-involved-yield surfaces describing anisotropic behaviors of sheet metals under tension/compression

A quadratic yield function which can describe the anisotropic behaviors of sheet metals with tension/compression symmetry and asymmetry is proposed.Five mechanical properties are adopted to determine the coefficients of each part of the yield function.For particular cases,the proposed yield function can be simplified to Mises or Hill’s quadratic yield function.The anisotropic mechanical properties are expressed by defining an angle between the current normalized principal stress space and the reference direction with the assumption of orthotropic anisotropy.The accuracy of the proposed yield function in describing the anisotropy under tension and compression is demonstrated.

Criteria of limiting temperature and parametric analysis of the large deflection behavior for fully restrained steel beams in fire

This paper mainly involve 3 parts:1) To apply the minimum principle of acceleration in dynamics of elastic-plastic continua at finite deformation to the statics problems,a computing model is presented for the restrained steel beams exposed to the fire.In this model,both effects of large deflection and thermal expansion deformation are taken into account,and the constitutive equations with the temperature effects are used.Then a dynamic finite difference(DFD) method is presented by using the dis-crete technique,which can be used in simulating the response of the steel beams at elevated temperature,and the large deflec-tion behavior and catenary action effects of the beams can be adequately expressed.The primary numerical results show that the method is valid and credible.Compared with other methods,this technique is very simple,and it can also be further devel-oped to simulate the behavior of steel beams subjected to the coupling loading of explosion and fire when both effects of strain rate and inertia are considered.2) By using this DFD method,detailed parametric analysis are presented so as to check the consistency of response results for several different formulas of thermal expansion deformation and retention factors of steel at elevated temperature,the influence of these parameters on the critical temperature is examined.3) Based on the analysis for the curves of temperature-generalized yield function comprised by the axial force and bending moment,both criteria to determine the limiting temperature(or failure temperature) of large deflection steel beams are presented more explicitly,that is,both lim-iting temperatures can be determined by if the catenary force begins to appear or arrives at the maximum value,respectively.It is shown by numerical results that both limiting temperatures are close to the both critical temperatures which are correspond-ing to the maximum deflections equal to span/20 and span/10,respectively.This conclusion may be helpful to make rational fire resisting design for the steel beams.

Coupled elasto-plasticity damage constitutive models for concrete

The paper is to design and construct a coupled elasto-plasticity damage constitutive model for concrete.Based on the energy dissipation principle,the Hsieh-Ting-Chen four-parameter yield function is used.The model can reflect different strength characteristics of concrete in tension and compression,and reduce the limitation and lacuna of the traditional damage constitutive models for concrete.Furthermore,numerical test for concrete stress-strain relation under uniaxial tension and compression is given.Moreover,the damage process of concrete gravity dam is calculated and analyzed in seismic load.Compared with other damage constitutive models,the proposed model contains only one unknown parameter and the other parameters can be found in the Hsieh-Ting-Chen four-parameter yield function.The same damage evolution law,which is used for tension and compression,is good for determining stress-strain constitutive and damage characteristics in complex stress state.This coupled damage constitutive models can be applied in analyzing damage of concrete gravity dam and arch dam.

CONSTITUTIVE MODELING OF ROLLED SHAPE MEMORY ALLOY SHEETS TAKING INTO ACCOUNT PRE-TEXTURE AND ANISOTROPIC HARDENING

The drawing or rolling process endows polycrystal shape memory alloy with a crys- tallographic texture, which can result in macroscopic anisotropy. The main purpose of this work is to develop a constitutive model to predict the thermomechanical behavior of shape memory alloy sheets, which accounts for the crystallographic texture. The total macroscopic strain is decom- posed into elastic strain and macro-transformation strain under isothermal condition. Considering the transformation strain in local grains and the orientation distribution function of crystallo- graphic texture, the macro-transformation strain and the effective elastic modulus of textured polycrystal shape memory alloy are developed by using tensor expressions. The kinetic equation is established to calculate the volume fraction of the martensite transformation under given stress. Furthermore, the Hill＇s quadratic model is developed for anisotropic transformation hardening of textured SMA sheets. All the calculation results are in good agreement with experimental data, which show that the present model can accurately describe the macro-anisotropic behaviors of textured shape memory alloy sheets.

Prediction of Forming Limit Diagrams for Materials with HCP Structure

The forming limit diagram（FLD） is an important tool to be used when characterizing the formability of metallic sheets used in metal forming processes. Experimental measurement and determination of the FLD is timeconsuming and therefore the analytical prediction based on theory of plasticity and instability criteria allows a direct and efficient methodology to obtain critical values at different loading paths, thus carrying significant practical importance.However, the accuracy of the plastic instability prediction is strongly dependent on the choice of the material constitutive model [1–3]. Particularly for materials with hexagonal close packed（HCP） crystallographic structure, they have a very limited number of active slip systems at room temperature and demonstrate a strong asymmetry between yielding in tension and compression [4, 5]. Not only the magnitude of the yield locus changes, but also the shape of the yield surface is evolving during the plastic deformation [4]. Conventional phenomenological constitutive models of plasticity fail to capture this unconventional mechanical behavior [4, 6]. Cazacu and Plunkett [6] have proposed generic yield criteria, by using the transformed principal stress, to account for the initial plastic anisotropy and strength differential（SD） effect simultaneously. In this contribution, a generic FLD MATLAB script was developed based on Marciniak–Kuczynski analytical theory and applied to predict the localized necking. The influence of asymmetrical effect on the FLD was evaluated. Several yield functions such as von Mises, Hill, Barlat89, and Cazacu06 were incorporated into analysis. The paper also presents and discusses the influence of different hardening laws on the formability of materials with HCP crystal structures. The findings indicate that the plastic instability theory coupled with Cazacu model can adequately predict the onset of localized necking for HCP materials under different strain paths.

A numerical and an analytical method for optimum planting date determination

Apart from number and size of machines in a farm,operations scheduling can also affect timeliness costs.In this study a new equation was presented for determination of timeliness costs and it was proven that the new equation is a generalization of the well-known ASABE standard equation.Based on the new equation,a parameter namely,timeliness index was defined that indicates the distribution of an operation around the optimum time of performing the operation.By minimizing the index,the whole timeliness cost is minimized.Since the planting operation is highly sensitive to its time of accomplishment,timeliness cost was determined accordingly.In this study the optimum planting starting date(opls)regarding the concept of timeliness costs,was determined.If for any reason,the planting operation cannot be performed in the minimum planting period,an optimization method is required to determine opls.For this,a numerical approach and an analytical method were presented for determination of opls and a computer model was developed based on the numerical method.opls was determined for the Research Farm of the University of Tehran in Karaj–Iran and both methods showed good agreement with each other.