Finite element analysis using elasto-visco-plastic self-consistent polycrystal model for E-form Mg sheet subjected to bending

The mechanical behavior of a magnesium alloy E-form under bending was investigated using the elasto-visco-plastic polycrystal model(ΔEVPSC) and its finite element(FE) implementation(ΔEVPSC-FE) developed in Jeong et al. and Jeong and Tomé. The crystallographic orientation distribution(COD) obtained from X-ray diffraction was used to represent the initial texture, and the Voce hardening parameters were calibrated by fitting the uniaxial tension and the compression flow stress curves. A quasi-static FE analysis of a miniaturized V-bending operation was conducted using the ΔEVPSC-FE model. The bending induced an inhomogeneous stress response along the through-thickness and the lateral directions, which was well captured by the model. Moreover, the predictive capability of the model was validated by comparing with various experimental results such as(1) force vs. displacement curves;(2) the through-thickness variations in the twin volume fraction;and(3) the changes in crystallographic texture as a function of displacement. Additional bending simulation was performed using an isotropic texture, the result of which suggests that the potential improvement in bendability of the magnesium alloy is attainable by weakening the initial texture. Moreover, the simulation results imply that the crystallographic texture, which may affect the twin activation across the thickness direction, plays a significant role in the shifting direction of the neutral layer.

Polycrystalline model for FE-simulation of micro forming processes

A new polycrystal model was presented from the viewpoint of polycrystal structure of the billets considering free surface effects.In the model,the billet was divided into three portions,such as free surface portion,transition portion and internal portion.The grains in free surface portion were considered the single grains,and the anisotropy of the grains was taken into account by introducing grain orientation to explain the inhomogeneous deformation.In the transition portion,the effects of the neighbouring grains were adopted in the model.The grains in the internal portion were considered the polycrystalline material.With the developed model,the upsetting deformation process was simulated by the MSC Superform software.The scatter of the flow stress and inhomogeneous deformation was observed by analysis of the model.The comparisons show that the computational results are good agreed with the experimental results.This means that the presented model is effective.

Deformation mechanisms of Mg-3Al-1Zn alloy by polycrystal plasticity modeling

A polycrystal plasticity model was developed to analyze the room-temperature deformation behaviors of Mg-3A1-1Zn alloy（AZ31）.The uniaxial tension and compression tests at room temperature were conducted using cast and extruded AZ31 rods with different textures and combined with the proposed model to reveal the deformation mechanisms.It is shown that,different flow curves of two specimens under tension and compression tests can be simulated by this model.The flow curves of AZ31 extrusions exhibit different shapes for tension and compression due to different activities of tensile twinning and pyramidalc＋a slip.The metallographic and TEM observations showed the equal twinning activities at the initial stage in tension and compression tests and the occurrence of pyramidalc＋a slip in compression of as-cast Mg-3A1-1Zn alloy with increasing the strain,which is consistent with the simulated results by the proposed model.

Polycrystal modeling of hot extrusion texture of AZ80 magnesium alloy

The visco-plastic self-consistent (VPSC) model is extended to take the dynamical recrystallization (DRX) into account so that the hot extrusion texture of AZ80 magnesium alloy can be properly modeled. The effects of extrusion temperatures and imposed boundary conditions on the resulting textures were investigated, and good agreement can be found between the simulated and the measured extrusion textures. The simulated results show that the DRX grains are responsible for the formation of the {2110} fiber component since the {1010} poles of the DRX grains are tilted away from those of the unrecrystallized grains during the formation of their high angle boundaries (HABs). Furthermore, the basal poles of the grains are favorably oriented to the transversal direction (TD) where the imposed deformation is larger due to lower slip resistance of the basal slip. The elevated temperature enhances the activity of pyramidal ?c+a? slip modes and gives rise to a larger recrystallized volume fraction, resulting in a weakened extrusion texture.

Constitutive relation of an orthorhombic polycrystal with the shape coefficients

An orthorhombic polycrystal is an orthorhombic aggregate of tiny crystallites. In this paper, we study the effect of the crystalline mean shape on the constitutive relation of the orthorhombic polycrystal. The crystalline mean shape and the crystalline orientation arrangement are described by the crystalline shape function （CSF） and the orientation distribution function （ODF）, respectively. The CSF and the ODF are expanded as an infinite series in terms of the Wigner D-functions. The expanded coefficients of the CSF and the ODF are called the shape coefficients s^lm0 and the texture coefficients c^lmn respectively. Assuming that Ceff in the constitutive relation depends on the shape coefficients s^lm0 and the texture coefficients c^lmn by the principle of material frame-indifference we derive an analytical expression for C^eff up to terms linear in s^lmo and c^lmn and the expression would be applicable to the polycrystal whose texture is weak and whose crystalline mean shape has weak anisotropy. C^cff contains six unspecified material constants （λ, μ, c, s1, s2, s3）, five shape coefficients （s^2 00, s^2 20, s^4 00, s^4 20, s^4 40）, and three texture coefficients （c^4 99,c^4 20, c^4 40）, The results based on the perturbation approach are used to determine the five material constants approximately. We also find that the shape coefficients 2 and a s^2mo and s^4m0 are all zero if the crystalline mean shape is a cuboid. Some examples are given to compare our computational results.

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.

Experimental Study and Finite Element Polycrystal Model Simulation of the Cold Rolling Textures in a Powder Metallurgy Processed Pure Aluminum Plate

Ingot metallurgy (IM) aluminum has long been the subject and attracted the attention of many metallurgists and textural researchers of materials. Due to the introduction of large amounts of ex situ interfaces, however, the textures in powder metallurgy (PM) processed aluminum has been rarely reported. In this article, a pure aluminum plate was prepared via PM route. The starting billet was first produced with uni-axially cold compaction and flat hot-extrusion and then followed by cold rolling processes. The hot-extruded and cold rolling deformation textures of the pure PM aluminum at 50%, 80% and 90% cold rolling reductions were studied by orientation distribution functions (ODFs) analysis. The finite element polycrystal model (FEPM) was finally utilized to simulate the cold rolling textural evolution at various stages of cold rolling. In FEPM simulation, the initial hot-extruded textures were taken into account as inputs. The results showed that typical β-fiber texture formed in pure PM aluminum with the cold rolling reduction increased till 80%, and there was not much change after excessive cold rolling deformation. Homogeneous slip is not the only deformation mode in PM processed pure aluminum plate at over 80% cold rolling reduction. The experimental results were qualitatively in good agreement with the simulated ones.

Force-Field Derivation and Atomistic Simulation of HMX/Graphite Interface and Polycrystal Systems

Interface is the key issue to understand the performance of composite materials.In this work,we study the interface between octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine(HMX) and graphite,try to find out its contribution to mixture explosives.The work starts from the force-field derivation.We get ab initio based pair potentials across the interface,and then use them to study the interface structural and mechanical properties.A series of large scale molecular dynamics simulations are performed.The structure evolution,energy variation and elastic/plastic transformation of interface and polycrystal systems are calculated.The desensitizing mechanism of graphite to HMX is discussed.

Influence of Al on the magnetostriction of Fe-Ga polycrystal alloys under compressive stress

Fe80Ga20-xAlx （x = 0, 6, 9, 14） ingots were prepared from high purity elements using a vacuum induction system. X-ray diffraction patterns show that the alloys are A2 disordered structures. The influence of the partial substitution of Ga in Fe-Ga alloys with A1 on their magnetostrictive properties was investigated, and the effects of different heat treatment conditions on the magnetostriction and microstructure of the alloy rods were also examined. The saturation magnetostriction value of FesoGa2o can reach to 240 x 10-6 under a compressive stress of 20 MPa. The Fe80GallA19 alloy has many good properties, such as low hysteresis, high linearity of the magnetostriction curve, and low saturated magnetic field, which make it a potential candidate for magnetostrictive actuator and transducer applications. It is found that subgrains have little influence on the magnetostriction of Fe-Ga alloys.

CYCLIC HARDENING BEHAVIOR OF POLYCRYSTALS WITH PENETRABLE GRAIN BOUNDARIES:TWO-DIMENSIONAL DISCRETE DISLOCATION DYNAMICS SIMULATION

A two-dimensional discrete dislocation dynamics （DDD） technology by Giessen and Needleman （1995）, which has been extended by integrating a dislocation-grain boundary interaction model, is used to computationally analyze the micro-cyclic plastic response of polycrystals containing micron-sized grains, with special attentions to significant influence of dislocationpenetrable grain boundaries （GBs） on the micro-plastic cyclic responses of polycrystals and underlying dislocation mechanism. Toward this end, a typical polycrystalline rectangular specimen under simple tension-compression loading is considered. Results show that, with the increase of cycle accumulative strain, continual dislocation accumulation and enhanced dislocation-dislocation interactions induce the cyclic hardening behavior; however, when a dynamic balance among dislocation nucleation, penetration through GB and dislocation annihilation is approximately established, cyclic stress gradually tends to saturate. In addition, other factors, including the grain size, cyclic strain amplitude and its history, also have considerable influences on the cyclic hardening and saturation.

Synthesis of AgGa_(1-x)In_(x)Se_(2) Polycrystalline Materials

AgGa_(1-x)In_(x)Se_(2)polycrystals were synthesized by the method of mechanical oscillation and temperature oscillation.X-ray diffraction spectra of polycrystal powder are conformable with the JCPDS cards.Lattice constants a and c calculated from the XRD were found to obey Vegard's law.The melting point of AgGa_(0.8)In_(0.2)Se_(2)obtained by means of differential scanning calorimetry(DSC)is 796.53℃.The DSC curve also show that there are no other transformation points below the melting point.The results indicate that polycrystalline materials synthesized by the method mentioned above are high-quality and can be used to grow single crystals by the vertical Bridgman technology.

Giant Magnetostrictions of Tb-Dy-Fe Polycrystals with < 110 > Axial Alignment

Preparing method and processing of Tb-Dy-Fe alloy samples with [110] axial orientation as well as their magnetostrictive properties have been studied. It has been found that the magnetostrictive strains of polycrystal samples with [110] axial orientation can reach (1550-1900) ×10~-6 in a low magnetic field less than 80 kA/m, which are equal to or somewhat better than that of the polycrystal samples with [112] axial orientation.

Constitutive relation of weakly anisotropic polycrystal with microstructure and initial stress

Man （Nondestr Test Eval 15：191-214, 1999） derived the constitutive relation of a weakly-textured orthorhombic aggregate of cubic crystallites with effects of microstructure and initial stress. In this paper, a computational expression on the integration ∫SO（3） Q^× D^1m0dg is given. Then, by means of the computational expression, the general constitutive relation of a weakly-textured anisotropic polycrystal with the consideration of microstructure and initial stress is derived. As special cases of our general constitutive relation, two constitutive relations are given for an isotropic polycrystal and a weakly-textured anisotropic aggregate of cubic crystallites. The acoustoelastic tensor of the reference cubic crystal is derived to determine the material constants of the polycrystal. Two examples are given for understanding the physical meaning of the texture coefficients and the constitutive relations.

Mechanical properties of irradiated multi-phase polycrystalline BCC materials

Structure materials under severe irradiations in nuclear environments are known to degrade because of irradiation hardening and loss of ductility,resulting from irradiation-induced defects such as vacancies,interstitials and dislocation loops,etc.In this paper,we develop an elastic-viscoplastic model for irradiated multi-phase polycrystalline BCC materials in which the mechanical behaviors of individual grains and polycrystalline aggregates are both explored.At the microscopic grain scale,we use the internal variable model and propose a new tensorial damage descriptor to represent the geometry character of the defect loop,which facilitates the analysis of the defect loop evolutions and dislocation-defect interactions.At the macroscopic polycrystal scale,the self-consistent scheme is extended to consider the multiphase problem and used to bridge the individual grain behavior to polycrystal properties.Based on the proposed model,we found that the work-hardening coefficient decreases with the increase of irradiation-induced defect loops,and the orientation/loading dependence of mechanical properties is mainly attributed to the different Schmid factors.At the polycrystalline scale,numerical results for pure Fe match well with the irradiation experiment data.The model is further extended to predict the hardening effect of dispersoids in oxide-dispersed strengthened steels by the considering the Orowan bowing.The influences of grain size and irradiation are found to compete to dominate the strengthening behaviors of materials.

CRACK PROPAGATION IN POLYCRYSTALLINE ELASTIC-VISCOPLASTIC MATERIALS USING COHESIVE ZONE MODELS

Cohesive zone model was used to simulate two-dimensional plane strain crack propagation at the grain level model including grain boundary zones. Simulated results show that the original crack-tip may not be separated firstly in an elastic-viscoplastic polycrystals. The grain interior＇s material properties （e.g. strain rate sensitivity） characterize the competitions between plastic and cohesive energy dissipation mechanisms. The higher the strain rate sensitivity is, the larger amount of the external work is transformed into plastic dissipation energy than into cohesive energy, which delays the cohesive zone rupturing. With the strain rate sensitivity decreased, the material property tends to approach the elastic-plastic responses. In this case, the plastic dissipation energy decreases and the cohesive dissipation energy increases which accelerates the cohesive zones debonding. Increasing the cohesive strength or the critical separation displacement will reduce the stress triaxiality at grain interiors and grain boundaries. Enhancing the cohesive zones ductility can improve the matrix materials resistance to void damage.

Effect of Relative Grain Size on the Flow Stress of Polycrystalline FCC Sheets

A dynamic explicit finite element code and rate-dependent elastic-viscoplastic polycrystalline model were used to simulate the simple tension test of annealing FCC polycrystal and 6111-T4 aluminum alloy sheet metal. The variability of flow stress was investigated, which was induced by various grain boundary constraints when the ratio of thickness-to-grain size was changed. The simulated results show that, when the relative grain size increases, the constraint of grain boundary will increase accordingly, which results in the increase of the flow stress of polycrystal. The results agree with experiments.

Phase and structure of polycrystal Sr_(0.69) La_(0.31)F_(2.31)+SrS solid electrolyte material

The phase and the structure of polycrystal material, which was prepared by calcining the co precipitated fluoride powder of Sr and La with a ratio of 0.69∶0.31 mixed with SrS powder, were investigated by X ray diffraction and electron probe scanning. In the materials, three phases were found, they are Sr 0.69 La 0.31 F 2.31 solid solution phase with a pure SrF 2 cubic structure whose lattice constant is 5.843 ?, SrS single phase with a NaCl cubic structure, and an unknown phase that is produced by the interaction of SrS and co precipitated powder. It was also found that SrS has no influence on the structure of Sr 0.69 La 0.31 F 2.31 solid solution.

A micromechanics-based finite element model for the constitutive behavior of polycrystalline ferromagnets

A micromechanics-based finite element model for the constitutive behavior of polycrystalline ferromagnets is developed. In the model, the polycrystalline solid is assumed to comprise numerous single crystals with randomly distributed crystallographic orientations, and the single crystals, in turn, consist of ferromagnetic domains, each of which is represented by a cubic element. The dipole directions of the domains are randomly assigned to simulate the crystallographic nature of ferromagnetic polycrystals. A switching criterion for the domains is specified at the microscopic level. The macroscopic constitutive behavior is obtained by averaging the microscopic/local behavior of each domain. The developed model has been applied to the simulation of a ferromagnetic material. With appropriate material parameters adopted, hysteresis loops of the predicted magnetic induction versus magnetic field and those of the strain versus magnetic field are shown to agree well with experimental observations.

Anomalies in Young's modulus behavior after annealing in polycrystalline SmS

In this paper,the dependencies of Young's modulus and attenuation decrement on samarium sulfide polycrystals(SmS)under various annealing temperatures are studied by the piezoelectric ultrasonic composite oscillator technique at a frequency of 100 kHz in the temperature range of 80-300 K.A decrease in Young's modulus with an increase of the annealing temperature due to the texturing of the material was revealed.At the same time,attenuation peaks were observed at temperatures about 90 and 125 K,presumably due to Niblett-Wilks and Bordoni relaxations.

STUDY OF POSITRON ANNIHILATION ONE DIMENSION ANGULAR-CORRELATION RADIATION ON POLYCRYSTAL Na^+ CONDUCTOR Na_5Y_(1-x)Cr_xSi_4O_(12)

With positron annihilation radiation one dimension angular-correlation device, it is measured that positron annihilation radiation one dimension angular-correlation curves of polycrystal sodium ion conductor Na5Y1-x CrxSi4O12 (NYCS) system. After electron momentum distribution curves are normalized, linear parameters are calculated. The parameters H, W and S show the change of Na+ ion vacancy concentration in NYCS series samples. The results show that parameters H, W and S of one dimension angular-correlation curves of those samples vary greatly with Cr2O3 contents. With Cr2O3 content increasing, H and S parameters increase, but W decreases, and reaches extremes at x=0.05; then with Cr2O3 adding continually, parameters H and S decrease gradually, parameter W increases gradually. This shows that, in addtion to Cr2O3, the conductivity has close relation with the concentration of Na+ ion vacancy.