Study on the Deformation Behavior of Mg-Gd-Y-Zn-Mn Wrought Magnesium Alloys by Visco-plastic Self-consistent Modeling

The plastic deformation behavior of new Mg-Gd-Y-Zn-Mn magnesium alloys gains great necessity to clarify and understand the mechanism deeply. In the present work,the tensile mechanical property test and visco-plastic self-consistent (VPSC) model are used to investigate the activities of deformation modes of VW84M and VW94M magnesium alloys during the tensile deformation. The results show that the mechanical properties of the above extruded alloys are similar but VW94M has higher strength than VW84M after the same aging process. Compared with the extruded alloys,the as-aged alloys have significantly higher activation of pyramidal slip at the later stage of plastic deformation. In addition,the as-aged VW94M alloy with higher strength has the largest activity of pyramidal slip. In summary,the addition of Gd increases the critical resolved shear stress (CRSS)in each slip system of VW94M,while the increase in the strength and the decrease in the elongation of as-aged alloys are associated with the significant activation of pyramidal slip.

A bounding surface visco-plasticity model considering generalized spacing ratio of soils

The non-unique critical state of soils with time-dependent behaviors is a significant issue in geotechnical engineering problems.However,previous bounding surface plasticity models cannot predict accurately the non-unique critical state of soils,because the distance between the compression line and critical state line charged by strain-rate effect is basically neglected.To fill this gap,a generalized spacing ratio of soils is defined in the elasto-viscoplastic framework,and a bounding surface visco-plasticity model is formulated and verified,which can consider the generalized spacing ratio.Specifically,the generalized spacing ratio of soils reflects the distance between the compression line and the critical state line of soils with time-dependent behaviors.Then,the generalized spacing ratio is introduced into an improved anisotropic bounding surface.A new expression of the visco-plastic multiplier is derived by solving the consistency equation of an anisotropic bounding surface.In the expression,a strain rate index is proposed to account for the strain-rate effect on visco-plastic strain increment,and a visco-plastic hardening modulus is derived to predict the visco-plastic response of soils in overconsolidation conditions.The model is then verified through constant strain rate tests and creep tests.Notably,it can capture the non-unique critical states of soils with time-dependent behaviors due to the generalized spacing ratio and the creep rupture of soils due to the visco-plastic multiplier that considers the stress ratio and visco-plastic strain rate.

Fractional-order visco-plastic constitutive model for uniaxial ratcheting behaviors

This paper proposes a novel unified visco-plastic constitutive model for uniaxial ratcheting behaviors. The cyclic deformation of the material presents remarkable time-dependence and history memory phenomena. The fractional(fractional-order)derivative is an efficient tool for modeling these phenomena. Therefore, we develop a cyclic fractional-order unified visco-plastic(FVP) constitutive model. Specifically, within the framework of the cyclic elasto-plastic theory, the fractional derivative is used to describe the accumulated plastic strain rate and nonlinear kinematic hardening rule based on the Ohno-Abdel-Karim model. Moreover, a new radial return method for the back stress is developed to describe the unclosed hysteresis loops of the stress-strain properly.The capacity of the FVP model used to predict the cyclic deformation of the SS304 stainless steel is verified through a comparison with the corresponding experimental data found in the literature(KANG, G. Z., KAN, Q. H., ZHANG, J., and SUN, Y. F. Timedependent ratcheting experiments of SS304 stainless steel. International Journal of Plasticity, 22(5), 858–894(2006)). The FVP model is shown to be successful in predicting the rate-dependent ratcheting behaviors of the SS304 stainless steel.

Self-Consistent Model for Pulsed Direct-Current N_2 Glow Discharge

A self-consistent analysis of a pulsed direct-current (DC) N2 glow discharge is presented. The model is based on a numerical solution of the continuity equations for electron and ions coupled with Poisson's equation. The spatial-temporal variations of ionic and electronic densities and electric field are obtained. The electric field structure exhibits all the characteristic regions of a typical glow discharge (the cathode fall, the negative glow, and the positive column). Current-voltage characteristics of the discharge can be obtained from the model. The calculated current-voltage results using a constant secondary electron emission coefficient for the gas pressure 133.32 Pa are in reasonable agreement with experiment.

A UNIFIED ENERGY APPROACH TO A CLASS OF MICROMECHANICS MODELS FOR COMPOSITE MATERIALS

Several micromechanics models for the determination of composite moduli are investigated in this paper,including the dilute solution,self-consistent method,generalized self-consistent method,and Mori-Tanaka's method.These mi- cromechanical models have been developed by following quite different approaches and physical interpretations.It is shown that all the micromechanics models share a common ground,the generalized Budiansky's energy-equivalence framework.The dif- ference among the various models is shown to be the way in which the average strain of the inclusion phase is evaluated.As a bonus of this theoretical development,the asymmetry suffered in Mori-Tanaka's method can be circumvented and the applica- bility of the generalized self-consistent method can be extended to materials contain- ing microcracks,multiphase inclusions,non-spherical inclusions,or non-cylindrical inclusions.The relevance to the differential method,double-inclusion model,and Hashin-Shtrikman bounds is also discussed.The application of these micromechanics models to particulate-reinforced composites and microcracked solids is reviewed and some new results are presented.

Effective electroelastic constants for three-phase confocal elliptical cylinder model in piezoelectric quasicrystal composites

A three-phase confocal elliptical cylinder model is proposed to analyze micromechanics of one-dimensional hexagonal piezoelectric quasicrystal （PQC） compos- ites. Exact solutions of the phonon, phason, and electric fields are obtained by using the conformal mapping combined with the Laurent expansion technique when the model is subject to far-field anti-plane mechanical and in-plane electric loadings. The effective elec- troelastic constants of several different composites made up of PQC, quasicrystal （QC）, and piezoelectric （PE） materials are predicted by the generalized self-consistent method. Numerical examples are conducted to show the effects of the volume fraction and the cross-sectional shape of inclusion （or fiber） on the effective electroelastic constants of these composites. Compared with other micromechanical methods, the generalized self- consistent and Mori-Tanaka methods can predict the effective electroelastic constants of the composites consistently.

Collective Hamiltonian for Multi-O（4） Model

The collective Bamiltonian up to the fourth order for multi-O（4） model is derived based on the self-consistent collective-coordinate （SCC） method, which is formulated in the framework of the time-dependent Hartree-Bogoliubov （TDHB） theory. The validity of the collective Hamiltonian is checked in the two special cases of the multi-O（4） model： the case where the number of the shells is equal to one （a single j-shell case）, and the case where the Hartree-Bogoliubov equilibrium point is spherical （the spherical case）. The collective Hamiltonian constitutes a good starting point to study nuclear shape coexistence.

Temperature-dependent constitutive modeling of a magnesium alloy ZEK100 sheet using crystal plasticity models combined with in situ high-energy X-ray diffraction experiment

A multiscale crystal plasticity model accounting for temperature-dependent mechanical behaviors without introducing a larger number of unknown parameters was developed.The model was implemented in elastic-plastic self-consistent(EPSC)and crystal plasticity finite element(CPFE)frameworks for grain-scale simulations.A computationally efficient EPSC model was first employed to estimate the critical resolved shear stress and hardening parameters of the slip and twin systems available in a hexagonal close-packed magnesium alloy,ZEK100.The constitutive parameters were thereafter refined using the CPFE.The crystal plasticity frameworks incorporated with the temperature-dependent constitutive model were used to predict stress–strain curves in macroscale and lattice strains in microscale at different testing temperatures up to 200℃.In particular,the predictions by the crystal plasticity models were compared with the measured lattice strain data at the elevated temperatures by in situ high-energy X-ray diffraction,for the first time.The comparison in the multiscale improved the fidelity of the developed temperature-dependent constitutive model and validated the assumption with regard to the temperature dependency of available slip and twin systems in the magnesium alloy.Finally,this work provides a time-efficient and precise modeling scheme for magnesium alloys at elevated temperatures.

Ion population fraction calculations using improved screened hydrogenic model with l-splitting

Ion population fraction（IPF） calculations are very important to understand the radiative spectrum emitted from the hot dense matter. IPF calculations require detailed knowledge of all the ions and correlation interactions between the electrons of an ion which are present in a plasma environment. The average atom models, e.g., screened hydrogenic model with l-splitting（SHML）, now have the capabilities for such calculations and are becoming more popular for in line plasma calculations. In our previous work [Ali A, Shabbir Naz G, Shahzad M S, Kouser R, Rehman A and Nasim M H 2018 High Energy Density Phys. 26 48], we have improved the continuum lowering model and included the exchange and correlation effects in SHML. This study presents the calculation of IPF using classical theory of fluctuation for our improved screened hydrogenic model with l-splitting（I-SHML） under local thermodynamic equilibrium conditions for iron and aluminum plasma over a wide range of densities and temperatures. We have compared our results with other models and have found a very good agreement among them.

Self-consistent mean field approximation and application in three-flavor NJL model

In this study,we apply a self-consistent mean field approximation of the three-flavor Nambu–Jona-Lasinio(NJL)model and compare it with the two-flavor NJL model.The self-consistent mean field approximation introduces a new parameter,α,that cannot be fixed in advance by the mean field approach itself.Due to the lack of experimental data,the parameter,α,is undetermined.Hence,it is regarded as a free parameter and its influence on the chiral phase transition of strong interaction matter is studied based on this self-consistent mean field approximation.αaffects numerous properties of the chiral phase transitions,such as the position of the phase transition point and the order of phase transition.Additionally,increasingαwill decrease the number densities of different quarks and increase the chemical potential at which the number density of the strange quark is non-zero.Finally,we observed thatαaffects the equation of state(EOS)of the quark matter,and the sound velocity can be calculated to determine the stiffness of the EOS,which provides a good basis for studying the neutron star mass-radius relationship.

A coupled elastoplastic and visco-plastic damage model for hard clay and its application for the underground gallery excavation

The numerical modelling of the excavation of an underground gallery in hard clay has been discussed in current article.A constitutive model is proposed to describe poromechanical behaviour of the hard clay.The main features of the hard clay observed in laboratory and in-situ experimental investigation have been taken into account in the proposed constitutive model,in particular the plastic deformation,the visco-plastic deformation,the damage,etc.The influence of the initial in-situ stress and the pore pressure has been taken into consideration.The numerical modelling of the underground excavation has been implemented by using a fully coupled hydro-mechanical finite element calculation code.The performance of the model is examined by comparing numerical simulations with in situ measurements.The proposed model and the calculation procedure for the modelling of the excavation of an underground gallery have the capacity to reproduce well the excavation damaged/distributed zone and other main features and phenomena observed during the excavation process.However,the in-situ observed convergence could not be reproduced correctly.More effort on the discontinuous problem should be made for the reproduce the observed convergence.

Understanding Depletion Induced Like-Charge Attraction from Self-Consistent Field Model

The interaction force between likely charged particles/surfaces is usually repulsive due to the Coulomb interaction.However,the counterintuitive like-charge attraction in electrolytes has been frequently observed in experiments,which has been theoretically debated for a long time.It is widely known that the mean field Poisson-Boltzmann theory cannot explain and predict this anomalous feature since it ignores many-body properties.In this paper,we develop efficient algorithm and perform the force calculation between two interfaces using a set of self-consistent equations which properly takes into account the electrostatic correlation and the dielectric-boundary effects.By solving the equations and calculating the pressure with the Debye-charging process,we show that the self-consistent equations could be used to study the attraction between like-charge surfaces from weak-coupling to mediate-coupling regimes,and that the attraction is due to the electrostatics-driven entropic force which is significantly enhanced by the dielectric depletion of mobile ions.A systematic investigation shows that the interaction forces can be tuned by material permittivity,ionic size and valence,and salt concentration,and that the like-charge attraction exists only for specific regime of these parameters.

Two-dimensional simulation on the rolling process of semi-solid 60Si2Mn by finite element method

The effect of various process variables on the law of metal flow for semi-solid rolling 60Si2Mn was studied by finite element method. Semi-solid 60Si2Mn can be described as compressible rigid visco-plastic porous material saturated with liquid. In terms of ther-mo-mechanical coupling condition, the distributions of stress, velocity and temperature were studied using software MARC. The simulation results show that the rigid visco-plastic model can accurately describe the semi-solid 60Si2Mn rolling process. The great deformation can achieve completely in view of low flow stress of semi-solid slurry.

Pressure dissociation of dense hydrogen

The self-consistent fluid variational model （SFVM） has been used to describe the pressure dissociation of dense hydrogen at high temperatures. This paper focuses on a mixture of hydrogen atoms and molecules and is devoted to the study of the phenomenon of pressure dissociation at finite temperatures. The equation of state and dissociation degree have been calculated from the free energy functions in the range of temperature 2000-10,000K and density 0.02-1.0g/cm^3, which can be compared with other approaches and experiments. The pressure dissociation is found to occur in higher density range, while temperature dissociation is a more gradual effect.

MESO APPROACHES FOR THE CREEP DAMAGE BEHAVIOR OF NICKEL-BASE DIRECTIONALLY SOLIDIFIED SUPERALLOYS

A self-consistent creep damage constitutive model and a finite element model have been developed for nickel-base directionally solidified superalloys. Grain degradation and grain boundary voiding are considered. The model parameters are determined from the creep test data of a single crystal and a directionally solidified superalloy with a special crystallographic orientation. The numerical analysis shows that the modeled creep damage behaviors of nickel-base directionally solidified super-alloys with different crystallographic orientations are in good agreement with the experimental data.

Radiative properties of matter based on quantum statistical method

We present the preliminary results of our code OPAQS（opacity calculation using quantum statistical model） that is based on the self consistent Hartree-Fock-Slater model for the average atom. The code is capable of performing robust calculations of average charge state, frequency-dependent and mean opacities. The accuracy of the atomic model is verified by comparing the calculations of average charge state with various published results. The monochromatic opacities for iron computed at different sets of temperatures and densities are compared with LEDCOP. The Rosseland and Planck opacities for iron and aluminum are validated with some state-of-the-art codes. The results are in good agreement with the published data.

Numerical Calculations of Some Plasma Parameters of the Capacitively Coupled <i>RF</i>Discharge

Numerical calculations by using a self-consistent model of the collisional sheath for the capacitively coupled RF discharge are our target. The results indicated that, at high pressure, the ohmic heating is usually the dominant heating mechanism in the discharge. The power dissipated in the sheath is calculated and compared with the measured data. Moreover, we indicated that, when the gas pressure is increased, the calculated dissipated power is decreased also while the measured input RF power is increased. Furthermore the sheath thickness of the capacitively coupled discharge is calculated and in the same order of the electron oscillation amplitude in the RF field, while the ionization mean free path is shorter than it.

Sub-external cavity effect and elimination method in laser self-mixing interference wave plate measurement system

Laser self-mixing interference（SMI） wave plate measurement method is a burgeoning technique for its simplicity and efficiency. But for the non-coated sample, the reflected light from the surface can seriously affect the measurement results.To analyze the reason theoretically, a self-consistent model for laser operation with a sub-external and an external cavity is established, and the sub-external cavity formed by the sample and a cavity mirror is proved to be the main error source.A synchronous tuning method is proposed to eliminate the sub-external cavity effect. Experiments are carried out on the synchronously tuning double external cavities self-mixing interference system, and the error of the system is in the range of -0.435°~0.387° compared with the ellipsometer. The research plays an important role in improving the performance and enlarging the application range of the laser self-mixing interference system.

Some Mathematical Properties of the Dynamically Inconsistent Bellman Equation： A Note on the Two-Sided Altruism Dynamics

This article describes some dynamic aspects on dynastic utility incorporating two-sided altruism with an OLG setting. The special case is analyzed where the weights of two-sided altruism are dynamically inconsistent. The Bellman equation for two-sided altruism proves to be reduced to one-sided dynamic problem, but the effective discount factor is different only in the current generation. It is shown that a contraction mapping result of value function cannot be achieved in general, and that there can locally exist an infinite number of self-consistent policy functions of the class C＂ with distinct steady states （indeterminacy of self-consistent, differentiable policy functions）.

An Analytical and Numerical Approach to the Self-Consistent Method for Computing the Proportion of F₂ⁿ/F₂^pUsing the 3_Heand 3_HNucleuses’ Structure Function and EMC Ratio

The following article has been retracted due to the investigation of complaints received against it. Mr. Mohammadali Ghorbani (corresponding author and also the last author) cheated the author’s name: Alireza Heidari. The scientific community takes a very strong view on this matter and we treat all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No.1 124-128, 2012, has been removed from this site.