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.

ANALYSIS OF SLAB EDGING BY A 3-D RIGID VISCO-PLASTIC FINITE ELEMENT METHOD

3-D rigid visco-plastic finite element method (FEM) is used in the analysisof metal forming processes, including strip and plate rolling, shape rolling, slab edging, specialstrip rolling. The shifted incomplete Cholesky decomposition of the stiffness matrix with thesolution of the equations for velocity increment by the conjugate gradient method is combined. Thistechnique, termed the shifted ICCG method, is then employed to solve the slab edging problem. Theperformance of this algorithm in terms of the number of iterations, friction variation, shiftedparameter psi and the results of simulation for processing parameters are analysed. Numerical testsand application of this technique verify the efficiency and stability of the shifted ICCG method inthe analysis of slab edging.

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.

Constitutive Laws for Visco-plastic Porous Medium Shaped by Regularly Distributed Circular Particles

A numerical study is presented,using a homogenization technique to consider the plain strain problem of visco-plastic porous medium shaped by regularly distributed circular particles. Based on a rigid plastic material,the paper derives the macroscopic constitutive laws for homogenous equivalent medium. By changing the shape parameter of circular particles,the effect of pore shape on macroscopic constitutive laws is explored. Yield surfaces with different pore shapes are obtained. About voids,a two-scale conception is introduced,which regards main void as macroscopic scale and secondary cavities as microscopic scale. The macroscopic potential involving main and secondary voids is achieved. The proposed macroscopic constitutive law taking microscopic features as influence factors is helpful for exploring the macroscopic mechanical properties of porous medium when numerical simulation is required.

The Compactions of Elasto-Plastic and Visco-Plastic Granular Assemblies

In this paper, the compactions of the elasto-plastic and the visco-plastic granular assemblies are simulated using the finite element method. Governing equations for motion and deformation for particles, including coupling of rigid body motion and deformation for deformable bodies, are investigated. An implicit discrete element method for block systems is developed to make visco-plastic analysis for the assemblies. Among particles, three different contact types, cohering, rubbing and sliding, are taken into account. To verify accuracy and efficiency of the numerical method, some numerical example is simulated and the results are in a satisfactory agreement with the solutions in literatures. The effects of frictional condition, the initial solid volume ratio, the number of particles in the assembly, and different types of compact- tion on the compaction of the elasto-plastic and the visco-plastic aggregates are investigated. It is demonstrated that the effect of frictional condition, the initial solid volume ratio, the number of particles in the assembly, and different types of compaction on the global behavior of the elasto-plastic the visco-plastic granular assemblies under compacting are considerable. The numerical model is extended to simulate the compaction of aggregates consisting of mixed particles of different viscous incompressible materials. It is indicated that, with minor modification, the method could be used in a variety of problems that can be represented using granular media, such as asphalt, polymers, aluminum, snow, food product, etc.

Relation between viscoplastic flow, periodic feature and Joule heat validity for electrically assisted friction stir welding

Electrically assisted friction stir welding is a promising way to improve liquidity of viscoplastic metal. However, this local heat source only can take into effect in a certain contact interface status. Semi-analytical model and FEM are adopted to analyze materials flow in electrically assisted FSW. Semi-analysis results show that Joule heating is validity with rotation speed 1 400 r/min and travel speed 400 mm/min. The maximum flow velocity is 0.033 m/s when travel speed is 400 mm/min, and it increases to 0.043 m/s with current assistant. Visco-plasticizing efficiency is a key factor to decide whether Joule heat is significant, and viscoplastic flow can periodically make circuit short. Periodic torque, axial force and onion rings surface show dynamic flow process, which can be used to illustrate the dynamic contact resistance feature and correct the calculation equation of Joule heat. This paper is aim to point out the potential relation between viscoplastic flow, periodic torque and Joule heating validity.

Modeling strain rate sensitivity and high temperature deformation of Mg-3Al-lZn alloy

Increasing the plastic deformation temperature of Mg alloys results in higher strain rate sensitivity,easier activation of secondary slip modes,and impeded twinning.In this study,the strain rate sensitivity is estimated for each deformation mode,and visco-plastic self-consistent modeling is used to reproduce the plastic deformation behavior of an Mg-3Al-lZn O-temper plate from 150 to 450℃.Twinning and basal slip have relatively low strain rate sensitivity,whereas secondary slip modes are highly strain rate sensitive at high temperature.The texture evolution and plastic anisotropy are modeled at different temperatures and strain rates.Results show that when the strain rate sensitivity is taken into account,compared with rate independent critical resolved shear stresses,the material parameters and predictions are different.In particular,this study shows that,for hot deformation,there is a critical strain rate above which secondary slip modes predominate,and beyond which tension twinning is activated.A similar transition is expected for modes that have different strain rate sensitivity.

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.

STUDY ON THE PROBLEMS OF CONTACT IN THE NUMERICAL SIMULATION OF SHEET FORMING

This study is concerned with the problems of contact in the process of numerical simulation of sheet metal forming in rigid visco-plastic shell FEM. In respect of analysis of sheet deep drawing process,for the tool model described by triangular elements, a kind of contact judging algorithm about the correlation between the node of deformed mesh and the triangular element of a tool is presented. In SPF/DB Lagrangian multiplier method is adopted to solve the contact problem between deformed meshes, and a new reliable practical dynamic contact checking algorithm is presented. As computation examples, the simulation results of metal sheet deep drawing and SPF/DB are introduced in this paper.

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.

Efect of Pre‑stretch Strain at High Temperatures on the Formability of AZ31 Magnesium Alloy Sheets

High-temperature pre-stretching experiments were carried out on the AZ31 Mg alloy at 723 K with strain levels of 2.54%,6.48%,10.92%,and 19.2%to alter the microstructure and texture for improving room-temperature formability.The results showed that the strain-hardening coefcient increased,while the Lankford value decreased.In addition,the Erichsen values of all pre-stretch sheets were enhanced compared with that of the as-received sheet.The maximum Erichsen value increased from 2.38 mm for the as-received sample to 4.03 mm for the 10.92%-stretched sample,corresponding to an improvement of 69.32%.This improvement was mainly attributed to the gradual increase in grain size,and the(0001)basal texture was weakened due to the activated non-basal slip as the high-temperature pre-stretching strain levels increased.The visco-plastic self-consistent analysis was performed on the as-received and high-temperature pre-stretched samples.Results confrmed the higher activity of the prismatic slip in 10.92%-stretched sample,leading to divergence and weakening of basal texture components.This results in an augmentation of the Schmid factor under diferent slip systems.Therefore,it can be concluded that high-temperature pre-stretching technology provided an efective method to enhance the formability of Mg alloy sheets.

Micromechanical Modeling of Elastic-Viscoplastic Behavior of Armco-Fe at High Strain Rate

Heterogeneous dynamical stress-strain response of Armco-Fe was investigated at high strain rates through the Split Hopkinson Pressure Bar （SHPB） testing. It was found that the viscoplastic deformation in BCC ferrite grains is affected by the strain rate. Thermal softening and variation in crystal orientations under high-strain-rate loading were used in the elastic-viscoplastic modeling. The micromechanical analysis with self-consistent transition and homogenization was used for estimation of the global impact response of the material. The results from modeling were found in good agreement with the experimental data.

ＯＰＥＲＡＴＯＲ－ＳＰＬＩＴＴＩＮＧＭＥＴＨＯＤＳＦＯＲＴＨＥＳＩＭＵＬＡＴＩＯＮＯＦＢＩＮＧＨＡＭＶＩＳＣＯ－ＰＬＡＳＴＩＣＦＬＯＷ

This article discusses computational methods for the numerical simulation of unsteady Bingham visco-plastic flow. These methods are based on time-discretization by operator-splitting and take advantage of a characterization of the solutions involving some kind of Lagrange multipliers. The full discretization is achieved by combining the above operator-splitting methods with finite element approximations, the advection being treated by a wave-like equation 'equivalent' formulation easier to implement than the method of characteristics or high order upwinding methods. The authors illustrate the methodology discussed in this article with the results of numerical experiments concerning the simulation of wall driven cavity Bingham flow in two dimensions.