ON CORRECT ACCOUNT OF FINITE ROTATIONS IN FINITE PLASTICITY THEORY

The non-uniqueness of the transition from nonobjective constitutive relations to objective ones with the use of the principle of material frame-indifference(PMFI)is shown.To eliminate it,the concept of finite strain without rotations(FSWR)for a given material type and each strain component(elastic,plastic) is introduced.In FSWR the rotation is excluded with respect to the natural preferred configuration for a given material.Considered are a simple solid,a liquid,a mouocrystal,a polycrystal and a composite.The procedure is proposed lbr consistent generalization of known infinitesimal relations for finite strains and rota- tions.The structure of constitutive relations is derived for anisotropic elasto-plastic mono-and polycrystalline materials.

Prediction of grain scale plasticity of NiTi shape memory alloy based on crystal plasticity finite element method

Grain scale plasticity of NiTi shape memory alloy(SMA)during uniaxial compression deformation at 400℃was investigated through two-dimensional crystal plasticity finite element simulation and corresponding analysis based on the obtained orientation data.Stress and strain distributions of the deformed NiTi SMA samples confirm that there exhibits a heterogeneous plastic deformation at grain scale.Statistically stored dislocation(SSD)density and geometrically necessary dislocation(GND)density were further used in order to illuminate the microstructure evolution during uniaxial compression.SSD is responsible for sustaining plastic deformation and it increases along with the increase of plastic strain.GND plays an important role in accommodating compatible deformation between individual grains and thus it is correlated with the misorientation between neighboring grains,namely,a high GND density corresponds to large misorientation between grains and a low GND density corresponds to small misorientation between grains.

Simulation of bulk metal forming processes using one-step finite element approach based on deformation theory of plasticity

The bulk metal forming processes were simulated by using a one-step finite element(FE)approach based on deformation theory of plasticity,which enables rapid prediction of final workpiece configurations and stress/strain distributions.This approach was implemented to minimize the approximated plastic potential energy derived from the total plastic work and the equivalent external work in static equilibrium,for incompressibly rigid-plastic materials,by FE calculation based on the extremum work principle.The one-step forward simulations of compression and rolling processes were presented as examples,and the results were compared with those obtained by classical incremental FE simulation to verify the feasibility and validity of the proposed method.

On Numerical Modelling of Industrial Powder Compaction Processes for Large Deformation of Endochronic Plasticity at Finite Strains

Compaction processes are one the most important par ts of powder forming technology. The main applications are focused on pieces for a utomotive, aeronautic, electric and electronic industries. The main goals of the compaction processes are to obtain a compact with the geometrical requirements, without cracks, and with a uniform distribution of density. Design of such proc esses consist, essentially, in determine the sequence and relative displacements of die and punches in order to achieve such goals. A.B. Khoei presented a gener al framework for the finite element simulation of powder forming processes based on the following aspects; a large displacement formulation, centred on a total and updated Lagrangian formulation; an adaptive finite element strategy based on error estimates and automatic remeshing techniques; a cap model based on a hard ening rule in modelling of the highly non-linear behaviour of material; and the use of an efficient contact algorithm in the context of an interface element fo rmulation. In these references, the non-linear behaviour of powder was adequately desc ribed by the cap plasticity model. However, it suffers from a serious deficiency when the stress-point reaches a yield surface. In the flow theory of plasticit y, the transition from an elastic state to an elasto-plastic state appears more or less abruptly. For powder material it is very difficult to define the locati on of yield surface, because there is no distinct transition from elastic to ela stic-plastic behaviour. Results of experimental test on some hard met al powder show that the plastic effects were begun immediately upon loading. In such mater ials the domain of the yield surface would collapse to a point, so making the di rection of plastic increment indeterminate, because all directions are normal to a point. Thus, the classical plasticity theory cannot deal with such materials and an advanced constitutive theory is necessary. In the present paper, the constitutive equations of powder materials will be discussed via an endochronic theory of plasticity. This theory provides a unifi ed point of view to describe the elastic-plastic behaviour of material since it places no requirement for a yield surface and a ’loading function’ to disting uish between loading an unloading. Endochronic theory of plasticity has been app lied to a number of metallic materials, concrete and sand, but to the knowledge of authors, no numerical scheme of the model has been applied to powder material . In the present paper, a new approach is developed based on an endochronic rate independent, density-dependent plasticity model for describing the isothermal deformation behavior of metal powder at low homologous temperature. Although the concept of yield surface has not been explicitly assumed in endochronic theory, it is shown that the cone-cap plasticity yield surface (Fig.1), which is the m ost commonly used plasticity models for describing the behavior of powder materi al can be easily derived as a special case of the proposed endochronic theory. Fig.1 Trace of cone-cap yield function on the meridian pl ane for different relative density As large deformation is observed in powder compaction process, a hypoelastic-pl astic formulation is developed in the context of finite deformation plasticity. Constitutive equations are stated in unrotated frame of reference that greatly s implifies endochronic constitutive relation in finite plasticity. Constitutive e quations of the endochronic theory and their numerical integration are establish ed and procedures for determining material parameters of the model are demonstra ted. Finally, the numerical schemes are examined for efficiency in the model ling of a tip shaped component, as shown in Fig.2. Fig.2 A shaped tip component. a) Geometry, boundary conditio n and finite element mesh; b) density distribution at final stage of

Numerical Analysis of Finite Deformation of Overbroken Rock Mass in Gob Area Based on Euler Model of Control Volume

The overbroken rock mass of gob areas is made up of broken and accumulated rock blocks compressed to some extent by the overlying strata. The beating pressure of the gob can directly affect the safety of mining fields, formarion of road retained along the next goaf and seepage of water and methane through the gob. In this paper, the software RFPA＇2000 is used to construct numerical models. Especially the Euler method of control volume is proposed to solve the simulation difficulty arising from plastically finite deformations. The results show that three characteristic regions occurred in the gob area： （1） a naturally accumulated region, 0-10 m away from unbroken surrounding rock walls, where the beating pressure is nearly zero; （2） an overcompacted region, 10-20 m away from unbroken walls, where the beating pressure results in the maximum value of the gob area; （3） a stable compaction region, more than 20 m away from unbroken walls and occupying absolutely most of the gob area, where the beating pressures show basically no differences. Such a characteristic can exolain the easy-seeoaged “O”-ring phenomena around mining fields very well.

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.

ANALYSIS OF ROLLING BY ELASTO-PLASTIC FINITE DEFORMATION CONTACT BOUNDARY ELEMENT METHOD

A multinonlinear boundary element method is established dealing with elasto plastic finite deformation contact problem, and it is employed to analysis rolling process. With rollers as elastic bodies, workpieces as elastio plastic bodies, rolling problem can be viewed as a frictional elasto plastic contact problem. With fewer assumptions in the simulation of the rolling process, a novel and accurate method is proposed for analysis of rolling problems.

Thermo-kinetic characteristics on stabilizing hetero-phase interface of metal matrix composites by crystal plasticity finite element method

Using dislocation-based constitutive modeling in three-dimension crystal plasticity finite element(3D CPFE)simulations,co-deformation and instability of hetero-phase interface in different material systems were herein studied for polycrystalline metal matrix composites(MMCs).Local stress and strain fields in two types of 3layer MMCs such as fcc/fcc Cu-Ag and fcc/bcc Cu-Nb have been predicted under simple compressive deformations.Accordingly,more severe strain-induced interface instability can be observed in the fcc/bcc systems than in the fcc/fcc systems upon refining to metallic nanolayered composites(MNCs).By detailed analysis of stress and strain localization,it has been demonstrated that the interface instability is always accompanied by high-stress concentration,i.e.,thermodynamic characteristics,or high strain prevention i.e.,kinetic characteristics,at the hetero-phase interface.It then follows that the thermodynamic driving forceG and the kinetic energy barrier Q during dislocation and shear banding can be adopted to classify the deformation modes,following the so-called thermo-kinetic correlation.Then by inserting a high density of high-energy interfaces into the Cu-Nb composites,such thermo-kinetic integration at the hetero-phase interface allows a successful establishment of MMCs with the high△G-high Q deformation mode,which ensures high hardening and uniform strain distri-bution,thus efficiently suppressing the shear band,stabilizing the hetero-phase interface,and obtaining an exceptional combination in strength and ductility.Such hetero-phase interface chosen by a couple of thermodynamics and kinetics can be defined as breaking the thermo-kinetic correlation and has been proposed for artificially designing MNCs.

Numerical Simulation of Extrusion Pressure in the Process of Hydrostatic Extrusion

In order to study the laws of the extrusion pressure changing with the extrusion parameters in the process of hydrostatic extrusion for the tungsten alloys, the large deformation elasto plastic theory and the software of ANSYS 5 5 are used to carry out the numerical simulation research. The laws of the extrusion pressure changing with the extrusion parameters, such as the die angle, extrusion ratio, and friction coefficient, are obtained. The simulation results are in good agreement with the experimental ones, and the simulated results are believable.

Grain-scale deformation in a Mg-0.8wt% Y alloy using crystal plasticity finite element method

Magnesium(Mg) alloys with hexagonal close-packed(HCP) structure usually have a poor ductility at room temperature. The addition of yttrium(Y) can improve the ductility of Mg alloys. To understand the underlying mechanism, crystal plasticity finite element method(CPFEM) was employed to simulate the tensile deformation of a Mg-0.8 wt% Y alloy. The simulated stress–strain curve and the grain-scale slip activities were compared with an in-situ tensile test conducted in a scanning electron microscope.According to the CPFEM result, basal slip is the dominant deformation mode in the plastic deformation stage, accounting for about 50% of total strain. Prismatic slip and pyramidal a slip are responsible for about 25% and 20% of the total strain, respectively. Pyramidal c + a slip and twinning, on the other hand,accommodate much less strain.

Multi-scale crystal plasticity finite element simulations of the microstructural evolution and formation mechanism of adiabatic shear bands in dual-phase Ti20C alloy under complex dynamic loading

A dynamic compression test was performed on α+β dual-phase titanium alloy Ti20C using a split Hopkinson pressure bar.The formation of adiabatic shear bands generated during the compression process was studied by combining the proposed multi-scale crystal plasticity finite element method with experimental measurements.The complex local micro region load was progressively extracted from the simulation results of a macro model and applied to an established three-dimensional multi-grain microstructure model.Subsequently,the evolution histories of the grain shape,size,and orientation inside the adiabatic shear band were quantitatively simulated.The results corresponded closely to the experimental results obtained via transmission electron microscopy and precession electron diffraction.Furthermore,by calculating the grain rotation and temperature rise inside the adiabatic shear band,the microstructural softening and thermal softening effects of typical heavily-deformed α grains were successfully decoupled.The results revealed that the microstructural softening stress was triggered and then stabilized(in general)at a relatively high value.This indicated that the mechanical strength was lowered mainly by the grain orientation evolution or dynamic recrystallization occurring during early plastic deformation.Subsequently,thermal softening increased linearly and became the main softening mechanism.Noticeably,in the final stage,the thermal softening stress accounted for 78.4% of the total softening stress due to the sharp temperature increase,which inevitably leads to the stress collapse and potential failure of the alloy.

Texture evolution and slip mode of a Ti-5.5Mo-7.2Al-4.5Zr-2.6Sn-2.1Cr dual-phase alloy during cold rolling based on multiscale crystal plasticity finite element model

The complex micromechanical response among grains remains a persistent challenge to understand the deformation mechanism of titanium alloys during cold rolling.Therefore,in this work,a multiscale crystal plasticity finite element method of dual-phase alloy was proposed and secondarily developed based on LS-DYNA software.Afterward,the texture evolution and slip mode of a Ti-5.5Mo-7.2Al-4.5Zr-2.6Sn-2.1Cr alloy,based on the realistic 3D microstructure,during cold rolling(20%thickness reduction)were systematically investigated.The relative activity of the■slip system in theαphase gradually increased,and then served as the main slip mode at lower Schmid factor(<0.2).In contrast,the contribution of the■slip system to the overall plastic deformation was relatively limited.For theβphase,the relative activity of the<111>{110}slip system showed an upward tendency,indicating the important role of the critical resolved shear stress relationship in the relative activity evolutions.Furthermore,the abnormally high strain of very fewβgrains was found,which was attributed to their severe rotations compelled by the neighboring pre-deformedαgrains.The calculated pole figures,rotation axes,and compelled rotation behavior exhibited good agreement to the experimental results.

Mechanical Anisotropy of Selective Laser Melted Ti-6Al-4V Using a Reduced-order Crystal Plasticity Finite Element Model

In this study,a reduced-order crystal plasticity finite element(CPFE)model was developed to study the effects of the microstructural morphology and crystallographic texture on the mechanical anisotropy of selective laser melted(SLMed)Ti-6Al-4V.First,both hierarchical and equiaxed microstructures in columnar prior grains were modeled to examine the influence of the microstructural morphology on mechanical anisotropy.Second,the effects of crystallographic anisotropy and textural variability on mechanical anisotropy were investigated at the granular and representative volume element(RVE)scales,respectively.The results show that hierarchical and equiaxed CPFE models with the same crystallographic texture exhibit the same mechanical anisotropy.At the granular scale,the significance of crystallographic anisotropy varies with different crystal orientations.This indicates that the present SLMed Ti-6Al-4V sample with weak mechanical anisotropy resulted from the synthetic effect of crystallographic anisotropies at the granular scale.Therefore,combinations of various crystallographic textures were applied to the reduced-order CPFE model to design SLMed Ti-6Al-4V with different mechanical anisotropies.Thus,the crystallographic texture is considered the main controlling variable for the mechanical anisotropy of SLMed Ti-6Al-4V in this study.

Settlement prediction and behaviour of pile foundations in deep clayey soil deposits

A new measurement technique is used to determine the settlement of bridge pile foundation and the thickness of deep compressed soft layer. The finite element Plaxis 3D foundation program is used in the analysis with a proposed empirical equation to modify the input parameters represented by the soil compression modulus. The results of the numerical analysis using the proposed empirical equation provide insight to the settlement analysis of pile groups in soft clayey soils; consequently, the finite element Plaxis 3D program can be a useful tool for numerical analysis. The numerical analysis is modified by adjusting the calculation of compression modulus from those obtained under pressure between 100-200 kPa by which the results of the settlement are modified and thus matching the realistic measurements. The absolute error is 3 mm which is accepted compared with the last researches. This scenario can be applied for the similar problems in the theoretical applications of deep foundations.

Analysis of the mechanism of orientations evolution during hot rolling and mechanical properties of TiBw/TA15 composites based on crystal plasticity finite element model

An in-depth understanding of the crystal orientation evolution during hot rolling of TiB whisker(TiBw)/TA15 composites and the anisotropy of the as-rolled plates can help fully utilize the material proper-ties.In this paper,the crystal plasticity finite element models of high-temperature(HT)β-phase and room-temperature(RT)α-phase were constructed from electron backscattering diffraction data.Based on this,the orientation evolution during hot rolling in the single-phase region and the effects of the matrix texture on the mechanical properties of the as-rolled plates were analyzed.The effect of TiBw on the anisotropy was studied by the composites finite element model.Results showed that theα-fiber texture of theβ-phase was formed during HT rolling.This texture was converted to the T-texture of theα-phase at RT during cooling according to the Burgers orientation relationships.The TiBw had little effect on the matrix texture composition.The TiBw and matrix texture caused the matrix to have higher strength along the rolling direction and the transverse direction,respectively.The matrix texture dominated the difference in mechanical properties because its effect exceeded that of TiBw.The effect of the matrix on the mechanical properties was caused by the Schmid factors(SFs)and the critical resolved shear stress(CRSS)of the slip system together.The slip mode was influenced by SFs determined by the angular rela-tionship between the crystal orientation and the loading direction.The CRSS of the activated slip system determined the yield strength.

STABILITY ANALYSIS OF PILLARS IN CONSIDERATION OF RHEOLOGICAL BEHAVIOUR OF ROCK

The mined-out area of a gypsum mine is right un-derneath civil constructions of a township, threatening the safety of the latter. To evaluate the long-term stability of the mined-out area, a visco-elastic plastic finite element analysis is carried out,combined with in situ measurements. The visco-elastic plastic coefficients have been determined through laboratory rock creep tests. Noticing the lim-itations of conventional element failure criteria,the authors proposed a new method to evaluate the stability of the element.i. e. ,by a si-multaneous control of the energy density and strain of the element. Computation showed that at stable state,one third of the pillars are in the visco-plastic state,the rest of the pillars ,the roof and floor are still in the visco-elastic state. The stress concentration coefficient at the boundary of pillars and roof is 2. 3,and the maximum verti-cal stress on the pillars is 11. 8 MPa. Data measured on site are con-sistent with the computation results, indicating that the proposed cal-culation method is correct. Therefore, the current mined-out area is stable,and the dimension of pillars is reasonable. The next-step ex-traction work should be carried out maintaining the current parame-ters,with only a moderate increase in pillar sizes to enhance the sta-bility of the pillars.

Development of Integrated Computational Materials Engineering(ICME)Model for Mg Alloy Design and Process Optimization

Integrated computational materials engineering(ICME)has emerged to be one of the most powerful materials genome engineering(MGE)approaches in designing new materials and manufacturing processes in recent years.It has successfully deployed many new products for the electronic,automotive,and aerospace industries.This paper reviews the current status of research on first principles in the design of high-strength Mg alloys,discusses the application of crystal plasticity finite element models to the microscale slip,twinning,microstructure morphology,texture evolution,and macroscopic forming of Mg alloys,and introduces the research progress of crystal plasticity finite element models and phase field models,meta cellular automata models and first principles coupled models respectively,around the need for multi-scale coupled simulations of Mg alloys.The key technology obstacles of integrating the first principles,crystal plasticity finite element,and microstructure models for Mg alloys have been solved.This paper can provide a reference for the design of new Mg alloy compositions and the development of high-performance Mg alloys.

A Modified Symmetric and Antisymmetric Decomposition-Based Three-Dimensional Numerical Manifold Method for Finite Elastic-Plastic Deformations

There are relatively few studies on large rotation or deformation by means of the three-dimensional(3D)numerical manifold method(NMM).A new modified symmetric and antisymmetric decomposition(MSAD)theory is developed and implemented into the 3D NMM,eliminating the false-volume expansion and false-rotation strain/stress problems.The Jaumann rate is used to measure the material rotation,and the geometric stiffness built on the Jaumann rate is deduced.The incremental formulas of the MSAD-based 3D NMM and a practical guide on the implementation of the MSAD theory are given in detail and exemplified.The new theory and formulas can be applied to analyze both large rotation and large deformation problems.Based on the hypoelasto-plasticity theory and the unified strength theory,the unified yield criterion with associated flow rule is implemented into the MSAD-based 3D NMM.Several typical examples are studied,showing the advantage and potential of the new MSAD theory and the MSAD-based 3D NMM.

Phase field simulation of the stress-inducedαmicrostructure in Ti–6Al–4 V alloy and its CPFEM properties evaluation

Variant selection under specific applied stresses during precipitation of a plates from prior-βmatrix in Ti-6 Al-4 V was investigated by 3 D phase field simulations.The model incorporates the Burgers transformation path fromβto a phase,with consideration of interfacial energy anisotropy,externally applied stresses and elastic interactions among a variants andβmatrix.The Gibbs free energy and atomic mobility data are taken from available thermodynamic and kinetic databases.It was found that external stresses have a profound influence on variant selection,and the selection has a sensitive dependence,as evidenced by both interaction energy calculations and phase field simulations.Compared with normal stresses,shear stresses applied in certain directions were found more effective in accelerating the transformation,with a stronger preference to fewer variants.The volume fractions of various a variants and the final microstructure were determined by both the external stress and the elastic interaction among different variants.The a clusters formed by variants with Type2 misorientation([11-20]/60°)relation were found more favored than those with Type4([-1055-3]/63.26°)under certain applied tensile stress such as along<111>β.The mechanical properties of different microstructures from our phase field simulation under different conditions were calculated for different loading conditions,utilizing crystal plastic finite element simulation.The mechanical behavior of the various microstructures from phase field simulation can be evaluated well before the alloys are fabricated,and therefore it is possible to select microstructure for optimizing the mechanical properties of the alloy through thermomechanical processing based on the two types of simulations.

Mesoscopic Analysis of Deformation Heterogeneity and Recrystallization Microstructures of a Dual-Phase Steel Using a Coupled Simulation Approach

Microstructure-based numerical modeling of the deformation heterogeneity and ferrite recrystallization in a cold-rolled dual-phase(DP)steel has been performed by using the crystal plasticity finite element method(CPFEM)coupled with a mesoscale cellular automaton(CA)model.The microstructural response of subsequent primary recrystallization with the deformation heterogeneity in two-phase microstructures is studied.The simulations demonstrate that the deformation of multi-phase structures leads to highly strained shear bands formed in the soft ferrite matrix,which produces grain clusters in subsequent primary recrystallization.The early impingement of recrystallization fronts among the clustered grains causes mode conversions in the recrystallization kinetics.Reliable predictions regarding the grain size,microstructure morphology and kinetics can be made by comparison with the experimental results.The influence of initial strains on the recrystallization is also obtained by the simulation approach.