IMPROVEMENT ON THE CALCULATION OF PLASTIC STRAIN RATIO IN BCC MONOCRYSTALS

Two improvements have been made on the calculation of plastic strain ratio (r value) in BCC monocrystals by considering the differences in the critical shear stresses among the three slip systems and the rotation of crystal lattice. It is found that the results calculated by the improved method are more rational.

STRAIN-DEPENDENCE OF PLASTIC STRAIN RATIO OF DEEP-DRAWING ALUMINIUM-KILLED STEEL SHEET

The change of width and length of an aluminium-killed(AK)steel sheet was measured in detail at various tensile strain levels.The effects of tensile strain on the conventional strain ratio,rc-value,and the instantaneous strain ratio,r^(1)-value,were analyzed.It was shown that the strain ratio of the AK steel sheet had obvious strain-dependency.The individual r^(c)-values for all tested directions tended to unity with increasing strain so that the planar anisotropy decreased with increasing strain.The r^(1)-value had overall straidenpendency similar to that of r^(c)-value,though it was overly sensitive to the experimental errors and showed significant variation with strain.In the representation of average strain ratio.the linear regression strain ratio,r^(r)-value,which was obtained by fitting a straight line to the εw vs εt curve,is preferable to the r^(c)-value measured at some specfic extension.

Analysis of bending mechanism in multi-scanning laser bending process based on plastic strain development

By using multi-pass straight-line scan strategies,a larger bending angle can be achieved.There is,however,a limited understanding of the variation in bending angle per pass during multi-pass under various process parameters.In multi-pass laser scanning,the bending angle cannot always linearly increase with scanning passes and this phenomenon can be observed mostly in low heat input.Strain hardening is the common explanation for this phenomenon.However,it could not explain why this bending angle reduction phenomenon occurs at low heat input scanning rather than at high heat input scanning.In this study,this phenomenon is discussed based on strain development in experiments and numerical simulation.The different growing mechanism of plastic strain is analyzed to reveal the effects of laser power and scanning velocity.Furthermore,the opposite bending trend that occurred at larger laser power is discussed in comparison to the plastic strain development.The study shows that relatively larger heat input below 6.7 J/mm can help to avoid the bending angle reduction phenomenon and the opposite bending trend is highly dependent on the larger laser power.For achieving the expected cumulative bending angle in multi-pass laser bending,it is recommended to decrease the scanning velocity at a relatively low laser power level while increase the scanning velocity at a high level of laser power.

Material Parameters of a Structural Steel with Plastic Strain Memory

The present work is concerned with the characterization of hardening parameters for an elasto-plastic continuum model, taking into account the memory effect of plastic strain amplitude, in order to predict the hysteretic responses of a ferritic steel. This elasto-plastic three-dimensional model is based on the internal thermodynamic variables which composed of the nonlinear kinematic hardening and isotropic hardening with the plastic strain memorization. The emphasis is put on the determination of strain memory parameters along with other material parameters of the proposed model in order to better simulate the behavior of the material at different strain range. The material parameters are calibrated with the experimental stabilized loops of stress-strain curves available in the literature. The predicted stabilized loops from the simulation with the determined parameters show good agreement with the experimental results signifying the validity of the considered model.

SOME MISUNDERSTANDINGS ON ROTATION OF CRYSTALS AND REASONABLE PLASTIC STRAIN RATE

It is pointed out that crystals are discrete but not continuous materials. Hence the rotation R in decomposition F=RU and spin W in F -1  are not correct. Errors will arise in plastic deformation rate if it is directly expressed with amounts of velocity of slips in glide systems such as vn. The geometrical figure of crystal lattices does not change after slips and based on this idea a simple way in mechanics of continuous media to get the plastic deformations rate induced by slips is proposed. Constitutive equations are recommended.

A work-hardening and softening constitutive model for sand:modified plastic strain energy approach

The paper describes an energy-based constitutive model for sand, which is modified based on the modified plastic strain energy approach, represented by a unique relationship between the modified plastic strain energy and a stress parameter, independent of stress history. The modified plastic strain energy approach was developed based on results from a series of drained plastic strain compression tests along various stress paths on saturated dense Toyoura sand with accurate stress and strain measurements. The proposed model is coupled with an isotropically work-hardening and softening, non-associtated, elasto-plastic material description. The constitutive model concerns the inherent and stress system-induced cross-anisotropic elastic deformation properties of sand. It is capable of simulating the deformation characteristics of stress history and stress path, the effects of pressure level, anisotropic strength and void ratio, and the strain localization.

SOME MISUNDERSTANDINGS ON ROTATION OF CRYSTALS AND REASONABLE PLASTIC STRAIN RATE

It is pointed out that crystals are discrete but not continuous materials. Hence the rotation R in decomposition F = RU and spin TY in (F) over dot F-1 ore not correct. Errors will arise in plastic deformation rare if it is directly expressed with amounts of velocity of slips in glide systems such as (gamma) over dot upsilon circle times n. The geometrical figure of crystal lattices does nor change after slips and based on this idea a simple way in mechanics of continuous media to get the plastic deformations rare induced by slips is proposed. Constitutive equations are recommended.

A refined deviatoric hardening plastic model for sand

The classical deviatoric hardening models are capable of characterizing the mechanical response of granular materials for a broad range of degrees of compaction.This work finds that it has limitations in accurately predicting the volumetric deformation characteristics under a wide range of confining/consolidation pressures.The issue stems from the pressure independent hardening law in the classical deviatoric hardening model.To overcome this problem,we propose a refined deviatoric hardening model in which a pressure-dependent hardening law is developed based on experimental observations.Comparisons between numerical results and laboratory triaxial tests indicate that the improved model succeeds in capturing the volumetric deformation behavior under various confining/consolidation pressure conditions for both dense and loose sands.Furthermore,to examine the importance of the improved deviatoric hardening model,it is combined with the bounding surface plasticity theory to investigate the mechanical response of loose sand under complex cyclic loadings and different initial consolidation pressures.It is proved that the proposed pressure-dependent deviatoric hardening law is capable of predicting the volumetric deformation characteristics to a satisfactory degree and plays an important role in the simulation of complex deformations for granular geomaterials.

An improved strain-softening constitutive model of granite considering the effect of crack deformation

This paper presents an improved strain-softening constitutive model considering the effect of crack deformation based on the triaxial cyclic loading and unloading test results.The improved model assumes that total strain is a combination of plastic,elastic,and crack strains.The constitutive relationship between the crack strain and the stress was further derived.The evolutions of mechanical parameters,i.e.strength parameters,dilation angle,unloading elastic modulus,and deformation parameters of crack,with the plastic strain and confining pressure were studied.With the increase in plastic strain,the cohesion,friction angle,dilation angle,and crack Poisson's ratio initially increase and subsequently decrease,and the unloading elastic modulus and the crack elastic modulus nonlinearly decrease.The increasing confining pressure enhances the strength and unloading elastic modulus,and decreases the dilation angle and Poisson's ratio of the crack.The theoretical triaxial compressive stress-strain curves were compared with the experimental results,and they present a good agreement with each other.The improved constitutive model can well reflect the nonlinear mechanical behavior of granite.

Quantification of grain boundary effects on the geometrically necessary dislocation density evolution and strain hardening of polycrystalline Mg-4Al using in situ tensile testing in scanning electron microscope and HR-EBSD

In situ tensile testing in a scanning electron microscope(SEM)in conjunction with high-resolution electron backscatter diffraction(HR-EBSD)under load was used to characterize the evolution of geometrically necessary dislocation(GND)densities at individual grain boundaries as a function of applied strain in a polycrystalline Mg-4Al alloy.The increase in GND density was investigated at plastic strains of 0%,0.6%,2.2%,3.3% from the area including 76 grains and correlated with(i)geometric compatibility between slip systems across grain boundaries,and(ii)plastic incompatibility.We develop expressions for the grain boundary GND density evolution as a function of plastic strain and plastic incompatibility,from which uniaxial tensile stress-strain response of polycrystalline Mg-4Al are computed and compared with experimental measurement.The findings in this study contribute to understanding the mechanisms governing the strain hardening response of single-phase polycrystalline alloys and more reliable prediction of mechanical behaviors in diverse microstructures.

New forming method of manufacturing cylindrical parts with nano/ultrafine grained structures by power spinning based on small plastic strains

A new spinning method to manufacture the cylindrical parts with nano/ultrafine grained structures is proposed, which consists of quenching, power spinning and recrystallization annealing. The microstructural evolution during the different process stages and macroforming quality of the spun parts made of ASTM 1020 steel are investigated. The results show that the microstructures of the ferrites and pearlites in the ASTM 1020 steel are transformed to the lath martensites after quenching. The martensite laths obtained by quenching are refined to 87 nm and a small amount of nanoscale deformation twins with an average thickness of 20 nm is generated after performing a 3-pass stagger spinning with 55% thinning ratio of wall thickness, where the equivalent strain required is only 0.92. The equiaxial ferritic grains with an average size of 160 nm and nano-carbides are generated by subsequent recrystallization annealing at 480°C for 30 min. The spun parts with high dimensional precision and low surface roughness are obtained by the forming method developed in this work, combining quenching with 3-pass stagger spinning and recrystallization annealing.

Generalizing J_2 flow theory: Fundamental issues in strain gradient plasticity

It has not been a simple matter to obtain a sound extension of the classical J2 flow theory of plasticity that incorporates a dependence on plastic strain gradients and that is capable of capturing size-dependent behaviour of metals at the micron scale. Two classes of basic extensions of classical J2 theory have been proposed： one with increments in higher order stresses related to increments of strain gradients and the other characterized by the higher order stresses themselves expressed in terms of increments of strain gradients. The theories proposed by Muhlhans and Aifantis in 1991 and Fleck and Hutchinson in 2001 are in the first class, and, as formulated, these do not always satisfy thermodynamic requirements on plastic dissipation. On the other hand, theories of the second class proposed by Gudmundson in 2004 and Gurtin and Anand in 2009 have the physical deficiency that the higher order stress quantities can change discontinuously for bodies subject to arbitrarily small load changes. The present paper lays out this background to the quest for a sound phenomenological extension of the rateindependent J2 flow theory of plasticity to include a de- pendence on gradients of plastic strain. A modification of the Fleck-Hutchinson formulation that ensures its thermo- dynamic integrity is presented and contrasted with a comparable formulation of the second class where in the higher or- der stresses are expressed in terms of the plastic strain rate. Both versions are constructed to reduce to the classical J2 flow theory of plasticity when the gradients can be neglected and to coincide with the simpler and more readily formulated J2 deformation theory of gradient plasticity for deformation histories characterized by proportional straining.

Strain gradient plasticity: energetic or dissipative?

Abstract For an infinite slab of strain gradient sensitive material subjected to plane-strain tensile loading, compu- tation established and analysis confirmed that passivation of the lateral boundaries at some stage of loading inhibits plastic deformation upon further loading. This result is not surprising in itself except that, remarkably, if the gradient terms contribute to the dissipation, the plastic deformation is switched off completely and only resumes at a clearly defined higher load, corresponding to a total strain ec, say. The analysis presented in this paper confirms the delay of plastic deformation following passivation and determines the exact manner in which the plastic flow resumes. The plastic strain rate is continuous at the exact point ec of resumption of plastic flow and, for the first small increment Ae = e - ec in the imposed total strain, the corresponding increment in plastic strain, AeP, is proportional to （Ae）2. The constant A in the relation AeP（0） = A（Ae）2, where AeP（0） denotes the plastic strain increment at the centre of the slab, has been determined explicitly; it depends on the hardening modulus of the material. The presence of energetic gradient terms has no effect on the value of ec unless the dissipative terms are absent, in which case passivation reduces the rate of plastic deformation but introduces no delay. This qualitative effect of dissipative gradient terms opens the possibility of experimen- tal discrimination of their presence or absence. The analysisemploys an incremental variational formulation that is likely to find use in other problems.

A Model of Dynamic Recrystallization in Alloys during High Strain Plastic Deformation

Recrystallized grains, less than 200 nm in diameter were observed in heavily shear zones of a high strength low alloy steel and a Ni-based alloy, and Also grain refinement, less than 3 μm in diameter was made in high purity aluminum by ECAE at ambient temperature. The experimental results showed that high strain rate and large deformation could induce dynamic recrystallization.Based on dislocation dynamics and grain orientation change enhanced by plastic deformation,a model for the recrystallization process is developed. The model is used to explain the ultra fine grains which are formed at a temperature still much lower than that for the conventional recrystallization

A SEPARATED LAW OF HARDENING IN STRAIN GRADIENT PLASTICITY

This paper presents a separated law of hardening in plasticity with strain gradient effects. The value of the length parameter l contained in this model was estimated from the experimental data for copper.

On the homogenization of metal matrix composites using strain gradient plasticity

The homogenized response of metal matrix composites（MMC） is studied using strain gradient plasticity.The material model employed is a rate independent formulation of energetic strain gradient plasticity at the micro scale and conventional rate independent plasticity at the macro scale. Free energy inside the micro structure is included due to the elastic strains and plastic strain gradients. A unit cell containing a circular elastic fiber is analyzed under macroscopic simple shear in addition to transverse and longitudinal loading. The analyses are carried out under generalized plane strain condition. Micro-macro homogenization is performed observing the Hill-Mandel energy condition,and overall loading is considered such that the homogenized higher order terms vanish. The results highlight the intrinsic size-effects as well as the effect of fiber volume fraction on the overall response curves, plastic strain distributions and homogenized yield surfaces under different loading conditions. It is concluded that composites with smaller reinforcement size have larger initial yield surfaces and furthermore,they exhibit more kinematic hardening.

Improvements of the crystallographic approach to plastic strain ratio in deep drawing steel sheets

Among various methods for calculation of the plastic strain ratio (γ value) of deep drawing steel sheet, the crystallographic approach is rather preferred because it is founded on the slip action during the crystal plastic deformation, while the crystal deformation mechanisms are fully taken into account. Thus it possesses a more soundly theoretical basis. However, its two assumptions, i.e. the same critical shear stresses for the three different slip systems in BCC and no orientation changes for all crystallites in tensile test samples in elongation up to 15％, are inconsistent with the experimental evidence.

Flow stress model considering the transformation-induced plasticity effect and the inelastic strain recovery behavior

On the basis of continuum mechanics and the Mori-Tanaka mean field theory, a micro-mechanical flow stress model that considered both the transformation-induced plasticity （TRIP） effect and the inelastic strain recovery behavior of TRIP multiphase steels was presented. The relation between the volume fraction of constituent phases and plastic strain was introduced to characterize the transformation-induced plasticity effect of TRIP steels. Loading-unloading-reloading uniaxial tension tests of TRIP600 steel were carried out and the strain recovery behavior after unloading was analyzed. From the experimental data, an empirical elastic modulus expression is extracted to characterize the inelastic strain recovery. A comparison of the predicted flow stress with the experimental data shows a good agreement. The mechanism of the transformation-induced plasticity effect and the inelastic recovery effect acting on the flow stress is also discussed in detail.

LOCALIZED SUPERPLASTIC BEHAVIOUR INα-TITANIUM AT HIGH STRAIN RATE

The microstructure of x-Ti/ mild steel composite fabricated by using constant stand-off cladding technique was observed with optical microscopy, SEM and TEM analyses. Very fine equiaxed grains (<0.1um) with a low dislocation density were observed in the adiabatic shear bands (ASB) this enables a thermomechanical response that may lead to a super plastic de formation.

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