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.

DEFORMATION ANALYSIS OF SHEET METAL SINGLE-POINT INCREMENTAL FORMING BY FINITE ELEMENT METHOD SIMULATION

Single-point incremental forming （SPIF） is an innovational sheet metal forming method without dedicated dies, which belongs to rapid prototyping technology. In generalizing the SPIF of sheet metal, the deformation analysis on forming process becomes an important and useful method for the planning of shell products, the choice of material, the design of the forming process and the planning of the forming tool. Using solid brick elements, the finite element method（FEM） model of truncated pyramid was established. Based on the theory of anisotropy and assumed strain formulation, the SPIF processes with different parameters were simulated. The resulted comparison between the simulations and the experiments shows that the FEM model is feasible and effective. Then, according to the simulated forming process, the deformation pattern of SPIF can be summarized as the combination of plane-stretching deformation and bending deformation. And the study about the process parameters＇ impact on deformation shows that the process parameter of interlayer spacing is a dominant factor on the deformation. Decreasing interlayer spacing, the strain of one step decreases and the formability of blank will be improved. With bigger interlayer spacing, the plastic deformation zone increases and the forming force will be bigger.

Analysis of localized shear deformation of ductile metal based on gradient-dependent plasticity

Shear localization in linear strain softening heterogeneous material under simple shear was investigated analytically. The closed-form solutions obtained based on gradient plasticity theory considering interactions and interplaying among microstructures due to heterogeneity of metal material show that in the normal direction of shear band, elastic shear displacement is linear; while plastic and total shear displacement are non-linear. Elastic shear strain in the band is uniform and the non-uniformity of total shear displacement stems from localized plastic shear displacement. In the center of the band, plastic and total shear displacement all reach their maximum values. In strain-softening process, elastic displacement decreases as flow shear stress decreases. Contrarily, plastic and total shear displacement increase and manifest shear localization occurs progressively. Under the same shear stress level, plastic and total shear displacement increase as strain softening modulus and elastic shear modulus decrease. The present analytical solutions were compared with many experimental results and the agreement is good.

Room temperature plastic deformation behavior of ZrCuNiAl bulk metallic glasses

The Zr62.55Cu17.55Ni9.9Al10 bulk metallic glass （BMG） was prepared by using copper-mold suction-casting. X-ray diffraction and differential scanning calorimetry were utilized to determine its structure and thermal stability. Uniaxial compression and Rockwell indenta- tion tests were adopted to study the plastic deformation behavior at room temperature. The results show that the glass transition temperature and the onset temperature of exothermic reaction of the BMG are 651.5 and 748 K, respectively. During the compression test, the BMGs undergo an engineering strain of about 2.5%, i.e., true strain of 2.8%, and then fracture. The BMGs deform via the formation and propagation of shear bands. Under indentation loading, the BMGs deform through the formation of radiation-like and circular shear bands. The circular shear bands form earlier than the radiation-like ones, The formation mechanism of shear bands in the BMGs was analyzed and discussed.

Deformation Behavior of Zr_(65)Cu_(17.5)Ni_(10)Al_(7.5)in Superplastic Forming with Silicon Mould: Simulation and Application

We investigated the deformation behaviors of Zr_65Cu_17.5Ni_10Al_7.5 in superplastic forming in silicon mould via numerical modeling and experiments. The data needed for the constitutive formulation were obtained from compressive tests to establish a material library for finite-element simulation using a DEFORM 3D software. A constant speed forming process of a micro gear was modeled where the loading force, feature size and amount of deformation in the micro gear in silicon mould were analyzed in detail for the optimal requirements of micro gear forming and the protection of silicon mould. Guided by the modeling parameters, an amorphous metal micro gear was successfully obtained by our home-made superplastic forming system with the optimized parameters （temperature of 683 K, top speed of 0.003 mm/s until the load force reaching limiting value at 1960 N, and a gradually decelerating process for holding the force to the end）. Our work gives a good example for optimization of superplastic forming and fabrication of BMGs in microparts.

Numerical simulation of ductile fracture behavior for aluminum alloy sheet under cyclic plastic deformation

A numerical analysis of mechanical behavior of aluminum alloy sheet under cyclic plastic deformation was investigated.Forming limit at fracture was derived from Cockcroft-Latham ductile damage criterion.The strain path of bending center of incremental roller hemming could be accepted as a kind of plane strain bending deformation process.Incremental rope roller hemming could be used to alleviate ductile fracture behavior by changing the stress state of the hemming-effected area.SEM observation on the fracture surface indicates that cyclic plastic deformation affects ductile fracture mechanism.

Influence of Transverse Normal Pressure on Deformation Behavior of Sheet Metal

To investigate the influence of magnitude and distribution of the transverse normal pressure on deformation behavior of sheet metal,viscous pressure bulge test (VPB) of overlapping sheet metals is proposed,where the overlapped sheet metal is deformed under the dual-sided normal pressure provided by viscous medium and the overlapping sheet.The transverse normal pressure loading features provided by overlapping sheet metals are first simulated by DEFORM-2D.It shows that the magnitude and space distribution of transverse normal pressure are dependent on strain hardening exponent n-,strength coefficient K-and thickness t-values of the overlapping sheet metal.Based on the stress,deviator stress and strain distribution resulted from the finite element simulation,it indicated that the uniform transverse normal pressure has no effect on deviator stress,the figure and strain distribution of bulge specimens have no change.The non-uniform transverse normal pressure can remarkably change the figure and metal flow of specimens,and the formability of sheet metal can be improved by controlling the transverse normal pressure distribution.

Theory and Method of Optimum Path Forming for Sheet Metal

Ideal forming results will be achieved if the sheet metal is formed along an optimum forming path. Such a path can be realized by multi-point forming technique. On the basis of the theory of the ideal forming path (or minimum plastic work path), the concept of an optimum forming path is proposed in this paper. The forming path can be described by the initial configuration, objective configuration and a series of intermediate configurations. According to the deformation theory and constitutive equation in ideal path forming, a finite element method to calculate the initial configuration is set up. The functional to determinate intermediate configurations is introduced and the numerical method to solve the configuration is presented. Based on the method presented in the paper, multi-step multi-point forming tests for sheet metal are designed. The test results demonstrate that when the sheet is deformed along an approximate optimum forming path, the maximum deformation curvature for the sphere objective shape and saddle objective shape are 11%∼40% and 15%∼50% greater than those of a sheet deformed along a common path respectively.

Zr-Co(Cu)-Al bulk metallic glasses with optimal glass-forming ability and their compressive properties

The formation of bulk metallic glasses（BMGs） in the ternary Zr（56） Co（28-x）Al（16） and quaternary Zr（56） Co（28-x）CuxAl16（x=2, 4, 5, 6, 7, mole fraction, %） glassy alloys was investigated via the copper mold suction casting method. The main purpose of this work was to locate the optimal BMG-forming composition for the quaternary Zr Co（Cu）Al alloys and to improve the plasticity of the parent alloy. The X-ray diffractometry（XRD）, transmission electron microscopy（TEM） and differential scanning calorimetry（DSC） were used to investigate the glassy alloys structure and their glass forming ability（GFA）. In addition, the compression test, microhardness, nano-indentation and scanning electron microscopy（SEM） were utilized to discuss the possible mechanisms involved in the enhanced plasticity achievement. The highest GFA among Cu-containing alloys was found for the Zr（56） Co（22） Cu6 Al（16） alloy, which was similar to that of the base alloy. Furthermore, the plasticity of the base alloy increased significantly from 3.3% to 6% for the Zr（56） Co（22） Cu）6 Al（16） BMG. The variations in the plasticity and GFA of the alloys were discussed by considering the positive heat of mixing within Cu and Co elements.

Deformation and fracture of a Zr-Al-Cu metallic glass ribbon under tension near glass transition temperature

The high temperature tensile and fracture behavior of Zr50Al40Cu10 metallic glass at the temperature range in the vicinity of glass transition were investigated. Tensile tests were carried out at room temperature, 350-420 ℃, and in the supercooled liquid region temperature range, respectively. Obvious plastic deformation was initiated at temperature about 80 °C lower than the glass transition temperature. The ultimate tensile strength decreases with the increase of testing temperature and the ductility increases with temperature. At temperature higher than Tg, viscous flow of Non-Newtonian fluid led to super plastic deformation behavior. The deformation process under tension was inhomogeneous, and remarkable serrations were observed on the stress-strain curve near glass transition temperature.

Mechanics and forming theory of liquid metal forging

On the basis of steel liquid forging and aluminium alloy liquid forging, liquid metal forging was investigated, such as the assembly model, metal plastic flowing, the force displacement curves, the harmonious equation, calculation of value of altitude deformation and determination of specific pressure of liquid metal forging. On the basis of the theory of metal plastic forming and the characteristics of liquid metal forging, the achievements on the mechanics and forming theory of liquid metal forging were given out by combining the theory and experiments systematically, and an important preparation for establishing liquid metal forging theory was suggested.

Sheet Bulk Forming of Thin-Walled Components with External Gearing through Upsetting Using Controllable Deformation Zone Method

Sheet-bulk metal forming(SBMF)is a promising process for manufacturing complex sheet components with functional elements.In this study,the entire forming process for a typical thin-walled component with external gearing is investigated,including sheet forming and bulk forming processes.Deep drawn cups are prepared during sheet forming;subsequently,upsetting is performed on the sidewall to form external gearing.The upsetting method performed is known as upsetting with a controllable deformation zone(U-CDZ).Compared with the conventional upsetting method,a floating counter punch with a counter force is used in the U-CDZ method such that the forming mechanism is changed into the accumulation of the deformation zone instead of deformation throughout the entire sidewall.The effects of the counter force and material flow are investigated to understand the mechanism.The forming quality,i.e.,the formfilling and effective strain distribution,improved,whereas a high forming load is avoided.In addition,a punch with a lock bead is used to prevent folding at the inner corner during the experiment.

PREDICTION OF PATH-DEPENDENT FAILURE IN ALUMINUM SHEET METALS UNDER FORMING OPERATIONS

An approximate macroscopic yield criterion for anisotropic porous sheet metals is adopted in a failure prediction methodology that can be used to investigate the failure of sheet metals under forming operations. This failure prediction methodology is developed based on the Marciniak-Kuczynski approach by assuming a slightly higher void volume fraction inside randomly oriented imperfecte analysis. Here, a nonproportional deformation history including relative rotation of principal stretch directions is identified in a selected critical element of an aluminum sheet from a FEM fender forming simulation. Based on the failure prediction methodology, the failure of the critical sheet element is investigated under the non-proportional deformation history. The results show that thiven non-proportional deformation history.

Deforming analysis of sheet metal based on stereo vision and coordinate grid

A new approach based on stereo vision technology is introduced to analyzesheet metal deformation. By measuring the deformed circle grids that are printed on the sheetsurface before forming, the strain distribution of the workpiece is obtained. The measurement andanalysis results can be used to verify numerical simulation results and guide production. To getgood accuracy, some new techniques are employed: camera calibration based on genetic algorithm,feature abstraction based on self-adaptive technology, image matching based on structure feature andcamera modeling pre-constrains, and parameter calculation based on curve and surface optimization.The experimental values show that the approach proposed is rational and practical, which can providebetter measurement accuracy with less time than the conventional method.

Parallel Deformation of the Metals

The metal goes into the plastic deformation after the application of external load. Most of the metal forming industries work on this principle of plastic deformation. Thus the understanding of plastic deformation in the metal forming industry is important. The research on the single material plastic deformation has been carried out from many centuries before the era of Tresca. In this study the two metals 0.05% C steel annealed (soft metal) and 0.6% C steel quenched and tempered (hard metal) were deformed plastically in the parallel combination in the composite form. This study has been carried out with simple mathematical theory and simulated numerical model. The comparison shows the exact match between the mathematical and numerical results. It is also observed that the individual metal thickness affects the deformation flow curve.

Casting effect on compressive brittleness of bulk metallic glass

An interesting phenomenon of cooling-rate induced brittleness in Zr52.5Cu17.9Ni14.6Al10Ti5 bulk metallic glass （BMG） was reported. It was found that the as-cast BMG specimens exhibited a brittle-ductile transition when the larger specimens were machined into smaller specimens through removing the cast-softening surface layer by layer. After compression tests, the as-machined small specimens, owing to the absence of the cast-softening surface, displayed highly dense and intersecting shear bands, and extensive plastic deformation. This is in contrast to the catastrophic failure and low deformability in the as-cast large specimens. More free volume was detected in the smaller as-fractured specimens, by differential scanning calorimetry, which may be attributed to the occurrence of strain softening and increased plasticity. Compared with the relatively smooth fracture surface in the smaller specimens, the larger specimens showed more diverse features on the fracture surface due to their graded structures.

Effect of flow stress—strain relation on forming limit of 5754O aluminum alloy

A modified Swift type flow stress—strain relation was presented in order to describe the uniaxial tension test curve reasonably. The FLD-strain （forming limit diagram made up of limit strain） of 5754O aluminum alloy sheet was calculated based on the two flow stress—strain relations using Yld2000-2d yield function. By comparing the theoretical and experimental results, it is found that the calculated FLD-strain based on the modified Swift flow stress—strain relation can reasonably describe the experimental results. However, though the common Voce flow stress—strain relation can describe the deformation behavior during homogenous deformation phase accurately, the FLD-strain calculated based on it is obviously lower than the experimental result. It is concluded that the higher the hardening rate of sheet metal is, the higher the forming limit is. A method for determining the reasonable flow stress—strain relation is recommended for describing the material behavior during inhomogenous phase and the forming limit of sheet metal.

Characterization of the Elastic-plastic Region Based on Magnetic Memory Effect

Detecting stress concentration, especially critical stress state leading to structure damage or failure, is one of the most important tasks of equipment diagnosis. Metal magnetic memory technique needs further research to evaluate stress concentration quantitatively due to ambiguous physical mechanism, though it has potential to detect early defects in ferromagnetic materials. Mild Q235 steel defective specimens in demagnetization state were loaded in tension up to visible necking, with magnetic memory signals measurement made at increasing stress levels. Magnetic signals varied greatly under first several loadings and subsequently tended to stability in the elastic region, which showed that the magnetization always approaches the anhysteretic magnetization curve and was explained by the theory of magnetomechanical effect. In the plastic stage, an abnormal wave occurred in the stress concentration zone and its height value was sensitive to plastic deformation levels and dependent on the distance between the probe and defect, in accordance with the simulation results based on the magnetic dipole model. Different magnetic signal characteristics in the elastic-plastic region indicate that the magnetic memory technique can identify macroyielding and early damage, which is of profound significance for ensuring safe operation of equipment in service.

Mechanical Properties,Damage and Fracture Mechanisms of Bulk Metallic Glass Materials

The deformation, damage, fracture, plasticity and melting phenomenon induced by shear fracture were investigated and summarized for Zr-, Cu-, Ti- and Mg-based bulk metallic glasses （BMGs） and their composites. The shear fracture angles of these BMG materials often display obvious differences under compression and tension, and follow either the Mohr-Coulomb criterion or the unified tensile fracture criterion. The compressive plasticity of the composites is always higher than the tensile plasticity, leading to a significant inconsistency. The enhanced plasticity of BMG composites containing ductile dendrites compared to monolithic glasses strongly depends on the details of the microstructure of the composites. A deformation and damage mechanism of pseudo-plasticity, related to local cracking, is proposed to explain the inconsistency of plastic deformation under tension and compression. Besides, significant melting on the shear fracture surfaces was observed. It is suggested that melting is a common phenomenon in these materials with high strength and high elastic energy, as it is typical for BMGs and their composites failing under shear fracture. The melting mechanism can be explained by a combined effect of a significant temperature rise in the shear bands and the instantaneous release of the large amount of elastic energy stored in the material.

Hot shear deformation constitutive analysis of fine-grained ZK60 Mg alloy sheet fabricated via dual equal channel lateral extrusion and sheet extrusion

Dual equal channel lateral extrusion(DECLE)process with various passes followed by sheet extrusion process was performed to produce fine-grained ZK60 alloy sheets.The coarse grain structure of the annealed sample after applying sheet extrusion(size:68μm)changed to fine grains of 6.0 and 5.2μm after 3 and 5 passes of DECLE and following extrusion.The hot shear deformation behavior of samples was studied by developing constitutive equations based on shear punch test(SPT)results.SPT was carried out in the temperature range of 200−300℃ and strain rate range of 0.003−0.33 s^(–1).The activation energy of 125−139 kJ/mol and the stress exponent of 3.5−4.2 were calculated for all conditions,which indicated that dislocation creep,controlled by dislocation climb and solute drag mechanism,acted as the main hot deformation mechanism.It was concluded that material constants of n and Q are dependent on the microstructural factors such as grain size and second phase particle fraction,and the relationship of which was anticipated using a 3D surface curve.Moreover,the similar strong basal texture of extruded sheets gave rise to the same deformation mechanisms during SPT and similar n and Q values for ZK60 alloy.