Numerical analysis of superplastic bulging for cavity-sensitive materials

A simulation of the thinning development until fracture for superplastic material bulging deformation under hydrostatic pressure is realized by the rigid-viscoplastic finite-element method by introducing a model of cavity growth. The deformation and the failure are considered as a combination and interaction process between the inhomogeneous geometric thinning development and the internal cavity evolution, which are controlled by the strain-rate sensitivity and the cavity growth-rate of the material.     

Analysis of superplastic blow-forming in a conical closed die

A mathematical model using the finite-difference method has been proposed in this work to examine the plastic deformation behavior of the sheet during blow-forming in a conical closed die. In the formulation of this mathematical model, nonuniform thinning in the free bulged region and the contact condition including the sticking and sliding friction modes between the sheet and die are considered. Effects of various forming parameters such as the die entry radius, friction coefficient, inclined angle of the die, etc., upon the optimized pressurization profile, forming time and the thickness distribution of products were discussed systematically. Furthermore, experiments on superplastic blow-forming in a conical closed die were carried out using 8090 Al-Li sheets. It is found that the theoretical predictions agree with experimental results. The thickness distributions of the SPF-ed product obtained with different friction coefficients along the die entry, sidewall and bottom are closer to the experimental data than those obtained with a constant friction coefficient.     

Accurate determination of biaxial stress-strain relationships from hydraulic bulging tests of sheet metals

The meridional strain gradient in hydraulic bulging of sheet metal through a circular aperture is severe. The resulting thickness gradation affects the bulge shape and complicates the evaluation of representative strain and stress at the pole of the bulge. An earlier solution for calculation of polar strain is extended to provide accurate explicit formulations of the thickness variation and the effective radius of curvature near the pole of the bulge. The representative stress—strain relationship determined for the biaxial stress state at the pole is shown to be significantly affected by these corrections.     

Damage evolution in creep bulging of thin sheet metal

The creeping motion of thin sheet metal, damaged by artificial cavities is observed in bulging tests and simulated ‘semi’-analytically. The sheet metal satisfies Norton’s Law for secondary creep and is subjected to a bi-directional stretch. The stretch is produced by creep bulging through elliptical dies with the virtue of sustaining nearly uniform background stress ratio for each aspect ratio of the die axes. In order to reach large deformations with significant shape evolution of the cavities, the tests were conducted at superplastic conditions. The sheet is double layered (only one layer is cavitated) made of Tin–Lead (50–50 Pb–Sn). The measured damage growth is compared to an approximate simulation. The simulation of the damage evolution, throughout its time history, makes repeated use of a so-called “Green-function solution” for the motion of a single isolated cavity in an infinite viscoplastic continuum. The solution is modified from Muskhelishvili’s elastic solution by replacing the elastic shear modulus by a “viscous-like” variable (“plastic shear modulus”) which depends (non-linearly) on the evolved average strain-rate. Similarly, the stresses in the ligaments between cavities were averaged to approximate the local stress concentrations. Due emphasis is given to the rotation of each elliptical cavity, beside its expansion (contraction) and elongation.     

Numerical simulation of electromagnetic sheet bulging based on FEM

A sequential coupling method has been used to analyze the electromagnetic sheet bulging. The adaptive remeshing technique is used in air meshes to make it change regularly according to the deformation result of the sheet. The deformed sheet is imported into electromagnetic model to calculate the magnetic force in next time step. Therefore, the method solves the problem of electromagnetic?Cstructure coupling analysis. According to the research results, with the increase of the sheet deflection, the effects of the radial component of the magnetic force on sheet deformation increase gradually. The optimum value of the time step is found, which corresponds to the better simulation result and less computational time. The simulative deflections at the center and 20?mm from the center with time are good in agreement with the experimental ones.     

Plastic bulging of sheet metals at high strain rates

The biaxial bulge test is a material test for sheet metals to evaluate formability and determine the flow stress diagram. Due to the biaxial state of stress induced in this test, the maximum achievable strain before fracture is much larger than in the uniaxial tensile test. A new dynamic bulge testing technique is simulated and analyzed in this study which can be performed on a conventional split Hopkinson pressure bar (SHPB) system to evaluate the strain-rate dependent strength of material at high impact velocities. Polyurethane rubber as pressure carrying medium is used to bulge the OFHC copper sheet. The use of hyperelastic rubber instead of fluid as a pressure medium makes the bulge test simple and easy to perform. The input bar of SHPB is used to apply and measure the bulging pressure. The finite element simulation using ABAQUS/explicit and analytical analysis are compared and show good correlation with each other. The results clearly show that as the strain-rate increases, the strength of the OFHC copper increases. From the study, a robust method to determine the material behavior under dynamically biaxial deformation conditions has been developed.     

Numerical simulation of the electromagnetic sheet metal bulging process

Electromagnetic forming (EMF) is an uncommon metal working process that relies on the use of electromagnetic forces to deform metallic workpieces at high speeds. It is expected to overcome some formability barriers of materials. EMF process analysis is the foundation of theoretical analysis. However, the electromagnetic sheet metal process is very difficult to describe, because of the complexity of magnetic pressure distribution. In this paper, a numerical modeling of the electromagnetic sheet metal process is performed using a finite element method, and a series of simulations on free bulging are carried out using the FEA program ADINA. The dynamic deformation process of sheet metal is investigated. At last, some experiments are made and those simulations agree well with the experimental results.     

A new formulation for the bulging of viscous sheet metals

The creep bulging of clamped circular thin shells subjected to one-sided hydrostatic pressure is examined. Contrary to the previous treatments of the problem this one does not assume a spherical shape but only an axisymmetric one. The theoretical results are compared with experiments in which sheets of Zn-Al eutectoïd alloy are deformed at various temperatures.     

Viscous pressure bulging of aluminium alloy sheet at warm temperatures

Improving the formability of aluminium alloy sheet metal by using warm or elevated temperature has become a valid approach. In this paper, viscous pressure bulging (VPB) at warm temperature is proposed. The coupled thermo-mechanical finite element method and experimental method were used to investigate the VPB of aluminium alloy AA3003 at warm temperature. The temperature distributions of sheet metal and viscous medium were analyzed for non-isothermal VPB. The influence of forming temperature on thickness distribution, forming load and failure location of sheet metal were investigated. Research results show the temperature gradient field in sheet metal forms when the initial temperature of viscous medium is lower than that of sheet metal. The formability and failure location of sheet metal changes with initial temperature of viscous medium.     

A simple model to simulate electromagnetic sheet free bulging process

Electromagnetic sheet forming is a high-velocity forming process driven by the coupled electromagnetic and mechanical phenomena. The deformation of the workpiece is governed by the body forces (Lorentz forces) that results from a pulsed magnetic field produced by a flat spiral coil. Formability can be increased using this high-velocity forming technique due to the inertial forces and high strain rates. In this study, we consider the electromagnetic and the mechanical aspect of the process as two independent problems. The finite difference method has been employed to solve the electromagnetic equations. The pressure acting on the sheet and due to the Lorentz forces is estimated neglecting the influence of the sheet velocity on the magnetic field. Then it has been treated as a load in the mechanical problem. Numerical simulations of the mechanical problem have been performed with the commercial finite element code ABAQUS/Explicit. The magnetic pressure has been introduced in ABAQUS/Explicit as an analytical pressure distribution. The general objective of this study is to better understand the complex phenomenon of deformation and the influence of viscoplastic material behaviour during the simulation of a free bulging electromagnetic sheet forming process.     

Numerical and experimental study on the three-dimensional extrusion of square section from square billet through a polynomial shaped curved die

The geometry of die profile plays a major role in reducing the extrusion pressure and ensuring the smooth flow of material. In general, the extrusion process is mostly affected by billet geometry, die geometry, and interface frictional force at the die billet geometry. In the present investigation, an analysis using three-dimensional upper bound method using fifth-order die profile function has been carried out for extrusion of square sections from square billet. The extrusion pressure and optimum die length have been computed by multivariable optimization technique. The present die shape profile is found to be superior to many other profiles. The results obtained will help in design of optimum die profile and investigation of its performance.     

Analysis of the bulging process of an AZ31B magnesium alloy sheet with a uniform pressure coil

As the lightest metal material, magnesium alloy is widely used in the aerospace, automobile, and consumer electronic industries. However, magnesium alloy sheet has poor formability at room temperature. Electromagnetic forming is a high velocity forming technique that can promote the formability of low ductility materials, improve the strain distribution of workpieces, and reduce their wrinkling and springback. In this work, a uniform pressure coil was used to bulge AZ31B magnesium alloy sheets. The finite element method was then used to analyze this bulging process. The bulging contours and displacements of AZ31B magnesium alloy sheets were consistent with the experiment results. The distribution of the magnetic field intensity and magnetic field forces were found to be better than using a flat spiral coil. The deformation rule of AZ31B magnesium alloy sheet using the uniform pressure coil differed from that using the flat spiral coil. The largest strain occurred at the center of the sheet.     

A quantitative model of the blow-forming of spherical surfaces in superplastic sheet metal

The blow-forming of a flat superplastic metal sheet to a spherical surface is analysed with a mathematical model based on the classical theory of liquid bubbles. The model enables a quantitative account to be given of the effect of the strain-rate sensitivity, flow stress and temperature of the metal on the rate of blow-forming and the replication of detail. Formulae are derived which enable the superplastic flow stress and strain-rate sensitivity to be calculated from simple blow-forming tests.     

Rigid viscoplastic finite element analysis of the gas-pressure constrained bulging of superplastic circular sheets into cone disk shape dies

This paper describes the development of a rigid viscoplastic finite element formulation for analysing the gas-pressure constrained bulging processes of superplastic circular sheets in cone disk shape dies. In this formulation, the effects of strain hardening and strain-rate sensitivity of materials are included, and the boundary friction condition is introduced into the formulation in the form of friction functional. The finiteelement model based on the membrane theory is developed, and then applied to simulate superplastic constrained bulging processes. The solutions by the rigid viscoplastic finite element method are compared with existing experimental data. The influences of the geometrical parameters of the dies, the friction factor in the friction functional, the strain hardening and the strain-rate sensitivity on the inhomogeneity of thickness distribution are studied in detail.     

Finite element correction matrices in metal forming analysis (with application to hydrostatic bulging of a circular sheet)

This paper presents a condensed review of finite element applications in metal forming processes. Difficulties in large strain-elastoplastic analysis of these processes are identified. Correction techniques for potential sources of errors, such as lack of nodal equilibrium, violation of yield conditions, overstiff performance of finite elements, and improper formulation of configuration-dependent problems, are discussed. A main feature of the paper is the account of mixed boundary data in the updated Lagrangian formulation variational procedure. The code developed is applied to the process of the hydrostatic bulging of a circular sheet clamped at its periphery. This is based on a convenient explicit form of the hydrostatic-pressure load correction stiffness matrix for isoparametric and allied types of elements.     

Experimental and FE simulation validation of sheet thickness optimization in superplastic forming of Al alloy

Superplasticity is the ability of a polycrystalline materials to exhibit very large elongations without necking prior to failure. In this paper, the superplastic forming potential of fine grained 7075 aluminium alloy was studied. The process parameters like pressure, forming time and initial sheet thickness were selected, using the design of experiments technique. The same condition of formation process was attempted in the finite element simulation using ABAQUS software. The deviation of the thickness distribution between the simulation and experiment was made and the variation lies within 8%.

     

无缝门板的冲切工艺与模具

通过对无缝门板类零件的工艺分析,提出解决此类中厚板外观件的强力弹压冲切工艺方案与模具结构,为此类零件的冲压提供较具经济价值的参考.     

Hydrostatic bulging of a circular aluminium diaphragm

A numerical method of solution is presented for the plastic deformation of a circular metal diaphragm. The analysis is applied to the bulging of soft commercial purity aluminium sheet and the results correlated with experiment. It is shown the correlation is good for pressure, strain and geometrical relationships when plastic yielding is based on a new anisotropic yield function proposed by Hill.