Introduction Metal forming process Analysis and technology in metal forming Plasticity and viscoplasticity Methods of analysis The finite element method (1) The finite element method (2) Plane-strain problems Axisymmetric isothermal forging Steady state processes of extrusion and drawing Sheet metal forming Thermo-viscoplastic analysis Compaction and forging of porous metals Three dimensional problems Preform design in metal forming Solid formulation, comparison of two formulations, and concluding remarks Index.

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Metal Forming and the Finite-Element Method

http://digitalknowledge.cput.ac.za/bitstream/11189/4942/3/Makinde_Oluwole_D_Aziz_A_Eng_2011.pdf

Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition

Publisher Summary This chapter describes the material failure by coalescence of microscopic voids. The voids nucleate mainly at second phase particles, by decohesion of the particle-matrix interface or by particle fracture, and subsequently the voids grow because of plastic straining of the surrounding material. The growth of voids to coalescence by plastic yielding of the surrounding material involves so large geometry changes that finite strain formulations of the field equations are a necessary tool. A convected coordinate formulation of the governing equations is used. Convected coordinates are introduced, which serve as particle labels. The convected coordinate net can be visualized as being inscribed on the body in the reference state and deforming with the material. It is found that after nucleation, cavities elongate along the major tensile axis and that two neighboring cavities coalesce when their length has grown to the order of magnitude of their spacing. This local failure occurs by the development of slip planes between the cavities or simply necking of the ligament. A detailed micromechanical study of shear band bifurcation that accounts for the interaction between neighboring voids and the strongly nonhomogeneous stress distributions around each void has been carried out, and are also elaborated in this chapter.

Material Failure by Void Growth to Coalescence

Bulk metal working processes are carried out at elevated temperatures where the occurrence of simultaneous softening processes would enable the imposition of large strains in a single step or multi...

Modelling of hot deformation for microstructural control

Theoretical concepts of sintering were originally based upon ideas of the discrete nature of particulate media. However, the actual sintering kinetics of particulate bodies are determined not only by the properties of the particles themselves and the nature of their local interaction with each other, but also by macroscopic factors. Among them are externally applied forces, kinematic constraints (e.g. adhesion of the sample's end face and furnace surface), and inhomogeneity of properties in the volume under investigation (e.g. inhomogeneity of initial density distribution created during preliminary forming operations). Insufficient treatment of the questions enumerated above was one of the basic reasons hindering the use of sintering theory. A promising approach is connected with the use of continuum mechanics, which has been successfully applied to the analysis of compaction of porous bodies. This approach is based upon the theories of plastic and nonlinear-viscous deformation of porous bodies. Similar ideas have recently been embodied in a continuum theory of sintering. The main results of the application of this theory for the solution of certain technological problems of sintering are introduced including their thermo–mechanical aspects.

Theory of sintering: from discrete to continuum

A new method of modeling material behavior which accounts for the dynamic metallurgical processes occurring during hot deformation is presented. The approach in this method is to consider the workpiece as a dissipator of power in the total processing system and to evaluate the dissipated power co-contentJ = ∫o σ e ⋅dσ from the constitutive equation relating the strain rate (e) to the flow stress (σ). The optimum processing conditions of temperature and strain rate are those corresponding to the maximum or peak inJ. It is shown thatJ is related to the strain-rate sensitivity (m) of the material and reaches a maximum value(J max) whenm = 1. The efficiency of the power dissipation(J/J max) through metallurgical processes is shown to be an index of the dynamic behavior of the material and is useful in obtaining a unique combination of temperature and strain rate for processing and also in delineating the regions of internal fracture. In this method of modeling, noa priori knowledge or evaluation of the atomistic mechanisms is required, and the method is effective even when more than one dissipation process occurs, which is particularly advantageous in the hot processing of commercial alloys having complex microstructures. This method has been applied to modeling of the behavior of Ti-6242 during hot forging. The behavior of α+ β andβ preform microstructures has been exam-ined, and the results show that the optimum condition for hot forging of these preforms is obtained at 927 °C (1200 K) and a strain rate of 1CT•3 s•1. Variations in the efficiency of dissipation with temperature and strain rate are correlated with the dynamic microstructural changes occurring in the material.

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Modeling of dynamic material behavior in hot deformation: Forging of Ti-6242

Briefly reviews the basic principles of metal forming but major emphasis is on the latest developments in the design of metal-forming operations and tooling. Discusses the position of metal forming in manufacturing and considers a metal-forming process as a system consisting of several interacting variables. Includes an overall review and classification of all metal-forming processes. The fundamentals of plastic deformation - metal flow, flow stress of metals and yield criteria - are discussed, as are significant practical variables of metal- forming processes such as friction, temperatures and forming machines and their characteristics. Examines approximate methods of analyzing simple forming operations, then looks at massive forming processes such as closed-die forging, hot extrusion, cold forging/ extrusion, rolling and drawing (discussion includes the prediction of stresses and load in each process and applications of computer-aided techniques). Recent developments in metal-forming technology, including CAD/CAM for die design and manufacture, are discussed, and a review of the latest trends in metal flow analysis and simulations.

Metal Forming : Fundamentals and Applications

A new yield function for compressible PM materials

The workability of a material during deformation processing is determined by (a) the die geometry which, in turn, determines the flow field during deformation, and, (b) the inherent workability of the material under the imposed processing conditions of strain rate and temperature. Most common alloys have good inherent workability and can be successfully formed over wide ranges of temperature and strain rate. Products can be successfully formed from these alloys even with dies which impose large variations in strain rate during deformation. However, many of the new alloys and composites can be deformed only in very narrow processing regimes, and control of the strain rate during deformation of such materials becomes important. For example, extrusion of a whisker-reinforced aluminum alloy composite is possible only when the strain rate is controlled to within one order of magnitude. This paper describes the development of a method for obtaining preliminary shapes of controlled strain rate extrusion dies, a special case being the constant strain rate die. The theoretical basis for such die design processes is presented, followed by some examples of die geometries. Since this design procedure ignores the material flow properties, the designed die shapes must be verified using the finite element method or physical modeling. Results of simulations with the program ALPID are also presented.

H. L. Gegel

Papers

Modeling of dynamic material behavior in hot deformation: Forging of Ti-6242

Metal Forming : Fundamentals and Applications

A new yield function for compressible PM materials

Extrusion Through Controlled Strain Rate Dies

Computer-aided design of extrusion dies by metal-flow simulation