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This paper gives a review of the finite element techniques (FE) applied in the area of material processing. The latest trends in metal forming, non‐metal forming and powder metallurgy are briefly discussed. The range of applications of finite elements on the subjects is extremely wide and cannot be presented in a single paper; therefore the aim of the paper is to give FE users only an encyclopaedic view of the different possibilities that exist today in the various fields mentioned above. An appendix included at the end of the paper presents a bibliography on finite element applications in material processing for the last five years, and more than 1100 references are listed.

Numerical modelling and simulation of metal forming is rapidly gaining prominence in many industries all over the world due to its effective saving of production time, effort and economy. In order to meet this need a special finite element code FORGE2 has been developed at CEMEF. In this work the theoretical basis of the FORGE2 along with its features such as thermo‐viscoplastic coupling, material compressibility and automatic mesh regeneration is reviewed and an attempt is made to simulate a few industrial forming processes taking into account the complex friction phenomena and thermal environment.

The constitutive equations for the deformation of elastoplastic, viscoplastic or compressible materials are presented for the small strain approximation and for the large strain theory of Hill. A velocity approach is proposed for time discretization, which leads to a second order approximation for small strain, and an incrementally objective second order approximation for large deformation processes. Two other quasi second order formulations are discussed. The finite element space discretization is outlined and the solution procedure is described.

The analysis of error estimation is addressed in the framework of viscoplasticity problems, this is to say, of incompressible and non‐linear materials. Firstly, Zienkiewicz—Zhu (Z²) type error estimators are studied. They are based on the comparison between the finite element solution and a continuous solution which is computed by smoothing technique. From numerical examples, it is shown that the choice of a finite difference smoothing method (Orkisz’ method) improves the precision and the efficiency of this type of estimator. Then a Δ estimator is introduced. It makes it possible to take into account the fact that the smoothed solution does not verify the balance equations. On the other hand, it leads us to introduce estimators for the velocity error according to the L² and L^∞norms, since in metal forming this error is as important as the energy error. These estimators are applied to an industrial problem of extrusion, demonstrating all the potential of the adaptive remeshing method for forming processes.

A finite‐element model for calculating the die temperature profile for a hot‐forging operation is presented. The workpiece is modelled as a thermo‐viscoplastic material, while the dies are considered undeformable. Heat transfer between the dies and the workpiece is modelled using an iteratively coupled, fixed‐point calculation of the temperature in each domain. Transfer of temperature boundary conditions across contact interfaces is performed for non‐coincident meshes, using a boundary integration point contact analysis. Two industrial‐type examples are presented. In the first example, the effectiveness of the transfer of the temperature boundary conditions for a non steady‐state forging process is evaluated and determined to be satisfactory. Then weakly‐ and strongly‐coupled temperature resolutions are compared. It was found that the strongly‐coupled resolution may be necessary in order to obtain reasonably accurate results. In the second example, the weakly‐coupled resolution is compared to a constant‐temperature die approach for a relatively slow forging process, which shows the influence of the die temperature on the flow of the material.

This paper gives a review of the finite element techniques (FE) applied in the area of material processing. The latest trends in metal forming, non‐metal forming, powder metallurgy and composite material processing are briefly discussed. The range of applications of finite elements on these subjects is extremely wide and cannot be presented in a single paper; therefore the aim of the paper is to give FE researchers/users only an encyclopaedic view of the different possibilities that exist today in the various fields mentioned above. An appendix included at the end of the paper presents a bibliography on finite element applications in material processing for 1994‐1996, where 1,370 references are listed. This bibliography is an updating of the paper written by Brannberg and Mackerle which has been published in Engineering Computations, Vol. 11 No. 5, 1994, pp. 413‐55.

A finite element model for numerical simulation of non‐steady but continuous chip formation under orthogonal cutting conditions is described. The problem is treated as coupled thermo‐mechanical. A velocity approach has been adopted for the proposed solution. The computational algorithm takes care of dynamic contact conditions and makes use of an automatic remeshing procedure. The results of simulation yield complete history of chip initiation and growth as well as distributions of strain rate, strain, stress and temperature. The paper includes a detailed presentation of computational results for an illustrative case.

A technique for computing free surfaces by a steady state approach has been included in the hot rolling code ROLL3. It has been described in a previous paper, along with applications to some simple rolling passes. In the present text, new developments are included to deal with more complex geometries, in particular when several potentially free surfaces exist. The problem of contact with flanks of grooves is given special care. Application to dog bone formation and flattening is presented. Then a case with two free surfaces is computed and compared to experiments. An application is then performed to beam roughing passes.

A two‐grid iterative method for 3D linear elasticity problems, discretized using quadratic tetrahedral elements is proposed. The conjugate‐gradient method is used as smoother. As compared to the conjugate‐gradient alone, it is shown, via numerical examples, that the method is much more efficient on the basis of computing time and memory allocation. The convergence property of the method is sensitive to the regularity of the problem.

This paper presents the results of the simulation of the forging of a connecting rod. The calculation has been carried out by the code FORGE3 developed at the CEMEF laboratory. FORGE3 is a three‐dimensional finite element computer program that can simulate hot forging of industrial parts. The flow problem is solved using a thermomechanical analysis. The mechanical resolution and the thermal one are coupled by the way of the consistency K which is thermodependent, the plastic deformation in the volume of the material and the friction heat flux on the surface. The material behaviour is assumed to be incompressible and viscoplastic (Norton—Hoff law) with the associated friction law. The thermal resolution includes the case of non‐linear physical properties and boundary conditions. An explicit Euler scheme is used for the mechanical resolution and two‐step schemes for the thermal one. For the computation of other parameters, it is necessary to have a good approximation for the strain rate tensor. The Orkisz method has been used to determine the deviatoric stress tensor and p is calculated by an original smoothing method. The results show that it is possible to get good information on the flow and on the physical properties during forging of automotive parts. Comparisons have been made with experimental measurements with a reasonably good agreement.