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Hexahedral elements are computationally efficient for three-dimensional modelling of metal forming processes but its utilization is still below expectations due to significant barriers caused by remeshing. Remeshing of hexahedral meshes is generally time consuming when performed manually or semi-automatically, suffers from lack of robustness when performed automatically and is commonly regarded as the bottleneck of the finite element analysis of metal forming processes. This paper presents an algorithm for the automatic generation of all-hexahedral meshes that is capable of representing the deformed geometry of a workpiece during updated Lagrangian finite element calculations without loosing geometrical as well as mechanical consistency. Topics to be addressed include the extraction of the basic geometrical features of the deformed mesh, construction of the core mesh, generation of the boundary mesh linking the core with the surface of the workpiece, application of smoothing procedures to edges, surfaces and volumes and transfer of field variables from the old to the new mesh. The emphasis is focused on providing detailed description of the algorithms and programming solutions for the benefit of those who want to design similar softwares for supporting their metal forming finite element simulation systems. The effectiveness of the proposed algorithm is discussed through its application to a simple but illustrative example derived from the cylindrical side pressing of a rod. Additional and more complex metal forming examples are included to enrich the presentation and to illustrate its scope of application.

A new approach is put forwards for the numerical simulation of steady and non-steady state bulk metal forming processes. The approach is based on the utilization of the reproducing kernel particle method in conjunction with the flow formulation for slightly compressible rigid-plastic materials.The effectiveness of the proposed approach is discussed by comparing theoretical predictions with finite-element calculations and experimental data for three different bulk metal forming operations: flat rolling (under steady-state conditions), compression of rods and heading of cylindrical billets. The overall comparisons comprise a wide range of topics such as material flow, geometry, strain distribution and forming load/torque. It is shown that, the proposed approach is capable of efficiently handling large plastic deformations without the need of remeshing procedures and providing results that are in close agreement with both finite-element predictions and experimental measurements.

This paper discusses the utilisation of the slightly compressible finite element formulation to the numerical analysis of the vertical-horizontal rolling process. The first part of the paper details the basis of the plasticity theory for slightly compressible materials and presents an overview of its numerical implementation. Of particular interest in vertical-horizontal rolling are topics related to the prediction of the dog-bone shape when using a Eulerian formulation, the treatment of the frictional boundary conditions along the three-dimensional roll-workpiece contact interfaces and the modelling of the material streamlines within the plastically deforming region.The second part of the paper presents a comparison between theoretical predictions obtained by means of a special purpose computer program developed under the proposed approach and experimental results taken from the literature. Assessment is made in terms of the cross-sectional shapes, roll separating force and torque.

In most cold forging operations, formability is limited by ductile fracture. This paper describes the utilisation of ductile fracture criteria in conjunction with the finite element method to predict when and where material is likely to fracture during cold forging. Several previously published ductile fracture criteria are selected, and their values of critical damage at the levels of deformation at which fracture starts are obtained through a series of experimental upset tests comprising cylindrical, tapered and flanged geometries. The experiments are also used to investigate the validity and the relative accuracy of each criterion under loading conditions of stress and strain similar to those usually found in cold forging.

A heat transfer model developed to predict the temperature distributions in the billets during the initial stages of a hot forging cycle is presented. The model takes into account the heating of billets, the moving of billets from the furnace to the press and the free resting of the billets on the die. The analysis includes the characteristics of different types of heating equipments currently utilised in forging companies: fuel-fired furnaces, induction and direct resistance electrical systems. The paper presents an example that illustrates the application of the proposed heat transfer model in the prediction of the temperature distribution inside the billets at the beginning of the hot forging cycle. The potential, capabilities and shortcomings of the model are discussed and recommendations for promoting a full utilisation of the capabilities of the finite element method in the simulation of metal forming processes are made.

This paper draws from fundamental research on precision forging for the development of a flexible tool system for producing gear parts. The overall investigation makes use of conventional spur gears. Fundamental research is undertaken by using virtual prototyping modeling techniques based on the finite element method. The utilization of such techniques provides a better insight into the deformation mechanics during the forging process, by giving an accurate description of the material flow, filling conditions and corresponding geometrical profiles. The finite element method also enables the prediction of stresses and forces exerted on tools as well as the distribution of the major field variables in the forged parts. The application of tool design expertise in conjunction with the virtual prototyping modeling techniques made possible the development of a tool system for performing the experiments. The experimental work is mainly utilized for supporting and validating the theoretical investigation but a later stage can be further developed in order to put the proposed forging concept on an industrial basis.

In this paper the three-dimensional forward extrusion of a square section from a round billet through a straight converging die is analysed using both the updated Lagrangian and the combined Eulerian–Lagrangian finite element formulations. The theoretical background for both formulations is reviewed, and the numerical results obtained with the two formulations are compared with experimental data obtained through the utilisation of physical modelling. Assessment is made in terms of flow pattern and strain distribution for two different cross-sections corresponding to the axial symmetry planes of the three-dimensional extrusion profile. The experimental distribution of strain is determined from the shape change of quadrilateral grids previously printed on the surface of the axial cross-sections of the undeformed billets by means of large deformation square-grid analysis. Good agreement is obtained between physical and numerical modelling.

This paper presents an effort to provide basic features for the fully automatic generation of graded initial quadrilateral finite element meshes to be applied in the analysis of metal forming processes. A grid-based approach is utilised for generating an initial coarse mesh with well-shaped internal elements, and in cases where non-rectangular shapes are to be discretised, linking with the boundary is performed on the basis of constrained Delaunay triangulation. Local refinement of the mesh is undertaken in zones where plastic deformation is expected to take place during the initial stages of simulation. Improvement of the general shape of the resulting mesh elements is performed by means of an iterative Laplacian smoothing procedure. An example is given to illustrate the feasibility of the approach.

This paper presents an innovative approach for analysing three-dimensional flat rolling. The proposed approach is based on a solution resulting from the combination of the finite element method with the boundary element method. The finite element method is used to perform the rigid–plastic numerical modelling of the workpiece allowing the estimation of the roll separating force, rolling torque and contact pressure along the surface of the rolls. The boundary element method is applied for computing the elastic deformation of the rolls. The combination of the two numerical methods is made using the finite element solution of the contact pressure along the surface of the rolls to define the boundary conditions to be applied on the elastic analysis of the rolls. The validity of the proposed approach is discussed by comparing the theoretical predictions with experimental data found in the literature.