F.R. Hall

Benchmark tests for 3-D, elasto-plastic, finite-element codes for the modelling of metal forming processes

Abstract Today the finite-element method is the most widely used tool in the prediction of both linear and nonlinear structural behaviour. An inherent danger of such widespread use, however, is an overconfidence in the accuracy and correctness of the results obtained. It is necessary to produce simple benchmark tests which may be performed to justify the users faith in such finite-element packages. The results of these benchmarks should compare favourably with experimental results, exact theoretical models or with recognised finite-element standards. In linear elastic problems it is relatively straightforward to find exact solutions to which the finite-element results may be compared. In nonlinear elasto-plastic analyses in general, and particularly for 3-dimensional forming, analyis it is extremely difficult to determine suitable benchmarks. However, in these cases it is even more important to establish a set of benchmarks to which quantitative or qualitative comparisons may be made. A series of such tests are presented for both single and multi-element analyses, which may be applied to 3-dimensional, elasto-plastic, large strain, finite-element codes. Further benchmarks are introduced which provide standards for friction, isotropic and anisotropic materials, and multi-material problems. It is hoped that the application of these benchmarks will help finite-element users to develop their analyses with legitimized assurance in the validity of their results.

Anisotropic Finite-Element Analysis of Plastic Metalforming Processes

This paper describes some aspects of the incorporation of plastic anisotropy of textured materials into an elastic-plastic finite-element program in order to simulate the deformation of such materials.

A three-dimensional study of flow in the fullering process using an elastic-plastic finite-element simulation

Abstract This paper describes research work concerned with the three-dimensional finite-element simulation of the fullering process. The main objectives of this preliminary study are to provide the details of metal flow during the process in order to investigate the effects of various parameters, to examine the correlation between the finite-element results and those of empirical relationships and to evaluate some aspects of empirical methods of fuller die design for a typical forging component. The activities carried out to achieve these objectives are explained in this paper.

Elastic-plastic finite-element modelling of metal forming with damage evolution

A model for damage accumulation proposed by Lemaitre has been incorporated in an elastic-plastic finite-element simulation of the plane-strain side pressing of an aluminium rod. Predictions of failure site agree closely with experimental observations. The level of deformation at which failure is predicted shows a small difference to experiment. Further predictions of failure were undertaken with variations on the basic Lemaitre model, (i) with no damage accumulation permitted for compressive triaxiality, and (ii) with an exponential dependence on triaxiality. When combined with a suitable fracture criterion the latter model showed very close correlation with experiment.

Metal forming of titanium: Experimentation, microstructure and computer simulation

Abstract Hot rolled titanium plate (IMI125) has been uni-axially compressed at 400°C. Test results are presented showing in-plane anisotropy and non-uniform deformation in the normal plate. It is thought that the non-uniform deformation in the normal plane is due to a combination of normal anisotropy and inhomogeneity. It is observed that the thicker plate material allows a greater tilt of the c-axis of the hexagonal unit cell in the normal/transverse plane than thinner sheet material. Yield loci for two specific slip/twinning systems using computer simulations of experimental pole figures measured from the centre of the titanium plate are presented.

THE INCORPORATION OF AN ANISOTROPIC YIELD LOCUS DERIVED FROM THE CRYSTALLOGRAPHIC TEXTURE IN FE MODELLING OF FORMING

In the last decades, classical elastic finite elements (FE) methods have served as a basis for the development of more general methods that can also treat plastic deformation and are able to simulate complex metal forming processes. Most of these models still use the isotropic von Mises yield criterion and its associated flow law. It will be shown how the latter can be replaced by an anisotropic yield criterion and its associated flow law which are directly derived from the crystallographic texture of the metal that is the cause of the anisotropy. The first stage of the procedure is the determination of the orientation distribution function (ODF) that describes the texture. The next stage is the calculation of the anisotropic yield locus that corresponds to it by means of the Taylor-Bishop Hill theory. The final stage is the implementation of this yield locus in the FEM code.