Anne Habraken

Contact between deformable solids: The fully coupled approach

This paper presents a finite element technique to handle frictional contact between bodies submitted to large deformations. Contact finite elements, based on a penalty method, are derived from the virtual work principle. The originality lies in the fact that the contact conditions (Signorinis conditions and Coulomb friction law) are expressed at some integration points and not at the nodal points. The development of contact introduces a coupling between the Degrees Of Freedom (DOF) of the bodies. In certain cases, this coupling can be neglected in the numerical strategy.

A fully coupled elastoplastic damage modeling and fracture criteria in metalforming processes

Abstract In this paper a fully coupled elastoplastic damage theory at finite strain is presented. The energy-based Von Mises yield criterion and the damage evolution criterion with two damage variables are postulated through the hypothesis of energy equivalence. The local distributions of variables connected with the history of stress, strain and damage are determined by numerical simulation. These values are then used with six previously published fracture criteria to predict fracture initiation sites and to simulate the propagation of fracture in metalforming processes.

Automatic adaptive remeshing for numerical simulations of metal forming

Abstract An automatic, adaptive remeshing scheme with a new, independent mesh has been developed to enable finite element simulations of forming processes with complicated die geometries. The different features of this technique are presented with one industrial example of forging. We especially focus on the fully automatic aspect of the procedure. The results are obtained with 8 node quadratic, isoparametric elements and 4 node mixed elements. For some practical applications, the implementation of this scheme is necessary to perform a complete analysis.

Modelling the plastic anisotropy of metals

SummaryThis work is an overview of available constitutive laws used in finite element codes to model elastoplastic metal anisotropy behaviour at a macroscopic level. It focuses on models with strong links with the phenomena occurring at microscopic level. Starting from macroscopic well-known models such as Hill or Barlats laws, the limits of these macroscopic phenomenological yield loci are defined, which helps to understand the current trends to develop micro-macro laws. The characteristics of micro-macro laws, where physical behaviour at the level of grains and crystals are taken into account to provide an average macroscopic answer are described. Some basic knowledge about crystal plasticity models is given for non-specialists, so every one can understand the microscopic models used to reach macroscopic values. The assumptions defining the transition between the microscopic and macroscopic scales are summarized: full constraint or relaxed Taylors model, self-consistent approach, homogenisation technique. Then, the two generic families of micromacro models are presented: macroscopic laws without yield locus where computations on discrete set of crystals provide the macroscopic material behaviour and macroscopic laws with macroscopic yield locus defined by microscopic computations. The models proposed by Anand, Dawson, Miehe, Geers, Kalidindi or Nakamachi belong to the first family when proposals by Montheillet, Lequeu, Darrieulat, Arminjon, Van Houtte, Habraken enter the second family. The characteristics of all these models are presented and commented. This paper enhances interests of each model and suggests possible future developments.

Finite element modeling of incremental forming of aluminium sheets

Incremental forming is an innovative and flexible sheet metal forming technology for small batch production and prototyping, which does not require any dedicated die or punch to form a complex shape. This paper investigates the process of single point incremental forming of an aluminum cone with a 50-degree wall angle both experimentally and numerically. Finite element models are established to simulate the process. The output of the simulation is given in terms of final geometry, the thickness distribution of the product, the strain history and distribution during the deformation as well as the reaction forces. Comparison between the simulation results and the experimental data is made.

Comparison of FEM simulations for the incremental forming process

Incremental forming is an innovative and highly flexible sheet metal forming technology for small batch production and prototyping that does not require any adapted dies or punches to form a complex shape. The purpose of this article is to perform FEM simulations of the forming of a cone with a 50-degree wall angle by incremental forming and to investigate the influence of some crucial computational parameters on the simulation. The influence of several parameters will be discussed: the FEM code used (Abaqus or Lagamine, a code developed at the University of Liège), the mesh size, the potential simplification due to the symmetry of the part and the friction coefficient. The output is given in terms of final geometry (which depends on the springback), strain history and distribution during the deformation, as well as reaction forces. It will be shown that the deformation is localized around the tool and that the deformations constantly remain close to a plane strain state for this geometry. Moreover, the tool reaction clearly depends on the way the contact is taken into account.

Forming Limit Predictions for Single-Point Incremental Sheet Metal Forming

A characteristic of incremental sheet metal forming is that much higher deformations can be achieved than conventional forming limits. In this paper it is investigated to which extent the highly non‐monotonic strain paths during such a process may be responsible for this high formability. A Marciniak‐Kuczynski (MK) model is used to predict the onset of necking of a sheet subjected to the strain paths obtained by finite‐element simulations. The predicted forming limits are considerably higher than for monotonic loading, but still lower than the experimental ones. This discrepancy is attributed to the strain gradient over the sheet thickness, which is not taken into account in the currently used MK model.

Analysis of Texture Evolution and hardening Behavior during Deep drawing with an improved mixed type FEM Element

In the present study, deep drawing simulations were investigated using a recently developed mixed type finite element (FE): the BWD3D. The main formulation of the element is described, with particular focus on the shear locking treatment. Two hardening models used in the presented simulations are described: the isotropic Swift’s model and the physically based microstructural Teodosiu and Hu model. Finally, deep drawing results, in terms of earing profile, are compared to experiment. Special attention is paid to the effects of texture evolution and hardening models; the method used to implement Teodosiu and Hu hardening model is also discussed.

Simulation of square-cup deep-drawing with different finite elements

In this paper, the simulation of square-cup deep-drawing is done using an 8-node brick 3-D solid element with one integration point, which is a mixed element based on the Hu-Washizu principle with hourglass control, and a 4-node quadrangular 3-D shallow shell element. The material is assumed to be rate-independent elastoplastic. The die, punch and blank-holder are assumed rigid, with the geometry discretized by facet triangular elements. The Coulomb law is used to model the friction between the sheet and the tools. A non-symmetric Newton-Raphson scheme is used to solve the system equations. Numerical results are obtained and compared.

NUMERICAL MODELLISATION OF CONTACT WITH FRICTION PHENOMENA BY THE FINITE ELEMENT METHOD

Abstract Finite element modelling contact with friction in two-dimensional, axisymmetric and three-dimensional cases are proposed. They take in account large displacements and rotations between a strained body and a so-called tool or between two strained bodies. The interface behaviour is based on a penalty method and on the COULOMB dry friction law, and is developed using the elasto-plastic formalisms. Due to the algorithm modularity it seems to be easy to introduce other interface behaviours as instance including dilatancy. The time integration of the generalised contact stresses and the objectivity treatment are discussed. At the end an application is proposed which could serve as comparison test between algorithms modelling same problems.