Katia Mocellin

NUMERICAL FORMULATIONS AND ALGORITHMS FOR SOLVING CONTACT PROBLEMS IN METAL FORMING SIMULATION

The problem of contact between a part and a tool or between two deforming bodies is analysed in view of metal-forming processes. For simplicity, only the case of viscoplastic materials is considered. The velocity formulation is presented. The contact with a rigid tool is considered first and various forms of contact formulations are described: nodal contact, integral or discrete formulation with a penalty or with a Lagrange multiplier method. The time integration is considered which results in various explicit or implicit contact formulations. A special attention is paid to the contact between two deforming bodies or to the self-contact when a fold is generated in the work-piece. Some 2-D and 3-D application examples illustrate the effectiveness of the proposed formulations and algorithms. Copyright

Numerical treatment of contact and friction in FE simulation of forming processes

Abstract The problem of contact between a part and a tool or between two deforming bodies is analysed in view of metal forming processes. For simplicity, only the case of viscoplastic materials is considered. The velocity formulation is presented, with different time integration schemes. The contact with a rigid tool is considered first and various forms of contact formulations are described: nodal contact, integral formulation with a penalty or with a Lagrange multiplier method. Time integration is considered which results in various explicit or implicit contact formulations. Special attention is paid to the contact between two deforming bodies or to the self contact when a fold is generated in the workpiece.

An application of a master-slave algorithm for solving 3D contact problems between deformable bodies in forming processes

We consider a finite element approximation of frictional contact problem between deformable bodies undergoing large deformations. The fully 3D mechanical coupling problem is expressed with a mixed velocity-pressure formulation. The multi-bodies contact problem is set as a linear complementary problem solved by a penalty method. The corresponding nonpenetration condition is approximated using a finite element meshes which do not necessarily fit on the contact zone. The local approach used to take into account unilateral contact on non-matching meshes is an extension of the master-slave algorithm. The mechanical system is solved using iterative methods. The associatedmodel and algorithm are implemented inside the 3D software Forge3®. The selected application is the process of viscoplastic metal forging.

2D high speed machining simulations using a new explicit formulation with linear triangular elements

This paper presents the several advantages of a new explicit formulation using modified linear tetrahedral elements non-sensitive to volumetric locking in the scope of high speed machining simulations. First, the explicit time integration allows obtaining very interesting computational time in very dynamic cases with complex behaviour laws. Then, the use of a tetrahedral mesh permits to use robust non-structured adaptive remeshers too. No chip separation criteria or damage model is used. Our 2D orthogonal cutting model detects automatically the apparition of an adiabatic shear band, and simulates very precisely its evolution and the chip formation. Phenomena relative to adiabatic shearing bands already described in the literature can be observed in detail in the simulation. This model is a powerful tool to improve the understanding of chip formation and adiabatic shear band propagation, and to simplify the optimisation of high speed machining processes in industries.

Numerical Modeling of Tube Forming by HPTR Cold Pilgering Process

For new fast-neutron sodium-cooled Generation IV nuclear reactors, the candidate cladding materials for the very strong burn-up are ferritic and martensitic oxide dispersion strengthened grades. Classically, the cladding tube is cold formed by a sequence of cold pilger milling passes with intermediate heat treatments. This process acts upon the geometry and the microstructure of the tubes. Consequently, crystallographic texture, grain sizes and morphologies, and tube integrity are highly dependent on the pilgering parameters. In order to optimize the resulting mechanical properties of cold-rolled cladding tubes, it is essential to have a thorough understanding of the pilgering process. Finite Element Method (FEM) models are used for the numerical predictions of this task; however, the accuracy of the numerical predictions depends not only on the type of constitutive laws but also on the quality of the material parameters identification. Therefore, a Chaboche-type law which parameters have been identified on experimental observation of the mechanical behavior of the material is used here. As a complete three-dimensional FEM mechanical analysis of the high-precision tube rolling (HPTR) cold pilgering of tubes could be very expensive, only the evolution of geometry and deformation is addressed in this work. The computed geometry is compared to the experimental one. It is shown that the evolution of the geometry and deformation is not homogeneous over the circumference. Moreover, it is exposed that the strain is nonhomogeneous in the radial, tangential, and axial directions. Finally, it is seen that the dominant deformation mode of a material point evolves during HPTR cold pilgering forming.

Finite Element Modeling and Optimization of Mechanical Joining Technology

The main scientific ingredients are recalled for developing a general finite element code and model accurately large plastic deformation of metallic materials during joining processes. Multi material contact is treated using the classical master and slave approach. Rupture may occur in joining processes or even be imposed in self piercing riveting and it must be predicted to evaluate the ultimate strength of joins. Damage is introduced with a generalized uncoupled damage criterion, or by utilizing a coupled formulation with a Lemaitre law. Several joining processes are briefly analyzed in term of specific scientific issues: riveting, self piercing riveting, clinching, crimping, hemming and screwing. It is shown that not only the joining process can be successfully simulated and optimized, but also the strength of the assembly can be predicted in tension and in shearing.

A PARTLY-EXPLICIT FINITE ELEMENT FORMULATION FOR THE FORGING PROCESS

This paper presents different finite element formulations for the large deformation modelling of a viscoplastic material. A partly-explicit acceleration-pressure formulation is investigated. As the velocity is supposed to be known, we do not have to deal with the possible non-linear feature of the material. Consequently, there is no need to use any Newton-Raphson iteration. The mixed finite element discretization is based on a simple triangular mini-element P1 + /P1. Analysis concerning the bubble properties and its influences on the equation system have been done in order to simplify the formulation. This new dynamic formulation has been successfully implemented in a viscoplastic version of the code Forge2®. Comparisons with implicit static and implicit dynamic algorithms have been performed. Numerical examples are provided to compare the different formulations. A good agreement is noticed on final results.

Modelling the strength of self-piercing riveted joints

Abstract: Predicting the mechanical strength of self-piercing riveted structures is of prime importance in industry. This chapter describes how numerical simulation can be used to obtain accurate predictive results. First, it is important to account for the mechanical history of the material resulting from the SPR process as input data for the mechanical strength simulation. The use of a coupled damage approach to account for the progressive mechanical degradation of the materials’ properties is recommended. The materials’ properties and damage parameters have to be carefully identified. Inverse analysis is an efficient methodology to obtain the materials’ parameters. Finally, some finite element simulations are presented and validated with respect to mechanical tests. The numerical approach presented here also enables the equivalent elements that can be used at the structure scale to be defined.

Development of Adapted Material Testing for Cold Pilgering Process of ODS Tubes

Development of fast-neutron sodium-cooled Generation IV reactors is resulting in extremely severe environment conditions for cladding tubes [1]. Both temperature and irradiation level will increase compared to the nowadays conditions. Due to their characteristics in irradiated environment, the oxide dispersion strengthened (ODS) ferritic and martensitic steels are natural candidate cladding materials[2]. However, they exhibit low deformation capabilities at room temperature, leading to problematic issues for forming such as pilgering. In order to improve the fabrication route for tubes, both metallurgical and numerical approaches can be conducted [3,4,5]. To reach predictive description of damage location and evolution, an adapated Latham and Cockoft model has been developed. This model is, of course, highly depending on the stress and strain prediction of the numerical model which itself is linked to the behavior law. In this work, we will describe an adapted material test developed in order to reproduce the cyclic, non uniform loading of the material during pilgering. An advanced cyclic beahvior law is introduced in the software. The model of Chaboche using 2 isotropic and 2 kinematic variables is chosen[6]. An inverse analysis procedure is used to identify both isotropic and kinematic hardening parameters. The results obtained using the identified behavior law are compared to both experimental observation and to other models including monotonic or cyclic laws identified on traditional test.

Numerical modeling of electrical upsetting manufacturing processes based on Forge® environment

The present work reviews the latest developments done within Forge®, finite element numerical simulation software for all bulk metal forming processes, to deal with electric processing of materials. We present a complete parallel finite-element coupled Electrical-Thermal-Mechanical model for two-dimensional and three-dimensional electro forming applications. The electro-thermal modeling is considered by sequential-coupling in which the Joule heating term computed from the electric resolution is used as a source term for the thermal problem. For the experimental comparison we use an electric upsetting forming case developed at the Osnabruck University of Applied Sciences. The forming process consists in a closed die hot forging case in which an electric current is passed through the billet to heat it up. At the same time, it is deformed by an applied pressure on the billets end surface. We compare the experimental set-up with 2D and 3D numerical simulations.The present work reviews the latest developments done within Forge®, finite element numerical simulation software for all bulk metal forming processes, to deal with electric processing of materials. We present a complete parallel finite-element coupled Electrical-Thermal-Mechanical model for two-dimensional and three-dimensional electro forming applications. The electro-thermal modeling is considered by sequential-coupling in which the Joule heating term computed from the electric resolution is used as a source term for the thermal problem. For the experimental comparison we use an electric upsetting forming case developed at the Osnabruck University of Applied Sciences. The forming process consists in a closed die hot forging case in which an electric current is passed through the billet to heat it up. At the same time, it is deformed by an applied pressure on the billets end surface. We compare the experimental set-up with 2D and 3D numerical simulations.