Elisabeth Massoni

An inverse analysis using a finite element model for identification of rheological parameters

Abstract In order to reduce the discrepency between experimental and numerical development, a parameter automatic identification procedure from rheological test is formulated as an inverse problem. The direct model which permits to simulate the large strain behaviour during the rheological test is a Finite Element Code. The inverse problem is formulated as finding a set of rheological parameters starting from a known constitutive equation. The goal is to compute the parameter vector which minimizes an objective function representing, in the least square sense, the difference between experimental and numerical data. The high nonlinearity of the problem to be solved, requires the use of an accurate evaluation of the sensitivity matrix by analytical differentiation of governing equations with respect to the parameters. Thus the optimisation algorithm is strongly coupled with the finite element simulation. This method, namely a Computer Aided Rheology (CAR) methodology is possible in principle for all tests able to be simulated. This paper concerns the thermoviscoplastic deformation during torsion and tension tests.

Finite element modelling of the inertia friction welding process between dissimilar materials

Abstract The present study concerns the development and experimental validation of a finite element code to simulate the inertia friction welding (IFW) process. The mechanical equations take into account, among others, the physics in terms of inertia, forces and friction. They are solved for velocity and pressure through the P1 + /P1 formulation. Due to the rotational movement of the workpiece, a third nodal unknown V θ , the rotational velocity, is added to the variables V r and V z . The thermal calculation influences the rheological and tribological parameters and is coupled to the mechanical solution. Powerful contact algorithm and automatic remeshing are implemented to model the flash formation at the joint interface, its self-contact with the workpiece and the multi-body contact between dissimilar materials. A novel formulation for the friction law is implemented to suitably represent the physical phenomena in IFW. A residual stress analysis is carried out.

Forming limits prediction using rate-independent polycrystalline plasticity

The purpose of this paper is the prediction of forming limits computed from an initial defect approach combined with a rate-independent polycrystalline plasticity model. The algorithm used for the integration of the material behaviour inside and outside the localization band is presented. Results are compared with the forming limit curves at necking and at failure for 6116-T4 aluminium.

Estimation of constitutive parameters using an inverse method coupled to a 3D finite element software

Abstract Forming process simulations require a precise knowledge of the input material parameters. These parameters are usually estimated from mechanical tests. The classical analysis of these tests are usually based on a few assumptions: material flow homogeneity, isothermal conditions, etc. But in some cases with strain localisation or self-heating, these assumptions overestimate material strength. Analysis techniques using inverse methods are then good alternatives. This paper deals with the estimation of mechanical parameters using an inverse method. The direct model is a 3D forming process simulation software (FORGE3 ® ). The numerical formulation is based on a mixed finite element method using two unknowns, the velocity and the pressure. The tetrahedron element is linear in velocity and pressure and the thermal problem is solved using a linear element. The inverse problem associated with the estimation of mechanical parameters is expressed as a least square problem. The aim is to obtain output of the direct model which fits experimental data measured during the mechanical test. The optimisation problem is solved using a Gauss–Newton algorithm. At the end of the optimisation, an estimation of confidence intervals is done. A Gauss–Newton algorithm requires the computation of the derivatives of the output with respect to the parameters to be identified. In this work, a semi-analytical differentiation is performed. The proposed method is first validated on artificial experimental data obtained from direct simulations of hot uniaxial compressions for a viscoplastic cylinder. The confidence interval is provided by the algorithm for different configurations with additional random noise. Finally a real steel compression test is analysed to provide parameters for the Norton–Hoff viscoplastic law.

Finite element simulation of the inertia welding of two similar parts

A complete thermo‐mechanical model for the simulation of the inertia welding process of two similar parts is described. The material behaviour is represented by an incompressible viscoplastic Norton—Hoff law in which the rheological parameters are dependent on temperature. The friction law was determined experimentally and depends on the prescribed pressure and the relative rotating velocity between the two parts. The mechanical problem is solved considering the virtual work principle including inertia terms. The computation of the three components of the velocity field such as radial, longitudinal and rotational velocity, in an axisymmetric approximation allows to take into account the torsional effects. The domain is updated based on a Lagrangian formulation. The non‐linear heat transfer equation with boundary conditions (convection, radiation and friction flux) is solved separately for each time step. Error estimators on mechanical and thermal computation are devised to adapt the mesh in an automatic w...

Inverse problems in finite element simulation of metal forming processes

Focuses on the inverse problems arising from the simulation of forming processes. Considers two sets of problems: parameter identification and shape optimization. Both are solved using an optimization method for the minimization of a suitable objective function. The convergence and convergence rate of the method depend on the accuracy of the derivatives of this function. The sensitivity analysis is based on a discrete approach, e.g. the differentiation of the discrete problem equations. Describes the method for non‐linear, non‐steady‐state‐forming problems involving contact evolution. First, it is applied to the parameter identification and to the torsion test. It shows good convergence properties and proves to be very efficient for the identification of the material behaviour. Then, it is applied to the tool shape optimization in forging for a two‐step process. A few iterations of the inverse method make it possible to suggest a suitable shape for the preforming tools.

Rate-independent crystalline and polycrystalline plasticity, application to FCC materials

Abstract This paper deals with the simulation of the mechanical response and texture evolution of cubic crystals and polycrystals for a rate-independent elastic–plastic constitutive law. No viscous effects are considered. An algorithm is introduced to treat the difficult case of multi-surface plasticity. This algorithm allows the computation of the mechanical response of a single crystal. The corresponding yield surface is made of the intersection of several hyper-planes in the stress space. The problem of the multiplicity of the slip systems is solved thanks to a pseudo-inversion method. Self and latent hardening are taken into account. In order to compute the response of a polycrystal, a Taylor homogenization scheme is used. The stress–strain response of single crystals and polycrystals is computed for various loading cases. The texture evolution predicted for compression, plane strain compression and simple shear are compared with the results given by a visco-plastic polycrystalline model.

Inverse analysis of thermomechanical upsetting tests using gradient method with semi-analytical derivatives

Abstract The starting point of this work is the need of precise and correct input data for material forming codes. The use of these codes as a direct model for inverse analysis of the processes permits to extend the validity range of the thermomechanical parameters in terms of temperature, strain and strain rate. The identification software was developed on the basis of the 2D and of a 3D finite element code (FORGE2 ® and FORGE3 ® ) simulating forming processes and using a thermo–elasto–viscoplastic behaviour. The optimisation problem is based on a Gauss Newton algorithm and necessitates the evaluation of the derivatives of the cost function and of the sensitivity matrix to solve the system. Different methods are proposed to evaluate these derivatives. We have studied deeply analytical evaluation, finite difference techniques and recently semi-analytical derivatives. In this paper we present the main feature of the semi-analytical derivatives and the comparison with numerical ones on the parameter identification during upsetting tests. The semi-analytical method of sensitivity analysis for inverse problems is very attractive thanks to the compromise between computational time and ease of derivatives evaluation. Especially for parameter identification in material forming domain, this technique seems to be promising.

On thermo-elastic-viscoplastic analysis of cooling processes including phases changes

Abstract This paper deals with the modelling and calculation of thermal, metallurgical and mechanical phenomena which occur in the quenching of steels. Especially the influence of the mechanical behaviour law of the material, either thermo-elasto-plastic or thermo-elasto-viscoplastic, on the development of internal stresses during cooling is analysed using the specific case of cooling of a cylinder made of eutectoid carbon steel.

3D inverse analysis model using semi-analytical differentiation for mechanical parameter estimation

An inverse method is developed in order to estimate constitutive parameters of a material from compression tests. The direct model used to simulate mechanical tests is FORGE3®. It solves a transient thermo-mechanical problem using a finite element method. From velocity, pressure and temperature fields, any output of a mechanical test can be computed and compared with experimental data. A Gauss-Newton algorithm is implemented to solve the least-square problem associated with the inverse problem. The optimisation module is coupled with a semi-analytical sensitivity analysis method. This method is fast and stable when using a remeshing algorithm. A confidence interval estimator is proposed. The stability of the optimisation module and the confidence interval estimation are tested for numerical test cases. Finally, constitutive parameters of a steel grade are estimated for two elastic-viscoplastic constitutive laws.