Keywords: multi-physics couplings, forming processes, electromagnetism, computational plasticity, thermal coupling, induction heating, microstructure.

Computer modelling of metal forming processes started more than thirty years ago [1,2,3]. At the beginning it was essentially focused on direct mechanical modelling of large deformations, and it remains largely based on the use of the finite element method [4,5]. However, the different stages of the manufacturing processes for industrial metal parts often involve, beyond the mechanical deformation processes, other physical coupled problems such as heat transfer, fluid-solid coupling, electromagnetism or metallurgy. An accurate modelling of forming processes thus needs to consider these problems and to couple them.

Regarding heat transfer coupling, in most software tools coupling between mechanical and thermal equations is not performed at the increment level, as the scheme consists of first computing the thermal field then the mechanical field (without a fixed-point iteration algorithm). If thermal and mechanical coupling is quite strong, such as in processes where localization in narrow shear bands can occur (for example, high speed machining) the previous method is not satisfactory and a fixed-point algorithm may not converge. In this case it is preferable to solve simultaneously the mechanical and thermal equations.

Fluid-solid coupling is an important issue. During heating in a furnace we must take into account the flow of the surrounding gas, and heat exchange between the gas and the preforms, in order to determine precisely the temperature field inside the worked pieces that will be formed. The problem is even more complicated when one wants to predict the quenching process with water which will be vaporised on contact with a hot piece. The prediction of the temperature evolution is important, as it will be responsible for the geometric change of the part and the microstructure evolution. An analogous situation arises in the casting of large work pieces during the cooling process, when a solid fraction interacts with a moving fluid with complicated thermal and mechanical evolutions. An efficient frame for this coupling is to use an ALE formulation for the liquid phase where the material velocity v is different from the mesh velocity vg, which will be defined by a smoothing operator.

Electromagnetic couplings may be involved through the use of direct or induced currents for thermal purposes: (a) in order to generate heat inside a work piece to obtain either a prescribed temperature field or some given mechanical or metallurgical properties through an accurate control of temperature evolution with respect to time, or (b) for solid or fluid mechanics purposes, in order to create magnetic forces such as in fluid mechanics (for example, electromagnetic stirring) or solid mechanics (for example, magneto-forming). Global coupled finite element approaches can be used, as in induction heating for instance [6]. The advantage of using an integrated software tool is even more obvious when one wishes to carry out a global optimisation approach [7].

Metallurgical coupling also needs to be carried out, as the microstructure of the materials may change significantly during forming operations. For instance in metals, dynamic or static recovery and recrystallisation can take place. These evolutions need to be modelled when the final microstructure is to be optimized, or when the behaviour of the metal must be described accurately during forming. Several strategies can be developed to compute microstructure evolutions in forming processes with large spatial heterogeneity of strain rate, strain and temperature fields.

1

G.C. Cornfield and R.H. Johnson, "Theoretical prediction of plastic flow in hot rolling including the effect of various temperature distributions", J. Iron Steel Inst., 211, 567 (1973).

2

C.H. Lee and S. Kobayashi, "New solutions to rigid plastic deformation problems using a matrix method", Trans. ASME, J. Eng. Ind., 95, 865 (1973).

3

O.C. Zienkiewicz, S. Valliapan, and I.P. King, "Elasto-solution of engineering problems: initial stress, finite element approach", Int. J. Num. Meth. Eng., 1, 75-100 (1969). doi:10.1002/nme.1620010107

4

R.H. Wagoner and J.-L. Chenot, Metal forming analysis, Cambridge University Press, Cambridge (2001).

5

J.-L. Chenot and F. Bay, "An overview of Numerical Modelling Techniques", Journal of Materials Processing Technology, (1998). doi:10.1016/S0924-0136(98)00205-2

6

F. Bay, V. Labbe, Y. Favennec and J-L. Chenot, "A numerical model for induction heating processes coupling electromagnetism and thermomechanics", International Journal for Numerical Methods in Engineering, 58, 839-867 (2000). doi:10.1002/nme.796

7

Y. Favennec, V. Labbe and F. Bay, "Induction Heating Processes Optimization - A General Optimal Control Approach", Journal of Computational Physics, vol. 187, pp 68-94, 2003. doi:10.1016/S0021-9991(03)00081-0

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