3. Numerical simulation of welding

Everything that is written, afterwards, can be implemented in two study situations:

• When simulating, of course, the welding of two parts;

• But also, when simulating the application of a coating on a room. The same methodology as that adopted for a welding operation can be applied.

3.1. Visual representation of a welding operation

• The reality: we have two parts A and B that we want to solder to obtain a part AB using a suitable welding process (for example by adding heat). The two pieces are never welded at once but not in successive steps, the first pass being called the root pass.

• The numerical representation: the first root pass is never modeled. It is therefore assumed that initially, the two pieces A and B are in a single block. Later, we will see that there are several methods to activate the passes. Most often (this is the configuration shown in the drawing below), we choose to represent all the passes in the initial model and we activate them gradually.

The reality		Digital representation
	The welder
	The heat source provided by the welding process, with filler metal here
	The two parts to be soldered		The initial part to be modelled, with here all the passes represented initially in the model
	1st pass = Root pass
	2nd pass		Activation of the 1st pass to be simulated
	3rd pass		Activation of the 2nd pass to be simulated
	4th pass		Activation of the 3rd pass to be simulated
	5th pass		Activation of the 4th pass to be simulated
	6th pass Welded AB part		5th pass Simulated AB coin

3.2. What are we trying to calculate?

The final aim of the simulation is to determine the fields of residual stresses and deformations. To do this, it is necessary to couple or chain thermal, possibly metallurgical and finally mechanical calculations.

3.3. What are the main challenges of simulation?

The major difficulties, questions and methodological choices that the engineer will face can be summed up in six points:

• 2D or 3D representation of the studied structure?

• What mesh size was adopted?

• How to take heat input into account?

• How to manage the addition of material, thermally or mechanically?

What mechanical behavior model (for metallurgical transformations, there is a unique model in*Code_Aster)?

• What physical data?

Note: The choices that will ultimately be adopted for the simulation depend on a lot of the experimental data in the engineer’s possession. This data includes:

• Material data; As in any simulation, it is important to have material data to identify the laws of behavior (thermal, metallurgical and mechanical) as accurately as possible. Since welding involves very high temperatures (up to the melting of the material), it is necessary, if possible, on the one hand, to have parameters between 20° C. and the melting temperature, and on the other hand, tests to characterize viscous phenomena.

Data on welding conditions; Among the many uncertainties in the input data that occur during the numerical simulation of a welding operation or coating removal operation, the indeterminacy of the heat input is the most penalizing. In fact, even when it comes to automated welding, and when the welding parameters are well known, modeling the heat input remains difficult anyway, and calibration is almost always necessary (on temperature measurements or on macrographs of melted zones) if a**predictive numerical simulation is targeted*.

In paragraph 3 and for each of these points, we will present the different possible methodologies and, sometimes, the recommended choices.

3.4. The specificities of Code_Aster

3.4.1. What are the combinations considered?

In Code_Aster, it is currently possible to take into account most of the phenomena but in a decoupled manner, through thermal, then metallurgical (possibly) and finally mechanical calculations.

Any metallurgical calculation is thus carried out by post-processing the thermal calculation, without taking into account the influence of metallurgy on thermal energy (difference in thermo-physical properties according to the phases and latent heats of transformation).

Likewise, mechanical calculation is decoupled from thermal and metallurgical calculations: the influence of intrinsic dissipation on thermal fields is neglected, as well as the influence of the stress state on metallurgical transformations.

To summarize, here are the interactions taken (OUI) or not (NON) taken into consideration:

• Influence of Thermal Engineering on Metallurgy: OUI

• Influence of Metallurgy on Thermal Engineering: NON

• Influence of Thermics on Mechanics: OUI

• Influence of Mechanics on Thermics: NON

• Influence of Metallurgy on Mechanics: OUI

• Influence of Mechanics on Metallurgy: NON

3.4.2. Typical schema for a Code_Aster command file

To summarize, here are the main steps of calculating a welding operation in Code_Aster:

	A thermal calculation is carried out which makes it possible to obtain the temperature field at each node of the mesh.
	If the material in question undergoes metallurgical transformations: after processing the thermal calculation, the metallurgical calculation is carried out, which makes it possible to obtain the proportion of the various metallurgical phases (and possibly the associated hardness) at each node of the mesh.
	From the temperature field and possibly from the metallurgical phases, the mechanical calculation is carried out by choosing a behavior model that possibly takes into account the various possible effects of metallurgical transformations. We thus obtain the fields of stresses, deformations and internal variables at each Gauss point.

3.4.3. Code_Aster restrictions [5]

• Thermal calculation

• • The resolution of the heat equation as a moving coordinate system by the THER_NON_LINE_MO [U4.53.03] command (useful for setting the heat source for an unsteady 3D thermal calculation) is only available in the case of a rectilinear path of the heat source, and not in the case of an axisymmetric path, as when welding cylindrical pipes for example.

  It is currently impossible to define a function of more than two variables with*Code_Aster, while « classical » heat sources (Gaussian, double ellipsoid, source CIN) are volume or surface flow densities, a function of space and time. If the source is a function of time (at least, except if the calculation is performed using a moving coordinate system), there is only one space parameter left available.

• Metallurgical calculation

• • The tempering phenomenon (which in particular results in a decrease in the elastic limit) of the crude tempering phases is not taken into account. We can possibly get around this problem. If the number of phases formed during cooling makes it possible to leave internal metallurgical variables « free », we can then assign proportions of returned phases to these internal variables and model the tempering kinetics by introducing a fictional TRC.

• Mechanical calculation

  • It would be interesting to develop, for a material comprising only one metallurgical phase, models equivalent to META_XXX_XXX (several phases). This currently requires a metallurgical miscalculation to benefit from these laws. In 3D, this can pose significant problems of calculation time and memory capacity, provided that a model with kinematic work hardening is used, for example (a tensor is stored as an internal variable for each calculation step and for each phase).