4. Simulation methodology#
The feedback given in this section is mainly based on the following three studies:
A chamfered 316L pipe welded by the TIG [:ref:`2 <2>`] process, with filler metal in thirteen passes (sheet CEA/EDF/FRAMATOME 3488); the first 2 passes of this example constitute a test case*Code_Aster [V7.42.100]);
A 316L chamfered plate welded by the TIG [:ref:`4 <4>`] process, with filler metal in two welding passes (sheet CEA/EDF 2425); the various command files associated with this study are stored in the*Code_Aster study base (SERVICE/BDD Studies);
A non-chamfered 316L plate, with the creation of a fusion line by the TIG [3] process, but without a filler metal (thesis INSA from Lyon by L. Depradeux defended in 2004).
For the sake of simplicity, we will later name them sheet 3488, sheet 2425 and thesis L.D 2004.
4.1. Type of modeling: 2D or 3D?#
Strictly speaking, the welding process is strictly three-dimensional, the supply of heat and possibly of material being mobile and often of constant speed. The temperature and mechanical fields generated are therefore three-dimensional and transitory.
It is therefore preferable to perform a three-dimensional transitory analysis.
However, this choice is not always possible due to the complexity, calculation time and memory capacity required by 3D calculations, 2D modeling is often used in numerical simulation of welding (in particular for multi-pass welding with a large number of passes).
Case of 2D modelling
In the majority of cases, 2D simulations consider a transverse section, perpendicular to the direction of the welding torch. These simulations are carried out with the hypothesis of plane deformations;
2D axisymmetric calculations are also adopted for the case of welding cylindrical pipes.
The weak point of the two previous models is that the speed effect of welding is overlooked and that it is assumed that the bead (or heat) is deposited simultaneously over the entire length of the part to be welded.
Other, less conventional, choices are also possible: one can choose for example to mesh a longitudinal section (in the direction of welding) or else, if one considers that the temperatures are constant over the thickness, one can choose to mesh the mean plane of the plate. These simulations are then carried out with the hypothesis of plane constraints.
Feedback
Sheet 3488: The calculation of the chamfered pipe is carried out axisymmetrically. Comparisons between this 2D axisymmetric approach and a 3D approach were made in [1] and show the good representativeness of the 2D approach, even if it does not take into account speed effects.
Thesis L.D 2004: On the non-chamfered plate, several models are tested:
Complete thermo-mechanical 3D calculation;
2D calculation in plane deformation where a section perpendicular to the advance of the torch is modelled;
2D calculation under plane stress where the mean plane of the plate is modelled.
It is noted, in this case, that the 2D calculation in plane deformation does not reproduce well the results obtained on the 3D calculation, in terms of displacements and residual stresses, except for the latter in the central zone of the plate. As for the 2D calculation in plane stress, it gives results that are very similar in terms of residual stresses to the 3D calculation.
4.2. The mesh#
General advice
Like any numerical study, it is always difficult to give precise values on the density of the mesh; it depends a lot on the physical problem in question. In the case of welding, the mesh must be sufficiently fine around the heat source (solder beads and molten zone) to correctly understand the strong thermal and mechanical gradients in this zone.
In the case of a quasi-stationary thermal modeling in a moving coordinate system (see § 3.3.2), the speed of the calculations allows for a greater mesh density, especially around the source.
In the case of welding on steels with metallurgical phase transformations, it is necessary to mesh ZAT finely enough. This is all the more important since the maximum of stresses is generally reached at the periphery of ZAT, in a partially austenitized zone. The mesh density in this zone is therefore essential. Welding simulations on steel that presents phase transformations therefore require, in principle, meshes that are larger in number of elements compared to simulations of welding on steels without transformations (with an identical study).
For 3D mechanical calculations, it is very important to deraffine the mechanical mesh as much as possible when moving away from the welded zone. In fact, the high non-linearity of the problem (and the computation times that go with it) and the transitory aspect (requiring many time steps) in practice limit the number of nodes in the model.
As with any problem, it is necessary to plan, as early as the meshing stage, the groups intended to receive the thermal and mechanical boundary conditions (source path, exchange surface, etc.), as well as the areas intended for post-treatment. This is all the more true for the thermal mesh where the load (heat source) and the boundary conditions (convection and radiation) move as the beads are deposited.
For the molten zone, it is often difficult to represent it because, in the absence of macrography, its shape is unknown.
Feedback
Sheet 3488: Weld beads can be represented geometrically and meshed in more or less complex ways. There are 3 possible choices, going from the most complicated to the simplest:
You can choose to respect both the volume and the shape of the pass. Since the shape of the beads is curved, surfaces with curved edges must be meshed, so use finite elements of at least degree 2;
We only respect the volume of the pass;
We respect the volume of the pass as best as possible.
Comparisons have been made in [2] with these three possibilities. It turns out that the results of mechanical calculations differ very little from one mesh to another (at equivalent thermal values). In conclusion, a curved mesh does not provide anything significant in terms of results compared to a polygonal mesh. On the other hand, it is important to respect approximately the volume of cords deposited.
4.3. Thermal calculation#
The critical point for the thermal part concerns the modeling of the heat supply.
4.3.1. Introduction#
In Code_Aster, the calculation of the thermal evolution is carried out by the non-linear resolution of the heat equation (operator THER_NON_LINE [R5.02.02]) in the volume of the room, given an initial condition and thermal boundary conditions on the borders. The resolution is transitory, the heat source moves on the mesh.
Heat diffusion is treated by an enthalpy formulation, which is the integral of specific heat over temperature \(\beta (T)=\underset{0}{\overset{T}{\int }}\rho {C}_{p}(u)\mathrm{du}\). It is therefore possible to provide either the conductivity and the specific heat \(\rho {C}_{p}\) as a function of the temperature, or, and this is preferable (see note below), the conductivity and the enthalpy as a function of the temperature.
Note on choosing an enthalpy formulation
At the melting temperature, the heat capacity (which is the energy to be supplied to raise the body’s temperature) undergoes a discontinuity which results in the latent heat of fusion, which represents the energy to be provided to cross the phase change temperature. In the case of a mixture of components (this is the case with alloys), the fusion takes place between liquidus and solidus temperatures \(\mathrm{Tl}\) and \(\mathrm{Ts}\). An « enthalpy » formulation of the heat equation is useful for taking into account the phenomena of latent heat and phase change. In fact, this formulation avoids « missing » the transformation, which is likely to happen for the capacity formulation if the time steps are not sufficiently small.
4.3.2. Management of the addition of material (welding beads)#
Description of the various methods
There are several methods for taking into account, in the transient thermal model, the successive addition of material during the various welding passes:
The first method consists in considering only one model (in the sense of*Code_Aster defined by the command AFFE_MODELE) containing all the passes and in artificially « deactivating » the cords not yet deposited by imposing zero thermal conductivity on them (\({10}^{-5}W/m°C\) in practice).
The second method consists in interlocking the thermal models (in the sense of*Code_Aster): an overall mesh of all the cords is used, but the thermal model is only assigned to the part of the mesh corresponding to the metal already deposited (during step AFFE_MODELE). Cords that have not yet been removed are not included in the model. In this case, it is necessary to have as many thermal models as there are cords deposited. The various models are nested one inside the other, that is to say that the thermal model I contains the passes from \(1\) to \(I\) and the thermal model \(I+1\) contains the passes \(1\) to \(I\) and the pass \(I+1\). This method is cleaner than the previous one in that the elements not deposited do not interfere with the calculation of the current pass, since they are not included in the model. On the other hand, this poses a problem during the sequence of thermal calculations, since the temperature fields of model \(I\) are not defined in all the nodes of the model corresponding to the next pass \(I+1\). It is therefore necessary to extend the calculated fields from one model to another. To do this, we proceed in 4 steps:
We start by creating an ambient temperature field (\(\mathrm{T20}\)) on the entire mesh using the CREA_CHAMP command (operation “AFFE”),
The first temperature field calculated in pass I (order number 1) is extended by completing \(\mathrm{T20}\) on the new cells (CREA_CHAMP operations” EXTR “then” ASSE “),
This field is stored in a new evol_ther data structure using the command CREA_RESU,
⇒ we loop over the remaining order numbers and repeat operations 2 and 3 for each order number by enriching the data structure created in 3 (reuse keyword from CREA_RESU).
Finally, the third method consists, on a single thermal model (in the sense of*Code_Aster), in splitting the nodes at the interface of each cord, which must be provided for in the mesh construction stage. When assigning the thermal load (AFFE_CHAR_THER), only the part of the model that corresponds to the metal already present is affected. Thus, the undeposited cords do not see the load, and the splitting of the nodes prevents the transfer of heat at the interface of the undeposited cords (a temperature equal to ambient is applied in the cords not yet deposited). When adding a new cord, the corresponding knots are glued back together by applying equal temperatures to the knots split by the LIAISON_GROUP command. This method is certainly the most reliable, but the construction of the mesh becomes tedious if the number of passes is large.
Feedback
The advantage of the first method (a single model and almost zero conductivity for the cord not yet deposited) is its simplicity of implementation. On the other hand, it can lead to numerical temperature oscillations due to the discontinuity of conductivity at the interfaces between the cords, as noted in sheet 3488 [2]. Nevertheless, this method is often chosen because of its simplicity.
All three methods were tested on plate 2425 [4] and compared to experimental temperature measurements. The three calculations lead to results that are substantially identical at the measurement points.
4.3.3. Heat source modeling#
The truly complete modeling of the thermal problem would require taking into account electro-thermo-fluid heat transfers in the electric arc, with taking into account electromagnetic phenomena, and the modeling of convective movements in the molten bath, in interaction with the blanket plasma, and heat transfers in the solid part. Although an extensive literature exists concerning the consideration of arc and melt pool modeling in simulation, we will subsequently move to a modeling perspective with an industrial calculation code, which does not make it possible to model the phenomena present in the arc and melt pool. These are replaced by the definition of an appropriately shaped heat source. Only the conduction of heat is therefore modelled, which is why no reference will be made to the modeling of the arc and the bath later.
Description of the two possible methods
The first method consists in**imposing temperature cycles* on the material that is deposited. These imposed temperatures can be applied either to the single cord deposited, or to the entire cord deposited plus molten zone.
For reasons of simplicity, the imposed temperature function \({T}^{\mathrm{imp}}\) is chosen, in most cases, which is constant in space but variable over time, i.e. \({T}^{\mathrm{imp}}={T}^{\mathrm{imp}}(x,y,z;t)={T}^{\mathrm{imp}}(t)\);
In addition, this temperature is often imposed only on the deposited cord: in fact, the shapes and sizes of melted zones are rarely known, and even if they are, this makes the construction of the mesh tedious, especially if the number of cords is high;
The temperature method is recommended in the case of 2D models or when no data is available on welding parameters. The \({T}^{\mathrm{imp}}(t)\) function often takes the following form:
\({T}^{\mathrm{imp}}(t)=\{\begin{array}{cc}\frac{{T}^{\mathrm{max}}}{{t}_{1}}t+{T}^{\mathrm{ini}}& \text{si}t\le {t}_{1}\\ {T}^{\mathrm{max}}& \text{si}{t}_{1}\le t\le {t}_{2}\\ \text{éventuellement,}\frac{-({T}^{\mathrm{max}}-{T}^{\mathrm{min}})}{{t}_{3}-{t}_{2}}(t-{t}_{2})+{T}^{\mathrm{max}}& \text{si}{t}_{1}\le t\le {t}_{3}\end{array}\) A rise from the initial temperature \({T}^{\mathrm{ini}}\) to the melting point or a temperature possibly higher than \({T}^{\mathrm{max}}\) for a period of time \({t}_{1}\) (the prescribed temperature rise may be linear or non-linear, exponential for example), then maintenance at this temperature for a period of time (\({t}_{2}-{t}_{1}\)) is prescribed, and finally possibly, we can prescribe the start of cooling until the Temperature \({T}^{\mathrm{min}}\). Parameters \(({t}_{\mathrm{1,}}{t}_{\mathrm{2,}}{t}_{\mathrm{3,}}{T}^{\mathrm{min}})\) can be identified if temperature measurements exist;
The rest of the cooling takes place with exchanges by convection and radiation.
The second method consists in**imposing a surface heat flow (*:math:`J/{mathrm{sm}}^{2}`**) or volume heat flow (:math:`J/{mathrm{sm}}^{3}`) ** on the modelled solder seam.
It is preferentially used when the welding energy delivered is known: this is the case for arc welding, for which it is possible to estimate the delivered power UI (with \(U\) the voltage and \(I\) the current intensity). Of this power delivered, only a fraction \(\eta \mathrm{UI}\) actually enters the room and participates in the heating and melting of the materials. For method TIG, for example, the parameter \(\eta\) is of the order of 0.6 to 0.9;
It is then possible to distribute this power, in area or in volume (or both), over the mesh. The distribution of this heat flow can be extremely simple (constant in space in the deposited metal), or more elaborate (double-ellipsoid model with Gaussian distribution developed by J. Goldak). The calibration of the parameters of the selected heat source requires temperature measurements.
Next, we detail the procedure to be followed in the case of heat flow modeling, distinguishing between 3D and 2D simulations. It is assumed that temperature data is available.
Case of 3D modeling with heat flow
Below are some possible forms for the spatial representation of volume or surface flows:
Example of a volume flow, constant according to \(y\) and \(z\) and variable in the welding direction, here \(x\). \({Q}^{V}={Q}^{V}(x,y,z;t)={Q}^{V}(x;t)=\{\begin{array}{cc}\frac{{Q}^{\mathrm{max}}}{L/2}x& \text{si}0\le x\le \frac{L}{2}\\ \frac{-{Q}^{\mathrm{max}}}{L/2}(x-L)& \text{si}\frac{L}{2}\le x\le L\end{array}\)
Example of a cylindrical \({Q}^{S}={Q}^{S}(x,y;t)\) surface flow with a circular base with radius \(R\) and maximum intensity \({Q}^{\mathrm{max}}\).
When temperature measurements are available, the parameters of this heat input (sizes, values of maximum injected power) can be adjusted in order to best reproduce, by calculation, the measured thermal cycles.
This calibration step can be carried out easily and with low calculation times using a semi-stationary calculation in a moving coordinate system (THER_NON_LINE_MO). This assumes that the source path is uniform, rectilinear, at a constant speed. In this case, we assume that a steady state is established, and the heat equation written in this coordinate system becomes independent of time. We therefore obtain the temperature field in this coordinate system (a function of space only). It is possible to recover the time dimension by changing the variable (\(X=x–\mathrm{V.t}\)). It is therefore possible to quickly (a single step of time) identify the source parameters, which are then reused in the case of the transitory calculation.
Once the identification has been carried out and if the power of the welding process is known, it is possible to derive/to establish the value of the parameter \(\eta\) in the net power (in order to verify the consistency of the value obtained with respect to the process). In fact, the integral of the volume density (respectively surface area) of heat flow over the selected volume (respectively the selected surface) must be equal to the net power, i.e.
\(\underset{V}{\int }{Q}^{V}(x,y,z;t)\mathrm{dv}=\eta \mathrm{UI}\text{et}\underset{S}{\int }{Q}^{S}(x,y,z;t)\mathrm{ds}=\eta \mathrm{UI}\)
In the two examples shown above, this gives:
Example of volume flow: \(S\underset{0}{\overset{L}{\int }}{Q}^{V}(x;t)\mathrm{dx}=S\ast \frac{L}{2}\ast {Q}^{\mathrm{max}}=\eta \mathrm{UI}\) where \(S\) is the surface of the bead deposited perpendicular to the welding direction.
Example of surface flow: \(\underset{S}{\int }{Q}^{S}(x,y,z;t)\mathrm{ds}=\pi \ast {R}^{2}\ast {Q}^{\mathrm{max}}=\eta \mathrm{UI}\).
Since the heat flow is identified spatially, it is now necessary to implement the movement of this source on the mesh for the transitory thermal calculation. A function in the welding direction, here \(x\), and of time is thus defined by the operator DEFI_NAPPE: a flux that is a function of time is applied successively to the meshes located under the path of the welding torch, considering an increase to maximum value, followed by a decrease to zero. The descent of the flow on one mesh corresponds to the increase in the flow on the next adjacent mesh. Thus, the sources are « switched on » successively along the welding axis during the passage of the torch, which corresponds to a heat source of constant intensity that travels in space along the welding axis.
Case of 2D modeling with heat flow
In the case of 2D modeling, the approach is different because it is necessary to choose a flow (volume or surface) that varies over time in order to take into account, in the 2D calculation, the approach and the distance of the torch. For the spatial distribution of this flow, a constant flow in space is often chosen. An example of surface flow is given below:
\({Q}_{r}={Q}_{r}(x,y,z;t)={Q}_{r}(x;t)=\{\begin{array}{cc}\frac{{Q}^{\mathrm{max}}}{{t}_{1}}t& \text{si}t\le {t}_{1}\\ {Q}^{\mathrm{max}}& \text{si}{t}_{1}\le t\le {t}_{2}\\ -{Q}^{\mathrm{max}}\frac{(t-{t}_{2})}{({t}_{3}-{t}_{2})}& \text{si}{t}_{2}\le t\le {t}_{3}\end{array}\)
Again, it will be necessary to identify, based on temperature measurements, the parameters of the chosen flow (in our example, the moments \({t}_{1}\), \({t}_{2}\) and \({t}_{3}\) as well as the value \({Q}^{\mathrm{max}}\)).
If the power delivered by the method is known, it is also possible to derive/to establish the parameter. For our example, this gives:
\(\underset{t}{\int }\left\{\underset{S}{\int }{Q}_{r}(t)\mathrm{ds}\right\}=S\underset{t}{\int }{Q}_{r}(t)\mathrm{dt}=\frac{\eta \mathrm{UI}}{V}\iff \underset{t}{\int }{Q}_{r}(t)\mathrm{dt}=\frac{\eta \mathrm{UI}}{\mathrm{SV}}\)
That makes:
\(\underset{t}{\int }{Q}_{r}(t)\mathrm{dt}={Q}^{\mathrm{max}}\ast \frac{1}{2}({t}_{3}+{t}_{2}-{t}_{1})=\frac{\eta \mathrm{UI}}{\mathrm{SV}}\)
where \(V\) is the known welding speed and \(S\) is the known surface area of the deposited cord. To refine the identification of the source parameters, it is possible to use the parameter \(\eta\) found by an almost stationary 3D calculation in a moving coordinate system.
Feedback
Thesis INSA L.D 2004:
For the 3D transient modeling of the plate, several forms of surface fluxes were tested: triangular in the direction of welding, cylindrical with a circular and Gaussian base. For these three flows, the temperature distribution proved to be approximately identical.
For 2D modeling (plane deformation), three representations were tested: imposed temperature, surface flow and volume flow with identification of the parameters on measurements. Only modeling with imposed temperature led to the melting of the deposited metal. With a volume flow, the molten zone has not been reproduced.
Sheet 3488: The imposed temperature approach was used on the axisymmetric calculation of the tube. The results of this simulation show that the calculations overestimate the melt zone and the maxima of the thermal cycles. The imposed temperature approach is therefore too energetic and it is the flow approach that is recommended for this study.
4.3.4. Thermal boundary conditions with the environment#
The thermal boundary conditions are modelled by convective and radiative exchanges between the welded part and the environment, which are written as:
\(-\lambda \frac{\partial T}{\partial n}=h(T-{T}_{\mathrm{air}})+\varepsilon \sigma ({T}^{4}-{T}_{\mathrm{air}}^{4})\)
where \(n\) is the external normal, \(h\) the convective exchange coefficient, \(\sigma\) the Stefan-Boltzman constant and \(\varepsilon\) the emissivity of the material.
Remarks
In the case of welding relatively thick parts, the values taken for the exchange coefficient and the emissivity often have only a secondary influence on thermal calculations: in fact, the heat flow exchanged with the ambient air during heating and cooling is very low, compared to the heat flow by conduction in the part coming from the heat input.
In the immediate vicinity of the source, the flux emitted by radiation is not negligible in reality, but the corresponding unknowns can be integrated into the definition of the size and distribution of the heat source.
The thermal problem is therefore most often reduced to a purely conductive problem and the non-consideration of radiative and convective exchanges with the environment is not essential.
4.3.5. Thermophysical characteristics#
The thermophysical properties involved in the heat equation are a function of temperature. These are thermal conductivity \(\lambda (T)\) and specific heat \(\rho {C}_{p}\) or enthalpy.
Remarks
As far as thermal conductivity is concerned, it is sometimes customary to increase it artificially for temperatures above the melting point, in order to « take into account » convective phenomena inside the bath, and to homogenize the temperature of this one. In the literature, conductivity is thus increased by a factor of 2, 10 or 100 according to the authors (this is what is done in the 3488 tube with a factor of 100). In practice, it is often reasonable to take a constant conductivity from the melting temperature, and it is considered that it is not necessary to increase it artificially, since the unknowns concerning the melt pool (convective phenomena, etc.) are included in the definition of an ad hoc heat source.
During welding, the latent heat of fusion (see note in paragraph 3.3.1) is low compared to the heat input from the process, and it is not necessarily useful to take it into account. Furthermore, this latent heat of fusion may also be included implicitly in the definition of heat supply.
4.4. Metallurgical calculation#
The critical point for the metallurgical part concerns, essentially, the knowledge of experimental data in order to correctly identify metallurgical behavior models.
4.4.1. Introduction#
In this part, we are only interested in the steel-type material, in particular 16 MND5, which can comprise five different metallurgical phases: ferrite, pearlite, bainite, martensite, called cold phase or \(\alpha\), and austenite, called hot phase or \(\gamma\).
When a material is heated, phases \(\alpha\) are transformed into phase \(\gamma\). When the material is cooled, the austenite is transformed, depending on the cooling rate, into ferrite and/or pearlite and/or bainite and/or martensite. It is therefore necessary to define for heating the kinetics of transformation \(\alpha \to \gamma\) and for cooling the nature and kinetics of the possible transformations \(\gamma \to \alpha\).
The metallurgical phases present therefore depend on the temperature and on the temperature rate. The calculation of these phases is carried out by post-processing a mechanical calculation, by the command CALC_META. The initial metallurgical state must be specified in this order.
4.4.2. Heating and cooling behavior models#
Currently in Code_Aster, for steel-type materials, there is only one behavior model that makes it possible to calculate, at each time step, the proportions of the various phases. Nevertheless, this model is different in heating and cooling. A detailed expression of the heating and cooling kinetics can be found in [R4.04.01].
4.4.3. Thermal interaction => Metallurgical#
As we have already specified before, there is no coupling between thermal and metallurgical calculations. However, the thermo-physical properties (conductivity, specific heat or enthalpy) of the material point depend on the proportions of the various phases present: while this is generally not too prejudicial to mechanical predictions, it may be so for a detailed forecast of the final metallurgy (but this is not, in general, the objective of a numerical simulation of welding).
4.5. Mechanical calculation#
The critical points for the mechanical part concern the choice of the law of behavior and the identification of the parameters of this law.
4.5.1. Principle of mechanical calculation#
The mechanical calculation is carried out by solving the equilibrium equations (operator STAT_NON_LINE), taking into account the dependence of mechanical properties on temperature and, possibly, on the proportions of the metallurgical phases.
4.5.2. Management of the addition of material (welding beads)#
In mechanics, there are two methods for managing the addition of material, equivalent in principle to those of thermal engineering.
One can consider a single mechanical model comprising all the cords, where the knots at the interface between cords are split. When a new cord is added, conditions are assigned to the interface relating to the increment of movements (LIAISON_DDL). As in thermal engineering, this method is certainly the most reliable but the construction of the mesh becomes tedious if the number of passes is high. We have no**recent* feedback on this method.
The most commonly used method in mechanics is the one where we have a single mechanical model for all the passes, the elements not yet present being artificially deactivated by assigning a « virtually zero » Young’s modulus (\(E={10}^{-11}\mathrm{.}E(20°C)\) in practice)). The Young’s modulus value to be assigned in the non-deposited metal results from a compromise: if the value is too high, stresses will be generated in the metal not yet deposited, but if it is too low, this can lead to convergence problems.
4.5.3. Law of behavior#
In Code_Aster, there are various laws of behavior to describe the non-linear behavior of a material (isotropic, kinematic, mixed, viscous effects,…). The user will find the inventory of these models in the document [U4.51.11]. Since these models are not specific to welding simulations alone, we will not describe them.
Note
However, we can cite mechanical models with the effect of structural transformations, which have been developed for steels, such as 16 MND5 and especially in the context of welding activities.
These models, which are described in detail in documents [R4.04.02] and [R4.04.03], make it possible to model the following phenomena: plastic behavior or viscous behavior, linear or non-linear isotropic work hardening or linear kinematic work hardening, transformation plasticity, transformation plasticity, restoration of work-hardening of metallurgical origin, restoration of work hardening of viscous origin. A calculation can be carried out in small deformations but also in large deformations, either with option PETIT_REAC, or with option SIMO_MIEHE (models with kinematic work hardening do not exist with SIMO_MIEHE).
The two important questions in terms of choosing the law of behavior relate to:
Do we have to take into account the viscous effects due to the high temperatures generated during welding?
What type of work hardening should we consider (isotropic, kinematic or mixed)? This question is important in welding because this process involves cycles of traction and compression;
Viscous effects are often overlooked mainly due to the lack of experimental data. A plastic model may then be sufficient if its identification is carried out on the basis of tests where the loading speed is close to that encountered in the structure studied [6]. Otherwise, it is preferable to take a viscous model, especially if one wishes to simulate a loading such as an expansion.
For the type of work hardening, it was found in [3], [4] and [6] that an isotropic work hardening model generally leads to a very high final stress level (compared to measurements). The maximum final stress level will be all the higher the more numerous the plasticization cycles in traction-compression are numerous. This is why the higher the number of passes modelled, the higher will be the residual stresses predicted by modeling with isotropic work hardening. This result can be mitigated by using isotropic work hardening with viscous restoration, which will compensate for the effect of isotropic work hardening. On the contrary, a kinematic work hardening model tends to underestimate residual stresses. The actual behavior of the material is often a combination of the two workings.
4.5.4. Note on large deformations#
Taking into account large deformations is in general not essential for a simulation of welding on thick structures. On the other hand, if the structures are thin (strong distortions), it is necessary to take them into account.
In Code_Aster, there are two ways to account for large deformations in the STAT_NON_LINE operator:
Option PETIT_REAC suitable when rotations are small;
Option SIMO_MIEHE for an exact formulation of large deformations, but restricted to isotropic work hardening models.
4.5.5. Boundary conditions#
Feedback
Sheet 3488: Axisymmetric modeling of pipe welding implicitly incorrectly assumes that welding takes place simultaneously around the entire circumference of the tube, and therefore that the temperature rises everywhere in the chamfer. In reality, the heat source progresses towards a part of the structure that has remained cold, which necessarily limits the welded zone. The room, at the level of the heat source, cannot therefore expand freely. This self-clamping effect should disappear when the heat diffuses and disappear during the cooling phase. To remedy this problem, it is possible to impose an axial clamping on the tube, only during the heating phase. The tube is thus prevented from expanding freely upon heating; on the other hand, it is free to deform upon cooling.
4.6. Calculation time#
We note (in version STA9), through various welding studies conducted in recent years, that most of the calculation time is consumed in mechanical calculation. To give an order of magnitude, we give two examples below:
Test case HTNA100Aqui considers a chamfered pipe welded in two passes with the TIG process (sheet called 3488):
Number of knots = 3632
Modeling: axisymmetric
Time CPU of the thermal calculation = 307s
Metallurgical calculation time CPU = 25s
Time CPU of mechanical calculation = 5169s
Study on a chamfered plate welded in two passes with process TIG (sheet called 2425)
Number of knots = 11600
Modeling: 3D
Time CPU of the thermal calculation = 951s
Time CPU of mechanical calculation = 64601s
Remarks
The possible metallurgical calculation does not cost anything in terms of calculation time because it is only a question of integrating behavioral models; there are no equilibrium equations to solve.
Mechanical time could certainly be improved if we consider (when solving the mechanical equilibrium equations by operator STAT_NON_LINE), in the prediction phase, the dependence of the module of YOUNG and perhaps of the thermal expansion coefficient, on temperature. Currently, only thermal deformation (in fact the derivative) is taken into account in the second member.
Since the mechanical part is a highly non-linear problem, it is often necessary to use linear research in module STAT_NON_LINE in order to facilitate convergence. In addition, an adapted division of the time step according to the evolution of temperatures makes it possible to facilitate convergence.