FE-model for prediction of welding distortions in components made of preformed stainless steel sheets

(1)

FE-model for prediction of welding distortions in components made of preformed stainless steel sheets

TOM GLANSHOLM

KTH

SKOLAN FÖR TEKNIKVETENSKAP

(2)

(3)

Abstract

This master thesis was carried out at Scania CV AB. The focus for this thesis is the prediction of welding distortions that can cause problems in the manufacturing process of Scania’s after- treatment system. The after-treatment system is mainly assembled by sheet metal plates of the ferritic stainless steel EN 1.4509. The plates are welded together.

When welding, distortions and residual stresses occur, and they also depend on the sequence in the component was welded together. The distortions and residual stresses can cause tolerance related issues and a lower lifetime for the welded components. Experiments are expensive and therefore it is desirable to simulate the welding process, thereby controlling distortions and optimizing welding sequences.

To simulate the welding process and predict the welding distortions a thermo-mechanical FE- model was created for two typical welds found on the after-treatment system. The first scenario was two thin plates welded onto each other in an overlap weld joint and the second scenario was a thin plate welded onto a thick plate in a overlap weld joint. After the FE-model was compared to the experiments. An optimization of the welding sequences was also made on a larger component typically found on the after-treatment system.

The FE-model can predict the distortion shape with good accuracy for the T-fillet weld, while the model predicted a more symmetric distortion shape on the overlap weld compared to a more asymmetric shape found on the experiments, but the error is still not very large. The Fe-model can also be used to optimize the welding sequence for bigger components on the after-treatment system within a reasonable time span compared to doing the opimization manually in an experiment.

(4)

Sammanfattning

Detta examensarbete gjordes för Scania CV AB. Fokus for detta examensarbete har varit kvarvarande deformationer efter svetsning som kan skapa problem vid tillverkningen av Scanias avgasefterbehandlingssystem. Avgasefterbehandlingssystemet är till mesta dels konstruerat av stålplåtar av det ferritiska rostfria stålet EN 1.4509, plåtarna är svetsade ihop och då uppstår kvarvarande deformationer.

När komponenter svetsas samman uppstår deformationer och restspänningar. Dessa deformationer och restspänningar är också beroende på i vilken sekvens komponenterna har svetsats ihop.

Deformationerna och restspänningarna kan skapa problem med toleranser och sänka livsläng- den för komponenterna som sammanfogats. Experiment är kostsamma och därför är det önskvärt att simulera svetsprocessen, och därav kontrollera deformationerna som uppstår och optimera i vilken sekvens som komponenterna ska svetsas ihop.

För att simulera svetsprocessen och prediktera de kvarvarande deformationerna efter svetsning så gjordes termo-mekanisk FE-model för två vanliga svetsscenarion för avgasefterbehandlingssystemet. Det ena scenariot är två tunna plåtar som svetsas ihop i en överlappande position och det andra var en tunn plåt som svetsas på en tjockare plåt. Ett experiment gjordes sedan för båda svetstyperna. Efter att svetstyperna hade jämförts med experimentet så gjordes en optimering av svetssekvensen för en större komponent likt komponenter funna på avgasefterbehandlingssystemet.

Den termomekaniska FE-modelen kunde prediktera de kvarnvarande deformationerna och deras form med bra noggrannhet jämfört med experimentet med undantag för en deformationsform på de tunna plåtarna som var mer symmetrisk i FE-modellen jämfört med den asymmetriska formen i experimentet. FE-modellen kunde också användas för att optimera svetssekvensen för den större komponenten inom en rimlig tidsrymd.

(5)

Acknowledgements

I would like to express my gratitude to the Alejandro Lípiz Fernández and Peter Nerman who helped me with a lot of practical issues to setup an experiment.

I also want to thank my supervisor Tomas Hansson for helping me with a lot of modelling issues and guidance in this project, and thanks to my fellow student Markus Johansson-Näslund for great and helpful discussions.

Last, I want to thank my examiner Jonas Neumeister for all the help with the report.

Tom Glansholm

Stockholm, 21-10-2020

(6)

1 Introduction

Background

The European emission regulations has increased a lot over the past two decades which has led to high demands on the after-treatment system on heavy vehicles. In order to provide trucks that fulfill new demands for costumers in Europe, the after-treatment components on Scania trucks has gone from being a silencer to a complex system to reduce particles and unwanted gases from the exhausts. Figure 1.1 a) shows the after-treatment system and the engine on a Scania truck to the right.

Figure 1.1: Aftertreatment system and the engine a), a close-up view off three weld beads on the silencer b).

The after-treatment system on Scania trucks is by now a complex welded component with high demands on the materials in terms of structural integrity, fatigue and corrosion. Some of the the weld beads are shown figure 1.1 b). To prevent leakage many weld beads acts as a sealing for exhaust gases on the after-treatment system, and the weld beads become very long. This results in a total length of 50 meters of weld beads on the after-treatment system.

When welding, distortion and residual stresses in the structure are inevitable, and these phenomena can cause tolerance related issues and decrease in fatigue life. Due to the high cost of experiments to validate designs and welding sequences it is desirable to simulate and control the welding process with computational methods.

Rapid increase in computer speed and the evolvement of numerical methods in the past 30 years have made it possible to simulate the welding process and predict distortions, residual stresses and metallurgical phenomena with the FE-method.

(10)

1.1 Project objective

This master thesis is commissioned from Scania CV AB and the objectives with this thesis are to

• Setup a FE-model to predict welding distortions on a ferritic stainless steel 1.4509 plate

• Construct and validate the FE-model with a welding experiment

• Optimize welding sequences for a component on the after-treatment system to minimize the welding distortions

(11)

2 Theory

2.1 Welding techniques

Welding is a technique for melting parts together by heating. For joining metals together common techniques used are tungsten inert gas welding (TIG), gas metal arc welding (GMAW) and submerged arc welding (SAW). The mentioned techniques are driven by an electrical current that runs through the materials of the components meant to be joined. The electrical current produces heat due to the electrical resistance in the materials. The heat melts the parts together.

The after-treatment system on the Scania vehicles are welded with the GMAW-technique, therefore this theory section will be focused on this technique.

(12)

GMAW-process

The GMAW-process is sometimes referred to as metal inert gas (MIG) or metal active gas (MAG) welding, which are two subcategories of GMAW. The process can be summarized by the generation of heat which fuses the material together and the addition of filler material.

The generation of heat is achieved according to figure 2.1 energy is supplied by the power source (5), which provides an electrical current that runs through the metal electrode, the base material (2) and the ground wire (6).

Figure 2.1: Principle of GMAW-welding process.

The electrical resistance will build up due to the by the gap between the weld torch (4) and the base material (2) causes very high temperatures that creates an arc (1) which is melting the base material (2) and the metal electrode (3), causing a molten base and filler material which is called weld metal. The volume that contains the weld metal is called the weld fusion zone.

The addition of filler material is done by the metal electrode which acts both as a filler material and as an electrical conductor. In order to continuously add filler material the metal electrode is continuously fed through the weld torch (4). In order to ensure good weld quality, the weld bead needs to be shielded with a shielding gas (7).

(13)

2.2 Sheet metal Weld joint types

There are several configurations available to join components together with welding. Figure 2.2 shows the cross section of common weld joint types for sheet metal plates mentioned in this report.

Figure 2.2: Cross section of three weld joint types. overlap weld joint a), T-fillet weld joint b) and Butt weld joint c).

2.3 Impact on the weld material during the welding pro- cess

The description in sections 2.4 and 2.5 regarding welding distortions and residual stresses is good for the knowledge of how they occur, but to predict welding distortions and residual stresses from the welding process, a more accurate description is needed of the material behavior. This is done in the proceeding sections of this theory chapter. The important properties that have a big temperature dependence and therefore might be needed to consider can be divided into three different categories, thermal, metallurgical and mechanical. The difference in steel grades can change the response of the material substantially during welding, therefore it is important to have the correct properties as input for the simulation.

Thermal properties

The common thermal properties of importance are thermal conductivity, the specific heat capacity, convection and radiation.

Convection is the transfer of heat by motion of mass from a fluid from one region to another, it could either be free or forced [1]. Forced convection occurs for example in welding when shielding gas is employed, and the gas is moving the surrounding air. Free convection occurs when the air is moving due to the uneven temperature distribution of the surrounding air and is not driven by any external factors.

Thermal conduction is the phenomena that describes the movement of heat from a high temperature region to a region with a lower temperature, this is driven by two things; the lattice vibration and the free electron movement. The free electron movement is the main contributor to thermal conductivity in metals. When metals are heated up the free electrons start to vibrate more, which increases the kinetic energy of the electrons. The electrons are then moving around to different regions transferring the kinetic energy to atoms at adjacent regions [2].

The specific heat capacity is a measure that can be explained as follows, when temperature rises

(14)

more energy can be stored in the material, the amount of energy stored per change in temperature is proportional to the mass and a the specific heat capacity of the material [3].

Radiation is the phenomena where heat is transferred by electromagnetic waves, the transport of heat by radiation does not require a material to move heat [1].

Figure 2.3 (a) and 2.3 (b) shows thermal conductivity and the specific heat capacity as a function of temperature for some common austenitic, ferritic and carbon steels.

(a) (b)

Figure 2.3: Conductivity at different temperatures a) and specific heat capacity at different temperatures b) for different metals from [4].

Figure 2.3 (a) shows that thermal conductivity is much lower for ferritic stainless steels compared to carbon steels. The specific heat for the ferritic steel has a similar behavior as the carbon steel but the austenitic stainless steel has a completely different temperature behavior.

Microstructural properties

When the base material is heated rapidly by the welding process the base material undergoes several different temperature activated microstructural changes. The main microstructural changes present are shown in figure 2.4. Figure 2.4a) shows a plot of the hardness of the material, peak temperatures are plotted in figure 2.4 b) and a carbon phase diagram in figure 2.4 c). The lower part of figure 2.4 b) shows an illustration of the weld bead and the base materials cross section.

From this illustration of the cross section it can be seen that the microstructure is layered from a coarse-grained microstructure to a finer grained microstructure further away from the fusion zone. This region is called the heat affected zone.

The large variety of different metallurgical phases shown in the bottom left of the picture are dependent on peak temperature and the duration of the certain temperature present for the material. The area close to the weld will be subjected to different peak temperatures depending on the distance from the fusion zone, the closer to the fusion the higher peak temperature. How

(15)

steep the temperature curve is also dependent on the distance to the fusion zone and will affect the duration at which certain temperatures are present.

Figure 2.4: Three diagrams that describes the microstructural effects of welding for a low-alloy quenched and tempered steel from [5]. The hardness of the material a), the peak temperature b) and a phase diagram c).

As seen in figure 2.4 the hardness of the base material is dependent on the temperature history as well. Before modelling the metallurgical phenomena, it is important to know what the subject of interest is. It could either be the strength and ductility of the welded component or the distortions and stresses. The austenite grain growth at certain temperature histories can lower strength and ductility [6]. The transformation from ferrite to austinite and martensite transformation will cause stresses and distortions due to volume change [7].

Mechanical properties

To predict the distortions and residual stresses, the mechanical properties are of high importance.

The mechanical properties affected by the welding process are yield stress, thermal expansion, Young’s modulus and the hardening behavior. Thermal expansion cannot always be interpreted as a mechanical property due to some metallurgical phenomena. Figure 2.5 below shows the dilatometer curves that are recorded during the heating and cooling process of two different steels. Figure 2.5 a) shows an austenitic steel without phase transformations and a perlite steel without phase transformation is shown in figure 2.5 b).

(16)

Figure 2.5: Dilatometer curves for two different steels during the heating and cooling process from D. Radaj [8]. Austenitic steel in figure a) and perlitic steel in figure b).

As mentioned above, the yield strength is also highly affected by the temperature. Figure 2.6 shows the measured stress strain curves at different temperatures for a low carbon steel.

Figure 2.6: Measured stress strain curve at temperatures from 25 from to 1100^◦C, with a strain rate of 10⁻³s⁻¹[9].

The yield stress is decreasing with temperature, and the hardening is lowered when the temperature increases.

2.4 Welding residual stresses

When the weld torch passes through the base metal, the material in the vicinity of the weld torch is heated up rapidly compared to the surrounding material. Figure 2.7 shows the uneven temperature distribution.

(17)

Figure 2.7: Temperature field isotherms around welding heat source moving uniformly and linearly along the x-axis towards the right in an infinite plate from [10].

As mentioned above the material is heated up locally and the material will expand. Due to the colder surrounding material the expansion becomes restricted and high stresses develops which often exceeds the yield limit locally. This will cause tensile residual stresses at the weld and compressive residual stresses in the surrounding material after the material has cooled down.

This principle can only be used as a rule of thumb as some metallurgical phenomena such as γα-transformations can change the stress distribution in the near field of the weld [10].

If phase dependent strains are neglected, the residual stresses due to welding can be interpreted using a simple model of three bars and two rigid plates as in figure 2.8 below.

Figure 2.8: A bar model, with a weld cross section below that describes the cause of residual stresses during the welding process. a) shows the initial state were no weld metal has been added, b) describes the heating state and c) shows the cooled down state.

At the initial state, all bars are in equilibrium. The middle plate represents the weld metal and the left and the right bars represents the surrounding material. The rigid plates represent the

(18)

connection between the weld and the surrounding material. At state 2, the heating state, the component is welded and the heat from the weld arc will cause thermal strains and the middle bar(weld metal) will try to expand, but as the left and right bar (surrounding material) will try to hold it back the middle will be subjected to high compressive stresses and start to yield. During the cooling (state 3), the heated bar will try to contract but the left and right bar will hold it back, causing residual tensile stresses in the middle bar.The left and right bar will develop compressive residual stresses. This is how residual stresses develop during welding, and these stresses can affect the fatigue life of the structure, by either increase or decrease the life depending if they are compressive or tensile respectively [11].

2.5 Welding distortions

Depending on how restrained the structure is, the structure will either be impacted by high residual stresses or large distortions on a global level. If the structure is unrestrained, large distortions will arise but if the structure is restrained the residual stresses will be dominant [12]. The welding distortions can be either temporarily or permanently. In this work the meaning off welding distortions means that they are permanent distortions. The welding distortions occur basically due to the shrinkage of the weld metal. The weld metal consists both molten filler and base material show in figure 2.8.Figure 2.9 below shows four basic distortions that can occur when welding a plate. [10]. During cooling the weld metal shrinks both in longitudinal direction and in the transverse direction, causing distortions in both directions respectively.

Figure 2.9: Distorted Butt welded plate with four types of shrinkages, transverse shrinkage a), longitudinal shrinkage b), bending shrinkage c) and angular shrinkage d) from [10].

It should be noted that the angular distortions only occur due to the through-thickness asymmetry of the weld bead, where the top of weld bead is thinner than the lower, which means that more material will shrink on the lower part of the plate than on the upper surface.

(19)

2.6 Computational welding mechanics

The first thing to consider is the degree of coupling needed for the analysis, since welding is a multi physical phenomena. The welding process includes electromagnetism, thermodynamics, fluid mechanics and solid mechanics [13]. Most of the analysis made ignores the fluid flow to simplify the model. Also, the thermo-mechanical coupling which has most impact is the heat generated by the plastic work done which also can be neglected for most welding processes except explosion welding [14].

For the physics of heat generation from the arc, the most common way is to use a weakly coupled model, where the physics of heat generated is by a heat input model with predefined distribution, this heat input must be calibrated with testing to predict distortions and residual stresses accurately [15]. With these mentioned simplifications, the Computional welding mechanics (CWM)-model can be described as in figure 2.10 below.

Figure 2.10: Flow chart diagram that describes the sequentially coupled thermo-mechanical model. The thermodynamic analysis with a heat input model gives a temperature history for the solid mechanical model.

This approach is called the sequentially coupled approach, where the heat transfer analysis with a moving heat source is solved first. thermal analysis gives a prescribed temperature field that drives the mechanical analysis. It could also be done in a staggered approach where the mechanical analysis is one increment step behind thermal analysis. This approach is the same except that the mechanical analysis does not need to wait for thermal analysis. A sequentially coupled analysis gives the benefit of evaluating the temperature distributions with experiments before running the mechanical analysis [13].

(20)

Thermal analysis

In order to get the temperature distribution T (x, y, z), the heat transfer equation below needs to be solved, where

cρ∂T

∂t = k ∂²T

∂x²

+ ∂²T

∂y²

+ ∂²T

∂z²

+ ˙Q. (2.1)

Where c is the heat capacity, and ρ is the density, t is the time, k is thermal conductivity andQ˙ is the prescribed heat flux. To solve equation 2.1 above, initial and boundary conditions need to be defined. The initial condition is an initial prescribed temperature and should be applied to all points,

T (x, y, z, 0) = T₀(x, y, z). (2.2)

The boundary condition that needs to be formulated is the radiation and convection on the boundary, where

k(∂T

∂xNx+∂T

∂yNy +∂T

∂zNz

= −hc− hR. (2.3)

Where Nx, Ny and Nz are the components of vector n = (Nx, N_y, N_z ) pointing in the normal direction of the surface where the bondary condition is applied. The thermal convection hc is often modeled with Newtons law of cooling, where

h_c= −h(T_s− T_a). (2.4)

Here h is the film coefficient, T^s is the surface temperature and T^a is the ambient temperature, in Newtons law of cooling the convection is proportional to the temperature difference between the plate temperature and the surrounding temperature. The heat radiation hRin equation 2.3 is often modelled by Stefan-Boltzmann’s law, where

hR = Γ · (Ts− Ta)⁴. (2.5)

Here Γ is the Stefan-Boltzmann constant and T^sis the surface temperature and T^rtis the ambient temperature. In [16] it was shown that thermal convection and the radiation is so small that they could either be combined in the convection definition or neglected for carbon steel plates with thickness >2.5mm. Convection and the radiation is too small near the weld pool compared to the heat transfer in the solid, and can be neglected [17].The specific heat capacity is the most importance property in thermal analysis for accurately predicting the distortions for low carbon steel grades S355, S700 and S900 steels [18].

Heat sources

There are three common ways of modelling the heat input in CWM, either the prescribed temperature on the elements that defines the weld bead, distributed heat flux models, or uniformly distributed heat source on the weld bead elements. All these methods so far not been able to predict the temperature distribution accurately without calibration [19].

The prescribed temperature heat model is applied by adding a prescribed temperature at the melting temperature to match the fusion zone in the weld bead, it has been shown by several authors that this method has a fairly accurate when comparing with experimental measurements [20].

(21)

The uniform heat distribution is a simple approach which prescribes a uniform heat flux to prescribed elements that represents the weld fusion zone. Bhatti et al [18] used a uniform heat source that applied heat flux to the fusion zone on a T-fillet weld and was able to predict angular distortions and residual stresses at the weld bead with good accuracy.

There are many distributed heat flux models such as the Gaussian distributed models, spheri- cal or the Goldak double ellipsoid model, or for example the cylindrical model. The double ellipsoid model is used in many studies and will be discussed below. The heat source model has shown good agreement with experimental results in terms of temperature histories, distortions and residual stresses [21] . The Goldak double ellipsoid model can be defined in a moving Cartesian coordinate system according to figure 2.11 with coordinates x⁰, y⁰ and z⁰.

Figure 2.11: Goldak double ellipsoid dimensions and the local coordinate system.

The heat flux distribution is defined for positive z⁰-values according to equation 2.6 below qF(x⁰, y⁰, z⁰) = f1

6√ 3 abc₁π^3/2

Q˙se^−3(x⁰^/a)²e^−3(y⁰^/a)²e^−3(z⁰^/a)², (2.6)

and for negative z⁰-values according to equation 2.7 below, where q_R(x⁰, y⁰, z⁰) = (2 − f₂) 6√

3

abc₂π^3/2Q˙_se^−3(x⁰^/a)²e^−3(y⁰^/a)²e^−3(z⁰^/a)². (2.7) The variables, a, b,c1,c2 are the dimensions of the double ellipsoid. Q˙_sis the prescribed heat flux, the distribution for heat flux between positive and negative z⁰values are defined by ff and fr. The Goldak double ellipsoid model needs at least 4 hexahedral elements along each half plane in figure 2.11 to ensure a continuous distribution of heat flux [22]. If continuity along the z⁰-axis should be fulfilled, then

(2 − fr) c_r = f1

c₁, (2.8)

(22)

and if the total heat flux from the front and the rear distribution should be equal to the total heat fluxQ˙_sthen

f_f + f_r = 2 (2.9)

By combining equation (2.8) and (2.9) the independent variables f^f and f^rcan be reduced as f_f = 2

1 + ^c_c^r

f

(2.10) and

fr = 2 − ff. (2.11)

Power input

The heat flux generated by the welding process is introduced by the electrical current I and the voltage U . But the heat flux applied to the weld is lower, therefore an arc efficiency factor η has been defined. The arc efficiency factor differs for different welding techniques and has not been accurately established [23]. But some guidelines have been made and for GMAW-process it has been estimated to be between 0.75-0.93 with CO2shielding gas and between 0.66-0.7 with Argon shielding gas [24]. With the arc efficiency factor η the net heat flux can be written as

Q˙_s= ηIU. (2.12)

Where I is the current and U is the electrical potential in the welding electrode.

Mechanical analysis

For sequentially coupled thermo-mechanical models, the mechanical analysis uses the thermal strains as input, this means that the total incremental strain can be written as a sum of the thermal strains and all other components, where

dε^tot = dε^th+ dε^ph+ dε^e+ dε^pl. (2.13) The thermal, phase change, elastic and the non-reversible plastic strain increment are denoted dε^th, dε^ph, dε^e, and dε^plrespectively. If the body forces are ignored the solid mechanical problem can be described by the equilibrium equation 2.14, the relationship between displacement and strain in equation 2.15 and the constitutive equation 2.16 below. Where

∇σ = 0, (2.14)

ε = ∇u (2.15)

and

dσ = C(dε^tot− dε^th− dε^ph− dε^pl). (2.16) Where ∇ is the Laplace operator and σ is the stress matrix, ε is the strain matrix, u is the displacement vector and C is the elastic material matrix. Equations 2.14, 2.15 and 2.16 are then written on weak form and solved incrementally by FEM. The mechanical properties often used as input during simulation of the welding process are the yield stress, yield hardening, Young’s modulus, Poisson’s ratio and coefficient of thermal expansion [25]. Most authors use rate independent plasticity with von Mises yield surface due to lack of material data even though the problem is rate dependent [26]. However Goldak et al [27] investigated the effect of kinematic hardening and found that the hardening behavior has a large effect for the residual stresses in the weld pool while the results were identical far away from the weld fusion zone.

(23)

2.7 Finite element implementation

Addition of weld metal

In order to not stiffen the structure subjected to welding in a non-physical way the weld bead needs to be added sequentially. This can be done in different ways in FEM, either by the quiet or the inactive element approach [28].

The quiet approach is done by setting the material properties such as Young’s modulus at a low value before the weld bead elements are added. The values need to be small enough to not affect the stiffness of the structure but large enough to not create zero stiffness elements which will cause convergence problems.

The inactive element approach adds the elements to the elastic stiffness matrix when activated, this approach has not the same convergence issues as the previous approach, but the construction of the elastic stiffness matrix is time consuming [28].

Mesh and elements

One common way to construct a FE-model is to use the same mesh for the heat transfer and the static analysis [29]. The input for the static analysis is the temperature distribution from the heat transfer analysis. The temperature distribution is interpolated within the elements with shape functions. If the same shape functions are used in the static analysis as in the thermodynamic analysis, the shape function for the temperature will serve as shape functions for the displacement field. The total strains in the static analysis is one order lower as the strains are the derivative of the displacement. Equation 2.17 below shows the total strains as a sum of the independent strains.

ε^tot = ε^th+ ε^ph+ ε^e+ ε^pl (2.17) If the order of elements is the same in the thermodynamic model as the solid mechanical model this will cause an inconsistency between the total strains and thermal strains. For instance, assume that the shape functions are linear, this will give a linear distribution of thermal strains, but the total strains must then be constant. Oddy et al [30] showed that the residual stress field in the weld cannot always be correctly predicted if the strain field is inconsistent, by using a higher order shape functions for the static analysis a more accurate prediction could be made.

But as mentioned above, welding simulations are highly non-linear causing large deformations and large plastic strains causing convergence problems for higher order elements, therefore it is common in turn use more linear elements for the static analysis [29].

2.8 Simplified CVM-models

The previous section discussed the sequentially coupled thermo-mechanical model. This method is time consuming and it is possible to simplify it and still predict residual stresses and distortions from welding processes accurately. The simplified approaches can be divided into two categories, the ones who take the transient behaviour into account and those who neglect the transient behaviour.

(24)

Block dumping

The ’block dumping’ method is a transient sequentially coupled thermo-mechanical approach where the weld bead is divided into bigger blocks and added sequentially. A uniform heat distribution is added to each block to simulate the heat from the weld torch. Figure 2.12 shows the weld bead added sequentially as blocks.

Figure 2.12: Sequentially added blocks, the first block is added sequentially in time from left to right from [31].

For a T-fillet weld with sufficient number of blocks this method can predict the residual stresses and distortions with the same accuracy as the moving heat source models and reduce computational time with 47 % [32].

One similar technique is called rapid dumping, where the whole weld bead is added in a single step. This method can also be used to predict residual stresses for butt-welds and T-fillet welds and can reduce computational time by 90 % [31]. But the sequence dependency is lost.

Shrinkage volume approach

The ’Shrinkage volume’ approach assumes that the welding distortions are driven by the elastic contraction of the material in the weld fusion zone and the contraction of material close to the fusion zone.

Bachorski et al [33] used the assumption that the material heated to 900^◦C, and above are only responsible for the welding distortions. The elements within this region are set to shrink linearly from 900^◦C to room temperature. This means that thermal strains above 900^◦C do not contribute to the shrinkage as the yield strength is very low above 900^◦C, which can be seen in figure 3.23.

To match the fusion zone a welding experiment needs to be done and a welding macro is needed.

This method is much faster than the thermo-mechanical approach, as it only needs a linear elastic FE-model to compute the distortions, but the sequence dependency is lost.

(25)

2.9 Testing techniques

The computational models need to be validated with testing. There are several subjects that could be of interest to validate such as distortions, residual stresses, temperature distribution, microstructural changes and so on. The focus of this study is welding distortions and temperature distributions therefore the testing techniques for evaluating these properties will be discussed but others will not be discussed here.

The common way to setup an experiment is by taking a practical weld scenario and make a specimen of it, such as T-fillet welds or overlap welds.

There are two ways to measure the temperature, either by thermocouples which is the most common way, or by thermographic cameras.

Thermocouples could either be welded onto the plate or placed in drilled holes [34]. The placement of thermocouples is important and a small error in placement can give a significant temperature difference [35].

Thermography cameras can capture the whole surface area as opposed to thermocouples which only can capture temperature at one point. They are, despite the advantages seldom used, because of reasons such as the area of interest cannot be captured if welding equipment is in the way of the camera. One other problem is that the emissivity of the surfaces changes with temperature and thus needs to be calibrated [35].

(26)

3 Method

The method is divided into three sections, the first section contains the experimental procedure for two typical welds found on the after-treatment system. The second section describes the FE-model that simulates the welding process from the test for both type of welding scenarios.

Several simplifications of the material model are evaluated as well as a mesh convergence study was done. The third section uses the calibrated Fe-model on a larger welded component on the after-treatment system and the welding sequence is optimized.

3.1 Experimental setup

The two most common welds on the after-treatment system is an overlap weld with two thin 1.5 mm plates, and a thin 1.5 mm thickness plate with a 90^◦ bend welded onto a thick 5 mm plate.

Figure 3.1 a) shows the Overlap weld and figure 3.1 b) the thin plate welded onto the thick plate.

Figure 3.1: The two thin plates welded in a overlap joint a), and the thin plate welded onto a thick plate b). The weld beads are coloured yellow.

The thin plates welded with an overlap weld will be called overlap (OL)-plate and the thin plate welded together with the thick plate will be called thin-thick (TT)-plate in this report. The material for the experiment was the ferritic stainless steel EN 1.4509. The dimensions of the plates were set according to figure 3.2.

(27)

Figure 3.2: The dimensions of the TT-plate in [mm] a) and the dimensions of the OL-plate in [mm] b)

Before the welding experiment the plates where tack welded together in each end of the plate according to figure 3.3 below.

Figure 3.3: Tack welds for the OL-plate a), and TT-plate b).

Due to insufficient fixture during the tack welding for the OL-plates, they had some initial distortions and there was also a gap between the plates. Figure 3.4 shows the initial displacement measured for the OL-plates.

Figure 3.4: Initial displacement of the OL-plates after tack welding.

(28)

The initial displacement e for the three plate were 0.8, -0.5 and 0.1 mm for plate 1,2 and 3 respectively.

During the welding experiment the temperature was measured with k-type thermocouples, welded onto the middle of the plates according to the figure 3.5 below.

Figure 3.5: Thermocouples welded onto the surface of the OL-plate a), and the TT-plate b). The wires where held in place an aluminum tape on both plates.

The placements of the thermocouples where set according to the figure 3.6 and 3.7 below. The thermocouples are named S1, S2, S3 and S4.

Figure 3.6: Placement of the thermocouples for the OL-plate with dimensions in [mm].

(29)

Figure 3.7: Placement of the thermocouples for the TT-plate with dimensions in [mm].

In order to not introduce unwanted fixture and heat distribution the plates where laying on a grid weld table. The weld filler material for the experiment was a 308LSi 0,8mm wire, which is a austenitic stainless steel. The plates where manually welded with a Kempi Miniarc evo 200.

The power was calculated as equation 3.1 below, where

Q = U · I (3.1)

Where I is the current and U is the voltage. These properties where estimated from the digital display of the welding machine. The temperature histories were recorded using IPemotion software. The sampling rate was 10 Hz. The distortions were measured using gauge blocks and a flat steel table.

Experimental results

The average weld time of each weld is shown in table 3.1 below.

Table 3.1: Measured welding time and power.

Specimen Power [W] Welding time [s]

TT 3944 9.6

OL 2309 17.59

The average power and welding time were calculated from table A.1 in appendix A.1.

Figure 3.8 a), b), c) and d) shows the temperature histories for thermocouples S1, S2, S3 and S4 on the OL-plate respectively. It can be seen that the temperature is overall much higher for run 3 compared to run 1 and 2.

(30)

Figure 3.8: Measured temperature histories for S1 a), S2 b), S3 c) and S4 d) on the OL-plate.

Figure 3.9 a), b), c) and d) shows the temperature histories for thermocouples S1, S2, S3 and S4 on the TT-plate respectively. The temperature history has less scatter than for the OL-plate.

Figure 3.9: Measured temperature histories for S1 a), S2 b), S3 c) and S4 d) on the TT-plate.

Figure A.1 in appendix A.1 shows the average temperature for the sensors S1, S2, S3 and S4 for the TT and OL-plate.

The welding settings caused some weld spatter and the weld is quite uneven along the length as shown in figure 3.10 below.

(31)

Figure 3.10: Photo of the Weld beads for specimen 1 of the TT-plate a) and the OL-plate b).

Weld specimen 3 was then cutted and the cross section where etched and macro pictures where taken. Figure 3.11 shows the macro for the OL and the TT-plate. The weld settings caused a weld bead with quite high toe angles. It’s also clear that there is a large gap between the plates for the OL-weld

Figure 3.11: Macro picture of the cross section for the TT-plate a) and the OL-plate b).

The weld almost burned through the lower plate on the OL-plate. All these mentioned features are seen on all plates.

The distortions on the TT-plate is mainly an angular distortion on the thick plate. Figure 3.12 shows the distortions for plate 1 and the edge at which the distortion was measured.

(32)

Figure 3.12: Distortions on the TT-plate with the measured edge coloured red.

Figure 3.13 shows the distortion measurements for TT-plates 1,2 and 3 at 0,50 and 100 mm along the red edge in figure 3.12.

Figure 3.13: Distortions on the TT-plate along the in 3.12 with the average and the standard deviation calculated.

The standard deviation is calculated with Bessel’s correction,

s = v u u t

1 N − 1

3

X

i=1

d_i− ¯d2

(3.2)

(33)

where s is the standard deviation, diis the distortion measurement for plate i andd is the average¯ value.

The distortions off the OL-plate is of a more complex shape with bending, angular and transverse distortions combined. The distortions were measured along the red edge according to figure 3.14.

Figure 3.14: Distortions on the OL-plate with the measured edge coloured red.

Figure 3.15 shows the distortion measurements for OL-plates 1,2 and 3 at 0,37.5,75,110 and 150 mm along the red edge in figure 3.14.

Figure 3.15: Distortions on the OL-plate along the in 3.14 with the average and the standard deviation calculated.

(34)

3.2 FE-model

A sequentially coupled thermo-mechanical Fe-model was constructed to predict the distortions.

The moving heat source was first calibrated against the thermal histories and with the calibrated model the distortions were calculated compared with the distortions measured in the experiment.

Thermodynamic model

The thermodynamic model was setup in the commercial FE-software Abaqus 2019 by solving weak form of equation 2.1. The equation is solved incrementally and Abaqus was set to automatically increase or decrease the increment size dependent if the convergence is reached.

Material properties

The material properties used as input for the thermodynamic model was conductivity and specific heat capacity. Figure 3.16 shows the specific heat capacity and conductivity as a function of temperature.

Figure 3.16: Specific heat capacity and conductivity for the ferritic stainless steel EN 1.4509, from [36].

The filler material used in the experiment was an AISI 308LSi which is an austenitic steel with other thermodynamic properties than the rest of the plates, the filler material is only a small part of the model and therefore another material model for the weld bead is not used.

Mesh and elements

The mesh for both plate models consists of 2735 DC3D6 prism and 51965 DC3D8 hexahedral elements with linear shape functions for the TT-plate and 5393 DC3D6 prism and 102457 DC3D8 hexahedral elements with linear shape functions for the OL-plate. Both plates were meshed with a finer mesh close to the weld bead. Figure 3.17 and 3.18 below shows the mesh for the OL and the TT plate respectively.

(35)

Figure 3.17: Mesh for OL-plate with a close-up figure of the weld bead geometry.

Figure 3.18: Mesh for TT-plate with a close-up figure of the weld bead geometry.

The weld bead was meshed to match the weld bead macros in figure 3.11. Figure 3.19 shows the mesh with the weld macro in the background for the TT and the OL-plate.

(36)

Figure 3.19: The cross section of the mesh and the weld macros in the background for comparison for the TT-plate a) and the OL-plate b).

Initial and boundary conditions

The initial conditions for the thermal analysis was to set the all nodal temperatures in equation 2.2 to Ta= 26.5^◦C which was the ambient temperature for the experiment. A convection boundary condition where set to all the free surfaces on the plates to model transport of heat from the surrounding air. This boundary condition is described in (2.3), where the convection coefficient where set to h = 20W/(m² · K), which is the same value used in [34] [37] [18]. The cooling from radiation on the surfaces was neglected.

Activation of weld bead elements

The weld bead is added sequentially each time step using Abaqus AM table collections which are tables that define the weld path, speed and size of a box. If the elements are within the box, they will be activated for the rest of the analysis. The box is defined by the dimensions and the position in a local coordinate system. Figure 3.20 below shows the box, activated elements and the welding direction.

Figure 3.20: Activation box is shown in a transparent grey color.

(37)

The quiet element approach is used which means that the material properties are set to 10 times their initially defined values before the activation. After activation they will be set to their nominal values.

Heat source calibration

The Goldak double ellipsoid was used as heat input model. The heat input model was calibrated by calculating the root mean square error (RMSE) of the difference between the FE nodal temperature and temperature measurement for each measurement point S1,S2 and S4. This can be described as

RSi(x) =

3

X

Si=1

v u u t

1 N

N

X

j=1

(SSi,j − FSi,j(x))². (3.3)

Where Si refers to thermocouple Si and j denotes each calculated value in the temperature history. This is an unconstrained optimization problem where the sum of each RMSE-value R_Si(x) should be minimized, that is

min

3

X

Si=1

R_Si(x) x_min≤ x ≤ x_max.

(3.4)

Where x = (a, b, cf, c_r, x, z)^T is a vector that contains all the dimensions a, b, cf and cr off the Goldak double ellipsoid according equation (2.6) and (2.7). By using equation (2.10) and (2.11) f^f and f^r can be set to be dependent variables of c^f and c^r, and thus reducing number of input variables. The placement of the ellipsoid in the weld cross section was varied with x and z according to figure 3.21 below.

Figure 3.21: The cross section of weld geometry and the placement of the double ellipsoid.

The power Q˙_saccording to equation (2.12) were also used as input variables where the arc efficiency was set to η = 0.8. In order to rapidly fit the simulation temperature histories with the experiment measurements, the optimization software Heeds was used. The adaptive optimization algorithm SHERPA was used which is a built-in algorithm that uses the following optimization algorithms:

• Genetic algorithm

• Sequential quadratic programming

• Simulated annealing

(38)

• Response surface methodology

• Multi-start local search

• Particle swarm optimization

• Nelder-Mead Simplex

Sherpa uses these search strategies simultaneously and can therefore find an optimum faster. The lower and upper limits and the initial guess for each input variables are defined in table A.3 and A.4 in appendix A.4.

Solid mechanical model

The solid mechanical model was setup solving weak form of equations 2.14, 2.15 and 2.16 in Abaqus 2019. The temperature histories from the tuned heat source model in chapter 3.2 are used as input. The incremental size was chosen automatically dependent on convergence.

Material properties

The temperature dependent material properties used as input for the solid mechanical model was the Young’s modulus and the coefficient of thermal expansion. Figure 3.22 shows the coefficient of thermal expansion and Young’s modulus as a function of temperature.

Figure 3.22: Youngs modulus and thermal expansion as a function of temperature.

The yield surface was modelled with the von Mises yield criteria, where

f (σ − α) − σ₀ = 0. (3.5)

Where f (σ − α) is the yield criteria, and σ0is the initial yield limit is plotted against temperature according to figure 3.23.

(39)

Figure 3.23: Yield limit as a function of temperature.

The von Mises yield criteria with backstress in equation 3.5 is defined as f (σ − α) =

r3

2(S − α^dev) : (S − α^dev). (3.6) Where S is the deviatoric stress tensor and α^dev deviatoric part of the back stress. The plastic behaviour of the material was modelled with a combined isotropic kinematic hardening model to account for both yielding at heating and cooling of the material during the welding process.

The incremental back stress in this model is defined in equation 3.7 below, where

˙

α = C 1

σ₀ε˙^pl− γα ˙ε^pl− ξ |α|

R¯

m−1

α, (3.7)

where ˙ε^plis the effective plastic strain rate and |α| = q3

2α^dev : α^dev. The parameters C, γ ξ and R, m and the initial yield stress σ¯ 0 are defined for each evaluated temperature in table A.3 in appendix A.2. As the heating and cooling and rapid during the welding process, the hardening behaviour might be affected, therefore a rate dependence was also considered by a Chaboche rate dependent model [38] where

ε˙^pl = ˙ε0

σ − σ⁰ K

n

, (3.8)

where ˙ε₀, K and n are material properties defined in table A.2 in appendix A.2.

(40)

Mesh

The solid mechanical model uses the same mesh as the thermodynamic model but with C3D6 prism and C3D8 hexahedral structural elements with linear shape functions.

Boundary conditions

During the experiments the plates where placed on a weld table which enabled the plates to move and distort freely without any clamping. The boundary conditions were therefore set to imitate the free motion of the plate without causing rigid body motion. By setting node 1,2,3 and 4 in 3.24 below as in table 3.2 these conditions are assumed to be modelled correctly.

Figure 3.24: Nodes for the boundary conditions on the TT-plate.

Table 3.2: The boundary conditions for the TT-plate.

Node \Coordinate x y z

1 0 0 0

2 0 0 free

3 0 free 0

4 0 free free

The OL-plate was also laying on a table while welded. The boundary was set the same was as for the TT-plate by setting the bottom nodes of each corner 1,2,3 and 4 in 3.25 according to table 3.2

(41)

Figure 3.25: Nodes for the boundary conditions on the OL-plate.

Mesh convergence study

With the properties from the heat source calibration the number of elements was increased in the through thickness direction and in the length direction of the plates to evaluate the convergence of the solution. Figure 3.26 a) and 3.26 b) shows the number of elements and the distortions for the TT-plate and OL-platet, respectively. The distortion were measured at 50 mm and 75 mm on edge the edge in figure 4.3 and figure 4.5 for the TT-plate and the OL-plate, respectively. The number of elements chosen for the rest of the analysis are marked with a square in both plots.

(42)

Figure 3.26: Mesh convergence study with the TT-plate a) and the OL-plate b). The square indicates the elements used for from now on.

Simplified Material models

The computational time can sometimes be the limiting factor in larger mechanical models, and sometimes complex material models can increase computational time. This section investigates the influence of the temperature properties specific heat capacity, conductivity, Young’s modulus, coefficient of thermal expansion and yield stress

The specific heat capacity, coefficient of thermal expansion and the yield limit was simplified in three ways by:

• Using fewer data points, and interpolating between the chosen values

• Using only the room temperature value and the value at 800^◦C , and interpolating between the values

• Neglecting the temperature dependence and setting the specific heat capacity to the room temperature value

Figure 3.27 a), figure 3.28 a) and 3.29 shows the three different simplifications for the specific heat capacity, coefficient of thermal expansion and the yield limit respectively. The conductivity and the Young’s modulus were simplified in two ways by

• Use only the room temperature value and the value at 800^◦C , and interpolate between the values

• Neglect the temperature dependence and set the specific heat capacity to the room temperature value

(43)

Figure 3.27 b) and figure 3.28 b) shows the simplifications for the conductivity and the Young’s modulus respectively.

Figure 3.27: Simplifications for specific heat capacities a), and the conductivities b).

Figure 3.28 shows simplifications evaluated for the coefficient of thermal expansion to the left and simplifications evaluated for the Young’s modulus.

Figure 3.28: Simplifications for the coefficient of thermal expansion a), and Youngs modulus b).

Figure 3.29 shows the simplifications made for the yield stress.

(44)

Figure 3.29: Simplifications of the temperature dependent yield stress.

The computational time for the thermodynamic and the structural mechanical analysis was then compared with the computational time without changes. The effect of those simplifications were calculated by comparing the distortion results to the non-simplified model.

Tetrahedral elements

There are automated 3-D meshing algorithms for which gives the advantage of a more rapid and simpler meshing procedure. To evaluate the accuracy of tetrahedral elements the TT-plate was meshed with tetrahedral elements with linear shape functions according to figure 3.30 below.

Figure 3.30: The TT-plate meshed with first order tetrahedral elements, and a close up of the refined area around the weld.

The heat input model used the calibrated input variables according to table A.5. The thermal histories where calculated and compared with the experimental measured values for S1, S2, S3 and S4 in figure A.1.

Both linear and second order shape order functions where used in the solid mechanical analysis.

(45)

With the linear shape functions, the solid mechanical analysis used the same mesh but for the second order shape functions the component was re-meshed according to figure 3.31.

Figure 3.31: The TT-plate meshed with second order tetrahedral elements and a refined view to the left.

The temperature histories where interpolated from the thermal analysis, as this analysis used a different mesh. To evaluate the accuracy the distortions was compared to the experiment.

Optimization of start/stop positions on a full size component

This part of the report is about applying the methods used in the previous sections on a full size component typically found in the after-treatment system. The component evaluated is typically found on the silencer with a thin plate structure welded onto a thick plate. Figure 3.32 a) shows an isometric view of the component with the weld bead in yellow, and figure 3.32 b) shows the top view with dimensions.

Figure 3.32: Isometric view of the component a) and top view b), with three dimensions in [mm].

The weld is emplaced in one pass with only one start and stop position, this is due to that the weld works as a sealing for exhaust gases on the after-treatment system. Only one start and stop position minimize the number of fatigue initiation spots to one.

(46)

The start and stop positions for the welding process are then varied in 10 different configurations to evaluate if a change in start and stop position could decrease the distortions after welding.

Thermodynamic model

The moving heat input model parameters used was the same as for the TT-plate according to table A.3. The thermodynamic properties were taken from 3.16. The start and position for the moving heat source was varied with 5 different positions. The direction was also varied for each start and stop position, either clockwise or counterclockwise direction. Figure 3.33 shows the different start and stop positions and the direction of welding.

Figure 3.33: Weld paths and arrows describing the welding path in clockwise direction.

After the welding sequence has been finished second step of 17 minutes was applied to simulate the cooling of the plates. During this step no heat input was applied and the was heat is distributed only due to the conduction in the material and the convection of the surfaces.

The component was meshed with hexahedral elements close to the weld bead to retain the distortion accuracy. Further away from the weld bead the component was meshed with tetrahedral elements by an automated meshing algorithm. Figure 3.34 shows the cross section of the weld bead with the transition to tetrahedral elements.

(47)

Figure 3.34: Cross section of the meshed bigger component.

The total number element is 194 037.

Solid mechanical model

The temperature histories from the thermodynamic model was used as input for the solid mechanical analysis. To simulate clamping during the welding process, each node at the surface of the holes 1,2,3 and 4 in figure 3.35 was set to a zero-displacement constraint during welding.

Figure 3.35: Clamping positions of the component and a coordinate system.

After the cooling step the zero-displacement constraint on the nodes on the surfaces of the holes 1,3 and 4 was released. The maximum displacement was then calculated in the z-direction for each configuration.

(48)

4 Results

4.1 Heat source calibration

The temperature histories for the tuned FEM simulation and the measured temperature history for the OL-plate and the TT-plate is shown in Figure 4.1 a) and b), respectively. All four thermocouples S1,S2, S3 and S4 are in good agreement with the experiment for the OL-plate, for the TT-plate however, the thermocouples S2, S3 and S4 shows good agreement with the simulated temperature history but S1 has a much higher peak temperature compared to the simulation.

Figure 4.1: FEM and average experiment temperature histories for OL-plate a), and the TT-plate b).

The tuned parameters for the OL-plate and the TT-plate for each heat source are shown in table A.5 in appendix A.5.

(49)

4.2 Distortions

The simulated distortions show a similar distorted shape as the experiment with substantial angular distortions. Figure 4.2 shows the distortions in the z-direction.

Figure 4.2: Distortions in the z-direction for the TT-plate (with 3x scaling).

The distortions along the edge shown in figure 3.12 are shown in figure 4.3 below for hexahedral elements, first and second order tetrahedral elements compared with the average value with standard deviation for the 4 measurement points from the experiment.

Figure 4.3: Distortions in the z-direction in [mm] for the TT-plate along the edge in figure 3.14.

The tetrahedral elements with second order shape functions shows the best agreement with the

(50)

experiment followed by the hexahedral elements. The distortion shape is captured, but the experiment exhibits more bending distortions.

The OL-plate has a more complex distorted shape with both angular and bending distortions.

Figure 4.4 below shows the deformation for the OL-plate in the z-direction.

Figure 4.4: Deformation in the z-direction in [m] for the OL-plate (with 3x scaling).

The distortions along the edge shown in figure 3.14 are shown in figure 4.5 below for hexahedral elements compared with the average value with standard deviation for the four measurement points from the experiment.

Figure 4.5: Distortions in the z-direction in for the OL-plate along the edge length in figure 3.12.

The distortion shape is a bit different for the experiment as the simulation has a more symmetrical shape with almost the same distortions at the ends.

(51)

4.3 Simplified thermal models

Figure 4.6 shows a comparison between the non-simplified model and the simplified models in temperature histories for point S2. From this plot it can be concluded that the conductivity can be set to be constant and that the specific heat capacity can also be simplified, but not as a linear or a constant without losing accuracy.

Figure 4.6: Comparison of the temperature histories for the location S2 between several simplifications in the thermal material model.

Table 4.1 shows a comparison between the computational time for each simplification.

Table 4.1: Comparison between computational time for each simplification.

Simplification Computational time [s]

No Simplification 962.19

Simplified specific heat capacity 886.25 Constant conductivity 903.44

(52)

4.4 Simplified mechanical models

Table 4.2 shows the difference in distortion in z-direction in the middle of the TT-plate edge as well as the computational time for each simplification.

Table 4.2: Comparison between computational time and deformation for each simplification on the mechanical model.

Simplification Computational time [minutes] deformation [%]

No Simplification 100 100

Simplified thermal expansion 102.3 100.2

Constant thermal expansion 68.7 77.2

Simplified Young’s modulus 217.8 101.9

Constant Young’s modulus 506 98.8

Simplified yield stress 99.3 92.9

Constant yield stress 18 40.2

(53)

4.5 Optimization of start/stop positions on a full size component

Figure 4.7 a) shows the distortions in the z-direction after the plate has cooled down for start and stop position 1, before the clamping were released. Figure 4.7 b) shows the distortions after clamping were released.

Figure 4.7: Displacement in z-direction before and after release of clamping.

Figure 4.8 shows the maximum distortions after the clamps were released for five different start and stop positions.

Figure 4.8: Distortions for the edge of the plate at different welding start and stop positions.

The CPU-time for the thermal analysis was 27 hours and five hours for the structural analysis.

The computational time to evaluate ten design was 320 CPU-hours, with the Scania cluster it was possible to evaluate four designs in parallel which gave a total time of 80 hours or three days.

(54)

5 Discussion and conclusions

The distortion modes are captured with the FE-model with good accuracy for the TT-plate, but the distortion shape is more symmetric in the simulation results compared to the experiments for the OL-plate. The distortions are overestimated the OL-plate and slightly underestimated for the TT-plate.

The TT-plate model with the tetrahedral elements with second order shape functions shows the best agreement with the experiment, but with hexahedral elements with linear shape functions does also predict the distortions with quite good accuracy. The tetrahedral elements with linear shape functions are most off from the experimental measurements. This result is not surprising as the tetrahedral elements with second order shape functions do not have the strain inconsistency mentioned in theory section 2.7. The second order tetrahedral elements do not have the same problem of artificial stiffening.

The temperature histories recorded from the test show a quite substantial scatter for both plates.

The scatter can be due to several causes, one is the that the plates were manually welded, and the welding speed and power input differs for each specimen. If the welding time in table 3.1 and temperature histories figure A.1 and 3.9 are compared, the longer welding time the higher temperatures are in general. This correlation seems reasonable as the welding power is almost constant, which means that more heat is inserted into the plate and therefore resulting in more distortions.

The temperature histories from the FE-model is quite good agreement with the tests for OL-plate.

The TT-plate is in good agreement with the test but the simulated temperature history for thermocouple S1 is off by 22 % at the peak temperature compared to testing. The other temperature histories S2, S3 and S4 for the TT-plate are very close to the experimental temperature histories.

This might mean that the material properties are modelled correctly but the behaviour close to the weld fusion zone is not accurately captured. One reason could be that the gap between the thick and the thin plate shown in figure 3.11 for the TT-plate is not modelled, this means that heat can be transferred within the material in the simulation and not in the experiment, and thus resulting in a different behaviour close to the weld fusion zone.

As mentioned in the theory section 2.6, at least four hexahedral elements are needed in each half plane in figure 2.11. Therefore, the need for many elements when tuning the heat source is important as one does not know the size of the heat source and therefore do not know how many elements are needed. But when the heat source is tuned it is possible to reduce the number of elements and still accurately predict the distortions with a decrease in computational time, as shown in the mesh convergence study.

FE-model for prediction of welding distortions in components made of preformed stainless steel sheets