Simulation of laser welding in sandwich rocket nozzle

Abstract

This bachelor thesis has been carried out at GKN Aerospace. GKN is a member of European Space Agency, designing and manufacturing rocket-nozzles for the Ariane rockets. The

manufacturing process entails many welds. Weld-simulations have been made to investigate

stresses and plastic strains on simplified geometries. Plastic strains have been evaluated

parallel and normal to the weld for plate geometries of shell-elements with rectangular cross-

section and sandwich-cross-section, using the FEM-program MSC.marc. Results shows that

plate width and length have negligible effect on the plastic strains when one weld is made. A

comparison between a sandwich-sector cone and a sandwich plate was made, to investigate

how plastic strains and stresses were affected of geometry. Plastic strains and stresses parallel

the weld are the same. Plastic strains and stresses normal the weld are affected by changing

geometry. Studies on differences in stresses between solid and shell elements propose use of

solid elements near the weld region, if stresses are of interest.

Fakulteten för teknik- och naturvetenskap

Simulation of laser welding in sandwich rocket nozzle

Filip Elfving

Examensarbete vid maskiningenjörsprogrammet

2015-05

Contents

1 Introduction ... 1

1.1 Restrictions ... 1

1.2 Background ... 1

1.3 Purpose/goals ... 2

1.4 Problem formulation ... 2

2 Method ... 3

2.1 Sandwich nozzle ... 3

2.2 Manufacturing ... 4

2.3 Welding ... 5

2.4 Programming tools/Theory ... 6

2.4.1 Analysis-type ... 6

2.4.2 Loads ... 7

2.4.3 Heat input ... 7

2.4.4 Convection and radiation ... 8

2.4.5 Material properties ... 8

3 Simulations ... 9

3.1 Simple-plate ... 10

3.1.1 Results ... 14

3.2 Sandwich plate ... 16

3.2.1 Sandwich plate with shell elements ... 17

3.2.2 Sandwich plate with solid elements ... 24

3.3 Sandwich-sector cone ... 28

3.4 Comparison of Sandwich sector cone and Sandwich plate of shell elements ... 33

3.4.1 Results ... 35

4 Discussion and conclusions ... 38 5 Recommendations for further work ... 39 6 Referensces ... 40

Nomenclature:

T-joint: geometry shaped like a T

SW: sandwich-plate

SP: single-plate

1

1 Introduction

This is a bachelor thesis. The work has been carried out at GKN Aerospace in Trollhättan, Sweden, where Eva Stenström has been my mentor. Göran Karlsson has been my mentor on the University of Karlstad at the department of engineering and physics. This thesis is a part of the program in mechanical engineering. For this course is Nils Hallbäck the examinant.

1.1 Restrictions

Material properties, exact dimensions of sandwich-cross-section and weld parameters are not included in this public version.

1.2 Background

GKN was founded in England on 19th September of 1759. The company grew fast. 1855 it became the world's largest ironwork. Since then the company has changed orientation more than one time. 2012 GKN acquired the Volvo Aero Group. GKN in Trollhättan (former Volvo Aero Corporation) has participated in the European Ariane launcher programme with the production of the thrust chambers for the Viking rocket engines and the Vulcain rocket engines. Today the company plays a growing role in the development of the world’s future space transportation systems mainly through assignments from ESA (European Space Agency), such as Ariane 5.

The studied product in this thesis is the sandwich wall of a rocket-nozzle. The sandwich- technology for the rocket-nozzle is a channel wall concept based on channels milled in a thick inner cone. The channels are closed by laser welding of a thin outer cone to the mid walls [1].

The nozzle is 2 m long, have a top diameter of approximately 0,5 m and a bottom diameter of 2 meter.

At GKN welding simulations has been carried out for several years. With welding simulations,

residual deformations and stresses due to welding can be estimated.

2

1.3 Purpose/goals

The heat input from welding leads to residual deformations and residual stresses, which must be handled from a manufacturing and design point of view. The weld tooling and welding sequence have a large impact on the residual deformations and stresses respectively. FE modeling and coupled (thermo-mechanical) analyses of the T weld sequence can be helpful for the understanding of the deformation and stress behavior.

In the development phase, T weld tests are performed, first on simplified specimen, then on components more and more like the final product.

Some questions on deformations and residual stresses from welding can be predicted on the simplified specimen, but others cannot due to differences e.g. in constraints.

The purpose of the Thesis is to analyze and evaluate residual deformations and stresses from T welding of plate and cone geometries with sandwich cross-section and to describe how and why they differ.

The job will be limited to studies of plane plates, plane sandwich models and downsized sandwich –sector cones.

1.4 Problem formulation

Residual stresses and deformations will be evaluated with coupled (thermo-mechanical) finite element analysis performed with the commercial code Marc.

A full size nozzle consists of around 1000 laser welds, each with a length of 2 m. An FE model of a sandwich wall of that size should be far too big to handle in a coupled analysis, why problems have to be broken down and solved using much smaller models.

The weld simulations treated in this report are first made on single shell geometries of plane plates, then increasing them in complexity to sandwich plates made by shell elements. A limited number of analyses will be made with solid elements models of sandwich plates in order to estimates residual stresses. Finally some studies will be carried out on downscaled sandwich cones, modeled with shell elements.

In order to study a number of different geometries in shell and solid element models within

the thesis work, the analysis time should preferably not be longer than 1 hour.

3

2 Method

In this section the different parts of a sandwich-nozzle will be described. There will be a review of the manufacturing process. The welding process will be explained more detailed.

2.1 Sandwich nozzle

Figure1 shows three different rocket nozzles, with the Sandwich nozzle in the middle. All nozzles are made of GKN. Major characteristics of these nozzles are low weight, large

dimensions in length and width compared to thickness. Reference [2] gives more information of rocket nozzles from GKN. Figure 2 shows the cross-section of a SW. Figure 3 shows the T-joint which is investigated, seen in the section of simulations. Figure 4 shows a sector of a sandwich nozzle. The blue areas indicate the wall that the outer sheet is to be welded on. The red area indicates places were the two of the other three sectors is to be merged.

Figure 1. Three different rocket nozzle extensions from GKN

4

2.2 Manufacturing

The green areas of figure 2 are milled channels. Red areas represent the inner-wall of a SW.

The outer wall is represented by blue color. The outer-wall is merged to the inner-wall by T- welding; seen in figure 3.

Figure 2. Cross-section of a SW

Figure 3. T-joint, where the yellow color symbolize molten metal. The arrow show welding direction

Figure 4. Inner sector of rocket-nozzle

5

2.3 Welding

The procedure of joining metal pieces involves a process where metal has to be molten. There are several methods available. All methods have their pros and cons. Welding of thin and large structures, like rocket nozzles, demands a welding method which induces little relative heat to avoid large deformations and/or stresses. The welding handbook, [3], shows that laser-beam welding (LBW), electron-beam welding (EBW), plasma-arc welding (PMA) and gas tungsten arc- welding (GTAW) are possible methods. EBW, LBW and PMA can merge material at a depth of more than 3 mm [3]. The use of GTAW is useful for manual adjustments of structures thinner than 3 mm [3].

In the following content laser welding will be described more detailed, since it's used for the sandwich nozzle T-joints. The high power-density of the laser beam is transported via

radiation. When temperature is elevated enough the metal melts. Sokolov and Salminen show how a proper melt should look like [4]. Laser welding has the advantage of deep penetration because it can focus the high power to a small area. It makes the metal to vaporize where the beam interacts. This allows for deeper welding. The phenomenon which occurs is making a characteristic “keyhole” [4]. A channel is then made by the moving laser. The channel is filled by molten metal as the laser bypass. Figure 5 shows a cross-section of a work piece. The characteristic described above is showed in figure 5. The blue area above the work piece is vaporized metal, the red color is the laser and weld-direction is indicated by an arrow.

Figure 5. Characteristics of a laser weld. The keyhole is symbolized by the light gray area.

6

2.4 Programming tools/Theory

Some features that is essential to understand when doing Coupled analysis is shown below 2.4.1 Analysis-type

For the analysis the FEM program MSC.Marc have been used. Marc was founded by Marcal and Hibbit; pioneers in the field of solving nonlinear FEM problems. Marcal [5] stated, “Welding is perhaps the most nonlinear problem encountered in structural mechanics”. To face this nonlinear problem, a coupled analysis is used by Marc. A coupled analysis is needed when deformations result in a change in the associated heat transfer problem. Such a change can be due to either large deformations or contact with conducting materials. MSC.Marc uses a staggered solution procedure in the coupled thermo-mechanical analysis. It first performs a heat transfer analysis then a stress analysis. This procedure is seen in figure 6 where X and Y indicate two separated physical fields. The substitution (S) and the predictor (P) connect the physical fields. Söderberg [6] gives a good description of how the staggered approach works in detail. In welding-simulations elasto-plastic material properties is used since the simulated body undergoes both elastic and plastic deformation.

Time

Figure 6. Sequential staggered solution of coupled problem [6]

Time step h

X

P S P S P S

Y

7 2.4.2 Loads

Applied loads to the model are in form of heat-input from the weld and heat-output by convection and radiation. The heat input to the model is active as long as the weld is present.

Heat energy is transported within the body by conduction. The energy is then dissipated by convection and radiation until it reaches ambient temperature. A quasi-static analysis is made.

The coupled problem is divided in many but small static problems. In Figure5 above, each of the two physic-fields X and Y is constant during the time step h. Before MARC continue to next time-step, force -and temperature-equilibrium is checked. The basic equations are:

Söderberg [6] show how both of these conditions are meet. An incremental numerical approach is then used to solve these equations (Marc uses the Newton-Raphson method).

2.4.3 Heat input

The heat-source from the weld is modeled as a volume heat flux. Goldak [7] proposes a volume heat flux to be modeled as a double ellipsoid. This definition for heat input is used by MARC.

Figure 7 accompanied by equation (3) and (4) [6], present the heat-distribution from the weld.

Equation (4) is used for the frontal ellipse, where Z > 0, [8]

and the other for the rear ellipse, Equation (5) z < 0.

Figure 7. Geometrical definition of the double ellipsoid heat source

C

(4)

Weld-direction

Cr

8 2.4.4 Convection and radiation

Energy dissipating from the body due to convection is stated in equation (6):

Where A is the surface area, h is the heat transfer coefficient, refers to the surface temperature and to the ambient temperature.

The energy loss from radiation is expressed by:

is Stefan-Boltzmann’s constant and ε is the emissivity factor, varying from [0,1].

2.4.5 Material properties

Material properties can be divided into physical properties and elasto-plastic data for different temperatures. Appendix A show diagrams of material properties as function of temperature (only given for the internal GKN report). Phase changes and hardening of the material due to plastic deformation occur in the material. The area around the weld region is affected since the temperature changes rapidly there.

(5)

(6)

9

3 Simulations

Parameter studies have been made on one or combinations of the following:

 Dimensions

- Width - Length

 Geometric shape

 Mesh density

Each sub section describes problems treated with one type of FE model at the time, starting with a description of the problem, the model used and results.

Before getting into the analysis and result sections, it should be pointed out:

- The sandwich plane plate models and the sandwich cone models had no weld gaps between the inner wall and outer sheet. The reason was to reduce the complexity of the models and analyses.

- None of the models had a weld fixture (bottom plate under the plane models or

inner, rigid fixture in the cone models). In some cases this reflects the true behavior

of the real hardware, in others it does not.

10

3.1 Simple-plate

Purpose of the simulations

 Do plate dimensions affect plastic strains along and across the weld Geometry/ FE model

The simple-plate (SP) is described by a 3 mm thick single shell elements with rectangular shapes. The width (B) and length (L) have been varied for the SP, seen in table 4. There is one weld in the middle of the plates starting and ending 5 mm from the ends, seen in figure 8.

Figure 8. Characteristics of SP

Table 1. Different models of SP

SP Dimensions [BxL] mm 1 452x115

2 45x115

3 116x115

4 200x115

5 200x150

6 200x215

11 Properties for the elements used:

Mechanical element (ID 75 in Marc)

 Bilinear, four-node shell element

 Six degrees of freedom per node

 Constant transverse shear-stress through thickness

Thermal element (ID 85 in Marc)

 Linear temperature distribution through thickness- two degrees of freedom per node

Other properties:

Material properties: Haynes 230, see Appendix A (only given in the GKN version of the report). The same weld power, speed and weld parameters were used for all analyses. Data was given by GKN weld engineers and typical for laser welding of T welds in Haynes 230.

Constraints

Mechanical boundary conditions were used so the plate could be as free to move as possible, in order to compare to other geometries. BC_fix is the applied mechanical boundary conditions shown in Figure 9.

Figure 9. Constraints for SP’s

12 Loads and load cases

Loads were the same in all SP simulations. The analysis included one weld load-case followed by a cooling load case, where the geometry was cooled down by convection and radiation to initial temperature (293 K). Radiation and convection loads were applied on all faces of the models. Table 2 below shows the applied loads, where Rad_conv are the loads from radiation and convection; weld_0 is the load from the weld. Indices w=weld and c=cooling describing the load cases in the left column of table 2. The convection load has a typical value for simulation of root gas or shielding gas. Radiation takes place between the metal and surrounding air.

Table 2: Load sequence, loads and constraints, all SP analyzes

Load-case BC_fix Rad_conv Weld_0

w_weld_0 X X X

c_weld_0 X X

Evaluation of results

Results are evaluated as indicated in figure 10. Strains are measured along path P1, black arrows indicate the strain components. The components directions are parallel and normal the weld. The measure is just outside the weld-pool.

Figure 10. Show were plastic strains are measured (path1)

13 HAZ

Figure 11 shows the temperature distribution during welding. The white area represents the molten metal. A fine mesh is needed in the melted area and in the HAZ (Heat Affected Zone).

Outside the weld and HAZ, figure 12b, the element size can be increased, since lower stresses and deformations are expected here. There is a large temperature difference around the weld.

At raised temperature the material expands in proportion to the temperature. The temperature distribution is not constant. Plastic strains occur when material is constrained to expand. Figure 12a shows plastic deformation after welding, measured across the width (B) of the plate, seen in figure 8 and 10. As seen the plastic area is concentrated to the weld and HAZ area.

Figure 11. Temperature distribution during welding

Figure 12. Plastic deformation measured across the weld a) and heat affected zone b) [3]

14 3.1.1 Results

Figure 13 and 14 show how different plate widths and lengths affect plastic strains. Plastic stains normal and parallel the weld are measured along path p1, figure 10.

Figure 13. Plastic strain normal weld along path 1. The labels (e.g. 452x115) equal the width x length of the plates.

Figure 14. Plastic strain parallel weld along path 1

15

Figure 15 show two plates with different widths. The narrow plate gets an elevated temperature at its borders. The plastic strains are then affected, seen in figure 13 and 14 for the plate of 45x115 mm.

Figure 15. Welding of two plates with different widths

Conclusions from the simulations of the simple plates

 The plastic strain normal the weld is not dependent of plate dimensions (as long as the plate is sufficiently wide). It is local and appearing in the HAZ.

 The plastic strain parallel the weld is proportional to the length of the weld (a short

start/stop distance of typically 10-20 mm should be excluded when calculating the

shrinkage).

16

3.2 Sandwich plate

Two different element types have been used for the sandwich plate (SW). Shell elements are used when comparing deformations and solid elements is used when comparing stresses around the weld region [9]. General information of the SW that applies for both shell and solid (SW) are listed below.

Geometry/FE-model

Sandwich plate (SW) is defined by two plates with mid walls between them. Different width (B) and length (L) have been varied. Height (h) does not change, see figure 16. All surfaces have the same thickness.

Figure 16. Characteristics of SW

Loads

A weld load case was first applied, where the heat source is moving straight across the plate along a weld path, see figure 16. Weld parameters have been given by GKN weld engineers, convection and radiation loads are the same as used for SP in previous chapter. The simulations had the same basis as for the SP. The analyses included weld load-cases followed by cooling load-cases, seen in table 1. Initial temperature of (293 K) was set as the limit for all cooling load-cases.

K

17 Constraints

The SW is constrained in the same manner as for SP in previous chapter. The yellow arrows indicate constraints of motion in its direction (x,y,z).

Figure 17. Constraints symbolized by yellow arrows

Evaluation of results

Results are evaluated along path p1, which is next to the weld and outside the weld pool. The component directions are parallel and normal the weld, se figure 17.

3.2.1 Sandwich plate with shell elements

For the SW-shell the effect of dimensions on plastic strains are investigated. Two SW-shell models have been made for latter comparison with the sandwich-sector cone, chapter (3.4).

They have the same length (L) but different plate widths (B) and channel width (K). They will not be compared to the other SW-shell models and are presented in its own chapter.

Properties for the shell-elements are seen in previous chapter (3.1). Same shell-elements are used as for the SP.

z

x

y

18

3.2.1.1 Sandwich plate with different width and length

Purpose of simulation

 Investigate plastic strains for different plate dimensions (B,L)

 Investigate shrinkage straight over the weld as function of welds made

Table 3 shows the different dimensions of the analyzed sandwich plates. Results are evaluated as seen in figure 17, along path 1. Figure 18 show three weld-paths parallel to each other in the middle of the top side of the SW. The weld paths are spaced 11 mm apart.

Table 3. SW-shell simulations

SW Dimensions Number of welds made

1 116x115 1-3

2 452x116 1-3

3 116x240 1-3

4 12x115 1-3

Figure 18. Three weld-paths parallel to each other

19

3.2.1.1.1 Results of sandwich plate with different width and length

Plastic strains normal weld direction is seen in figure 19. The SW-shell plates 452x115 and 115x120 have the same plastic strain. The longer plate (240 mm) have almost the same plastic strain value compared to the shorter plates at 50% of the its normed length. Figure 20 show plastic strain parallel to the weld, around the middle of the graph it is seen that the plastic strains not differ so much. The SW-shell with a length of 240 mm has a steeper curve at the start/stop of the graphs after normalizing the length.

Figure 19. Plastic strains normal weld for different SW-shell dimensions

Figure 20. Plastic strains parallel weld for different SW-shell dimensions

20

The length shrinkage is measured over the plate length (L) straight across the weld. Figure 21 show shrinkage as function of number of welds made on a plate with the same dimensions. The shrinkage rise when more welds are made.

Figure 21. Length shrinkage straight across the weld as more welds are made

Conclusions

 The plastic strain normal the weld is almost the same for the different plates. Plastic strain parallel weld are the same. The trends are seen to be the same as for the simple plate in previous chapter.

 The length shrinkage along the plate length (L) measured across the weld rise when

more welds are made.

21 3.2.1.2 Sandwich shells with different channel width

The SW-shells with different channel widths are used in a comparison of stresses and plastic strains with a sandwich sector cone model in chapter (3.4). To make a more accurate

comparison the channel width’s impact on stresses and strains measured parallel the weld has to be made. The channel of the cone varies with its height. The width of the channels has been chosen to capture the variation from the large channels at the bottom and the small channels at the top of the cone. More description seen in chapter (3.4)

Purpose of simulation

 Investigate plastic strains for different channel width (K)

 Investigate stresses for different channel widths

Table 4 shows the different channel widths (K) and the overall plate width (B), se figure 16.

Loads, constraints and evaluation of the results are described in chapter 3.2. The widths of the two plates in Table 4 are chosen so they are the same as the width of the cone sector at two given heights, see further section 3.4.

Table 4. SW-shell simulations made for latter comparison

SW denomination Dimensions [mm] Channel width (K) [mm]

Smal 95,628x111 K=5,626

Bred 136,487x111 K=8,03

22

3.2.1.2.1 Results of sandwich plate with different channels widths

Plastic strains parallel weld direction is seen in figure 22. The definition of “bred” and “smal” is seen in table 4. The plastic strain component parallel the weld is the same. The plastic strain component normal the weld is difference for the SW-shells seen in figure 23. The curve has the same form but have different plastic strains.

Figure 22. Plastic strain measured at path plot1, plastic strain component parallel the weld

Figure 23. Plastic strain measured at path plot 1, plastic strain component normal to the weld

-0,02 -0,01 -0,01 0,00 0,01 0,01

0 20 40 60 80 100 120

p l s tr ai n [ -]

plastic strain in the weld direction

eppl22_bred_1400W eppl22_smal_1400W

-0,030 -0,025 -0,020 -0,015 -0,010 -0,005 0,000

0 20 40 60 80 100 120

p l s tr ai n [ -]

path [mm]

plastic strain normal to the weld direction

eppl11_bred_1400W

eppl11_smal_1400W

23

The stresses are seen to not vary so much seen in figure 24 and 25

Figure 24. Stresses measured at path plot 1, stress component normal to the weld

Figure 25. Stresses measured at path plot1, stress component parallel to the weld

-600 -500 -400 -300 -200 -100 0 100 200 300

0 20 40 60 80 100 120

stre sss [ M P a]

stress normal to the weld direction

S11_bred_1400W S11_smal_1400W

-100 0 100 200 300 400 500 600 700

0 20 40 60 80 100 120

stre ss [M p a]

path [mm]

stress in the weld direction

S22_bred_1400W S22_smal_1400W

24 3.2.2 Sandwich plate with solid elements

Solid and shell elements have not the same FEM formulation therefore may the results be differently.

Temperature gradients and stresses at the weld region are investigated for these element types. Loads, constraints and dimensions of the models are kept the same. Stresses are evaluated in cool condition along a path plot parallel and next to the weld.

Purpose of simulation

 How differ the temperature gradients with respect to element type at the weld region

 How differ the stresses with respect to element type at the weld region

Figure 26 show the components of normal stresses on a solid element. The shell element has no component in the y-direction (out of plane).

Figure 26. The x,y,z- axes show the direction of stresses for solid element

25

Figure 27 shows the temperature distribution on top of the SW-plate of shell elements. The gauge to the left shows temperature scale in [K]. Figure 28 show temperature through the thickness of SW-plates, solid element to the left and shell elements to the right. In the shell definition used for the heat transfer problem it’s assumed that the temperature is constant through thickness whereas the temperature varies linearly for the SW-solid. The SW-shell is seen to get higher temperatures at the bottom side compared to SW-solid. Mid walls and the top side have almost the same temperature distribution.

Figure 27. Welding of SW-shell, where the temperature distribution is seen on the top of the SW-plate

Figure 28. Temperature measured through the thickness of a SW-plate with solid and shell elements

top

Bottom

26

Figure 29 to figure 31 shows a quite big change in stresses for the element types. Note that the shell element has no component in the y-direction seen in figure 26.

Figure 29. Stress component normal weld measured at a path plot next to and parallel weld

Figure 30. Stress component parallel weld measured at a path plot next to and parallel weld

Figure 31. Stress component in y-direction measured at a path plot next to and parallel weld -600

-400 -200 0 200 400

0% 20% 40% 60% 80% 100% 120%

Ϭ[Mpa]

Length

stresses normal weld

solid shell

-200 0 200 400 600 800

0% 20% 40% 60% 80% 100% 120%

Ϭ[Mpa]

Length

stresses parallel weld

solid shell

-10 0 10 20 30 40 50

0% 20% 40% 60% 80% 100% 120%

Ϭ[Mpa]

Length

stresses through thickness of weld

solid shell

27 Conclusions

 If stresses are the desired result solid element should be used.

 The temperature distribution through the thickness of the outer wall showed to be

quite small (around 50 K). Therefore the approximation with a constant temperature

used in the shell element models gives a fair approximation.

28

3.3 Sandwich-sector cone

Purpose of simulation

 Evaluate plastic strains normal and parallel weld

 Evaluate residual stresses normal and parallel weld

Geometry/FE-model

The sandwich-sector cone is built of the same cross-section as SW seen in figure 16. The cone has a diameter that varies from D_bot to D_top with the height (h), seen in figure 32a. A 90 degree sector is used for simulations, figure 32b. Thickness for all surfaces is the same as for the plane model (SW), (1, 5 mm). The height (h) of the cone has been kept constant. The mesh in the weld and HAZ zone is also the same as on the plate models in chapter 3.2.1, the elements of this area has a constant width and length. The model is built of shell-elements that have the same properties as the ones used for SW-shell. Material used is Haynes 230.

Figure 32. Cone a) and sector of cone b)

29 Constraints

The sector of the cone is completely constrained tangentially at its borders. No movement is allowed in that direction, see figure 33, but the model can move in the radial and axial direction.

The cone is constrained axially and radially at the black dots at the top of the sandwich-sector, seen in figure 33. Totally four nodes are constrained axially and two nodes radially.

Figure 33. Sector of sandwich-cone with constraints

30 Loads

A weld load case was first applied, where the weld was moving from bottom and up. When finished a cooling load case cooled the sector down to initial temperature. The sector model used the same weld parameters, convective and radiation loads as for SW-shell “smal” and

“bred”, for which comparisons with respect to plastic strains and stresses are presented in subsequent chapter.

Evaluation of results

Stresses and strains are evaluated along a path plot just beside and outside the weld pool, se figure 34. The stress and plastic strain components used are parallel and normal the weld. All results are evaluated in cool condition.

Figure 34. Sector of sandwich cone during welding

31 3.3.1.1 Results of sandwich sector cone

Plastic strains measured as indicated in figure 34 are showed in figure 35 and 36.

Figure 35. Plastic strain component parallel to the weld

Figure 36. plastic strain component normal to the weld -1,4%

-1,2%

-1,0%

-0,8%

-0,6%

-0,4%

-0,2%

0,0%

0,2%

0,4%

0,6%

0 20 40 60 80 100 120

ε

[%]

length[mm]

plastic strain parallel weld

eppl22_kon_1400W

-2,0%

-1,8%

-1,6%

-1,4%

-1,2%

-1,0%

-0,8%

-0,6%

-0,4%

-0,2%

0,0%

0 20 40 60 80 100 120

ε

[%]

length[mm]

plastic strain normal weld

eppl11_kon_1400W

32

Stresses measured as indicated in figure 34 are showed in figure 37 and 38.

Figure 37. Stress component parallel to the weld

Figure 38. Stress component normal to the weld -200

-100 0 100 200 300 400 500 600 700

0 20 40 60 80 100 120

Ϭ[Mpa]

length[mm]

stresses parallel weld

S22_kon_1400W

-600 -500 -400 -300 -200 -100 0 100 200 300

0 20 40 60 80 100 120

Ϭ[Mpa]

length[mm]

stresses normal weld

S11_kon_1400W

33

3.4 Comparison of Sandwich sector cone and Sandwich plate of shell elements

To make a comparison between the sector-cone and SW every parameter of the models compared has to be as equal as possible.

Purpose of simulation

 Compare plastic strains of sandwich-sector and sandwich-plate

 Compare stresses of sandwich-sector and sandwich-plate

Geometry/FE-model comparison

Two different SW plane plate models were made to investigate the effect of the varying channel width on the sector-cone. The SW model ‘bred’ seen in chapter 3.2.1 with the large channels K2 has the same channel width as the cone a distance from the bottom. They also has the same width S2=B, see figure 39. The SW model ‘smal’ has same channel width (K1) and global width (S1=B1) as the sector-cone a short distance from it’s top. The geometry of the SW and sector- cone is described in chapter 3.2 and 3.3 respectively. Note that the element size is the same in both the sector cone and SW around the weld region.

Figure 39. The comparison of the SW and cone model

top

Bottom

34 Constraints

The constraints of the Sector-cone and the SW are seen in figure 40. Figure a) showing two pictures of the sector-cone. The left picture show the constraints at the top of the cone and the right showing the completely tangentially constrained borders. Figure b) show the constraints for the SW. The weld starts at the bottom and moves forward to the top of the sector cone and SW.

Figure 40. Two pictures of the sector cone standing and lying a) SW b)

Loads

The same weld parameters have been used for the sector cone and SW. The load sequence is the same as for all previous analyses, as well as radiation and convection parameters.

Evaluation of results

Plastic strains and stresses are evaluated at the same distance from the weld for both models.

The path plot used is P1, seen in figure 40.

P1

P1

35 3.4.1 Results

Plastic strain normal the weld for the SW and sector cone have the same form on the plastic strain curve, figure 41. The small SW plate has largest plastic strain and the sector cone has the least. The plastic strain normal the weld is increasing along the path plot from (20 to 80-90 mm) for all the analyzed models. Figure 42 show that the plastic strain parallel weld is the same for SW and sector cone.

Figure 41. plastic strain component normal to the weld

Figure 42. Plastic strain component parallel to the weld

-0,030 -0,025 -0,020 -0,015 -0,010 -0,005 0,000

0 20 40 60 80 100 120

p l s tr ai n [ -]

path [mm]

plastic strain normal to the weld direction

eppl11_kon_1400W

eppl11_bred_1400 W

weld direction

-0,015 -0,010 -0,005 0,000 0,005 0,010

0 20 40 60 80 100 120

p l s tr ai n [ -]

path [mm]

plastic strain in the weld direction

eppl22_kon_1400W eppl22_bred_1400W eppl22_smal_1400W

weld direction

36

The stress curve of the component normal the weld is seen to differ for the cone compared with the SW, figure 43. The stress value is almost the same for all models when looking at the middle of the curve. Stress components parallel the weld are the same for the SW and sector cone seen in figure 44.

Figure 43. Stress component normal to the weld

Figure 44. Stress component parallel to the weld

-600 -500 -400 -300 -200 -100 0 100 200 300

0 20 40 60 80 100 120

stre sss [ M P a]

path [mm]

stress normal to the weld direction

S11_kon_1400W S11_bred_1400W S11_smal_1400W

weld direction

-200 -100 0 100 200 300 400 500 600 700

0 20 40 60 80 100 120

stre ss [M p a]

path [mm]

stress in the weld direction

S22_kon_1400W S22_bred_1400W S22_smal_1400W

weld direction

37 Conclusions

 Stresses and strains parallel the weld is not changing when going from SW to a sector cone model. Both models are free to move in the axial direction therefore are the results the same.

 The change of geometry affects the value of the plastic strain component normal to the weld. The curves have the same shape, so tests with sandwich plates can be used for a first estimate of results. If more accurate results are needed, tests should be carried out on sandwich cones.

 Stress component curve normal weld have different forms for the SW and sector cone.

The value is almost the same in the middle of the path plot and a distance from that

point and forward.

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4 Discussion and conclusions

 Simulations show that the studied single plate width and length do not affect plastic strains in the weld-region for plates in a way that make it necessary to account for.

Sandwich plates are seen to have the same trends. In a modeling point of view it's seen that the mesh density is important in the weld region since large temperature, stress and strain gradients are seen here.

 When the sandwich-sector cone and sandwich plate was compared where all

parameters not regarding the geometric properties the same. In the theory is the cone not able to move in its tangential direction it was therefore completely constrained there. The cone has a diameter and a channel width that varies with its height. Two plates with different channel widths were made to investigate the channel width effect on the results. Results shows that the plate and sector cone is similar in the directions were both are free to expand. Plastic strains and stresses have different values in the direction were the cone and plate not are equally free to move, i.e. in the tangential direction.

The key-point is to know what to obtain from a simulation. If stresses are investigated, solid elements should be used. When looking for deformation trends that could be useful in an early design stage, it is enough to use shell element models to get results faster.

From simulations carried out one can state that weld simulations are time consuming, since

they involve coupled analyses with large deformations and plasticity. Some recommendations

to reduce the analysis time are given in the final section.

39

5 Recommendations for further work

From the performed weld analyses, the following topics are recommended for future studies:

 A core is used for the rocket nozzle to fixture it during welding. The constraints of the fixture may have an impact on stresses and it affects the residual deformations and stresses.

 Model and analyze sandwich wall models with weld gap between the inner and outer wall

Some proposes to speed up the analysis time are showed below. Lindgren [10] and Lundbäck [8] give information about the stated areas below.

 use of adaptive mesh

 use of super-elements

 Submodelling

40

6 Referensces

1. The Sandwich Nozzle Extension Demo: A milestone on the route to sandwich nozzle production. IAC-06-C4.3.08

2. Nørgaard, Jakob. New concept for Rocket engines. FORCE TECHNOLGY. http://f- m-v.dk/documents/00324.pfd (Hämtad 2015-05-16).

3. Weman, Klas. 1997. SVETS-HANDBOK, Karlebo. Askersund: Liber AB

4. Sokolov, M. and Salminen, A. (2014) Improving Laser Beam Welding Efficiency.

Engineering, 6, 559-571. doi: 10.4236/eng.2014.69057.

5. Marcal, P.V., Weld problems. Structural Mechanics Computer Programs,1974: p.

191-206.

6. Söderberg, Magnus. (2014). Coupled Models Related to Manufacturing Simulations. Lic.-avh., Luleå University of Technology

7. Goldak John, Aditya Chakravarti, Malcom Bibby, A new finite element model for welding heat sources, Metallurgical Trans B, Vol. 15B,june,1984, pp.209-305.

Goldak J, Patel B, Bibby M and Moore J: Computational weld mechanics, ASGARD Workshope – Structures and Materials 61:st Panel meeting, Oberammergau, Germany, Sep., 1985.

8. Lundbäck, Andreas. (2010). Modelling and Simulations of Welding and Metal Deposition.

Diss., Luleå University of Technology

9. Lars-Erik Lindgren( 2001): FINITE ELEMENT MODELING AND SIMULATION OF WELDING.PART2:IMPROVED MATERIAL MODELING, Journal of Thermal Stresses, 24:3, 195-231

10. Lars-Erik Lindgren(2005): Numerical modeling of welding. Division of Computer Aided Design, Luleå University of Technology, S-97187 Luleå, Sweden.

tillgänglig: www.sciencedirect.com, Comput. Methods Appl. Mech. Engrg. 195

(2006) 6710-6736

Appendix A

Information about material data used in marc is stated below. Not to be seen for public version.

32