chapter 6 finite element analysis of fsw process to...

137

CHAPTER 6

FINITE ELEMENT ANALYSIS OF FSW PROCESS TO PREDICT

TEMPERATURE DISTRIBUTION

6.1 INTRODUCTION

FSW process is a complicated process which involves many variables. The

important component of the process is the amount of temperature generated during

the process. The heat input due to this temperature decides the quality of the joint.

Sufficient temperature should be generated to plasticize the material and to make it

flow and then it is forged on the other side so that a sound weld is achieved. Low

temperature as well as high temperature is detrimental to the quality of the weld. To

find out the temperature distribution during FSW in a specific material, many trials

are to be carried out which consume a lot of time and money. Thus it becomes

essential to go by modelling and simulation route to find out the temperature

distribution. This will also lead to predicting the thermal stress that is induced

during the process. Here, an attempt has been made to predict the temperature

distribution across the plate during welding using the commercially available

simulation software - ANSYS.

138

6.2 EXPERIMENTAL PROCEDURE

6.2.1 Mathematical Modeling of FSW Process

Developing a mathematical model for FSW process is the ideal beginning to

simulate the process using simulation software. The model will aid in calculating

the approximate heat generated during the process which can be used as the input

for evaluating the temperature distribution using ANSYS. Understanding the FSW

process is essential to develop a sound mathematical model. Many researchers over

the years have tried developing mathematical models to predict the heat generation.

The most suitable being the model developed by Hamilton et al 2008 which is used

to calculate the heat flux. This model has been used for calculating the heat flux and

used as the input during the simulation process. As per the model, heat is generated

at a constant rate during the intermediate period of welding. During the beginning

and end, the process is highly dynamic. When the welding is started, the heat

increases exponentially and when it ends, it decreases in the same manner. This

process depicts a quasi-steady behaviour during the entire process (Yeong-Maw et

al 2008). The mass flow is treated as a flow of a non-Newtonian, incompressible,

yield yield, is based on distortion energy theory for

plane stress.

approximation. Partial sticking condition was assumed at the surface between the

tool and the work piece. The tilt angle of the tool is taken as zero. Also, the tool

shoulder is assumed to be flat.

FSW process involves transfer of plasticized material from the front to the

back of the tool pin as the tool traverses along the joint. It is basically an extrusion

process followed by forging which joins the plates. Therefore, it is appropriate to

use the following equations for FSW. The calculation of heat generation is done

with help of following parameters:

139

1. F - Force Applied during welding, kN.

2. µ - Coefficient of friction.

3. Mechanical efficiency.

4. N - Tool rotational speed, rps.

5. S Tool traverse speed, mm/s.

6. D - Diameter of shoulder Pin, mm.

In FSW process, the governing heat equation for a moving heat source is

(Song et al 2003a and Schmidt et al 2004):

p (dT / dt) = - (K. grad T) + q (6.1)

Where q is the power generated by friction between the tool and the top of

and Cp is the heat capacity. The heat flux, q, at the tool/work piece interface may be

derived from the following expression:

µ x x N x S x D (kW) (6.2)

By using the above equation (6.2), the heat flux was calculated for the

different runs as per the design matrix. The respective values of the process

parameters corresponding to a particular run is substituted and the resultant values

are presented in Table 6.1

140

Table 6.1 Heat Flux Values for the 31 Runs of Experiments

Run No. FSW Process Parameters

Heat Flux (kW) N

(rpm) S

(mm/min) F

(N) R

(%) 1 1475 75 11750 11 3047.908 2 1825 75 11750 11 3771.14 3 1475 105 11750 11 4267.071 4 1825 105 11750 11 5279.596 5 1475 75 17250 11 4474.588 6 1825 75 17250 11 5536.355 7 1475 105 17250 11 6264.424 8 1825 105 17250 11 7750.897 9 1475 75 11750 13 3047.908

10 1825 75 11750 13 3771.14 11 1475 105 11750 13 4267.071 12 1825 105 11750 13 5279.596 13 1475 75 17250 13 4474.588 14 1825 75 17250 13 5536.355 15 1475 105 17250 13 6264.424 16 1825 105 17250 13 7750.897 17 1300 90 14500 12 3977.998 18 2000 90 14500 12 6119.997 19 1650 60 14500 12 3365.998 20 1650 120 14500 12 6731.997 21 1650 90 9000 12 3133.86 22 1650 90 20000 12 6964.134 23 1650 90 14500 10 5048.997 24 1650 90 14500 14 5048.997 25 1650 90 14500 12 5048.997 26 1650 90 14500 12 5048.997 27 1650 90 14500 12 5048.997 28 1650 90 14500 12 5048.997 29 1650 90 14500 12 5048.997 30 1650 90 14500 12 5048.997 31 1650 90 14500 12 5048.997

141

6.2.2 Finite Element Analysis of FSW Process

6.2.2.1 Pre-Processing

As mentioned in section 4.2.2, the work piece of size 100 mm X 50 mm X 6

mm is modelled in the ANSYS software. For conducting the simulation using the

software, two different meshes are required. One of the elements selected is SOLID

70 which is a solid 3D element to predict the nodal solutions and another one is the

SURFACE 152 which is a surface element used for allocating convection properties

to the model. Figure 6.1 shows the meshed model of the Al-TiB2 MMC which

shows that the elements are meshed in an orderly manner with brick shaped

elements. To improve the accuracy of the solution, a finer mesh of element size 2

mm is applied to the meshed model.

Figure 6.1 Meshed Model of the Al-TiB2 MMC Plate

Figure 6.2 shows the displacement boundary condition applied to the model

wherein all DOF of one edge is constrained. Figure 6.3 shows the displacement and

142

convection boundary condition which is applied to the surface of the modelled plate

using the surface mesh.

Figure 6.2 ANSYS Model of the Al-TiB2 MMC Plate Showing Displacement

Boundary Condition

Figure 6.3 ANSYS Model Showing of the Al-TiB2 MMC Plate Showing

Displacement and Convection Boundary Condition

143

Figure 6.4 shows the temperature distribution in the Al-TiB2 MMC after first

load step. The material properties such as thermal conductivity, density and the

convection properties are defined for the problem. The following are the thermal

conductivity values: a) Al-10wt.%TiB2 = 160 W/m K; b) Al-11wt.%TiB2 = 155

W/m K; c) Al-12wt.%TiB2 = 149 W/m K; d) Al-13wt.%TiB2 = 143 W/m K; e) Al-

14wt.%TiB2 = 138 W/m K (Yih & Chung 1997)

Figure 6.4 Temperature Distribution in the Al-TiB2 MMC Plate after First

Load Step

6.2.2.2 Solution

The processing of the solution for this problem is based on transient thermal

condition. Additionally a moving heat source model is tried in this analysis to

visualize the welding process throughout the plate. Therefore the regular method

using GUI cannot be applied for this problem. The solving methodology was

written in ANSYS Parametric Design Language (APDL) and was executed. In

section 6.2.3 the APDL program is explained in detail. The heat flux is applied first

°C

144

at one location on the first element as shown in Figure 6.4, then it is solved and the

solution is stored as rtf file. The load step for carrying out the analysis is calculated

using the welding speed (S). The time taken for the tool to travel 100 mm for given

tool traverse speed is calculated and applied as the load step for the respective

analysis. This rtf file is used as the input for the next iteration at the next location

(the second element in the column). Meanwhile the heat source in the first element

is deleted so that there will not be any interference of that heat source in the second

iteration. This process is continued until the solver reaches the last element.

6.2.2.3 Post Processing

In the post processing of the results, the nodal solution at every interval is

plotted and the temperature distribution is plotted as a contour plot. An animation of

the moving heat source is also captured for the nodal solution. The section 6.3 deals

with the result and discussion on the contour plots that is obtained using post

processor of ANSYS Software.

6.2.3 APDL Programming

Finite Element Analysis (FEA) is carried out using ANSYS software with

programming language APDL in ANSYS command mode. Table 6.2 shows the

programme for finding the temperature distributions along the work piece and

explains the process carried out to solve the FSW problem using APDL

Table 6.2 APDL Program with Explanation

Line No.

Command Explanation

1. /BATCH The problem is started in Batch Mode (Command Mode)

2. /clear Clear the screen

145

3. /prep7 Processing set to thermal problem

4. et,1,70 SOLID 70 element is selected from the list

5. et,2,152,,,,1 SURFACE 152 element is selected from the list

6. keyopt,2,8,2 Key points are plotted

7. block,,0.1,,-0.006,,-0.05 A block is modelled using the key points

8. esize,0.002 Element size is set to 2 mm

9. vmesh,1 Volume mesh is done using the first element

10. mp,kxx,1,160 Material property input 1 - Thermal conductivity

11. mp,dens,1,2700 Material property input 2 - density of the material

12. type,2 Second element type is chosen

13. esurf Surface element meshed on the surface

14. esel,s,type,,2,2 Surface element is selected

15. sfe,all,1,conv,1,15 Convection properties are given as initial condition

16. sfe,all,1,conv,2,30 Convection properties are given as final condition

17. esel,all All the elements are selected to apply this condition

18. FINISH Pre-processing is done

19. /SOL Solution phase is started

20. antype,trans Transient type problem is defined

21. toffst,273

Transient problem set up done like setting the solution control, setting the time limit, setting the minimum and maximum intervals, etc.,

22. tunif,30

23. nropt,full

24. autots,on

25. nsub,1,1,1

26. solcontrol,on

27. outres,nsol,all

28. timint,on

29. kbc,0

146

30. *SET,tim,1 Delimiting the time setting

31. *SET,dt,1 Set dt as 1 second

32. *do,i,3701,3750,1 Select the 1st element

33. sfe,i,4,hflux,1,3050300 Apply the heat flux in that element

34. time,tim Select time

35. *SET,tim,tim+dt Set it as increment of 1 seconds

36. solve Solve the problem

37. sfedele,i,4,hflux Delete the heat flux from the 1st element

38. *enddo End the problem

39. FINISH Finish the solution

40. /POST1 Start post processing

41. ! PLNSOL, TEMP,, 0 Print nodal solution

42. ! SAVE, therm,db, Save the file

43. !LGWRITE,'Run-1' Write the log file so that it can be used for the next run.

6.3 RESULT AND DISCUSSION

6.3.1 Temperature Distribution in Al-TiB2 MMC

Figures 6.5 to 6.8 show typical contour plots indicating temperature

distribution in the FS welded plates. The welding is initiated at the left end of the

plate as mentioned in section 4.2.2 and the heat source is moved along the edge and

reaches the right end of the plate. The temperature distribution along the transverse

direction for various load steps is calculated and the predicted maximum

temperature at the end of the last load step for all the 31 runs is presented in

Table6.3. It is evident from the figures that the predicted maximum temperature

increases when the input heat flux is increased. Since the heat flux was calculated as

a function of FSW process parameters (Eqn. 6.2), the predicted maximum

temperature is dependent on FSW process parameters.

147

Figure 6.9 shows typical time history plots drawn from the temperature data

acquired from the FEA analysis. The data for the plot is taken from the FEA model

at the exact point where the thermocouples were placed during actual welding. The

figure shows that as the time progresses, the temperature increases. The temperature

reaches the maximum value at around 7 seconds. The temperature remains at

maximum temperature up to 12 seconds. After that as the time increases the

temperature decreases gradually. The reason for this may be attributed to position of

the FSW tool and the location of the thermocouple. In the beginning of the welding,

the position of the FSW tool is away from the location of the thermocouple because

of which the temperature is less. As the time increases, the FSW tool move forward

and reaches near the location of the thermocouple, thus the temperature increases.

After 12 seconds, the FSW tool moves beyond the location of the thermocouple.

Since the FSW tool moves beyond the location of the thermocouple, the weldment

begins to cool down due to convection. Therefore the temperature decreases

gradually with respect to the further increase in time.

Figure 6.5 Temperature Distribution in FS Welded Al6061-11wt.%TiB2 MMC

(Run 1, Heat Flux - 3047.9 kW)

°C

148





°C

°C

149


(Run 20, Heat Flux 6731.9 kW)

Figure 6.9 Typical Time History Plot for FS Welded Al6061-TiB2 MMC Plates

6.3.2 Validation of the FEA Model

Table 6.3 shows the maximum temperature obtained using the

thermocouples which were placed on top of the weldment and the data acquisition

100

150

200

250

300

350

400

450

500

0 5 10 15 20 Time (Sec)

Run 1 Run 10 Run 14 Run 20

°C

6731.9 kW

5536.35 kW

3771.14 kW

3047.9 kW

150

system (NI Kit-NI cDAQ-9178 & NI 9211) with LABVIEW software as mentioned

in section 4.2.2.

Table 6.3 Comparison between the Actual Temperature and Predicted Temperature

Run No. FSW Process Parameters Experimental

Max Temp (°C)

Predicated Max Temp

(°C)

% Error N S F R

1 -1 -1 -1 -1 154 150.9 2.05434 2 1 -1 -1 -1 201 199.2 0.90361 3 -1 1 -1 -1 210 207.5 1.20482 4 1 1 -1 -1 285 278.5 2.33393 5 -1 -1 1 -1 244 239.5 1.87891 6 1 -1 1 -1 342 337.5 1.33333 7 -1 1 1 -1 477 468 1.92308 8 1 1 1 -1 482 480 0.41667 9 -1 -1 -1 1 155 150.9 2.71703 10 1 -1 -1 1 205 199.2 2.91165 11 -1 1 -1 1 212 207.5 2.16867 12 1 1 -1 1 288 278.5 3.41113 13 -1 -1 1 1 246 239.5 2.71399 14 1 -1 1 1 342 337.5 1.33333 15 -1 1 1 1 478 468 2.13675 16 1 1 1 1 483 480 0.625 17 -2 0 0 0 207 199.3 3.86352 18 2 0 0 0 354 350.3 1.05624 19 0 -2 0 0 186 179.5 3.62117 20 0 2 0 0 478 475 0.63158 21 0 0 -2 0 184 179.5 2.50696 22 0 0 2 0 480 477 0.62893 23 0 0 0 -2 254 249.5 1.80361 24 0 0 0 2 254 249.5 1.80361 25 0 0 0 0 254 249.5 1.80361 26 0 0 0 0 254 249.5 1.80361 27 0 0 0 0 254 249.5 1.80361 28 0 0 0 0 254 249.5 1.80361 29 0 0 0 0 254 249.5 1.80361 30 0 0 0 0 254 249.5 1.80361 31 0 0 0 0 254 249.5 1.80361

151

The predicted maximum temperature obtained from FEA is also presented in

the same table. The % error in predicting the maximum temperature is calculated

and tabulated for validating the FEA model. From the table it is evident that the

experimental maximum temperature and the predicted maximum temperature

values lie close to each other and the % error in predicting the maximum

temperature is less than 4%.

The time history plots for the temperature distribution at the point where the

thermocouples were placed during weldment were obtained using the data

acquisition system (Section 4.2.2) and are presented in Figures 6.10 to 6.13. The

time history plots obtained from the FEA analysis (section 6.3.1) are also

superimposed in same figures for comparison and validation. The graphs show that

the path traced by both the actual and predicted temperature lie close to each other

with very little variation. The reason for the variation between the actual and

predicted maximum temperature is due to the non-availability of temperature

dependant properties of the MMCs and the use of room temperature thermal

properties of the MMCs for the analysis.

Figure 6.10 Time History Plot for FS Welded Al6061-11wt.%TiB2 MMC


100

120

140

160

0 5 10 15 20

Tem

pera

ture

(C

)

Time (S)

Simulation Experiment

152





130

150

170

190

210

0 5 10 15 20

Tem

pera

ture

(C

)

Time (S)


220

240

260

280

300

320

340

0 5 10 15 20

Tem

pera

ture

(C

)

Time (S)


153


(Run 20, Heat Flux 6731.9 kW)

6.4 SUMMARY

The following are the summary of the results of Chapter 6:

i. The FSW process was analysed using FEA Process with the help of ANSYS

software.

ii. A thermal transient type analysis with moving heat source model was carried

out to understand the process better.

iii. The contours plots indicated that the temperature distribution was along the

transverse direction of the FS welded MMC plate.

iv. Time history plots indicated that the path traced by the experimental value

and the simulated value lie close to each other showing very little variation.

v. It was found that the simulated values of the maximum temperature varied

with respect to the change in FSW process parameters.

vi. It was found that the error was within 4% which validated the FEA

procedure followed to analyse the FSW process.

280

330

380

430

480

0 5 10 15 20

Tem

pera

ture

(C

)

Time (S)


chapter 6 finite element analysis of fsw process to...

Documents