Numerical simulation of electron beam welding process of Inconel 706

sheets

P. Lacki1,a, K. Adamus1,b, K. Wojsyk1,c, M. Zawadzki2,d

1Częstochowa University of Technology, al. Armii Krajowej 21, 42-200 Częstochowa, Poland

2WSK "PZL-Rzeszów" S.A., ul. Hetmańska 120, 35-078 Rzeszów, Poland

apiotr@lacki.com.pl, bkonrad.adamus@gmail.com, c kwojsyk@spaw.pcz.pl,

dmarcin.zawadzki@wskrz.com

Keywords: sheet welding, electron beam welding, weld pool geometry prediction, numerical

simulation

Abstract. Welding operation of aircraft engine sheet part will be analyzed in this paper. The sheet

part is made of narrow Inconel 706 sheet pieces. During manufacturing process first sheets undergo

the process of bending. Subsequently they are welded to produce the final shape. Finite element

analysis will be used to model welding operation. The thermal field and its impact on the stress field

will be analyzed. The produced results will be used to design the actual welding process. Sheets will

be welded using electron beam welding, EBW, method. This method is characterized by high

concentration of power which instantly melts metal. As a result small HAZ is produced and

comparatively small distortions are introduced. EBW process is characterized mainly by three input

parameters: beam voltage, beam current and welding speed. The goal of numerical simulation is to

identify the values of input parameters that produce full-depth fusion zone. As a guideline for

simulation the actual dependency between input parameters and weld pool geometry will be taken

from calibration data for EB welding unit. Calibration was performed using 18-8 steel. Partial least

square method will be used to project those data on Inconel 706 alloy.

Introduction

Inconel 706 is nickel-iron-chromium alloy. It was based on Inconel 718 alloy and it has similar

characteristics, also similar welding procedures apply [1]. Inconel 706 maintains high strength and

offers high creep and rupture resistance at high temperatures up to 704° C. Additionally nickel and

chromium give it good oxidation and corrosion resistance. These properties allow it to be

successfully applied in aerospace industry for elements that work at elevated temperatures. It is

used for discs, shafts, cases of turbines, diffusers, compressors and other components. In such

applications joining by welding is necessary. High power density welding technologies such as laser

and electron beam welding are preferred method of fusion welding for Inconel alloys [2, 3]. The

advantage of using these technologies follows from the fact that heat input is relatively low and

produced fusion zone, FZ, and heat affected zone, HAZ, have minimal size. This results in

reduction of distortions and residual stresses which contribute to occurrence of hot cracking

phenomena [4].

In the paper engine part welding process will be analyzed. The engine part outline is presented in

Fig. 1. It comprises two sheet pieces made of Inconel 706 each 50 mm wide and 1 mm thick. First

sheets undergo bending process. Subsequently they are welded to produce final shape of the engine

part. In the process two welds are created.

Key Engineering Materials Vol. 473 (2011) pp 540-547Online available since 2011/Mar/28 at www.scientific.net© (2011) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/KEM.473.540

All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,www.ttp.net. (ID: 130.15.241.167, Queen's University, Kingston, Canada-31/08/13,16:48:57)

Fig. 1. Overall view of sheet part and weld trajectories

Electron beam welding

EBW is a technology that utilizes electrons for fusion and joining of metals and alloys. Few key

properties of electron allow it to be successfully applied in welding applications [5]:

• electrons have electric charge (-1,6 ·10-19

C) and can be accelerated using electric field, their

kinetic energy will be converted to heat upon collision with welded material,

• electrons exist at external atom shells and can be easily detached.

Key aspects of EBW technology were described in [6]. EBW is characterized by very high

power density (107 W/cm

2). The size of beam spot in focusing condition is about (10

-7cm

2). High

power density and small spot size allow achieving very narrow and deep welds. As the beam power

is increased the ratio of fusion zone depth to width has value of 10:1 to 15:1. The mechanism

behind deep welds creation is not entirely known. Electrons have the capability of penetrating

through external material layers at depth of about 10-2

mm. Once electrons penetrate external layer

they start to heat up metal. Metal is melted and subsequently vaporized. Under high pressure the

bubble of metal vapor bursts and external material layer is destroyed. Electron beam starts to

refocus and penetrates through next layer. The cycle is repeated many times and deep welds are

created.

The unique feature of EBW is that it is carried out in vacuum. There are two primary reasons for

this. Collisions of electrons with gas particles would cause beam defocus and loss of beam power.

Additionally electron beam would lead to air ionization which would cause destruction of cathode

emitting electrons. There are versions of EB units operating in partial vacuum and in atmospheric

gases. Due to poorer performance they are supplementary method and can't be treated as

replacement.

There are following advantages of using EBW technology [7]:

• no pre-heating is required for materials that have high melting point,

• capability of welding materials that have high thermal conductivity,

• since welding is performed in vacuum it is possible to weld materials that react with

atmospheric gases, for instance titanium,

• capability of welding materials that tend to reflect laser beam,

• ease of controlling welding parameters that allows for welding of small and large objects.

The main disadvantage of using EBW is use of vacuum chamber. Welded objects must fit into

chamber. Additionally, there is significant time required for chamber empting.

Weld pool geometry model

Weld pool geometry depends on the welding process parameters. It is often required that the

produced weld has the specified fusion zone depth. Application of predictive model helps to

identify process parameters that will satisfy this requirement.

Bollig et al. [8] used artificial neural network as model predictive controller, MPC, for laser

beam welding process. The impact of beam power and welding speed on plasma emission, which is

sheet part 1

sheet part 2

joint 1

joint 2

Key Engineering Materials Vol. 473 541

correlated with beam penetration depth, was analyzed. Since welding process was performed in

three dimensions welding speed varied depending on the welding trajectory. The goal of MPC was

to dynamically modify beam power so that it compensated for changes of speed during welding

process. Application of neural network as predictive controller requires definition of input

regression vector and calibration of neural network parameters such as number of hidden neurons,

weight values. Regression vector is built from history of the latest power, speed, and emission

measurements as well as from known future value of speed, and predicted future value of emission.

Yang et al. [9] suggested application of partial least square method, PLS, for prediction of weld

pool geometry for gas metal arc welding process. Impact of 6 input parameters: wire feed rate, wire

extension, welding speed, gas flow, welding voltage, and welding current on weld pool width, weld

pool depth, and weld reinforcement was analyzed. Cai et al. [10] used PLS for on-line prediction of

spatter rate of gas metal arc welding in short-circuit transfer mode. The error between estimation

and measured value is less than 11%. According to Cai advantages of PLS include: effective

dealing with multicollinearity among input variables, and fast response time in on-line applications.

For the purpose of this work it was decided that PLS method will be used to build model

predicting weld pool geometry.

Partial least square method. PLS method is described in [11]. Concise description can be found in

[12] and [13]. PLS combines extraction of latent variables and ordinary least square, OLS,

regression which is performed on latent variables. Latent variables are linear combination of

original variables. They are created one by one in such manner that they explain the highest amount

of variation among explanatory variables X=X1 and response variables Y=Y1. First hidden variable

t1=X1w1 is a linear combination of X1, similarly first hidden variable u1=Y1q1 is a linear

combination of Y1. Variables t1 and u1 are created in such way that covariation t1Tu1 has maximal

value. Vectors w1 and q1 are first eigenvectors of matrices X1TY1Y1

TX1 and Y1

TX1X1

TY1

respectively.

In next step variables X1 and Y1 are regressed onto t using vectors p1, c1:

��� = �����, where ��

� = (�����)

������

��� = �����, where ��

� = (�����)

������

The calculated values of ��� and ��� correspond to first hidden variable which explains the highest

amount of variation. Each consecutive hidden variable explains the highest amount of variation that

was not explained by previous hidden variables assuming that it is orthogonal to already calculated

hidden variables. In practical applications only first few hidden variables are used. They usually

explain about 90% of variation among data.

The next hidden variables are created in the same way as first hidden variables. The only

difference is that instead of variables X1 and Y1 the new variables X2 and Y2 are used. In order to

calculate X2 and Y2 the variables ��� and ���obtained using regression must be subtracted from X1

and Y1:

� �� = � − ��

� �� = � − ��

The results obtained using PLS method will never be more accurate than results obtained using

OLS method. However OLS can lead to over-fitting of the model to training data and produce

worse results using test data. The advantage of PLS method is that relatively good results will be

produced using only few first hidden variables that account for highest amount of variation. Thus it

is possible to choose the number of hidden variables in such a way that model is fitted only to data

where the variation is well explained and ignore data where the variation is poorly explained.

Training data. Training data for PLS model were obtained from calibration process of EB unit.

Impact of 6 control parameters on weld pool geometry was indentified. Control parameters include:

542 Sheet Metal 2011

welding speed, beam current, frequency, accelerating voltage, distance of beam focus from surface,

beam deflection. Weld pool geometry was identified by: depth, width and reinforcement height.

During calibration 49 welds were created which were grouped into 7 series. The reference set of

control parameters was selected. In each series only one parameter in the reference set was modified

and its impact on FZ geometry was analyzed. In case of distance of beam focus two series were

performed, one for focus above surface and one for focus below surface. Experiments were done

using 14-mm thick plates made of 18-8 steel.

Fig. 2. PLS model predicted values and actual values of weld pool depth

Since PLS model assumes linear dependencies between data and dependencies among analyzed

data are nonlinear data preprocessing was required. For the purpose of modeling second order

polynomial dependencies were assumed. In order to linearize the problem f(x) = ax2+bx+c

dependency was changed into f(x1, x2)= ax1+bx2+c, where x1=x2 and x2=x. Thus 12 variables were

used as independent variables, six variables corresponding to 6 control parameters and their 6

square counterparts. In the model first 5 hidden variables were used that account for 94% of

variation among data.

PSL model results were presented in Fig. 2 as the scatter plot of actual depth and PLS predicted

depth. Distance between points and the reference line, f(x) = x, in vertical direction represents error

introduced by the model. The errors follow from assumption about character of dependency

between particular control parameter and depth.

Test data. The model built on the basis of 18-8 steel was applied to control data reported for

Inconel 706 in [4]. For the set of parameters: voltage - 150 kV, current - 10 mA, speed - 10 mm/s,

focus distance - 2mm above surface, frequency - 0 Hz, authors obtained FZ depth of 6.2 mm. There

was no information about value of deflection. For the same set of control parameter values and

value of deflection set to 0, PLS model predicted depth of 5.7 mm. Error introduced by the PLS

model is 8%. The error might be caused by 2 factors:

• different material properties such as thermal conductivity and heat capacity,

• training data contained information only about impact of single parameter change on weld

pool geometry, there was no information about impact of more than 1 parameter change on

pool geometry, for instance, there was no information about impact of focus change on

current-depth dependency.

0

2

4

6

8

10

0 2 4 6 8 10

predicted depth, mm

actual depth, mm

Key Engineering Materials Vol. 473 543

Projected data. It was assumed that FZ for the purpose of engine part welding should have depth

of 1.5 mm. On the basis of the PLS model the following set of parameters was suggested: voltage -

133 kV, current - 5mA, speed - 20 mm/s, focus - 0 mm, deflection - 0, frequency - 0 Hz. The

predicted FZ is 1.5 mm deep and 1.5 mm wide.

FEM model

FEM model was built to simulate the process of sheet welding using program ADINA. The finite

element procedures used in the program were described in [14]. Fourier-Kirchoff equation was used

to describe heat propagation: ��

��= �∇�T +

��

��� (11)

where: a – thermal diffusivity, ρ – density, cp – specific heat, qv – efficiency of inner volume heat

source.

544 Sheet Metal 2011

Fig. 3. Stress and temperature field for first joint at time: a) 0.25s b) 1.5s c) 2.5s d) 75s

During EBW process heat is produced inside volume of the material thus three-dimensional heat

model was applied. Volume representing heat source has the shape of hexahedron. Uniform power

distribution was used in heat source volume. The motion of heat source is represented by heat

production in consecutive heat source volumes along welding trajectory. At any time heat is

produced only inside one heat source volume. Mesh along welding trajectories was thickened to

capture changes introduced by heat source. Two welding trajectories were built as presented in Fig.

1. The welding pause time between 2 trajectories was assumed to be 10 seconds. The welding time

EFFECTIVESTRESS

3.500E+083.250E+083.000E+082.750E+082.500E+082.250E+082.000E+081.750E+081.500E+081.250E+081.000E+087.500E+075.000E+072.500E+070.000E+00

TEMPERATURE

1350.1260.1170.1080.990.900.810.720.630.540.450.360.270.180. 90.

TIME 0.25052

EFFECTIVESTRESS

MAXIMUM2.756E+08

MAXIMUM

MAXIMUM

MAXIMUM

a)

b)

d)

c)

2.500E+08TIME 1.5005

TIME 2.500002.334E+08

TIME 75.003.660E+08

MAXIMUM2678.

MAXIMUM

MAXIMUM

MAXIMUM

TEMPERATURE

2679.

3455.

96.01

Key Engineering Materials Vol. 473 545

for single welding trajectory is 2.5 s. As initial condition temperature of sheets was set to 20°C. On

the sheet surfaces convection coefficient was set to 0 as welding is performed in vacuum in short

time.

Thermo-mechanical coupled, TMC, analysis was used to determine the magnitude of thermal

stresses. Thermal elasto-plastic material model was assumed in the numerical model.

The results simulation are presented in Fig. 4. Temperature field and its impact on stress field

can be seen. In the beginning FZ develops in non-stationary way. Subsequently stationary stage is

achieved for FZ. During stationary period FZ doesn't change its shape and only changes its position

along welding trajectory. Maximal temperature calculated by model is 2679 °C and it increases

toward the end of welding trajectory up to 3455 °C which is caused by the fact that near the sheet

edge heat is not distributed in all directions. After 75 s from the beginning of the process

temperature drops below 180 °C.

The lowest values of stress occur in the area of molten pool. The higher values of stress surround

welding pool. As welding pool moves and metals starts to solidify stress values start to increase.

During welding highest stress values of about 275 MPa occur in the beginning of the process and

they decrease to 233 MPa toward the end of welding. The highest values of stresses occur after

welding process ends. After 75 s from the beginning of the process stress values along welding

trajectory have values in the range 325-350 MPa. The highest stress value of 366 MPa occurs near

the edge at the beginning of welding trajectory.

Summary

In the paper the set of parameters for welding of sheet part made of Inconel 706 was suggested.

In order to identify parameter values PLS model was used. The model was built based on EB unit

calibration process performed for 18-8 steel. The model was applied to results reported by Ferro et

al. The error introduced by the model is expected to follow from the fact that 18-8 steel and Inconel

706 have different properties and EB calibration process didn't take into account dependencies

caused by changing more than 2 parameters simultaneously.

The following conclusions can be drawn:

• Application of PLS method is relatively simple. PLS model must be trained using

selected data. No calibration of model parameters is required.

• The limitation of using PLS method follows from the fact that it assumes linear

dependencies. If nonlinear dependencies between data are expected variables should be

modified so that linear model input variables represent nonlinear characteristics. In some

cases appropriate data linearization might be impossible.

• PLS method is useful extension of FEM. It allows for identification of process

parameters that will produce required weld pool depth. Once the set of parameters is

identified value of beam power can be used to define FEM heat source that has the main

impact on the results of welding process simulation.

Acknowledgements

Financial support of Structural Funds in the Operational Programme - Innovative Economy (IE OP)

financed from the European Regional Development Fund - Project "Modern material technologies

in aerospace industry", No POIG.01.01.02-00-015/08-00 is gratefully acknowledged.

References

[1] Technical bulletin: Inconel alloy 706 (Publication number SMC-091), Special Metals

Corporation (http://www.specialmetals.com), September 2004.

546 Sheet Metal 2011

[2] Huang C.A., Wang T.H, Lee C.H., Han W.C., A study of heat-affected zone (HAZ) of an

Inconel 718 sheet welded with electron-beam welding (EBW), Materials Science and

Engineering A, 398 (2005) 275-281

[3] Egbewande A.T., Buckson R.A., Ojo O.A., Analysis of laser beam weldability of Inconel 738

superalloy, Materials characterization, 61 (2010) 569-574

[4] Ferro P., Zambon A., Bonollo F., Investigation of electron beam welding in wrought Inconel

706 - experimental and numerical analysis, Materials Science and Engineering A, 392 (2005) 94-

105

[5] Nikolaev G., Olshansky N., Advanced welding processes, Mir, Moscow, 1977

[6] Schultz H., Electron beam welding, Woodhead Publishing, Abington, 1994.

[7] Chattopadhyay R., Advanced thermally assisted surface engineering processes, Springer, 2004.

[8] Bollig A., Rake H., Kratzsch Ch., Kaierle S., Application of neuro-predictive control to laser

beam welding, IFAC 15th Triennial World Congress, Spain, 2002

[9] Yang H., Cai Y., Bao.Y, Zhou Y., Analysis and application of partial least square regression in

arc welding process, Journal of Central South University of Technology, 12 (2005) 453-458

[10] Cai Y., Wang G., Yang H., Hua X., Wu Y., Spatter rate estimation of GMAW-S based on

partial least square regression, Journal of Central South University of Technology, 13 (2008)

695-701

[11] Esposito Vinzi V., Chin W.W., Hensler J., Wang H., Handbook of partial least squares.

Concepts, methods and applications, Springer, 2010

[12] Kourti T., Process analysis and abnormal situation detection: from theory to practice, IEEE:

Control Systems Magazine, 22 (2005) 10-25

[13] SAS Online Doc, Version 8, The PLS Procedure

[14] Bathe K.J., Finite Element Procedures, Prentice-Hall Inc. Upper Saddle River, New Jersey,

1996.

Key Engineering Materials Vol. 473 547

Sheet Metal 2011 10.4028/www.scientific.net/KEM.473 Numerical Simulation of Electron Beam Welding Process of Inconel 706 Sheets 10.4028/www.scientific.net/KEM.473.540

DOI References

[7] Chattopadhyay R., Advanced thermally assisted surface engineering processes, Springer, 2004.

doi:10.1111/j.0022-3840.2004.120_14.x [9] Yang H., Cai Y., Bao.Y, Zhou Y., Analysis and application of partial least square regression in rc welding

process, Journal of Central South University of Technology, 12 (2005) 453-458

doi:10.1007/s11771-005-0181-z [2] Huang C.A., Wang T.H, Lee C.H., Han W.C., A study of heat-affected zone (HAZ) of an Inconel 718

sheet welded with electron-beam welding (EBW), Materials Science and Engineering A, 398 (2005) 275-281

doi:10.1016/j.msea.2005.03.029 [9] Yang H., Cai Y., Bao.Y, Zhou Y., Analysis and application of partial least square regression in arc

welding process, Journal of Central South University of Technology, 12 (2005) 453-458

doi:10.1007/s11771-005-0181-z [11] Esposito Vinzi V., Chin W.W., Hensler J., Wang H., Handbook of partial least squares. Concepts,

methods and applications, Springer, 2010

doi:10.1007/978-3-540-32827-8